Valence Interactions

The core electrons are replaced by a gaussian expansion which reproduces electrostatic and exchange core-valence interactions. 

Nylon fibers are semicrystalline, that is, they consist of crystallites separated by amorphous regions. Hydrogen bonding is an important secondary valence interaction in nylon-6 and nylon-6,6. Individual chains in the microcrystalline regions of nylons are held together by hydrogen bonds. Nylons are resistant to aqueous alkali but deteriorate more readily on exposure to mineral acids. 

As shown in Fig. 4.69, the HfFLi- alkene complex exhibits expected parallels with the HfFLi- H2 complex (Fig. 4.59), both in terms of molecular shape and in terms of valence interactions. The characteristic features of such weak dative bonding include long Hf—C distances (2.82 A), normal C=C bond length (1.34 A), planar alkene bond angles, and small binding energy (15.1 kcalmol-1)-... 

An important point is that the electrochemically driven charge transport in these polymeric materials is not dependent on the presence of mixed valence interactions which are well known to give rise to electronic conductivity — in a number of cation radical crystalline salts. This is clearly seen from the absorption spectrum of the electrochemically oxidized pyrazoline films (Figure 8) which show no evidence for the mixed valence states that are the structural electronic prerequisites for electrical conductivity in the crystalline salts. A more definitive confirmation of this point is provided by the absorption spectrum (Figure 10) of electrochemically oxidized TTF polymer films which shows... 

The generalization of the pseudopotential method to molecules was done by Boni-facic and Huzinaga[3] and by Goddard, Melius and Kahn[4] some ten years after Phillips and Kleinman s original proposal. In the molecular pseudopotential or Effective Core Potential (ECP) method all core-valence interactions are approximated with l dependent projection operators, and a totally symmetric screening type potential. The new operators, which are parametrized such that the ECP operator should reproduce atomic all electron results, are added to the Hamiltonian and the one electron ECP equations axe obtained variationally in the same way as the usual Hartree Fock equations. Since the total energy is calculated with respect to this approximative Hamiltonian the separability problem becomes obsolete. 

This has enabled these authors to derive a computational means for obtaining the effective core-valence interaction ((7eore) as a local one-electron operator.)... 

Having described the variety of ways in which the core-valence interaction may be parameterized it is clear that we should examine how they perform in actual calculations. Generally the advances in the complexity of the parameterization have produced commensurate improvements in the accuracy of the results. However, by introducing a large number of parameters the simplicity of the core-valence concept is lost and, in practice, the fitting of the parameters themselves can be expensive in terms of computer time, although they only need to be obtained once for each atom. 

The semi-local pseudopotential24 used for the calculations of Table 3 was based on a parameterization for the neutral atom. Melius, Olafson, and Goddard also included in their paper some calculations based on the single valence electron ion Fe7+. As expected, this parameterization leads to far worse results, which differ on average from the all-electron results by 0.05 a.u., thus emphasizing the importance of the contribution of valence-valence interaction to the effective potential [equation (51)]. 

The complexes are unique in that they involve (a) platinum in three different formal oxidation states and (b) both class I and class II mixed-valence interactions within a single complex. 

It has been recently reported that the E-form of bis(ferrocenylethynyl)-ethane, 97a, can undergo photoisomerization to the Z-form, 97b, by excitation of a charge transfer band with visible light [82]. This structural change affords a decrease in the through bond mixed-valence interaction between two ferrocenes. 

The one-center approximation allows for an extremely rapid evaluation of spin-orbit mean-field integrals if the atomic symmetry is fully exploited.64 Even more efficiency may be gained, if also the spin-independent core-valence interactions are replaced by atom-centered effective core potentials (ECPs). In this case, the inner shells do not even emerge in the molecular orbital optimization step, and the size of the atomic orbital basis set can be kept small. A prerequisite for the use of the all-electron atomic mean-field Hamiltonian in ECP calculations is to find a prescription for setting up a correspondence between the valence orbitals of the all-electron and ECP treatments.65-67... 

A similar situation was described recently in an other context by Houk, K. N., Rondan, N. G., Mareda, J. J. Am. Chem. Soc. 106, 4291 (1984) Houk, K. N., Rondan, N. G. ibid. 4293. We have reasons to assume that another, sandwich-like arrangement finds some stabilization by secondary valence interactions... 

Once a nodeless orbital has been generated the one-electron atomic Fock equation is easily inverted to produce a (radially) local operator, the EP, which represents the core-valence interactions (22,23). 

More generally, the potential energy of a model can be expressed as a sum of bonded (valence) interactions and nonbonded interactions that depends only on the distance between the atoms according to the expression ... 

The valence interactions consist of bond stretching, bond angle bending, and dihedral angle torsion, active in nearly all force-fields for covalent systems. The nonbonded interactions consist of van der Waals, electrostatic and hydrogen bond terms, and the form of each expression depends on the particular force-field [67,62]. 

Sc and Lu derivatives are isomorphous and polymeric containing [r/5-(C5H5)2Ln(p,-r] -CsHs)]. In the case of SmCp3, two crystallographically independent molecules bonded to each other by non-valence interactions has been observed [25]. 

The expression for the anisotropic part of hyperfine coupling involves an integral over the spatial distribution of the unpaired electron, which is relatively easy to compute accurately even at a relatively low level of theory. The contact term, however, includes a delta-function that chips out the wave function amplitude at the nucleus point. The latter is quite difficult to compute both because standard Gaussian basis sets do not reproduce the wavefunction cusp at the nucleus point and because additional flexibility has to be introduced into the core part of the basis to account for the now essential core valence interaction. " ... 

I. D. Brown, The program VALENCE for calculating bond valences interactively 2001, http //www.ccpl4.ac.uk/ccp/ web mirrors/i.d brown. 

The potential function U(r) has at least two terms, an attractive term U+ reflecting valence interactions, and a repulsive term U- due to core electrostatic repulsions (Figure 5). Thus... 

Force fields which predicted the observed frequency data most satisfactorily have been those for which certain approximations were made about the valence interaction constants F. . Jones related a number of such interaction constants by the use of simple valence theory ( resonance interaction valence force field ) and obtained a satisfactory set of force constants for the compounds M(CO)6 (M = Cr, Mo, or W) (190, 191, 192, 193) and NiC(0)4 (189). However, the secular equations for governing the vibrations of these systems have most usually been solved by neglecting certain interaction force constants For instance,... 

The valence interactions consist of intramolecular bond stretching, bond angle bending, dihedral angle torsion, and inversion as shown in Figure 1. 

IV. Valence interaction between atoms and linear rotors. J. Chem. Phys. 108, 5265 (1998)... 

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