Geometry optimization of large biomolecules in redundant internal coordinates

We present an improved version of our recent algorithm [B. Paizs, G. Fogarasi, and P. Pulay, J. Chem. Phys. 109, 6571 (1998)] for optimizing the geometries of large molecules. The approximate Cholesky factorization technique has been generalized to the case of redundant coordinates, and an alternative approach involving use of the B†B matrix in the iterative coordinate back transformation is described. The generalized full Cholesky factors of B†B are very sparse and the corresponding force and geometry transformations are fast and numerically stable, permitting us to apply this technique for internal coordinate geometry optimization of molecules containing thousands of atoms. As an example we present optimization data on alpha-helical alanine polypeptides, and various globular proteins. Results for the alanine polypeptides indicates that internal coordinate optimization is clearly superior to the first-order Cartesian optimization techniques generally used in force field calculations. The largest system i...

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

[2]  Peter Pulay,et al.  Systematic AB Initio Gradient Calculation of Molecular Geometries, Force Constants, and Dipole Moment Derivatives , 1979 .

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

[4]  Jon Baker,et al.  The generation and use of delocalized internal coordinates in geometry optimization , 1996 .

[5]  A. Komornicki,et al.  Rapid geometry optimization for semi-empirical molecular orbital methods , 1971 .

[6]  Peter Pulay,et al.  Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules , 1969 .

[7]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[8]  Peter Pulay,et al.  Geometry optimization in redundant internal coordinates , 1992 .

[9]  R. Ahlrichs,et al.  Geometry optimization in generalized natural internal coordinates , 1999 .

[10]  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 .

[11]  M. Frisch,et al.  Using redundant internal coordinates to optimize equilibrium geometries and transition states , 1996, J. Comput. Chem..

[12]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[13]  William H. Press,et al.  Numerical recipes , 1990 .

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

[15]  Peter Pulay,et al.  The calculation of ab initio molecular geometries: efficient optimization by natural internal coordinates and empirical correction by offset forces , 1992 .