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CHM695March 14

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Optimizing the TS

min.max.

qn+1 = qn c

d2E

dq2

1

q=qn

dE

dq

q=qn

+

normal mode withimaginary freq.q

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%chk=job.chk#hf/3-21Gopt=(ts,CalcFc,Z-matrix)freq

TSOPT

-11ch1hch1hc2120.0h1hc3120.02180.0cl1clc290.0490.0

cl1clc290.0390.0

hc1.089000clc2.000000

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Intrinsic Reaction

Coordinate (IRC)

qn+1 = qn c dE

dqq=qn

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Nudge Elastic Band MethodPlane-elastic band

orchain of states model:

Fuki & Wolynes:

S(R(1),R(2),

,R(P)) =

P

i=1

V(R(i))+

P

i=2

Pk

2

R(i) R

(i1)2

Minimise Sw.r.t. R(i)keeping

replica 1 and replica P

fixed.

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Fs,(i)I = P

(i+1)k

R(i+1)I

R(i)I

P

(i)k

R(i)I R

(i1)I

Pk = 1.0 P

k = 0.5

cuts the corner

and thus

overestimatebarrier

cuts the corner bit lesser than k=1 case.

Still overestimate barrier, as images slide

down towards the minima, and less

resolution at saddle point.

F(i)I

= IV(R(i)) + F

s,(i)I

where,

(negative of gradient=force)

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spring force component perpendicular to

path&true force component paralle l to the path

Needs to omit

F(i)I = IV(R(1)) + Fs,(

i)I

IV(R(i)) = IV(R

(i))IV(R

(i)) ||

||

unit vector along the path

Fs,(i)I =

F

s,(i)I

||

||

unit vector along the path

Correcting forces:

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Refs.

G. Mills and H. Jonsson, Phys. Rev. Letters 72, 1124 (1994)

G. Mills, H. Jonsson and G. Schenter, Surf. Sci. 324, 305 (1995).

http://theory.cm.utexas.edu/henkelman/pubs/jonsson98_385.pdf

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Exercise

Predict reaction rate for the forward and backward? (DFT/

B3LYP, 6-31G**(d,p) )

At 300 K, at what is the timescale for this reaction? (Eyrings

equation, assume potential energy difference = free energy

difference)

When this reaction occurs, is the electron flowing from diene

to dienophile, or viceversa? (HOMO & LUMO)

Using NBO, identify sigma bonds and double bonds (and

verify the bonds drawn in the diagram above)