Fragment-Based Restricted Active Space Configuration Interaction with Second-Order Corrections Embedded in Periodic Hartree–Fock Wave Function

2020 ◽  
Vol 16 (11) ◽  
pp. 7100-7108
Author(s):  
Hung-Hsuan Lin ◽  
Lorenzo Maschio ◽  
Daniel Kats ◽  
Denis Usvyat ◽  
Thomas Heine
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Second Order ◽  
Active Space ◽  
Hartree Fock

On the basis of orbital theories

1955 ◽  
Vol 232 (1188) ◽  
pp. 114-135 ◽  
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Singlet Ground State ◽  
New Techniques ◽  
Hartree Fock ◽  
Basic Set ◽  
Spin Eigenfunctions ◽  
Spin Degeneracy ◽  
One And Many ◽  
Reduced Density

In molecular theory the wave function is usually constructed from antisymmetrized products, or ‘Slater determinants’, of one-electron ‘orbitals’. A single determinant of suitably chosen, doubly occupied orbitals is often a fair approximation to a singlet ground state; but when more general products are admitted, as in ‘configuration interaction’ calculations, it is first necessary to resolve a high ‘spin degeneracy’ by constructing spin eigenfunctions (SE’s). In §1, the fundamental basis of recent methods (McWeeny 1954 b ) is clarified by a group theoretical approach. Next, in §2, the energy expression, using as wave function an arbitrary mixture of similar SE’s, is written very simply in terms of the reduced density matrices for one and two particles, and formulae for the calculation of these matrices are given. The remaining problem is to get a ‘best’ wave function, usually with limited configuration interaction, by (i) variation of SE coefficients and (ii) variation of the orbitals appearing in the SE’s; this problem is formally solved in §3. (i) is the usual configuration interaction process; but (ii) is new and leads, when the orbitals are expressed in terms of a standard basic set (e.g. of atomic orbitals), to a complete generalization of the Roothaan 1951) equations. These (matrix) equations are simple in appearance, but their numerical solution calls for new techniques; and it is possible that the Roothaan (i.e. Hartree–Fock) approach, followed by configuration interaction, provides about the best working compromise between (i) and (ii). In §4, some points of contact between one- and many-configuration theories are noted. In particular, certain density matrix elements provide appropriate generalizations of the ‘charges’ and ‘bond orders’ of Coulson and Longuet-Higgins and continue to describe the response of a system to changes in its ‘Coulomb’ and ‘resonance’ integrals.

Transition probability approach for direct calculation of coefficients of Configuration Interaction wave function

2017 ◽  
Author(s):  
Arijit Bag
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Correlation Energy ◽  
Transition Probability ◽  
Direct Calculation ◽  
Energy Curve ◽  
Equilibrium Bond Length ◽  
Hydrogen Water ◽  
Hartree Fock ◽  
A New Technique

To reduce the computation cost of Configuration Interaction (CI) method, a new technique is used to calculate the coefficients of doubly excited determinants directly from orbital energies, orbital overlap matrix and electron population obtained from Hartree Fock level run. This approach to approximate the coefficients of CI wave function is termed as <b>transition probability approximated CI (TPA-CI).</b> In principle, calculated dynamical electron correlation energy of TPA-CI and Full CI (FCI) are equivalent. It is observed that computed TPA-CI correlation energies of hydrogen, water, ammonia and ozone are very close to FCI values, within 5% error. The potential energy curve of the hydrogen molecule is also studied and it is found that the energy is minimum at its equilibrium bond length.<br><br>

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function

2015 ◽  
Vol 11 (9) ◽  
pp. 4064-4076 ◽  
Author(s):  
Ward Poelmans ◽  
Mario Van Raemdonck ◽  
Brecht Verstichel ◽  
Stijn De Baerdemacker ◽  
Alicia Torre ◽  
...  
Keyword(s):  
Wave Function ◽  
Density Matrix ◽  
Configuration Interaction ◽  
Second Order ◽  
Variational Optimization

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.

Transition probability approach for direct calculation of coefficients of Configuration Interaction wave function

2017 ◽  
Author(s):  
Arijit Bag
Keyword(s):  
Wave Function ◽  
Configuration Interaction ◽  
Correlation Energy ◽  
Transition Probability ◽  
Direct Calculation ◽  
Energy Curve ◽  
Equilibrium Bond Length ◽  
Hydrogen Water ◽  
Hartree Fock ◽  
A New Technique

To reduce the computation cost of Configuration Interaction (CI) method, a new technique is used to calculate the coefficients of doubly excited determinants directly from orbital energies, orbital overlap matrix and electron population obtained from Hartree Fock level run. This approach to approximate the coefficients of CI<br>wave function is termed as <b>transition probability approximated CI (TPA-CI).</b> In principle, calculated dynamical electron correlation energy of TPA-CI and Full CI (FCI) are equivalent. It is observed that computed TPA-CI correlation energies of hydrogen, water, ammonia and ozone are very close to FCI values, within 5% error. The potential energy curve of the hydrogen molecule is also studied and it is found that the energy is minimum at its equilibrium bond length.<br><br>

scholarly journals Fragment-Based Restricted Active Space Configuration Interaction with Second-order corrections Embedded in Periodic Hartree-Fock Wavefunction

2020 ◽  
Author(s):  
Hung-Hsuan Lin ◽  
Lorenzo Maschio ◽  
Daniel Kats ◽  
Denis Usvyat ◽  
Thomas Heine
Keyword(s):  
Perturbation Theory ◽  
Potential Energy Surfaces ◽  
Fluorine Atom ◽  
Second Order ◽  
Strongly Correlated ◽  
Active Space ◽  
Hartree Fock ◽  
Dissociation Energies ◽  
Energy Surfaces ◽  
Second Order Perturbation Theory

<div><div><div><p>We present a computational scheme for restricted-active-space configuration inter- action (RASCI) calculations combined with second-order perturbation theory (RASCI- PT2) on a fragment of a periodic system embedded in the periodic Hartree-Fock (HF) wavefunction. This method allows one to calculate the electronic structure of localized strongly-correlated features in crystals and surfaces. The scheme was implemented via an interface between the Cryscor and Q-Chem codes. To evaluate the performance of the embedding method, we explored dissociation of fluorine atom from a lithium flu- oride surface and partially fluorinated graphane layer. The results show that RASCI and RASCI-PT2 embedded in periodic HF are able to produce well-behaved potential energy surfaces and accurate dissociation energies.</p></div></div></div>

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.

The Study of Bond Selective Photochemistry in CH2BrCl

2013 ◽  
Vol 699 ◽  
pp. 107-110
Author(s):  
Lan Li ◽  
Zong He Li
Keyword(s):  
Configuration Interaction ◽  
Oscillator Strengths ◽  
Bond Breaking ◽  
Complete Active Space ◽  
Active Space ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

The photodissociation of chlorobromomethane (CH2BrCl) has been studied using unrestricted Hartree-Fock (UHF), configuration-interaction-singles (CIS), and complete active space self-consistent field (CASSCF) levels. The result of oscillator strengths indicate that the photochemistry reactions of CH2BrCl are processes where the n(Br)→σ*(C-Br) transition are excited to repulsive states leading to direct carbon-bromine bond breaking reactions. And the 1A’ →1A’ state is the important transition in photolysis of chlorobromomethane.

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