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Physical Review A

Bivariational coupled-cluster method: Equations for first-order property

Keya Basu Ghose, Sourav Pal

Published Aug 1, 1987• 18 citations
Publisher

Abstract

Equations are presented for the first-order property using our recently developed bivariational coupled-cluster approach for calculation of static property in a two-body approximation of the cluster parameters.
DOI
10.1103/physreva.36.1539

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The Journal of Physical Chemistry A•Apr 6, 2025•5 citations
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.
Real-time propagation methods for chemistry and physics are invariably formulated using variational techniques. The time-dependent bivariational principle (TD-BIVP) is known to be the proper framework for coupled-cluster type methods, and is here studied from a differential geometric point of view. It is demonstrated how two distinct classical Hamilton's equations of motion arise from considering the real and imaginary parts of the action integral. This in turn leads to two distinct bivariational principles for real bivariational approximation submanifolds. Conservation laws and Poisson brackets are introduced, completing the analogy with classical mechanics. Furthermore, the time-dependent univariational principles (the time-dependent variational principle, the McLachlan principle, and the Dirac-Frenkel principle) are reconstructed using the TD-BIVP and a bivariational submanifold on product form. An overview of established real-time propagation methods is given in the context of our formulation of the TD-BIVP, namely time-dependent traditional coupled-cluster theory, orbital-adaptive coupled-cluster theory, time-dependent orthogonal optimized coupled-cluster theory, Brueckner coupled-cluster theory, and equation-of-motion coupled cluster theory.