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[[VB_workshop_tutorials_program|<< Return to the program]]
+
[[VB_tutorial|<<< VB tutorials main page]]
  
  
<font color=red> '''How to modify this page''' : </font>
 
* first : '''<font color=blue>log in</font>''' (top right of this page) ;
 
* click on '''[<font color=blue>edit</font>]''' (far right) to edit a section of the page ;
 
* write your text directly in the wiki page, and click on the "Save page" button (bottom left) to save your modifications
 
Pictures : [[Insert a picture| how to insert a picture]] in your text
 
  
See also [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet this page] for an introduction to the basics of the wiki syntax
+
=BLW method & HuLiS program=
  
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''BLW within GAMESS (Version: MAR-25-2010 R2)'''</big>
 +
|-
 +
|
 +
[[BLW | BLW ]] is provided by [http://homepages.wmich.edu/~ymo/ Yirong Mo]  (Western Michigan University - USA). It allows to optimize local wave functions. DFT approaches allow to include a part of correlation into the structure.
 +
Gradients are available for geometry optimization. Structures can interact with $BLWCI group.
  
 +
During the workshop, a BLW computation of file.inp is obtained with the command "blwrun  file "
 +
file.log and file.blw are in the current directory.
  
<center><big><big><big> '''BLW method & HuLiS program''' </big></big></big></center>
+
[[BLW | BLW help]]
  
 +
|}
  
= To the Tutors =
 
'''[[Sason_remarks|Sason remarks and prospective 2 hours talk]]'''
 
+
 
  
Philippe's remark on the initially proposed tutorial. are included in '''bold'''.  
+
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''HuLiS : a Huckel-based code'''</big>
 +
|-
 +
|
 +
[[File:hulis.png|thumb|right| 100px|alt=Huckel - Lewis alt text | Huckel - Lewis]]
  
'''Qualitative'''
+
HuLiS is provided by [http://www.ism2.univ-cezanne.fr/equipes/CTOM_1.htm Stephane Humbel ]  (Aix-Marseille Université - France).
* ?...
 
  
'''Computational'''
+
This is a graphical java applet that deals with Huckel and Lewis structures. It computes coefficients and weights of mesomeric structures through two different approaches: the energy related approach is a simulated CI (HL-CI - deprecated); the wave function approach is a projection of Lewis structures onto a Huckel derived wave function(HLP). This second approach is more reliable.
  
Proposal from Yirong
+
HuLiS is launch with the command "java -jar ~/bin/hulis.jar" or via the web site [http://www.hulis.free.fr/ HuLiS ]
# benzene and formamide - focus is on the structural and energetic impact from conjugation, and how to correlate the results with experimental evidences;
 
# butadiene - focus is on the conjugation in the planar structure and the hyperconjugation in the staggered structure, and their impact on the rotational barrier;
 
# acid-base and H-bonding systems: BLW energy decomposition analyses.
 
# visualize the results. I have been using GaussView and ChemDraw, but other graphical software should be fine with me as well.
 
# Questions from any participant can be discussed and tested on site.
 
  
= BLW within GAMESS (Version: MAR-25-2010 R2) =
+
Details of the principles are written at
BLW is provided by [http://homepages.wmich.edu/~ymo/ Yirong Mo] (Western Michigan University - USA). It allows to optimize local wave function.
+
[http://www.hulis.free.fr/huckel_theory_delocalization/index.shtml HL-CI and HLP explanations].
Gradients are available for geometry optimization. DFT approaches allow to include a part of correlation into the structure.
+
Seminal papers are [http://wiki.lct.jussieu.fr/workshop/images/4/43/HL-CI-JCEp1056.pdf HL-CI] and [http://wiki.lct.jussieu.fr/workshop/images/d/d3/HLP2008.pdf HLP].
  
During the workshop, a BLW computation is obtained with the command "rungms file.inp -v BLW "
+
|}
  
Note: Eigenvalues and compositions of BLW-MOs are stored in $SCR/*.blw.
 
