A Caltech Library Service

Improved Quantum Theory of Many-Electron Systems. V. The Spin-Coupling Optimized GI Method

Ladner, Robert C. and Goddard, William A., III (1969) Improved Quantum Theory of Many-Electron Systems. V. The Spin-Coupling Optimized GI Method. Journal of Chemical Physics, 51 (3). pp. 1073-1088. ISSN 0021-9606. doi:10.1063/1.1672106.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


The previously developed GI methods have an arbitrary aspect since they are based on a particular representation of the symmetric group. Here we remove this arbitrariness by optimizing the representation, that is, optimizing the spin‐coupling scheme simultaneously with the optimization of the orbitals. The resulting wavefunctions, called the spin‐coupling optimized GI or SOGI wavefunctions, have all of the general properties of GI wavefunctions including the independent particle interpretation and are found as the solutions to a set of coupled differential equations which differ from the GI equations only in that the equations are constructed from a different representation of the symmetric group. We have applied this method to the ground state and some excited states of Li, to the ground states of Be^+ and B^(++) and to the ground state of LiH. In each of these cases, we found that the SOGI wavefunction was only slightly different from the G1 wavefunction and led to very similar energies and other spatial properties. For the spin density at the nucleus, however, SOGI led to much better results. In order to illustrate the effects of spatial symmetry on the SOGI orbitals, we examined the lowest ^1B_(1g), ^3A_(2g), and ^3E_u states of square H_4 and the ^2Σ_u^+ state of linear symmetrical H_3. We find that in three of these cases optimization of the spin representation is crucial to providing an adequate description of the state. To investigate how the SOGI method would describe chemical reactions, the SOGI wavefunctions were computed for several other nuclear configurations of the H_3 system along the reaction path. These calculations showed that the spin coupling changed significantly during the reaction H_2 + H⇆H + H_2 and that the variation of the SOGI orbitals provides a clear description of the changes in bonding which occur during this reaction.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle
Goddard, William A., III0000-0003-0097-5716
Additional Information:© 1969 American Institute of Physics. Received 6 February 1969. Online Publication Date: 5 September 2003. Partially supported by a grant (GP-6965) from the National Science Foundation. National Science Foundation Predoctoral Fellow. Alfred P. Sloan Fellow. Contribution No. 3807. We thank W. E. Palke and Richard Blint for the use of the four-electron Gl program, W. E. Palke and R. M. Pitzer for the use of the Cambridge Slater integrals program, R. M. Stevens for the use of the Nesbet-Stevens diatomic integrals program, Thomas Dunning for the use of his version of the Murray Geller Gaussian integrals program, and A. D. McLean for the use of the McLYOSH linear polyatomic integrals program. In addition we thank S. L. Guberman for help with the plot programs and RCL thanks Albert Fordyce Wagner for helpful discussions.
Funding AgencyGrant Number
NSF Predoctoral FellowshipUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Caltech Arthur Amos Noyes Laboratory of Chemical Physics3807
Issue or Number:3
Record Number:CaltechAUTHORS:20120905-103928118
Persistent URL:
Official Citation:Improved Quantum Theory of Many‐Electron Systems. V. The Spin‐Coupling Optimized GI Method Robert C. Ladner and William A. Goddard J. Chem. Phys. 51, 1073 (1969);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33854
Deposited By: Ruth Sustaita
Deposited On:05 Sep 2012 18:16
Last Modified:09 Nov 2021 23:05

Repository Staff Only: item control page