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Best harmonic approximation

Common spectroscopic techniques test small portions of the ground and/or excited state PES either around the gs minimum (IR and non-resonant Raman spectra, electronic absorption spectra.) or in the proximity of the excited state minimum (steady-state fluorescence). These spectra are then satisfactorily described in the best harmonic approximation, a local harmonic approach that approximates the PES with parabolas whose curvatures match the exact curvatures calculated at the specific position of interest [78]. Anharmonicity in this approach manifests itself with the dependence of harmonic frequencies and relaxation energies on the actual nuclear configuration [79]. Along these lines we predicted softened (hardened) vibrational frequencies for the ground (excited) state [74], amplified and p-dependent infrared and Raman intensities [68, 74], different Frank-Condon... [Pg.262]

It has been noticed [37] that A is positive for any attractive power-law potential e(a)r , where e is the sign function. In particular, if the popular Coulomb-plus-linear potential is split into its best harmonic approximation (for N = 2) and a correction to it, say... [Pg.46]

Within the above Gaussian approximation, the r.m.s. separation between quarks, = experiences the same value in the baryon as in the pseudomeson with constituent masses m. This approximation corresponds to choosing the best harmonic approximation ar + b to the potential V. When one treats the anharmonicity Au(r) in perturbation, the pseudomesons, in comparison to baryons, receive large contributions from higher states of the harmonic oscillator. This results in larger shifts. [Pg.57]

The best fit harmonic approximation, on the other hand, gives... [Pg.159]

These comparisons teach us about the performance of this simplest physical theory. An important point is how the iimer shell should be defined to make reasonable statistical thermodynamic predictions. As with the K" (aq) case of Fig. 8.15, a naive eyeball analysis of a radial distribution function might not be the wisest for this assignment. On physical groimds, it has been argued that the inner-shell volume should be chosen aggressively small so that subsequent approximations such as a harmonic approximation for the optimized structure have the best chance of being valid (Pratt and Rempe, 1999). But the discussion of Section 7.4, p. 153, pointed out that this question has a variational answer - see Fig. 7.6,... [Pg.207]

The differences in barrier heights are even more dramatic. This is best exemplified by calculations on porphycenes 1 and la the inclusion of zero point energy results in the transition state energy being lower than that of the cis form in 1 and of both forms in la. These results show that the harmonic approximation is not appropriate for the vibrations involved in the hydrogen transfer path in porphycenes (NH stretch, in particular) and that the barriers to tautomerization must be very low. [Pg.258]

Consideration of the effect of electron correlation is needed to arrive at predicted intensities comparable in quantitative terms with experimental values. Since the number of molecules treated in calculations accounting for large proportion of correlation energy is limited, definite conclusions as to what approach is best for quantitative IR intensity predictions are still to come. Analytical derivative methods for higher order perturbation frieory proaches, configuration interaction treatment and, especially, coupled cluster theory, tq>pear to be the best hopes. Whether such calculations would become a routine exercise is yet to be seen. Fortunately, the studies carried out show that die double harmonic approximation works quite well as far as ab initio intensity predictimis are concerned. [Pg.187]

AMorse function best approximates a bond potential. One of the obvious differences between a Morse and harmonic potential is that only the Morse potential can describe a dissociating bond. [Pg.24]

The last task is to calculate the area of the independent pieces S0, which is provided by eq 6 only for a harmonic interaction. To accomplish this, we will seek a harmonic potential Hdz) = (l/2)Bdz — zdj2 4- C (with Bo, zo, and C independent of z), which best approximates H(z) and use So = mdBo)m. [Pg.349]

The above discussion of Equations 2 and 3 has been predicted on the assumption of harmonic frequencies for all 3N modes. More realistically, these are at best described as slightly anharmonic frequencies which we approximate with an effective harmonic force field. For lattice frequencies in particular, anharmonicity is expected to be important here it arises both from the anharmonic curvature in the potential and from the expansion of the lattice on warming. Consequently, the force constants used to describe the lattice modes become temperature dependent. The approach amounts to a simple extension of the ideas at the basis of the pseudoharmonic theory of solid lattices (2, 3) to the condensed phases which interest us. One phenomenological result of such anharmonicity is that Equation 3 now takes the form ... [Pg.103]


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