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== Exercise 1 : Computation of state correlation Diagrams for a 3 centers / 4 electrons system ==
 
== Exercise 1 : Computation of state correlation Diagrams for a 3 centers / 4 electrons system ==
In this exercise the <math>\textrm{S}_{\textrm{N}}2</math> reaction Cl<math>{}^{-}</math> + CH3Cl -> ClCH3 + Cl<math>{}^{-}</math> will be studied in both vacuum and solution. Valence Bond State Correlation Diagrams (VBSCD) will be constructed at <math>\pi</math>-D-BOVB level. There are two parts in this exercise: basic part and optional part. The basic part is performed with MCP-DZP basis set in which the inner orbitals in Cl and C are described with MCP pseudo potential. The optional part is performed with 6-31+G* basis set, using the general specification for the xmvb input (expert users). Only reactant and transition state will be computed in this exercise, which is sufficient to build the VBSCD diagrams. <br>
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In this exercise the <math>\textrm{S}_{\textrm{N}}2</math> reaction Cl<math>{}^{-}</math> + CH<math>{}_3</math>Cl -> ClCH<math>{}_3</math> + Cl<math>{}^{-}</math> will be studied in both vacuum and solution. Valence Bond State Correlation Diagrams (VBSCD) will be constructed at <math>\pi</math>-D-BOVB level. There are two parts in this exercise: basic part and optional part. The basic part is performed with MCP-DZP basis set in which the inner orbitals in Cl and C are described with MCP pseudo potential. The optional part is performed with 6-31+G* basis set, using the general specification for the xmvb input (expert users). Only reactant and transition state will be computed in this exercise, which is sufficient to build the VBSCD diagrams. <br>
  
 
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==== 1. Compute the Energies and Wavefunctions at Reactant and Transition State with Different Sets of VB Structures====
 
==== 1. Compute the Energies and Wavefunctions at Reactant and Transition State with Different Sets of VB Structures====
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We advise you to create the first xmvb input file (''.xmi'' file) for this study starting from a ''.xmi'' file taken from tutorial1 as a template. Alternatively, you may copy the input file corresponding for the first calculation of this study (L-VBSCF on reactant state geometry in vacuum) from the ''answer'' folder of this exercise (''cp answer/rs_vac_vbscf.xmi .''), run directly the first calculation, inspect input/outputs, and then use this ''.xmi'' file as a template for the following calculations.
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# Write the following VB structure sets for a 3 centers / 4 electrons system :
 
# Write the following VB structure sets for a 3 centers / 4 electrons system :
 
## all structures;
 
## all structures;
 
## minimal structures for reactant;
 
## minimal structures for reactant;
 
## minimal structures for product.
 
## minimal structures for product.
 +
# How would you define your different fragment orbitals for this calculation (''$frag'' section) ? You will find the answer for this case is in the [[General_guidelines_for_BOVB_calculations#Recommended_definition_for_the_orbital_blocks|"recommended definition for the orbital blocks" section of the "practical for BOVB calculations" document]]
 
# Perform <math>\pi</math>-D-BOVB calculation for reactant [[General_guidelines_for_BOVB_calculations#High_symmetry_case:|(see "high symmetry cases" here)]]:
 
# Perform <math>\pi</math>-D-BOVB calculation for reactant [[General_guidelines_for_BOVB_calculations#High_symmetry_case:|(see "high symmetry cases" here)]]:
 
