QM/MM tutorial

QM/MM calculations on a Diels-Alder antibody catalyst.

I. Optimization of the product, reactant and transition state geometries in vacuo, using a quantum chemistry software package

Introduction

A transition state for a chemical reaction can be found in many ways. With some intuition, a good guess can be made of what the transition state should look like and start the optimization from there. Another possibily is to define a coordinate which transforms the reactants into product and optimize the system while varying that coordinate. The latter approach is called a Linear Transit and will be discussed and used in the next part of this tutorial.

Here we will do a straight-forward search for the transition state, using a good guess as a starting geometry. We will also try to optimize the reactant and product minima.

Optimizing the transition state geometry in vacuo, starting with a good guess.

We will start by optimizing the transition state of the Diels-Alder reaction in vacuo at the semi-empirical PM3 level. This is easy since we already have the struture of the transition state analogue. We simply take the coordinates of that analogue from the x-ray structure (1C1E.pdb) and modify them a bit, such that we get the appropriate input coordinates for a Gaussian98 transition-state optimization calculation. We will use the semi-empirical PM3 hamiltonian throughout this tutorial, because of its cost-efficiency. Note that in the x-ray structure the -R group of the analogue (Figure 1) is not resolved. We ignore that group for the moment and focus on the system with -R = -CH3.

The following steps will lead us to the transition state geometry of the reaction in vacuo.

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Optimizing the reactant state geometry in vacuo

Now that we have the transition state, we are going to optimize the reactant state geometry in vacuo. We start from the input file we created for optimizing the transition state.

We simple increase a bit more the bond lengths of the bonds that are to be formed upon the cycloaddition reaction and start an geometry optimization.

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Optimizing the product state geometry in vacuo

Again, we start from the Transition state optimization input. This time we want to have the product geometry in vacuo. We now decrease slightly the bond lengths of the bonds that are to be formed upon the cycloaddition reaction and start an geometry optimization.

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Conclusions

We have now optimized the geometries and energies of the transition state, the reactant state and the prodcut state of the Diels-Alder cycloaddition. The energies of these structures can be found by scanning the gaussian output files (.log) for lines that start with "Energy". The last one is the energy of the optimized structure. Note, the energies are reported in atomic units (au): 1 au = 2625.4999999 kJ/mol. Table 1 lists the potential energies of the optimized geomtries.

Table 1. Energies of the optimized
structures in vacuo at the PM3 level
of theory. The last column lists the
energy differences with respect to
the reactant state.

E(au)E(kJ/mol)ΔE(kJ/mol)
Reactant-0.145-380.700.0
Trans. St.-0.068-178.53202.17
Product-0.158-414.83-34.13

The structures we optimized here at a semi-empirical level are a good starting point for optimizations at higher levels of theory. A good rule of the thumb in optimizing structures is to start with a very low level of theory an gradually increase the level of theory using the optimized geometry of the previous level (i.e. PM3, STO-3G, 3-21G, 3-21G*, ...., 6-31G*, ..., ...)

Next:II. Optimization of the product, reactant and transition state geometries in vacuo, using Linear Transit in gromacs
Previous: Introduction

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updated 27/07/04