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637. MAXWELL: Calculation of Electrostatic Interaction
Energies
by Mihaly Mezei, Department of Physiology and Biophysics, Mount Sinai School of Medicine, CUNY, New York, New York 10029 and Edwin S. Campbell, Department of Chemistry, New York University, New York, New York 10003 The programs described herein can calculate the interaction energies of either a finite set or a crystal of polarizable molecules. They were written by Mihaly Mezei in collaboration with Professor Edwin S. Campbell at NYU on the CDC in 1975-76 and are based on algorithms deleloped either jointly or earlier by Professor Campbell. They have been converted to the current FORTRAN 77 version from 1988 to 1992 at Hunter College, CUNY, and at Mount Sinai School of Medicine, CUNY. It now runs on the IBM, VAX/VMS, CRAY and on any generic UNIX system. The charge distribution at each lattice site is assumed to be characterized by a multipole expansion about the site in the formalism of Maxwell which computes the interaction energy in the form of general directional derivatives. Cooperativity is introduced through the dipole polarizability tensor of each charge distribution. For a given charge distribution, the poles (scalar mulipliers for each harmonic order) and characteristic directions (used in the directional derivatives) are obtained with the program CHARDIR. This algorithm requires the Taylor series coefficients in the multipole expansion for the charge distribution. These coefficients can be computed for a one-determinant wave-function expanded over a Gaussian basis set with the program MOMENTS. The program MOMENTS can perform the multipole expansion at the position of any of the atoms or it can partition the electron density into atomic contributions in a number of different ways and thus perform the multipole expansion on each separately.If necessary, the moments can be translated and rotated by the program MOMTRNSF. The program MULTIPOL computes three types of contributions to the interaction energies between a finite set of molecules. The permanent multipole interaction energies are calculated with recursion algorithms. The nonadditive induction energies are calculated in the induced dipole approximation. Pairwise additive interaction energies, which have the form of a linear combination of inverse powers of the distance between pairs of centers on each pair of molecules, can be used to model dispersion and repulsive contributions. These algorithms were used to develop a cooperative potential function for water- water interactions. The same three types of contributions to the lattice energy of a crystal of polarizable molecules can also be computed. The permanent multipole contribution is calculated with Campbell's generalization of the Ewald method for ionic lattices to lattices of multipoles of arbitrary order and an efficient algorithm for a sequence of calculations on the same lattice but different molecular orientations.The algorithm proceeds in two steps. For each spherical harmonic order a set of quantitites, called crystal constants (completely determined by the geometry of the lattice sites), is calculated. These crystal constants are combined with characteristic directions and multipole moments in a much shorter step to obtain the permanent multipole interaction energy. The program CRYSCON executes the "crystal constant" calculations, and the program CRYSTAL calculates the permanent multipole and, if desired, the induction contributions to the lattice energy. The program CRYSPOT computes pairwise additive contributions for each molecule in the unit cell.It sums the interactions over all other molecules in a crystallographic parallelepiped about each molecule. The potential used has the form of inverse powers of the distance between the interacting centers. The programs are written in FORTRAN 77 and are very portable. The programs should run on any UNIX machine as is.For non-UNIX systems, the CALL SYSTEM statements have to be eliminated. Lines required by IBM (MVS or VM) are given prefixed with CIBM and by VAX/VMS with CVAX--these have to be blanked out, as appropriate.The program MULTIPOL requires a preprocessor (see Sec. E.6 of the documentation) to set the dimensions as needed. The current version uses single-precision arithmetic in most places. This limited the precision of the calculated moments to 4-5 significant figures for a water molecule in a calculation with 32-bit arithmetic. If increased precision is needed, the program should be converted to double precision (by declaring all real variables as REAL*8 with the IMPLICIT declaration and changing the intrisic fuction calls to their REAL*8 counterpart). On the Convex the -p8 compiler option automatically doubles the word sizes. Lines of Code: 7251 FORTRAN 77 |