Many-body perturbation theory size-consistent methods

If one wishes to use RSPT to perform ab initio quantum-chemical calculations that yield size-consistent energies, then care must be taken in computing the factors that contribute to any given E For example, if were calculated as in Eq. (3.28), limitations of numerical precision might not give rise to the exact cancellation of size-inconsistent terms, which we know should occur. This would certainly be the case for an extended system (for which the size-inconsistent terms would dominate). In addition, it is unpleasant to have a formalism in which such improper terms arise in the first place. It is therefore natural to attempt to develop approaches to implementing RSPT in which the size-inconsistent factors are never even computed. Such an approach has been developed and is commonly referred to as many-body perturbation theory (MBPT). The method of implementing MBPT is discussed once we have completed the present treatment of RSPT. 

The ab initio HF treatment with correlation of large molecules is by no means a simple problem. On the other hand, without taking into account correlation effects only the ground state properties of a molecule in its equilibrium geometry can be calculated in a more or less reliable way. Further the standard method for the treatment of correlation, the configuration interaction (Cl) method, cannot be used well even for medium size systems, because it is not size consistent. Therefore, one has to apply either some form of many body perturbation theory (MBPT) or the coupled cluster (CC) approach, both in a certain approximation (both methods are size consistent). 

This requirement is satisfied by two of the methods most frequently used to calculate correlation effects Many body perturbation theory (MBPT) and coupled cluster theory (CC). In principle, configuration interaction (Cl) is also size consistent, but only if it is not truncated at a certain excitation level. Since untruncated Cl expansions become untractably large even for medium-size systems. Cl is not a method that can be used for the calculation of molecule/ surface interactions. 

Although a wide variety of theoretical methods is available to study weak noncovalent interactions such as hydrogen bonding or dispersion forces between molecules (and/or atoms), this chapter focuses on size consistent electronic structure techniques likely to be employed by researchers new to the field of computational chemistry. Not stuprisingly, the list of popular electronic structure techniques includes the self-consistent field (SCF) Hartree-Fock method as well as popular implementations of density functional theory (DFT). However, correlated wave function theory (WFT) methods are often required to obtain accmate structures and energetics for weakly bound clusters, and the most useful of these WFT techniques tend to be based on many-body perturbation theory (MBPT) (specifically, Moller-Plesset perturbation theory), quadratic configuration interaction (QCI) theory, and coupled-cluster (CC) theory. 

It was seen in Section 5.3 that to determine the QP band structures of a polymeric chain one must use a size-consistent method to determine the major part of the correlation [many-body perturbation theory (MBPT) in the Moller-Plesset partitioning, coupled-cluster theory, etc.]. Suhai, in his QP band-structure calculation on polyacetylenes and polydiace-tylenes, used second-order (MP/2) Moller-Plesset MBPT. For polydiacetylenes he obtained 5.7 eV as first ionization potential (using the generalized Koopmans theorem) for the PTS structure (see Figure 8.1), in reasonable agreement with experiment (A = 5.5 0.1 while the HF value (the simple Koopmans theorem) is 6.8 eV.< > For the TCDU diacetylene structure the theoretical value is 5.0 eV (HF value, 6.2 eV). Unfortunately, there is no reliable experimental ionization-potential value available for the TCDU structure of polydiacetylene. 

As I have argued, errors are seldom computed by independent ab inito criteria in any of the calculations in theoretical chemistry which I discuss. Only the Self-Consistent Field calculations provide an upper bound whereas Many-Body Perturbation Theory and Coupled Cluster methods do not. More importantly perhaps, none of these methods computes a lower bound. As was remarked earlier the calculation of the ground state energies of atoms has been achieved to a remarkable degree of accuracy and similarly calculations on small or even medium sized molecules have given encouraging results. However, whether one can draw the conclusion that chemistry has been reduced rather depends on one s criteria of reduction. If we are to define approximate reduction as has been suggested in this paper then it must be concluded that chemistry is not even approximately reduced to quantum mechanics. The point I wish to emphasize is that we should not be misled by the apparent quantitative successes achieved and should appreciate the full nature of the approximation procedures employed. 

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