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<div id="introdiv" style="text-align: left;">
<div id="titlediv" style="text-align: center;">Hydrogen Bromide
</div>
<br />
</div>
<table style="width: 100%;" border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td>
<div style="margin: 0pt; padding: 0pt;">&nbsp;</div>
<div id="divHBr_with_bond_length">
<div id="tableHBr_with_bond_length" class="floatRightDiv">
<table style="text-align: left; width: 300px;" border="1"
cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td
style="vertical-align: top; width: 300px; height: 300px;">
<div id="Jmol0" class="JmolDiv"
style="width: 300px; height: 300px; background-image: url(HBr_with_bond_length.png);">
<script type="text/javascript">
putJmolDiv(0, "HBr_with_bond_length.spt", "HBr_with_bond_length.png", 300, 300);
</script>
</div>
<br />
</td>
</tr>
<tr>
<td style="vertical-align: top;"> Figure 1 - HBr with bond
length displayed. </td>
</tr>
</tbody>
</table>
</div>
<div id="textHBr_with_bond_length">Here are the results of the
computations on HBr. &nbsp;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. &nbsp;This is demonstrated by comparing the calculated
bond lengths and dipole moments with the literature.
</div>
</div>
</td>
</tr>
<tr>
<td>
<div style="margin: 0pt; padding: 0pt;">&nbsp;</div>
<div id="divHBr_with_HOMO">
<div id="tableHBr_with_HOMO" class="floatLeftDiv">
<table style="text-align: left; width: 300px;" border="1"
cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td
style="vertical-align: top; width: 300px; height: 300px;">
<div id="Jmol1" class="JmolDiv"
style="width: 300px; height: 300px; background-image: url(HBr_with_HOMO.png);">
<script type="text/javascript">
putJmolDiv(1, "HBr_with_HOMO.spt", "HBr_with_HOMO.png", 300, 300);
</script>
</div>
<br />
</td>
</tr>
<tr>
<td style="vertical-align: top;">Figure 2 - HBr with HOMO
displayed. </td>
</tr>
</tbody>
</table>
</div>
<div id="textHBr_with_HOMO">Here is displayed HBr's HOMO.
&nbsp;It's difficult to evaluate the accuracy of this result without a
basis for comparison.
</div>
</div>
</td>
</tr>
</tbody>
</table>
<div style="margin: 0pt; padding: 0pt;">&nbsp;
<table style="text-align: left; width: 743px; height: 124px;" border="1"
cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="vertical-align: top;">Basis Set<br />
</td>
<td style="vertical-align: top;">Bond Length<br />
</td>
</tr>
<tr>
<td style="vertical-align: top;">3-21G<br />
</td>
<td style="vertical-align: top;">1.432407</td>
</tr>
<tr>
<td style="vertical-align: top;">6-31G<br />
</td>
<td style="vertical-align: top;">1.429702</td>
</tr>
<tr>
<td style="vertical-align: top;">DZV<br />
</td>
<td style="vertical-align: top;">1.416607</td>
</tr>
<tr>
<td style="vertical-align: top;">Literature<br />
</td>
<td style="vertical-align: top;">1.4145<small><sup>1</sup></small></td>
</tr>
</tbody>
</table>
Table 1 - We see that with increasing basis size going down the table
the bond length becomes closer to the measured value.<br />
<br />
<table style="text-align: left; width: 898px; height: 164px;" border="1"
cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td>Number of diffuse orbital <br />
functions included in basis set</td>
<td>3-21G</td>
<td>6-31G</td>
<td>DZV</td>
</tr>
<tr>
<td>0</td>
<td>1.322598</td>
<td>1.429702</td>
<td>1.500531</td>
</tr>
<tr>
<td>3</td>
<td>failure</td>
<td>1.146224</td>
<td><span
style="font-size: 12pt; line-height: 115%; font-family: &quot;Helvetica&quot;,&quot;sans-serif&quot;;">1.0979278</span></td>
</tr>
<tr>
<td>5</td>
<td>failure</td>
<td><span
style="font-size: 12pt; line-height: 115%; font-family: &quot;Helvetica&quot;,&quot;sans-serif&quot;;">0.978147</span></td>
<td>0.<span
style="font-size: 12pt; line-height: 115%; font-family: &quot;Helvetica&quot;,&quot;sans-serif&quot;;">951230</span></td>
