Energy function parameters, consistency

A short presentation of the Consistent Force Field is given, with emphasis on parametrization and optimization of energy function parameters. For best possible calculation of structure, potential energy functions with parameter values optimized on both structural and other properties must be used. Results from optimization with the Consistent Force Field on alkanes and ethers are applied to glucose, gentiobiose, maltose and cellobiose. Comparison is made with earlier and with parallel work. The meaning and use of conformational maps is discussed shortly. 

CHARMM is the first program system published which deserves the designation "molecular mechanics , in the sense that it treats static, kinematic and dynamic properties. All other programs available are much more limited in scope. A few warnings for the uninitiated are in place The more complicated a system is, and here I mean only modern well-structured and well-documented systems, the more attention is required to maintain and operate it, and that cannot be left solely to the computer people. Also, know-how does not come by itself or on a tape. For many prospective applications, potential energy function parameters, or even the functions themselves, are lacking, just as for the simpler systems. Parameters must be found by trial and error, as is usual, or, preferably, by optimisation, which cannot be done in CHARMM a program of the consistent force field family is necessary. 

All members of the consistent force field family of programs are available, from QCPE or from the authors they are described under section 3.4 They are all singular in a way they allow for optimisation of potential energy function parameters on many types of observable, and are therefore splendid tools in the hands of a skilled worker. 

A molecular system consists of electrons and nuclei. Their position vectors are denoted hereafter as rel and qa, respectively. The potential energy function of the whole system is V(rel, qa). For simplicity, we skip the dependence of the interactions on the spins of the particles. The nuclei, due to their larger mass, are usually treated as classical point-like objects. This is the basis for the so called Bom-Oppenheimer approximation to the Schroedinger equation. From the mathematical point of view, the qnuc variables of the Schroedinger equation for the electrons become the parameters. The quantum subsystem is described by the many-dimensional electron wave function rel q ). 

This initial guess may then be inserted on the right-hand sides of the equations and subsequently used to obtain new amplitudes. The process is continued until self-consistency is reached. For the special case in which canonical Hartree-Fock molecular orbitals are used, the Fock matrix is diagonal and the T2 amplitude approximation above is exactly the same as the first-order perturbed wave-function parameters derived from Moller-Plesset theory (cf. Eq. [212]). In that case, the Df and arrays contain the usual molecular orbital energies, and the initial guess for the T1 amplitudes vanishes. 

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