Conventional effective potential calculation

We find that the 5d bands are 7-8 eV wide for the trivalent metals and somewhat narrower, 6—7eV, for divalent Eu and Yb. The 4f complements of Eu and Yb are larger by one than trivalency would imply (a consequence of the energetic favora-bility of a half-filled or filled 4f shell), and the relatively smaller effective nuclear charge is responsible for larger lattice constants and correspondingly narrower 5d bands. Our 5d bandwidths are in reasonable agreement with those of conventional band structure calculations (see the review by Liu (1978)), even though the methods of potential construction are quite different. 

Simple self-interaction corrected approximations have been shown to provide viable alternative to accurate polarizability calculations of long-chain polymers within DFT." The schemes have been applied to (H2) chains with n = 2-6 in comparison with HF, conventional DFT, and high-level electron correlation schemes. SIC functionals have been shown to exhibit a field counteracting term in the response part of the XC potential as a result of which the calculated polarizabilities are much improved in comparison to normal LDA and GGA functionals. In a related investigation, it has been demonstrated that a self-interaction correction implemented rigorously within Kohn-Sham theory via the optimized effective potential... 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

---