Configuration excitation hierarchy

One can so define a hierarchy of Cl methods, called CI-SD, CI-SDT, CISDTQ etc. where S, D, T, Q stands for singly, doubly, triply, quadruply excited configurations. This hierarchy has the advantage over MP-PT that it does converge to full Cl if one let the excitation rank go to the number of electrons. This is, however, just what one wants to avoid. 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

H. Koch, O. Christiansen, P. Jorgensen, and J. Olsen, Chem. Phys. Lett., 244, 75 (1995). Excitation Energies of BH, CH2, and Ne in Full Configuration Interaction and the Hierarchy CCS, CC2, CeSD, and CC3 of Coupled-Cluster Models. 

States whose zero-order labels are configurations, which are multiply excited (e.g., doubly, triply, or even quadruply excited) with respect to the ground main configuration, for example, see Ref. [10]. They can be created by the absorption of one or more photons. It is important to stress that these states are determined as solutions of their state-specific Schrbdinger equations and do not correspond, except perhaps by occasional accident, to the hierarchy of virtual excitations that appear in the many-electron treatments of electron correlation in ground states by the conventional methods of computational chemistry. 

The hierarchy of the MMCC(myt,mB) approximations is obtained, when we restrict the wave functions 4 b ) in eqs (7) and (22) to functions that do not contain higher-than-ms-tuply excited configurations in the corresponding Cl expansions. The nonzero values of corrections are ob-tmned only when me > tha- The energy expressions describing the resulting MMCC(myi,ms) approximations are as follows (7,16,17,98) ... 

The Cl approach to the many-electron problem suffers from two main disadvantages. First, since the Cl model is not manifestly separable, it does not provide size-extensive energies. In Section 4.3.2, we found that size-extensivity follows only when the variational space of the compound system is equal to the direct product of the fragment spaces. This requirement cannot be satisfied for Cl wave functions truncated at a fixed excitation level relative to the reference configuration. For example, if two fragments are each described at the CISD level, then a size-extensive treatment of the compound system requires the wave function to be augmented with certain triples and quadruples - namely, those that represent products of single and double excitations in the two subsystems. Such wave functions are not defined within the hierarchy of truncated Cl wave functions based on excitation levels. 

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