  
[[BLW | BLW help]]
 
  
= HuLiS : a Huckel-based code =
+
{| class="collapsible collapsed wikitable"
[[File:hulis.png|thumb|right| 100px|alt=Huckel - Lewis alt text | Huckel - Lewis]]
+
|-
 +
!<big><big><big>'''Main exercises'''</big></big></big>
 +
|-
 +
|  
 +
== Exercice 1 (Lewis structures of benzene, resonance) ==
  
HuLiS is provided by [http://www.ism2.univ-cezanne.fr/equipes/CTOM_1.htm Stephane Humbel ] (Aix-Marseille Université - France).
+
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''Topic'''</big>
 +
|-
 +
|
 +
The benzene molecule is commonly represented as the resonance between the two Kékulé structures. The aim of the exercise is to understand the relative importance of the different Lewis structures in the benzene molecule using BLW and [http://www.hulis.free.fr/ HuLis].  
  
This is a "Click-click-get" java applet that deals with Huckel and Lewis structures It computes coefficients and weights of mesomeric structures through two different approaches: the energy related approach is a simulated CI (HL-CI - deprecated); the wave function approach is a projection of Lewis structures onto a Huckel derived wave function(HL-P). This second approach is better.  
+
According to IUPAC’s Goldbook, resonance energy is defined as “The difference in potential energy between the actual molecular entity and the contributing structure of lowest potential energy”.  However this definition does not precise what is the geometry of the contributing structure of lowest potential energy. Consequently, we can define two types of resonance energy: the vertical resonance energy (VRE) and the adiabatic resonance energy (ARE). This exercice tutorial will guide us toward Lewis structures and resonance of benzene.
 +
|}
  
HuLiS is launch with the command "java hulis.jar" or via the web site [http://www.hulis.free.fr/ HuLiS ]
+
The 6-31G(d) basis set will be used in the following.  
  
= Paper Exercices =
+
1/ Vertical Resonance Energy - at the geometry of benzene.
Here two HuLiS exercices : compute weight in formamide with both HL-CI and HL-P (2x2) mesomery.
 
  
Extend to allyl radical ? find the anti-resonant ground state. Show why HL-CI is deprecated.
+
With the BLW program, and using the provided optimized geometry of benzene molecule, define one 1,3,5-cyclohexadiene Lewis structure, and optimize it's orbitals. 4 blocks need to be defined : 3 blocks for 3 pi bond, and 1 for all the sigma electrons.
 +
Using benzene energy, calculate the Vertical Resonance Energy (VRE).
  
= Computer Exercices =
 
  
== Exercice 1 (Lewis structures of benzene, resonance) B3LYP/6-311+G* level ==
+
2/ Adiabatic Resonance Energy (ARE)- relax the Lewis structure geometry
=== Subject ===
 
The benzene molecule is commonly represented as the resonance between the two Kékulé structures. The aim of the exercise is to understand the relative importance of the different Lewis structures in the benzene molecule using BLW and [http://www.hulis.free.fr/ HuLis].
 
  
According to IUPAC’s Goldbook, resonance energy is defined as “The difference in potential energy between the actual molecular entity and the contributing structure of lowest potential energy”.  However this definition does not precise what is the geometry of the contributing structure of lowest potential energy. Consequently, we can define two type of resonance energy: the vertical resonance energy (VRE) and the adiabatic resonance energy (ARE). This exercice tutorial will guide us toward Lewis structures and resonance of benzene.
+
With the BLW program, relax the Lewis' structure geometry.
 
 
=== To do ===
 
1/ Vertical Resonance Energy - at the  geometry of benzene:
 
<html><pre> $DATA
 
B3LYP/6-311+G*
 
C1 
 
C    6.0    0.000000    0.000000    1.395201
 
C    6.0    1.208090    0.000000    0.697640
 
C    6.0    1.208090    0.000000    -0.697640
 
C    6.0    0.000000    0.000000    -1.395201
 
C    6.0    -1.208090    0.000000    -0.697640
 
C    6.0    -1.208090    0.000000    0.697640
 
H    1.0    0.000000    0.000000    2.481104
 
H    1.0    2.148596    0.000000    1.240288
 
H    1.0    2.148596    0.000000    -1.240288
 
H    1.0    0.000000    0.000000    -2.481104
 
H    1.0    -2.148593    0.000000    -1.240288
 
H    1.0    -2.148593    0.000000    1.240288
 
$END</pre></html>
 
2/ Adiabatic Resonance Energy - relax the Lewis structure geometry
 
 
 
3/ With HuLiS, evaluate the space spanned by Lewis structures compared to that of delocalized wave functions.
 