</tr>
<tr>
<td>7</td>
<td>failure</td>
<td><span
style="font-size: 12pt; line-height: 115%; font-family: &quot;Helvetica&quot;,&quot;sans-serif&quot;;">0.951641</span></td>
<td>0<span
style="font-size: 12pt; line-height: 115%; font-family: &quot;Helvetica&quot;,&quot;sans-serif&quot;;">.970366</span></td>
</tr>
</tbody>
</table>
<br />
<div style="text-align: center;">Table 2 - Dipole moments, Debye.</div>
Literature Value: &nbsp;0.827 Debye<br />
The
failures of the 3-21G basis set can likely be attributed to the
insufficient size of the set. &nbsp;There is a general trend of more
diffuse functions leading to more accurate results, with the exception
of the DZV with 7 difuse functions. &nbsp;This is another example of
how care must be taken when performing these calculations.<br />
<br />
<div style="text-align: center;">UV VIS data<br />
</div>
<table
style="width: 537px; height: 172px; text-align: left; margin-left: auto; margin-right: auto;"
border="1" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td>3-21G</td>
<td>6-31G</td>
<td>DZV</td>
<td>Literature</td>
</tr>
<tr>
<td>62460.53</td>
<td>62625.91</td>
<td>61888.18</td>
<td>2500</td>
</tr>
<tr>
<td>113392.79</td>
<td>110478.65</td>
<td>110387.62</td>
<td><br />
</td>
</tr>
<tr>
<td>194016.17</td>
<td>117185.39</td>
<td>169565.38</td>
<td><br />
</td>
</tr>
<tr>
<td>194281.11</td>
<td>129661.68</td>
<td>171294.34</td>
<td><br />
</td>
</tr>
<tr>
<td>197612.77</td>
<td>133333.86</td>
<td>171821.6</td>
<td><br />
</td>
</tr>
<tr>
<td>198249.03</td>
<td>133687.31</td>
<td>178705.02</td>
<td><br />
</td>
</tr>
<tr>
<td>202884.99</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</tbody>
</table>
<div style="text-align: center;">Table 3 - ultraviolet visual range
electronic transition frequencies, cm^-1.<br />
</div>
<div style="text-align: left;"><br />
<div style="text-align: center;">Below
is a graph of potential energy vs. bond stretch. &nbsp;In general it is
accepted that the larger the basis set, the lower the calculated energy
will be. &nbsp;However, these results are an exception to that trend,
as the DZV set is larger than the 6-31G set. &nbsp;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.</div>
</div>
<div style="text-align: center;"><img
style="width: 547px; height: 346px;" alt="PE vs Bond Stretch"
src="../HBr%20with%20two%20views/3potentialgraphs.png" /><br />
</div>
<div style="text-align: center;">Figure
3 - Graph of potential energy vs. bond stretch. &nbsp;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. &nbsp;</div>
<div style="text-align: center;"><br />
Below is a table of vibrational frequencies for HBr. <br />
</div>
<table
style="width: 597px; height: 144px; text-align: left; margin-left: auto; margin-right: auto;"
border="1" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="text-align: center;">3-21G</td>
<td style="text-align: center;">6-31G</td>
<td style="text-align: center;">DZV</td>
<td style="text-align: center;">Literature</td>
</tr>
<tr>
<td style="text-align: center;">2491</td>
<td style="text-align: center;">2672</td>
<td style="text-align: center;">2654.5</td>
<td style="text-align: center;">2649</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">14.01</td>
<td style="text-align: center;">2505</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">13.55</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><font face="Calibri" size="3">4.17<br />
</font></td>
<td style="text-align: center;"><br />
</td>
</tr>
</tbody>
</table>
Table 4 - Vibrational frequencies, cm^-1. &nbsp;Each basis set came
close to the literature value of 2649,<br />
&nbsp;with the largest&nbsp;basis set DZV coming the closest in this
instance.<br />
<div style="text-align: center;">UV VIS data<br />
</div>
<table
style="width: 537px; height: 172px; text-align: left; margin-left: auto; margin-right: auto;"
