Multiple solutions of the valence‐universal coupled‐cluster equations for Be, B⁺, and C²⁺

Abstract

Sets of nonlinear equations for the cluster amplitudes of the valence-universal coupled-cluster (VU-CC) method have been solved to obtain physically meaningful multiple solutions for Be, B', and Cz+. The wave operator is taken in Lindgren's normal ordered exponential form and the completeness of the model space is postulated. The cluster operator is restricted to its one-and two-electron components that are represented in terms of radial amplitudes defined by the configurational excitations (VU-CCSD/R method). Five solutions giving rise to 10 approximate energies of four ' S states are obtained and discussed. These are the first multiple solutions documented for a nonmodel system. Some attention is paid to the problem of the efficiency of various methods in obtaining alternative solutions and to some consequences of the availability of alternative solutions. 0 1993 John Wiley & Sons, Inc.

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

“…Consequently, the multiplicity at a given valence rank level will propagate into the higher levels (cf. [95,228,268] where T ( j ) now designates a connected-cluster operator* associated with the reference I@j ) E Mo. Thus, as in the SR case, we express each T ( j ) in terms of the excitation operators and corresponding amplitudes; that is, (2.129) where the superscript indicates the excitation level relative to i @ j ) , while the subscript enumerates distinct excitation operators or the corresponding configurations I @$)) = GY) 0') l @ j ) .…”

Coupled‐cluster corrected MR‐CISD method with noniterative evaluation of connected triples

“…The effective Hamiltonian formalism underlying both MR‐CC formulations requires description of several states at a time and that restricts applicability of the methods to relatively small and simple systems. Moreover, it has been found that one can face such problems like the intruder state problem 38 or multiplicity of the solutions 34, 39 in their numerical applications. In spite of the significant progress that has been made 40–47, obtaining a MR‐CC scheme that is simple, dependable and resistant to intruder states is still one of the most challenging problems of the computational quantum chemistry.…”

Visualization of the effective potential and Coulomb correlations in finite metallic systems

“…The work, started in the late 1970s by Rehmus, Kellman, Roothaan and Berry, 5,6 provides a generalization of other quantitative descriptions of electron correlation. [8][9][10][11][12][13][14][15][16] At this point, reference must be made to the important progress in studying the correlation effects in atoms and molecules that followed from the two-particle densitymatrix approach, 17 d-dimensional theory, 18-20 the coupledcluster method, [21][22][23] and the density-functional approach. …”

“…The work, started in the late 1970s by Rehmus, Kellman, Roothaan and Berry, 5,6 provides a generalization of other quantitative descriptions of electron correlation. [8][9][10][11][12][13][14][15][16] At this point, reference must be made to the important progress in studying the correlation effects in atoms and molecules that followed from the two-particle densitymatrix approach, 17 d-dimensional theory, 18-20 the coupledcluster method, [21][22][23] and the density-functional approach. [24][25][26] For a system of more particles, we have yet to find a comparably powerful approach because so much information is contained in the wave function and we do not know how to extract what is relevant in a manner adaptable to pictures.…”