Coupled cluster method, trial

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

One of the main advantages of the Monte Carlo method of integration is that one can use any computable trial function, including those going beyond the traditional sum of one-body orbital products (i.e., linear combination of Slater determinants). Even the exponential ansatz of the coupled cluster (CC) method [27, 28], which includes an infinite number of terms, is not very efficient because its convergence in the basis set remains very slow. In this section we review recent progress in construction and optimization of the trial wavefunctions. 

Among MO-based theories, dynamic correlation is better described by perturbation theory or coupled cluster approaches [123] which are both accurate and computationally affordable, at least for small to medium-size molecules. Despite their prevalence in quantum chemistry, these methods will not be described here because the number of determinants required to evaluate their wave functions is presently too large for use as QMC trial functions. 

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