Ionic relaxation first step is a steepest descent step with line minimisation Conjugate gradient search directions are "conjugated"to the previous search directions 共轭梯度法 1.gradient at the current position g() 2.conjugate this gradient to the previous search direction using: N=+5-1 Y=g--》-y (g(N-1)·gN-) 3. line minimisation along this search direction s 4.continue with step 1),if the gradient is not sufficiently small. the search directions satisfy: sBM=δNM YN,M the conjugate gradient algorithm finds the minimum of a quadratic function with k degrees of freedom in k+1 steps exactly
Ionic relaxation 共轭梯度法
Ionic relaxation instead of using a fancy minimization algorithms it is possible to treat the Damped molecular dynamics minimization problem using a simple "simulated annealing algorithm" Regard the positions as dynamic degrees of freedom Behaves like a rolling ball with a friction The forces serve as accelerations and an additional It will accelerate initially,and then deaccelerate when friction term is introduced close to the minimum if the optimal friction is chosen the ball will glide Equation of position motion right away into the minimum 元=-2*0g()-成 for a too small friction it will overshoot the minimum CAP using a velocity Verlet algorithm this becomes and accelerate back for a tool large friction relaxation will also slow down +1V2=(1-2)v-1/2-2*a)/1+2) (behaves like a steepest descent) N+1=N+1+N+1/2 For u=2,this is equivalent to a simple steepest descent step
Ionic relaxation instead of using a fancy minimization algorithms it is possible to treat the minimization problem using a simple “simulated annealing algorithm” • Regard the positions as dynamic degrees of freedom • The forces serve as accelerations and an additional friction term is introduced • Equation of position motion using a velocity Verlet algorithm this becomes For µ = 2, this is equivalent to a simple steepest descent step • Behaves like a rolling ball with a friction • It will accelerate initially, and then deaccelerate when close to the minimum • if the optimal friction is chosen the ball will glide right away into the minimum • for a too small friction it will overshoot the minimum and accelerate back • for a tool large friction relaxation will also slow down (behaves like a steepest descent)