In the present approach the high reliability of ab initio techniques is combined with the easily amenable phenomenological core polarization concept for an efficient treatment of intershell correlation effects in all-electron SCF and valence CI calculations. By use of only a single adjustable atomic parameter, which is related to the radius of the core and determines the cutoff at short range, our effective core polarization potential (CPP) accounts quantitatively for dynamical intershell correlation as well as exclusion effects on the correlation energy of the core. The applications refer to alkali and alkaline earth atoms (Li to K and Be to Ca) and a detailed analysis is performed for core polarization effects on ionization energies, electron affinities, oscillator strengths, polarizabilities, van der Waals coefficients, the valence electron density, and spin densities. Very accurate results are obtained for well-known energetic properties and spin densities at the nucleus. With respect to the other applications we consider our results as the most reliable to date with an estimated uncertainty of 1%–2%.
A quadratically convergent MCSCF method is described which allows one to optimize an energy average of several states with arbitrary weight factors. An analysis of the problems connected with the variational determination of excited states is given and it is concluded that the averaging method is a natural solution to these problems. In the energy expansion minimized in each iteration, certain cubic and higher order terms can be included. It is demonstrated that this greatly facilitates convergence in cases where the Hessian matrix of second energy derivatives has many negative eigenvalues. Several approximations to the exact quadratically convergent scheme, which are useful when calculating potential surfaces, are discussed.
Potential energy, dipole moment, and transition moment functions have been calculated for the two lowest 1Σ+ states of LiF using MCSCF wave functions. By optimizing both states simultaneously with a particular choice of configurations it is possible to account for the major part of the correlation energy difference of the neutral and ionic states and to obtain the correct separation of the states at infinite internuclear distance. A simple method to obtain a diabatic description of the two states is proposed. In the crossing region nonadiabatic coupling elements have been calculated.
The three lowest adiabatic potential energy curves for each of the two dipole-allowed symmetries, Σu+1 and Πu1, are calculated in the multireference configuration–interaction framework. Diabatic potentials and corresponding coupling elements are obtained by diagonalizing the electronic operator r2 which serves to discriminate Rydberg and valence type states. A large basis set and judiciously chosen active orbital and configuration spaces furnish smooth and reliable potential curves. However, a vibrational analysis of the coupled systems in diabatic representation still shows some disappointing deviations from the experimental interference patterns of overlapping absorption bands that are highly sensitive to potential energy differences. Starting from the calculated curves, a fitting procedure accounting also for empirical information yields potential energy curves and diabatic coupling elements that reproduce all details of the experiment very well. These recommended results also serve to identify residual defects in the ab initio curves mainly as vertical shifts. The performance of other commonly used ab initio methods for the calculation of excited states is briefly discussed.
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