1
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Sibaev M, Polyak I, Manby FR, Knowles PJ. Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing. J Chem Phys 2020; 153:124102. [DOI: 10.1063/5.0018930] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Marat Sibaev
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Iakov Polyak
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Frederick R. Manby
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom
| | - Peter J. Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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2
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McLaughlin PF, Chakraborty A. Compact Real-Space Representation of Excited States Using Frequency-Dependent Explicitly Correlated Electron–Hole Interaction Kernel. J Chem Theory Comput 2020; 16:5762-5770. [DOI: 10.1021/acs.jctc.9b01238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Peter F. McLaughlin
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Arindam Chakraborty
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
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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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Pavošević F, Culpitt T, Hammes-Schiffer S. Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method. Chem Rev 2020; 120:4222-4253. [DOI: 10.1021/acs.chemrev.9b00798] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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5
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Culpitt T, Yang Y, Schneider PE, Pavošević F, Hammes-Schiffer S. Molecular Vibrational Frequencies with Multiple Quantum Protons within the Nuclear-Electronic Orbital Framework. J Chem Theory Comput 2019; 15:6840-6849. [PMID: 31618582 DOI: 10.1021/acs.jctc.9b00665] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The nuclear-electronic orbital (NEO) approach treats all electrons and specified nuclei, typically protons, on the same quantum mechanical level. Proton vibrational excitations can be calculated using multicomponent time-dependent density functional theory (NEO-TDDFT) for fixed classical nuclei. Recently the NEO-DFT(V) approach was developed to enable the calculation of molecular vibrational frequencies for modes composed of both classical and quantum nuclei. This approach uses input from NEO-TDDFT to construct an extended NEO Hessian that depends on the expectation values of the quantum protons as well as the classical nuclear coordinates. Herein strategies are devised for extending these approaches to molecules with multiple quantum protons in a self-contained, effective, and computationally practical manner. The NEO-TDDFT method is shown to describe vibrational excitations corresponding to collective nuclear motions, such as linear combinations of proton vibrational excitations. The NEO-DFT(V) approach is shown to incorporate the most significant anharmonic effects in the molecular vibrations, particularly for the hydrogen stretching modes. These theoretical strategies pave the way for a wide range of multicomponent quantum chemistry applications.
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Affiliation(s)
- Tanner Culpitt
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Yang Yang
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Patrick E Schneider
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Fabijan Pavošević
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States
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6
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Pavošević F, Culpitt T, Hammes-Schiffer S. Multicomponent Coupled Cluster Singles and Doubles Theory within the Nuclear-Electronic Orbital Framework. J Chem Theory Comput 2018; 15:338-347. [DOI: 10.1021/acs.jctc.8b01120] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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7
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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8
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Brorsen KR, Schneider PE, Hammes-Schiffer S. Alternative forms and transferability of electron-proton correlation functionals in nuclear-electronic orbital density functional theory. J Chem Phys 2018; 149:044110. [DOI: 10.1063/1.5037945] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kurt R. Brorsen
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Patrick E. Schneider
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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9
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Bayne MG, Scher JA, Ellis BH, Chakraborty A. Linked-Cluster Formulation of Electron–Hole Interaction Kernel in Real-Space Representation without Using Unoccupied States. J Chem Theory Comput 2018; 14:3656-3666. [DOI: 10.1021/acs.jctc.8b00123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michael G. Bayne
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Jeremy A. Scher
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Benjamin H. Ellis
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
| | - Arindam Chakraborty
- Department of Chemistry, Syracuse University, Syracuse, New York 13244 United States
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10
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Mandal A, Shakib FA, Huo P. Investigating photoinduced proton coupled electron transfer reaction using quasi diabatic dynamics propagation. J Chem Phys 2018; 148:244102. [DOI: 10.1063/1.5030634] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Farnaz A. Shakib
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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11
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Goli M, Shahbazian S. Developing effective electronic-only coupled-cluster and Møller-Plesset perturbation theories for the muonic molecules. Phys Chem Chem Phys 2018; 20:16749-16760. [PMID: 29881845 DOI: 10.1039/c8cp02489h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the nuclear-electronic orbital theory [Phys. Chem. Chem. Phys., 2018, 20, 4466]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Møller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.
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Affiliation(s)
- Mohammad Goli
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), 19395-5531, Tehran, Iran.
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12
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Rayka M, Goli M, Shahbazian S. Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules. Phys Chem Chem Phys 2018; 20:4466-4477. [PMID: 29372727 DOI: 10.1039/c7cp07599e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.
