Spectroscopic force constants

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.). 

A number of force fields used in organic chemistry have been fitted to thermodynamic data, and most force fields used in inorganic chemistry are based on these. Also, initial guesses for parameters are often based on spectroscopic force constants and therefore related to physically meaningful parameters. Thus, in many cases reasonably accurate thermodynamic data may be obtained1161. 

Steepness of a potential energy function, for instance, spring strength in Hookes law. Empirical force constants are different from spectroscopic force constants (see molecular mechanics, force field). 

In Eq. [2] s, is an internal coordinate (or a linear combination thereof) and As, is the deviation of that coordinate from its equilibrium value. The second derivatives that appear in Eq. [2] are the spectroscopic force constants. They determine the shape of the potential near the equilibrium point. Again, because there are an infinite number of sets [s,], the associated force constants are not the universal parameters we seek. However, they are well defined. 

One obvious way to attack the problem is simply to reduce the value of the bending force constant sufficiently so that the heat of formation can be accurately reproduced. While the heat of formation can be taken care of in this way, the cyclobutane ring by such a calculation will be planar, or nearly so, rather than puckered. In order to get the pucker and the energy both right, we need a smaller value for the curve at 90 degrees than we would get from the spectroscopic force constants, and we also need a smaller slope to the... 

In principle, it would be possible to use just this Taylor series expansion directly in force field calculations. Howevei we cannot do this because the spectroscopic force constants of Eqs. [20]-[22] are not unique. 

An MM energy function, whose second derivatives at a minimum are the spectroscopic force constants, is generally represented as a sum of quadratic and non-quadratic terms. The former encompass the valence-type deformations, such as bond stretching and angle bending, while the latter involve torsions, dispersion interactions, electrostatic interactions, and possible hydrogen-bond terms. 

The first applications of the moleeular mechanies method were to hydroearbons, for the good reason that spectroscopic force constants were more readily available. When heteroatom-containing molecules began to be eonsidered, with presumable permanent electrostatic polarizations, a further elaboration of the formulation led to the inclusion of coulomb-type interaetions ... 

When the molecular mechanics method is applied in its full functional extension, it has moved a long way from the initial assumption of a minimization of vibrational strain energy, and there are a large number of parameters to be adjusted. Once one starts adjusting parameters, the method becomes parametric, and there is no point in defending first-principle derivations or in preserving a strict correspondence between molecular mechanics force constants and spectroscopic force constants. The most sensible attitude is to readjust all parameters all together, and this is what has been done, since the pioneer years, in more recent times for the preparation of the most popular and widely applied force fields. One is not restricted to functional forms that... 

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