Quantum-mechanical consistent force field

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. 

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>. 

A. Warshel, in Sentiempirical Methods of Electronic Structure Calculation. G. A. Segal, Ed., Modern Theoretical Chemistry, Vol. 7, Plenum, New York, 1977, p. 133. The Consistent Force Field and Its Quantum Mechanical Extension. 

An alternative approach to parametrisation, pioneered by Lifson and co-workers in the development of their consistent force fields, is to use least-squares fitting to determine the set of parameters that gives the optimal fit to the data [Lifson and Warshel 1968]. Again, the first step is to choose a set of experimental data that one wishes the force field to reproduce (or calculate using quantum mechanics, if appropriate). Warshel and Lifson used thermodynamic data, equilibrium conformations and vibrational frequencies. The error for a given set of parameters equals the sum of squares of the differences between the observed and calculated values for the set of properties. The objective is to change the force field parameters to minimise the error. This is done by assuming that the properties can be related to the force field by a Taylor series expansion ... 

CFF = consistent force field QMFF = quantum mechanical force field. 

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 ... 

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. 

---