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Affiliation(s)
- Milad Rayka
- Department of Physics and Department of Physical and Computational Chemistry, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, Tehran, 19839, Iran.
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13
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Brorsen KR, Yang Y, Hammes-Schiffer S. Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries. J Phys Chem Lett 2017; 8:3488-3493. [PMID: 28686449 DOI: 10.1021/acs.jpclett.7b01442] [Citation(s) in RCA: 78] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF-. The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pKa's, optimized geometries, and reaction paths.
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Affiliation(s)
- Kurt R Brorsen
- Department of Chemistry, University of Illinois at Urbana-Champaign , 600 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Yang Yang
- Department of Chemistry, University of Illinois at Urbana-Champaign , 600 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, University of Illinois at Urbana-Champaign , 600 South Mathews Avenue, Urbana, Illinois 61801, United States
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14
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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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15
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Gharabaghi M, Shahbazian S. Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study. J Chem Phys 2017; 146:154106. [PMID: 28433028 DOI: 10.1063/1.4979994] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.
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Affiliation(s)
- Masumeh Gharabaghi
- Faculty of Chemical and Petroleum Sciences, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, 19839 Tehran, Iran
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, 19839 Tehran, Iran
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16
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Cassam-Chenaï P, Suo B, Liu W. A quantum chemical definition of electron–nucleus correlation. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2081-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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17
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Brorsen KR, Pak MV, Hammes-Schiffer S. Calculation of Positron Binding Energies and Electron–Positron Annihilation Rates for Atomic Systems with the Reduced Explicitly Correlated Hartree–Fock Method in the Nuclear–Electronic Orbital Framework. J Phys Chem A 2017; 121:515-522. [DOI: 10.1021/acs.jpca.6b10124] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kurt R. Brorsen
- Department of Chemistry, 600 South Mathews Avenue, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Michael V. Pak
- Department of Chemistry, 600 South Mathews Avenue, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, 600 South Mathews Avenue, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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18
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Goli M, Shahbazian S. Extending the Domain-Averaged Exchange-Correlation Energies Within the Context of the MC-QTAIM: Tracing Subtle Variations Induced by Isotope Substitution. Chemphyschem 2016; 17:3875-3880. [PMID: 27778433 DOI: 10.1002/cphc.201600986] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Indexed: 11/06/2022]
Abstract
Recently, it has been demonstrated that the domain-averaged exchange-correlation energies, Vxc , are capable of tracing the covalent character of atom-atom interactions unequivocally and thus pave the way for detailed bonding analysis within the context of the quantum theory of atoms in molecules (QTAIM) [M. García-Revilla, E. Francisco, P. L. Popelier, A. Martín Pendás, ChemPhysChem 2013, 14, 1211-1218]. Herein, the concept of Vxc is extended within the context of the newly developed multicomponent QTAIM (MC-QTAIM). The extended version, Veexc , is capable of analyzing nonadiabatic wavefunctions and thus is sensitive to the mass of nuclei and can trace "locally" the subtle electronic variations induced by isotope substitution. To demonstrate this capability in practice, ab initio nonadiabatic wavefunctions for three isotopically substituted hydrogen cyanide molecules, in which the hydrogen nucleus was assumed to be a proton, deuterium, or tritium, were derived. The resulting wavefunctions were then used to compute Veexc and it emerged that for the hydrogen-carbon bond, the Veexc was distinct for each isotopic composition and varied in line with chemical expectations. Indeed, the introduction of Veexc paves the way for the investigation of vast numbers of structural and kinetic isotope effects within the context of the MC-QTAIM.
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Affiliation(s)
- Mohammad Goli
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran, 19839, P.O. Box 19395-4716, Iran
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19
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Culpitt T, Brorsen KR, Pak MV, Hammes-Schiffer S. Multicomponent density functional theory embedding formulation. J Chem Phys 2016; 145:044106. [DOI: 10.1063/1.4958952] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Tanner Culpitt
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801, USA
| | - Michael V. Pak
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801, USA
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20
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Tsukamoto Y, Ikabata Y, Romero J, Reyes A, Nakai H. The divide-and-conquer second-order proton propagator method based on nuclear orbital plus molecular orbital theory for the efficient computation of proton binding energies. Phys Chem Chem Phys 2016; 18:27422-27431. [DOI: 10.1039/c6cp03786k] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
An efficient computational method to evaluate the binding energies of many protons in large systems was developed.
