A spin-adapted linear response theory in a coupled-cluster framework for direct calculation of spin-allowed and spin-forbidden transition energies
01 Nov 1982-Vol. 72, Iss: 1, pp 161-176
TL;DR: In this paper, a spin-adapted linear response theory in a coupled-cluster framework was proposed to calculate the spin-allowed and spin-forbidden transition energies from a single methodology.
Abstract: In this paper, we have spin-adapted our recently formulated linear response theory in a coupled-cluster framework. This allows us to calculate directly both the spin-allowed and the spin-forbidden transition energies from a single methodology. We have introduced rank-zero and rank-one spin operators to construct excitation operators for singlet-singlet and singlet-triplet transitions respectively and utilised the graphical methods of spin algebra to integrate the spin variables. It has been shown how a suitable parameterisation of the reduced Hugenholtz matrix elements of the excitation operator in terms of Goldstone matrix elements makes the resulting system of equations simple, compact and suitable for computer implementation. A pilot calculation has been performed to test the applicability of the theory.
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TL;DR: The coupled cluster based linear response theory which is applicable to the direct calculation of atomic and molecular properties are presented and applied to compute the ionization potentials and excitation energies of light and moderately heavy atoms.
Abstract: The coupled cluster based linear response theory which is applicable to the direct calculation of atomic and molecular properties are presented and applied to compute the ionization potentials and excitation energies of light and moderately heavy atoms. The e®ect of electron correlation on the ground and excited states is studied using Hartree-Fock, Dirac-Fock and approximate two-component relativistic spinors.
2 citations
TL;DR: In this article, a set of non-orthogonal and orthogonal spin-adapted substitution operators are generated and used in consecutive Configuration Interaction (CI) and CC calculations.
Abstract: In spin-adapted open-shell coupled cluster (CC) theory, the choice of spin-free spatial substitution operators is generally not unique. Due to an increasing linear dependence of the cluster operator (with increasing substitution level), the options to span identical linear spaces increase rapidly. In this work several sets of non-orthogonal as well as orthogonal spin-adapted substitution operators are generated and used in consecutive Configuration Interaction (CI) and CC calculations. All (full) operator sets were generated to span the same linear space. The results are analyzed in terms of the produced wave function quality and the amount of recovered correlation energy w.r.t. full CI. In particular, the influence of different amounts of spectators, the influence of orthogonality as well as the effect of spin incompleteness was investigated. It was found that CC calculations involving fewer spectators lead to more accurate results in general. Here correlation energy differences of up to 0.32\% for minimal to maximal spectating sets were obtained. As expected, all conducted calculations led to identical results for non-orthogonal and orthogonal operator sets. Spin completeness on the other hand was found to be of great importance. Spin-incomplete Cluster operators led to significant errors in both the correlation energies and the FCI overlap.
1 citations
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TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.
Abstract: A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one‐electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman‐like diagrams. The connection of this method with the configuration‐interaction method as well as with the perturbation theory in the quantum‐field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration‐interaction method considering all possible configurations within the chosen basis of one‐electron functions.
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TL;DR: In this paper, a response function approach to the direct determination of transition energy in a multiple-cluster expansion formalism has been developed, in a way reminiscent of the Fourier-transformed version of a response-function theory.
311 citations
TL;DR: In this article, a non-perturbative approach to the calculation of correlation energies of open-shell systems is presented, which utilizes an Ursell-type expansion about a multi-determinant starting wave function.
Abstract: In this paper we present a non-perturbative approach to the calculation of correlation energies of open-shell systems. The formulation utilizes an Ursell-type expansion about a multi-determinant starting wavefunction. We have proved a theorem which enables us to derive an effective hamiltonian for the system consisting entirely of linked terms. In the symmetry-degenerate case this effective hamiltonian acts within the subspace of a set of symmetry-degenerate functions, and generates the energy eigenvalues of the system. The present theory has been cast in a diagrammatic language which facilitates the analysis of the correlation problem. The workability of the theory has been tested on a 4 π electron problem, transbutadiene, for which we have calculated the lowest π-π* singlet and triplet energies. The agreement between the results of the present theory and that found from a full CI calculation is excellent. The desirable feature of the theory is that the effective hamiltonian is energy-independent. We hav...
260 citations