For the case of one molecule in the unit cell (space group p1, for example), the total crystal geometrical parameters are nine ,as we mentioned earlier. While for the case of two or more molecules in the unit cell(e.g. space group p1 bar), six more parameters (tx,ty,tz,rx,ry,rz) for each additional molecule are needed to define the rest of molecules in the unit cell. For example, benzene crystal which has four molecules in the unit cell, there are total of 27 parameters to define the whole crystal system.

In this program, the molecule itself was treated as rigid molecule during the lattice parameters optimization.

The CRSTL program use SIMPLEX optimization method.

NONBONDED INTERACTION FORMULATION AND FORCE FIELD.

Nonbonded interactions arise from the interactions among electrons and nuclei of atoms which are not bonded together, and in our formulation, not bonded to a common atom either. There are total of four kinds of nonbonded interactions used in the CRSTL program. They are van der waals, hydrogen bonding, dipole/ dipole and charge/charge interactions. (Note: dipole/dipole and charge/charge interactions can not calculated in the same time)

• van der waals and hydrogen bonding interaction.

A modified hill"s potential which is governed by two parameters, the van der waals distance, rvdw, and depth of potential well, es, is adapted for the van der waals and hydrogen bonding interaction through out the program. In hydrogen bonding interaction, the depth of potential well, es, is governed by the dielectric constant as well.

evdw = es *(a1*(rvdw/r)**6+a2*100000*exp(-a3*r/rvdw))
ehb = (es/d) *(cosa*a1*(rvdw/r)**6+a2*100000*exp(-a3*r/rvdw))

evdw : van der waals interaction energy (in kcal/mole).
ehb : hydrogen bonding interaction energy (in kcal/mole).
a1 : -2.25 for mm2; -2.25 for mm3 and others.
a2 : 2.90 for mm2; 1.84 for mm3 and others.
a3 : 12.50 for mm2; 12.00 for mm3 and others.
es : the depth of potential well (in kcal/mole).
rvdw : van der waals distance (in ang.).
r : the effective distance between interacting centers of two atoms (in ang.).
d : the dielectric constant.
cosa : the cosine of angle a,


• dipole/dipole interaction.

A classical electrostatics, the so-called jean's formula is used in the program.

edip = 14.39418*ua*ub/(d*r**3)*(cos(x)-3*cos(y)*cos(z))

edip : dipole/dipole interaction energy (in kcal/mole).
ua, ub : the dipole moments of dipoles a and b (in deby).
d : the dielectric constant.
r : the distance between the midpoints of the two dipoles (in ang.).
x : the angle between the two dipoles (in degree).
y, z : the angles between the line along which r is measured and the dipole axes of dipole ua and ub (in degree).


• charge/charge interaction.

A classical electrostatics is used in the program.

echg = 14.39418*4.80298*4.80298*qa*qb/(d*r)

echg : charge/charge interaction energy (in kcal/mole).
qa, qb : charge of point charges a and b (in electron charge).
d : dielectric constant.
r : the distance between two point charges (in ang.).

The default MM2 nonbonded parameters are stored in VDW.MM2 file.
The default MM3 nonbonded parameters are stored in VDW.MM3 file.

(1) The maximun numbers of molecules in the unit cell is 4 (isp=4).
(2) The maximum numbers of atoms for each molecule is 400/isp.
(3) The maximum crystal size for lattice parameter refinement is 3 x 3 x 3.
(4) The maximum number of attached atoms is 4.
(5) Program can not handle more than one conformation in the unit cell.

Written by:

Dr. Jenn-Huei Lii(robert@europa.chem.uga.edu)
CCMSD
Chemistry Department
University of Georgia
Athens, Georgia
(706)543-2044