TY - JOUR

T1 - An efficient newton‐like method for molecular mechanics energy minimization of large molecules

AU - Ponder, Jay W.

AU - Richards, Frederic M.

PY - 1987

Y1 - 1987

N2 - Techniques from numerical analysis and crystallographic refinement have been combined to produce a variant of the Truncated Newton nonlinear optimization procedure. The new algorithm shows particular promise for potential energy minimization of large molecular systems. Usual implementations of Newton's method require storage space proportional to the number of atoms squared (i.e., O(N2)) and computer time of O(N3). Our suggested implementation of the Truncated Newton technique requires storage of less than O(N1.5) and CPU time of less than O(N2) for structures containing several hundred to a few thousand atoms. The algorithm exhibits quadratic convergence near the minimum and is also very tolerant of poor initial structures. A comparison with existing optimization procedures is detailed for cyclohexane, arachidonic acid, and the small protein crambin. In particular, a structure for crambin (662 atoms) has been refined to an RMS gradient of 3.6 × 10−6 kcal/mol/Å per atom on the MM2 potential energy surface. Several suggestions are made which may lead to further improvement of the new method.

AB - Techniques from numerical analysis and crystallographic refinement have been combined to produce a variant of the Truncated Newton nonlinear optimization procedure. The new algorithm shows particular promise for potential energy minimization of large molecular systems. Usual implementations of Newton's method require storage space proportional to the number of atoms squared (i.e., O(N2)) and computer time of O(N3). Our suggested implementation of the Truncated Newton technique requires storage of less than O(N1.5) and CPU time of less than O(N2) for structures containing several hundred to a few thousand atoms. The algorithm exhibits quadratic convergence near the minimum and is also very tolerant of poor initial structures. A comparison with existing optimization procedures is detailed for cyclohexane, arachidonic acid, and the small protein crambin. In particular, a structure for crambin (662 atoms) has been refined to an RMS gradient of 3.6 × 10−6 kcal/mol/Å per atom on the MM2 potential energy surface. Several suggestions are made which may lead to further improvement of the new method.

UR - http://www.scopus.com/inward/record.url?scp=84988112508&partnerID=8YFLogxK

U2 - 10.1002/jcc.540080710

DO - 10.1002/jcc.540080710

M3 - Article

AN - SCOPUS:84988112508

SN - 0192-8651

VL - 8

SP - 1016

EP - 1024

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

IS - 7

ER -