Users.Programs.mol_Optimize

mol_Optimize: Find minimum energy conformations

Starting from (more or less) randomly chosen initial configuration, the MATLAB function mol_Optimize finds minima of the potential energy hypersurface of a molecular system by means of multivariate optimization (typically unconstrained). Most often local minima are found. Hence it is recommended to run many minimizations to increase the chance of finding the global minimum energy structure.

As an alternative, in particular for very high-dimensional problems, we recommend to use the simulated annealing technique, which is built in as a variant in our mol_MonteCarlo code

Source codes

The MATLAB function mol_Optimize.m can be found here

Initial conformations are generated by one of the following functions

• ini_spheroid.m: Randomly putting all molecules on the surface of a spheroid of given radius

• ini_cuboid.m: Randomly putting all molecules inside a cuboid of given size

• ini_icosahedral.m: Putting all molecules to center and 12 vertices of an icosahedron of given size

• ini_fcc.m: Set up a face-centered cubic (fcc) lattice with given lattice constant (scalar) and given numbers of unit cells

• ini_hcp.m: Set up a hexagonal close packed (hcp) lattice with given lattice constants (vector) and given numbers of unit cells

Note that conformations are discarded where molecules come too close to one another.

File I/O

The resulting optimized geometries are written to an xyz-file named minima...xyz. Upon repeated runs of mol_Optimize.m additional data are appended to the end of that file. These results can be visualized (e.g. using JMOL or VMD software) and/or the geometries can be sorted according to energy by our MATLAB function mol_SortMimima.m

Variables

Note that function mol_Initialize has to be run previously in order to initialize all variables in use. Of particular interest are the following structures:

• simulation
• initial
• molecule
• intra
• inter
• optimize

Algorithms

Minimization of potential energy (unconstrained multivariable function)

• fminsearch (part of MATLAB standard distribution)
  Nelder-Mead Simplex method
  Lagarias, J.C., J. A. Reeds, M. H. Wright, and P. E. Wright,
  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions
  SIAM Journal of Optimization, Vol. 9 Number 1, pp. 112-147, 1998.
• fminunc (from MATLAB optimization toolbox, if available)
  BFGS Quasi-Newton method