Post-HF methods

In principle, the deficiencies of HF theory can be overcome by so-called correlated wavefunction or post-HF methods. In the majority of the available methods, the wavefunction is expanded in terms of many Slater-determinants instead of just one. One systematic recipe to choose such determinants is to perform single-, double-, triple-, etc. substitutions of occupied HF orbitals by virtual orbitals. Pictorially speaking, the electron correlation is implemented in this way by allowing the electrons to jump out of the HF sea into the virtual space in order... 

It is apparent that the Hartree-Fock level is characterized by an enormous average deviation from experiment, but standard post-HF methods for including correlation effects such as MP2 and QCISD also err to an extent that renders their results completely useless for this kind of thermochemistry. We should not, however, be overly disturbed by these errors since the use of small basis sets such as 6-31G(d) is a definite no-no for correlated wave function based quantum chemical methods if problems like atomization energies are to be addressed. It suffices to point out the general trend that these methods systematically underestimate the atomization energies due to an incomplete recovery of correlation effects, a... 

Having these severe approximations in mind, SCC-DFTB performs surprisingly well for many systems of interest, as discussed above. However, it has a lower overall accuracy than DFT or post HF methods. Therefore, applying it to new classes of systems should be only done after careful examination of its performance. This can be done e.g. by conducting reference calculations on smaller model systems with DFT or ab initio methods. A second source of errors is related to some intrinsic problems with the GGA functionals also used in popular DFT methods (SCC-DFTB uses the PBE functional), which are inherited in SCC-DFTB. This concerns the well known GGA problems in describing van der Waals interactions [32], extended conjugate n systems [45,46] or charge transfer excited states [47, 48],... 

It is, however, for the transition metals themselves that DFT has proven to be a tremendous improvement over HF and post-HF methods, particularly for cases where tlie metal atom is coordinatively unsaturated. The narrow separation between filled and empty d-block orbitals typically leads to enormous non-dynamical correlation problems with an HF treatment, and DFT is much less prone to analogous problems. Even in cases of a saturated coordination sphere, DFT methods typically significantly ouqierform HF or MP2. Jonas and Thiel (1995) used the BP86 functional to compute geometries for the neutral hexacarbonyl complexes of Cr, Mo, and W, the pentacarbonyl complexes of Fe, Ru, and Os, and the tetracarbonyl... 

The choice of a basis set can be crucial and is particularly important for post-HF methods. HF itself and DFT methods are not so basis set dependent, but this should not be taken as an excuse for not checking a few basis sets even for these levels. The popular Pople-type basis sets [26], e.g. 6-31G(d), have proven their value for HF and DFT, and are well behaved for structures involving first row and many heavier elements. The cc-p VXZ b asis sets [ 19 ], which are also sometimes used in conjunction with DFT computations, were explicitly designed to recover as much correlation energy as possible for highly correlated methods and are, therefore, not necessarily guaranteed to perform well with DFT methods. 

The post-HF methods can be very accurate, but require so much computer time that they are restricted to molecules with less than about 15 atoms. Hence, post-HF methods are generally impractical for studying degradation of pharmaceutically interesting molecules. 

There are various post-HF methods for obtaining a wave function for an excited state (38). However, a molecule has so many excited states that it may be computationally difficult to determine the wave functions for each of these except when symmetry (i.e., the irreproducible representation in group theory) can be used to distinguish the states. 

For drug-sized molecules, an MO calculation is more practical than post-HF methods. Such a calculation will give you a set of filled MOs and a set of unoccupied (so-called virtual) MOs (and, in the case of radicals, one or more singly occupied MOs). Simplistically, electronic excitations can be thought of as promoting an electron from one of the occupied MOs to an unfilled one. In reality, of course, the MOs would adjust to the excitation so that the ground state MOs are only an approximation to the excited state MOs. 

In practical terms, a post-HF method (38) that is able to reliably optimize ground and excited states must be used. One such method is CASSCF, which is available in ab initio programs such as Gaussian. The drawback of modeling with a post-HF method is that the computer time requirements are heavy. Molecules with 10-15 first-row atoms are about as large as can be handled accurately. 

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