Intro Simulation

7/28/2019 Intro Simulation

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r ()

-4 -3 -2 -1 0 1 2 3 4

-300

-200

-100

0

-5 5

100

V(r)an

dE

n,

kca

l/mo

l


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x ()

-.4 -.3 -.2 -.1 0 0.1 0.2 0.3 0.4

1

2

3

4

5

6

-.5 0.50

*,

ClassicalR

esult


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T (K)

100 200 300 400 500

1

2

3

4

0 6000

5

U=

(kca

l/mo

l),C

V=

dU/dT


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Log (f / Hz)

11 12 13 14

1

2

3

4

10 150

5

U

an

dC

V

at30

0K

-

-


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T (K)

100 200 300 400 500

.001

.002

.003

.004

.005

0 6000

sca

led(

2)

-

-

-


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rij / aij

1 2

-300

-200

-100

0

0 3

Gpolarization

(kcal/mol)

-


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-

-


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- -

-


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-


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Empirical Potential Energy Function

Bonds

Angles

ImproperDihedrals

ll

0

V

V

0

l

Torsions

V

0

Electrostatics

van der Waals

V

V

r

Vr+


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-


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-


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-

-

- -

-

-

-

-


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MC compares energies. No forces calculated.

In equilibrium at T:

= (EE) / kTe

p(E)

p(E)

eE / kT

ER~~

R

V

V


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Monte Carlo Algorithm

Generate initial structure R. Calculate V(R).~~

If V < V then

End if

else

Generate random number RAND:

0 1RAND

p(RAND)R~

R~

If > RAND (VV) / kT

e

~ ~R R

End if

Repeat for N steps.

V V,

V V,

Modify structure to R. Calculate V=V(R).~~

-


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(Pure Translation)

Examples of Normal Modes

Guitar stringfixed at both ends

Balls & Springsin 1D

L

m mM

k k

mode

= 2L / n

n = 1, 2, 3

0

(k/m)1/2

[(k/m)(1+2m/M)]1/2

Proteins

Low frequencyGLOBAL High frequencyLOCAL

C H

(Center at Rest)


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Intro Simulation

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