 
 
'''Step by step help :'''
 
 
 
1/ With the BLW program, and using the provided optimized geometry of benzene molecule, define one 1,3,5-cyclohexadiene Lewis structure, and optimize it's orbitals. 4 blocks need to be defined 3 blocks for 3 pi bond, one for all the sigma electrons.
 
: by compairison to benzene energy, calculate the Vertical Resonance Energy (VRE).
 
 
 
2/ With the BLW program, relax the Lewis' structure geometry.
 
 
: Compare the C-C bond distances to benzene's. Ensure that it is consistent with the Lewis structure.
 
: Compare the C-C bond distances to benzene's. Ensure that it is consistent with the Lewis structure.
 
: Compute the Adiabatic Resonance Energy (ARE) and comment.
 
: Compute the Adiabatic Resonance Energy (ARE) and comment.
 
: Compare the resonance energies computed by the BLW method to the conventional experimental resonance energy based on the hydrogenation heats of benzene and cyclohexene (36 kcal/mol).
 
: Compare the resonance energies computed by the BLW method to the conventional experimental resonance energy based on the hydrogenation heats of benzene and cyclohexene (36 kcal/mol).
  
3 With the hulis program:
+
 
 +
3/ With HuLiS, evaluate the space spanned by Lewis structures compared to that of delocalized wave functions.
  
 
: Draw the benzene with the Huckel tools (blue, left) and create two Kekules structures with the Lewis tools. Double bonds are obtained by clicking a single bond - A second click returns to the Single bond.
 
: Draw the benzene with the Huckel tools (blue, left) and create two Kekules structures with the Lewis tools. Double bonds are obtained by clicking a single bond - A second click returns to the Single bond.
Ligne 107 : Ligne 85 :
 
::Note the value of <math>{\tau}</math>, and the weight of all Lewis structures needed ([Results]).
 
::Note the value of <math>{\tau}</math>, and the weight of all Lewis structures needed ([Results]).
  
=== Access to files : ===
+
[[VBFile 4-1 | FILES FOR BENZENE]]
[[VBFile 4-1 | all input files are there]]
 
]]
 
 
 
  
 
== Exercice 2 (allyl) ==
 
== Exercice 2 (allyl) ==
 +
[[File:Allyl.png|400px|thumb|right]]
  
1 With BLW code calculate the relative energy of the three Lewis structure of the allyl cation at the HF level. By comparison with the energy of the allyl cation, determine the VRE and the ARE. Compare the C-C bond distances.
+
*1/ With the BLW code calculate the relative energies of the three Lewis structures of the allyl cation at the HF level. By comparison with the energy of the allyl cation, determine the VRE and the ARE. Compare the C-C bond distances.
 
 
2 – Repeat the first question at the B3LYP level.
 
 
 
3 - Repeat question 1 and 2 for the allyl radical.
 
 
 
4 -
 
  
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!'''Hints'''
 +
|-
 +
|
 +
* Starting from the delocalized geometry, the first iteration of the optimization of the localized structure will give the VRE.
 +
|}
  
 +
*2/ Repeat the first question at the B3LYP level.
  
 +
*3/ Repeat questions 1 and 2 for the allyl radical.
  
