1
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Woźniak AP, Adamowicz L, Pedersen TB, Kvaal S. Gaussians for Electronic and Rovibrational Quantum Dynamics. J Phys Chem A 2024; 128:3659-3671. [PMID: 38687971 PMCID: PMC11089519 DOI: 10.1021/acs.jpca.4c00364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 03/23/2024] [Accepted: 04/08/2024] [Indexed: 05/02/2024]
Abstract
The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.
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Affiliation(s)
| | - Ludwik Adamowicz
- Department
of Chemistry and Biochemistry, University
of Arizona, 1306 E University Blvd, Tucson, Arizona 85721-0041, United States
| | - Thomas Bondo Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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2
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Nasiri S, Shomenov T, Bubin S, Adamowicz L. Dissociation energy and the lowest vibrational transition in LiH without assuming the non-Born–Oppenheimer approximation. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2147105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Saeed Nasiri
- Department of Physics, Nazarbayev University, Nur-Sultan, Kazakhstan
| | | | - Sergiy Bubin
- Department of Physics, Nazarbayev University, Nur-Sultan, Kazakhstan
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
- Department of Physics, University of Arizona, Tucson, AZ, USA
- Centre for Advanced Study (CAS), the Norwegian Academy of Science and Letters, Oslo, Norway
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3
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Muolo A, Baiardi A, Feldmann R, Reiher M. Nuclear-electronic all-particle density matrix renormalization group. J Chem Phys 2020; 152:204103. [PMID: 32486651 DOI: 10.1063/5.0007166] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We introduce the Nuclear-Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schrödinger equation simultaneously for electrons and other quantum species. In contrast to the already existing multicomponent approaches, in this work, we construct from the outset a multi-reference trial wave function with stochastically optimized non-orthogonal Gaussian orbitals. By iterative refining of the Gaussians' positions and widths, we obtain a compact multi-reference expansion for the multicomponent wave function. We extend the DMRG algorithm to multicomponent wave functions to take into account inter- and intra-species correlation effects. The efficient parameterization of the total wave function as a matrix product state allows NEAP-DMRG to accurately approximate the full configuration interaction energies of molecular systems with more than three nuclei and 12 particles in total, which is currently a major challenge for other multicomponent approaches. We present the NEAP-DMRG results for two few-body systems, i.e., H2 and H3 +, and one larger system, namely, BH3.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Alberto Baiardi
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Robin Feldmann
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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4
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Charry J, Pedraza-González L, Reyes A. On the physical interpretation of the nuclear molecular orbital energy. J Chem Phys 2017; 146:214103. [PMID: 28576090 PMCID: PMC5453789 DOI: 10.1063/1.4984098] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 05/11/2017] [Indexed: 11/14/2022] Open
Abstract
Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.
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Affiliation(s)
- Jorge Charry
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
| | - Laura Pedraza-González
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
| | - Andrés Reyes
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
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5
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Yang Y, Kylänpää I, Tubman NM, Krogel JT, Hammes-Schiffer S, Ceperley DM. How large are nonadiabatic effects in atomic and diatomic systems? J Chem Phys 2015; 143:124308. [DOI: 10.1063/1.4931667] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yubo Yang
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Ilkka Kylänpää
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
- Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland
| | - Norm M. Tubman
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Jaron T. Krogel
- Oak Ridge National Laboratory, Materials Sciences & Technology Division, Oak Ridge, Tennessee 37831, USA
| | | | - David M. Ceperley
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
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6
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Simmen B, Mátyus E, Reiher M. Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory. J Chem Phys 2014; 141:154105. [PMID: 25338879 DOI: 10.1063/1.4897632] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X (1)Σ(g)(+) and B (1)Σ(u)(+) electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.
