Premium
Constrained numerical gradients and composite gradients: Practical tools for geometry optimization and potential energy surface navigation
Author(s) -
Stenrup Michael,
Lindh Roland,
Fdez. Galván Ignacio
Publication year - 2015
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.23987
Subject(s) - convergence (economics) , mathematical optimization , numerical analysis , space (punctuation) , surface (topology) , computer science , energy (signal processing) , degrees of freedom (physics and chemistry) , optimization problem , rigid body , mathematics , connection (principal bundle) , algorithm , geometry , mathematical analysis , physics , classical mechanics , statistics , quantum mechanics , economics , economic growth , operating system
A method is proposed to easily reduce the number of energy evaluations required to compute numerical gradients when constraints are imposed on the system, especially in connection with rigid fragment optimization. The method is based on the separation of the coordinate space into a constrained and an unconstrained space, and the numerical differentiation is done exclusively in the unconstrained space. The decrease in the number of energy calculations can be very important if the system is significantly constrained. The performance of the method is tested on systems that can be considered as composed of several rigid groups or molecules, and the results show that the error with respect to conventional optimizations is of the order of the convergence criteria. Comparison with another method designed for rigid fragment optimization proves the present method to be competitive. The proposed method can also be applied to combine numerical and analytical gradients computed at different theory levels, allowing an unconstrained optimization with numerical differentiation restricted to the most significant degrees of freedom. This approach can be a practical alternative when analytical gradients are not available at the desired computational level and full numerical differentiation is not affordable. © 2015 Wiley Periodicals, Inc.