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An efficient newton‐like method for molecular mechanics energy minimization of large molecules
Author(s) -
Ponder Jay W.,
Richards Frederic M.
Publication year - 1987
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540080710
Subject(s) - energy minimization , quadratic equation , newton's method , convergence (economics) , minification , atom (system on chip) , mathematics , nonlinear system , algorithm , chemistry , computer science , physics , mathematical optimization , computational chemistry , geometry , quantum mechanics , economics , embedded system , economic growth
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 ( N 2 )) and computer time of O ( N 3 ). Our suggested implementation of the Truncated Newton technique requires storage of less than O ( N 1.5 ) and CPU time of less than O ( N 2 ) 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.