Some Recent Advances in the use of Propagator Methods in Quantum Chemistry. From AMO to AGP

  • Osvaldo Goscinski
Part of the Académie Internationale Des Sciences Moléculaires Quantiques / International Academy of Quantum Molecular Science book series (QUCH, volume 3)


A survey of recent developments in the use of propagator methods in quantum chemistry is made. Particular emphasis is devoted to balanced approximations of both states and operators in order to get a consistent description of both static and dynamic properties. A systematic procedure provides, in particular, an alternative derivation of a significant result by Linderberg and Öhrn: the antisymmetrized geminal power wave function (AGP): ΨAGP = NAg(1,2)g(3,4)…g(N-1,N) is the correct ground state of the self-consistent particle-hole propagator (SCPHP) (N is a normalization constant, A an antisymmetrizer and g an antisymmetric, normalized geminal). This AGP function was previously dismissed as a reasonable approximation on account of the limited amount of correlation energy it seemed to yield or because its inability to lead to proper dissociation. It is shown that on the contrary, provided no restrictions on the geminal are made, it contains as particular cases the different orbitals for different spins (DODS) scheme and the alternant molecular orbital method (AMO) of Löwdin - both capable of high accuracy. It is argued that the current theories of chemical reactions can have the AGP function as an optimal framework, with AMO as the simplest level of formalization of the methods of Bader, Fukui, Pearson, Woodward and Hoffman. It encompasses also the more advanced level proposed by Ruedenberg in terms of orbital reaction space and natural reaction orbitals. Some consequences of the AGP function being the ground state of the SCPHP are: the excitation spectrum is easily obtainable; the excited states are obtained by “one-electron excitation operators”; the validity of the Hellman-Feynman theorem which leads to a simple description of the response to external perturbations.

Essential to the previous aspects is the non-singlet character of the geminal. This “broken symmetry” allows the inclusion of a major part of the correlation energy. At the orbital level and the Hartree-Fock (HF) self-consistent (SCF) level of approximation these low-symmetry orbitals provide reasonable transition energies and probabilities in core-holem ionization as well as in n-п* transitions through the use of orbitals adapted to the excitation process: transition orbitals.


Quantum Chemistry Correlation Energy Configuration Interaction Spin Orbital Propagator Method 
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© D. Reidel Publishing Company 1980

Authors and Affiliations

  • Osvaldo Goscinski
    • 1
  1. 1.Department of Quantum ChemistryUppsala UniversityUppsalaSweden

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