3. We
measure
the
rate
(constant)
But
compute
the
ac0va0on
free
energy
d[4] d[4p]
− = = k[4]
dt dt
0.69
t1/2 =
k
The
connecGon
is
Transi0on
State
Theory
k≈
kBT − ΔG ≠ / RT
h
e (
10 -1 −1
= 2.1 × 10 s K T ⋅ e − ΔG ≠ / RT
)
(
k ≈ 10 s 10 13 -1
) − ΔG ≠ /1.4
(room
T,
ΔG
in
kcal/mol)
4. To
compute
the
rate
constant
we
need
to
find
the
transi0on
state
Image:
h4p://en.wikipedia.org/wiki/TransiGon_state_theory
5. Since
bonds
are
broken/formed
we
must
use
quantum
mechanics
to
find
the
TS
(methods
like
B3LYP/6-‐31G(d)
and
PM3)
Source:
Patrick
Rydberg
Finding
the
TS
is
much
trickier
than
finding
the
reactant
and
product
(minima)
structures
Finding
minima:
minimize
E
along
all
degrees
of
freedom
Finding
TS:
maximize
E
along
one*
degree
of
freedom
and
minimize
along
rest
*but
which
one?
h4p://en.wikipedia.org/wiki/Saddle_point
6. The
free
energy
has
two
contribuGons:
PotenGal
(electronic)
energy
and
vibraGonal
free
energy
Approximate
TS
as
maximum
on
Minimum
(PotenGal)
Energy
Path
(MEP)
G X ≈ Eele + Gvib
X X
Poten0al
energy
E
7. Approximate
TS
as
maximum
on
Reac0on
Coordinate
scan
the
Poten0al
Energy
Surface
(PES)
G X ≈ Eele + Gvib
X X
Poten0al
energy
E
O-‐C
Distance
O-‐C
distance
is
kept
fixed
during
energy
minimizaGon
8. Approximate
TS
can
then
serve
as
a
starGng
point
for
finding
the
real
transi0on
state
This
requires
an
(expensive)
frequency
calcula0on
G X ≈ Eele + Gvib
X X
Poten0al
energy
E
9. Once
the
real
transiGon
state
is
found
the
vibraGonal
free
energy
can
be
calculated
to
yield
the
ac0va0on
free
energy
This
requires
another
(expensive)
frequency
calculaGon
G X ≈ Eele + Gvib
X X
10. Building
a
TransiGon
State:
The
movie
h4p://molecularmodelingbasics.blogspot.com/2009/06/building-‐transiGon-‐state.html
h4p://molecularmodelingbasics.blogspot.com/search/label/transiGon%20state
11. Modeling
Chemical
Reac0ons
in
Enzyme
Ac0ve
Sites
Enzymes
are
too
large
to
be
treated
quantum
mechanically
image:
10.1080/01442350903495417
Source:
Patrick
Rydberg
Image:
10.1021/jp805137x
12. image:
10.1080/01442350903495417
One
opGon
is
to
make
a
small
(gas
phase)
model
of
the
acGve
site
Problems:
Key
interacGons
missing
System
is
too
floppy
Can
by
fixed
by
going
to
larger
models
but
expensive
Image:
10.1021/jp805137x
13. image:
10.1080/01442350903495417
Another
opGon
is
QM/MM
Red:
QM
region
Yellow
&
Green:
MM
Problems:
QM/MM
Boundary
Set-‐up
is
difficult
Schrodinger’s
QM/MM:
Qsite
Source:
10.1021/jp805137x
14. Ques0ons
Now?
Ques0ons
Later?
Leave
a
comment
on
h4p://proteinsandwavefuncGons.blogspot.com/2011/02/modeling-‐chemical-‐reacGons-‐in-‐enzyme.html
