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[[VB_workshop_tutorials_program|<< Return to the program]]
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[[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
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=BLW method & HuLiS program=
  
 
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{| class="collapsible collapsed wikitable"
 
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|-
<center><big><big><big> '''BLW method & HuLiS program''' </big></big></big></center>
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!<big>'''BLW within GAMESS (Version: MAR-25-2010 R2)'''</big>
 
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|-
 
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= To the Tutors =
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[[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.
'''[[Sason_remarks|Sason remarks and prospective 2 hours talk]]'''
+
Gradients are available for geometry optimization. Structures can interact with $BLWCI group.  
+
 
 
 
Philippe's remark on the initially proposed tutorial. are included in '''bold'''.
 
 
 
'''Qualitative'''
 
* ?...
 
 
 
'''Computational'''
 
 
 
Proposal from Yirong
 
# 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.
 
 
 
<big>
 
 
 
= BLW within GAMESS (Version: MAR-25-2010 R2) =
 
[[BLW | BLW ]] is provided by [http://homepages.wmich.edu/~ymo/ Yirong Mo]  (Western Michigan University - USA). It allows to optimize local wave function.
 
Gradients are available for geometry optimization. DFT approaches allow to include a part of correlation into the structure.
 
 
 
Structures can interact with $BLWCI group.  
 
  
 
During the workshop, a BLW computation of file.inp is obtained with the command "blwrun  file "
 
During the workshop, a BLW computation of file.inp is obtained with the command "blwrun  file "
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[[BLW | BLW help]]
 
[[BLW | BLW help]]
  
= HuLiS : a Huckel-based code =
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|}
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{| class="collapsible collapsed wikitable"
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|-
 +
!<big>'''HuLiS : a Huckel-based code'''</big>
 +
|-
 +
|
 
[[File:hulis.png|thumb|right| 100px|alt=Huckel - Lewis alt text | Huckel - Lewis]]
 
[[File:hulis.png|thumb|right| 100px|alt=Huckel - Lewis alt text | Huckel - Lewis]]
  
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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].
 
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].
  
= Paper Exercices =
+
|}
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>
 
 
Formamide as a Huckel energy <math>E_{Huckel}= 4\alpha + 6.548\beta</math>
 
  
The (localized) Lewis structures '''I''' and '''II''' have an energy of
+
{| class="collapsible collapsed wikitable"
** <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> 
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!<big><big><big>'''Main exercises'''</big></big></big>
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|-
 +
|
 +
== Exercice 1 (Lewis structures of benzene, resonance) ==
  
These values are used as  <math>H_{I-I}</math> and <math>H_{II-II}</math> for the CI matrix.  
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{| class="collapsible collapsed wikitable"
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|-
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!<big>'''Topic'''</big>
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|-
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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].  
  
*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).
+
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.
 +
|}
  
*2/ Resolve the secular equations of the CI and find that
+
The 6-31G(d) basis set will be used in the following.  
<math> \Psi_{HL-CI}=0.81\Psi_{I}+0.58\Psi_{II}</math>, hence the weights of the structures (I/II)=(66%/34%).
 
  
====Allyl Radical with HLP====
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1/ Vertical Resonance Energy - at the geometry of benzene.
[[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 :
 
  
** <math> \phi_1=0.5 p_1 + 0.7 p_2 + 0.5 p_3 </math>
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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.
** <math> \phi_2=0.7 p_1 + 0.0 p_2 - 0.7 p_3 </math>
+
Using benzene energy, calculate the Vertical Resonance Energy (VRE).
** <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>
 
 
 
= Computer Exercices =
 
 
 
== Exercice 1 (Lewis structures of benzene, resonance)  B3LYP/6-311+G* level ==
 
=== 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 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.
 
  
=== To do ===
 
1/ Vertical Resonance Energy - at the  geometry of benzene.
 
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/ Adiabatic Resonance Energy (ARE)- relax the Lewis structure geometry
  
2/ Adiabatic Resonance Energy - relax the Lewis structure geometry
 
 
With the BLW program, relax the Lewis' structure geometry.
 
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.
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3/ With HuLiS, evaluate the space spanned by Lewis structures compared to that of delocalized wave functions.
 
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.
 
::Note the low value of the trust factor <math>{\tau}</math>.
 
::Note the low value of the trust factor <math>{\tau}</math>.
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::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 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.
 
