Linearized canonical transformation theory

To summarize the theory dynamic correlations are described by the unitary operator exp A acting on a suitable reference funchon, where A consists of excitation operators of the form (4). We employ a cumulant decomposition to evaluate all expressions in the energy and amphtude equations. Since we are applying the cumulant decomposition after the first commutator (the term linear in the amplimdes), we call this theory linearized canonical transformation theory, by analogy with the coupled-cluster usage of the term. The key features of the hnearized CT theory are summarized and compared with other theories in Table II. 

In the current work, we consider primarily two theoretical models the linearized canonical transformation with doubles (L-CTD) and linearized canonical transformation with singles and doubles (L-CTSD) theories. These are defined by the choice of operators in A. The L-CTD theory contains only two-particle... 

As an example of the application of matrix methods to MO theory, consider the transformation between the set of delocalized canonical Hartree-Fock MOs energy-localized MOs linear combinations of the canonical MOs ... 

Finding canonical forms for each of the A s, is an easier task than for any general form A. A technique has been developed at Princeton [189-191] for finding such canonical forms using an algebraic method in nonlinear perturbation theory. For the application of this technique the leading operator Aq must be chosen to be in canonical form. The basic approach is then to find a non-linear transformation C such that the resultant operator. 

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