Download - Lecture March14
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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)