Parallel algorithm for efficient calculation of second derivatives of conformational energy function in internal coordinates

Abstract

A parallel algorithm for efficient calculation of the second derivatives (Hessian) of the conformational energy in internal coordinates is proposed. This parallel algorithm is based on the master/slave model. A master processor distributes the calculations of components of the Hessian to one or more slave processors that, after finishing their calculations, send the results to the master processor that assembles all the components of the Hessian. Our previously developed molecular analysis system for conformational energy optimization, normal mode analysis, and Monte Carlo simulation for internal coordinates is extended to use this parallel algorithm for Hessian calculation on a massively parallel computer. The implementation of our algorithm uses the message passing interface and works effectively on both distributed-memory parallel computers and shared-memory parallel computers. We applied this system to the Newton–Raphson energy optimization of the structures of glutaminyl transfer RNA (Gln-tRNA) with 74 nucleotides and glutaminyl-tRNA synthetase (GlnRS) with 540 residues to analyze the performance of our system. The parallel speedups for the Hessian calculation were 6.8 for Gln-tRNA with 24 processors and 11.2 for GlnRS with 54 processors. The parallel speedups for the Newton–Raphson optimization were 6.3 for Gln-tRNA with 30 processors and 12.0 for GlnRS with 62 processors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1716–1723, 1998