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Feldmann R, Muolo A, Baiardi A, Reiher M. Quantum Proton Effects from Density Matrix Renormalization Group Calculations. J Chem Theory Comput 2022; 18:234-250. [PMID: 34978441 DOI: 10.1021/acs.jctc.1c00913] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
We recently introduced [J. Chem. Phys. 2020, 152, 204103] the nuclear-electronic all-particle density matrix renormalization group (NEAP-DMRG) method to solve the molecular Schrödinger equation, based on a stochastically optimized orbital basis, without invoking the Born-Oppenheimer approximation. In this work, we combine the DMRG method with the nuclear-electronic Hartree-Fock (NEHF-DMRG) approach, treating nuclei and electrons on the same footing. Inter- and intraspecies correlations are described within the DMRG method without truncating the excitation degree of the full configuration interaction wave function. We extend the concept of orbital entanglement and mutual information to nuclear-electronic wave functions and demonstrate that they are reliable metrics to detect strong correlation effects. We apply the NEHF-DMRG method to the HeHHe+ molecular ion, to obtain accurate proton densities, ground-state total energies, and vibrational transition frequencies by comparison with state-of-the-art data obtained with grid-based approaches and modern configuration interaction methods. For HCN, we improve on the accuracy of the latter approaches with respect to both the ground-state absolute energy and proton density, which is a major challenge for multireference nuclear-electronic state-of-the-art methods.
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Affiliation(s)
- Robin Feldmann
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Andrea Muolo
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - Alberto Baiardi
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Wang C, Ulusoy IS, Aebersold LE, Wilson AK. Multi-configuration electron-nuclear dynamics: An open-shell approach. J Chem Phys 2021; 155:154103. [PMID: 34686063 DOI: 10.1063/5.0063478] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The multi-configuration electron-nuclear dynamics for open shell systems with a spin-unrestricted formalism is described. The mean fields are evaluated using second-order reduced density matrices for electronic and nuclear degrees of freedom. Applications to light-element diatomics including equilibrium geometries, electronic energies, dipole moments, and absorption spectra are presented. The von Neumann entropies for different spin states of a LiH molecule are compared.
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Affiliation(s)
- Cong Wang
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
| | - Inga S Ulusoy
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
| | - Lucas E Aebersold
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
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Aebersold LE, Ulusoy IS, Wilson AK. Electron-nuclear quantum dynamics of diatomic molecules: nonadiabatic signatures in molecular spectra. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1988743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Lucas E. Aebersold
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
| | - Inga S. Ulusoy
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
- Scientific Software Center, Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany
| | - Angela K. Wilson
- Department of Chemistry, Michigan State University, East Lansing, MI, USA
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Chen Z, Yang J. Nucleus-electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization. J Chem Phys 2021; 155:104111. [PMID: 34525813 DOI: 10.1063/5.0056773] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We formulate an exact self-consistent nucleus-electron embedding potential from the single product molecular wavefunction and demonstrate that the fundamental behavior of the correlated nucleus-electron can be computed for mean-field electrons that are responsive to a quantal anharmonic vibration of selected nuclei in a discrete variable representation. Geometric gauge choices are discussed and necessary for formulating energy invariant biorthogonal electronic equations. Our method is further applied to characterize vibrationally averaged molecular bonding properties of molecular energetics, bond lengths, and protonic and electron densities. Moreover, post-Hartree-Fock electron correlation can be conveniently computed on the basis of nucleus-electron coupled molecular orbitals, as demonstrated for correlated models of second-order Møllet-Plesset perturbation and full configuration interaction theories. Our approach not only accurately quantifies non-classical nucleus-electron couplings for revising molecular bonding properties but also provides an alternative time-independent approach for deploying non-BO molecular quantum chemistry.
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Affiliation(s)
- Ziyong Chen
- Department of Chemistry, The University of Hong Kong, Hong Kong, People's Republic of China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong, People's Republic of China
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White AF, Gao Y, Minnich AJ, Chan GKL. A coupled cluster framework for electrons and phonons. J Chem Phys 2020; 153:224112. [DOI: 10.1063/5.0033132] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Alec F. White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Yang Gao
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Austin J. Minnich
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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Dresselhaus T, Bungey CBA, Knowles PJ, Manby FR. Coupling electrons and vibrations in molecular quantum chemistry. J Chem Phys 2020; 153:214114. [PMID: 33291918 DOI: 10.1063/5.0032900] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
We derive an electron-vibration model Hamiltonian in a quantum chemical framework and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and we make preliminary steps at applying standard quantum chemical methods to evaluate its properties, including mean-field theory, linear response, and a primitive correlated model. The Hamiltonian can be compared to standard vibronic Hamiltonians, but it is constructed without reference to potential energy surfaces through direct differentiation of the one- and two-electron integrals at a single reference geometry. The nature of the model Hamiltonian in the harmonic and linear-coupling regime is investigated for pyrazine, where a simple time-dependent calculation including electron-vibration correlation is demonstrated to exhibit the well-studied population transfer between the S2 and S1 excited states.
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Affiliation(s)
- Thomas Dresselhaus
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Callum B A Bungey
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Frederick R Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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Sasmal S, Vendrell O. Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: Application within the framework of the MCTDH method. J Chem Phys 2020; 153:154110. [PMID: 33092359 DOI: 10.1063/5.0028116] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear coordinates is introduced. This procedure circumvents the introduction of potential energy surfaces and non-adiabatic couplings, providing an alternative to the Born-Oppenheimer approximation. An important feature of the molecular Hamiltonian in the mixed first quantized representation for the nuclei and the SQR representation for the electrons is that all degrees of freedom, nuclear positions and electronic occupations, are distinguishable. This makes the approach compatible with various tensor decomposition Ansätze for the propagation of the nuclear-electronic wavefunction. Here, we describe the application of this formalism within the multi-configuration time-dependent Hartree framework and its multilayer generalization, corresponding to Tucker and hierarchical Tucker tensor decompositions of the wavefunction, respectively. The approach is applied to the calculation of the photodissociation cross section of the HeH+ molecule under extreme ultraviolet irradiation, which features non-adiabatic effects and quantum interferences between the two possible fragmentation channels, He + H+ and He+ + H. These calculations are compared with the usual description based on ab initio potential energy surfaces and non-adiabatic coupling matrix elements, which fully agree. The proof-of-principle calculations serve to illustrate the advantages and drawbacks of this formalism, which are discussed in detail, as well as possible ways to overcome them. We close with an outlook of possible application domains where the formalism might outperform the usual approach, for example, in situations that combine a strong static correlation of the electrons with non-adiabatic electronic-nuclear effects.
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Affiliation(s)
- Sudip Sasmal
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuneheimer Feld 229, 69120 Heidelberg, Germany
| | - Oriol Vendrell
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuneheimer Feld 229, 69120 Heidelberg, Germany
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