CHEMISTRY 51
MOLECULAR MODELING
INTRODUCTION. This set of laboratory exercises is designed to acquaint you
with selected but instructive techniques of molecular modeling. Computational
chemistry has evolved to the point that a good calculation can be the full equivalent of an
experiment. The contemporary chemical literature makes frequent reference to in silico
chemistry that is chemistry performed on a computer. The following exercises are
designed as a series of experiments in which you will use computational methods to
answer chemical questions.
Computational chemistry covers a broad range of methods and theory and no
attempt will be made to provide an exhaustive coverage of the field. However, we shall
address problems that most scientists identify as central to the evolving discipline of
molecular modeling. This set of exercises will primarily focus on applications that use
techniques from quantum mechanics. The central result is the Schrödinger wave
equation:
H = E
where the wave function  is a mathematical representation of the system, i.e. a virtual
molecule, H represents the measurement of the energy, and E is the experimental value of
the energy. Physicists and physical chemists assert that the principles of quantum
mechanics are sufficient for the understanding of all chemical phenomena. When Dirac
made this bold claim in the early 1920’s, there was no means of solving the Schrödinger
equation for any non-trivial chemical system. Although the theory was complete in
principle, it was useless in practice as the equation could not be solved. Nearly a century
of intense theoretical effort and the development of computers have solved this problem
and it is now possible to obtain chemically useful results from a numerical solution of the
Schrödinger equation. Several programs have been developed to this end. Gaussian is
the leading program for serious quantum chemistry but it is particularly difficult to use.
We shall be using Spartan ‘02, a powerful yet user-friendly program. The College has a
site license for Spartan that supports up to 15 simultaneous users. Although we shall be
using it in one of the department’s computer labs, you can also run the software on any
computer in a campus computer lab that is running under Windows 2000.
PLAN OF ATTACK. We shall be using the computers in Seaver North 113 and
will take advantage of the physical arrangement of the hardware. Two computers are
located at each of the 6 tables in the room. Accordingly, each problem involves
calculations and analysis for two molecules. You will work in pairs. In each pair, one
student will use his/her computer to study one of the molecules while the partner will
work with the second molecule on her/his computer. Each group will compare results of
the calculations. This format is well suited to the practice of molecular modeling where
informative results are usually obtained when some parameter is changed.
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This document will not outline every keystroke. Rather, the instructor will
demonstrate the use of the program and will be available to handle problems as they
develop. If you wish to familiarize yourself with the program before lab, consult the
tutorial, Spartan ’02 Tutorial and User’s Guide. A copy is on reserve in the Seeley G.
Mudd Library. An electronic version of the tutorial is available through the Help
function of the program. Spartan is relatively easy to use and you will be able to fly solo
after the lab session. There are more exercises in this document than we can cover during
the lab period. We encourage you to pursue them and to use Spartan in cases where the
application of molecular modeling is instructive. Those of you who take Organic
Chemistry next year will make additional use of Spartan.
When you arrive in lab (Seaver North 113 for this exercise), select a computer
and log on. Click on the Spartan ikon to start Spartan. We encourage you to save all the
work in your own space since the disk on a public computer is cleaned up when the user
logs off. You are probably familiar with this routine from your use of Excel.
MODELING EXPERIMENTS
1) Validation of Valence-Bond Models of Acids and Conjugate Bases
In class, we used valence-bond theory in its Lewis electron-dot form to discuss
bonding theory. However, chemical bonds are a useful human construction developed to
understand the properties of molecules and electrons in molecules. That is, electrons, not
bonds, are real. In this experiment, you will compare the predictions from a VB
treatment for formic acid (HCOOH) and its conjugate base, the formate anion
(HCOO-) with the results of quantum mechanical calculations, i.e. virtual experiments.
