Some theoretical questions about the G-particle-hole hypervirial equation

• Published in: International journal of quantum chemistry Vol. 111; no. 2; pp. 245 - 255
• Main Authors: Valdemoro, C., Alcoba, D. R., Tel, L. M., Pérez-Romero, E.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.02.2011
• Subjects: contracted Schrödinger equation; correlation matrix; electronic correlation effects; G-particle-hole matrix; reduced density matrix
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.22678

By applying a matrix contracting mapping, involving the G‐particle‐hole operator, to the matrix representation of the N‐electron density hypervirial equation, one obtains the G‐particle‐hole hypervirial (GHV) equation (Alcoba, et al., Int J Quant Chem 2009, 109, 3178). This equation may be solved by exploiting the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Fernández and Castro, Hypervirial Theorems., Lecture Notes in Chemistry Series 43, 1987) and by following the general lines of Mazziotti's approach for solving the anti‐Hermitian contracted Schrödinger equation (Mazziotti, Phys Rev Lett 2006, 97, 143002), which can be identified with the second‐order density hypervirial equation. The accuracy of the results obtained with this method when studying the ground‐state of a set of atoms and molecules was excellent when compared with the equivalent full configuration interaction (FCI) quantities. Here, we analyze two open questions: under what conditions the solution of the GHV equation corresponds to a Hamiltonian eigenstate, and the possibility of extending the field of application of this methodology to the study of excited and multiconfigurational states. A brief account of the main difficulties that arise when studying this type of states is described. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011