Coupling force constant

Figure 4. Phonon dispersion for fee FesNi (renormalized with the eleetron-phonon coupling). Force constants have been obtained from ab initio calculations. Diamonds mark experimental results .

The largest discrepancy between our prediction and experiment, is the 70 cm" (5%) overestimate of the V14 bzu CC-stretching frequency. This vibrational mode can be characterized as an alternating expansion and contraction of the CC bonds, in which the CC-stretching coupling force constants are of primary importance [10b]. This frequency is underestimated by the HF and... 

Molecular Vibration. Coriolis Coupling. Force Constants Fundamental Vibrations V in cm ... 

True quasi-Newton schemes attempt to sidestep any calculation of the exact Hessian. In such cases, an approximate Hessian must be estimated by the program or by the user. How should such an estimate be obtained One attractive possibility is to utilize experimental data on vibrational frequencies, or to transfer estimates from one system to a related system. Here is where the choice of coordinate system can be crucial. In general, such estimates are likely to provide information only about, in effect, the normal modes of vibration of a system they specify only the diagonal elements of the Hessian in a particular coordinate system. There are few sources of empirical information about coupling force constants, for example, and few sources about force constants expressed in Cartesian coordinates. Also Hessian information in Cartesian coordinates is rarely transferable from one molecule to another. Hence, for first-order methods the choice of coordinate system in which the optimization is performed is strongly influenced by the need to obtain Hessian information. 

---