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: In this paper, an equation of motion coupled-cluster (EOM-CC) method for the calculation of excitation energies is presented, which is based upon representing an excited state as an excitation from a ground state and the excitation energy is obtained by solving a non-Hermitian eigenvalue problem.
588 citations
TL;DR: In this paper, expressions for static and dynamic properties in coupled-cluster (CC) theory are derived using diagrammatic techniques and shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects.
Abstract: Expressions for static and dynamic properties in coupled-cluster (CC) theory are derived. In the static case, using diagrammatic techniques, it is shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects. For the dynamic case, excitation energy expressions are obtained without consideration of orbital relaxation effects and shown to be equivalent to an equation of motion (EOM) approach subject to a coupled-cluster ground-state wave function and an excitation operator consisting of single and double excitations. Illustrative applications for excited states of ethylene are reported.
586 citations
TL;DR: The electron attachment equation of motion coupled cluster (EA•EOMCC) method is derived in this paper, which enables determination of the various bound states of an (N+1)-electron system and the corresponding energy eigenvalues relative to the energy of an N•electron CCSD reference state.
Abstract: The electron attachment equation of motion coupled cluster (EA‐EOMCC) method is derived which enables determination of the various bound states of an (N+1)‐electron system and the corresponding energy eigenvalues relative to the energy of an N‐electron CCSD reference state Detailed working equations for the EA‐EOMCC method are derived using diagrammatic techniques for both closed‐shell and open‐shell CCSD reference states based upon a single determinant The EA‐EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations The results from EA‐EOMCC calculations are compared to other EOMCC approaches, starting from different reference states, as well as other theoretical methods and experimental values, where available We have investigated electron affinities for a wide selection of both closed‐shell and open‐shell systems Excitation spectra of atoms and molecules with an odd number of electrons are obtained, taking the closed‐shell ground state of the ion as a reference in the EA‐EOMCC calculation Finally we consider excitation spectra of some closed‐shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way
505 citations
TL;DR: In this article, the authors study the open-shell coupled-cluster theories and examine the current theoretical status regarding the existence or non-existence of a linked-clusters theorem, ensuring the connectedness of the cluster amplitudes and the effective Hamiltonian.
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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