Hydrogen Bromide

 
Figure 1 - HBr with bond length displayed.
Here are the results of the computations on HBr.  In general the larger the basis set the more accurate the calculation, although some basis sets are more well suited to certain types of calculations than others.  This is demonstrated by comparing the calculated bond lengths and dipole moments with the literature.
 
Figure 2 - HBr with HOMO displayed.
Here is displayed HBr's HOMO.  It's difficult to evaluate the accuracy of this result without a basis for comparison.
 
Basis Set
 Bond Length
3-21G
 1.432407
6-31G
 1.429702
DZV
 1.416607
Literature
 1.41451
Table 1 - We see that with increasing basis size going down the table the bond length becomes closer to the measured value.

Number of diffuse orbital
functions included in basis set		 3-21G 6-31G DZV
0 1.322598 1.429702 1.500531
3 failure 1.146224 1.0979278
5 failure 0.978147 0.951230
7 failure 0.951641 0.970366

Table 2 - Dipole moments, Debye.
Literature Value:  0.827 Debye1
The failures of the 3-21G basis set can likely be attributed to the insufficient size of the set.  There is a general trend of more diffuse functions leading to more accurate results, with the exception of the DZV with 7 difuse functions.  This is another example of how care must be taken when performing these calculations.


Below is a graph of potential energy vs. bond stretch.  In general it is accepted that the larger the basis set, the lower the calculated energy will be.  However, these results are an exception to that trend, as the DZV set is larger than the 6-31G set.  Heavier atoms are harder to deal with in computations, and this result may be explained by an inability to accurately compute the properties of bromine.
PE vs Bond Stretch
Figure 3 - Graph of potential energy vs. bond stretch.  The larger basis set DZV calculated a higher energy than the 6-31G basis set, which is contrary to the expectation that larger basis sets produce lower energies.  

Below is a table of vibrational frequencies for HBr.
3-21G 6-31G DZV Literature
2491 2672 2654.5 26492


14.01 25052


13.55


4.17
Table 4 - Vibrational wavenumbers, cm^-1.  Each basis set came close to the literature value of 2649,
 with the largest basis set DZV coming the closest in this instance.


Below is a graph of potential energy vs. bond stretch.  In general it is accepted that the larger the basis set, the lower the calculated energy will be.  However, these results are an exception to that trend, as the DZV set is larger than the 6-31G set.  Heavier atoms are harder to deal with in computations, and this result may be explained by an inability to accurately compute the properties of bromine.
PE vs Bond Stretch
Figure 3 - Graph of potential energy vs. bond stretch.  The larger basis set DZV calculated a higher energy than the 6-31G basis set, which is contrary to the expectation that larger basis sets produce lower energies.  




(1)  Lide, D. R., CRC Handbook of Chemistry and Physics, 77th Edition, CRC Press, 1996-1997.

(2)  "UV-VIS Absorption Spectra of Gaseous Molecules and Radicals: Catalogue Spectra." Atmospheric Chemistry: Start Page. Web. 31 Mar. 2010. <http://www.atmosphere.mpg.de/enid/0,e0818c5350454b5452554d5f7375626b6174092d09093a095350454b5452554d
5f6b6174092d09487964726f67656e2b68616c69646573093a095350454b5452554d5f73746f66666e616d65092d09687
964726f67656e2b62726f6d696465093a095f7472636964092d093531363935/Spectra/Catalogue_5p4.html>.
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