scholarly journals Stochastic Generalized Active Space Self-Consistent Field: Theory and Application

2021 ◽  
Author(s):  
Oskar Weser ◽  
Kai Guther ◽  
Khaldoon Ghanem ◽  
Giovanni Li Manni
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Electron Correlation ◽  
Spin Exchange ◽  
Occupation Number ◽  
Heat Bath ◽  
Wave Functions ◽  
Density Matrices ◽  
Direct Evaluation ◽  
Active Space

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.

scholarly journals Stochastic Generalized Active Space Self-Consistent Field: Theory and Application

2021 ◽  
Author(s):  
Oskar Weser ◽  
Kai Guther ◽  
Khaldoon Ghanem ◽  
Giovanni Li Manni
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Electron Correlation ◽  
Spin Exchange ◽  
Occupation Number ◽  
Heat Bath ◽  
Wave Functions ◽  
Density Matrices ◽  
Direct Evaluation ◽  
Active Space

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.

scholarly journals A study of some atomic properties for He-like selected ions

2007 ◽  
Vol 4 (2) ◽  
pp. 301-304
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Configuration Interaction ◽  
Diamagnetic Susceptibility ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Hartree Fock ◽  
Atomic Properties ◽  
Atomic Form Factor ◽  
He Atom

The atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained.

Rational orbitals for two-electron S states

1981 ◽  
Vol 59 (10) ◽  
pp. 1552-1556
Author(s):  
F. W. Birss ◽  
W. den Hertog
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Orthogonal Transformation ◽  
Open Shell ◽  
Wave Functions ◽  
Natural Orbitals ◽  
S States ◽  
Single Configuration

The concept of rational orbitals is introduced, based upon finding that pair of orbitals which yield the single configuration function which maximally overlaps with a configuration interaction wave function. They are simply obtained from the natural orbitals by an elementary orthogonal transformation and are more appropriate than natural orbitals to analysis of functions for open-shell states. The CI wave functions of a number of lS states of helium are analyzed and the nature of the rational orbitals investigated.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

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