## Perform all-structure <math>\pi</math>-D-BOVB calculation as following:
 
## Perform all-structure <math>\pi</math>-D-BOVB calculation as following:
### Perform L-VBSCF calculation with "''orbtyp=hao frgtyp=sao guess=mo''", in which the orbitals are all localized on the Cl and CH<math>{}_3</math> groups;
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### Perform L-VBSCF (file name: rs_vac_vbscf) calculation with "''orbtyp=hao frgtyp=sao guess=mo''", in which the orbitals are all localized on the Cl and CH<math>{}_3</math> groups;
### Perform π-D-VBSCF calculation where <math>\pi</math> orbitals are delocalized in the whole system and the <math>\sigma</math> orbitals are kept localized. Use the L-VBSCF orbitals as initial guess;
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### Perform π-D-VBSCF calculation where <math>\pi</math> orbitals are delocalized in the whole system and the <math>\sigma</math> orbitals are kept localized (file name: rs_vac_d-vbscf). Use the L-VBSCF orbitals as initial guess;
### Perform π-D-BOVB calculation with π-D-VBSCF orbitals as initial guess.
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### Perform π-D-BOVB (file name: rs_vac_d-bovb) calculation with π-D-VBSCF orbitals as initial guess.
## Perform <math>\pi</math>-D-BOVB calculations with minimal structures for reactant and product with the same procedure as all-structure calculation.
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## Perform <math>\pi</math>-D-BOVB calculations with minimal structures for reactant (file names: rs_vac_*_rs) and product (file names: rs_vac_*_ps) with the same procedure as all-structure calculation.
# Perform <math>\pi</math>-D-BOVB calculation for transition state. The procedure is the same as step 2.
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# Perform <math>\pi</math>-D-BOVB calculation for transition state (file names: ts_vac_*). The procedure is the same as step 2.
 
# Perform <math>\pi</math>-D-BOVB/PCM calculations for reactant:
 
# Perform <math>\pi</math>-D-BOVB/PCM calculations for reactant:
## Perform all-structure <math>\pi</math>-D-BOVB/PCM calculation for the reactant in following steps: 
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## Perform all-structure <math>\pi</math>-D-BOVB/PCM (file name: rs_pcm_d-bovb) calculation for the reactant, starting directly from the <math>\pi</math>-D-BOVB orbitals computed in vacuum (2.1)
### Perform L-VBSCF/PCM calculation with L-VBSCF orbitals as initial guess;
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## Perform <math>\pi</math>-D-BOVB/PCM calculations with minimal structures for reactant (file name: rs_pcm_d-bovb_rs) and product (file name: rs_pcm_d-bovb), also starting from the corresponding <math>\pi</math>-D-BOVB orbitals computed in vacuum (2.2)
### Perform π-D-VBSCF/PCM calculation with L-VBSCF/PCM orbitals as initial guess;
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# Perform BOVB/PCM calculations for transition state (file names: rs_pcm_d-bovb*) with the same procedure as step 4.
### Perform π-D-BOVB/PCM calculation with π-D-VBSCF/PCM orbitals as initial guess.
 
## Perform <math>\pi</math>-D-BOVB/PCM calculations with minimal structures for reactant and product in the sames steps as all structure calculation.
 
# Perform BOVB/PCM calculations for transition state with the same procedure as step 4.
 
  
 
==== 2. Analysis: Wavefunctions and Energies====
 
==== 2. Analysis: Wavefunctions and Energies====
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# Compute the Barrier height of the <math>\textrm{S}_{\textrm{N}}2</math> reaction in both vacuum and solution. See the difference of the barrier heights, and find out the reason.
 
# Compute the Barrier height of the <math>\textrm{S}_{\textrm{N}}2</math> reaction in both vacuum and solution. See the difference of the barrier heights, and find out the reason.
 
# Compare the energies of reactant and product structures at reactant and transition state geometries, in both vacuum and solution. What's the difference of the energies at different points? Why?
 
# Compare the energies of reactant and product structures at reactant and transition state geometries, in both vacuum and solution. What's the difference of the energies at different points? Why?
# Compute the resonance energies at both reactant and transition state points, see the difference of the resonance energies.
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# Compute the resonance energy at the crossing point of diabatic curves state points in vacuum.
  
 
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|-
 
|-
 
! scope="row"    | BOVB
 
! scope="row"    | BOVB
| 0.228 || 0.228 || 0.041 || 0.494 || 0.004 || 0.004
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| 0.228 || 0.228 || 0.041 || 0.502 ||   ||  
 
|-
 
|-
 
! scope="row"      | VBSCF/PCM
 
! scope="row"      | VBSCF/PCM
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|-
 
|-
 
! scope="row"      | BOVB/PCM
 
! scope="row"      | BOVB/PCM
|0.215 || 0.215 || 0.035 || 0.528 || 0.003 || 0.003
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|0.215 || 0.215 || 0.034 || 0.536 ||   ||  
 
|}
 
|}
 
</center>
 
</center>
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|-
 
|-
 
! scope="row"    | Trasition State
 
! scope="row"    | Trasition State
| -36.98034  || -37.02691 || -37.06980 || -37.11506
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| -36.98034  || -37.02508 || -37.06980 || -37.11346
 
|-
 
|-
 
! scope="row"      | Barrier
 
! scope="row"      | Barrier
| 33.6 || 16.9 || 41.8 || 25.4
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| 33.6 || 16.2 || 41.8 || 25.2
 
|}
 
|}
 
</center>
 
</center>
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! scope="col" | VBSCF
 
