Electron correlation multiconfiguration-based methods

When the HF wave function gives a very poor description of the system, i.e. when nondynamical electron correlation is important, the multiconfigurational SCF (MCSCF) method is used. This method is based on a Cl expansion of the wave function in which both the coefficients of the Cl and those of the molecular orbitals are variationally determined. The most common approach is the Complete Active Space SCF (CASSCF) scheme, where the user selects the chemically important molecular orbitals (active space), within which a full Cl is done. 

Next are methods based on zeroth-order wave functions that are linear combinations of Slater determinants that again may or may not include a treatment of residual electron correlation effects. In these multiconfigurational (MC) approaches, the starting wave function is presupposed to be given by a determinantal expansion... 

A b initio quantum chemical studies of hyperfine structures (hfs) were initiated some 25 years ago, with the pioneering work of Meyer and others [127]. However, results from the early Hartee-Fock-based methods deviated considerably from experimentally determined hf parameters. It was not until the configuration interaction (Cl) techniques were fully developed for hfs calculations, that theoretical predictions of high accuracy were possible for atomic and molecular radicals [20]. This is mainly associated with the importance of electron correlation and with the development of new and fax larger basis sets. In later years, hfs calculations have also been carried out with great success using various levels of multiconfiguration SCF (MCSCF) [21], multireference Cl (MRCI) [22] and coupled cluster (CC) theory [23]. 

As in the Hartree-Fock molecular orbital theory, which is based on the independent particle model, the above Hartree product method also lacks enough correlation among the orbitals, and thereby the resultant accuracy is limited. To overcome the drawback, one can take account of the interaction among possible configurations (or the Hartree products) as in the configuration interaction method and multiconfiguration SCF methods in electronic structure theory. The multiconfigulational time-dependent Hartree... 

Eq. (5.75) in Tables 13.4 to 13.6 as examples. The emphasis is here on the comparison of some of the methods introduced in Chapters 10 to 12 and in particular on the effect of electron correlation, meaning the difference in the results obtained with methods based on the Hartree-Fock wavefunction, like SCF linear response (section 11.2) or RPA (section 10.3) and CHF (section 11.1) on one side and with methods based on multiconfigurational (sections 10.4 and 11.2), Mpller-Plesset (sections 10.3 and 12.2) or coupled cluster wavefunctions (sections 10.3, 11.4 and 12.2) on the other side. Only results for small molecules are discussed here. 

Coupling of quantum mechanical molecular subsystems with larger classically treated subsystems has traditionally involved electronic structure models describing molecules embedded in a dielectric medium and this is a research area that has expanded tremendously over the last three decades [2-36]. Most of this work has involved electronic structure methods that have been based on uncorrelated electronic structure methods [2-12,15-19]. Accurate description of the electronic structure of molecular systems requires that the correlated electronic motion in the molecule is incorporated and therefore a number of correlated electronic structure methods have been developed such as the second order Moller-Plesset (MP2) [28,30,90,91], the multiconfigurational self-consistent reaction field (MCSCRF) [13,20] and the coupled-cluster self-consistent reaction field (CCSCRF) method [36]. 

Ab initio MO methods based on HF or small multiconfigurational wave-functions have been the method of choice, up to the present, for studies of organic systems and other molecules with light nuclei. The properties of stable species on the PES are often reproduced very well by calculations with just HF wavefunctions. Studies of reactions usually require the more sophisticated and expensive techniques, such as Cl or MP perturbation theory, that take into account the effects of the correlation between the electrons that is omitted from the HF approximation. The additional energy lowering computed with these methods with respect to that obtained with an HF calculation is called the correlation energy. A detailed and up-to-date discussion of the accuracy of state-of-the-art MO methods when applied to a variety of problems may be found in the book by Hehre et al. 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

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