Restricted Hartree Fock using complexvalued orbitals: A longknown but neglected tool in electronic structure theory
Abstract
Restricted Hartree Fock using complexvalued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and realvalued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a WoodwardHoffmann violating reaction, and a symmetrydriven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague realvalued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.
 Authors:
 Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
 Publication Date:
 OSTI Identifier:
 22415819
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CHEMICAL BONDS; ELECTRONIC STRUCTURE; EQUILIBRIUM; HARTREEFOCK METHOD; HYDROGEN; IMPLEMENTATION; MATHEMATICAL SOLUTIONS; MOLECULES; OXYGEN; POTENTIAL ENERGY; SINGULARITY; SURFACES; SYMMETRY; VALENCE
Citation Formats
Small, David W., Sundstrom, Eric J., and HeadGordon, Martin. Restricted Hartree Fock using complexvalued orbitals: A longknown but neglected tool in electronic structure theory. United States: N. p., 2015.
Web. doi:10.1063/1.4905120.
Small, David W., Sundstrom, Eric J., & HeadGordon, Martin. Restricted Hartree Fock using complexvalued orbitals: A longknown but neglected tool in electronic structure theory. United States. doi:10.1063/1.4905120.
Small, David W., Sundstrom, Eric J., and HeadGordon, Martin. 2015.
"Restricted Hartree Fock using complexvalued orbitals: A longknown but neglected tool in electronic structure theory". United States.
doi:10.1063/1.4905120.
@article{osti_22415819,
title = {Restricted Hartree Fock using complexvalued orbitals: A longknown but neglected tool in electronic structure theory},
author = {Small, David W. and Sundstrom, Eric J. and HeadGordon, Martin},
abstractNote = {Restricted Hartree Fock using complexvalued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and realvalued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a WoodwardHoffmann violating reaction, and a symmetrydriven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague realvalued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.},
doi = {10.1063/1.4905120},
journal = {Journal of Chemical Physics},
number = 2,
volume = 142,
place = {United States},
year = 2015,
month = 1
}

Characteristics of the calculations for molecules with a partially filled pair of degenerate molecular orbitals in the restricted HartreeFock approximation using the MINDO/3 method. Monocyclic antiaromatic polymethynes (CH)/sub n/
In calculations for molecules with a partially filled pair of degenerate MO's in the restricted HartreeFock approximation, within the framework of the onedeterminant scheme, an incorrect initial filling will lead to solutions with artifact character which do not correspond to a stationary point on the potential energy surface. In their work they have considered as an example the calculations using the MINDO/3 method; but it is obvious that ignoring the methodological problem of the initial filling leads to an incorrect result even when they use different calculation methods. As a consequence of this, they give results of calculations for cyclobutadienemore » 
Calculation of the electronic structure of metalloporphyrin dianions by the restricted HartreeFock method 
The metalloporphine dianions (MeP)/sup 2 / with D/sub 4/h symmetry for the nuclear skeleton have an e/sub g/ /sup 2/ electronic configuration, which generates the triplet state /sup 3/A/sub 2g/ and the three single states /sup 1/B/sub 1g/, /sup 1/B/sub 2g/, and /sup 1/A/sub 1g/. With the aid of projection operators of the symmetry group, SCF equations have been formulated for such systems with open shells of degenerate orbitals, where the Roothaan method is not directly applicable. Calculations of the individual states of (MeP)/sup 2 / and its analogs have been performed by the proposed method in the ..pi..electronic approximation.more » 
Electronic responses of long chains to electrostatic fields: HartreeFock vs. densityfunctional theory: A model study
The response to an electrostatic field is determined through simple model calculations, within both the restricted HartreeFock and density functional theory methods, for long, finite as well as infinite, periodic chains. The permanent dipole moment, μ{sub 0}, the polarizability, α, and the hyperpolarizabilities β and γ, calculated using a finitefield approach, are extensively analyzed. Our simple model allows for treatment of large systems and for separation of the properties into atomic and unitcell contributions. That part of the response properties attributable to the terminations of the finite system change into delocalized current contributions in the corresponding infinite periodic system. Specialmore » 
Molecular electronic structure theory: 19721975. [HartreeFock method]
In this review of molecular electronic structure theory the emphasis is placed on the most important and innovative contributions. The HartreeFock and correlation problems as well as applications of the theory are treated. 269 references. (JFP)