! scope="col" | VBSCF
 
! scope="col" | BOVB
 
! scope="col" | BOVB
! scope="col" | VBSCF/PCM
 
 
! scope="col" | BOVB/PCM
 
! scope="col" | BOVB/PCM
 
|-  
 
|-  
 
! scope="row"    | All Structures
 
! scope="row"    | All Structures
| -36.98034 ||-37.02691 || -37.06980 || -37.11506
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| -36.98034 ||-37.02508 || -37.11346
 
|-
 
|-
 
! scope="row" | Reactant
 
! scope="row" | Reactant
| -36.95812 || -36.97494 || -37.05258 || -37.06909
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| -36.95984 || -36.98719 || -37.07951
 
|-
 
|-
 
! scope="row" | Product
 
! scope="row" | Product
| -36.95812 ||-36.97494 ||-37.05258 || -37.06910
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| -36.95984 ||-36.98718  || -37.07949
 
|-
 
|-
 
! scope="row"      | Resonance Energy
 
! scope="row"      | Resonance Energy
| 13.9 || 32.6 || 10.8 || 28.8
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| 12.9 || 23.8 || 21.3
 
|}
 
|}
 
</center>
 
</center>
  
=====Resonance Energ of Transition State=====
 
<center>
 
{| border="1"
 
|+ Energies(a.u.) and Resonance Energies (kcal/mol) of Reactant
 
! scope="col" |
 
! scope="col" | VBSCF
 
! scope="col" | BOVB
 
! scope="col" | VBSCF/PCM
 
! scope="col" | BOVB/PCM
 
|-
 
! scope="row"    | All Structures
 
| -37.03384 || -37.05387 || -37.13644 || -37.15552
 
|-
 
! scope="row" | Reactant
 
| -37.03354 || -37.05085 || -37.13626 ||-37.15356
 
|-
 
! scope="row" | Product
 
| -36.59694 ||-36.59694 || -36.88408 || -36.88750
 
|-
 
! scope="row"      | Resonance Energy
 
| 0.2 || 1.9 || 0.1 || 1.2
 
|}
 
</center>
 
|}
 
  
|}
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In this part, calculations with BFI section are performed with 6-31+G* basis set, which is desired for the experienced users. The inner orbitals are frozen as HF orbitals in all VB calculations and the valence basis functions are reorganized to hybrid basis functions so that the <math>\sigma</math>, <math>\pi_x</math> and <math>\pi_y</math> spaces can be separated well. A D-BOVB calculation is performed in 2 steps:
+
In this part, calculations with BFI section are performed, which is a technique for the experienced users. The 6-31+G* basis set is used. The inner orbitals are frozen as HF orbitals in all VB calculations and the valence basis functions are reorganized to hybrid basis functions so that the <math>\sigma</math>, <math>\pi_x</math> and <math>\pi_y</math> spaces can be separated well. A D-BOVB calculation is performed in 2 steps:
 
# Perform a VBSCF calculation with <math>\pi</math> orbitals delocalized in the whole system and <math>\sigma</math> orbitals localized on the Cl and CH<math>{}_3</math> groups;
 
# Perform a VBSCF calculation with <math>\pi</math> orbitals delocalized in the whole system and <math>\sigma</math> orbitals localized on the Cl and CH<math>{}_3</math> groups;
 
# Perform a BOVB calculation with VBSCF orbitals as initial guess.
 
# Perform a BOVB calculation with VBSCF orbitals as initial guess.
The VB calculations are the same as the calculations performed above. Try to understand the BFI section, perform the calculations and compare the differences of barrier heights, resonance energies and performances with and without $BFI.
+
The VB calculations are the same as the calculations performed above. Try to understand the BFI section, perform the calculations and compare the differences of barrier heights, resonance energies and cpu performances with and without $BFI.
  
