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If you recall from previous discussions, we've made a number of assumptions about atoms and molecules that are chemically "suspect". We've done this in order to conserve computing time and resources. In many cases, our standard has been in the range of "ballpark" -- meaning that we're interested in getting values that are close to exact but not quite. One of the assumptions made in previous calculations -- energies and geometry optimizations -- has been that we'll ignore movement of the nuclei. We do this with the full knowledge that the nuclei are indeed mobile, but that compared to electrons, they're not moving very much. Nuclei vibrate when they absorbed energy, and these vibrations are characteristic of the molecule. These vibrations can be calculated, albeit at some computational expense.
Gaussian94 calculates vibrational frequencies through the use of the "Freq" keyword. A typical input file is as follows:
# RHF/6-31G(D) Freq Test
Formaldehyde Frequencies
0,1
C
O,1,AB
H,1,AH,2,HAB
H,1,AH,2,HAB,3,180.
Variables:
AB=1.18429
AH=1.09169
HAB=122.13658One important point: frequency calculations are only valid for an optimized geometry, i.e., at a stationary point. Not only that, but frequencies are only valid if the basis set used to calculate the frequency is the same basis set used to calculate the optimized geometry. In the formaldehyde example above, we used the 6-31G(D) basis set to perform the calculation. This file assumes that the values given are optimized and represent the stationary point. We could have done this by running two separate runs: one for the geometry optimization and one for the frequency calculation. You can combine both of these files into one file by using the "--Link1--" separator, and can reduce computing and wall-clock time through the use of a "checkpoint" file. The complete input file is as follows:
%CHK=/flyer/edu/d/tng60/g94/formaldehyde # RHF/6-31G(D) Opt Test (blank line) Formaldehyde Frequencies (blank line) 0,1 C O 1 AB H 1 AH 2 HAB H 1 AH 2 HAB 3 180. Variables: AB=1.18 AH=1.09 HAB=122.0 (blank line) --Link1-- %CHK=/flyer/edu/d/tng60/g94/formaldehyde # RHF/6-31G(D) Freq Geom=CheckPoint Test (blank line) Formaldehyde Frequencies (blank line) 0 1 (blank line)
The first line requests that a checkpoint file titled "formaldehyde" be created. This file will store intermediate results as well as the final optimized geometry. Checkpoint files are non-human-readable that can be used to restart a run (if the system dies, you underestimate the size of a job, or for other "accidental" reasons). There are a series of utilities that can be used, such as "newzmat" and "formchk", to modify the checkpoint file for other purposes. In this example, we'll use the checkpoint file as the starting values for the frequency run. In the example above, we've specified where the checkpoint file is going to be stored. The phrase "/flyer/edu/d/tng60/g94" is the full pathname of a sample student's directory. The file will be called "formaldehyde.chk". I next request the optimization using a particular basis set. Typical starting values for the optimization are then entered. I'll implore you to pay attention to blank lines! Then you should enter the "--Link1--" separator, followed by the name of the checkpoint file to be used (and it better be the same as the name used at the top!). Notice that in the routing request, the basis set used for the optimization is also the one used for the frequency calculation. If you switch horses, your results will be meaningless! Following the "Freq" keyword, I've requested that the geometry come from the checkpoint file. I maintain the usual title line, and I maintain the charge and the multiplicity, followed by a final blank line.
Output for frequeny calculations is relatively straightforward. The output reports the frequencies and the intensities of the infrared peaks.
1 2 3
B1 B2 A1
Frequencies -- 1336.0041 1383.6449 1679.5843
Red. masses -- 1.3689 1.3442 1.1039
Frc consts -- 1.4395 1.5162 1.8348
IR Inten -- 0.3694 23.1589 8.6240
Raman Activ -- 0.7657 4.5170 12.8594
Atom AN X Y Z X Y Z X Y Z
1 6 0.17 0.00 0.00 0.00 0.15 0.00 0.00 0.00 0.00
2 8 -0.04 0.00 0.00 0.00 -0.08 0.00 0.00 0.00 0.08
3 1 -0.70 0.00 0.00 0.00 -0.25 -0.65 0.00 -0.35 -0.61
4 1 -0.70 0.00 0.00 0.00 -0.25 0.65 0.00 0.35 -0.61
(data removed)
4 5 6
A1 A1 B2
Frequencies -- 2028.0971 3159.3259 3231.2614
Red. masses -- 7.2497 1.0490 1.1206
Frc consts -- 17.5690 6.1692 6.8934
IR Inten -- 150.1861 49.7083 135.8583
Raman Activ -- 8.1124 137.7307 58.2883
Atom AN X Y Z X Y Z X Y Z
1 6 0.00 0.00 0.58 0.00 0.00 0.06 0.00 0.10 0.00
2 8 0.00 0.00 -0.41 0.00 0.00 0.00 0.00 0.00 0.00
3 1 0.00 -0.46 -0.19 0.00 0.61 -0.35 0.00 -0.60 0.37
4 1 0.00 0.46 -0.19 0.00 -0.61 -0.35 0.00 -0.60 -0.37
-------------------
You should be reminded that even though we are now looking at the movement of the nuclei, we are still not computing the effect that electrons have on each other (the electron correlation). As a result, the frequencies calculated using the Hartree-Fock method are going to be high, by as much as 15%. You may wish to consider scaling down the values that you obtain for the frequencies, as was suggested for results from MacSpartan.
