scholarly journals Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation

Computation ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 135
Author(s):  
Carmelo Naim ◽  
Claudio Amovilli
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Density Matrix ◽  
Quantum Monte Carlo ◽  
Valence Bond ◽  
Reduced Density Matrix ◽  
Electronic Density ◽  
Complete Active Space ◽  
Energy Functionals ◽  
Reduced Density

In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Self Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.

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>

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