Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. II. Simple Open‐Shell Case

1970 ◽  
Vol 52 (6) ◽  
pp. 2919-2936 ◽  
Author(s):  
J. Paldus ◽  
J. Čĺžzek
Keyword(s):  
Open Shell ◽  
Stability Conditions ◽  
Molecular Systems ◽  
Hartree Fock

An algebraic method for solving Hartree-Fock equations. II. Open-shell molecular systems

1993 ◽  
Vol 90 ◽  
pp. 1999-2005 ◽  
Author(s):  
RM Teixeira Filho ◽  
LAC Malbouisson ◽  
JDM Vianna
Keyword(s):  
Algebraic Method ◽  
Open Shell ◽  
Molecular Systems ◽  
Hartree Fock

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.

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