An efficient method for the coordinate transformation problem of massively three-dimensional networks

A new and efficient algorithm is presented for the coordinate transformation problem of massively three-dimensional networks formed, e.g., by the atoms of crystal fragments or molecular clusters. The new algorithm is based on a divide-and-conquer technique to perform iterative coordinate transformation, applicable even for three-dimensional networks, with linear scaling memory and near linear scaling CPU time requirements. The new algorithm proved to be very fast in the coordinate transformation problems and geometry optimization of diamond fragments, water clusters, globular proteins, and proteins in solvent.

[1]  H. Bernhard Schlegel,et al.  Methods for geometry optimization of large molecules. I. An O(N2) algorithm for solving systems of linear equations for the transformation of coordinates and forces , 1998 .

[2]  J. H. Wilkinson,et al.  Reliable Numerical Computation. , 1992 .

[3]  G. Fitzgerald,et al.  Geometry optimization of solids using delocalized internal coordinates , 2001 .

[4]  Walter Thiel,et al.  Linear scaling geometry optimisation and transition state search in hybrid delocalised internal coordinates , 2000 .

[5]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[6]  Peter Pulay,et al.  An efficient direct method for geometry optimization of large molecules in internal coordinates , 1998 .

[7]  Jon Baker,et al.  Geometry optimization of large biomolecules in redundant internal coordinates , 2000 .

[8]  P. Pulay,et al.  Efficient geometry optimization of molecular clusters , 2000, J. Comput. Chem..

[9]  Olivier Coulaud,et al.  Linear scaling algorithm for the coordinate transformation problem of molecular geometry optimization , 2000 .

[10]  Gustavo E. Scuseria,et al.  A redundant internal coordinate algorithm for optimization of periodic systems , 2001 .

[11]  Matt Challacombe,et al.  A simplified density matrix minimization for linear scaling self-consistent field theory , 1999 .

[12]  S. Goedecker.  Linear scaling electronic structure methods , 1999 .

[13]  Michele Benzi,et al.  A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method , 1996, SIAM J. Sci. Comput..

[14]  Gustavo E. Scuseria,et al.  Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations , 1997 .

[15]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[16]  S. L. Mayo,et al.  DREIDING: A generic force field for molecular simulations , 1990 .

[17]  E. Bright Wilson,et al.  Some Mathematical Methods for the Study of Molecular Vibrations , 1941 .

[18]  Gustavo E. Scuseria,et al.  Linear Scaling Density Functional Calculations with Gaussian Orbitals , 1999 .