Lab 1: Symmetry
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"Symmetry, unity, regularity, and simplicity are essential elementary qualities of beauty in both complex and simple things." - Plato |
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"Symmetry, unity, regularity, and simplicity are essential elementary qualities of beauty in both complex and simple things." - Plato |
In his famous poem, William Blake asks, "Tyger Tyger burning bright, In the forests of the night, What immortal hand or eye, Could frame thy fearful symmetry?" From Plato, to DaVinci, to Blake, many of our greatest thinkers, artists, and poets have contemplated symmetry. Consciously or subconsciously, we all may consider issues of symmetry in determining beauty. Research suggests that animals and humans are influenced by symmetry in choosing mates. Does the six-fold symmetry axis of a flower make it more beautiful than the single reflection plane in a cockroach? Such questions are beyond the scope of this lab. Instead, we have a more modest goal, that of classifying the symmetry point groups of the molecules listed below.
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Purpose: To assign symmetry designations, called "symmetry point groups", to two conformations for each of the folowing molecules.
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ethane |
ammonia |
methyl amine, CH3NH2 |
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methyl ammonium, CH3NH3+ |
aniline, PhNH2 |
hydrogen peroxide, H2O2 |
| biphenyl, Ph-Ph |
The table below describes several symmetry elements and operations. Symmetry operations are operations that can be performed on a molecule and result in an equivalent structure. The simplest operation is to do nothing--the identity element, E, is the one element that all structures will have. Other examples of symmetry elements may be familiar to you from organic chemistry. Molecules that possess an internal plane of symmetry (σ) are unchanged by reflection through a mirror plane that bisects the molecule. A molecule in a specific geometry, or conformation, can be characterized by the set of all symmetry operations that will result in equivalent structures. Point groups are a type of "shorthand" that describe all of the possible symmetry operations. A table of point groups symmetries is helpful (and necessary at this stage) to decode this shorthand. For example, the C2v point group describes a molecule as having the identity element, a two-fold rotation axis, and two reflection planes.
| Symmetry Element | Symbol | Symmetry Operation (operation that produces an equivalent structure) |
| identity | E | N/A |
| plane | σ | mirror-like reflection through the plane |
| inversion center | i | inversion of all atoms through the center |
| proper axis | Cn | 360°/n rotation about the axis |
| improper axis | Sn | rotation followed by reflection through a perpendicular plane |
It is terribly ineficient to find point groups by determining all of the symmetry elements for a given geometry and looking through the tables until you find the point group. For a more fruitful method, try using the flowchart below. It is often helpful to have molecular models or at least to build 3D models on the computer to look for potential symmetry elements. Determine the symmetry of each molecule before even calculating anything. Each molecule will have more than one possible conformation so make sure to think about as many theoretical geometries as possible. For instance, one could draw ethane in either the eclipsed or staggered conformations. For ethane one of these conformations will be a minimum on the potential energy surface (PES) and the other will be a transition state. The goal for this lab is to find, for each molecule, the global minimum and at least one other conformation with which to compare it.
Note that it's usually much easier than this to figure out the symmetry. A linear molecules and platonic solids are usually identified on sight so the assignment comes down to a few critical questions (highlighted in yellow). If there's no rotation axis look for a plane of symmetry (Cs) or inversion center (Ci). Otherwise, the highest n rotation axis, Cn, is called the principal axis (n in this case is a variable and will be replaced by a number in the point group designation). The next critical step is to check for C2 axes perpendicular to Cn. If they exist then the molecule's designation is Dn?, if not Cn?. The "?" will be "h" if there is a horizontal symmetry plane perpendicular to Cn. Failing that, it will be Cnv or Dnd if there is a symmetry plane that contains Cn. If it has no planes of symmetry then it will be Cn or Dn.
Decide which conformations should be important for each molecule and build an input file for each. Determine the symmetry point group to which each conformation should belong and enforce that symmetry.
Enforcing Symmetry. Under normal conditions Gaussian will never change your symmetry point group, so if you start with ethane exactly eclipsed, guassian will not attempt to change the dihedral angle from 0 and the optimized geometry will be eclipsed despite the fact that this is not the optimum geometry. Gaussian, however, only recognizes symmetry when it is exact. If the two bond lengths for H2O are 1.0000 and 1.0001 they will not be considered equivalent. If symmetry is desired in the molecule select >Edit>Point Group and choose Enable Point Group Symmetry from the dialogue box (shown, right). Select the appropriate point group from the Approximate higher-order point groups drop box and click the Symmetrize button.
Submit the calculation.
After an input geometry is prepared, you will need to submit it by selecting >calculate>Gaussian. Change the
to >Optimization; change the
from Hartree-Fock to Semi-Empirical AM1; check to make sure that the charge and spin multiplicity are appropriate; and change the
to something descriptive.
For each calculation you should make sure that your output symmetry, assigned by Gaussian, agrees with what you thought it should be; make sure that the geometry is fully optimized; and write down the absolute energy to five decimal places. Compare your lowest energy with that of your classmates. If anyone has a lower energy then you probably haven't found the global minimum. Keep looking.
After all of this has been done, a frequency calculation will tell you whether each conformation is a minimum or transition state on the potential energy surface. To submit a frequency calculation you should open a successfully optimized log file in GaussView, click >calculate>Gaussian, change the to >frequency and specify >No Raman Intensities. After the frequency calculation is complete you can check under
Make sure you keep your notebook file updated as you work. The notebook file should contain all of the information that will end up in your results section. You will be required to submit your notebook file for each laboratory.
Results Format:
Your results should be summarized in an Excel table like the one below (download the template by clicking on the table image or here). Relative energy is the difference between two conformations of the same molecule (or two isomers). Normally, the global minimum is defined as 0 in relative energy. A second table should include a JPEG image of each structure in which the characteristic geometric features can easily be seen.
Questions to Think About:
