and Dewar structures among the full set of case 4 can be evaluated when one
removes them: the quality of the resonance scheme drops to 86 % when removing
only the Kekule structures (case 5) and 70 %, when removing both (case 6).
The NRT results reported in Table 13.4 were obtained with the full set of 35
structures (case 4) as initial structures, so that we can compare both methods with
the same mesomerism scheme. They indicate an overall good description of the
density of benzene (s ¼ 90 %). The best HL-P set of contributors (highlighted line
corresponding to s ¼ 97 % in Table 13.4) compares well with the NRT results as it
provides the same tendency regarding the relative importance of the structures: the
Kekule structures are dominant (weight of 22 % in HL-P against 19.5 % in NRT)
over the Dewar structures (weight of 5 % in both methods), and over the para ionic
structures (weight of 3 % in HL-P against 1 % in NRT). In the HL-P scheme, the 24
meta ionic/covalent structures have a small weight of 1 % each and contribute to the
resonance scheme (s is improved by 12 % when they are included) but are absent in
NRT. One has to keep in mind that the HL-P method relies on a Hückel wave
function and does not have as much flexibility as the NRT method to describe the
resonance of benzene. This explains the small discrepancies between both methods.
Moreover, as in the butadiene case, the major Kekule structures came along with 12
zwitterionic structures having adjacent charges. Two of these zwitterionic structures
have charges on carbon 1 and 2 and double bonds elsewhere, which leads to six
structures per inital Kekule structure when permuting charges and double bonds
(two such structures per double bond for the six double bonds of the Kekule
structures) and account for an overall weight of 20 %. Their weights are added to
the weight of the Kekule structures, as they contribute to their description.
As a summary of the two examples discussed in this section, the trust parameter
s designed in the HL-P method provides a excellent means of measuring how good
a given set of contributors is, to mimic the reference wave function.
13.4 HuLiS: An Easy-to-Use Code to Link Hückel
to Lewis Concepts
HuLiS started as a Java applet and evolves to a javascript/HTML5 script to increase
the ease of use [33]. The program is available as a web application at http://ism2.
univ-amu.fr/hulis,
4 and can also be downloaded as a standalone java applet. The
mobile version is available from the same address. In addition to the simple Hückel
method, HuLiS implements the two methods described herein and the topological
resonance module described in this section.
4
Note to the referee: at the moment HuLiS is at http://www.hulis.free.fr but it will migrate soon.
13 Localized Structures at the Hückel Level …
353
removes them: the quality of the resonance scheme drops to 86 % when removing
only the Kekule structures (case 5) and 70 %, when removing both (case 6).
The NRT results reported in Table 13.4 were obtained with the full set of 35
structures (case 4) as initial structures, so that we can compare both methods with
the same mesomerism scheme. They indicate an overall good description of the
density of benzene (s ¼ 90 %). The best HL-P set of contributors (highlighted line
corresponding to s ¼ 97 % in Table 13.4) compares well with the NRT results as it
provides the same tendency regarding the relative importance of the structures: the
Kekule structures are dominant (weight of 22 % in HL-P against 19.5 % in NRT)
over the Dewar structures (weight of 5 % in both methods), and over the para ionic
structures (weight of 3 % in HL-P against 1 % in NRT). In the HL-P scheme, the 24
meta ionic/covalent structures have a small weight of 1 % each and contribute to the
resonance scheme (s is improved by 12 % when they are included) but are absent in
NRT. One has to keep in mind that the HL-P method relies on a Hückel wave
function and does not have as much flexibility as the NRT method to describe the
resonance of benzene. This explains the small discrepancies between both methods.
Moreover, as in the butadiene case, the major Kekule structures came along with 12
zwitterionic structures having adjacent charges. Two of these zwitterionic structures
have charges on carbon 1 and 2 and double bonds elsewhere, which leads to six
structures per inital Kekule structure when permuting charges and double bonds
(two such structures per double bond for the six double bonds of the Kekule
structures) and account for an overall weight of 20 %. Their weights are added to
the weight of the Kekule structures, as they contribute to their description.
As a summary of the two examples discussed in this section, the trust parameter
s designed in the HL-P method provides a excellent means of measuring how good
a given set of contributors is, to mimic the reference wave function.
13.4 HuLiS: An Easy-to-Use Code to Link Hückel
to Lewis Concepts
HuLiS started as a Java applet and evolves to a javascript/HTML5 script to increase
the ease of use [33]. The program is available as a web application at http://ism2.
univ-amu.fr/hulis,
4 and can also be downloaded as a standalone java applet. The
mobile version is available from the same address. In addition to the simple Hückel
method, HuLiS implements the two methods described herein and the topological
resonance module described in this section.
4
Note to the referee: at the moment HuLiS is at http://www.hulis.free.fr but it will migrate soon.
13 Localized Structures at the Hückel Level …
353