Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

2007 ◽  
Vol 127 (24) ◽  
pp. 244105 ◽  
Author(s):  
Gergely Gidofalvi ◽  
David A. Mazziotti
Keyword(s):  
Wave Function ◽  
Low Rank ◽  
Reduced Density Matrix ◽  
Electron Wave Function ◽  
Electron Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Many ◽  
Reduced Density

A Heterogeneous CPU + GPU Algorithm for Variational Two-Electron Reduced-Density Matrix Driven Complete Active Space Self-Consistent Field Theory

2019 ◽  
Author(s):  
J. Wayne Mullinax ◽  
Elvis Maradzike ◽  
Lauren N. Koulias ◽  
Mohammad Mostafanejad ◽  
Evgeny Epifanovsky ◽  
...  
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Complete Active Space ◽  
Active Space ◽  
Consistent Field ◽  
Singlet States ◽  
Unpaired Electron Density ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Reduced Density

<div><div><div><p>We present a heterogeneous CPU+GPU algorithm for the direct variational optimization of the two-electron reduced-density matrix (2RDM) under two-particle N-representability conditions. This variational 2RDM (v2RDM) approach is the driver for a polynomially-scaling approximation to configuration-interaction-driven complete active space self-consistent field (CASSCF) theory. For v2RDM-based CASSCF com- putations involving an active space consisting of 50 electrons in 50 orbitals [denoted (50e,50o)], we observe a speedup of a factor of 3.7 when the code is executed on a combination of an NVIDIA TITAN V GPU and an Intel Core i7-6850k CPU, relative to the case when the code is executed on the CPU alone. We use this GPU-accelerated v2RDM-CASSCF algorithm to explore the electronic structure of the 3,k-circumacene and 3,k-periacene series (k=2–7) and compare indicators of polyradical character in the lowest-energy singlet states to those observed for oligoacene molecules. The singlet states in larger circumacene and periacene molecules display the same polyradical characteristics observed in oligoacenes, with the onset of this behavior occuring at smallest k for periacenes, followed by the circumacenes and then the oligoacenes. However, the unpaired electron density that accumulates along the zig-zag edge of the circumacenes is slightly less than that which accumulates in the oligoacenes, while periacenes clearly exhibit the greatest build-up of unpaired electron density in this region.</p></div></div></div>

A Heterogeneous CPU + GPU Algorithm for Variational Two-Electron Reduced-Density Matrix Driven Complete Active Space Self-Consistent Field Theory

2019 ◽  
Author(s):  
J. Wayne Mullinax ◽  
Elvis Maradzike ◽  
Lauren N. Koulias ◽  
Mohammad Mostafanejad ◽  
Evgeny Epifanovsky ◽  
...  
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Complete Active Space ◽  
Active Space ◽  
Consistent Field ◽  
Singlet States ◽  
Unpaired Electron Density ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Reduced Density

<div><div><div><p>We present a heterogeneous CPU+GPU algorithm for the direct variational optimization of the two-electron reduced-density matrix (2RDM) under two-particle N-representability conditions. This variational 2RDM (v2RDM) approach is the driver for a polynomially-scaling approximation to configuration-interaction-driven complete active space self-consistent field (CASSCF) theory. For v2RDM-based CASSCF com- putations involving an active space consisting of 50 electrons in 50 orbitals [denoted (50e,50o)], we observe a speedup of a factor of 3.7 when the code is executed on a combination of an NVIDIA TITAN V GPU and an Intel Core i7-6850k CPU, relative to the case when the code is executed on the CPU alone. We use this GPU-accelerated v2RDM-CASSCF algorithm to explore the electronic structure of the 3,k-circumacene and 3,k-periacene series (k=2–7) and compare indicators of polyradical character in the lowest-energy singlet states to those observed for oligoacene molecules. The singlet states in larger circumacene and periacene molecules display the same polyradical characteristics observed in oligoacenes, with the onset of this behavior occuring at smallest k for periacenes, followed by the circumacenes and then the oligoacenes. However, the unpaired electron density that accumulates along the zig-zag edge of the circumacenes is slightly less than that which accumulates in the oligoacenes, while periacenes clearly exhibit the greatest build-up of unpaired electron density in this region.</p></div></div></div>

Note on the Interpretation of the Density Matrix in the Many-Electron Problem

1931 ◽  
Vol 27 (2) ◽  
pp. 240-243 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Density Matrix ◽  
The Self ◽  
Transformation Theory ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Many

When we treat an atom containing a number n of electrons by the method of the self-consistent field, we assume that each electron has its own particular “orbit,” specified by a wave function (q|r) in four variables q. These four variables are usually taken to be the three coordinates of the electron together with a variable describing the spin, but according to the transformation theory of quantum mechanics, they may be any four independent commuting functions of the coordinates, momenta and spin variables.

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