The Coupled-Cluster Response Properties

The above described linear-response approach to calculating first- and cond-order properties can also be applied within the CC and RSPT frame-5rks. In the former (Monkhorst, 1977) theory we consider the CC working luations for a Hamiltonian to which a one-electron perturbation a/f, has en added  

The above first-order equation for 7 [Eq. (5.29)] expresses a set of linear gebraic equations for the cluster amplitudes in which can be written 

In principle, D and II, can be computed in terms of the known (unperturbed) cluster amplitudes and integrals involving the H, operator. The second-order equation that determines can also be expressed as a set of linear algebraic equations 

The RSPT or MBPT approach to computing response properties for atomic and molecular system is, in principle, straightforward (Kelly, 1969 Barlett and Silver, 1975). The perturbed Hamiltonian H 4- af/, is decomposed into an unperturbed part // , which is most commonly taken to be a HF Hamiltonian, and a perturbation that contains both olH, and (// - /7°)  

The desired first- and second-order response properties of the state y ire calculated by summing and respectively, over the index m 

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