In this paper we present a useful analysis for higher-order static properties involving three different response approaches based on coupled-cluster methods, namely, the nonvariational, the variational and the more recent bivariational methods.
The recently developed bivariational coupled-cluster approach was earlier used for the derivation of equations for first-order properties in a two-body approximation. In this paper we introduce a linearized form of this approach in which the bra vector is linearized. In such a form the bivariational coupled-cluster approach reduces to the nonvariational-response-type approach, and thus it can also be more easily generalized to any higher-order property in a more extended approximation. This also gives us an alternative variational derivation of the original nonvariational-response equations of Monkhorst.
An analysis of some of the coupled-cluster methods has been undertaken for the calculation of first-order properties. In particular, it has been shown that Arponen's variational extended exp(T) method truncated to the quadratic power in the cluster amplitudes gives a result identical to the average value of the property operator with the linearized coupled-cluster doubles (L-CCD) stationary state truncated to the quadratic power in amplitudes in the model where only two-body excitations have been included in the cluster amplitudes. In the same model it is also shown that Monkhorst's nonvariational method gives results identical to the previously mentioned average value again truncated to the quadratic power in amplitudes with a full CCD stationary-state wave function.