Calculating Surfaces using Arguslab

This exercise is intended primarily to be used in a three-hour drylab session, with active teaching by demonstrators.  Students are expected to have already learnt basic modelling operations using Arguslab, in the first drylab session, Drylab: Modelling using Arguslab, and instructions given there will not be repeated here.  As with the first exercise, the present one should be very useful for private study as a revision aid, and will particularly help students to understand the parts of the modelling lecture course dealing with surfaces.  Arguslab is available directly on Campus cluster PCs.  It may be run by Start, Programs, Departmental Software, Chemistry, ArgusLab3.

In this exercise, you will create a model of methyl vinyl ketone 1 and display some of its molecular orbitals as surfaces.  You will map its electrostatic potential onto one of these, and come to some conclusions about the reactivity of the molecule.

Building the model geometry

You should have an appropriately shaped skeleton.

Monitor some bond angles

Here you will measure the three bond angles at the carbonyl carbon, and set monitors on these, so that you can follow them when you improve the geometry.

Reoptimise the geometry at the PM3 level

Calculate some grid files for the properties you wish to display as surfaces

In this step you will calculate the values of some wavefunctions, and of the electrostatic potential, at each of a cubic grid of points covering the space occupied by the molecule.  For each function you select, Arguslab will store the resulting three-dimensional array of values as a separate file, which will be named automatically

Calculate and display surfaces for molecular orbitals

A contour is a line in two-dimensional space which connects points having a particular value, e.g. of a wavefunction.  Contour plots of wavefunctions in a plane through a molecule are used in elementary teaching of MO theory of symmetric molecules.  They may be useful for bigger molecules if a plane can be found which passes through a region of interest, e.g. it contains one or two bonds.  Generally, however, it is not possible, and hardly ever easy, to select a plane which contains all the features of interest of a delocalised MO.  We need to view the whole molecule, in three-dimensional space.

The three-dimensional counterpart of a contour is a surface which passes through all points in three-dimensional space, which have a particular value of some property.  In the previous section, you calculated some MOs and the ESP of the molecule at all points of a three-dimensional grid.  For an orbital which you want to display, Arguslab now just needs to select all the entries in its stored array which have your selected value of a contour level.  Just as it can draw on the screen a perspective view of a plastic ball to represent an atom, so it can draw a view of a surface connecting these selected coordinates.  As you rotate the model on the screen to see different atoms, so the surface will also rotate, so that you can see different features of it.

In real research, selecting the contour value usually needs to be done by trial and error, to explore what information different values will yield.  In a two-dimensional contour plot, several different contour values are often plotted at once, since any number of non-intersecting lines in the chosen plane can be seen at the same time.  In three dimensions, it is usually practicable to see only one surface at a time, or in the case of orbitals with nodes, one positive and one negative surface joining points with plus or minus a particular numerical value respectively.  This is because surfaces for orbitals (or ESP) are closed surfaces, so that you cannot see one inside the other. Now you can look at the other three MOs you have calculated, in the same way, as follows

Electrostatic Potential

Electrostatic potential is the repulsive or attractive energy felt by a unit positive charge as a result of the combined effect of nuclei and electrons in the molecule.  It is of interest when considering the attack of charged or dipolar nucleophiles or electrophiles on the molecule.  In an earlier section you have already calculated the ESP at every point of the cubic grid covering the molecule.  It does not depend on a knowledge of individual orbitals, but on the distribution of the whole electron density and of the nuclei.  In the absence of electronic method data, it can be calculated approximately from electronegativities.