Quantum-mechanical consistent force

The consistent force field (CFF) was developed to yield consistent accuracy of results for conformations, vibrational spectra, strain energy, and vibrational enthalpy of proteins. There are several variations on this, such as the Ure-Bradley version (UBCFF), a valence version (CVFF), and Lynghy CFF. The quantum mechanically parameterized force field (QMFF) was parameterized from ah initio results. CFF93 is a rescaling of QMFF to reproduce experimental results. These force fields use five to six valence terms, one of which is an electrostatic term, and four to six cross terms. 

Just as for an atom, the hamiltonian H for a diatomic or polyatomic molecule is the sum of the kinetic energy T, or its quantum mechanical equivalent, and the potential energy V, as in Equation (1.20). In a molecule the kinetic energy T consists of contributions and from the motions of the electrons and nuclei, respectively. The potential energy comprises two terms, and F , due to coulombic repulsions between the electrons and between the nuclei, respectively, and a third term Fg , due to attractive forces between the electrons and nuclei, giving... 

It should be clear that force field methods are models of the real quantum mechanical systems. The total neglect of electrons as individual particles forces the user to define explicitly the bonding present in the molecule prior to any calculations. The user must decide how to describe a given molecule in terms of the selected force field. The input to a calculation consists of three sets of information. 

In combined QM/MM potentials, the system is divided into a QM region and an MM region. The QM region typically includes atoms that are directly involved in the chemical step and they are treated explicitly by a quantum mechanical electronic structure method. The MM region consists of the rest of the system and is approximated by an MM force field. The QM/MM potential is given by ... 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

Yukawa proceeded by writing down a mathematical formula for the force. It wasn t especially difficult to do this. He looked for the simplest mathematical form that was consistent with experimental facts. He knew that, if necessary, refinements could be added later. Then, applying the principles of quantum mechanics, he deduced that, if the force did have that form, there had to exist a previously unobserved particle that had a mass approximately 200 times greater than that of the electron. 

Continuum models are the most efficient way to include condensed-phase effects into quantum-mechanical calculations, and this is typically accomplished by using the self-consistent reaction field (SCRF) approach for the electrostatic component. Therefore it is very common to replace the quantal problem by a classical one in which the electronic energy plus the coulombic interactions of the nuclei, taken together, are modeled by a classical force field—this approach usually called molecular mechanics (MM) (Cramer and Truhlar, 1996). 

Continued Quantum and Molecular Mechanical Simulations, In this technique, a molecular dynamics simulation includes the treatment of some part of the system wilh a quantum mechanical technique. This approach. yMf.MM. is similar to programs that Use quantum mechanical methods to treat the n-systems of the structures in question separately from the sigma framework. The results are combined ai ihe end to render a slructure which is optimized and energy-refined in satisfy both self-consistent field (SCF) and force field energy convergence. 

One modern theoretical approach consists in using the quantum-mechanical force-constants as atrial force field in the regularization functional (5), instead of empirical force-constants [2,10]. It is obvious that the reliability of this method depends crucially on the choice of a realistic quantum-mechanical force field. Unfortunately even the advanced quantum-chemical methods often fail to reproduce the molecular frequencies with sufficient accuracy to assign the experimental spectroscopic features to the corresponding normal vibrations. 

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