Molecular potential empirical

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

The profiles of the rototranslational absorption of CH4-CH4 in the far infrared have been reported [56] see Fig. 3.22 for an example. The treatment of the spectra is based on the multipolar induction model and an advanced isotropic potential empirical overlap-induced dipole components have also been included for fitting the experimental data at several temperatures (126 through 300 K). At the lower temperatures, satisfactory fits of the measurements are possible. The analysis seems to suggest that at temperatures near room temperature a significant rotation-induced distortion of the tetrahedral frames occurs which affects the properties of the individual molecules (multipole strengths, molecular symmetry, polarizabilities, and perhaps the interaction). 

A vast amount of empirical molecular potential energy functions and a series of corresponding programs (molecular mechanics and consistent force field programs) are available (for recent reviews see 203 205)). Unfortunately these energy functions are always the result of optimization on a rather limited group of compounds. No... 

Another fairly new method, using the electrostatic molecular potential, will not be discussed here since it is the subject of another contribution to this volume 50>. I will now consider methods that have had the widest application in the theoretical study of chemical reactivity, in order of increasing complexity a) molecular mechanics b) extended Htickel method c), d) empirical self-consistent field methods such as CNDO and MINDO e) the simplest ab initio approach f) the different S.C.F. methods, possibly including configuration interaction g) valence bond methods, and h) the dynamical approach, including the calculation of trajectories 61>. 

Low-coverage volumetric isotherm data [41, 42] were used to extract the isosteric heat of adsorption extrapolated to zero coverage, the gas-solid virial coefficient, and the two-dimensional second virial coefficient. It is found that fitting the two-dimensional virial coefficient obtained from the measurements in the vicinity of the surface in terms of Lennard-Jones inter-molecular potentials reduces the well depth obtained from the bulk by about 20%. In addition, the effective quadmpole moment of CO needs to be significantly reduced [42] by as much as about 50%. These fitted parameters are believed to account for various substrate mediation effects in some effective way (see Refs. 41 and 42 for more details concerning these param-eterizations). It is also concluded [41] that the asymmetric empirical parameterization of Ref. 238 should be replaced by models in which the similarity between the isoelectronic CO and N2 molecules is exploited for the non-electrostatic contributions as in Ref. 17. 

A NEW EMPIRICAL INTER MOLECULAR POTENTIAL ENERGY FUNCTION FOR HYDROGEN BONDING... 

KLEIN - We do indeed use a semi-empirical model for the various interaction potentials. First, we model the ammonia inter molecular potential with an effective pair potential which ignores many body polarization. Models of this type are remarkably successful in explaining the physical properties of polar fluids. Of course, we really should include many body forces, but at this stage we ignore them. The ammonia potential is fitted to the heat of evaporation and the zero-pressure density. The electron-alkali metal (Lithium) potential is represented by the Shaw pseudo potential fitted to the ionization energy. This is the simplest and crudest model possible. We have explored the effect of using (a) Heine-Abarenkov, (b) Ashcroft, and (c) Phillips-Kleinman forms. Our results are not very sensitive to the choice of pseudo potential. (In the case of Cs metal, which I did not discuss, the sensitivity to the potential is crucial). 

The reduced density or packing fraction t] is related to an effective and temperature-dependent co-volume b(T) by ti = ib(T)p/4, with p being the number density, i.e., the number of molecules per volume. However, PHSC-theoiy does not use an analytical inter-molecular potential to estimate the temperature dependence of a(T) and b(T). Instead, empirical temperature functions are fitted to experimental data of aigon and methane (see also" ). 

There are many large molecules whose mteractions we have little hope of detemiining in detail. In these cases we turn to models based on simple mathematical representations of the interaction potential with empirically detemiined parameters. Even for smaller molecules where a detailed interaction potential has been obtained by an ab initio calculation or by a numerical inversion of experimental data, it is usefid to fit the calculated points to a functional fomi which then serves as a computationally inexpensive interpolation and extrapolation tool for use in fiirtlier work such as molecular simulation studies or predictive scattering computations. There are a very large number of such models in use, and only a small sample is considered here. The most frequently used simple spherical models are described in section Al.5.5.1 and some of the more common elaborate models are discussed in section A 1.5.5.2. section Al.5.5.3 and section Al.5.5.4. 

For this reason, there has been much work on empirical potentials suitable for use on a wide range of systems. These take a sensible functional form with parameters fitted to reproduce available data. Many different potentials, known as molecular mechanics (MM) potentials, have been developed for ground-state organic and biochemical systems [58-60], They have the advantages of simplicity, and are transferable between systems, but do suffer firom inaccuracies and rigidity—no reactions are possible. Schemes have been developed to correct for these deficiencies. The empirical valence bond (EVB) method of Warshel [61,62], and the molecular mechanics-valence bond (MMVB) of Bemardi et al. [63,64] try to extend MM to include excited-state effects and reactions. The MMVB Hamiltonian is parameterized against CASSCF calculations, and is thus particularly suited to photochemistry. 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

Kurst G R, R A Stephens and R W Phippen 1990. Computer Simulation Studies of Anisotropic iystems XIX. Mesophases Formed by the Gay-Berne Model Mesogen. Liquid Crystals 8 451-464. e F J, F Has and M Orozco 1990. Comparative Study of the Molecular Electrostatic Potential Ibtained from Different Wavefunctions - Reliability of the Semi-Empirical MNDO Wavefunction. oumal of Computational Chemistry 11 416-430. 

---