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Title: Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

 [1];  [1];  [1]
  1. Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
Publication Date:
Sponsoring Org.:
OSTI Identifier:
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Journal Article: Publisher's Accepted Manuscript
Journal Name:
The Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 2; Related Information: CHORUS Timestamp: 2018-03-28 12:38:41; Journal ID: ISSN 0021-9606
American Institute of Physics
Country of Publication:
United States

Citation Formats

Small, David W., Sundstrom, Eric J., and Head-Gordon, Martin. Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory. United States: N. p., 2015. Web. doi:10.1063/1.4905120.
Small, David W., Sundstrom, Eric J., & Head-Gordon, Martin. Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory. United States. doi:10.1063/1.4905120.
Small, David W., Sundstrom, Eric J., and Head-Gordon, Martin. Fri . "Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory". United States. doi:10.1063/1.4905120.
title = {Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory},
author = {Small, David W. and Sundstrom, Eric J. and Head-Gordon, Martin},
abstractNote = {},
doi = {10.1063/1.4905120},
journal = {The Journal of Chemical Physics},
number = 2,
volume = 142,
place = {United States},
year = {Fri Jan 09 00:00:00 EST 2015},
month = {Fri Jan 09 00:00:00 EST 2015}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4905120

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Cited by: 6works
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  • Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued 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 Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecularmore » systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued 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.« less
  • In calculations for molecules with a partially filled pair of degenerate MO's in the restricted Hartree-Fock approximation, within the framework of the one-determinant 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 » using the PPP method, according to which the energy difference between the singlet and triplet states for the D/sub 4h/ structure is equal to 60.2 kJ/mole.« less
  • The metalloporphine dianions (Me-P)/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 (Me-P)/sup 2 -/ and its analogs have been performed by the proposed method in the ..pi..electronic approximation.more » In accordance with Hund's rule, it has been found that the lowest level in the multiplet is the triplet level and that the subsequent singlet levels of (Me-P)/sup 2 -/ are 340 (/sup 1/B/sub 1g/ ), 2560 (/sup 1/B/sub 2g/ ), and 3010 (/sup 1/A/sub 1g/ ) cm/sup -1/ above it. A comparison of the ..pi..-electron densities of (Me-P)/sup 2 -/ and Me-P has revealed, first, that the additional charge is distributed along the periphery of the macrocycle (the maximum increase takes place at the bridging atoms) and, second, that a number of bonds are strengthened, rather than weakened. The results obtained correlate well with the data on the reactivity and vibrational spectra of the dianions of porphyrins.« less
  • The response to an electrostatic field is determined through simple model calculations, within both the restricted Hartree-Fock 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 finite-field approach, are extensively analyzed. Our simple model allows for treatment of large systems and for separation of the properties into atomic and unit-cell 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 » emphasis is placed on analyzing the reasons behind the dramatic overestimation of the response properties found with density functional theory methods presently in common use.« less
  • In this review of molecular electronic structure theory the emphasis is placed on the most important and innovative contributions. The Hartree-Fock and correlation problems as well as applications of the theory are treated. 269 references. (JFP)