Before you come to lab, draw Lewis electron dot structures of formic acid and
the formate anion. One member of each group should select formic acid and the other
formate anion. Complete the following steps.
a) Draw the structure of the molecule by selecting Carboxylic Acid from
the Groups menu. The structure is complete in the case of formic acid. The
molecular editor will automatically add hydrogens to the yellow dangling
bonds. In the case of the formate anion, click on Delete in the Geometry
menu and delete the dangling bond connected to the carboxyl oxygen by
clicking on it. Then no hydrogen atom will be added to this oxygen when
you leave the molecular editor.
b) Set up a calculation. Specify the Task in the Calculate boxes as
Equilibrium Geometry at the Ground state. The method should be
Hartree-Fock with a 3-21G* basis functions. Also click on the box marked
E. Sol. This option will produce an estimate of the species’ electronic
energy in water. In the case of the formate anion, one more change is
necessary. Set the Total Charge box to read anion. Then click on the
Submit button and enter a file name and path as prompted.
c) When the calculations have been completed, measure the bond angles and
bond lengths of the two species. Discuss the comparative results. The
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values of the energy for each species in vacuo and in aqua are obtained by
accessing the Output submenu of the Results menu. Does hydration
stabilize or destabilize these species? Will solvation increase the extent of
dissociation?
2) Strength of Species with Lone Pairs as Ligands and Bases
G. N. Lewis defined a base as an electron donor. Bases can also function as
ligands as the basis for a coordinate-covalent bond between a ligand and a transition
metal species is the sharing of an electron pair between the two. Accordingly, ammonia
which has one lone pair acts as both a base and a ligand. Phosphorus is in the same
family as nitrogen and phosphine, PH3, should also have the same electronic properties.
However, this qualitative argument does not allow one to predict the relative reactivity of
these two species. The pKb’s of ammonia and phosphine are 4.75 and 25.67,
respectively; but both species are good ligands. The goal of this is exercise is to
understand these striking differences with the aid of molecular modeling.
One student should choose ammonia and the other phosphine. Perform the
following steps:
a) Draw the structure of your molecule.
b) Set up a calculation. In the Calculate windows, select Equilibrium
Geometry with Hartree-Fock and a 3-21G* basis set. Also click on Elect.
Charges. Click on the Submit button and provide a path and file name as
prompted.
c) When the calculation is finished, measure the bond angle in your
compound. Is the value consistent with bonding theory? Also, use the
Output function to read the charges on the atoms. The key strokes of this
and later steps will be demonstrated by the instructor with water as an
example. Are your results consistent with your notion of electronegativity?
d) An electron density surface can be an informative graphical presentation
of information. This is a surface with the property that the electrons in the
molecule will be found on or inside the surface a certain fraction of the time.
This fraction is given by one minus the isovalue parameter. Hence with the
default isovalue = 0.002, the electrons will be found on or inside the surface
with 99.8% probability.
Brønsted defined a base as a proton acceptor. A potential surface can show
the electrical attraction between a species and a proton. A potential surface
is a surface on which the electrical potential has a fixed value. Generate
these surfaces using the Setup menu and the Surfaces submenu. To prepare
for the generation of the surfaces, click on the Add button and select first
density from the menu of surfaces with potential as the property and then
potential from the menu of surfaces with no property. To actually generate
the surfaces selected above, click on the Submit submenu in the Setup
menu. When the process is completed, the unfilled square to the left of the
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name of the surface will turn yellow. To display the surface, click on the
square; a red check will appear. To undisplay, click on the square again.
e) Use the graphical and quantitative results of the modeling calculations to
discuss the chemistry of ammonia and phosphine.
3) The Molecular Structure of Sulfur Tetrafluoride (SF4)
We have used the VSEPR model, an extension of the valence-bond (VB) model,
to predict the three-dimensional structure of molecules. In its simplest form, the model
asserts that the arrangement of substituents and lone pairs attached to a central atom is
determined by repulsion between electrons. For example, in the case of BF3, three
groups of charge belonging to the three F atoms distribute themselves to form an
equilateral triangle. The well-known trigonal planar structure results. In many cases,
lone pairs of electrons compete with bonding pairs. The text book presents a hand
waving argument that lone pairs occupy more space than bonding pairs but the argument
is by no means convincing. In cases such as this, the VSEPR model provides a set of
alternatives and a plausibility argument for a preferred structure. An experiment is
required to provide a convincing case for or against the hypothesis. One experimental
approach would be the measurement of the microwave spectrum of the compound. This
spectrum yields the moments of inertia of the molecule. In the case of small, polar
molecules, this information is sufficient for the determination of its three-dimensional
structure. Molecular modeling provides an alternate experimental approach. Once
calculates the electronic energy for each molecular structure. The structure that yields the
lowest energy is the preferred form.