border="1" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td>3-21G</td>
<td>6-31G</td>
<td>DZV</td>
<td>Literature</td>
</tr>
<tr>
<td>62460.53</td>
<td>62625.91</td>
<td>61888.18</td>
<td>2500</td>
</tr>
<tr>
<td>113392.79</td>
<td>110478.65</td>
<td>110387.62</td>
<td><br />
</td>
</tr>
<tr>
<td>194016.17</td>
<td>117185.39</td>
<td>169565.38</td>
<td><br />
</td>
</tr>
<tr>
<td>194281.11</td>
<td>129661.68</td>
<td>171294.34</td>
<td><br />
</td>
</tr>
<tr>
<td>197612.77</td>
<td>133333.86</td>
<td>171821.6</td>
<td><br />
</td>
</tr>
<tr>
<td>198249.03</td>
<td>133687.31</td>
<td>178705.02</td>
<td><br />
</td>
</tr>
<tr>
<td>202884.99</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</tbody>
</table>
<div style="text-align: center;">Table 3 - ultraviolet visual range
electronic transition frequencies, cm^-1.<br />
</div>
<div style="text-align: left;"><br />
<div style="text-align: center;">Below
is a graph of potential energy vs. bond stretch. &nbsp;In general it is
accepted that the larger the basis set, the lower the calculated energy
will be. &nbsp;However, these results are an exception to that trend,
as the DZV set is larger than the 6-31G set. &nbsp;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.</div>
</div>
<div style="text-align: center;"><img
style="width: 547px; height: 346px;" alt="PE vs Bond Stretch"
src="../HBr%20with%20two%20views/3potentialgraphs.png" /><br />
</div>
<div style="text-align: center;">Figure
3 - Graph of potential energy vs. bond stretch. &nbsp;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. &nbsp;</div>
<div style="text-align: center;"><br />
Below is a table of vibrational frequencies for HBr. <br />
</div>
<table
style="width: 597px; height: 144px; text-align: left; margin-left: auto; margin-right: auto;"
border="1" cellpadding="2" cellspacing="2">
<tbody>
<tr>
<td style="text-align: center;">3-21G</td>
<td style="text-align: center;">6-31G</td>
<td style="text-align: center;">DZV</td>
<td style="text-align: center;">Literature</td>
</tr>
<tr>
<td style="text-align: center;">2491</td>
<td style="text-align: center;">2672</td>
<td style="text-align: center;">2654.5</td>
<td style="text-align: center;">2649</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">14.01</td>
<td style="text-align: center;">2505</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">13.55</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><font face="Calibri" size="3">4.17<br />
</font></td>
<td style="text-align: center;"><br />
</td>
</tr>
</tbody>
</table>
Table 4 - Vibrational frequencies, cm^-1. &nbsp;Each basis set came
close to the literature value of 2649,<br />
&nbsp;with the largest&nbsp;basis set DZV coming the closest in this
instance.</div>
<div id="authordiv" style="text-align: right;">
Based on template by A. Herráez as modified by J. Gutow
</div>
<div id="creationdiv" style="text-align: right;"> <small>Page skeleton
and JavaScript generated by export to web function using <a
href="http://jmol.sourceforge.net">Jmol 11.8.20 2010-02-28 19:28</a>
on Mar 31, 2010.</small><br />
</div>
<div id="logdiv" style="text-align: right; display: none;">
<pre>Using directory /Users/Shared/Wes and Natasha transferred/Website
adding JmolPopIn.js
...jmolApplet0
...adding HBr_with_bond_length.png
...copying
/Users/Shared/Wes and Natasha transferred/Hbr/HBr_minimal_DZV.log
to
/Users/Shared/Wes and Natasha transferred/Website/HBr_minimal_DZV.log
...copying
Jmol.js
to
/Users/Shared/Wes and Natasha transferred/Website/Jmol.js
...copying
JmolApplet.jar
to
/Users/Shared/Wes and Natasha transferred/Website/JmolApplet.jar
...adding HBr_with_bond_length.spt
...jmolApplet1
...adding HBr_with_HOMO.png
...adding HBr_with_HOMO.spt

</pre>
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