Vibrational force field methods

The various terms in this formula have the meaning of the potential function (force field) V(r1,r2,0) the vibrational, 7 rotational, fx, Ty, Tz and rotational-vibrational, Tvr kinetic energy terms. The latter are differential operators acting in the space of wave functions )/(/ ,r2,0 a,P,y). The potential function V(rur2,Q) is either calculated ab initio or parametrized in a suitable fashion. A commonly used parametrization is that provided by the force-field method... 

Vibrational frequencies of 1,4-benzodioxin using the density functional theory (DFT) method, as well as the conventional HF and MM3 force-field methods, were calculated to evaluate the frequency prediction capability of each computational method and get a better understanding of the vibrational spectra . 

The vibrational frequencies for the three lower lying states were calculated via the valence force field method using the force constants calculated by O Neil, Schaeffer, and Bender ( ). The geometry and vibrational levels for the c A state were estimated. The uncertainty in the entropy mainly reflects the uncertain position of the low lying electronic levels. 

For large molecules, however, the computer requirements become increasingly prohibitive, especially when conformationally flexible compounds are tackled. Alternative approaches to quantum-mechanical methods are known, based on potential functions and parameters derived from detailed analysis of vibrational spectra. These so-called force field methods are now joined in what is called molecular mechanics, an empirical method that considers the molecule as a collection of spheres (possibly deformable) bound by harmonic forces (eventually corrected with cubic and quartic potentials). The energy... 

The molecular configuration is a function of time. Molecular systems are not stationary molecules vibrate, rotate, and tumble. Force field calculations and the properties predicted by them are based on a. stationary model. What is needed is some way to predict what motions the atoms within a molecule will undergo at various temperatures. Molecular dynam-ics (MD) simulations use classical mechanics—force field methods—to study the atomic and molecular motions to predict macroscopic properties. "... 

A few non-conjugated polyenes have been studied by the force-field method. It was calculated that 1,4-cyclohcxadiene is planar (D2 ), although one electron diffraction study (Oberhammer and Bauer, 1969) on the molecule indicated a boat form (C2 ). An independent electron diffraction work indeed gave a planar structure (Dallingaand Toneman, 1967). The problem with the former electron diffraction study seems to have been a misinterpretation of the observed 3,6-distance, a problem related to what is sometimes referred to as shrinkage (see Bartell and Kohl, 1963 and references therein). This effect occurs because the atomic nuclei are undergoing vibrational motion. Thus, one mode of vibration of 1,4-cyclo-hexadiene is as shown in eqn (11). 

Studies of the isolated imidazolium cation have been undertaken primarily to produce parameters for use in force field methods. Shah et al., have calculated the [BMIM]+ cation at the HF/6-31G(d) level, and determined CHdpG [57] charges [58]. De Andrade et al., have calculated the [EMIM]+ and [BMIM] cations at the HF/6-31G(d) level, and determined the RESP charges using AMBER [59]. They also compared the ab initio dipole moments and vibrational frequencies with those obtained using force field methods [60]. 

Intramolecular charge transfer in 4-nitropyridine N-oxide has been investigated by spectroscopic methods and by comparison with AMI and MNDO semi-empirical methods to obtain the vibrational force field. The results obtained indicate that protic solvents (water, methanol) favour the mesomeric form 97 which is also favoured in the crystal, by an internal interaction between the nitro and A-oxide groups. ... 

The explicit expressions used for each of the terms in (16.94) define what is called a molecular-mechanics force field, since the derivatives of the potential-energy function determine the forces on the atoms. A force field contains analytical formulas for the terms in (16.94) and values for all the parameters that occur in these formulas. The MM method is sometimes called the empirical-force-field method. Empirical force fields are used not only for single-molecule molecular-mechanics calculations of energy differences, geometries, and vibrational frequencies, but also for molecular-dynamics simulations of liquids and solutions, where Newton s second law is integrated to follow the motions of atoms with time in systems containing hundreds of molecules. 

The MM method will be seen to be the most useful one for obtaining force constants that can be used for different conformations of the molecule. In this approach the force constants are obtained from the second derivatives of an assumed potential energy function consisting of quadratic bonded tenns and non-quadratic non-bonded terms. Although present MM functions are too crude to be spectroscopically reliable, a new method for deriving such functions holds the promise of providing a reliable vibrational force field for the polypeptide chain. 

Computational modelling of chemical stmctures began with force field methods, the foundations for which were laid with developments in vibrational spectroscopy in the 1930s [1]. It was not until the mid-1940s that there began to be apparent a coherent theory, when three groups came up with similar methods for describing molecular conformations and their interactions with respect to sterics. 

Compared with other time-resolved spectroscopic methods for measuring electronic transitions (electronic absorption, fluorescence, etc.) in molecules and molecular systems, time-resolved vibrational spectroscopy, which measures vibrational transitions, has the potential for simultaneously providing information on both the molecular structure (and vibrational force field) and the dynamics of a short-lived transient molecular species. Time-resolved vibrational spectroscopy is therefore considered to be one of the most effective means for monitoring changes in molecular structure over a wide time scale, particularly for condensed-phase studies. 

Torii, H., and M. Tasmni. 1995. Vibrational analysis of the squarate ion based on ab initio molecular orbital calculations. A practical method to calculate vibrational force fields of non-bond-altemating conjugated molecules. J. Mol. Struct. THEOCHEM 334 15-27. 

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