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Computational Chemistry: Conformational Analysis of Ethane and Butane

Objectives: To visualize molecules in 3-dimensions. To learn how to use the Spartan ES software. To compute and graph the relative conformational energies of ethane and butane.

Background:

One of the most successful theories of the 20th century is quantum mechanics, also called wave mechanics. The idea that energy in atoms occurs in discrete bundles is contrary to our everyday notion that energy flows smoothly into or out of a reaction. But on the atomic and molecular scale, our everyday notions must be set aside. Likewise, the notion that matter is composed of solid particles must give way to the idea that electrons and atoms have wave-like properties, and that the wavelength associated with the particle depends on the particle’s momentum. Describing the interactions of the waves corresponding to individual electrons is at the heart of molecular wave mechanics. When the electron waves in a region of the molecule overlap in a constructive way, like water waves reinforcing each other, there is greater likelihood of finding the electrons in that region.

The challenge is to describe this wavelike behavior in enough mathematical detail that we can accurately predict important features of the molecule such as bond lengths, bond energies, and force constants. For the hydrogen atom, the mathematical description of the electron can be written exactly. You have seen the wavelike pictures of the electron in the H atom - the s, p, d, and f orbitals. For larger atoms (and molecules), the problem is so complicated that it cannot be solved. Approximations must be used. Years of research have shown that we need to retain the approximate 3-dimensional shapes of the orbitals, but that we can simplify considerably how we describe the wavelike behavior of the electron with respect to distance from the nucleus.

Spartan is a computer program that uses the atomic orbitals on the individual atoms to describe the behavior of all the molecule’s electrons. An atom’s core electrons are closely held, while the atom’s valence electrons are shared among atoms. We will concentrate on calculating the total energy of the molecule. This large negative value represents how much energy is released when the molecule is formed by bringing together all its nuclei and all its electrons. What we want to find is how the total energy of the molecule changes as we change the molecular conformation. Notice that we are looking for relatively small changes in very large numbers. Thus, the calculations need to be very accurate. One of the challenges in the development of programs like Spartan is ensuring that the models are sufficiently accurate to give meaningful results but simple enough that the calculations can be performed in a reasonable amount of time. An additional feature of Spartan is that we can use the familiar Windows interface to build and manipulate the molecules. Programs like Spartan are now being used in a wide range of chemical research, including medical and pharmaceutical research.

Overview of the experiment:

We will use Spartan ES to determine the relative energies of several conformations of ethane and butane. For ethane, you will need to have Spartan vary the H-C-C-H dihedral angle from 0 to 120 degrees in 15( increments (i.e. 0(, 15(, 30(… 120(). For butane, you will need to vary the C-C-C-C dihedral angle in 20( increments from 0 to 360( (i.e. 0(, 20(, 40(… 360(.) Spartan will determine the overall energy of the molecule for each conformation. You will get a series of data points (dihedral angle and corresponding energy) that can be plotted in Excel to give a conformational energy diagram.

You will be taught how to use Spartan during the lab. You will be expected to enter your data into an Excel spreadsheet, carry out some energy unit conversions, and create a graph from your data. If you've never used Excel or it has been awhile since you've...
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