Valence force

Three-body and higher terms are sometimes incorporated into solid-state potentials. The Axilrod-Teller term is the most obvious way to achieve this. For systems such as the alkali halides this makes a small contribution to the total energy. Other approaches involve the use of terms equivalent to the harmonic angle-bending terms in valence force fields these have the advantage of simplicity but, as we have already discussed, are only really appropriate for small deviations from the equilibrium bond angle. Nevertheless, it can make a significant difference to the quality of the results in some cases. 

The atoms of a molecule are held together by primary bonds. The attractive forces which act between molecules are usually referred to as secondary bonds, secondary valence forces, intermolecular forces or van der Waals forces. 

Condition in which two surfaces are bonded together by interfacial forces caused by valence forces or interlocking forces or both (see mechanical adhesion and specific adhesion). 

Adhesion between surfaces whereby valence forces predominate that are similar to those promoting cohesion. 

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 refer to models where we write the total potential energy in terms of chemical endties such as bond lengths, bond angles, dihedral angles and so on as valence force field models. 

A Urey-Bradley force field is similar to a valence force field, except that we include non-bonded interactions. 

Valenz, /. valence, valency, -betatigung, /. valence activity, -einlieit, /. valence unit, valence, -kraft,/. valence (or valency) force, -lehre, /. doctrine of valence, -richtung, /. valence direction, -strich, m. valence line or dash. -8 tufe,/. valence stage. 

TPEs are materials that possess, at normal temperatures, the characteristic resilience and recovery from the extension of crosslinked elastomers and exhibit plastic flow at elevated temperatures. They can be fabricated by the usual techniques such as blow molding, extrusion, injection molding, etc. This effect is associated with certain interchain secondary valence forces of attraction, which have the effect of typical conventional covalent crosslinks, but at elevated temperatures, the secondary... 

The significance of force constants of general quadratic valence force fields application to Au(CN)2. PtCl42-, AuC14, AuBr4- and Au(CN)2Cl2. L. H. Jones, Coord. Chem. Rev., 1966,1, 351-378 (15). 

Kaplan and Thornton (1967) used three different sets of vibrational frequencies to estimate the zero-point energies of the reactants and products of the equilibrium, which provided three different isotope exchange equilibrium constants 1-163, 1-311 and 1-050. The value 1-311 is considered to be most reasonable, whereas the others are rejected as unrealistic for the case in hand. Calculations using the complete theory led to values that varied from 1-086 to 1-774 for different sets of valence-force constants for the compounds involved. 

These compounds contain two or more independent portions that are not bonded to each other by any valence forces but nevertheless must remain linked. Catenanes are made up of two or more rings held together as links in a chain, while in rotaxanes a... 

Force constants of have been calculated from the data in Table 2 using the general valence force field (GVFF) [148, 149] as well as the Urey-Bradley force field [80] (UBFF) although there is insufficient data to evaluate all the interaction constants since no isotopomers of Se have been measured by vibrational spectroscopy. The stretching and bond interaction force constants were reported as/r = 2.24 andf = 0.53 N cm, respectively [149]. However, because of the uncertainty regarding the Am mode of Se the published force constants [80, 148, 149] maybe unreliable. 

The spectra of S12 and Si2-CS2 clearly reflect the differing site symmetries of the S12 molecule The two Eg vibrations at 188 and 245 cm degenerate in Si2 CS2, split into their components in pure S12 with its non-degenerate site symmetry of C2h- The valence force constants calculated for S12 reproduce the observed wavenumbers within 14 cm [79]. The two most interesting constants are/r = 2.41 and/ r = 0.60 N cm ... 

The correlation of stretching wavenumbers to the bond lengths is a spec-troscopical expression of the dependence of the valence force constant fr from the bond length r [197-199] which is presented in Fig. 33 ... 

The absence of overlapping of bands of various matrix-isolated compounds and the possibility of freezing highly reactive intermediates make this method very convenient for the direct study of reaction mechanisms. Additionally, direct IR spectroscopy of intermediates allows estimation of important structural parameters, e.g. valence force fields, which show the character of bonds in these species. 

After the first unsuccessful attempts to record a matrix IR spectrum of the methyl radical, reliable data were obtained by the use of the vacuum pyrolysis method. IR spectra of the radicals CH3 and CD3 frozen in neon matrices were measured among the products of dissociation of CH3I, (CH3)2Hg and CD3I (Snelson, 1970a). The spectra contained three absorptions at 3162 (1 3), 1396 V2) and 617 cm (I l) belonging to the radical CH3 and three bands 2381, 1026 and 463 cm assigned to the radical CD3. Normal coordinate analysis of these intermediates was performed and a valence force field calculated. In accordance with the calculations, methyl radical is a planar species having symmetry >31,. 

IR absorptions of these species were assigned to fundamental modes by comparison with the spectra of stable perfluoroorganic compounds. Normal coordinate analysis of the perfluoroethyl radical was performed and the valence force field of C2F5 was calculated (Snelson et al., 1981). 

Mulliken (41) distinguishes two kinds of polarization. He calls Coulomb polarization what we are concerned with in this paper the polarization produced by an electric field, and he calls valence polarization a kind of polarization du to quantum-mechanical valence forces. In order to correctly describe the chemical bond in H2, it is necessary to include the valence polarization function as soon as one calculates energy with the unperturbed function (i.e. the 2p orbital). 

In the construction of the matrix F of Eq. (63), the symmetrical equivalence of the two O-H bonds was taken into account. Nevertheless, it contains four independent force constants. As the water molecule has but three fundamental vibrational frequencies, at least one interaction constant must be neglected or some other constraint introduced. If all of the off-diagonal elements of F are neglected, the two principal constants, f, and / constitute the valence force field for this molecule. However, to reproduce the three observed vibrational frequencies this force field must be modified to include the interaction constant... 

From the above example it is apparent that there may be (and usually are) more unknown force constants than observed frequencies. If no additional sources of data are available, it is necessary to make some assumptions to simplify the force field. Often all or some of the off-diagonal elements in the F matrix [Eq. (63)] are neglected, leading to the so-called valence force field (VFF) or modified valence force field (MVFF), respectively. 

Bonding forces Primary valence forces (intramolecular forces) Secondary valence forces (intermolecular forces)... 

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 ... 

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. 

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