Cheatography

# Energy Minimisation Cheat Sheet (DRAFT) by lemonbuzz

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

### 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 -

### 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)