BWCC theory

Single-root MR BWCC theory Hilbert space approach 9... 

SINGLE-ROOT MR BWCC THEORY HILBERT SPACE APPROACH. 

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]... 

Multireference Brillouin-Wigner coupled cluster (MR-BWCC) theory applied to the H8 model ... 

These two equations together are the basic equations of non-degenerate (singlereference) Brillouin-Wigner coupled cluster (Bwcc) theory. We emphasize that these equations are obtained directly from Brillouin-Wigner perturbation expansion. In particular, we have not used the linked cluster theorem and neither have we employed... 

Here we shall discuss two versions of the multi-reference Brillouin-Wigner coupled cluster (Bwcc) theory which are based on the use of effective Hamiltonians. 

To derive a multi-reference version of the bwcc theory, we shall follow a procedure which is similar to that used in the case of single-reference function. We begin again with eqs. (4.1)-(4.7) ... 

The formulation of a multi-reference bwcc theory can now proceed in two distinct ways. In the first option, we can formulate a multi-root version of the multi-reference BWCC theory which yields all roots of the d-dimensional 9 space simultaneously. This is the approach employed in most multi-reference coupled cluster formulations which are based on the Rayleigh-Schrodinger expansion. In the second option, we can use the state-specific wave operator (4.59) and formulate a state-specific (or single root) version of multi-reference bwcc theory [10]. 

If we now adopt an exponential ansatz for the wave operator 17, then we are lead to the multi-reference Brillouin-Wigner coupled-cluster (MR Bwcc) theory. 

Now let us begin the determination of exact energies within the multi-root multireference Bwcc theory. In the following analysis, we will work with the Hamiltonian in the normal-ordered product form, i.e. 

In Section 4.2.3.1, we have defined the wave operator, 12, in the Brillouin-Wigner form (4.92). If we adopt an exponential ansatz for the wave operator, 12, we can develop the single-root (state-specific) multi-reference Brillouin-Wigner coupled-cluster (MR Bwcc) theory. This is the purpose of the present section. 

In developing BWCCS.D theory, extensivity and size consistency have been a primary concern. In Table 1 a size-consistency test for the F2 molecule [131] is presented. The entries show that on applying the a posteriori extensivity correction the size-consistency error has been practically eliminated and that its absolute value does not increase with size of basis set. In other tests on CH2, SiH2 and twisted ethylene molecules [15] the extensivity error was smaller than 1 kcal/mol. This accuracy is suflScient for... 

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