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Abstract: Single reference coupled-cluster CC methods for electronic excitation arebased on a biorthogonal representation bCC of the shifted Hamiltonian interms of excited CC states, also referred to as correlated excited CE states,and an associated set of states biorthogonal to the CE states, the latter beingessentially configuration interaction CI configurations. The bCCrepresentation generates a non-hermitian secular matrix, the eigenvaluesrepresenting excitation energies, while the corresponding spectral intensitiesare to be derived from both the left and right eigenvectors. Using theperspective of the bCC representation, a systematic and comprehensive analysisof the excited-state CC methods is given, extending and generalizing previoussuch studies. Here, the essential topics are the truncation errorcharacteristics and the separability properties, the latter being crucial fordesigning size-consistent approximation schemes. Based on the general orderrelations for the bCC secular matrix and the left and right eigenvectormatrices, formulas for the perturbation-theoretical PT order of thetruncation errors TEO are derived for energies, transition moments, andproperty matrix elements of arbitrary excitation classes and truncation levels.In the analysis of the separability properties of the transition moments, thedecisive role of the so-called dual ground state is revealed. Due to the use ofCE states the bCC approach can be compared to so-called intermediate staterepresentation ISR methods based exclusively on suitably orthonormalized CEstates. As the present analysis shows, the bCC approach has decisive advantagesover the conventional CI treatment, but also distinctly weaker TEO andseparability properties in comparison with a full and hermitian ISR method.



Author: J. Schirmer, F. Mertins

Source: https://arxiv.org/







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