geometry optimization pertemuan vi. geometry optimization backgrounds real molecules vibrate...
Post on 19-Dec-2015
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Geometry Optimization
Backgrounds Real molecules vibrate thermally about their
equilibrium structures. Finding minimum energy structures is key to
describing equilibrium constants, comparing to experiment, etc.
Before GO After GO (PM3-Steepest Descent)
C-C Bond 1.34 Å 1.32197 Å
C-H Bond 1.08 Å 1.08604 Å
C-C-H Angle 120° 123.034°
Geometry Optimization
In its essence, geometry optimization is a problem in applied mathematics.
How does one find a minimum in an arbitrary function of many variables?
Example of paths taken when an angle changes in a geometry optimization.(a) Path taken by an optimization using a Z-matrix or redundant internalcoordinates. (b) Path taken by an optimization using Cartesian coordinates.
Optimization Algorithms Non Derivative methods
Simplex Method The Sequential Univariate Method
Derivative Methods First order derivative
Steepes Descent Conjugate gradient (The Fletcher-Reeves Algorithm) Line Search in One Dimension Arbitrary Step Approach
Second Order derivative Newton Raphson Quasy Newton
Which minimization should I use?
The choice of minimisation algorithm should consider: Storage and computational requirements The relative speed The availability of analytical derivatives and the
robustness of the method
Convergence Criteria In contrast to the simple analytical functions thet we
have used to illustrate the operation of the various minimisation methods, in real molecular modelling applications it is rarely possible to identify the exact location of minima.
We can only ever hope to find an approximation to the true minima.
Instruction to stop the minimisation step = convergence criteria Energy gradient Coordinate gradient Root Mean Square gradient