Biomedical Engineering Reference
In-Depth Information
constraint that the optimized structure retain the same relative position along the path (ortho-
gonal optimization). The method yields a series of energy estimates which progressively bound
the energy of the transition state from above and from below. High computational efficiency is
attainable, and sufficient flexibility is provided to deal with asynchronous processes. Compar-
isons are made to the alternative 'reaction coordinate' approach, which is shown to be subject
to several serious deficiencies. The method is applied to a model two-dimensional energy sur-
face and to the allowed electrocyclic interconversions of the cyclopropyl and allyl cations and
of cyclobutadiene and
cis
-butadiene.
As we saw in earlier chapters, early work in geometry optimization using electronic
structure methods used nonredundant internal coordinates (e.g. the Z-matrix). Pulay
et al.
(1979) demonstrated clearly that redundant internal coordinates are the best choice for
minimizing many molecules. Peng
et al.
(1996) reported similar conclusions for transition
state structures, especially when the initial steps of such calculations are guided by QST.
22.1 An Example
Gaussian 03 includes the
synchronous transit-guided quasi-Newton
method; that is, it uses
QST to get close to the quadratic region of the transition state and then quasi-Newton-
Raphson to complete the optimization. There are two flavours: Opt
=
QST2 requires
reactants and products as input structures, whilst Opt
=
QST3 requires in addition the
initial transition state.
The isomerization reaction
HCN
→
HNC
has been used frequently to test transition state optimizations and reaction path algorithms.
Here is the QST3 input:
%chk=c:/hcn.chk
# mp2/6-311g(2d,1p) opt=qst3 freq
HCN (Reactant)
01
C
0.0 0.0 -0.506777
H
0.0 0.0 -1.574099
N
0.0 0.0
0.659252
HNC (Product)
01
C 0.0 0.0 -0.743084
H 0.0 0.0 1.432195
N 0.0 0.0 0.432330
HCN --
>
HNC Transition State H above CN
01
C
0.0 0.0
-0.506777
H
0.0 1.07 -0.506777
N
0.0 0.0
0.659252
It is wise to allow for electron correlation when dealing with reactions that involve
bond breaking and bond making. I first optimized HCN and HNC and then made
