Force field calculations, vibrational

The observation of the variation of the SCH bands of thiazole with the nature and the position of the substituent has been interpreted as a proof of a fairly strong coupling between the various CH vibrators (203). The couplings are confirmed by the force-field calculation for thiazole that shows that the nature of the 1300-1000 band is rather complex. 

The potential energy expressions used for force field calculations are all descendants of three basic types originating from vibrational spectroscopy (5) the generalized valence force field (GVFF), the central force field, and the Urey-Bradley force field. General formulations for the relative potential energy V in these three force fields are the following ... 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

We have seen that for our calculations essentially two types of force fields have to be considered VFF- and UBFF-expressions. The main difference with repect to spectroscopic force fields consists in the superposition of nonbonded interactions. The force fields used so far for our purposes are almost exclusively simple valence force fields without cross terms, and a veriety of UB-force fields. Only recently could experiences be gathered with a valence force field that includes a number of important cross terms (79). Vibrational spectroscopic force fields of both types have been derived and tested with an overwhelming amount of experimental data. The comprehensive investigations of alkanes by Schachtschneider and Snyder (26) may be mentioned out of numerous examples. The insights gained from this voluminous spectroscopic work are important also when searching for suitable potentials for our force-field calculations. 

A force field is considered transferable from an arbitrary molecule A to another molecule B if the agreement of properties calculated fori (geometrical, vibrational, thermochemical, and other properties) with the respective experimental values is as good as for A. In our calculations we are dealing with force fields which describe entire families of molecules. Within these families, properties of only a fraction of their members are known experimentally while it is our aim to predict the others computationally. It is therefore clear that the problem of transferability is of decisive importance for force field calculations of unknown systems or those with unknown properties or. Traditional vibrational spectroscopic force fields in most cases reproduce well the frequencies of a single molecule or a family of closely related molecules however, they are not transferable to molecules of different strain. Subsequently we comment on this point in somewhat more detail. 

The simple cycloalkanes (CH2)n with n = 5 to 12 are the compounds most frequently studied by force field calculations (8, 9, 11, 12,17, 21). This preference results from their simple structure, from the abundant available experimental material (structural (46), thermo-chemical (47) and vibrational spectroscopic (27, 48, 49) data), and from the fact that, apart from bond length deformations, all other strain factors (angle deformations, unfavourable torsion angles, strongly repulsive nonbonded interactions) are important for the calculation of their properties. The cycloalkanes are thus good candidates for testing force fields. For a more detailed discussion we choose cyclodecane, a so-called medium-ring compound. 

Kofraneck and coworkers24 have used the geometries and harmonic force constants calculated for tram- and gauche-butadiene and for traws-hexatriene, using the ACPF (Average Coupled Pair Functional) method to include electron correlation, to compute scaled force fields and vibrational frequencies for trans-polyenes up to 18 carbon atoms and for the infinite chain. 

Entropies and heat capacities can thus now be calculated using more elaborate models for the vibrational densities of states than the Einstein and Debye models discussed in Chapter 8. We emphasize that the results are only valid in the quasiharmonic approximation and can only be as good as the accuracy of the underlying force-field calculation of such properties can thus be a very sensitive test of interatomic potentials. 

Forced-vibration instruments, 21 745 Force field calculations, 16 742 Force field energy, 16 742 Force field performance, 16 745 Force fields, 16 743-745 Force field simulations, 16 746-747 programs for, 16 746 Force modulation microscopy, 3 332 Forces, exponents of dimensions in absolute, gravitational, and engineering systems, 8 584t Forchlorfenuron, 13 43t, 53 Ford nuclear reactor, 17 594... 

Berces, A., Ziegler, T. Application of Density Functional Theory to the Calculation of Force Fields and Vibrational Frequencies of Transition Metal Complexes. 182, 41-85 (1996). Bersier, J., see Bersier, P.M. 170, 113-228 (1994). 

Spectroscopic methods such as IR and Raman have proven to be exceptionally powerful methods for solving many chemistry problems . However, the vibrational assignment, as well as the understanding of the relationship between the observed spectral features and molecular structure or reactivity of the sample, can be very difficult. Theoretical methods can certainly assist to obtain a deeper understanding of the vibrational spectra of new compounds. These are the well-established force field calculations, semi-empirical and ab initio methods . 

Raman studies have been made of the complexes Pt(CN)2-, Pt(13CN)4 , and Pt(C15N)4-. Many of the vibrational frequencies have been determined. From force field calculations it is found that the Pt—C o bond and Pt—CN back jt bond are both stronger than those found for the Ni and Pd analogs.275... 

Some of the potential energy functions used to calculate the total strain energy of a molecule are similar to the functions used in the analysis of vibrational spectra. Because the parameters used to derive the strain energies from these functions are fitted quantities, which are based on experimental data (for example X-ray structures), molecular mechanics may be referred to as empirical force field calculations (more often the simplification force field calculations is used). The quality of such calculations is strongly dependent on the reliability of potential energy functions and the corresponding parameters (the force field). Thus, the selection of experimental data to fit the force field is one of the most important steps in a molecular mechanics study. An empirical force field calculation is in essence a method where the structure and the strain energy of an unknown molecule are interpolated from a series of similar molecules with known structures and properties. 

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