Electron correlation, omission

A systematic analysis of the electrostatic interactions in the crystals of 40 rigid organic molecules was undertaken by Price and coworkers (D. S. Coombes et al. 1996). In this work, distributed (i.e., local) multipoles up to hexadecapoles, obtained from SCF calculations with 6-31G basis sets, scaled by a factor of 0.9 to allow for the omission of electron correlation, are used in the evaluation of the electrostatic interactions. The experimental lattice constants and structures are reproduced successfully, the former to within a few percent of the experimental... 

A number of important trends can be drawn from Table 4.1, which are trends that have influenced how computational chemists approach related (and sometimes even largely unrelated) problems. Hartree-Fock (HF) self-consistent field (SCF) computations vastly overestimate the barrier, predicting a barrier twice as large as experiment. The omission of any electron correlation more seriously affects the transition state, where partial bonds require correlation for proper description, than the ground-state reactants. Inclusion of nondynamical correlation is also insufficient to describe this reaction complete active space self-consistent field (CASSCF) computations also overestimate the barrier by some 20 kcal... 

If AEcorr is large, the one-electron starting point will be a relatively poor approximation. This is particularly true for the most popular ab initio technique, Hartree-Fock theory, where it turns out that for TM systems, the omission of complete electron correlation is serious and the HF scheme has to be improved significantly. In contrast, the correlation error for DFT-based methods seems to be much smaller3. 

Although the harmonic approximation is satisfactory for small displacements from the equifibrium position, ab initio harmonic force constants and vibrational frequencies are known to be typically overestimated as compared with those experimentally found [86]. Sources of this disagreement are the omission or incomplete incorporation of electron correlation, basis set deficiencies, and the neglect of anharmonicity effects. However, as the overestimation is fairly uniform, the appHcation of appropriate scahng procedures becomes feasible. Due to its simplicity, global scafing (using one uniform scale factor determined by a least-squares fit of the calculated to the experimental vibrational frequencies) has widely been used at different levels of theory [87]. However, for most spectro-... 

Initially, Dewar et al. " based their scheme on INDO, with modified expressions for the core-resonance integral, and ultimately, the core-core repulsion energy. Electron correlation effects were incorporated primarily through an alternative parametric formula for interatomic Coulomb repulsion. The third reparameterization, MINDO/3, became the preferred INDO-based semiempirical method. The most significant omission from MINDO/3 is the interatomic electron repulsion and core-electron attraction that arises from the nonsphericality of atomic charge distributions in molecules. Addition of these and reparameterization led first to MNDO in 1977, to AM1 ° in 1985, and to in 1988-1989. In passing from MINDO/3 to PM3 an overall... 

The only satisfactory solution at present appears to be the use of basis sets which are large enough to describe both molecules accurately. This is unfortunately often impracticable, since such a large basis can only be used for small molecules. Even in such cases difficulties remain, since electron correlation must be taken into account if dispersion effects are to be described. It is becoming clear that basis extension error is a much more serious problem in correlated calculations than in SCF ones[24], both because it is larger at a given level of basis and because it is difficult to correct for it in a consistent way[25]. A recent accurate calculation of the interaction between pairs of Be atoms[263 required s, p, d and f basis functions on each atom for a reasonably accurate result omission of the f functions led to a 40 error in the well depth. 

The most severe problem is most probably the large dynamic correlation effects inherent in a 3d shell with many electrons. Omission of these effects sometimes even leads to an incorrect qualitative description of the chemical bond. A drastic example is the Ct2 molecule, mentioned in the introduction. 

In square CB, (2/2)CASSCF places the triplet below the singlet (positive value of A st) because the wavefunction includes no correlation between the electrons in the NBMOs and those in the bonding n MO. This omission is rectified in the (4/4)CASSCF calculation, which gives AEjt = -10.6 kcal/mol. However, this calculation still does not include correlation between n and a electrons. If it is included by means of second-order multireference perturbation theory (CASPT2), AEjt is reduced to -4.1 kcal/mol (i.e., the triplet is apparently stabilized, relative to the singlet, by a-7t correlation). 

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