ASCF method

Although ASCF methods are more likely to be successful, it is critical that diffuse functions be included in the basis set so that the description of the radical anion is adequate with respect to the loosely held extra electron. In general, correlated methods are to be preferred, and DFT represents a reasonably efficient choice that seems to be robust so long as the radical anion is not subject to overdelocalization problems. Semiempirical methods do rather badly for EAs, at least in part because of their use of minimal basis sets. 

The most reliable method has proved to be the ASCF method, in which the core binding energies are obtained by subtracting the SCF energies of the ground state from the SCF energy of the system with one of the core electrons removed.24... 

A related topic is the computation of valence-shell ionization potentials (VSIP). The calculation of vertical ionization potentials via Koopmans theorem28 leads in many cases to serious errors, and a version of the ASCF method has been used to compute VSIP for several small molecules, including CH4.29 All the valence hole states of the molecule were computed. Agreement with experiment was substantially better than in the calculations using Koopmans theorem. 

Instead of the standard Hartree-Fock reference calculation, a grand-canonical Hartree-Fock calculation [35] is used with the occupation number of a single spin-orbital (i.e., the transition spin-orbital) set to 0.5. Upon convergence, appreciable corrections to the relaxation energy are included in the transition spin-orbital s energy [23, 24], Usually a very close agreement with the ASCF method [36] is obtained [26], The second order electron propagator is applied to the ensemble... 

Ionization potentials calculated by the ASCF method were studied by Guest and Saunders, who found that this combined SCF procedure successfully accounts for the relaxation energies computed by independent ASCF calculations. 

In the case of S.C.F. calculations this is termed the ASCF method. 

Conceptually, one of the simplest ways to study excited states at the correlated level of theory is by means of A methods, in which is obtained with some post-HF method. While the problems of variational collapse discussed above severely complicate efforts to calculate excitation energies by ASCF methods, it is actually straightforward to obtain ACI excitation energies, provided the same reference function is used for both states. In this case, the... 

The excitation energy by the ASCF method is given as follows ... 

The Perdew-Zunger or one-electron self-interaction error in the ASCF method is written as [63]... 

Table 14.2 summarizes CO core-excitation energies calculated by the ASCF and SIC-ASCF methods using HF and KS-DFT with BLYP, B3LYP, and BHHLYP. 

As is widely known, KS-DFT succeeds in reproducing standard enthalpies of formation of the small G2 set within 3-7 kcal/mol with commonly used functionals [71], Since the ASCF method estimates excitation energies from total energies of two different states, the accuracy for the core-excitation energies is predictable. 

We applied the SIC-ASCF and SIC-TDDFT methods to CO core excitations. The SIC-ASCF and SIC-TDDFT methods are supposed to provide more accurate coreexcitation energies than those of the ASCF and TDDFT methods because of the absence of self-interaction. However, the SIC-TDDFT severely overestimates coreexcitation energies, while the SIC-ASCF method slightly overestimates. These behaviors originate in the fact that the error cancellation occurs for the ASCF method but does not occur for TDDFT. The present analysis suggests that the reduction of self-interaction is important for the TDDFT calculations. Based on the analysis, we have developed a new XC functional, CV-B3LYP with the appropriate inclusion of HFx, which reduces self-interaction [50-52]. 

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