Force spectroscopically determined

S, Cl and Si-isotope fractionations for gas-phase molecules and aqueous moleculelike complexes (using the gas-phase approximation) are calculated using semi-empirical quantum-mechanical force-field vibrational modeling. Model vibrational frequencies are not normalized to measured frequencies, so calculated fractionation factors are somewhat different from fractionations calculated using normalized or spectroscopically determined frequencies. There is no table of results in the original pubhcation. 

Thus ra can be obtained from rg by a correction involving harmonic force constants only. If rg is extrapolated to T = 0, it is possible to obtain rz. This temperature extrapolation involves the anharmonic constants and is perhaps the most uncertain step in going from rg to rz in many cases. Determination of re from rg is also limited by a lack of knowledge of anharmonic constants. Thus, as with spectroscopic determinations, anharmonicity of vibrations is a major limiting factor. 

Expressions for the force constant, i.r. absorption frequency, Debye temperature, cohesive energy, and atomization energy of alkali-metal halide crystals have been obtained. Gaussian and modified Gaussian interatomic functions were used as a basis the potential parameters were evaluated, using molecular force constants and interatomic distances. A linear dependence between spectroscopically determined values of crystal ionicity and crystal parameters (e.g. interatomic distances, atomic vibrations) has been observed. Such a correlation permits quantitative prediction of coefficients of thermal expansion and amplitude of thermal vibrations of the atoms. The temperature dependence (295—773 K) of the atomic vibrations for NaF, NaCl, KCl, and KBr has been determined, and molecular dynamics calculations have been performed on Lil and NaCl. Empirical values for free ion polarizabilities of alkali-metal, alkaline-earth-metal, and halide ions have been obtained from static crystal polarizabilities the results for the cations are in agreement with recent experimental and theoretical work. 

Melander and Saunders (1980) have given a comprehensive description of the development of methods of computer calculations of isotope effects on the kinetics of chemical reactions. Such techniques, originally proposed by Wolfsberg and Stem (1964), Shiner (1975), Buddenbaum and Shiner (1977), and Schowen (1977), marry the methods ofEyring s absolute rate (activated complex) theory with detailed modeling of molecular vibrational properties. Input parameters are a mix of spectroscopically determined or quantum mechanically calculated force constants and/or force constant shifts. The method has resulted in informative and detailed molecular description of the molecular changes that occur as the system proceeds from reactant to product along the reaction coordinate. As a result, kinetic isotope effect studies now constitute one of the most important methods employed in the development of detailed... 

A force field that focusses on intramolecular interactions, and particularly on the force constants that determine vibrational frequencies, is the spectroscopically determined force field of Krimm and co-workers (50-52). They advocate very high level quantum calculations to fix the geometries, force constants, and electrostatic terms while using OPLS nonbond Lennard-Jones parameters. The recent focus of this work has been on highly polar molecules, as are discussed later. While this force field reproduces gas-phase IR data very accurately, it does not appear to have been tested on condensed phases. 

What is clearly needed is an approach that systematically incorporates spectroscopic agreement in the initial stages of the optimization of the MM parameters. This has been achieved by a procedure designed to produce a so-called spectroscopically determined force field (SDFF) [45, 46]. 

MM = molecular mechanics SDFF = spectroscopically determined force field. 

The latter development has taken two paths. In one, parameters are obtained by a least-squares fit to energies and first and second derivatives at a number of points on the ab initio potential energy surf ace.In this method, F,y terms in Kq are selected for their presumed relevance. In the second method, that of the spectroscopically determined force field (SDFF), a direct transformation is made from the ab initio structures and second derivatives into the MM function. All F,y are initially retained, with subsequent reduction being determined by preset conditions of frequency agreement. Ab initio energies... 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

Most spectroscopic binaries have periods ranging from days to months and are separated by distances of order 1 AU. A consequence of knowing the period of the star and separation, measured optically, is the determination of the mass of the stars. Assuming that the two stars are in circular orbit, for the sake of simplicity, then a centripetal force is required to keep them moving in orbit. Gravity provides this attraction and the two forces must be balanced. The complete solution of this problem is hard and only a combined mass can be derived without knowing some information other than the period of rotation. 

How should we, being interested in catalysis, look at phonons Lattice vibrations determine the spectral intensity in many spectroscopic techniques, and they often force us to take spectra at lower temperatures than we like often we... 

In the gas phase, ions may be isolated, and properties such as stability, metal-ligand bond energy, or reactivity determined, full structural characterization is not yet possible. There are no complications due to solvent or crystal packing forces and so the intrinsic properties of the ions may be investigated. The effects of solvation may be probed by studying ions such as [M(solvent) ]+. The spectroscopic investigation of ions has been limited to the photoelectron spectroscopy of anions but other methods such as infrared (IR) photodissociation spectroscopy are now available. 

---