[[VBFile 4-2 | butadiene.xmi]]
+
[[VBFile 4-2 | FILES FOR THE ALLYLS]]
  
== Exercice 3 (Butadiene deconjugation without hyperconjugation) ==
+
== Exercise 3 (BH3... NH3) electronics  at the B3LYP 6-31G(d) level ==
[[VBFile 4-2 | butadiene.xmi]]
 
== Exercice 4 (BH3... NH3) electronics  at the B3LYP 6-31G(d) level ==
 
  
 
BLW energy decomposition analysis can be used to shed light into the nature of intermolecular interactions. Example of NH3∙∙∙BH3. Visualize the polarization and electron transfer effects using the electron density difference (EDD) maps.
 
BLW energy decomposition analysis can be used to shed light into the nature of intermolecular interactions. Example of NH3∙∙∙BH3. Visualize the polarization and electron transfer effects using the electron density difference (EDD) maps.
  
1/ Make orbitals of BH3 alone (then NH3) in the geometry of the complex  
+
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''Geometry'''</big>
 +
|-
 +
|
 +
the geometry of the complex we use is
 
<html><pre>
 
<html><pre>
 
  $DATA
 
  $DATA
Ligne 148 : Ligne 130 :
 
  $END
 
  $END
 
</pre></html>
 
</pre></html>
2/ Let fragment orbitals to polarize in the full complex.
+
|}
 +
 
 +
*1/ Make orbitals of BH3 alone (then NH3) in the geometry of the complex  
  
3/ Let delocalize. This is just a standard DFT calculation. (TO CHECK with Yirong)
+
*2/ Let fragment orbitals to polarize in the full complex.
  
'''Preliminary Remarks :'''  
+
*3/ Let  delocalize. This is just a standard DFT calculation.
 +
 
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''Preliminary Remarks :'''</big>
 +
|-
 +
|
 
B3LYP calculation in Gamess is specified in $CONTRL :  
 
B3LYP calculation in Gamess is specified in $CONTRL :  
 
<pre> $CONTRL SCFTYP=RHF DFTTYP=B3LYP runtyp=energy maxit=200 icharg=0 $END</pre>
 
<pre> $CONTRL SCFTYP=RHF DFTTYP=B3LYP runtyp=energy maxit=200 icharg=0 $END</pre>
Ligne 158 : Ligne 148 :
 
<pre>  $BASIS  GBASIS=N31 NGAUSS=6 NDFUNC=1 $END</pre>
 
<pre>  $BASIS  GBASIS=N31 NGAUSS=6 NDFUNC=1 $END</pre>
  
'''Step by step help :'''
+
|}
 +
 
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''Step by step help :'''</big>
 +
|-
 +
|
  
1/ Perform a NH3  BLW calculation of the fragment alone in the geometry of the complex with  '''$BLW NBLOCK=1 $END''' and keep the generated .blw file for next step (same for BH3).
+
*1/ Perform a NH3  BLW calculation of the fragment alone in the geometry of the complex with  '''$BLW NBLOCK=1 $END''' and keep the generated .blw file for next step (same for BH3).
  
 
<font color=grey>  
 
<font color=grey>  
: We obtain
+
:: We obtain
: nh3.log: FINAL R-B3LYP ENERGY IS      -56.5111505350
+
:: nh3.log: FINAL R-B3LYP ENERGY IS      -56.5111505350
: bh3.log: FINAL R-B3LYP ENERGY IS      -26.5644674370  
+
:: bh3.log: FINAL R-B3LYP ENERGY IS      -26.5644674370  
 
= > summ = -83.07561797</font>
 
= > summ = -83.07561797</font>
  
2/ Do the complex in a NBLOCK=2 BLW calculation and see the energetic effect of the polarization of each fragment. The initial orbitals are obtained from .blw files of individual fragments
+
*2/ Do the complex in a NBLOCK=2 BLW calculation and see the energetic effect of the polarization of each fragment. The initial orbitals are obtained from .blw files of individual fragments
 
---ORBITALS (LOCAL BFS)---  part, and copied after the $BLWDAT fragments definition. A blank line separate each fragments’guess.
 
---ORBITALS (LOCAL BFS)---  part, and copied after the $BLWDAT fragments definition. A blank line separate each fragments’guess.
  
