Quantum mechanical force fields, for

Williams, R. W., V. F. Kalasinsky, and A. H. Lowrey. 1993. Scaled Quantum Mechanical Force Field for Cis- and Trans-glycine in Acidic Solution. J. Mol. Struct. (Theochem) 281, 157-171. 

A. Aamouche et al., Neutron inelastic scattering, optical spectroscopies and scaled quantum mechanical force fields for analyzing the vibrational dynamics of pyrimidine nucleic acid bases. 1. Uracil. J. Phys. Chem. 100, 5224-5234 (1996)... 

McNamara JP, AM Muslim, H Abdel-Aal, H Wang, M Mohr, IH Hillier, RA Bryce (2004) Towards a quantum mechanical force field for carbohydrates a reparametrized semi-empirical MO approach. Chem. Phys. Lett. 394 (4-6) 429-436... 

Scaled quantum-mechanical force fields for furan (and thiophene) and its isotopomers have been calculated with the B3LYP/6-31G method. Corresponding MP2 and FIE calculations gave less satisfactory results. Excellent agreement... 

Quantum mechanics is essential for studying enzymatic processes [1-3]. Depending on the specific problem of interest, there are different requirements on the level of theory used and the scale of treatment involved. This ranges from the simplest cluster representation of the active site, modeled by the most accurate quantum chemical methods, to a hybrid description of the biomacromolecular catalyst by quantum mechanics and molecular mechanics (QM/MM) [1], to the full treatment of the entire enzyme-solvent system by a fully quantum-mechanical force field [4-8], In addition, the time-evolution of the macromolecular system can be modeled purely by classical mechanics in molecular dynamicssimulations, whereas the explicit incorporation... 

Over the last decade, ab initio quantum-mechanical force fields have begun to be applied in theoretical stable isotope studies of molecules and dissolved species (Bochkarev et al. 2003 Driesner et al. 2000 Oi 2000 Oi and Yanase 2001). This method shows great promise for future studies, because ab initio calculations accurately describe chemical properties such as force constants without the necessity of assuming allowed force-constant types (which may not be universally applicable). Ab initio calculations are also ideally suited to molecules with... 

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. 

Nowadays a wide variety of quantum-chemical programs are disposable, which permit to calculate with high accuracy the equilibrium geometry of the molecules and their energy of formation. Theoretical methods have been developed for analytical calculation of the first and second derivatives of energy [8,9], so that the force-constant matrix FHT and the harmonic frequencies can be extracted from the quantum-mechanical calculations. Since as a rule the molecular orbitals (MO) obtained by the quantum-mechanical methods are spread around the entire molecule, the corresponding quantum-mechanical force fields incorporate the important effects of the off-diagonal interactions. 

The reasons for this discrepancies will be discussed shortly in the following sections. As a rule frequencies calculated on the Hartree-Fock (HF) or density functional theory (DFT) levels are upshifted with respect to the experimental values, and differences sometimes overwhelm 100 cm-1 [11-13], This makes the pristine quantum-mechanical force fields inadequate as a trial approximations in the regularization technique. Consequently some empirical corrections to the quantum-mechanical force-constants are unavoidable when analyzing the normal vibrations of the molecules. 

Therefore the scaling transformation of the quantum-mechanical force field is an empirical way to account for the electronic correlation effects. As far as the conditions listed above are not always satisfied (e.g. in the presence of delocalized 7r-electron wavefunctions) the real transformation is not exactly homogeneous but rather of Puley s type, involving n different scale constants. The need of inhomogeneous Puley s scaling also arises due to the fact that the quantum-mechanical calculations are never performed in the perfect Hartree-Fock level. The realistic calculations employ incomplete basis sets and often are based on different calculation schemes, e.g. semiempirical hamiltonians or methods which account for the electronic correlations like Cl and density-functional techniques. In this context we want to stress that the set of scale factors for the molecule under consideration is specific for a given set of internal coordinates and a given quantum-mechanical method. 

As a rule the quantum-mechanical force-fields and the corresponding normal frequencies are calculated in a harmonic approximation, while the experimentally accessible frequencies are influenced by anharmonic contributions. The Puley s scaling factors are also found to incorporate the relevant empirical corrections for the vibrational anharmonicity. 

Obviously, these structural changes make the transfer of force-constants from the neutral B3 molecule to the B3+ radical inadequate. Instead, we tentatively transferred the scale factors optimized for the neutral molecule to the quantum-mechanical force-field of B3+ and calculated the corresponding scaled normal frequencies. We obtained a clear correspondence between many of the frequencies experimentally observed in Cl doped B3 crystals (Fig. 3(a)) and the calculated scaled frequencies (Fig. 3(b)). We also observed that some of the calculated scaled frequencies in the neutral B3 molecule are present in the spectra of the Cl doped crystals (Fig. 3(c)). This fact tells us that there is some portion of unoxidized B3 molecules in the sample and gives additional proof for the validity of the SQMF calculations performed on the neutral B3 molecule. 

In the following sections, we summarize the theoretical formulation of the X-Pol model and illustrate the multilevel X-Pol method for studying intermolecular interactions. In addition, we discuss our work on using X-Pol as a quantum mechanical force field (QMFF) for liquid water simulations. 

The XP3P Mode I for Water as a Quantum Mechanical Force Field... 

There are three broad types of intermolecular forces of adhesion and cohesion (7) quantum mechanical forces, pure electrostatic forces, and polarization forces. Quantum mechanical forces account for covalent bonding. Pure electrostatic interactions include Coulomb forces between charged ions, permanent dipoles, and quadrupoles. Polarization forces arise from dipole moments induced by the electric fields of nearby charges and other permanent and induced dipoles. Ideally, the forces involved in the interaction at a release interface must be the weakest possible. These are the polarization forces known as London or dispersion forces that arise from interactions of temporary dipoles caused by fluctuations in electron density. They are common to all matter and their energies range from 0.1 to 40 kJ/mol. Solid surfaces with the lowest dispersion-force interactions are those that comprise aliphatic hydrocarbons, and fluorocarbons, and that is why such materials dominate the classification table (Table 1) and the surface energy table (Table 2). 

A three-step procedure was used to derive the CFF, resulting in a force field suitable for the calculation of properties of molecules in vacuo and in condensed phases. " First, non-bonded energy function parameters were derived from fits of crystal structures, sublimation energies, and gas phase dipole moment data. Then, a quantum mechanical force field was derived from fitting Hartree-Fock energies and energy derivatives of equilibrium and systematically distorted molecules... 

Direct dynamics calculations of the type just described, with all degrees of freedom included, are very expensive if the local quadratic approximations to the potential energy surface are obtained from an ab initio computation. In applications we have used a hybrid parameterized quantum-mechanical/force-field method, designed to simulate the CASSCF potential for ground and covalent excited states. A force field is used to describe the inert molecular a-framework, and a parameterized Heisenberg Hamiltonian is used to represent the CASSCF active orbitals in a valence bond space. Applications include azulene and benzene excited state decay dynamics. 

A descriptor for the 3D arrangement of atoms in a molceulc can be derived in a similar manner. The Cartesian coordinates of the atoms in a molecule can be calculated by semi-empirical quantum mechanical or molecular mechanics (force field) methods, For larger data sets, fast 3D structure generators are available that combine data- and rule-driven methods to calculate Cartesian coordinates from the connection table of a molecule (e.g., CORINA [10]). 

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