Before you come to lab, use the VB/VSEPR model to determine reasonable
hypotheses for the three-dimensional structure of SF4. In lab, each group of two
should select two candidate structures from the list and each member of the group will
choose a different structure. Complete the following steps for each structure:
a) Draw the structure. You will need to use the expert mode. Don't forget
to delete any unused dangling bonds. You don't draw in the lone pairs.
Their number and location are determined by quantum mechanics and the
program.
b) Set up a calculation. Specify the Task in the Calculate boxes as
Equilibrium Geometry at the Ground state. The method should be
Hartree-Fock with a 3-21G* basis functions. Also click on the Freq. box.
Accept the default values for the other options. Click the Submit button
and provide a path and file name as prompted. The program will accept the
structure that you input as the starting point of a routine in which the
electronic energy is calculated and the structure is adjusted to minimize this
energy. This procedure will determine the structure closest to the starting
point that has a minimum energy. This is called the local minimum.
c) When the calculation has completed, determine the energy using Display
menu and the Output submenu. Record the electronic energy in atomic
units. Also measure the bond angles and bond lengths of any stable species.
and check using the Display menu and the Vibrations submenu the list of
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vibrational frequencies calculated for your structure. All frequencies of a
stable molecule must be real numbers. An activated complex, a species that
we shall encounter in chemical kinetics, has one imaginary frequency.
d) Compare the results of the two calculations. They should allow us to
determine the most stable isomer or conformer of SF4. Does SF4 have more
than one stable form? We shall discuss the results in lab. Do the
calculations refute or support your hypothesis? Interpret the values of the
bond lengths and angles.
4) Carbon Monoxide and Cyanide as Ligands.
Most people know that cyanide and carbon monoxide are potent poisons but are
probably unaware of the chemical basis for this property. We have noted in class that
these species are poisons as they are strong ligands and bind to transition metal species
such as iron(II). We did not address the orientation of the ligand when it forms a
coordinate covalent bond. Is it M-CX or M-XC where X is N or O? The preference for
one orientation or isomer will be explored in this exercise. To answer the question, we
should display the molecular orbital with the highest energy, the so-called Highest
Occupied Molecular Orbital or HOMO for short. Species that are electron deficient
attack electrons in this orbital and hence of all the molecular orbitals in the molecule, the
HOMO is most indicative of the species chemistry. Fukui shared the Nobel Prize with
Hoffman and Woodward for developing the study of these “frontier” orbitals. Similarly,
in examining the chemistry in which a reagent donates charge to a molecule under study,
the most instructive orbital for this chemistry, i.e. the relevant frontier orbital, is the
Lowest Unoccupied Molecular Orbital or LUMO.
As in the previous exercises, one member of the pair should choose carbon
monoxide and the other cyanide. As before, complete the following steps:
a) Draw the structure of your compound. Use a triple bond between the two
atoms in the ligand. In the case of cyanide delete the dangling bond or a
hydrogen atom will be appended when you leave the molecular editor.
b) As before, set up an energy calculation. Use Hartree-Fock and a 3-21G*
basis set. Be sure to provide the charge if your ligand is an ion. Submit the
job as before.
c) When the calculation is completed, draw the HOMO. This is accessed
via Setup and Surfaces. You used this utility before to draw the electron
density and potential surfaces. This same approach is used in this case but
HOMO is selected as the surface.
d) Examine the HOMO. Which end of the ligand will be the preferential
site of attack?
mol_model_lab.doc, 27 June 2001, WES
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