Variational time‐dependent Hartree–Fock calculations. I. Applications to four‐electron atomic and molecular systems

1975 ◽  
Vol 63 (8) ◽  
pp. 3222-3227 ◽  
Author(s):  
R. F. Stewart ◽  
D. K. Watson ◽  
A. Dalgarno
Keyword(s):  
Time Dependent ◽  
Molecular Systems ◽  
Hartree Fock

DETERMINATION OF THE ELECTRONIC GROUND STATE OF MOLECULAR SYSTEMS WITH THE MULTI-CONFIGURATION TIME-DEPENDENT HARTREE–FOCK METHOD

2007 ◽  
Vol 06 (03) ◽  
pp. 563-574 ◽  
Author(s):  
M. NEST
Keyword(s):  
Ground State ◽  
Equations Of Motion ◽  
Electronic Ground State ◽  
Time Dependent ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Time Propagation ◽  
Core Excitations ◽  
Electronic Ground

In this paper, we present progress in the application of the explicitly time-dependent multi-configuration time-dependent Hartree–Fock (MCTDHF) method. The spin–orbitals and equations of motion are expressed in the basis of Gaussian Type Orbitals. MCTDHF is then applied to the calculation of the electronic ground state of various small molecules by imaginary time propagation. We were able to take between four and 12 active electrons into account. We discuss the suitability of a core guess as initial wave function, the possibility to obtain excited states, as well as the consequences of a neglect of core excitations.

scholarly journals Reduction of the molecular hamiltonian matrix using quantum community detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Susan M. Mniszewski ◽  
Pavel A. Dub ◽  
Sergei Tretiak ◽  
Petr M. Anisimov ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Community Detection ◽  
Slater Determinant ◽  
Hamiltonian Matrix ◽  
Approximate Methods ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Molecular Hamiltonian ◽  
Structure Problem ◽  
Modularity Maximization ◽  
Chemical Knowledge

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

scholarly journals Computational Methods for Ab Initio Molecular Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Eric Paquet ◽  
Herna L. Viktor
Keyword(s):  
Molecular Dynamics ◽  
Quantum Mechanics ◽  
Ab Initio ◽  
First Principles ◽  
Density Functional ◽  
Path Integrals ◽  
Ab Initio Molecular Dynamics ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Computational Perspective

Ab initio molecular dynamics is an irreplaceable technique for the realistic simulation of complex molecular systems and processes from first principles. This paper proposes a comprehensive and self-contained review of ab initio molecular dynamics from a computational perspective and from first principles. Quantum mechanics is presented from a molecular dynamics perspective. Various approximations and formulations are proposed, including the Ehrenfest, Born–Oppenheimer, and Hartree–Fock molecular dynamics. Subsequently, the Kohn–Sham formulation of molecular dynamics is introduced as well as the afferent concept of density functional. As a result, Car–Parrinello molecular dynamics is discussed, together with its extension to isothermal and isobaric processes. Car–Parrinello molecular dynamics is then reformulated in terms of path integrals. Finally, some implementation issues are analysed, namely, the pseudopotential, the orbital functional basis, and hybrid molecular dynamics.

scholarly journals Theoretical and experimental comparative studies of nonlinear optical properties for selected melaminium compounds

2010 ◽  
Vol 8 (6) ◽  
pp. 1192-1202 ◽  
Author(s):  
Marek Drozd ◽  
Mariusz Marchewka
Keyword(s):  
Optical Properties ◽  
Acetic Acid ◽  
Nonlinear Optical ◽  
Time Dependent ◽  
X Ray ◽  
Hartree Fock ◽  
Optical Applications ◽  
Experimental Values ◽  
Nonlinear Optical Applications ◽  
Theoretical Results

AbstractThe bis(melaminium) sulphate dihydrate, 2,4,6-triamine-1,3,5-triazin-1,3-ium tartrate monohydrate, 2,4,6-triamine-1,3,5-triazin-1-ium hydrogenphthalate, 2,4,6-triamine-1,3,5-triazin-1-ium acetate acetic acid solvate monohydrate, 2,4,6-triamine-1,3,5-triazin-1-ium bis(selenate) trihydrate, melaminium diperchlorate hydrate, melaminium bis(trichloroacetate) monohydrate and melaminium bis(4-hydroxybenzenesulphonate) dihydrate were discovered recently as perspective materials for nonlinear optical applications. On the basis of X-ray structures for eight melaminium compounds the time dependent Hartree Fock (TDHF) method was used for calculation of the polarizability, and first and second hyperpolarizability. Detailed directional studies of calculated hyperpolarizability for all investigated melaminium compounds are shown. The theoretical results are compared with experimental values of β.

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