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Stetzler J, Rassolov VA. Comparison of Born–Oppenheimer approximation and electron-nuclear correlation. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2106321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Julian Stetzler
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC, USA
| | - Vitaly A. Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC, USA
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2
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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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3
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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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4
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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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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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6
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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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7
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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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8
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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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Ellis BH, Aggarwal S, Chakraborty A. Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions. J Chem Theory Comput 2015; 12:188-200. [DOI: 10.1021/acs.jctc.5b00879] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Benjamin H. Ellis
- Department
of Chemistry, Syracuse University, Syracuse, New York 13244, United States
| | - Somil Aggarwal
- Jamesville-DeWitt
High School, DeWitt, New York 13214, United States
| | - Arindam Chakraborty
- Department
of Chemistry, Syracuse University, Syracuse, New York 13244, United States
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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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11
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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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12
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Flick J, Appel H, Rubio A. Nonadiabatic and Time-Resolved Photoelectron Spectroscopy for Molecular Systems. J Chem Theory Comput 2014; 10:1665-76. [PMID: 26580375 DOI: 10.1021/ct4010933] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We quantify the nonadiabatic contributions to the vibronic sidebands of equilibrium and explicitly time-resolved nonequilibrium photoelectron spectra for a vibronic model system of trans-polyacetylene. Using exact diagonalization, we directly evaluate the sum-over-states expressions for the linear-response photocurrent. We show that spurious peaks appear in the Born-Oppenheimer approximation for the vibronic spectral function, which are not present in the exact spectral function of the system. The effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states and also persists when either only initial or final states are replaced by correlated vibronic states. Only when correlated initial and final vibronic states are taken into account are the spurious spectral weights of the Born-Oppenheimer approximation suppressed. In the nonequilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wavepacket motion of the system can be traced in the time-resolved photoelectron spectra as a function of the pump-probe delay.
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Affiliation(s)
- Johannes Flick
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6, D-14195 Berlin-Dahlem, Germany
| | - Heiko Appel
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6, D-14195 Berlin-Dahlem, Germany
| | - Angel Rubio
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6, D-14195 Berlin-Dahlem, Germany.,Nano-Bio Spectroscopy group, Dpto. Física de Materiales, Universidad del País Vasco , Centro de Física de Materiales CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastián, Spain
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13
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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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14
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Aguirre NF, Villarreal P, Delgado-Barrio G, Posada E, Reyes A, Biczysko M, Mitrushchenkov AO, de Lara-Castells MP. Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems. J Chem Phys 2013; 138:184113. [DOI: 10.1063/1.4803546] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [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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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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16
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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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17
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Fedorov DG, Nagata T, Kitaura K. Exploring chemistry with the fragment molecular orbital method. Phys Chem Chem Phys 2012; 14:7562-77. [DOI: 10.1039/c2cp23784a] [Citation(s) in RCA: 290] [Impact Index Per Article: 24.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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18
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Ando K. Electron wave packet modeling of chemical bonding: Floating and breathing minimal packets with perfect-pairing valence-bond spin coupling. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2011.12.019] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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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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