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Title: Orbital-optimized opposite-spin scaled second order correlation: An economical method to improve the description of open-shell molecules

Abstract

Coupled cluster methods based on Brueckner orbitals are well-known to resolve the problems of symmetry-breaking and spin-contamination that are often associated with Hartree-Fock orbitals. However their computational cost is large enough to prevent application to large molecules. Here they present a simple approximation where the orbitals are optimized with the mean-field energy plus a correlation energy taken as the opposite-spin component of the second order many-body correlation energy, scaled by an empirically chosen parameter (recommended as 1.2 for general applications). This optimized 2nd order opposite spin (abbreviated as O2) method requires fourth order computation on each orbital iteration. O2 is shown to yield predictions of structure and frequencies for closed shell molecules that are very similar to scaled second order Moller-Plesset methods. However it yields substantial improvements for open shell molecules, where problems with spin-contamination and symmetry breaking are shown to be greatly reduced.

Authors:
;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
Chemical Sciences Division
OSTI Identifier:
950218
Report Number(s):
LBNL-1644E
Journal ID: ISSN 0021-9606; JCPSA6; TRN: US200910%%122
DOE Contract Number:
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ELECTRON CORRELATION; SPIN; SYMMETRY BREAKING

Citation Formats

Lochan, Rohini C., and Head-Gordon, Martin. Orbital-optimized opposite-spin scaled second order correlation: An economical method to improve the description of open-shell molecules. United States: N. p., 2007. Web. doi:10.1063/1.2718952.
Lochan, Rohini C., & Head-Gordon, Martin. Orbital-optimized opposite-spin scaled second order correlation: An economical method to improve the description of open-shell molecules. United States. doi:10.1063/1.2718952.
Lochan, Rohini C., and Head-Gordon, Martin. Mon . "Orbital-optimized opposite-spin scaled second order correlation: An economical method to improve the description of open-shell molecules". United States. doi:10.1063/1.2718952. https://www.osti.gov/servlets/purl/950218.
@article{osti_950218,
title = {Orbital-optimized opposite-spin scaled second order correlation: An economical method to improve the description of open-shell molecules},
author = {Lochan, Rohini C. and Head-Gordon, Martin},
abstractNote = {Coupled cluster methods based on Brueckner orbitals are well-known to resolve the problems of symmetry-breaking and spin-contamination that are often associated with Hartree-Fock orbitals. However their computational cost is large enough to prevent application to large molecules. Here they present a simple approximation where the orbitals are optimized with the mean-field energy plus a correlation energy taken as the opposite-spin component of the second order many-body correlation energy, scaled by an empirically chosen parameter (recommended as 1.2 for general applications). This optimized 2nd order opposite spin (abbreviated as O2) method requires fourth order computation on each orbital iteration. O2 is shown to yield predictions of structure and frequencies for closed shell molecules that are very similar to scaled second order Moller-Plesset methods. However it yields substantial improvements for open shell molecules, where problems with spin-contamination and symmetry breaking are shown to be greatly reduced.},
doi = {10.1063/1.2718952},
journal = {Journal of Chemical Physics},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analysed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn–Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite–spin OEP functional [I. Grabowski, E. Fabiano, and F. Della Sala, Phys. Rev. B 87, 075103 (2013)] which is the most advantageous from a computational point of view.more » We find that for high accuracy, a careful, system dependent, selection of the scaling coefficient is required. We analyse several size-extensive approaches for this selection. Finally, we find that a composite approach, named OEP2-SOSh, based on a post-SCF rescaling of the correlation energy can yield high accuracy for many properties, being comparable with the most accurate OEP procedures previously reported in the literature but at substantially reduced computational effort.« less
  • A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Moller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite spin second order energy (SOS-MP2) yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the 5th order computational steps associated with MP2 theory, even without exploiting any spatial locality. A 4th order algorithm is given for evaluating the opposite spin MP2 energy usingmore » auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.« less
  • Theoretical methods have been developed for the analytic determination of second energy derivatives (i.e., force constants) from restricted Hartree--Fock wave functions for certain types of open-shell systems. Specifically treated are systems for which all electrons outside closed shells have their spins parallel. Although the open-shell formalism is somewhat complicated, its application once implemented, is not greatly more arduous than the closed-shell theory presented in 1979 by Pople and co-workers. Like previous procedures for the evaluation of the second derivatives of electrons repulsion integrals, the present method exploits the Rys polynomial concept. Beyond this general framework, however, significant departures appear, andmore » these differences are described. Preliminary application of the new method has been to the two lowest triplet states of the formaldehyde molecule, for which both equilibrium geometry and harmonic vibrational frequencies have been evaluated.« less
  • Orbital-optimized second-order perturbation theory (OOMP2) optimizes the zeroth order wave function in the presence of correlations, removing the dependence of the method on Hartree–Fock orbitals. This is particularly important for systems where mean field orbitals spin contaminate to artificially lower the zeroth order energy such as open shell molecules, highly conjugated systems, and organometallic compounds. Unfortunately, the promise of OOMP2 is hampered by the possibility of solutions being drawn into divergences, which can occur during the optimization procedure if HOMO and LUMO energies approach degeneracy. In this work, we regularize these divergences through the simple addition of a level shiftmore » parameter to the denominator of the MP2 amplitudes. We find that a large level shift parameter of 400 mE{sub h} removes divergent behavior while also improving the overall accuracy of the method for atomization energies, barrier heights, intermolecular interactions, radical stabilization energies, and metal binding energies.« less