*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.
 +
 +
{| 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.
 
*2/ Repeat the first question at the B3LYP level.
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*3/ Repeat questions 1 and 2 for the allyl radical.
 
*3/ Repeat questions 1 and 2 for the allyl radical.
  
*4/ With XMVB, for the allyl cation put in resonance  structures I and II, then add the structure III. What is the gain in energy due to the inclusion of this third structure?
+
[[VBFile 4-2 | FILES FOR THE ALLYLS]]
 
 
 
 
 
 
 
 
[[VBFile 4-2 | butadiene.xmi]]
 
 
 
== Exercice 3 (Butadiene deconjugation without hyperconjugation) ==
 
[[File:planar_butadiene.png|right|150px|alt=butadiene - Lewis alt text | planar butadiene ]][[File:Rotated_butadiene.png|right|150px|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?
 
 
 
BLW shall be used
 
* to compute the deconjugated planar form, and compare to the conjugated form at the same geometry.
 
* to inhibit at will the hyperconjugaison in the perpendicular form, hence to mesure its stabilizing  contribution to the rotation barrier.
 
  
 
+
== Exercise 3 (BH3... NH3) electronics  at the B3LYP 6-31G(d) level ==
 
 
[[VBFile 4-2 | FILES ARE HERE]]
 
 
 
== Exercice 4 (BH3... NH3) electronics  at the B3LYP 6-31G(d) level ==
 
'''REMARK : BSSE is not taken into account. Shall we add it just a discussion? '''
 
  
 
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.
  
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big>'''Geometry'''</big>
 +
|-
 +
|
 
the geometry of the complex we use is  
 
the geometry of the complex we use is  
 
<html><pre>
 
<html><pre>
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  $END
 
  $END
 
</pre></html>
 
</pre></html>
 +
|}
  
 
*1/ Make orbitals of BH3 alone (then NH3) in the geometry of the complex  
 
*1/ Make orbitals of BH3 alone (then NH3) in the geometry of the complex  
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*3/ Let  delocalize. This is just a standard DFT calculation.  
 
*3/ Let  delocalize. This is just a standard DFT calculation.  
  
'''Preliminary Remarks :'''  
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{| 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>
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<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).
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<font color=grey>
 
<font color=grey>
 
::We obtain
 
::We obtain
::ITER  1  E(RBLW)      =      -83.059219
+
::ITER  1  E(RBLW)      =      -83.059219 </font>
::FINAL R-B3LYP ENERGY IS      -83.093218</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)
 
*3/ Let the delocalization of all electrons.  (NBLOCK=1 + read localized guess orbitals OR standard B3LYP calculation)
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<font color=grey>
 
<font color=grey>
 
::We obtain
 
::We obtain
::FINAL R-B3LYP ENERGY IS      -83.148013 </font>
+
::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.
+
'''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 this route card  
+
  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)
 
  #B3LYP/6-31G(d) 6D Nosymm  Guess=(Cards,'''only''') Cube=(81,Density,Full)
 
    
 
    
Ligne 236 : Ligne 192 :
 
  don't forget to name the cube file.   
 
  don't forget to name the cube file.   
 
  '''test.cube_BLW'''  
 
  '''test.cube_BLW'''  
  see also [[VBFile_4-4#gaussiancube.com | gaussiancube file]]
+
  see also [[VBFile_4-3#gaussiancube.com | gaussiancube file]]
  
 +
|}
  
[[VBFile 4-4 | all input files are there]]
+
[[VBFile 4-3 | FILES FOR THE NH3 ... BH3]]
 +
 
 +
|}
 +
 
 +
 
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!<big><big><big>'''Optional exercises - homework'''</big></big></big>
 +
|-
 +
|
 +
 
 +
== 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?
 +
 
 +
 +
* 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.
 +
* Compare the energies to calculate the conjugaison energy.
 +
 
 +
{| class="collapsible collapsed wikitable"
 +
|-
 +
!'''Planar geometry'''
 +
|-
 +
|
 +
<html><pre>
 +
C    6.0  0.0000000000  0.6097325637  1.7490045499
 +
C    6.0  0.0000000000  0.6038280097  0.4085967284
 +
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 :
 +
 
 +
** <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>
  
</big>
+
|}

Dernière version du 14 février 2013 à 08:27

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BLW method & HuLiS program