Hilbert space expansion theories

So far, we have specified the wave operator H in the BW form (15). If we adopt an exponential ansatz for the wave operator Cl, we can speak about the single-root multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory. The simplest way how to accomplish the idea of an exponential expansion is to exploit the so-called state universal or Hilbert space exponential ansatz of Jeziorski and Monkhorst [23]... 

FULL CLUSTER EXPANSION THEORIES IN HILBERT SPACE... 

As explained in Sec.2, the full cluster—expansion theories in Hilbert space are designed to compute wave-functions for the open-shell states that are explicitly size-extensive with respect to the total number of electrons N. The underlying cluster structure of all these developments is what was envisaged by Silverstone and Sinanoglu/48/s... 

This relation shows how the action of the antisymmetrizer can mix different orders in perturbation theory. Secondly, the projected functions AglO ) 0 > do not form an orthogonal set in the antisymmetric subspace of the Hilbert space L2(r3N) if we take all excited states a > and b > in order to obtain a complete set a > b >, the projections As a > b > form a linearly dependent set. Expanding a given (antisymmetric) function in this overcomplete set is always possible, but the expansion coefficients are not uniquely defined. How the different symmetry adapted perturbation theories that have been formulated since the original treatment by Eisenschitz and London in 1930 , actually deal with these two problems can be read in the following reviews Usually, the first order interaction... 

A strong numerical evidence supporting the above statements has been provided in Ref. [98]. Before discussing a few representative examples, let us emphasize that in all numerical calculations reported in Ref. [98] and reviewed here, we tested, for the first time ever, the exact theory, in which we used the unexpanded form of the exponential operator to define the E X) energy rather than the truncated power series expansion in X used in Ref. [97]. This was made possible by representing the operators H and X as matrices in the finite-dimensional 7V-electron Hilbert spaces relevant to a molecular system under consideration (using all symmetry-adapted Slater determinants ) and n = 1,..., TV, defining the... 

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