Simple valence force field

There are some systems for which the default optimization procedure may not succeed on its own. A common problem with many difficult cases is that the force constants estimated by the optimization procedure differ substantially from the actual values. By default, a geometry optimization starts with an initial guess for the second derivative matrix derived from a simple valence force field. The approximate matrix is improved at each step of the optimization using the computed first derivatives. 

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 qualitative view of the influence of the M-H-M angle on v 1, >2, and v can be drawn from a simple valence force field calculation in which the force... 

Simple valence force field calculations predict a difference of 20 cm-1 between a truly linear Cr-H-Cr array and the slightly bent array (159.8°), which has been observed by neutron diffraction for the Et4N+ salt. 

A simple valence force field leads to Equation 1 for relationship between a M-H terminal stretch, j/t, as compared with for a linear M-H-M system. 

In the conventional simple valence force field approximation, mixed derivatives of the type (d3E/dR1dd2)n2 and (33 /3/f2902)j x are neglected. In fact they are usually relatively small. Using these approximations, it follows from the above equations that... 

The bands at 1388 cm-1 might be explained by the presence of small amounts of P4OI0 due to the route of preparation (see Refs. 171 and 172). Force constants for the P406S4 molecule were calculated from Raman spectra and were improved later (113). Table XXVII gives the values obtained using the simple valence force field method (I) or the extended force field method (II) (113) the calculations have been carried out using interatomic distances and angles from electron diffraction data (178). 

Up to this point, the analysis is rigorously correct and general it is simply a restatement of the Born-Von Karman expansion of the energy in terms of relative displacements—.see Eq. (8-17). However, we shall now make a major approximation in taking the force constants from the very simple valence force field that we described in Chapter 8. This will give us a clear and correct qualitative description of the vibration spectra and will even give semiquantitativc estimates of the frequencies. Afterward, we shall consider the influence of the many terms that are omitted in this simple model. 

Force constant calculations are facilitated by applying symmetry concepts. Group theory is used to find the appropriate linear combination of internal coordinates to symmetry-adapted coordinates (symmetry coordinates). Based on these coordinates, the G matrix and the F matrix are factorized, which makes it possible to carry out separate calculations for each irreducible representation (c.f. Secs. 2.133 and 5.2). The main problem in calculating force constants is the choice of the potential function. Up until now, it has not been possible to apply a potential function in which the number of force constants corresponds to the number of frequencies. The number of remaining constants is only identical with the number of internal coordinates (simple valence force field SVFF) if the interaction force constants are neglected. If this force field is applied to symmetric molecules, there are often more frequencies than force constants. However, the values are not the same in different irreducible representations, a fact which demonstrates the deficiencies of this force field (Becher, 1968). 

As the application of this treatment depends on a knowledge of the function E r, a), which depends on the nature of the molecular force field, it is relevant next to enquire whether any simple force field leads to a simplification of the results. A good first approximation to the molecular force field is the simple valence force field (see Linnett toj, This approximation implies that dEjdrk for all... 

Spectroscopic Results.—The Raman spectra which we obtained for solid SF4-BFa and SF4-AsF5 and our assignments of the lines contained therein (Figure 1) are in essential agreement with those reported by earlier workers except that we observe an additional weak feature at 711 cm in the spectrum of SF4 AsFj. This new feature is attributable to a fundamental transition in the formally Raman-inactive mode 3(tiu) of the AsFs anion. Using a simple valence force field and the geometry established in this work, the fundamentals of SFa in... 

The proposed force constant calculations are also reviewed. Attention is drawn to some common errors. An approximate calculation is made according to a simple valence force field (SVFF) but experimental data are still too sparse to allow a more precise approach. 

A potential field consisting of stretching and bending force constants only is called a simple valence force field. 

Constants of the simple valence force field. Least-squares calculations with six HOF and DOF fundamentals of a simple three-parameter force field did not yield a converging set of force constants. With the addition of the OF stretch-bend interaction constant, an acceptable set of converging values was obtained [3]. (They comprise the third set of the table above.) The measured v, of HOF alone yielded foH = 7.10, fop = 4.27, and f = 0.87 (all in mdyn/A) [4]. For similar data, see [11]. 

In the keto form of 2,4-pentanedione, CH3—CO—CH2—CO—CH3, there will be C=0 interaction in that we will have in-phase and out-of-phase C=0 stretch vibrations. These appear at 1725 and 1707 cm at nearly the same frequency because the C=0, C=0 coupling is weak. If we replace this central CH2 with an oxygen to make an anhydride, CH3—CO—O—CO— CH3, the carbonyl vibrations should be mechanically similar. However, the C—O frequencies at 1833 cm (in-phase) and 1764 cm (out-of-phase) are further apart than expected. This unexpectedly large separation comes about because of an effect not taken into account in a simple valence force field. 

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