Orbital valence force field

In the course of fui ther development of these ideas, Heath and Linnett have introduced the concept of the orbital valency force field in which the bonding angles are essentially a measure of the decrease of electronic overlap. In the case of planar XYs molecules, for instance, the potential energy due to bending is proportional to the sum of squares of angles Si, representing the deflections of the XY directions from an assumed... 

Before it is possible to interpret on a rigorous basis the behavior of the carbonyl stretching frequencies of a series of isostructural and isoelectronic complexes complete vibrational analyses are necessary. However, it is only within the last few years that far-infrared 137) and laser Raman 84) spectrometers have become available generally. Hence, in the general absence of the data they have provided, earlier complete analyses were limited to the spectra of simple metal carbonyls (for which such information was available). Even for these complexes, the number of force constants exceeds the number of observable frequencies, and model force fields had to be used. Since Urey-Bradley type force fields proved to be unsuitable for carbonyl complexes 86,105, 106), Jones 80-82) developed a resonance interaction valence force field which reduced the number of force constants by interrelating several on the basis of orbital overlap. This approach is not readily adaptable to less symmetrical substituted carbonyl complexes. Alternative models had, therefore, to be investigated. 

For the analysis of the spectra of trans-(CH)x, valence-force-field calculations have been performed, the force constant being empirically fitted so as to reproduce the observed vibrational frequencies (Inagaki et al., 1975 Schiigerl and Kuzmany, 1981). The energy gradient scheme based on the ab initio crystal orbital method has also been attempted for the study of the vibrational structure of trans- and c -(CH)x (Teramae et al., 1984). The calculated result of the vibrational frequencies has been found to depend upon the quality of the basis set. It has been demonstrated that, e.g., for the 4-31G basis, a uniform scaling of the force constants, multiplying by 0.8, is required to adjust the vibrational frequencies of the trans-(CH), (Table III). 

Although the Urey-Bradley field has four force constants, F is usually taken as — on the assumption that the repulsive energy between nonbonded atoms is proportional to 1/r . Thus, only three force constants, K, H, and F, are needed to construct the F matrix. The orbital valence force (OVF) field developed by Heath and Linnett [83] is similar to the UBF field. The OVF field uses the angle (Ap), which represents the distortion of the bond from the axis of the bonding orbital instead of the angle between two bonds (Aa). 

MMVB is a hybrid force field, which uses MM to treat the unreactive molecular framework, combined with a valence bond (VB) approach to treat the reactive part. The MM part uses the MM2 force field [58], which is well adapted for organic molecules. The VB part uses a parametrized Heisenberg spin Hamiltonian, which can be illustrated by considering a two orbital, two electron description of a sigma bond described by the VB determinants... 

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). 

Keywords Polarizable force field, Molecular orbital and valence bond theory, Nuclear quantum... 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

Molecular Energetics. Molecular energies can be computed in a variety of ways including empirical fixed valence potentials, full force field potentials, and semi-empirical molecular orbital techniques (CNDO-2, INDO, MINDO-3, MNDO, PCILO). 

The EHM will require far fewer parameters. This is easy to see, because each atom requires just one parameter for each valence atomic orbital. For C, for example, we need an ionization energy for the 2s, and one for the 2p orbitals, just two parameters (strictly, valence state ionization energies, VSIEs - see Harder Question 9).3 Each H needs only one parameter, for its Is orbital. So for an EHM program that will handle hydrocarbons in general we need only three parameters (as in Hoffmann s pioneering paper on hydrocarbons [1]). In contrast, an early but viable molecular mechanics forcefield limited to alkanes had 26 parameters [2]. The Universal Force Field, which sacrifices accuracy for wide applicability, has about 800 parameters, and the accurate and quite broadly applicable Merck Molecular Force Field 1994 (MMFF94) has about 9,000 parameters [3]. 

The main difficulty with the valence-bond approach is that the atomic orbitals, whether hybridized or not, result from the interaction of electrons with a single central force field— that of the atomic nucleus. An electron that spends most of its time between two nuclei will find itself in a very different, two-center force field, and this will give rise to new types of orbitals that are better characterized as molecular, rather than as atomic orbitals. 

More recently, the Landis group" has used valence bond concepts to derive new angular potential energy functions and to develop rules for parameterization. The VALBOND force field angular energy function is based on Pauling s hybrid orbital nonorthogonality functions and can be derived for any arbitrary combination of s, p, d, and f orbitals. 

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