Ligne 175 : Ligne 171 :
  
 
<font color=grey>
 
<font color=grey>
We obtain
+
::We obtain
 +
::ITER  1  E(RBLW)      =      -83.059219 </font>
 +
::<font color=grey>FINAL R-B3LYP ENERGY IS      -83.093218</font> compared to the 1st iteration it is -21.3 kcal/mol= electronic relaxation
 +
 
 +
*3/ Let the delocalization of all electrons.  (NBLOCK=1 + read localized guess orbitals OR standard B3LYP calculation)
 +
[[File:EDD_map.png|right| 200px|alt=EDD map - EDD alt text | differential density]]
 +
<font color=grey>
 +
::We obtain
 +
::FINAL R-B3LYP ENERGY IS      -83.148013 </font> -34.4 kcal/mol charge transfer.
 +
'''Remark0''' : BSSE can be computed with CP approach and use to correct this energy. A ghost atom is noted with a negative Z (e.g. a ghost Carbone in noted as C -6.0  X Y Z  instead of C  6.0 X Y Z).
 +
 
 +
'''Remark''' : the electronic differential density can be mapped using BLW and DELOCALIZED cube files generate with gaussian for instance. An utility ('''edd''') substracts the two densities from the  cube files named '''test.cube_BLW''' and '''test.cube_HF''' and stores it in the file '''test.cub'''. The new cube file can be visualized with gaussview ('''gview''').
 +
 
 +
 
 +
to generate the cube file for BLW orbitals, use Gaussian ('''gaurun''') with this route card
 +
#B3LYP/6-31G(d) 6D Nosymm  Guess=(Cards,'''only''') Cube=(81,Density,Full)
 +
 
 +
and after the geometry specification,
 +
input the orbitals from the BLW file as cards,
 +
don't forget to name the cube file. 
 +
'''test.cube_BLW'''
 +
see also [[VBFile_4-3#gaussiancube.com | gaussiancube file]]
  
ITER  1  E(RBLW)      =      -83.059219
+
|}
  
FINAL R-B3LYP ENERGY IS      -83.093218</font>
+
[[VBFile 4-3 | FILES FOR THE NH3 ... BH3]]
  
3/ Let the delocalization of all electrons.  (NBLOCK=1 + read localized guess orbitals OR standard B3LYP calculation)
+
|}
  
<font color=grey>We obtain
 
  
FINAL R-B3LYP ENERGY IS      -83.148013 </font>
+
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big><big><big>'''Optional exercises - homework'''</big></big></big>
 +
|-
 +
|
  
'''Remark''' : the electronic differential density can be mapped using BLW and DELOCALIZED cube files generate with gaussian for instance. An utility ('''edd''') substracts the two densities from the  cube files named '''test.cube_BLW''' and '''test.cube_HF''' and stores it in the file '''test.cub'''. The new cube file can be visualized with gaussview for instance.[[File:EDD_map.png|thumb|right| 100px|alt=EDD map - EDD alt text | positive values of the differential density]]
+
== Exercise 4 (Butadiene deconjugation without hyperconjugation) ==
 +
[[File:Rotated_butadiene.png|right|150px|alt=butadiene - Lewis alt text | planar butadiene ]]
 +
[[File:planar_butadiene.png|right|200px|alt=butadiene - Lewis alt text | planar butadiene ]]
 +
Examine the conjugation in planar butadiene and the hyperconjugation in perpendicular butadiene, and explain the rotational barrier.
  
 +
Note that often people rotate one participating group to disable the conjugation and use the barrier to measure the conjugation energy. What is the inconvenience of this approach?
  
  to generate the cube file for BLW orbitals, use this route card
+
   
#B3LYP/6-31G(d) 6D Nosymm  Guess=(Cards,'''only''') Cube=(81,Density,Full)
+
* Compute the conjugated planar form with a standard B3LYP/6-31G(d) calculation
    
+
* Using BLW, localize the pi electrons on C1=C2 and on C3=C4 double bonds. (view the geometrie to verify that the pi system is along the X axis.
  and after the geometry specification, input the orbitals from the BLW file as cards, and the name of the cube file :  
+
* Compare the energies to calculate the conjugaison energy.
   (3E20.10)
+
 
