Quantum Chemistry
Computer Exercise IV
Autumn 2016
Transition state optimization
In this exercise you will learn how to find the transition state for a chemical reaction.
You will construct a potential energy diagram for a SN2 reaction between chloride
and bromomethane.
Quantum Chemistry
Computer Exercise IV
Autumn 2016
1. Introduction
In this exercise you will learn how to use quantum chemistry to construct an energy
profile for a simple reaction. This involves calculating reactants, transition state and
products. You will search for the transition state by scanning the reaction coordinate.
When you have found an approximate transition state you will use it as a starting
point for a full transition state optimization. You are then able to estimate the rate of
the reaction using Transition State Theory (TST) and the Eyring equation.
k= (kbT/h) exp(-ΔG#/RT)
In this exercise we consider a nucleophilic substitution reaction classified as SN2
(where 2 tells that the reaction is bimolecular, i.e. the rate depends on the
concentration of nucleophile and substrate). You are going to study the following SN2
reaction:
Cl- + CH3Br → Cl-----CH3Br → [Cl••• CH3•••Br]‡– → ClCH3---Br- → CH3Cl + Br-
As you can see from the above formulation of the reaction a so called supermolecule
is build prior and after the transition state. In this supermolecule the negatively
charged halide is attracted to the substrate by charge-dipole interaction. For your
investigation you will use DFT with the B3LYP functional and two different basis
sets. First you do all the calculations with the 6-31G(d,p) basis set. After you have
obtained all the necessary stationary points and drawn the potential energy surface you
should do single point calculations on the previously optimized structures with the
large 6-311++G(2df,2p) basis set. Finally you add solvation effects to predict how the
reaction would change if it would be done in presence of a solvent.
2. Optimization of reactant, product and supermolecules
Start by building the molecules CH3Cl and CH3Br with MOLDEN. Optimize the
geometries in GAUSSIAN and check the final structures. Note the bond length
between the halides and the carbon. Also compute the energies for the Br- and Clanions.
Next you take the optimized CH3Br molecule and place the chloride ion at
approximately 3.7 Å away from the carbon. Optimize the geometry to obtain the
supermolecule. For your gaussian input-file you should not forget that the total charge
of the supermolecule is -1. Note the distance between the chloride and the carbon for
the optimized supermolecule. Do exactly the same for CH3Cl and bromide.
2.1 Calculation of the zero point energies
Compute the zero point energy (ZPE) of the optimized molecules. In order to do this
you will use the checkpoint file from the previous optimization. The initial guesswave function and the optimized geometry will be read from the checkpoint file, so
your input file simply looks like this:
Quantum Chemistry
Computer Exercise IV
Autumn 2016
----------------------------------------------------------------------------------------------------%chk=/data/tk/YOUR_DIRECTORY/CH3Cl.chk
#p B3LYP/6-31G(d,p) freq guess=check geom=check
COMMENT LINE
01
----------------------------------------------------------------------------------------------------Specifying the keyword freq tells Gaussian to calculate the second derivatives of the
energy with respect to the nuclear coordinates. The matrix of the second derivatives is
called a Hessian. With the Hessian one can calculate vibrational frequency modes and
derive thermal properties like zero point vibrational energy, enthalpy and entropy.
Furthermore, if the Hessian has no negative eigenvalues (e.g. no negative frequencies)
the structure belongs to a minimum on the potential energy surface.
3. Searching the approximate transition state
The highest energy barrier on a reaction path determines the rate of the reaction. The
transition state is a saddle point on the potential energy surface, e.g. it is the highest
point along the reaction path and a minimum otherwise. Thus a transition state
structure is defined by having one imaginary frequency, which is along the reaction
path, and positive frequencies otherwise.
The search for the transition state starts by scanning the reaction coordinate. For the
SN2 reaction to take place the chloride has to come close to the bromomethane.
Your reaction coordinate is thus the Cl--C distance The scan involves various
optimizations with frozen Cl--C distance, use the opt(addredun) keyword (for
examples of inputs with frozen coordinates see exercise 2).
It is suggested that you choose 2.9 Å, 2.7 Å, 2.5 Å, 2.3 Å, 2.1 Å and 1.9 Å. By
plotting these values you obtain an energy profile for the Cl-C bond formation. The
highest point of this energy profile will now be used for the transition state
optimization.
