Linearized bivariational coupled-cluster approach: General scheme for derivation of static properties

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.