Vibrational frequencies force fields

Conformation of a System of Three Linked Peptide Units. Biopol. 6, 1425-1436. von Carlowitz, S., H. Oberhammer, H. Willner, and J. E. Boggs. 1986. Structural Determination of a Recalcitrant Molecule (S2F4). J. Mol. Struct. 100,161-177. von Carlowitz, S., W. Zeil, P. Pulay, and J. E. Boggs. 1982. The Molecular Structure, Vibrational Force Field, Spectral Frequencies, and Infrared Intensities of CH3POF2. J. Mol. Struct. (Theochem) 87, 113-124. 

A potentially much more adaptable technique is force-field vibrational modeling. In this method, the effective force constants related to distortions of a molecule (such as bond stretching) are used to estimate unknown vibrahonal frequencies. The great advantage of this approach is that it can be applied to any material, provided a suitable set of force constants is known. For small molecules and complexes, approximate force constants can often be determined using known (if incomplete) vibrational specha. These empirical force-field models, in effect, represent a more sophisticated way of exhapolating known frequencies than the rule-based method. A simple type of empirical molecular force field, the modified Urey-Bradley force field (MUBFF), is introduced below. 

S, Cl and Si-isotope fractionations for gas-phase molecules and aqueous moleculelike complexes (using the gas-phase approximation) are calculated using semi-empirical quantum-mechanical force-field vibrational modeling. Model vibrational frequencies are not normalized to measured frequencies, so calculated fractionation factors are somewhat different from fractionations calculated using normalized or spectroscopically determined frequencies. There is no table of results in the original pubhcation. 

The ground state force field, vibrational normal modes and frequencies have been obtained with MCSCF analytic gradient and hessian calculations [176]. Frequencies computed with the DZ basis set are compared with experimental ones in Table 16. The T - So transition moments were obtained using distorted benzene geometries with atomic displacements along the normal modes, and with the derivatives in Eq. 97 obtained by numerical differentiation. The normal modes active for phosphorescence in benzene are depicted in Fig. 12. The final formula for the radiative lifetime of the k spin sublevel produced by radiation in all (i/f) bands is (ZFS representation x,y,z is used [49]) ... 

It is apparent from Eq. (2), that this stretching force constant is highly sensitive to the value of due to the 1/R>b dependence of the second term. Therefore, in force-field and frequency calculations the equilibirum (rj geometries should ideally be used as a reference point, in order to reproduce experimental vibrational frequencies. 

Microwave studies also provide Important Information regarding molecular force fields, particularly with reference to low frequency vibrational modes in cyclic structures (74PMH(6)53). 

At this point, spectroscopists and molecular modellers part company because they have very different aims. Spectroscopists want to describe the vibradons of a molecule to the last possible decimal point, and their problem is how a force field should be determined as accurately as possible from a set of experimental vibrational frequencies and absorption intensities. This problem is well understood, and is discussed in definitive textbooks such as that by Wilson, Decius and Cross (1955). 

Halgren, T. A. Merck Molecular Force Field. HI. Molecular geometries and vibrational frequencies for MMFF94. J Comput Chem 1996,17 553-86. 

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