Gaussian94 also reports a variety of thermochemical values for the molecule (which may be of more interest than the frequency calculations for some of you!). Thermochemistry calculations are done at 298.15 K and 1 atmosphere of pressure. An abbreviated output (including E, thermal energy, Cv, the constant volume molar heat capacity, and S, the entropy) is as follows:
-------------------
- Thermochemistry -
-------------------
Temperature 298.150 Kelvin. Pressure 1.00000 Atm.
Atom 1 has atomic number 6 and mass 12.00000
Atom 2 has atomic number 8 and mass 15.99491
Atom 3 has atomic number 1 and mass 1.00783
Atom 4 has atomic number 1 and mass 1.00783
Molecular mass: 30.01056 amu.
(data removed....)
E CV S
KCAL/MOL CAL/MOL-KELVIN CAL/MOL-KELVIN
TOTAL 20.114 6.255 52.101
ELECTRONIC 0.000 0.000 0.000
TRANSLATIONAL 0.889 2.981 36.130
ROTATIONAL 0.889 2.981 15.921
VIBRATIONAL 18.337 0.294 0.049
You can rerun the thermochemical analysis for the frequency data stored in the checkpoint file by using the "freqchk" utility. You can also change the parameters of the thermochemical runs by using the ReadIsotopes option of the Freq keyword (Freq=ReadIsotopes).You can use this option to the Freq keyword to reset the values for the thermochemical calculations. Defaults are 298.15 K for temperature, 1 atm for pressure, and the most abundant isotopes. The format, which appears in a separate input section, is as follows:
temp pressure [scale] {must be real numbers}
isotope mass for atom 1
isotope mass for atom 2
....
isotope mass for atom nTemp and pressure are self-explanatory. Scale is the scale factor for the frequency data, which defaults to 0.89 if scale is omitted or set to zero. The isotope masses are self-explanatory, but the order must follow the order of the atoms in the geometry section. You can use integers, such as 18 for oxygen-18, and Gaussian94 will use the correct mass, in this case 17.99916 a.u.
You also get some information about the nuclei themselves, known as the "normal modes". The typical standard orientation information for the nuclei is shown. In the case of formaldehyde, all of the atoms are at zero on the x-dimension, and the molecule is defined by the yz plane. For each of the six spectral lines shown in the output, the vectors for each of the atoms are shown, giving displacement in a three-dimensional plane. If you have access to some type of scientific visualization/animation software (such as NIH Image), it is possible to create a small animation of the vibration of the molecule.
Standard orientation:
----------------------------------------------------------
Center Atomic Coordinates (Angstroms)
Number Number X Y Z
----------------------------------------------------------
1 6 0.000000 0.000000 -0.519556
2 8 0.000000 0.000000 0.664734
3 1 0.000000 0.924424 -1.100269
4 1 0.000000 -0.924424 -1.100269
----------------------------------------------------------
1 2 3
B1 B2 A1
Frequencies -- 1336.0041 1383.6449 1679.5843
IR Inten -- 0.3694 23.1589 8.6240
Atom AN X Y Z X Y Z X Y Z
1 6 0.17 0.00 0.00 0.00 0.15 0.00 0.00 0.00 0.00
2 8 -0.04 0.00 0.00 0.00 -0.08 0.00 0.00 0.00 0.08
3 1 -0.70 0.00 0.00 0.00 -0.25 -0.65 0.00 -0.35 -0.61
4 1 -0.70 0.00 0.00 0.00 -0.25 0.65 0.00 0.35 -0.61
(data removed)
4 5 6
A1 A1 B2
Frequencies -- 2028.0971 3159.3259 3231.2614
IR Inten -- 150.1861 49.7083 135.8583
Atom AN X Y Z X Y Z X Y Z
1 6 0.00 0.00 0.58 0.00 0.00 0.06 0.00 0.10 0.00
2 8 0.00 0.00 -0.41 0.00 0.00 0.00 0.00 0.00 0.00
3 1 0.00 -0.46 -0.19 0.00 0.61 -0.35 0.00 -0.60 0.37
4 1 0.00 0.46 -0.19 0.00 -0.61 -0.35 0.00 -0.60 -0.37
-------------------
[NOTE: fun technical tip: if you include the letter "P" after the pound sign ("#P"), your output will include an ASCII bar graph of your IR spectra.]
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