Lagrangians coupled-cluster methods

The reasons for not invoking the variation principle in the optimization of the wave function are given in Chapter 13, which provides a detailed account of coupled-cluster theory. We here only note that the loss of the variational property characteristic of the exact wave function is unfortunate, but only mildly so. Thus, even though the coupled-cluster method does not provide an upper bound to the FCI energy, the energy is usually so accurate that the absence of an upper bound does not matter anyway. Also, because of the Lagrangian method of Section 4.2.8, the complications that arise in connection with the evaluation of molecular properties for the nonvariational coupled-cluster model are of little practical consequence. 

In Section 12.2 it will be discussed that this approach for the calculation of expectation values is called the unrelaxed method, because the conditions for the molecular orbital coefficients were not included as additional constraints in the coupled cluster Lagrangian given in Eq. (9.95) or Eq. (9.98). A coupled cluster Lagrangian including orbital relaxation takes the following form... 

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