Publications of Sergiy Bubin

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    Author / Coauthor Title Journal / Proceedings / Book Year Web PDF
    S. Bubin and L. Adamowicz Variational calculations of excited states with zero total angular momentum (vibrational spectrum) of H$_2$ without use of the Born-Oppenheimer approximation J. Chem. Phys. 118, 3079 2003 DOI PDF
    Abstract: Very accurate, rigorous and fully variational, all-particle, non-Born--Oppenheimer calculations of the vibrational spectrum of the H$_2$ molecule have been performed. Very high accuracy has been achieved by expanding the wave functions in terms of explicitly correlated Gaussian functions with preexponential powers of the internuclear distance. An indicator of the high accuracy of the calculations is the new upper bound for the H$_2$ nonrelativistic nonadiabatic ground state energy equal to -1.1640250300 hartree.
    BibTeX:

    @article{bubin_jcp_118_3079_2003,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Variational calculations of excited states with zero total angular momentum (vibrational spectrum) of H$_2$ without use of the Born--Oppenheimer approximation},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2003},
    volume = {118},
    number = {7},
    pages = {3079-3082},
    doi = {10.1063/1.1537719}
    }
    M. Cafiero, S. Bubin and L. Adamowicz Non-Born-Oppenheimer calculations of atoms and molecules Phys. Chem. Chem. Phys. 5, 1491 2003 DOI PDF
    Abstract: We review a recent development in high-accuracy non-Born--Oppenheimer calculations of atomic and molecular systems in a basis of explicitly correlated Gaussian functions. Much of the recent progress in this area is due to the derivation and implementation of analytical gradients of the energy functional with respect to variational linear and non-linear parameters of the basis functions. This method has been used to obtain atomic and molecular ground and excited state energies and the corresponding wave functions with accuracy that exceeds previous calculations. Further, we have performed the first calculations of non-linear electrical properties of molecules without the Born--Oppenheimer approximation for systems with more than one electron. The results for the dipole moments of such systems as HD and LiH agree very well with experiment. After reviewing our non-Born--Oppenheimer results we will discuss ways this method can be extended to deal with larger molecular systems with and without an external perturbation.
    BibTeX:

    @article{cafiero_pccp_5_1491_2003,
    author = {Cafiero, M and Bubin, S and Adamowicz, L},
    title = {Non-Born-Oppenheimer calculations of atoms and molecules},
    journal = {Phys. Chem. Chem. Phys.},
    year = {2003},
    volume = {5},
    number = {8},
    pages = {1491-1501},
    doi = {10.1039/b211193d}
    }
    S. Bubin, M. Cafiero and L. Adamowicz Quantum mechanical calculations on molecules containing positrons Fundamental World of Quantum Chemistry 3, 521 2004
    BibTeX:

    @incollection{bubin_fwqc_2004,
    author = {S. Bubin and M. Cafiero and L. Adamowicz},
    title = {Quantum mechanical calculations on molecules containing positrons},
    booktitle = {Fundamental World of Quantum Chemistry},
    publisher = {Kluwer},
    year = {2004},
    volume = {3},
    pages = {521}
    }
    S. Bubin and L. Adamowicz Non-Born-Oppenheimer study of positronic molecular systems: $e^+$LiH J. Chem. Phys. 120, 6051 2004 DOI PDF
    Abstract: Very accurate non-Born--Oppenheimer variational calculations of the ground state of $e^+$LiH have been performed using explicitly correlated Gaussian functions with preexponential factors dependent on powers of the internuclear distance. In order to determine the positron detachment energy of $e^+$LiH and the dissociation energy corresponding to the $e^+$LiH fragmentation into HPs and Li$^+$ we also calculated non-BO energies of HPs, LiH, and Li$^+$. For all the systems the calculations provided the lowest ever-reported variational upper-bounds to the ground state energies. Annihilation rates of HPs and $e^+$LiH were also computed. The dissociation energy of $e^+$LiH into HPs and Li$^+$ was determined to be 0.036548 hartree.
    BibTeX:

    @article{bubin_jcp_120_6051_2004,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Non-Born--Oppenheimer study of positronic molecular systems: $e^+$LiH},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2004},
    volume = {120},
    number = {13},
    pages = {6051-6055},
    doi = {10.1063/1.1651056}
    }
    S. Bubin and L. Adamowicz Nonrelativistic molecular quantum mechanics without approximations: Electron affinities of LiH and LiD J. Chem. Phys. 121, 6249 2004 DOI PDF
    Abstract: We took the complete nonrelativistic Hamiltonians for the LiH and LiH$^-$ systems, as well as their deuterated isotopomers, we separated the kinetic energy of the center of mass motion from the Hamiltonians, and with the use of the variational method we optimized the ground-state nonadiabatic wave functions for the systems expanding them in terms of $n$-particle explicitly correlated Gaussian functions. With 3600 functions in the expansions we obtained the lowest ever ground-state energies of LiH, LiD, LiH$^-$, and LiD$^-$ and these values were used to determine LiH and LiD electrons affinities (EAs) yielding 0.33030 and 0.32713 eV, respectively. The present are the first high-accuracy ab initio quantum mechanical calculations of the LiH and LiD EAs that do not assume the Born-Oppenheimer approximation. The obtained EAs fall within the uncertainty brackets of the experimental results.
    BibTeX:

    @article{bubin_jcp_121_6249_2004,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Nonrelativistic molecular quantum mechanics without approximations: Electron affinities of LiH and LiD},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2004},
    volume = {121},
    number = {13},
    pages = {6249-6253},
    doi = {10.1063/1.1786580}
    }
    E. Bednarz, S. Bubin and L. Adamowicz Non-Born-Oppenheimer variational calculations of HT$^+$ bound states with zero angular momentum J. Chem. Phys. 122, 164302 2005 DOI PDF
    Abstract: We report fully nonadiabatic calculations of all rotationless bound states of HT$^+$ molecular ion ($t^+ p^+ e^-$) carried out in the framework of the variational method. We show that, in all the states, except the two highest ones, the bond in the system can be described as covalent. In the highest two states the bond becomes essentially ionic and HT$^+$ can be described as a T + H$^+$ complex. The wave function of the system was expanded in terms of spherically symmetric, explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance. Apart from the total energies of the states, we have calculated the expectation values of the $t-p$, $t-e$, and $p-e$ interparticle distances, their squares, and the nucleus-nucleus correlation functions.
    BibTeX:

    @article{bednarz_jcp_122_164302_2005,
    author = {Eugeniusz Bednarz and Sergiy Bubin and Ludwik Adamowicz},
    title = {Non-Born--Oppenheimer variational calculations of HT$^+$ bound states with zero angular momentum},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2005},
    volume = {122},
    number = {16},
    pages = {164302},
    doi = {10.1063/1.1884602}
    }
    E. Bednarz, S. Bubin and L. Adamowicz Integrals for non-Born-Oppenheimer calculations of molecules with three nuclei Mol. Phys. 103, 1169 2005 DOI PDF
    Abstract: Variational molecular calculations without assuming the Born--Oppenheimer approximation of states corresponding to zero total angular momentum require the use of spherically symmetric basis functions explicitly depending on the electron--electron, electron--nucleus, and nucleus--nucleus distances. In our calculations, such functions have been the explicitly correlated Gaussians. For molecules with three nuclei, the Gaussians have to be multiplied by powers of all three internuclear distances to describe the highly correlated motion of the nuclei. In this work we have derived formulae for the overlap and the Hamiltonian matrix elements for such basis functions. Implementation of the formulae presents some unconventional numerical difficulties related to maintaining the required precision of the calculation. The implementation problems are discussed.
    BibTeX:

    @article{bednarz_mp_103_1169_2005,
    author = {Bednarz, Eugeniusz and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Integrals for non-Born--Oppenheimer calculations of molecules with three nuclei},
    journal = {Mol. Phys.},
    publisher = {Taylor & Francis},
    year = {2005},
    volume = {103},
    pages = {1169-1182},
    doi = {10.1080/00268970512331339314}
    }
    S. Bubin, M. Cafiero and L. Adamowicz Non-Born-Oppenheimer variational calculations of atoms and molecules with explicitly correlated Gaussian basis functions Adv. Chem. Phys. 131, 377 2005 DOI PDF
    BibTeX:

    @article{bubin_acp_131_377_2005,
    author = {Bubin, Sergiy and Cafiero, Mauricio and Adamowicz, Ludwik},
    title = {Non-Born-Oppenheimer variational calculations of atoms and molecules with explicitly correlated Gaussian basis functions},
    journal = {Adv. Chem. Phys.},
    publisher = {Wiley},
    year = {2005},
    volume = {131},
    pages = {377-475},
    doi = {10.1002/0471739464.ch6}
    }
    S. Bubin and L. Adamowicz Nucleus-nucleus correlation function in non-Born-Oppenheimer molecular calculations: vibrationally excited states of HD$^+$ Chem. Phys. Lett. 403, 185 2005 DOI PDF
    Abstract: In the present work, we studied HD$^+$ ($dpe$) molecular ion in the framework of variational method without assuming the Born-Oppenheimer approximation. The non-adiabatic wave function was expanded in terms of explicitly correlated Gaussian basis functions. An algorithm for calculating the nucleus-nucleus correlation function (i.e., the probability density of one nucleus in the reference frame where the other one is at the origin) was derived, implemented, and used to depict all bound states of HD$^+$ with zero rotational energy.
    BibTeX:

    @article{bubin_cpl_403_185_2005,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Nucleus-nucleus correlation function in non-Born-Oppenheimer molecular calculations: vibrationally excited states of HD$^+$},
    journal = {Chem. Phys. Lett.},
    year = {2005},
    volume = {403},
    number = {1-3},
    pages = {185 - 191},
    doi = {10.1016/j.cplett.2005.01.009}
    }
    S. Bubin, E. Bednarz and L. Adamowicz Charge asymmetry in HD$^+$ J. Chem. Phys. 122, 041102 2005 DOI PDF
    Abstract: Expanding the wave functions of the ground and excited states of HD$^+$ (or $pde$) in terms of spherically symmetric explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance, and using the variational method, we performed very accurate nonadiabatic calculations of all bound states of this system corresponding to the zero total angular momentum quantum number (vibrational states; $v$=0-22). The total and the transition energies obtained agree with the best available calculations. For each state we computed the expectation values of the $d-p$, $d-e$, and $p-e$ interparticle distances. This is the first time these quantities were computed for HD$^+$ using rigorous nonadiabatic wave functions. While up to the $v$=20 state some asymmetry is showing in the $d-e$ and $p-e$ distances, for $v$=21 and $v$=22 we observe a complete breakdown of the Born--Oppenheimer approximation and localization of the electron almost entirely at the deuteron.
    BibTeX:

    @article{bubin_jcp_122_041102_2005,
    author = {Sergiy Bubin and Eugeniusz Bednarz and Ludwik Adamowicz},
    title = {Charge asymmetry in HD$^+$},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2005},
    volume = {122},
    number = {4},
    pages = {041102},
    doi = {10.1063/1.1850905}
    }
    S. Bubin, L. Adamowicz and M. Molski An accurate non-Born-Oppenheimer calculation of the first purely vibrational transition in LiH molecule J. Chem. Phys. 123, 134310 2005 DOI PDF
    Abstract: In this work we study the ground and the first vibrationally excited states of LiH molecule. We performed an extensive nonrelativistic variational calculations of the two states without using the Born--Oppenheimer approximation. The results are analyzed and compared with the data extracted from recent experiments. The 0$\leftarrow$1 transition energy obtained in the calculations converged to a value which is less than a wave number above the transition energy estimated from the available experimental data concerning the LiH rovibrational transitions. We discuss the remaining discrepancy and the procedure used to determine the ``experimental'' transition frequencies.
    BibTeX:

    @article{bubin_jcp_123_134310_2005,
    author = {Sergiy Bubin and Ludwik Adamowicz and Marcin Molski},
    title = {An accurate non-Born--Oppenheimer calculation of the first purely vibrational transition in LiH molecule},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2005},
    volume = {123},
    number = {13},
    pages = {134310},
    doi = {10.1063/1.2047487}
    }
    M. Pavanello, S. Bubin, M. Molski and L. Adamowicz Non-Born-Oppenheimer calculations of the pure vibrational spectrum of HeH$^+$ J. Chem. Phys. 123, 104306 2005 DOI PDF
    Abstract: Very accurate calculations of the pure vibrational spectrum of the HeH$^+$ ion are reported. The method used does not assume the Born--Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.
    BibTeX:

    @article{pavanello_jcp_123_104306_2005,
    author = {Michele Pavanello and Sergiy Bubin and Marcin Molski and Ludwik Adamowicz},
    title = {Non-Born--Oppenheimer calculations of the pure vibrational spectrum of HeH$^+$},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2005},
    volume = {123},
    number = {10},
    pages = {104306},
    doi = {10.1063/1.2012332}
    }
    S. Bubin and L. Adamowicz Matrix elements of $N$-particle explicitly correlated Gaussian basis functions with complex exponential parameters J. Chem. Phys. 124, 224317 2006 DOI PDF
    Abstract: In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.
    BibTeX:

    @article{bubin_jcp_124_224317_2006,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Matrix elements of $N$-particle explicitly correlated Gaussian basis functions with complex exponential parameters},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2006},
    volume = {124},
    number = {22},
    pages = {224317},
    doi = {10.1063/1.2204605}
    }
    S. Bubin and L. Adamowicz Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH$^+$ J. Chem. Phys. 125, 064309 2006 DOI PDF
    Abstract: Very accurate, rigorous, variational, non-Born-Oppenheimer (non-BO) calculations have been performed for the fully symmetric, bound states of the LiH$^+$ ion. These states correspond to the ground and excited vibrational states of LiH$^+$ in the ground electronic state. The non-BO wave functions of the states have been expanded in terms of spherical $N$-particle explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and 5600 Gaussians were used for each state. The calculations that, to our knowledge, are the most accurate ever performed for a diatomic system with three electrons have yielded six bound states. Average interparticle distances and nucleus-nucleus correlation function plots are presented.
    BibTeX:

    @article{bubin_jcp_125_064309_2006,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH$^+$},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2006},
    volume = {125},
    number = {6},
    pages = {064309},
    doi = {10.1063/1.2244563}
    }
    S. Bubin and L. Adamowicz Nonrelativistic variational calculations of the positronium molecule and the positronium hydride Phys. Rev. A 74, 052502 2006 DOI PDF
    Abstract: Highly accurate ground-state nonrelativistic variational calculations of Ps$_2$, $^1$HPs, and $^\infty$HPs are reported. The calculations have been performed using 5000 explicitly correlated Gaussian basis functions and yielded the lowest variational energy upper bounds for these systems to date. The relative accuracies of the energies obtained are of the order of 4$\times$10$^{-10}$ a.u. for Ps$_2$ and 2$\times$10$^{-9}$ a.u. for HP. Several expectation values have also been computed for each system, as well as electron-positron annihilation rates.
    BibTeX:

    @article{bubin_pra_74_052502_2006,
    author = {Bubin, Sergiy and Adamowicz, Ludwik },
    title = {Nonrelativistic variational calculations of the positronium molecule and the positronium hydride},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2006},
    volume = {74},
    number = {5},
    pages = {052502},
    doi = {10.1103/PhysRevA.74.052502}
    }
    D. Kedziera, M. Stanke, S. Bubin, M. Barysz and L. Adamowicz Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H$_2$ J. Chem. Phys. 125, 014318 2006 DOI PDF
    Abstract: The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H$_2$ using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.
    BibTeX:

    @article{kedziera_jcp_125_014318_2006,
    author = {Dariusz K\c{e}dziera and Monika Stanke and Sergiy Bubin and Maria Barysz and Ludwik Adamowicz},
    title = {Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H$_2$},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2006},
    volume = {125},
    number = {1},
    pages = {014318},
    doi = {10.1063/1.2209691}
    }
    D. Kedziera, M. Stanke, S. Bubin, M. Barysz and L. Adamowicz Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations J. Chem. Phys. 125, 084303 2006 DOI PDF
    Abstract: The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the internuclear distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD$^+$ ion.
    BibTeX:

    @article{kedziera_jcp_125_084303_2006,
    author = {Dariusz K\c{e}dziera and Monika Stanke and Sergiy Bubin and Maria Barysz and Ludwik Adamowicz},
    title = {Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2006},
    volume = {125},
    number = {8},
    pages = {084303},
    doi = {10.1063/1.2236113}
    }
    M. Stanke, D. Kedziera, M. Molski, S. Bubin, M. Barysz and L. Adamowicz Convergence of Experiment and Theory on the Pure Vibrational Spectrum of HeH$^{+}$ Phys. Rev. Lett. 96, 233002 2006 DOI PDF
    Abstract: Very accurate quantum mechanical calculations of the pure vibrational spectrum of the HeH$^+$ molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreement.
    BibTeX:

    @article{stanke_prl_96_233002_2006,
    author = {Stanke, Monika and K\c{e}dziera, Dariusz and Molski, Marcin and Bubin, Sergiy and Barysz, Maria and Adamowicz, Ludwik},
    title = {Convergence of Experiment and Theory on the Pure Vibrational Spectrum of HeH$^{+}$},
    journal = {Phys. Rev. Lett.},
    publisher = {American Physical Society},
    year = {2006},
    volume = {96},
    number = {23},
    pages = {233002},
    doi = {10.1103/PhysRevLett.96.233002}
    }
    S. Bubin and L. Adamowicz Calculations of the ground states of BeH and BeH$^+$ without the Born-Oppenheimer approximation J. Chem. Phys. 126, 214305 2007 DOI PDF
    Abstract: Non-Born-Oppenheimer variational calculations employing explicitly correlated Gaussian basis functions have been performed for the ground states of the beryllium monohydride molecule (BeH) and its ion (BeH$^+$), as well as for the beryllium atom (Be) and its ion (Be$^+$). An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed. The calculated energies were used to determine the ionization potential of BeH and the dissociation energies of BeH and BeH$^+$. Also, the generated wave functions were used to compute various expectation values, such as the average interparticle distances and the nucleus-nucleus correlation functions.
    BibTeX:

    @article{bubin_jcp_126_214305_2007,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Calculations of the ground states of BeH and BeH$^+$ without the Born-Oppenheimer approximation},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2007},
    volume = {126},
    number = {21},
    pages = {214305},
    doi = {10.1063/1.2736699}
    }
    S. Bubin, M. Stanke, D. Kedziera and L. Adamowicz Relativistic corrections to the ground-state energy of the positronium molecule Phys. Rev. A 75, 062504 2007 DOI PDF
    Abstract: The leading-order relativistic corrections to the ground-state energy of the positronium molecule (Ps$_2$) have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of Ps$_2$.
    BibTeX:

    @article{bubin_pra_75_062504_2007,
    author = {Bubin, Sergiy and Stanke, Monika and K\c{e}dziera, Dariusz and Adamowicz, Ludwik },
    title = {Relativistic corrections to the ground-state energy of the positronium molecule},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2007},
    volume = {75},
    number = {6},
    pages = {062504},
    doi = {10.1103/PhysRevA.75.062504}
    }
    S. Bubin, M. Stanke, D. Kedziera and L. Adamowicz Improved calculations of the lowest vibrational transitions in HeH$^{+}$ Phys. Rev. A 76, 022512 2007 DOI PDF
    Abstract: More accurate variational calculations of the lowest three pure vibrational states ($v$=0,1,2) of the $^4$HeH$^+$ molecular ion have been carried out without assuming the Born-Oppenheimer approximation. In the calculations we included the complete set of $\alpha^2$ relativistic corrections, i.e., mass-velocity, Darwin, spin-spin, and orbit-orbit. This allowed us to improve the agreement between the theory and the experiment for the vibrational frequencies of the 1$\leftarrow$0 and 2$\leftarrow$1 transitions as compared to our previous calculations [Stanke et al., Phys. Rev. Lett. 96, 233002 (2006)].
    BibTeX:

    @article{bubin_pra_76_022512_2007,
    author = {Bubin, Sergiy and Stanke, Monika and K\c{e}dziera, Dariusz and Adamowicz, Ludwik },
    title = {Improved calculations of the lowest vibrational transitions in HeH$^{+}$ },
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2007},
    volume = {76},
    number = {2},
    pages = {022512},
    doi = {10.1103/PhysRevA.76.022512}
    }
    M. Stanke, D. Kedziera, S. Bubin and L. Adamowicz Relativistic corrections to the non-Born-Oppenheimer energies of the lowest singlet Rydberg states of $^3$He and $^4$He J. Chem. Phys. 126, 194312 2007 DOI PDF
    Abstract: In this work the authors present an approach to calculate the leading-order relativistic corrections for ground and excited states of helium isotopomers. In the calculations they used variational wave functions expanded in terms of explicitly correlated Gaussians obtained without assuming the Born-Oppenheimer approximation.
    BibTeX:

    @article{stanke_jcp_126_194312_2007,
    author = {Monika Stanke and Dariusz K\c{e}dziera and Sergiy Bubin and Ludwik Adamowicz},
    title = {Relativistic corrections to the non-Born-Oppenheimer energies of the lowest singlet Rydberg states of $^3$He and $^4$He},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2007},
    volume = {126},
    number = {19},
    pages = {194312},
    doi = {10.1063/1.2735305}
    }
    M. Stanke, D. Kedziera, S. Bubin and L. Adamowicz Electron affinity of $^7$Li calculated with the inclusion of nuclear motion and relativistic corrections J. Chem. Phys. 127, 134107 2007 DOI PDF
    Abstract: Explicitly correlated Gaussian functions have been used to perform very accurate variational calculations for the ground states of $^7$Li and $^7$Li$^-$. The nuclear motion has been explicitly included in the calculations (i.e., they have been done without assuming the Born-Oppenheimer (BO) approximation). An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed. This led to a noticeable improvement of the previously determined variational upper bound to the nonrelativistic energy of Li$^-$. The Li energy obtained in the calculations matches those of the most accurate results obtained with Hylleraas functions. The finite-mass (non-BO) wave functions were used to calculate the $\alpha^2$ relativistic corrections ($\alpha = 1/c$). With those corrections and the $\alpha^3$ and $\alpha^4$ corrections taken from Pachucki and Komasa [J. Chem. Phys. 125, 204304 (2006)] , the electron affinity (EA) of $^7$Li was determined. It agrees very well with the most recent experimental EA.
    BibTeX:

    @article{stanke_jcp_127_134107_2007,
    author = {Monika Stanke and Dariusz K\c{e}dziera and Sergiy Bubin and Ludwik Adamowicz},
    title = {Electron affinity of $^7$Li calculated with the inclusion of nuclear motion and relativistic corrections},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2007},
    volume = {127},
    number = {13},
    pages = {134107},
    doi = {10.1063/1.2755767}
    }
    M. Stanke, D. Kedziera, S. Bubin and L. Adamowicz Ionization potential of $^{9}$Be calculated including nuclear motion and relativistic corrections Phys. Rev. A 75, 052510 2007 DOI PDF
    Abstract: Variational calculations employing explicitly correlated Gaussian functions have been performed for the ground states of $^9$Be and $^9$Be$^+$ including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation]. An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed, leading to energies of the two systems noticeably improved over those found in the recent paper of Pachucki and Komasa [Physical Review A 73, 052502 (2006)]. The non-BO wave functions were used to calculate the $\alpha^2$ relativistic corrections ($\alpha=e^2/ \hbar c$). With those corrections and the $\alpha^3$ and $\alpha^4$ corrections taken from Pachucki and Komasa, a new value of the ionization potential (IP) of 9Be was determined. It agrees very well with the most recent experimental IP.
    BibTeX:

    @article{stanke_pra_75_052510_2007,
    author = {Stanke, Monika and K\c{e}dziera, Dariusz and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Ionization potential of $^{9}$Be calculated including nuclear motion and relativistic corrections},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2007},
    volume = {75},
    number = {5},
    pages = {052510},
    doi = {10.1103/PhysRevA.75.052510}
    }
    M. Stanke, D. Kedziera, S. Bubin, M. Molski and L. Adamowicz Lowest vibrational states of $^{4}$He$^{3}$He$^{+}$: Non-Born-Oppenheimer calculations Phys. Rev. A 76, 052506 2007 DOI PDF
    Abstract: Very accurate quantum mechanical calculations of the first five vibrational states of the $^4$He$^3$He$^+$ molecular ion are reported. The calculations have been performed explicitly including the coupling of the electronic and nuclear motions [i.e., without assuming the Born-Oppenheimer (BO) approximation]. The nonrelativistic non-BO wave functions were used to calculate the $\alpha^2$ relativistic mass velocity, Darwin, and spin-spin interaction corrections. For the lowest vibrational transition, whose experimental energy is established with high precision, the calculated and the experimental results differ by only 0.16 cm$^{-1}$.
    BibTeX:

    @article{stanke_pra_76_052506_2007,
    author = {Stanke, Monika and K\c{e}dziera, Dariusz and Bubin, Sergiy and Molski, Marcin and Adamowicz, Ludwik },
    title = {Lowest vibrational states of $^{4}$He$^{3}$He$^{+}$: Non-Born-Oppenheimer calculations},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2007},
    volume = {76},
    number = {5},
    pages = {052506},
    doi = {10.1103/PhysRevA.76.052506}
    }
    M. Stanke, D. Kedziera, S. Bubin and L. Adamowicz Lowest Excitation Energy of $^{9}$Be Phys. Rev. Lett. 99, 043001 2007 DOI PDF
    Abstract: Variational calculations employing explicitly correlated Gaussian functions and explicitly including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation] have been performed to determine the lowest singlet transition energy in the 9Be atom. The non-BO wave functions were used to calculate the $\alpha^2$ relativistic corrections ($\alpha$=1/137.035999679). With those corrections and with the $\alpha^3$ and $\alpha^4$ QED corrections determined previously by others, we obtained 54677.35 cm$^{-1}$ for the $3 ^1 S \rightarrow 2 ^1 S$ transition energy. This result falls within the error bracket for the experimental transition of 54677.26(10) cm${-}1$. This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.
    BibTeX:

    @article{stanke_prl_99_043001_2007,
    author = {Stanke, Monika and K\c{e}dziera, Dariusz and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Lowest Excitation Energy of $^{9}$Be},
    journal = {Phys. Rev. Lett.},
    publisher = {American Physical Society},
    year = {2007},
    volume = {99},
    number = {4},
    pages = {043001},
    doi = {10.1103/PhysRevLett.99.043001}
    }
    S. Bubin and L. Adamowicz Energy and energy gradient matrix elements with $N$-particle explicitly correlated complex Gaussian basis functions with $L$ = 1 J. Chem. Phys. 128, 114107 2008 DOI PDF
    Abstract: In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an $N$-particle system with the $L$=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest $P$ state of the beryllium atom and the bound $P$ state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.
    BibTeX:

    @article{bubin_jcp_128_114107_2008,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Energy and energy gradient matrix elements with $N$-particle explicitly correlated complex Gaussian basis functions with $L$ = 1},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2008},
    volume = {128},
    number = {11},
    pages = {114107},
    doi = {10.1063/1.2894866}
    }
    M. Pavanello, M. Cafiero, S. Bubin and L. Adamowicz Accurate Born-Oppenheimer calculations of the low-lying $c ^3 \Sigma_g^+$ and $a ^3 \Sigma_u^+$ excited states of helium dimer Int. J. Quantum Chem. 108, 2291 2008 DOI PDF
    Abstract: Accurate variational Born--Oppenheimer calculations of the two lowest excited $\Sigma$ triplet states of the helium dimer at their respective equilibrium geometries are reported. The wave functions of the states are expanded in terms of explicitly correlated Gaussian functions with shifted centers. The obtained energies are the best variational estimates ever calculated for these states. One-electron densities are also presented and discussed. The results are compared with the experimental values and previous calculations.
    BibTeX:

    @article{pavanello_ijqc_108_2291_2008,
    author = {Michele Pavanello and Mauricio Cafiero and Sergiy Bubin and Ludwik Adamowicz},
    title = {Accurate Born--Oppenheimer calculations of the low-lying $c ^3 \Sigma_g^+$ and $a ^3 \Sigma_u^+$ excited states of helium dimer},
    journal = {Int. J. Quantum Chem.},
    publisher = {Wiley},
    year = {2008},
    volume = {108},
    pages = {2291-2298},
    doi = {10.1002/qua.21757}
    }
    M. Stanke, D. Kedziera, S. Bubin, M. Molski and L. Adamowicz Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H$_2$ J. Chem. Phys. 128, 114313 2008 DOI PDF
    Abstract: We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with $\sigma$ electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of $\alpha^2$ (where $\alpha = 1/c$). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H$_2$ molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in $\alpha$ to further improve the agreement between the theory and the experiment.
    BibTeX:

    @article{stanke_jcp_128_114313_2008,
    author = {Monika Stanke and Dariusz K\c{e}dziera and Sergiy Bubin and Marcin Molski and Ludwik Adamowicz},
    title = {Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H$_2$},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2008},
    volume = {128},
    number = {11},
    pages = {114313},
    doi = {10.1063/1.2834926}
    }
    M. Stanke, D. Kedziera, S. Bubin and L. Adamowicz Complete $\alpha^2$ relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of HeH$^+$ Phys. Rev. A 77, 022506 2008 DOI PDF
    Abstract: We report the implementation of the complete set of the lowest-order relativistic corrections of the order of $\alpha^2$ (where $\alpha$ is the fine structure constant) for calculating vibrational states of diatomic molecular systems within the framework that does not assume the Born-Oppenheimer approximation. To test the accuracy of the approach we have performed calculations for all rotationless vibrational states (also called pure vibrational states or $S$ states) of the HeH$^+$ ion in the ground electronic state. For the lowest transitions, where very precise experimental results are available, an excellent agreement with the experimental values has been achieved.
    BibTeX:

    @article{stanke_pra_77_022506_2008,
    author = {Stanke, Monika and K\c{e}dziera, Dariusz and Bubin, Sergiy and Adamowicz, Ludwik },
    title = {Complete $\alpha^2$ relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of HeH$^+$ },
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2008},
    volume = {77},
    number = {2},
    pages = {022506},
    doi = {10.1103/PhysRevA.77.022506}
    }
    M. Stanke, J. Komasa, D. Kedziera, S. Bubin and L. Adamowicz Three lowest $S$ states of $^{9}$Be$^{+}$ calculated with including nuclear motion and relativistic and QED corrections Phys. Rev. A 77, 062509 2008 DOI PDF
    Abstract: We have performed high-accuracy quantum mechanical calculations for the three lowest $S$ states of the beryllium ion ($^9$Be$^+$). The nonrelativistic part of the calculations was done with the variational approach and explicitly included the nuclear motion (i.e., the finite-nuclear-mass approach). The nonrelativistic wave functions were expanded in terms of explicitly correlated Gaussian functions. These nonrelativistic functions were subsequently used to calculate the leading $\alpha^2$ relativistic corrections ($\alpha=1/c$) and the $\alpha^3$ and $\alpha^4$ QED (quantum electrodynamics) corrections. In the $\alpha^4$ QED correction we only accounted for its dominant component typically contributing about 80\% of the correction. With those the present results are the most accurate ever obtained for $^9$Be$^+$. They also agree with the experimentally measured transitions within less than 0.1 cm$^{-1}$.
    BibTeX:

    @article{stanke_pra_77_062509_2008,
    author = {Stanke, Monika and Komasa, Jacek and K\c{e}dziera, Dariusz and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Three lowest $S$ states of $^{9}$Be$^{+}$ calculated with including nuclear motion and relativistic and QED corrections},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2008},
    volume = {77},
    number = {6},
    pages = {062509},
    doi = {10.1103/PhysRevA.77.062509}
    }
    M. Stanke, J. Komasa, D. Kedziera, S. Bubin and L. Adamowicz Accuracy limits on the description of the lowest $S$ excitation in the Li atom using explicitly correlated Gaussian basis functions Phys. Rev. A 78, 052507 2008 DOI PDF
    Abstract: We have performed very accurate quantum-mechanical calculations for the two lowest $S$ states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading $\alpha^2$ relativistic correction ($\alpha$ is the fine-structure constant) and the $\alpha^3$ QED correction. We also estimated the $\alpha^4$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.
    BibTeX:

    @article{stanke_pra_78_052507_2008,
    author = {Stanke, Monika and Komasa, Jacek and K\c{e}dziera, Dariusz and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Accuracy limits on the description of the lowest $S$ excitation in the Li atom using explicitly correlated Gaussian basis functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2008},
    volume = {78},
    number = {5},
    pages = {052507},
    doi = {10.1103/PhysRevA.78.052507}
    }
    S. Bubin, F. Leonarski, M. Stanke and L. Adamowicz Non-adiabatic corrections to the energies of the pure vibrational states of H$_2$ Chem. Phys. Lett. 477, 12 2009 DOI PDF
    Abstract: Nonrelativistic energies of all fifteen pure vibrational states of the H$_2$ molecule have been recalculated with much higher accuracy than before. In the calculations we employed explicitly correlated Gaussian functions and an approach where the Born-Oppenheimer (BO) approximation is not assumed. The wave function of each state was expanded in terms of 10000 Gaussians whose nonlinear parameters were optimized using a procedure involving the analytical energy gradient. The obtained non-BO energies combined with the recent BO adiabatic energies of Pachucki and Komasa [K. Pachucki, J. Komasa, J. Chem. Phys. 129 (2008) 034102] allowed us to determine new improved values of the non-adiabatic corrections for the considered states.
    BibTeX:

    @article{bubin_cpl_477_12_2009,
    author = {Sergiy Bubin and Filip Leonarski and Monika Stanke and Ludwik Adamowicz},
    title = {Non-adiabatic corrections to the energies of the pure vibrational states of H$_2$},
    journal = {Chem. Phys. Lett.},
    year = {2009},
    volume = {477},
    number = {1-3},
    pages = {12 - 16},
    doi = {10.1016/j.cplett.2009.06.060}
    }
    S. Bubin, F. Leonarski, M. Stanke and L. Adamowicz Charge asymmetry in pure vibrational states of the HD molecule J. Chem. Phys. 130, 124120 2009 DOI PDF
    Abstract: Very accurate variational calculations of all rotationless states (also called pure vibrational states) of the HD molecule have been performed within the framework that does not assume the Born--Oppenheimer (BO) approximation. The non-BO wave functions of the states describing the internal motion of the proton, the deuteron, and the two electrons were expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. Up to 6000 functions were used for each state. Both linear and nonlinear parameters of the wave functions of all 18 states were optimized with a procedure that employs the analytical gradient of the energy with respect to the nonlinear parameters of the Gaussians. These wave functions were used to calculate expectation values of the interparticle distances and some other related quantities. The results allow elucidation of the charge asymmetry in HD as a function of the vibrational excitation.
    BibTeX:

    @article{bubin_jcp_130_124120_2009,
    author = {Sergiy Bubin and Filip Leonarski and Monika Stanke and Ludwik Adamowicz},
    title = {Charge asymmetry in pure vibrational states of the HD molecule},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2009},
    volume = {130},
    number = {12},
    pages = {124120},
    doi = {10.1063/1.3094047}
    }
    S. Bubin, M. Stanke and L. Adamowicz Non-Born-Oppenheimer calculations of the BH molecule J. Chem. Phys. 131, 044128 2009 DOI PDF
    Abstract: Variational calculations employing explicitly correlated Gaussian basis functions have been performed for the ground state of the boron monohydride molecule (BH) and for the boron atom (B). Up to 2000 Gaussians were used for each system. The calculations did not assume the Born--Oppenheimer (BO) approximation. In the optimization of the wave function, we employed the analytical energy gradient with respect to the Gaussian exponential parameters. In addition to the total nonrelativistic energies, we computed scalar relativistic corrections (mass-velocity and Darwin). With those added to the total energies, we estimated the dissociation energy of BH. The non-BO wave functions were also used to compute some expectation values involving operators dependent on the interparticle distances.
    BibTeX:

    @article{bubin_jcp_131_044128_2009,
    author = {Sergiy Bubin and Monika Stanke and Ludwik Adamowicz},
    title = {Non-Born--Oppenheimer calculations of the BH molecule},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2009},
    volume = {131},
    number = {4},
    pages = {044128},
    doi = {10.1063/1.3195061}
    }
    S. Bubin, J. Komasa, M. Stanke and L. Adamowicz Isotope shift in the electron affinity of lithium J. Chem. Phys. 131, 234112 2009 DOI PDF
    Abstract: Very accurate electron affinity (EA) calculations of $^6$Li and $^7$Li (and $^\infty$Li) have been performed using explicitly correlated Gaussian functions and a variational approach that explicitly includes the nuclear motion in the calculations (i.e., the approach that does not assume the Born--Oppenheimer approximation). The leading relativistic and quantum electrodynamics corrections to the electron affinities were also calculated. The results are the most accurate theoretical values obtained for the studied systems to date. Our best estimates of the $^7$Li and $^6$Li EAs are 4984.9842(30) and 4984.9015(30) cm$^{-1}$, respectively, and of the $^7$Li/$^6$Li EA isotope shift is 0.0827 cm$^{-1}$.
    BibTeX:

    @article{bubin_jcp_131_234112_2009,
    author = {Sergiy Bubin and Jacek Komasa and Monika Stanke and Ludwik Adamowicz},
    title = {Isotope shift in the electron affinity of lithium},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2009},
    volume = {131},
    number = {23},
    pages = {234112},
    doi = {10.1063/1.3275804}
    }
    S. Bubin and L. Adamowicz Calculations of low-lying $^1 P$ states of the beryllium atom Phys. Rev. A 79, 022501 2009 DOI PDF
    Abstract: High-accuracy nonrelativistic variational calculations employing explicitly correlated Gaussian basis functions have been performed to determine the energies and the expectation values of some operators for the lowest four $^1 P_1$ states of the beryllium atom. The states correspond to the electron configurations $1 s^2 2 s^1 n p^1$, where $n$=2, 3, 4, and 5. The calculations were performed for both finite and infinite mass of the Be nucleus. The basis set for each state was grown to the level of 5000 Gaussians. With that many functions we achieved a tight energy convergence. The reported values, to the best of our knowledge, are the most accurate ever obtained for the four states.
    BibTeX:

    @article{bubin_pra_79_022501_2009,
    author = {Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Calculations of low-lying $^1 P$ states of the beryllium atom},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2009},
    volume = {79},
    number = {2},
    pages = {022501},
    doi = {10.1103/PhysRevA.79.022501}
    }
    K. L. Sharkey, M. Pavanello, S. Bubin and L. Adamowicz Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two $p$ electrons using all-electron explicitly correlated Gaussian basis functions Phys. Rev. A 80, 062510 2009 DOI PDF
    Abstract: A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two $p$ electrons or a single $d$ electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.
    BibTeX:

    @article{sharkey_pra_80_062510_2009,
    author = {Sharkey, Keeper L. and Pavanello, Michele and Bubin, Sergiy and Adamowicz, Ludwik },
    title = {Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two $p$ electrons using all-electron explicitly correlated Gaussian basis functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2009},
    volume = {80},
    number = {6},
    pages = {062510},
    doi = {10.1103/PhysRevA.80.062510}
    }
    M. Stanke, S. Bubin, M. Molski and L. Adamowicz Non-Born-Oppenheimer calculations of the lowest vibrational energy of HD including relativistic corrections Phys. Rev. A 79, 032507 2009 DOI PDF
    Abstract: In this work we report variational calculations of the two lowest vibrational states of the HD molecule within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states were corrected for the relativistic effects of the order of $\alpha^2$ (where $\alpha=1/c$), calculated as expectation values of the operators representing these effects with the nonrelativistic non-BO wave functions. The non-BO wave functions were expanded in terms of the one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. The $v=0 \rightarrow 1$ transition energy obtained in the calculations is compared with the previous calculations, as well as with the transition frequency obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in $\alpha$ to further improve the agreement between the theory and the experiment.
    BibTeX:

    @article{stanke_pra_79_032507_2009,
    author = {Stanke, Monika and Bubin, Sergiy and Molski, Marcin and Adamowicz, Ludwik},
    title = {Non-Born-Oppenheimer calculations of the lowest vibrational energy of HD including relativistic corrections},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2009},
    volume = {79},
    number = {3},
    pages = {032507},
    doi = {10.1103/PhysRevA.79.032507}
    }
    M. Stanke, S. Bubin and L. Adamowicz Fundamental vibrational transitions of the $^3$He$^4$He$^+$ and $^7$LiH$^+$ ions calculated without assuming the Born-Oppenheimer approximation and with including leading relativistic corrections Phys. Rev. A 79, 060501 2009 DOI PDF
    Abstract: Very accurate variational calculations of the fundamental pure vibrational transitions of the $^3He$^4He$^+$ and $^7$LiH$^+$ ions are performed within the framework that does not assume the Born-Oppenheimer (BO) approximation. The non-BO wave functions expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance are used to calculate the leading relativistic corrections. Up to 10000 Gaussian functions are used for each state. It is shown that the experimental $^3He$^4He$^+$ fundamental transitions is reproduced within 0.06 cm$^{-1}$ by the calculations. A similar precision is expected for the calculated, but still unmeasured, fundamental transition of $^7$LiH$^+$. Thus, three-electron diatomic systems are calculated with a similar accuracy as two-electron systems.
    BibTeX:

    @article{stanke_pra_79_060501_2009,
    author = {Stanke, Monica and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Fundamental vibrational transitions of the $^3$He$^4$He$^+$ and $^7$LiH$^+$ ions calculated without assuming the Born-Oppenheimer approximation and with including leading relativistic corrections},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2009},
    volume = {79},
    number = {6},
    pages = {060501},
    doi = {10.1103/PhysRevA.79.060501}
    }
    M. Stanke, J. Komasa, S. Bubin and L. Adamowicz Five lowest $^1S$ states of the Be atom calculated with a finite-nuclear-mass approach and with relativistic and QED corrections Phys. Rev. A 80, 022514 2009 DOI PDF
    Abstract: We have performed very accurate quantum mechanical calculations of the five lowest $S$ states of the beryllium atom. In the nonrelativistic part of the calculations we used the variational method and we explicitly included the nuclear motion in the Schr\"{o}dinger equation. The nonrelativistic wave functions of the five states were expanded in terms of explicitly correlated Gaussian functions. These wave functions were used to calculate the leading $\alpha^2$ relativistic correction ($\alpha$ is the fine structure constant) and the $\alpha^3$ quantum electrodynamics (QED) correction. We also estimated the $\alpha^4$ QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement.
    BibTeX:

    @article{stanke_pra_80_022514_2009,
    author = {Stanke, Monika and Komasa, Jacek and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Five lowest $^1S$ states of the Be atom calculated with a finite-nuclear-mass approach and with relativistic and QED corrections},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2009},
    volume = {80},
    number = {2},
    pages = {022514},
    doi = {10.1103/PhysRevA.80.022514}
    }
    S. Bubin, M. Stanke, M. Molski and L. Adamowicz Accurate non-Born-Oppenheimer calculations of the lowest vibrational energies of D$_2$ and T$_2$ with including relativistic corrections Chem. Phys. Lett. 494, 21 2010 DOI PDF
    Abstract: In this work we report very accurate variational calculations of the two lowest vibrational states of the D$_2$ and T$_2$ molecules within the framework that does not assume the Born-Oppenheimer approximation. The non-relativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of $\alpha^2$ calculated as expectation values of the operators representing these effects. The $v=0 \rightarrow 1$ transition energy of D$_2$ obtained in the calculations is compared with the transition frequency obtained from the experimental spectra. The comparison shows the need to include corrections higher than second-order in $\alpha$ to further improve the agreement between the theory and the experiment.
    BibTeX:

    @article{bubin_cpl_494_21_2010,
    author = {Sergiy Bubin and Monika Stanke and Marcin Molski and Ludwik Adamowicz},
    title = {Accurate non-Born-Oppenheimer calculations of the lowest vibrational energies of D$_2$ and T$_2$ with including relativistic corrections},
    journal = {Chem. Phys. Lett.},
    year = {2010},
    volume = {494},
    number = {1-3},
    pages = {21 - 25},
    doi = {10.1016/j.cplett.2010.05.081}
    }
    S. Bubin, M. Stanke and L. Adamowicz Lower vibrational transitions of the $^3$He$^4$He$^+$ ion calculated without the Born-Oppenheimer approximation and with leading relativistic corrections Chem. Phys. Lett. 500, 229 2010 DOI PDF
    Abstract: Very accurate variational calculations of the five lowest vibrational states of the $^3$He$^4$He$^+$ ion are carried out within a framework that does not assume the Born-Oppenheimer (BO) approximation, i.e., treating the two nuclei and three electrons forming the system on an equal footing. The non-BO wave functions are expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. The wave functions are used to calculate the leading relativistic corrections. The approach reproduces the experimental $^3$He$^4$He$^+$ fundamental transition within 0.055 cm$^{-1}$ and similar accuracy is expected for the higher yet unmeasured vibrational transitions determined in the present calculations.
    BibTeX:

    @article{bubin_cpl_500_229_2010,
    author = {Sergiy Bubin and Monika Stanke and Ludwik Adamowicz},
    title = {Lower vibrational transitions of the $^3$He$^4$He$^+$ ion calculated without the Born-Oppenheimer approximation and with leading relativistic corrections},
    journal = {Chem. Phys. Lett.},
    year = {2010},
    volume = {500},
    number = {4-6},
    pages = {229 - 231},
    doi = {10.1016/j.cplett.2010.10.021}
    }
    S. Bubin, J. Komasa, M. Stanke and L. Adamowicz Isotope shifts of the three lowest $^1 S$ states of the B$^+$ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections J. Chem. Phys. 132, 114109 2010 DOI PDF
    Abstract: We present very accurate quantum mechanical calculations of the three lowest $S$-states [$1s^2 2s^2 (^1 S_0)$, $1s^2 2p^2 (^1 S_0)$, and $1s^2 2s 3s (^1 S_0)$] of the two stable isotopes of the boron ion, $^{10}$B$^+$ and $^{11}$B$^+$. At the nonrelativistic level the calculations have been performed with the Hamiltonian that explicitly includes the finite mass of the nucleus as it was obtained by a rigorous separation of the center-of-mass motion from the laboratory frame Hamiltonian. The spatial part of the nonrelativistic wave function for each state was expanded in terms of 10000 all-electron explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians were variationally optimized using a procedure involving the analytical energy gradient determined with respect to the nonlinear parameters. The nonrelativistic wave functions of the three states were subsequently used to calculate the leading $\alpha^2$ relativistic corrections ($\alpha$ is the fine structure constant; $\alpha = 1/c$, where $c$ is the speed of light) and the $\alpha^3$ quantum electrodynamics (QED) correction. We also estimated the $\alpha^4$ QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement. The discrepancy is smaller than 0.4 cm$^{-1}$.
    BibTeX:

    @article{bubin_jcp_132_114109_2010,
    author = {Sergiy Bubin and Jacek Komasa and Monika Stanke and Ludwik Adamowicz},
    title = {Isotope shifts of the three lowest $^1 S$ states of the B$^+$ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2010},
    volume = {132},
    number = {11},
    pages = {114109},
    doi = {10.1063/1.3358999}
    }
    S. Bubin, Ká, lmá and n Varga Calculation of transmission probability by solving an eigenvalue problem J. Phys. Condens. Matter 22, 465306 2010 DOI PDF
    Abstract: The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.
    BibTeX:

    @article{bubin_jpcm_22_465306_2010,
    author = {Sergiy Bubin and K\'{a}lm\'{a}n Varga},
    title = {Calculation of transmission probability by solving an eigenvalue problem},
    journal = {J. Phys. Condens. Matter},
    year = {2010},
    volume = {22},
    number = {46},
    pages = {465306},
    doi = {10.1088/0953-8984/22/46/465306}
    }
    S. Bubin, J. Komasa, M. Stanke and L. Adamowicz Isotope shifts of the $1s^2 2s^2 (^1 S_0) \rightarrow 1 s^2 2p^2 (^1 S_0)$ transition in the doubly ionized carbon ion C$^{2+}$ Phys. Rev. A 81, 052504 2010 DOI PDF
    Abstract: Highly accurate quantum mechanical calculations are performed for the $1s^2 2s^2 (^1 S_0) \rightarrow 1 s^2 2p^2 (^1 S_0)$ transition energy in the isotopomers of C$^{2+}$ ion to determine the isotope shifts. Explicitly correlated Gaussian functions and a variational approach that explicitly includes the nuclear motion are employed in the calculations. The leading relativistic and quantum electrodynamics corrections to the transition energy are also calculated using the perturbation theory with the nonrelativistic wave function as the zero-order approximation. It is determined that the $^{12}$C$^{2+}$ transitions energy, which is obtained from the calculations to be 182519.031 cm$^{-1}$ (vs the experimental value of 182519.88 cm$^{-1}$ , an excellent sub-wave-number agreement) up-shifts by 1.755 cm$^{-1}$ for $^{13}$C$^{2+}$ and by additional 1.498 cm$^{-1}$ for $^{14}$C$^{2+}$. Those shifts are sufficiently large to be measured experimentally.
    BibTeX:

    @article{bubin_pra_81_052504_2010,
    author = {Bubin, Sergiy and Komasa, Jacek and Stanke, Monika and Adamowicz, Ludwik},
    title = {Isotope shifts of the $1s^2 2s^2 (^1 S_0) \rightarrow 1 s^2 2p^2 (^1 S_0)$ transition in the doubly ionized carbon ion C$^{2+}$},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2010},
    volume = {81},
    number = {5},
    pages = {052504},
    doi = {10.1103/PhysRevA.81.052504}
    }
    K. L. Sharkey, S. Bubin and L. Adamowicz Analytical energy gradient in variational calculations of the two lowest $^3 P$ states of the carbon atom with explicitly correlated Gaussian basis functions J. Chem. Phys. 132, 184106 2010 DOI PDF
    Abstract: Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating $n$-electron atomic systems with two $p$-electrons and ($n-2$) $s$-electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited $^3 P$ state of the carbon atom. For the former the lowest energy upper bound ever obtained is reported.
    BibTeX:

    @article{sharkey_jcp_132_184106_2010,
    author = {Keeper L. Sharkey and Sergiy Bubin and Ludwik Adamowicz},
    title = {Analytical energy gradient in variational calculations of the two lowest $^3 P$ states of the carbon atom with explicitly correlated Gaussian basis functions},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2010},
    volume = {132},
    number = {18},
    pages = {184106},
    doi = {10.1063/1.3419931}
    }
    S. Bubin, Ká, lmá and n Varga First-principles time-dependent simulation of laser assisted desorption of hydrogen atoms from H-Si(111) surface Appl. Phys. Lett. 98, 154101 2011 DOI PDF
    Abstract: The dynamics of hydrogen desorption from H-terminated silicon surface clusters has been simulated in the framework of real space time-dependent density functional theory complemented with molecular dynamics for ions. It has been demonstrated that by choosing an appropriate frequency and intensity of the laser it is possible to remove the hydrogen layer from the surface without destroying the structure of underlying silicon. At the laser field intensities used in the current study (0.5-2.0 V/\AA) the desorption process is notably nonlinear.
    BibTeX:

    @article{bubin_apl_98_154101_2011,
    author = {Sergiy Bubin and K\'{a}lm\'{a}n Varga},
    title = {First-principles time-dependent simulation of laser assisted desorption of hydrogen atoms from H--Si(111) surface},
    journal = {Appl. Phys. Lett.},
    publisher = {AIP},
    year = {2011},
    volume = {98},
    number = {15},
    pages = {154101},
    doi = {10.1063/1.3580563}
    }
    S. Bubin, Ká, lmá and n Varga Electron-ion dynamics in laser-assisted desorption of hydrogen atoms from H-Si(111) surface J. Appl. Phys. 110, 064905 2011 DOI PDF
    Abstract: In the framework of real time real space time-dependent density functional theory we have studied the electron-ion dynamics of a hydrogen-terminated silicon surface H-Si(111) subjected to intense laser irradiation. Two surface fragments of different sizes have been used in the simulations. When the intensity and duration of the laser exceed certain levels (which depend on the wavelength) we observe the desorption of the hydrogen atoms, while the underlying silicon layer remains essentially undamaged. Upon further increase of the laser intensity, the chemical bonds between silicon atoms break as well. The results of the simulations suggest that with an appropriate choice of laser parameters it should be possible to remove the hydrogen layer from the H-Si(111) surface in a matter of a few tens of femtoseconds. We have also observed that at high laser field intensities (2-4 V/A in this work) the desorption occurs even when the laser frequency is smaller than the optical gap of the silicon surface fragments. Therefore, nonlinear phenomena must play an essential role in such desorption processes.
    BibTeX:

    @article{bubin_jap_110_064905_2011,
    author = {Sergiy Bubin and K\'{a}lm\'{a}n Varga},
    title = {Electron-ion dynamics in laser-assisted desorption of hydrogen atoms from H-Si(111) surface},
    journal = {J. Appl. Phys.},
    publisher = {AIP},
    year = {2011},
    volume = {110},
    number = {6},
    pages = {064905},
    doi = {10.1063/1.3638064}
    }
    S. Bubin, M. Stanke and L. Adamowicz Vibrational transitions of the $^7$LiH$^+$ ion calculated without the Born-Oppenheimer approximation and with leading relativistic corrections J. Chem. Phys. 134, 024103 2011 DOI PDF
    Abstract: We recently presented very accurate calculations of the fundamental vibrational frequency of the $^7$LiH$^+$ and $^3$He$^4$He$^+$ ions [Stanke et al. Phys. Rev. A 79, 060501(R) (2009)] performed without the Born--Oppenheimer approximation and included leading relativistic corrections. The accuracy of those calculations was estimated to be of the order of 0.06 cm$^{-1}$. In the present work we extend the calculations to the remaining pure vibrational states of $^7$LiH$^+$ and similarly accurate results are generated. They may lead to the experimental search for still unidentified lines corresponding to those transitions.
    BibTeX:

    @article{bubin_jcp_134_024103_2011,
    author = {Sergiy Bubin and Monika Stanke and Ludwik Adamowicz},
    title = {Vibrational transitions of the $^7$LiH$^+$ ion calculated without the Born--Oppenheimer approximation and with leading relativistic corrections},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2011},
    volume = {134},
    number = {2},
    pages = {024103},
    doi = {10.1063/1.3525679}
    }
    S. Bubin and L. Adamowicz Accurate variational calculations of the ground $^2 P^{o} (1s^2 2s^2 2p)$ and excited $^2 S (1s^2 2s 2p^2)$ and $^2 P^{o} (1s^2 2s^2 3p)$ states of singly ionized carbon atom J. Chem. Phys. 135, 214104 2011 DOI PDF
    Abstract: In this article we report accurate nonrelativistic variational calculations of the ground and two excited states of C$^+$ ion. We employ extended and well optimized basis sets of all-electron explicitly correlated Gaussians to represent the wave functions of the states. The optimization of the basis functions is performed with a procedure employing the analytic gradient of the energy with respect to the nonlinear parameters of the Gaussians. The calculations explicitly include the effects due to the finite nuclear mass. The calculated transition energies between the three states are compared to the experimentally derived values. Finally, we present expectation values of some small positive and negative powers of the interparticle distances and contact densities.
    BibTeX:

    @article{bubin_jcp_135_214104_2011,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Accurate variational calculations of the ground $^2 P^{o} (1s^2 2s^2 2p)$ and excited $^2 S (1s^2 2s 2p^2)$ and $^2 P^{o} (1s^2 2s^2 3p)$ states of singly ionized carbon atom},
    journal = {J. Chem. Phys.},
    year = {2011},
    volume = {135},
    pages = {214104},
    doi = {10.1063/1.3664900}
    }
    S. Bubin, M. Stanke and L. Adamowicz Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D$_2$ with including relativistic corrections J. Chem. Phys. 135, 074110 2011 DOI PDF
    Abstract: In this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D$_2$ molecule performed within the framework where the Born-Oppenheimer (BO) approximation is not assumed. After the elimination of the center-of-mass motion, D$_2$ becomes a three-particle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of $\alpha^2$ (where $\alpha = 1/c$ is the fine structure constant) calculated as expectation values of the operators representing these effects.
    BibTeX:

    @article{bubin_jcp_135_74110_2011,
    author = {Sergiy Bubin and Monika Stanke and Ludwik Adamowicz},
    title = {Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D$_2$ with including relativistic corrections},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2011},
    volume = {135},
    number = {7},
    pages = {074110},
    doi = {10.1063/1.3625955}
    }
    S. Bubin and L. Adamowicz Correlated-Gaussian calculations of the ground and low-lying excited states of the boron atom Phys. Rev. A 83, 022505 2011 DOI PDF
    Abstract: Benchmark variational calculations of the four lowest $^2 P$ and $^2 S$ states of the boron atom (including the ground state) have been performed. The wave functions of the states have been expanded in terms of all-particle explicitly correlated Gaussian basis functions and the finite mass of the nucleus has been explicitly accounted for. Variational upper bounds for the nonrelativistic finite- and infinite-nuclear-mass energies of all considered states have been obtained with the relative convergence of the order of 10$^{-7}$--10$^{-8}$. Expectation values of the powers of the inter-particle distances and Dirac $\delta$ functions depending on those distances have also been computed. These calculations provide reference values that can be used to test other high-level quantum chemistry methods.
    BibTeX:

    @article{bubin_pra_83_022505_2011,
    author = {Bubin, Sergiy and Adamowicz, Ludwik },
    title = {Correlated-Gaussian calculations of the ground and low-lying excited states of the boron atom},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2011},
    volume = {83},
    number = {2},
    pages = {022505},
    doi = {10.1103/PhysRevA.83.022505}
    }
    S. Bubin, M. Stanke and L. Adamowicz Complete pure vibrational spectrum of HD calculated without the Born-Oppenheimer approximation and including relativistic corrections Phys. Rev. A 83, 042520 2011 DOI PDF
    Abstract: All 18 bound pure vibrational levels of the HD molecule have been calculated within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states have been corrected for the relativistic effects of the order of $\alpha^2$ (where $\alpha$ is the fine structure constant), calculated using the perturbation theory with the nonrelativistic non-BO wave functions being the zero-order approximation. The calculations were performed by expanding the non-BO wave functions in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and by performing extensive optimization of the Gaussian nonlinear parameters. Up to 10000 basis functions were used for each state.
    BibTeX:

    @article{bubin_pra_83_042520_2011,
    author = {Bubin, Sergiy and Stanke, Monika and Adamowicz, Ludwik},
    title = {Complete pure vibrational spectrum of HD calculated without the Born-Oppenheimer approximation and including relativistic corrections},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2011},
    volume = {83},
    number = {4},
    pages = {042520},
    doi = {10.1103/PhysRevA.83.042520}
    }
    S. Bubin, K. Varga, lmá and n Ground-state energy and relativistic corrections for positronium hydride Phys. Rev. A 84, 012509 2011 DOI PDF
    Abstract: Variational calculations of the ground state of positronium hydride (HPs) are reported, including various expectation values, electron-positron annihilation rates, and leading relativistic corrections to the total and dissociation energies. The calculations have been performed using a basis set of 4000 thoroughly optimized explicitly correlated Gaussian basis functions. The relative accuracy of the variational energy upper bound is estimated to be of the order of $2 \times 10^{-10}$, which is a significant improvement over previous nonrelativistic results.
    BibTeX:

    @article{bubin_pra_84_012509_2011,
    author = {Bubin, Sergiy and Varga, K\'{a}lm\'{a}n},
    title = {Ground-state energy and relativistic corrections for positronium hydride},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2011},
    volume = {84},
    number = {1},
    pages = {012509},
    doi = {10.1103/PhysRevA.84.012509}
    }
    J. A. Driscoll, B. Cook, S. Bubin, Ká, lmá and n Varga First-principles study of field emission from carbon nanotubes and graphene nanoribbons J. Appl. Phys. 110, 024304 2011 DOI PDF
    Abstract: A real-space, real-time implementation of time-dependent density functional theory is used to study electron field emission from nanostructures. Carbon nanotubes and graphene nanoribbons are used as model systems. The calculations show that carbon nanotubes with iron adsorbates have spin-polarized emission currents. Graphene nanoribbons are shown to be good field emitters with spatial variation of the emission current influenced by the presence of passivating hydrogen.
    BibTeX:

    @article{driscoll_jap_110_024304_2011,
    author = {Joseph A. Driscoll and Brandon Cook and Sergiy Bubin and K\'{a}lm\'{a}n Varga},
    title = {First-principles study of field emission from carbon nanotubes and graphene nanoribbons},
    journal = {J. Appl. Phys.},
    year = {2011},
    volume = {110},
    pages = {024304},
    doi = {10.1063/1.3610511}
    }
    J. A. Driscoll, S. Bubin, W. R. French and K. Varga Time-dependent density functional study of field emission from nanotubes composed of C, BN, SiC, Si, and GaN Nanotechnology 22, 285702 2011 DOI PDF
    Abstract: Field emission from various types of nanotubes is studied by propagating the electronic density in real space and time using time-dependent density functional theory. Capped (5, 5) C, BN, SiC, Si, and GaN nanotubes are considered. The GaN, SiC, and Si nanotubes were found to be significantly better field emitters than C and BN nanotubes, both in terms of current magnitude and sharpness of peaks in the energy spectra. By analyzing the electronic structure of the various systems it is seen that the nanotubes with the highest currents have electron densities that extend significantly from the nanotube in the emission direction.
    BibTeX:

    @article{driscoll_n_22_285702_2011,
    author = {Joseph A Driscoll and Sergiy Bubin and William R French and Kalman Varga},
    title = {Time-dependent density functional study of field emission from nanotubes composed of C, BN, SiC, Si, and GaN},
    journal = {Nanotechnology},
    year = {2011},
    volume = {22},
    number = {28},
    pages = {285702},
    doi = {10.1088/0957-4484/22/28/285702}
    }
    J. A. Driscoll, S. Bubin, K. Varga, lmá and n Laser-induced electron emission from nanostructures: A first-principles study Phys. Rev. B 83, 233405 2011 DOI PDF
    Abstract: Time-dependent density functional theory simulation of laser-induced ionization is presented. Various test systems including a small wire-like molecule, C$_{12}$H$_{14}$, as well as carbon nanotubes with varying diameter are studied. It has been demonstrated that significant ionization electron current is produced when a laser pulse is applied. Moreover, pulse-like patterns of the current have been observed, which suggests that short laser pulses can be used to create spatially and temporally localized electron sources.
    BibTeX:

    @article{driscoll_prb_83_233405_2011,
    author = {Driscoll, Joseph A. and Bubin, Sergiy and Varga, K\'alm\'an },
    title = {Laser-induced electron emission from nanostructures: A first-principles study},
    journal = {Phys. Rev. B},
    publisher = {American Physical Society},
    year = {2011},
    volume = {83},
    number = {23},
    pages = {233405},
    doi = {10.1103/PhysRevB.83.233405}
    }
    K. L. Sharkey, S. Bubin and L. Adamowicz An algorithm for calculating atomic $D$ states with explicitly correlated Gaussian functions J. Chem. Phys. 134, 044120 2011 DOI PDF
    Abstract: An algorithm for the variational calculation of atomic $D$ states employing $n$-electron explicitly correlated Gaussians is developed and implemented. The algorithm includes formulas for the first derivatives of the Hamiltonian and overlap matrix elements determined with respect to the Gaussian nonlinear exponential parameters. The derivatives are used to form the energy gradient which is employed in the variational energy minimization. The algorithm is tested in the calculations of the two lowest $D$ states of the lithium and beryllium atoms. For the lowest $D$ state of Li the present result is lower than the best previously reported result.
    BibTeX:

    @article{sharkey_jcp_134_044120_2011,
    author = {Keeper L. Sharkey and Sergiy Bubin and Ludwik Adamowicz},
    title = {An algorithm for calculating atomic $D$ states with explicitly correlated Gaussian functions},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2011},
    volume = {134},
    number = {4},
    pages = {044120},
    doi = {10.1063/1.3523348}
    }
    K. L. Sharkey, S. Bubin and L. Adamowicz Refinement of the experimental energy levels of higher $^2 D$ Rydberg states of the lithium atom with very accurate quantum mechanical calculations J. Chem. Phys. 134, 194114 2011 DOI PDF
    Abstract: Very accurate variational non-relativistic calculations are performed for four higher Rydberg $^2 D$ states ($1s^2 nd^1$, $n$ = 8, ..., 11) of the lithium atom ($^7$Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the $^2 S$ $1s^2 2s^1$ ground state.
    BibTeX:

    @article{sharkey_jcp_134_194114_2011,
    author = {Keeper L. Sharkey and Sergiy Bubin and Ludwik Adamowicz},
    title = {Refinement of the experimental energy levels of higher $^2 D$ Rydberg states of the lithium atom with very accurate quantum mechanical calculations},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2011},
    volume = {134},
    number = {19},
    pages = {194114},
    doi = {10.1063/1.3591836}
    }
    K. L. Sharkey, S. Bubin and L. Adamowicz Lower Rydberg $^{2}D$ states of the lithium atom: Finite-nuclear-mass calculations with explicitly correlated Gaussian functions Phys. Rev. A 83, 012506 2011 DOI PDF
    Abstract: Very accurate variational nonrelativistic calculations are performed for the five lowest Rydberg $^2 D$ states ($1s^2 nd^1$, $n$=3,...,7) of the lithium atom ($^7$Li). The finite-nuclear-mass approach is employed and the wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian function. Four thousand Gaussians are used for each state. The calculated relative energies of the states determined with respect to the $^2 S$ $1s^2 2s^1$ ground state are systematically lower than the experimental values by about 2.5 cm$^{-1}$. As this value is about the same as the difference between the experimental relative energy between $^7$Li$^+$ and $^7$Li in their ground-state energy and the corresponding calculated nonrelativistic relative energy, we attribute it to the relativistic effects not included in the present calculations.
    BibTeX:

    @article{sharkey_pra_83_012506_2011,
    author = {Sharkey, Keeper L. and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Lower Rydberg $^{2}D$ states of the lithium atom: Finite-nuclear-mass calculations with explicitly correlated Gaussian functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2011},
    volume = {83},
    number = {1},
    pages = {012506},
    doi = {10.1103/PhysRevA.83.012506}
    }
    K. L. Sharkey, S. Bubin and L. Adamowicz $^{1}D$ states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions Phys. Rev. A 84, 044503 2011 DOI PDF
    Abstract: Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five $^1 D$ states ($1s^2 2p^2$, $1s^2 2s^1 3d^1$, $1s^2 2s^1 4d^1$, $1s^2 2s^1 5d^1$, and $1s^2 2s^1 6d^1$) of the beryllium atom ($^9$Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular states.
    BibTeX:

    @article{sharkey_pra_84_044503_2011,
    author = {Sharkey, Keeper L. and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {$^{1}D$ states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2011},
    volume = {84},
    pages = {044503},
    doi = {10.1103/PhysRevA.84.044503}
    }
    S. Bubin and L. Adamowicz Explicitly correlated Gaussian calculations of the $^2 P^o$ Rydberg spectrum of the lithium atom J. Chem. Phys. 136, 134305 2012 DOI PDF
    Abstract: Accurate quantum-mechanical nonrelativistic variational calculations are performed for the nine lowest members of the $^2 P^o$ Rydberg series ($1s^2 np^1$, $n$=2,...,10) of the lithium atom. The effect of the finite nuclear mass is included in the calculations allowing for determining the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The calculated state energies are compared with the available experimental data.
    BibTeX:

    @article{bubin_jcp_136_134305_2012,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Explicitly correlated Gaussian calculations of the $^2 P^o$ Rydberg spectrum of the lithium atom},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2012},
    volume = {136},
    number = {13},
    pages = {134305},
    doi = {10.1063/1.3698584}
    }
    S. Bubin and L. Adamowicz Assessment of the accuracy the experimental energies of the $^1 P^o$ $1s^2 2s 6p$ and $1s^2 2s7p$ states of $^9$Be based on variational calculations with explicitly correlated Gaussians J. Chem. Phys. 137, 104315 2012 DOI PDF
    Abstract: Benchmark variational calculations are performed for the six lowest states of the $^1 P^o$ $1s^2 2s np$ state series of the $^9$Be atom. The wave functions of the states are expanded in terms of all-particle, explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations. The exponential parameters of the Gaussians are variationally optimized using the analytical energy gradient determined with respect to those parameters. Besides providing reference non-relativistic energies for the considered states, the calculations also allow to assess the accuracy of the experimental energies of the $^1 P^o$ $1s^2 2s 6p$ and $1s^2 2s 7p$ states and suggest their refinement.
    BibTeX:

    @article{bubin_jcp_137_104315_2012,
    author = {Sergiy Bubin and Ludwik Adamowicz},
    title = {Assessment of the accuracy the experimental energies of the $^1 P^o$ $1s^2 2s 6p$ and $1s^2 2s7p$ states of $^9$Be based on variational calculations with explicitly correlated Gaussians},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2012},
    volume = {137},
    number = {10},
    pages = {104315},
    doi = {10.1063/1.4742764}
    }
    S. Bubin, M. Atkinson, K. Varga, lmá, n, X. Xie, S. Roither, D. Kartashov, Baltu&scaron, A. ka and M. Kitzler Strong laser-pulse-driven ionization and Coulomb explosion of hydrocarbon molecules Phys. Rev. A 86, 043407 2012 DOI PDF
    Abstract: Field ionization and Coulomb explosion of small hydrocarbon molecules driven by intense laser pulses are studied in a combined theoretical and experimental framework. The spectra of ejected protons calculated by the time-dependent density functional approach are in good agreement with the experimental data. The results of the simulations give detailed insight into the correlated electron and nuclear dynamics and complement the experiment with a time-dependent physical picture. It is demonstrated that the Coulomb explosion in the studied molecular systems is a sudden, all-at-once fragmentation where the ionization step is followed by a simultaneous ejection of the charged fragments.
    BibTeX:

    @article{bubin_pra_86_043407_2012,
    author = {Bubin, Sergiy and Atkinson, Mackenzie and Varga, K\'alm\'an and Xie, Xinhua and Roither, Stefan and Kartashov, Daniil and Baltu\v{s}ka, Andrius and Kitzler, Markus},
    title = {Strong laser-pulse-driven ionization and Coulomb explosion of hydrocarbon molecules},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2012},
    volume = {86},
    pages = {043407},
    doi = {10.1103/PhysRevA.86.043407}
    }
    S. Bubin, K. Varga, lmá and n Electron and ion dynamics in graphene and graphane fragments subjected to high-intensity laser pulses Phys. Rev. B 85, 205441 2012 DOI PDF
    Abstract: In the framework of real-time real-space time-dependent density functional theory complemented with Ehrenfest molecular dynamics we have studied the response of small graphene and graphane fragments to intense femtosecond laser pulses. In particular, we have investigated how the response changes with laser pulses of different frequency (near IR, visible, and UV). The results of our simulations show that graphene has a very high immediate (i.e., within laser-pulse duration) damage threshold. They also suggest that, similar to the case of other hydrogenated surfaces, it should be possible to selectively desorb hydrogens from graphane without destroying the underlying carbon structure provided that the laser pulse parameters are properly chosen.
    BibTeX:

    @article{bubin_prb_85_205441_2012,
    author = {Bubin, Sergiy and Varga, K\'alm\'an},
    title = {Electron and ion dynamics in graphene and graphane fragments subjected to high-intensity laser pulses},
    journal = {Phys. Rev. B},
    publisher = {American Physical Society},
    year = {2012},
    volume = {85},
    pages = {205441},
    doi = {10.1103/PhysRevB.85.205441}
    }
    S. Bubin, B. Wang, S. Pantelides, K. Varga, lmá and n Simulation of high-energy ion collisions with graphene fragments Phys. Rev. B 85, 235435 2012 DOI PDF
    Abstract: The collision of energetic ions and graphene fragments is studied in the framework of real-space finite-difference time-dependent density functional theory (TDDFT) coupled with classical molecular dynamics for nuclei. The amount of energy transferred from the projectile to the target is calculated to explore the defect formation mechanisms as a function of the projectile's energy. It is found that creation of defects in graphene due to the interaction of a fast proton with valence electrons is unlikely. In the case of projectiles with higher charges, the transferred energy increases significantly, leading to higher probability of bond breaking.
    BibTeX:

    @article{bubin_prb_85_235435_2012,
    author = {Bubin, Sergiy and Wang, Bin and Pantelides, Sokrates and Varga, K\'alm\'an},
    title = {Simulation of high-energy ion collisions with graphene fragments},
    journal = {Phys. Rev. B},
    publisher = {American Physical Society},
    year = {2012},
    volume = {85},
    pages = {235435},
    doi = {10.1103/PhysRevB.85.235435}
    }
    S. Bubin, M. Pavanello, W.-C. Tung, K. L. Sharkey and L. Adamowicz Born-Oppenheimer and Non-Born-Oppenheimer, Atomic and Molecular Calculations with Explicitly Correlated Gaussians Chem. Rev. 113, 36 2013 DOI PDF
    BibTeX:

    @article{bubin_cr_113_36_2013,
    author = {Bubin, Sergiy and Pavanello, Michele and Tung, Wei-Cheng and Sharkey, Keeper L. and Adamowicz, Ludwik},
    title = {Born--Oppenheimer and Non-Born--Oppenheimer, Atomic and Molecular Calculations with Explicitly Correlated Gaussians},
    journal = {Chem. Rev.},
    year = {2013},
    volume = {113},
    number = {0},
    pages = {36--79},
    doi = {10.1021/cr200419d}
    }
    S. Bubin, K. L. Sharkey and L. Adamowicz Prediction of $^2 D$ Rydberg energy levels of $^6$Li and $^7$Li based on very accurate quantum mechanical calculations performed with explicitly correlated Gaussian functions J. Chem. Phys. 138, 164308 2013 DOI PDF
    Abstract: Very accurate variational nonrelativistic finite-nuclear-mass calculations employing all-electron explicitly correlated Gaussian basis functions are carried out for six Rydberg $^2 D$ states ($1s^2 nd$, $n=6, ..., 11$) of the $^7$Li and $^6$Li isotopes. The exponential parameters of the Gaussian functions are optimized using the variational method with the aid of the analytical energy gradient determined with respect to these parameters. The experimental results for the lower states ($n=3, ..., 6$) and the calculated results for the higher states ($n=7, ..., 11$) fitted with quantum-defect-like formulas are used to predict the energies of $^2 D$ $1s^2 nd$ states for $^7$Li and $^6$Li with $n$ up to 30.
    BibTeX:

    @article{bubin_jcp_138_164308_2013,
    author = {Sergiy Bubin and Keeper L. Sharkey and Ludwik Adamowicz},
    title = {Prediction of $^2 D$ Rydberg energy levels of $^6$Li and $^7$Li based on very accurate quantum mechanical calculations performed with explicitly correlated Gaussian functions},
    journal = {J. Chem. Phys.},
    publisher = {AIP},
    year = {2013},
    volume = {138},
    number = {16},
    pages = {164308},
    doi = {10.1063/1.4801855}
    }
    S. Bubin, A. G. Russakoff and K. Varga Interaction of electromagnetic fields and atomic clusters J. Phys. Conf. Ser. 436, 012084 2013 DOI PDF
    Abstract: In the framework of real-time real-space time-dependent density functional theory complemented with Ehrenfest molecular dynamics we have studied the response of nanostructures to intense femtosecond laser pulses. Examples of applications include laser desorption of hydrogen from graphene and Coulomb explosion of hydrocarbon molecules.
    BibTeX:

    @article{bubin_jpcs_436_12084_2013,
    author = {S Bubin and A G Russakoff and K Varga},
    title = {Interaction of electromagnetic fields and atomic clusters},
    journal = {J. Phys. Conf. Ser.},
    year = {2013},
    volume = {436},
    number = {1},
    pages = {012084},
    doi = {10.1088/1742-6596/436/1/012084}
    }
    S. Bubin and L. Adamowicz Prediction of $^2 S$ Rydberg energy levels of $^6$Li and $^7$Li based on quantum-mechanical calculations performed with explicitly correlated Gaussian functions Phys. Rev. A 87, 042510 2013 DOI PDF
    Abstract: Accurate variational quantum-mechanical calculations are performed for the nine lowest $^2 S$ ($1s^2 ns$), $n=2,..,10$ states of the lithium atom. The effect of the finite nuclear mass is explicitly included in the calculations allowing for the determination of the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and their exponential parameters are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The experimental results for the lower states ($n=3,...,6$) and the calculated results for the higher states ($n=7,...,10$) fitted with quantum-defect-like formulas are used to predict the energies of $^2 S$ $1s^2 ns$ states for $^7$Li and $^6$Li with $n$ up to 30.
    BibTeX:

    @article{bubin_pra_87_042510_2013,
    author = {Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Prediction of $^2 S$ Rydberg energy levels of $^6$Li and $^7$Li based on quantum-mechanical calculations performed with explicitly correlated Gaussian functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2013},
    volume = {87},
    pages = {042510},
    doi = {10.1103/PhysRevA.87.042510}
    }
    S. Bubin, O. V. Prezhdo, K. Varga, lmá and n Instability of tripositronium Phys. Rev. A 87, 054501 2013 DOI PDF
    Abstract: The stability of tripositronium, a system consisting of three electrons and three positrons, has been investigated systematically by varying the repulsion strength between like-charged particles. The possibility of the existence of a Ps$_3$ bound state that is stable against dissociation appears utterly unlikely based on the results of variational calculations employing all-particle explicitly correlated Gaussian basis functions.
    BibTeX:

    @article{bubin_pra_87_054501_2013,
    author = {Bubin, Sergiy and Prezhdo, Oleg V. and Varga, K\'alm\'an},
    title = {Instability of tripositronium},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2013},
    volume = {87},
    pages = {054501},
    doi = {10.1103/PhysRevA.87.054501}
    }
    S. Bubin and O. V. Prezhdo Excited States of Positronic Lithium and Beryllium Phys. Rev. Lett. 111, 193401 2013 DOI PDF
    Abstract: Using a variational method with an explicitly correlated Gaussian basis, we study the $e^+$-Li and $e^+$-Be complexes in the ground and lowest excited states with higher spin multiplicity. Our calculations provide rigorous theoretical confirmation that a positron can be attached to the excited states: $1s 2s 2p \, ^4 P^o$ and $1s^2 2s 2p \, ^3 P^o$ for $e^+$-Li and $e^+$-Be, respectively. The result is particularly notable for the $e^+$-Be complex, as the excited $^3 P^o$ state lies below the autoionization threshold. We report accurate binding energies, annihilation rates and structural properties of these positron-atom systems. The existence of the ground and metastable excited states with bound positron opens up a new route to the presently lacking experimental verification of stability of a positron binding to any neutral atom.
    BibTeX:

    @article{bubin_prl_111_193401_2013,
    author = {Bubin, Sergiy and Prezhdo, Oleg V.},
    title = {Excited States of Positronic Lithium and Beryllium},
    journal = {Phys. Rev. Lett.},
    publisher = {American Physical Society},
    year = {2013},
    volume = {111},
    pages = {193401},
    doi = {10.1103/PhysRevLett.111.193401}
    }
    J. Mitroy, S. Bubin, W. Horiuchi, Y. Suzuki, L. Adamowicz, W. Cencek, K. Szalewicz, J. Komasa, D. Blume, K. Varga, lmá and n Theory and application of explicitly correlated Gaussians Rev. Mod. Phys. 85, 693 2013 DOI PDF
    Abstract: The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.
    BibTeX:

    @article{mitroy_rmp_85_693_2013,
    author = {Mitroy, Jim and Bubin, Sergiy and Horiuchi, Wataru and Suzuki, Yasuyuki and Adamowicz, Ludwik and Cencek, Wojciech and Szalewicz, Krzysztof and Komasa, Jacek and Blume, D. and Varga, K\'alm\'an},
    title = {Theory and application of explicitly correlated Gaussians},
    journal = {Rev. Mod. Phys.},
    publisher = {American Physical Society},
    year = {2013},
    volume = {85},
    pages = {693--749},
    doi = {10.1103/RevModPhys.85.693}
    }
    S. Bubin and L. Adamowicz Prediction of $^1 P$ Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians J. Chem. Phys. 140, 024301 2014 DOI PDF
    Abstract: Benchmark variational calculations are performed for the seven lowest $1s^2 2s np (^1 P)$, $n = 2...8$, states of the beryllium atom. The calculations explicitly include the effect of finite mass of $^9$Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of $1s^2 2s np (^1 P) \rightarrow 1s^2 2s^2 (^1 S)$ transition is about 12 cm$^{-1}$. The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm$^{-1}$.
    BibTeX:

    @article{bubin_jcp_140_024301_2014,
    author = {Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Prediction of $^1 P$ Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians},
    journal = {J. Chem. Phys.},
    year = {2014},
    volume = {140},
    number = {2},
    pages = {024301},
    doi = {10.1063/1.4858275}
    }
    S. Bubin, M. Stanke and L. Adamowicz Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of ditritium using all-particle explicitly correlated Gaussian functions J. Chem. Phys. 140, 154303 2014 DOI PDF
    Abstract: Very accurate variational calculations of the complete pure vibrational spectrum of the ditritium (T$_2$) molecule are performed within the framework where the Born-Oppenheimer approximation is not assumed. After separating out the center-of-mass motion from the total laboratory-frame Hamiltonian, T$_2$ becomes a three-particle problem. States corresponding to the zero total angular momentum, which are pure vibrational states, are spherically symmetric in this framework. The wave functions of these states are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. In the calculations the total energies, the dissociation energies, and expectation values of some operators dependent on interparticle distances are determined.
    BibTeX:

    @article{bubin_jcp_140_154303_2014,
    author = {Bubin, Sergiy and Stanke, Monika and Adamowicz, Ludwik},
    title = {Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of ditritium using all-particle explicitly correlated Gaussian functions},
    journal = {J. Chem. Phys.},
    year = {2014},
    volume = {140},
    number = {15},
    pages = {154303},
    doi = {10.1063/1.4870935}
    }
    K. L. Sharkey, S. Bubin and L. Adamowicz Singlet-triplet energy splitting between $^1 D$ and $^3 D$ ($1s^2 2s nd$) $n$=3,4,5, and 6, Rydberg states of the beryllium atom ($^9 Be$) calculated with all-electron explicitly correlated Gaussian functions Chem. Phys. Lett. 616-617, 254 2014 DOI PDF
    Abstract: Abstract Accurate variational nonrelativistic quantum-mechanical calculations are performed for the five lowest $^1 D$ and four lowest $^3 D$ states of the $^9 Be$ isotope of the beryllium atom. All-electron explicitly correlated Gaussian (ECG) functions are used in the calculations and their nonlinear parameters are optimized with the aid of the analytical energy gradient determined with respect to these parameters. The effect of the finite nuclear mass is directly included in the Hamiltonian used in the calculations. The singlet--triplet energy gaps between the corresponding $^1 D$ and $^3 D$ states, are reported.
    BibTeX:

    @article{sharkey_cpl_616_254_2014,
    author = {Keeper L. Sharkey and Sergiy Bubin and Ludwik Adamowicz},
    title = {Singlet--triplet energy splitting between $^1 D$ and $^3 D$ ($1s^2 2s nd$) $n$=3,4,5, and 6, Rydberg states of the beryllium atom ($^9 Be$) calculated with all-electron explicitly correlated Gaussian functions},
    journal = {Chem. Phys. Lett.},
    year = {2014},
    volume = {616-617},
    pages = {254-258},
    doi = {10.1016/j.cplett.2014.10.012}
    }
    X. Xie, S. Roither, Schö, M. ffler, H. Xu, S. Bubin, Lö, E. tstedt, S. Erattuphuza, A. Iwasaki, D. Kartashov, K. Varga, lmá, n, G. , G. Paulus, Baltu&scaron, A. ka, K. Yamanouchi and M. Kitzler Role of proton dynamics in efficient photoionization of hydrocarbon molecules Phys. Rev. A 89, 023429 2014 DOI PDF
    Abstract: We experimentally investigate the ionization mechanism behind the formation of remarkably high charge states observed in the laser-pulse-induced fragmentation of different hydrocarbon molecules by Roither et al. [Phys. Rev. Lett. 106, 163001 (2011)], who suggested enhanced ionization occurring at multiple C-H bonds as the underlying ionization mechanism. Using multiparticle coincidence momentum imaging we measure the yield of multiply charged fragmenting ethylene and acetylene molecules at several intensities and pulse durations ranging from the few-cycle regime to 25 fs. We observe, at constant intensity, a strong increase of the proton energy with increasing laser pulse duration. It is shown that this is caused by a strong increase in the yield of highly charged parent molecular ions with pulse duration. Based on experimental evidence we explain this increase by the necessary population of precursor states in the parent ion that feature fast C-H stretch dynamics to the critical internuclear distance, where efficient ionization via enhanced ionization takes place. For increasing pulse duration these precursor ionic states are more efficiently populated, which leads in turn to a higher enhanced-ionization probability for longer pulses. Our work provides experimental evidence for the existence of a multiple-bond version of enhanced ionization in polyatomic molecules.
    BibTeX:

    @article{xie_pra_89_023429_2014,
    author = {Xie, Xinhua and Roither, Stefan and Sch\"offler, Markus and Xu, Huailiang and Bubin, Sergiy and L\"otstedt, Erik and Erattuphuza, Sonia and Iwasaki, Atsushi and Kartashov, Daniil and Varga, K\'alm\'an and G.~Paulus, Gerhard and Baltu\v{s}ka, Andrius and Yamanouchi, Kaoru and Kitzler, Markus},
    title = {Role of proton dynamics in efficient photoionization of hydrocarbon molecules},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2014},
    volume = {89},
    pages = {023429},
    doi = {10.1103/PhysRevA.89.023429}
    }
    A. Russakoff, S. Bubin, X. Xie, S. Erattupuzha, M. Kitzler, K. Varga, lmá and n Time-dependent density-functional study of the alignment-dependent ionization of acetylene and ethylene by strong laser pulses Phys. Rev. A 91, 023422 2015 DOI PDF
    BibTeX:

    @article{russakoff_pra_91_023422_2015,
    author = {Russakoff, Arthur and Bubin, Sergiy and Xie, Xinhua and Erattupuzha, Sonia and Kitzler, Markus and Varga, K\'{a}lm\'{a}n},
    title = {Time-dependent density-functional study of the alignment-dependent ionization of acetylene and ethylene by strong laser pulses},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2015},
    volume = {91},
    pages = {023422},
    doi = {10.1103/PhysRevA.91.023422}
    }
    S. Bubin, M. Formanek and L. Adamowicz Universal all-particle explicitly-correlated Gaussians for non-Born-Oppenheimer calculations of molecular rotationless states Chem. Phys. Lett. 647, 122 2016 DOI PDF
    Abstract: Complex explicitly correlated one-center all-particle Gaussian functions (CECGs) are tested as basis functions for molecular non-Born--Oppenheimer (non-BO) calculations. The tests concern the complete spectrum of the 23 bound pure vibrational states of the HD$^+$ ion. The tests show that CECGs are very effective in representing both the nuclear-nuclear correlation and the vibrational oscillation of the wave functions in terms of the internuclear distance. This finding is important because it paves the way for high-accuracy non-BO calculations of bound vibrational states of molecules with more than two nuclei that have never been performed before.
    BibTeX:

    @article{bubin_cpl_647_122_2016,
    author = {Sergiy Bubin and Martin Formanek and Ludwik Adamowicz},
    title = {Universal all-particle explicitly-correlated Gaussians for non-Born--Oppenheimer calculations of molecular rotationless states},
    journal = {Chem. Phys. Lett. },
    year = {2016},
    volume = {647},
    pages = {122-126},
    doi = {10.1016/j.cplett.2016.01.056}
    }
    S. Bubin, M. Stanke and L. Adamowicz Relativistic corrections for non-Born-Oppenheimer molecular wave functions expanded in terms of complex explicitly correlated Gaussian functions Phys. Rev. A 95, 062509 2017 DOI PDF
    Abstract: In our previous work S. Bubin et al., Chem. Phys. Lett. 647, 122 (2016), it was established that complex explicitly correlated one-center all-particle Gaussian functions (CECGs) provide effective basis functions for very accurate nonrelativistic molecular non-Born-Oppenheimer calculations. In this work, we advance the molecular CECGs approach further by deriving and implementing algorithms for calculating the leading relativistic corrections within this approach. The algorithms are tested in the calculations of the corrections for all 23 bound pure vibrational states of the HD$^+$ ion.
    BibTeX:

    @article{bubin_pra_95_062509_2017,
    author = {Bubin, Sergiy and Stanke, Monika and Adamowicz, Ludwik},
    title = {Relativistic corrections for non-Born-Oppenheimer molecular wave functions expanded in terms of complex explicitly correlated Gaussian functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2017},
    volume = {95},
    pages = {062509},
    doi = {10.1103/PhysRevA.95.062509}
    }
    S. Bubin and L. Adamowicz Lowest $^{2}S$ Electronic Excitations of the Boron Atom Phys. Rev. Lett. 118, 043001 2017 DOI PDF
    Abstract: A theoretical ab initio approach for calculating bound states of small atoms is developed and implemented. The approach is based on finite-nuclear-mass [non-Born-Oppenheimer (non-BO)] nonrelativistic variational calculations performed with all-particle explicitly correlated Gaussian functions and includes the leading relativistic and quantum electrodynamics energy corrections determined using the non-BO wave functions. The approach is applied to determine the total and transition energies for the lowest four $^2 S$ electronic excitations of the boron atom. The transition energies agree with the available experimental values within 0.2-0.3 cm$^{-1}$. Previously, such accuracy was achieved for three- and four-electron systems.
    BibTeX:

    @article{bubin_prl_118_043001_2017,
    author = {Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Lowest $^{2}S$ Electronic Excitations of the Boron Atom},
    journal = {Phys. Rev. Lett.},
    publisher = {American Physical Society},
    year = {2017},
    volume = {118},
    pages = {043001},
    doi = {10.1103/PhysRevLett.118.043001}
    }
    S. Erattupuzha, C. L. Covington, A. Russakoff, E. Lö, tstedt, S. Larimian, Vá, clav Hanus, S. Bubin, M. Koch, S. Grä, fe, A. Baltu&scaron, ka, X. Xie, K. Yamanouchi, Ká, lmá, n Varga and M. Kitzler Enhanced ionisation of polyatomic molecules in intense laser pulses is due to energy upshift and field coupling of multiple orbitals J. Phys. B 50, 125601 2017 DOI PDF
    Abstract: We present the results of a combined experimental and numerical study on strong-field ionisation of acetylene performed with the aim of identifying the mechanism behind the previously reported surprisingly large multi-electron ionisation probabilities of polyatomic molecules. Using coincidence momentum imaging techniques and time-dependent density functional simulations, we show that the reported efficient ionisation is due to the combined action of a significant geometrically induced energy upshift of the most relevant valence orbitals as the C--H distance stretches beyond about two times the equilibrium distance, and a strong increase in the coupling between multiple molecular orbitals concomitant with this stretch motion. The identified enhanced ionisation mechanism, which we refer to as EIC-MOUSE, is only effective for molecules aligned close to parallel to the laser polarisation direction, and is inhibited for perpendicularly aligned molecules because of a suppression of the C--H stretch motion during the onset of ionisation.
    BibTeX:

    @article{erattupuzha_jpb_50_125601_2017,
    author = {Sonia Erattupuzha and Cody L Covington and Arthur Russakoff and Erik L\"otstedt and Seyedreza Larimian and V\'aclav Hanus and Sergiy Bubin and Markus Koch and Stefanie Gr\"afe and Andrius Baltu\v{s}ka and Xinhua Xie and Kaoru Yamanouchi and K\'alm\'an Varga and Markus Kitzler},
    title = {Enhanced ionisation of polyatomic molecules in intense laser pulses is due to energy upshift and field coupling of multiple orbitals},
    journal = {J. Phys. B},
    year = {2017},
    volume = {50},
    number = {12},
    pages = {125601},
    doi = {10.1088/1361-6455/aa7098}
    }
    M. Stanke, A. Bralin, S. Bubin and L. Adamowicz Leading relativistic corrections for atomic $P$ states calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions Phys. Rev. A 97, 012513 2018 DOI PDF
    Abstract: In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the $L=1$ total orbital angular momentum ($P$ states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest $^1 P$ states of the helium atom and the four lowest $^1 P$ states of the beryllium atom.
    BibTeX:

    @article{stanke_pra_97_012513_2018,
    author = {Stanke, Monika and Bralin, Amir and Bubin, Sergiy and Adamowicz, Ludwik},
    title = {Leading relativistic corrections for atomic $P$ states calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions},
    journal = {Phys. Rev. A},
    publisher = {American Physical Society},
    year = {2018},
    volume = {97},
    pages = {012513},
    doi = {10.1103/PhysRevA.97.012513}
    }
    A. Bralin, S. Bubin, M. Stanke and L. Adamowicz The $^2 S$ Rydberg series of the lithium atom. Calculations with all-electron explicitly correlated Gaussian functions Chem. Phys. Lett. 730, 497 2019 DOI PDF
    Abstract: In this work we report very accurate variational calculations of the twelve lowest 2S Rydberg states of the lithium atom performed with the finite-nuclear-mass (FNM) approach and with all-electron explicitly correlated Gaussian functions. The FNM non-relativistic variational energies of the states are augmented with the leading relativistic and QED corrections. The calculated transition energies are compared with the previous works (only eight states of the series were calculated before) and with the available experimental results. Density distributions of the electrons and the nucleus in the center-of-mass frame are also shown.
    BibTeX:

    @article{bralin_cpl_730_497_2019,
    author = {Amir Bralin and Sergiy Bubin and Monika Stanke and Ludwik Adamowicz},
    title = {The $^2 S$ Rydberg series of the lithium atom. Calculations with all-electron explicitly correlated Gaussian functions},
    journal = {Chem. Phys. Lett.},
    year = {2019},
    volume = {730},
    pages = {497 - 505},
    doi = {10.1016/j.cplett.2019.06.051}
    }
    E. M. Chavez, S. Bubin and L. Adamowicz Implementation of explicitly correlated complex Gaussian functions in calculations of molecular rovibrational $J=1$ states without Born-Oppenheimer approximation Chem. Phys. Lett. 717, 147 2019 DOI PDF
    Abstract: In our previous work (Bubin et al., 2016) it was established that complex explicitly-correlated one-center all-particle Gaussian functions (CECGs) provide an effective basis set for very accurate non-relativistic molecular non-Born-Oppenheimer (non-BO) calculations for vibrational ground and excited states corresponding to the rotational ground state. In this work we advance the molecular CECGs approach further by implementing and testing the algorithms for calculating the vibrational states corresponding to the first rotational excited state (the $J=1$ state). The test concerns all bound $J=1$ rovibrational states of the HD$^+$ ion.
    BibTeX:

    @article{chavez_cpl_717_147_2019,
    author = {Erik M. Chavez and Sergiy Bubin and Ludwik Adamowicz},
    title = {Implementation of explicitly correlated complex Gaussian functions in calculations of molecular rovibrational $J=1$ states without Born-Oppenheimer approximation},
    journal = {Chem. Phys. Lett.},
    year = {2019},
    volume = {717},
    pages = {147-151},
    doi = {10.1016/j.cplett.2019.01.013}
    }
    M. Stanke, S. Bubin and L. Adamowicz Lowest ten $^1 P$ Rydberg states of beryllium calculated with all-electron explicitly correlated Gaussian functions J. Phys. B 52, 155002 2019 DOI PDF
    Abstract: In this work we report very accurate calculations of the ten lowest $^1 P$ ($L=1$) bound states of the beryllium atom performed with the finite-nuclear-mass (FNM) approach and with all-electron explicitly correlated Gaussian functions. The FNM non-relativistic variational energies of the states are augmented with the leading relativistic and quantum-electrodynamics (QED) corrections. The latter include the Araki–Sucher QED correction whose implementation for the $L=1$ states is featured in this work. The calculated energies for interstate transition energies are compared with the experimental results.
    BibTeX:

    @article{stanke_jpb_52_155002_2019,
    author = {Monika Stanke and Sergiy Bubin and Ludwik Adamowicz},
    title = {Lowest ten $^1 P$ Rydberg states of beryllium calculated with all-electron explicitly correlated Gaussian functions},
    journal = {J. Phys. B},
    year = {2019},
    volume = {52},
    number = {15},
    pages = {155002},
    doi = {10.1088/1361-6455/ab2510}
    }

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