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Affiliation(s)
- Yusuke Tsukamoto
- Department of Chemistry and Biochemistry
- School of Advanced Science and Engineering
- Waseda University
- Tokyo 169-8555
- Japan
| | - Yasuhiro Ikabata
- Department of Chemistry and Biochemistry
- School of Advanced Science and Engineering
- Waseda University
- Tokyo 169-8555
- Japan
| | - Jonathan Romero
- Department of Chemistry
- Universidad Nacional de Colombia
- Bogotá
- Colombia
| | - Andrés Reyes
- Department of Chemistry
- Universidad Nacional de Colombia
- Bogotá
- Colombia
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry
- School of Advanced Science and Engineering
- Waseda University
- Tokyo 169-8555
- Japan
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21
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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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22
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Sirjoosingh A, Pak MV, Brorsen KR, Hammes-Schiffer S. Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach. J Chem Phys 2015; 142:214107. [DOI: 10.1063/1.4921303] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Andrew Sirjoosingh
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Michael V. Pak
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
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23
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Brorsen KR, Sirjoosingh A, Pak MV, Hammes-Schiffer S. Nuclear-electronic orbital reduced explicitly correlated Hartree-Fock approach: Restricted basis sets and open-shell systems. J Chem Phys 2015; 142:214108. [DOI: 10.1063/1.4921304] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kurt R. Brorsen
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Andrew Sirjoosingh
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Michael V. Pak
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
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24
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Silkowski M, Lesiuk M, Moszynski R. Calculation of the molecular integrals with the range-separated correlation factor. J Chem Phys 2015; 142:124102. [DOI: 10.1063/1.4915272] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Michał Silkowski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Robert Moszynski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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25
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Sherman MC, Corcelli SA. Thermal equilibrium properties of surface hopping with an implicit Langevin bath. J Chem Phys 2015; 142:024110. [DOI: 10.1063/1.4905253] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- M. C. Sherman
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - S. A. Corcelli
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
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26
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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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27
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Romero J, Charry JA, Flores-Moreno R, Varella MTDN, Reyes A. Calculation of positron binding energies using the generalized any particle propagator theory. J Chem Phys 2014; 141:114103. [DOI: 10.1063/1.4895043] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan Romero
- Department of Chemistry, Universidad Nacional de Colombia, Av. Cra. 30 #45-03, Bogotá, Colombia
| | - Jorge A. Charry
- Department of Chemistry, Universidad Nacional de Colombia, Av. Cra. 30 #45-03, Bogotá, Colombia
| | - Roberto Flores-Moreno
- Departamento de Química, Universidad de Guadalajara, Blvd. Marcelino García Barragán 1421, Guadalajara Jal., C. P. 44430, Mexico
| | | | - Andrés Reyes
- Department of Chemistry, Universidad Nacional de Colombia, Av. Cra. 30 #45-03, Bogotá, Colombia
- Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, SP, Brazil
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28
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The two-component quantum theory of atoms in molecules (TC-QTAIM): the unified theory of localization/delocalization of electrons, nuclei, and exotic elementary particles. Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1410-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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29
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Sirjoosingh A, Pak MV, Swalina C, Hammes-Schiffer S. Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework: Theoretical formulation. J Chem Phys 2013; 139:034102. [DOI: 10.1063/1.4812257] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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The two-component quantum theory of atoms in molecules (TC-QTAIM): tensor formulation and its implications. Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1362-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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31
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Simmen B, Mátyus E, Reiher M. Elimination of the translational kinetic energy contamination in pre-Born–Oppenheimer calculations. Mol Phys 2013. [DOI: 10.1080/00268976.2013.783938] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Benjamin Simmen
- ETH Zurich, Laboratorium für Physikalische Chemie, , Zurich, Switzerland
| | - Edit Mátyus
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, Pázmány Péter sétány , Budapest, Hungary
| | - Markus Reiher
- ETH Zurich, Laboratorium für Physikalische Chemie, , Zurich, Switzerland
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32
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Elward JM, Thallinger B, Chakraborty A. Calculation of electron-hole recombination probability using explicitly correlated Hartree-Fock method. J Chem Phys 2012; 136:124105. [PMID: 22462833 DOI: 10.1063/1.3693765] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
The electron-hole explicitly correlated Hartree-Fock method (eh-XCHF) is presented as a general strategy for investigation of electron-hole correlation and computation of electron-hole recombination probability. The eh-XCHF method is a variational method which uses explicitly correlated wavefunction that depends on the electron-hole inter-particle distances. It is shown that the explicitly correlated ansatz provides a systematic route to variationally minimize the total energy. The parabolic quantum dot is used as the benchmark system and the eh-XCHF method is used for computation of the ground state energy and electron-hole recombination probability. The results are compared to Hartree-Fock and explicitly correlated full configuration interaction (R12-FCI) calculations. The results indicate that an accurate description of the electron-hole wavefunction at short electron-hole inter-particle distances is crucial for qualitative description of the electron-hole recombination probability. The eh-XCHF method successfully addresses this issue and comparison of eh-XCHF calculations with R12-FCI shows good agreement. The quality of the mean field approximation for electron-hole system is also investigated by comparing HF and R12-FCI energies for electron-electron and electron-hole systems. It was found that performance of the mean field approximation is worse for the electron-hole system as compared to the corresponding electron-electron system.
