NUMERICAL_DERIVATIVES


Function

Numerical_Derivatives contains procedures for calculating numerically the first and second derivatives of the potential energy of a system with respect to the atomic coordinates.

Full details about the use of this module can be found in chapters 4 and 5 of the book A Practical Introduction to the Simulation of Molecular Systems.

Dependencies

Module Variables
DEFINITIONS DP
ATOMS ATMCRD, ATMFIX, NATOMS, NFIXED, NFREE
POTENTIAL_ENERGY ATMDER, ENERGY, ETOTAL, GRADIENT


Public Variables

None.

Public Procedures

There are two public subroutines in this module.

SubroutinePurpose
NUMERICAL_GRADIENT Calculate the first derivatives.
NUMERICAL_HESSIAN Calculate the second derivatives.


NUMERICAL_GRADIENT

Argument Type Intent Optional Purpose
DELTA Real In No The finite-difference step size.
GRADIENT Real(1:3,1:NATOMS) Out No The numerical derivatives.
SELECTION Logical(1:NATOMS) In Yes A selection array.




NUMERICAL_HESSIAN

Argument Type Intent Optional Purpose
DELTA Real In No The finite-difference step size.
HESSIAN Real(1:(3*NFREE*(3*NFREE+1))/2) Out No The numerical derivatives.




Stability

Stable.



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