3.1 Optimization of the transition state
Use the geometry corresponding to the point highest in energy of the previously
determined energy profile as a guess structure for the transition state optimization.
First calculate the Hessian of this structure and check the frequencies. If the dominant
imaginary frequency has the correct character you can start the transition state
optimization.
To do this you need to use the checkpoint file from the Hessian calculation. It contains
all the information necessary to optimize the transition state.
Quantum Chemistry
Computer Exercise IV
Autumn 2016
--------------------------------------------------------------------------------------------------%chk=/data/tk/YOUR_DIRECTORY/approxTS_freq.chk
#p B3LYP/6-31G(d,p) opt=(ts, rcfc, noeigentest) guess=check geom=check
COMMENT LINE
-1 1
--------------------------------------------------------------------------------------------------The following options for the opt keyword are used:
ts
rcfc
requests optimization of a transition state rather than a local minimum
specifies that the computed force constants from a frequency calculation
are to be read from the checkpoint file
noeigentest needed for transition state optimization in case there are more than one
imaginary frequency
After the transition state is optimized, perform a frequency calculation in order to
check that you have obtained a true transition state. This new Hessian should be used
for your calculation of the potential energy surface.
Note: An error many students do in this step is to take the .chk-file from the previous
scan, instead of just the geometry, for the calculation of the initial Hessian. But since
you need the .chk-file from this Hessian for the subsequent transition state
optimization, it would contain the information of the frozen coordinate from the
previously done reaction coordinate scan. Thus the transition state optimization
would fail.
4. Draw the Potential Energy Surface
Now that you have all stationary points of this SN2 reaction (separated reactants and
products, the two supermolecules and the transition state) you are able to draw a 2dimensional potential energy surface. This surface should be drawn for the Gibbs free
energy, i.e. it contains zero point energy and thermal effects. (The Gibbs free energy is
found in the Thermochemistry section of the Gaussian output.)
5. Calculate all stationary points with the big basis set
Now you take all the optimized structures you have and perform a single point
calculation with the big basis set. Add the contribution to the Gibbs free energy from
your calculations with the small basis set and draw the potential energy surface.
You can do this because the geometries will not differ so much for these two different
basis sets. Which means that you don't have to optimize with the big basis set, and you
also don't have to recalculate the Hessian for the big basis set.
But the relative energy you obtain for your structures will be different for these two
basis sets, and this is the reason why your potential energy surface will look different.
Quantum Chemistry
Computer Exercise IV
Autumn 2016
6. Calculate the Solvent Effect
So far you did look at the gas phase reaction. Can you imagine what happens if this
SN2 reaction would be done in solution? How would the barrier change?
To estimate what might happen you should set up 3 single point calculations; one for
the transition state geometry, and one for each supermolecule. It would not make
sense to include the separated reactant and the separated product, because in this case
the cavity formed by the solvation model would be different sized, and it would thus
be hard to compare the solvent effect obtained for these with the solvent effect
obtained for the two supermolecules and the transition state, for which the cavity has
approximately the same size.
See Exercise 4 (ionization of H2O) for how to set up a single-point solvent
calculation. Use your optimized geometries obtained with the small basis set, and
calculate the solvent effects also with the small basis set. The dielectric constant of
the solvent should be ε=7.6, since we assume that the reaction is performed in
tetrahydrofuran instead of water.
7. Report
Your report should include following points:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Report the final energies of all stationary points for both basis sets
Report X-C bond lengths and Mulliken charge on X and C for these
structures (for the transition state and the supermolecules its X-C-Y)
Draw the Gibbs free energy profile for both basis sets and calculate the
reaction rate
Report the imaginary frequency of the transition state
What coordination does the carbon have at the transition state, and which
point group does it belong to?
How does the reaction barrier change if you include solvent effects.
Is the reaction endo- or exothermic?
This part is optional:
Compare your results to experiments and/or ab initio calculations.
Which basis set is better to describe the reaction? Why is that?
Experiements in gas phase:
J. Am. Chem. Soc., 1996, 118, 9360-9367.
Org. Mass Spectrom., 1974, 8 ,81.
J. Am. Chem. Soc., 1984, 106, 959-966.
Ab inito:
Int. J. Mass. Spectrom., 2000, 201, 277-282.
J. Am. Chem. Soc., 1995, 117, 9347-9356.