 
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|-
 
|
 
|
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=====Weights of Structures=====
 
=====Weights of Structures=====
 
<center>
 
<center>
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</center>
 
</center>
  
=====Resonance Energ of Transition State=====
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=====Resonance Energies of Reactant=====
 
<center>
 
<center>
 
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|-
 
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== Exercise 2 : computation of H—H + H. -> H. + H—H radical exchange VBSCD diagram ==
 
== Exercise 2 : computation of H—H + H. -> H. + H—H radical exchange VBSCD diagram ==
  
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b - Let us express the various energies and matrix elements in terms of the usual <big><math> \beta </math></big> and  <big><math> S </math></big> integrals between the X and H orbitals:
 
b - Let us express the various energies and matrix elements in terms of the usual <big><math> \beta </math></big> and  <big><math> S </math></big> integrals between the X and H orbitals:
  
<big><math> E_{ind} = 2 \beta S </math></big>
+
<big><math> E_{ind} = \beta S </math></big>
  
 
<big><math> S_{12} = 0.5 </math></big>
 
<big><math> S_{12} = 0.5 </math></big>
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## minimal structures for product.
 
## minimal structures for product.
 
# Perform VBSCF and VBCISD calculations for reactant:
 
# Perform VBSCF and VBCISD calculations for reactant:
## Perform a VBSCF calculation with "''orbtyp=hao''" and "''boys''";
+
## Perform a VBSCF calculation (file name: rs_vbscf) with "''orbtyp=hao''" and "''boys''";
## Perform a VBCISD calculation with VBSCF orbital as initial guess.
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## Perform a VBCISD calculation (file name: rs_vbcisd) with VBSCF orbital as initial guess.
## Perform VBSCF and VBCISD calculations with minimal structures for reactant and product.
+
## Perform VBSCF and VBCISD calculations with minimal structures for reactant (file names: rs_*_rs) and product (file names: rs_*_ps).
# Perform VBSCF and VBCISD calculations for transition state with the same procedure as in step 2.
+
# Perform VBSCF and VBCISD calculations for transition state (file names: ts_*) with the same procedure as in step 2.
  
 
<br>
 
<br>
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5- Allyl radical <math>\pi</math> system is isoelectronic to the <math>H_3</math> radical case.   
 
5- Allyl radical <math>\pi</math> system is isoelectronic to the <math>H_3</math> radical case.   
R correspond to one covalent right coupling (radical on the left carbone atom). P to the radical on the right carbone.  
+
R corresponds to the covalent right coupling (radical on the left carbone atom). P to the covalent right coupling.  
* <math> \Psi^{\neq}  </math> corresponds to the mesomery between these 2 bonding schemes.
+
* <math> \Psi^{\neq}  </math> corresponds to the resonance (mesomery) between these 2 bonding schemes.
 
* <math>\Psi^{\star} </math> to the "through space" (a,c) electronic coupling ("long bond", the radical is centered on the middle atom).
 
* <math>\Psi^{\star} </math> to the "through space" (a,c) electronic coupling ("long bond", the radical is centered on the middle atom).
  
... work in progress
+
The geometrical distortion to make the two states degenerated in allyl radical would be a rotation of the two CH2 end groups: by such a rotation, the resonance structures are destabilized (pi bonds break), and the a-c coupling is re-inforced (sigma bond forms).  
 
 
To make the state degenerated in allyl radical ....
 
  
The end product obtained  from the first excited state of allyl radical ... cyclopropyl radical, that would return to a open radical upon deexcitation.
+
The end product obtained  from the first excited state of allyl radical is a cyclopropyl radical (formation of the a-c bond).
  
  

Dernière version du 18 janvier 2013 à 15:56

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Valence Bond State correlation diagrams

Exercise 1 : Computation of state correlation Diagrams for a 3 centers / 4 electrons system

In this exercise the <math>\textrm{S}_{\textrm{N}}2</math> reaction Cl<math>{}^{-}</math> + CH<math>{}_3</math>Cl -> ClCH<math>{}_3</math> + Cl<math>{}^{-}</math> will be studied in both vacuum and solution. Valence Bond State Correlation Diagrams (VBSCD) will be constructed at <math>\pi</math>-D-BOVB level. There are two parts in this exercise: basic part and optional part. The basic part is performed with MCP-DZP basis set in which the inner orbitals in Cl and C are described with MCP pseudo potential. The optional part is performed with 6-31+G* basis set, using the general specification for the xmvb input (expert users). Only reactant and transition state will be computed in this exercise, which is sufficient to build the VBSCD diagrams.