BOMD Input

Molecular Dynamics

Molecular Dynamics Simulation For electrons we have to solve the quantum Schroedinger Equation For nuclei we only consider that they move classically

  F 



 ma

 d   x 2



m

2

d t 



  m x



d V   d  x

Force on nuclei can be obtained from potential derivative





 x t   t    x t 

   x

t t       x t   t    x t    x t t     x

t   

1 dV  

m d  x



 x t 

For example for harmonic oscillator

Initial Condition: You give starting geometry and velocity then you calculate the force from your potential energy surface. Using the force you calculate the velocity and position change, then continue on.

1 2 V  x   k  x   xeq  2 dV     k  x   x 

Types of Force Fields used in Molecular Mechanics

V    V 0 cosa 

V  x  

         V  x   4               12

6

1 2

k  x   xeq 

2

On the fly simulation At every time step solve the electronic Schrodinger equation Good Points 1. Accurate 2. Can describe reaction 3. Do not have to worry about fitting problems Bad Points 1. Computational time is great so can only be used for short time propagation 2. Can not perform detailed analysis

Gaussian 09 BOMD input

G09 BOMD output 1

G09 BOMD output 2

Method of Propagation1 Goal: dx

•

  f  x, t ;  xt 0    x0   xt  final   in time step t 

dt  Euler method (first order method take gradient)  xn 1   xn   f   xn , t n t 

4th order Runge-Kutta propagation : add up contribution along the way 1  xn 1   xn  k 1  2k 2  2k 3  k 4 t  6 k 1   f   xn ,t n ; k 2   f   xn  0.5k 1t , t n  0.5t  •

k 3   f  xn  0.5k 2 t , t n  0.5t ; k 4   f   xn  k 3t , t n  t 

Method of Propagation 2 •

Predictor Corrector : repeated Euler

 x1n 1   xn   f  xn , t n t   x

2 n 1

  xn 

 x

3 n 1

  xn 

1 2 1 2

 f  x , t     f  x  , t   t  n

n

1 n 1

n 1

 f  x , t     f  x n

2 n 1

 f  x , t     f  x

m 1 n 1

n

, t n 1 t 

...  x

m n 1

  xn 

1 2

n

n

stop if   xnm1  xnm11  threshold

, t n 1 t 

Method of Propagation 3 Symplectic Integrator: special integrator for classical mechanics made to satisfy Hamilton’s Equation dp dq  H   H    ; q dt  dt   p Second order Symplectic assume H=T(p)+V(q) •

  V qn   t   pn  0.5   pn  0.5 p n t    pn  0.5    q   T  pn0.5  qn 1  qn  t   p   V qn 1   t   pn 1   pn  0 5  0.5 

Intermolecular Interaction: Super Molecule Approximation

Super Molecule Approximation To obtain the interaction between two waters perform calculation of two waters

Two things to be careful Size Consistency Basis set super position erro • •

Size Consistancy •

Consider H2…H2 with CISD infinite far away result for H2…H2 is not equal to 2 H2!! Two electron excitation

H2A

H2A

H2B

H2B

H2A

H2B

Two electron excitation of two H2 has four electron excitation in H2…H2

Two electron excitation

H2A

;

H2A

H2A

H2B

Size Consistent Methods •

MP2

•

CCSD CCSD  exp

T 1  T 2

 D0

1  T 1 D0  T 2 D0  T 1T 1 D0  T 2T 2 D0  T 1T 2 D0  2 Pople et al. have defined an empirical estimation of the four electron excitation contribution MRSDCI had defined +Q so for bond dissociation and potential energy surface calculation people use MRSDCI+Q to approximately take care of the size consistancy problem

Basis Set Super Position Error •

When calculating the energy of a supermolecule we use the basis set of Molecule A and Molecule B together, when we calculate the separated products we calculate molecule A with basis of A, molecule B with basis of B

VS

Counter Poise Correction •

Boys Lanbardi method: use ghost atoms (no charge just position to put basis)and put the basis for the respective partner in the energy calculation for molecule A and B

VS

BSSE big for small basis sets

Gaussian CP Input

G09 CP output 1

G09 CP output2

G09 CP output3

G09 CP output4

G09 CP Output 5

G09 CP output 6

Optimized Geometry CP

W/O CP

with CP

Excited Electronic States Calculation

Method for Excited States •

•

Use more than one slater determinant •

CISD: Configuration Interaction Singles and Doubles

•

CCSD: Coupled Cluster Singles and Doubles

•

MCSCF: Multiconfigurational Self Consistent Field

•

MR-CISD: Multireference CISD

CAS MP2 •

MP2,3,4: Mollar Plesset perturbation theory

•

Equation of Motion CCSD

•

Time Dependent DFT