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Affiliation(s)
- Benjamin Simmen
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Eövtös University, Institute of Chemistry, P.O. Box 32, H-1518, Budapest 112, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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7
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Goli M, Shahbazian S. The two-component quantum theory of atoms in molecules (TC-QTAIM): foundations. Theor Chem Acc 2012. [DOI: 10.1007/s00214-012-1208-9] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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8
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Hoshino M, Nishizawa H, Nakai H. Rigorous non-Born-Oppenheimer theory: Combination of explicitly correlated Gaussian method and nuclear orbital plus molecular orbital theory. J Chem Phys 2011; 135:024111. [DOI: 10.1063/1.3609806] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Schmidling D. High accuracy interpolation of diatomic pseudo-potentials with high order Hermite splines. COMPUT THEOR CHEM 2011. [DOI: 10.1016/j.comptc.2010.10.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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10
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Sharkey KL, Bubin S, Adamowicz L. Analytical energy gradient in variational calculations of the two lowest P3 states of the carbon atom with explicitly correlated Gaussian basis functions. J Chem Phys 2010. [DOI: 10.1063/1.3419931] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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11
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Cooper IL, Dickinson AS. Construction of theoretical hybrid potential energy curves for LiH(XΣ+1). J Chem Phys 2009; 131:204303. [DOI: 10.1063/1.3259841] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Bubin S, Stanke M, Adamowicz L. Non-Born–Oppenheimer calculations of the BH molecule. J Chem Phys 2009; 131:044128. [DOI: 10.1063/1.3195061] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
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13
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Bubin S, Leonarski F, Stanke M, Adamowicz L. Non-adiabatic corrections to the energies of the pure vibrational states of H2. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.06.060] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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14
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Pachucki K, Komasa J. Nonadiabatic corrections to rovibrational levels of H2. J Chem Phys 2009; 130:164113. [DOI: 10.1063/1.3114680] [Citation(s) in RCA: 138] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Bytautas L, Matsunaga N, Nagata T, Gordon MS, Ruedenberg K. Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum. J Chem Phys 2008; 127:204313. [PMID: 18052433 DOI: 10.1063/1.2805392] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F(2) are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm(-1) over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm(-1) of the experimental value of 12 953+/-8 cm(-1). The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev. 41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.
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Affiliation(s)
- L Bytautas
- Department of Chemistry, Iowa State University, Ames, IA 50011, USA
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16
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Stanke M, Kȩdziera D, Bubin S, Adamowicz L. Electron affinity of Li7 calculated with the inclusion of nuclear motion and relativistic corrections. J Chem Phys 2007; 127:134107. [DOI: 10.1063/1.2755767] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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17
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Stanke M, Kedziera D, Bubin S, Adamowicz L. Lowest excitation energy of 9Be. PHYSICAL REVIEW LETTERS 2007; 99:043001. [PMID: 17678358 DOI: 10.1103/physrevlett.99.043001] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2007] [Indexed: 05/16/2023]
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 alpha2 relativistic corrections (alpha=1/137.035,999,679). With those corrections and with the alpha3 and alpha4 QED corrections determined previously by others, we obtained 54,677.35 cm(-1) for the 3(1)S-->2(1)S transition energy. This result falls within the error bracket for the experimental transition of 54,677.26(10) cm(-1). This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.
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Affiliation(s)
- Monika Stanke
- Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
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18
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Bubin S, Adamowicz L. Calculations of the ground states of BeH and BeH+ without the Born-Oppenheimer approximation. J Chem Phys 2007; 126:214305. [PMID: 17567194 DOI: 10.1063/1.2736699] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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.
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Affiliation(s)
- Sergiy Bubin
- Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
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19
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Hybrid treatment combining the translation- and rotation-free nuclear orbital plus molecular orbital theory with generator coordinate method: TRF-NOMO/GCM. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2006.11.054] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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20
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Kedziera D, Stanke M, Bubin S, Barysz M, Adamowicz L. Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations. J Chem Phys 2006; 125:084303. [PMID: 16965008 DOI: 10.1063/1.2236113] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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.
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Affiliation(s)
- Dariusz Kedziera
- Department of Chemistry, Nicholas Copernicus University, ul. Gagarina 7, PL 87-100 Toruń, Poland
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21
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Bubin S, Adamowicz L. Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH+. J Chem Phys 2006; 125:64309. [PMID: 16942288 DOI: 10.1063/1.2244563] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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 (2)Sigma(+) 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.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA.
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22
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Kedziera D, Stanke M, Bubin S, Barysz M, Adamowicz L. Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2. J Chem Phys 2006; 125:014318. [PMID: 16863309 DOI: 10.1063/1.2209691] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 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.
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Affiliation(s)
- Dariusz Kedziera
- Department of Chemistry, Nicholas Copernicus University, ul. Gagarina 7, PL 87-100 Toruń, Poland
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23
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Bubin S, Adamowicz L. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters. J Chem Phys 2006; 124:224317. [PMID: 16784284 DOI: 10.1063/1.2204605] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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 programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA.
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24
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Non-Born–Oppenheimer effects predicted by translation-free nuclear orbital plus molecular orbital method. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2006.01.064] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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