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Affiliation(s)
- Jennifer M Elward
- Department of Chemistry, Center for Science and Technology, Syracuse University, Syracuse, New York 13244, USA
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33
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Mátyus E, Reiher M. Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation. J Chem Phys 2012; 137:024104. [DOI: 10.1063/1.4731696] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Sirjoosingh A, Pak MV, Hammes-Schiffer S. Multicomponent density functional theory study of the interplay between electron-electron and electron-proton correlation. J Chem Phys 2012; 136:174114. [DOI: 10.1063/1.4709609] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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36
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Elward JM, Hoffman J, Chakraborty A. Investigation of electron–hole correlation using explicitly correlated configuration interaction method. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.03.050] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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37
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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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38
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Swalina C, Pak MV, Hammes-Schiffer S. Analysis of electron-positron wavefunctions in the nuclear-electronic orbital framework. J Chem Phys 2012; 136:164105. [DOI: 10.1063/1.4704124] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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39
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Development of the explicitly correlated Gaussian–nuclear orbital plus molecular orbital theory: Incorporation of electron–electron correlation. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.02.070] [Citation(s) in RCA: 16] [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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40
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Nishizawa H, Hoshino M, Imamura Y, Nakai H. Evaluation of electron repulsion integral of the explicitly correlated Gaussian-nuclear orbital plus molecular orbital theory. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2011.11.023] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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41
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Mátyus E, Hutter J, Müller-Herold U, Reiher M. Extracting elements of molecular structure from the all-particle wave function. J Chem Phys 2011; 135:204302. [DOI: 10.1063/1.3662487] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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42
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Sirjoosingh A, Pak MV, Hammes-Schiffer S. Derivation of an Electron–Proton Correlation Functional for Multicomponent Density Functional Theory within the Nuclear–Electronic Orbital Approach. J Chem Theory Comput 2011; 7:2689-93. [DOI: 10.1021/ct200473r] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Andrew Sirjoosingh
- Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Michael V. Pak
- Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, United States
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43
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Ko C, Pak MV, Swalina C, Hammes-Schiffer S. Alternative wavefunction ansatz for including explicit electron-proton correlation in the nuclear-electronic orbital approach. J Chem Phys 2011; 135:054106. [DOI: 10.1063/1.3611054] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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44
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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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45
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Komornicki A, King HF. A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions. J Chem Phys 2011; 134:244115. [DOI: 10.1063/1.3600745] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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46
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Chakraborty A, Pak MV, Hammes-Schiffer S. Erratum: “Inclusion of explicit electron-proton correlation in the nuclear-electronic orbital approach using Gaussian-type geminal functions” [J. Chem. Phys. 129, 014101 (2008)]. J Chem Phys 2011. [DOI: 10.1063/1.3555041] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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47
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Hammes–Schiffer S, Stuchebrukhov AA. Theory of coupled electron and proton transfer reactions. Chem Rev 2010; 110:6939-60. [PMID: 21049940 PMCID: PMC3005854 DOI: 10.1021/cr1001436] [Citation(s) in RCA: 578] [Impact Index Per Article: 41.3] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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48
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Auer B, Hammes-Schiffer S. Localized Hartree product treatment of multiple protons in the nuclear-electronic orbital framework. J Chem Phys 2010; 132:084110. [DOI: 10.1063/1.3332769] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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49
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Varganov SA, Martínez TJ. Variational geminal-augmented multireference self-consistent field theory: Two-electron systems. J Chem Phys 2010; 132:054103. [DOI: 10.1063/1.3303203] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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50
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KANEKO M, UDAGAWA T, TACHIKAWA M. Geometric Isotope Effect on Low Barrier Hydrogen-Bonding Systems of Acetic Acid Dimer, Formic Acid Dimer, and Their Anionic Clusters by Using the Multi-Component Molecular Orbital Method. ACTA ACUST UNITED AC 2010. [DOI: 10.2477/jccj.h2124m] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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