   1
+
{| class="collapsible collapsed wikitable"
    0.9926747455E+00   0.3486271161E-01   0.3593065246E-09
+
|-
    0.3887252782E-07   0.8398088273E-03   0.4264961672E-02
+
!'''Planar geometry'''
  etc ..
+
|-
    0.2753682661E-03   -0.5377658935E-04   0.5519598115E-02
+
|
    0.2723760658E+00   0.3016686057E+00   -0.1384931403E+00
+
<html><pre>
  -0.1533710684E+00  -0.1339008317E+00  -0.1482888468E+00
+
C    6.0  0.0000000000  0.6097325637  1.7490045499
  0
+
C    6.0  0.0000000000  0.6038280097  0.4085967284
  '''test.cube_BLW'''
+
C    6.0  0.0000000000  -0.6038307169  -0.4085950903
 +
C    6.0  0.0000000000  -0.6097309803  -1.7490029472
 +
H    1.0  0.0000000000  1.5343833559  2.3190652626
 +
H    1.0  0.0000000000  -0.3149186339  2.3230080652
 +
H    1.0  0.0000000000  1.5514513284  -0.1322302753
 +
H    1.0  0.0000000000  -1.5514569088  0.1322266423
 +
H   1.0  0.0000000000  -1.5343794820  -2.3190677945
 +
  H    1.0  0.0000000000  0.3149214640  -2.3230051413
 +
</pre></html>
 +
|}
 +
* Use the perpendicular form given below to compute the "deconjugated" system. The comparairison with the planar standard calculation gives an estimate of the conjugaison, which is contaminated by some hyperconjugaison.
 +
* To inhibit hyperconjugaison in the perpendicular form, localize the electrons on the C1=C2 and on C3=C4 double bond. (note that the C3=C4 vinyl group has rotated along the XZ plane; hence its pi system is along the Y axis.
 +
 
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!'''Twisted (perpendicular) geometry'''
 +
|-
 +
|
 +
 
 +
<html><pre>
 +
  C    6.0  0.000000  -1.086858    2.236154
 +
C    6.0   0.000000    0.000000   1.489418
 +
C    6.0  0.000000    0.000000   0.000000
 +
C    6.0  -1.086858   0.000000  -0.746736
 +
H    1.0  0.967527    0.000000  -0.478451
 +
H   1.0  0.000000   0.967527    1.967869
 +
  H    1.0  -2.072275    0.000000   -0.314213
 +
H    1.0  -1.029400   0.000000  -1.820913
 +
H    1.0   0.000000  -2.072275    1.803631
 +
H   1.0  0.000000   -1.029400    3.310331
 +
$END
 +
 
 +
</pre></html>
 +
[[File:Rotated_butadiene.png|right|250px|alt=butadiene - Lewis alt text | planar butadiene The C3=C4 has rotated along the XZ plane; hence its pi system is along the Y axis.]]
 +
 
 +
|}
 +
[[VBFile 4-4 | FILES FOR THE BUTADIENE DECONJUGAISON ]]
 +
 
 +
== Exercise 5 : formamide and allyl radical with HuLiS ==
 +
 
 +
Here are two HuLiS  exercices : find the weights in formamide with HL-CI and use HLP to get coefficients for the allyl radical.
 +
 
 +
====Formamide with HL-CI====
 +
[[File:Formamide.png|400px|thumb|right]]
 +
Formamide can be written as a resonance between two Lewis strutures. We shall find the weights of this scheme using HL-CI.
 +
 
 +
In HL-CI we define an effective CI hamiltonian that concerns the interaction between  the (localized) Lewis structures <math> \Psi_{I}</math> and <math> \Psi_{II}</math>: <math> \Psi_{HL-CI}=c_{I}\Psi_{I}+c_{II}\Psi_{II}</math>. This CI must give the Huckel energy of the delocalized wave function. <math> E_{HL-CI}=E_{Huckel}</math>
 +
 
