Cheatography
https://cheatography.com
Structural Bioinformatics – Slide 7
This is a draft cheat sheet. It is a work in progress and is not finished yet.
Definitions
Minimisation algorithm |
Identifies geometries corresponding to minimum points on the energy surface |
Saddle point |
Highest points on the path between two minima/maxima i.e. a transition structure |
At a minimum point, first derivatives are zero, and second derivatives are positive |
Parameter coordinates |
Molecular mechanics – Cartesian (3N)
Quantum mechanics – Internal (3N-6) |
Categories of min algo |
1. Derivative
2. Non-derivative |
Derivative methods |
- Obtained analytically or numerically
- Analytical preferred
- If only numerical, non-derivative may be more effective |
Numerical derivative |
Change in energy divided by change in coordinates |
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Non-derivative methods
Simplex method |
- Non derivative (zeroth order)
- Locates minimum on energy surface by moving around like an amoeba |
Simplex |
M cartesian coord => M+1 vertices
M internal coord => M-5 vertices |
- Direction of first derivative => Minima location
- Magnitude of deriv. => Steepness of local slope |
Movements |
Reflection -
Reflection and Expansion -
Contraction - |
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Derivative methods
- Direction of first derivative => Minima location
- Magnitude of deriv. => Steepness of local slope
- Second derivative => curvature of function |
Force = -dV(r)/dr |
First order algos |
- steepest descent
- conjugate gradient |
STEEPEST DESCENT |
- moves in dir. || net force (walking straight downhill
- both gradient and direction orthogonal
1) line search (2) arbitrary step (3) lanrange multipliers
- robust when starting point is far from minimum
- relieves higest energy features |
1D Line search |
- bracket search
- computationally expensive |
Arbitrary step |
- random step size
- if lower energy, step size increased by multiplication factor
- higher energy, step size reduced
- more steps but less function evaluations |
Cons |
- forced to make right angles
- path oscillates, overcorrects, and reintroduces errors |
CONJUGATE GRADIENT |
- no oscillation
- gradient orthogonal but direction conjugate
- for quadratic function of M variables, min reached in M steps
- can be used from 2nd step (1st step SD) |
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