Urey-Bradley force fields

The results given by a Urey-Bradley force field are very similar, although not identical, to those given by a force field utilizing stretch-bend cross terms. One is likely to need many cross terms in the force field anyway, apart from the stretch-bend interactions, so it is more convenient for most purposes just to add stretch-bend terms here as well. The Urey-Bradley force field is consequently seldom used anymore, but it is mentioned here because it is conceptually useful. 

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In a Urey-Bradley force field, angle bending is achieved using 1,3 non-bonded interaction rather than an explicit angle-bending potential. The stretch-bond term in such a forci field would be modelled by a harmonic function of the distance between the 1,3 atoms ... 

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

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 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 ... 

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. 

Figure 4. Schematic illustration of force-constant parameters used in Modified Urey-Bradley Force-Field (MUBFF) vibrational modeling (Simanouti (Shimanouchi) 1949). The MUBFF is a simplified empirical force field that has been used to estimate unknown vibrational frequencies of molecules and molecule-like aqueous and crystalline substances. Here, three force constants (K, H, and describe distortions of a tetrahedral XY molecule, [Cr04] due to bond stretching (Cr-O), bond-angle bending (Z O-Cr-O), and repulsion between adjacent non-bonded atoms (0..0). Less symmetric molecules with more than one type of bond or unequal bond angles require more parameters, but they will belong to the same basic types.

Table 1. Block diagonalized G and F matrices for tetrahedral XY4 and octahedral XYn molecules, using the modified Urey-Bradley force field. Adapted from Nakmoto (1997). nix and nij are the masses of atoms ofX and Y, and r is the length of the X-Y bond. K, H, and are force constants for bond stretching, bond-angle bending, and non-bonded repulsion, respectively.

Some authors use the terms valence force field and Urey-Bradley force field in the sense of molecular mechanics. The former refers to the force field taking no explicit account of 1,3-interactions, which are intended in the latter. 

CONFl. Simple force field program released by QCPE (35). MUB-2. Bartell s latest version of his modified Urey-Bradley force field model (36). 

The Raman spectrum of the reaction product of titanocene pentasulfide and dichlorodiselane shows the presence of l,2,3-Se3Sj as the main species (sea Fig. 3). The normal coordinate treatment using a modified Urey-Bradley force field with 12 independent force constants resulted in a complete assignment of the spectrum and in a very good agreement between the observed and calculated wave numbers. The composition of the phase as determined from the HPLC data, molecular weight measurement, and selenium analysis agrees with the vibrational analysis. 

A selection of bond stretching force constants, G, taken from the literature is plotted in Fig. 9.2 as a function of the bond valence, S. What is surprising is not that there is some scatter (this is expected from the crudeness of the Urey-Bradley force field) but that an expression such as eqn (9.5) gives such a good fit ... 

Force-constant (F) calculations for the dimeric rhenium anion Re2Br were performed using both a valence force field and a Urey-Bradley force field (30). Neither analysis was considered entirely satisfactory by the authors, but both treatments led to very similar values for FReBr of 1.63 0.02 mdyne A"1. Of more interest with regard to the strength of the quadruple bond is the fact that the results of both calculations suggested that FReRe lies somewhere in the... 

Debeau and Poulet 2S1> reported an interesting study of 31 crystalline hexa-chloro MC16 and hexabromo MBr6 metallates and the force constants are calculated with a modified Urey-Bradley force field the relation between the metal-X stretching frequency and the MX covalency is discussed. 

Let us consider the description of a simple three-atom molecule by the three most frequently used spectroscopic parameterization schemes, the general central force field (GCF), the general valence force field (GVF) and the Urey-Bradley force field (UBF Fig. 2.14). 

Srivastava et al. carried out a complete study of the vibrational spectrum of acetylglycine, and evaluated its relation to the spectrum of acetylcholine [13]. A normal coordinate analysis of acetylglycine was carried out using the Wilson s GF matrix method. Vibrational frequencies were assigned, and the infrared spectra of acetylglycine and acetylcholine compared. Conformation-sensitive modes of acetylcholine were identified, and a transferable Urey-Bradley force field was also obtained. 

Infrared and Raman spectra of Se6 have been measured, and the observed wave numbers have been assigned to the eight fundamental vibrations by comparison with the wave numbers calculated from force constants taken from Se8 and using a modified Urey-Bradley force field. The spectra of S8 and Se6 are completely analogous (see Table III). The four g vibrations are Raman active, the three a2u and eu vibrations are active in the infrared while the am mode cannot be observed directly. 

Using an extended Urey-Bradley force field with six force constants,... 

Figure 13. Calculated v(M—S) frequencies for trigonal-prismatic MS6 unit as a function of trigonal-twist distortion. Calculation based on a Urey-Bradley force field for M = Nb with the bidentate bite b = 1.31, K° = 1.57 mdyn A-1 and F = 0.22 mdyn A-1. [Reprinted with permission from K. Tatsumi, I. Matsubara, Y. Sekiguchi, A. Nakamura, and C. Mealli, Inorg. Chem., 28, 773 (1989). Copyright 1989 American Chemical Society.]...

Note. I, simple force field II, extended force field (113). A determination carried out by Chapman (114) using a modified Urey-Bradley force field yielded similar results. In the case of P4O10, a slight improvement of the force field has been achieved by Muldagaliev and coworkers (120). 

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