 +
*1/ Write the expression of the CI secular determinant that has the energy ot the delocalized wave function, and show that the off-diagonal term is <math>H_{I-II}=0.71\beta</math>. (in HL-CI the off diagonal term is supposed <0).
 +
 
 +
*2/ Resolve the secular equations of the CI and find that
 +
<math> \Psi_{HL-CI}=0.81\Psi_{I}+0.58\Psi_{II}</math>, hence the weights of the structures (I/II)=(66%/34%)
 +
 
 +
Note that in HL-CI <math><\Psi_{I}|\Psi_{II}>=0</math>
 +
  {| class="collapsible collapsed wikitable"
 +
|-
 +
!'''help'''
 +
|-
 +
|
 +
Formamide's Huckel energy <math>E_{Huckel}= 4\alpha + 6.548\beta</math>
 +
 
 +
The (localized) Lewis structures '''I''' and '''II''' have an energy of
 +
** <math>E_{I}= 2*(\alpha + 1.370\beta)+2*(\alpha+1.651\beta)= 4\alpha + 6.041\beta</math> 
 +
** <math>E_{II}= 2*(\alpha + 1.808\beta)+2*(\alpha+0.970\beta)= 4\alpha + 5.556\beta</math> 
 +
 
 +
These values are used as  <math>H_{I-I}</math> and <math>H_{II-II}</math> for the CI matrix.
 +
|}
 +
 
 +
====Allyl Radical with HLP====
 +
[[File:Allyl_radical.png|250px|thumb|right]]
 +
Allyl radical can be written as a resonance between two Lewis strutures: <math> \Psi_{HLP}=c_{I}\Psi_{I}+c_{II}\Psi_{II}</math>.
 +
We shall find the coefficients of this CI via HLP. The Huckel orbitals are considered as :
  
see also [[VBFile_4-4#gaussiancube.com | gaussiancube file]]
+
** <math> \phi_1=0.5 p_1 + 0.7 p_2 + 0.5 p_3 </math>
 +
** <math> \phi_2=0.7 p_1 + 0.0 p_2 - 0.7 p_3 </math>
 +
** <math> \phi_3=0.5 p_1 - 0.7 p_2 + 0.5 p_3 </math>
 +
In the following the Huckel wave function is expressed as a Salter determinant: <math> \Psi_{Huckel}=|\phi_{1}\bar{\phi_{1}}\phi_2|</math>
 +
In the HLP scheme we search the coefficient of the structures I and II by projection of the Huckel wave function  onto the localized structures <math> \Psi_{I}=|\pi_{12}\bar{\pi_{12}}p_3|</math> and <math>\Psi_{II}=|p_1\pi_{23}\bar{\pi_{23}}|</math>.
 +
======Overlap between Lewis structures ======
 +
Within Huckel approximation, (<math> <p_{i}|p_{j}>=\delta_{ij}</math>)
 +
*1/ Find that <math> <\Psi_{I}|\Psi_{II}>=-0.25</math>.
 +
*2/ Suppose that <math> <\Psi_{I}|\Psi_{Huckel}>=-0.73</math> and <math><\Psi_{II}|\Psi_{Huckel}>=+0.73</math>.
 +
Find <math>c_I</math> and <math>c_{II}</math> by solving the equations that derive from
 +
**<math><\Psi_I|\Psi_{Huckel}>=<\Psi_I|\Psi_{HLP}></math>
 +
**<math><\Psi_{II}|\Psi_{Huckel}>=<\Psi_{II}|\Psi_{HLP}></math>
 +
*3/ Compute the trust factor <math>\tau=<\Psi_{HLP}|\Psi_{huckel}></math>
  
 +
*4/ Remark: HL-CI fails to give the correct signs because it supposes <math>H_{I-II}<0</math>.
 +
This drawback can be shown using the energies of the occupied Huckel orbitals <math> \epsilon_1=\alpha+1.41\beta</math> and<math> \epsilon_2=\alpha</math>
  
[[VBFile 4-4 | all input files are there]]
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|}

Dernière version du 14 février 2013 à 08:27

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BLW method & HuLiS program