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= '''Basics of VB theory and XMVB program''' =
 
= '''Basics of VB theory and XMVB program''' =
  
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== Exercise 1 : HF molecule weights ==
  
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The Gamess and XMVB input files for the HF molecule are provided in the ''Exercise'' folder on the tutorial machines. These are VBSCF calculations with the 6-31G(d,p) basis set, with the fragment specification in terms of symmetry-adapted orbitals (''frgtyp=sao''). Then these input files could serve you as templates for the next exercises.
  
{| class="collapsible collapsed wikitable"
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# Just inspect these inputs, run the gamess-xmvb program (using : ''vbrun hf-scf''), and analyze the outputs. Which structure(s) should be kept in further BOVB calculations ?
|-
 
!<big><big><big>'''Computer exercises'''</big></big></big>
 
|-
 
|
 
== Exercise 1 : Starting up with the H<math>{}_2</math> molecule ==
 
 
 
Two Gamess and XMVB input files for the H<math>{}_2</math> molecule are provided in the ''Exercise'' folder on the tutorial machines :
 
* the file ''h2-atom.xmi'' input uses the fragment specification in terms of atoms (''frgtyp=atom'') ;
 
* the file ''h2-sao.xmi'' input uses the fragment specification in terms of symmetry-adapted orbitals (''frgtyp=sao'').
 
 
 
There are VBSCF calculations with the 6-31G(d,p) basis set. Just inspect these inputs, run the gamess-xmvb program (using : ''vbrun h2-atom'' and : ''vbrun h2-sao'', and analyze the outputs.
 
 
 
Then these input files could serve you as templates for the next exercises.
 
 
 
== Exercise 2 : HF molecule : weights and bond energy ==
 
 
 
# Compute a VBSCF three structure wave function for the HF molecule, using the ''frgtyp=sao'' specification, automatic guess (''guess=auto''), and ''boys'' keyword. Which structure(s) should be kept in further BOVB calculations ?
 
 
# Using VBSCF orbitals as guess orbitals :
 
# Using VBSCF orbitals as guess orbitals :
 
## Compute a L-BOVB wave function on a selected subset of structures ;  
 
## Compute a L-BOVB wave function on a selected subset of structures ;  
 
## Compute a VBCISD wave function, freezing the 1s core orbital of fluorine in the VBCI calculation (''NCOR=1'' option), and printing only structures which have a coefficient superior to 0.01 (''ctol=0.01'' option) ;
 
## Compute a VBCISD wave function, freezing the 1s core orbital of fluorine in the VBCI calculation (''NCOR=1'' option), and printing only structures which have a coefficient superior to 0.01 (''ctol=0.01'' option) ;
 
## Compare structure weights at the VBSCF, L-BOVB and VBCI levels
 
## Compare structure weights at the VBSCF, L-BOVB and VBCI levels
# Compute bond energies at the L-BOVB and VBCISD levels.
 
 
{| class="collapsible collapsed wikitable"
 
|-
 
!'''Remark'''
 
|-
 
|
 
We do not recommend to use the ''frgtyp=atom'' specification together with the automatic guess (''guess=auto''). With ''frgtyp=atom'' you should specify orbital guess from HF MOs through an extra $gus section (see manual, and next exercises).
 
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{| class="collapsible collapsed wikitable"
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* To compute the bond energy at the BOVB level, you can simply use the ROHF energies computed with Gamess for the separate H and F atoms, as the L-BOVB wave function dissociate to uncorrelated H+F fragments.
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* To go from L-VBSCF to L-BOVB level, starting from the input of the VBSCF input file (.xmi) as a template, you should simply make the following changes in it :
* To compute the bond energy at the VBCISD level, you should however compute the separate fragments at this level of theory.
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*# add the ''bovb'' keyword in "$ctrl" section ;
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*# change ''iscf=5'' by ''iscf=2'' ;
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*# suppress structures with minor weights at the VBSCF level (e.g 1% or less) from the '$str'' section
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*# use "guess=read" option to read previous converged VBSCF orbitals
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* Then to use L-VBSCF orbitals as guess orbitals, copy the file: ''file_name-l-vbscf.orb'' which was created in the VBSCF step, to a new file : ''file_name-l-bovb.gus''.
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* To go from L-VBSCF to the VBCI wave functions, starting from the input of the VBSCF input file as a template, you should simply make the following changes :
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*# add the corresponding VBCI keyword in the ''$ctrl'' section (''VBCISD'' here) ;
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*# use "guess=read" option and previous converged VBSCF orbitals as ''input.gus'' guess file
 
|}
 
|}
  
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<big>[[General_guidelines_for_BOVB_calculations| >> general guidelines for BOVB calculations]]</big>
 
<big>[[General_guidelines_for_BOVB_calculations| >> general guidelines for BOVB calculations]]</big>
  
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== Exercise 2 : F<math>{}_2</math> molecule and bond energy ==
  
== Exercise 3 : F<math>{}_2</math> molecule and charge-shift resonance energy ==
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To answer the first two questions below, we strongly recommend you to comment your input files as extensively as what was done in the input files of the previous exercise. This will allow you to clearly see if you understand all components of an XMVB input.
 
 
# Compute a VBSCF wave function for the F<math>{}_2</math> molecule, using the cc-pvtz basis set, and with inactive orbitals localized on only one of the fluorine atoms ;
 
## first using the ''frgtyp=sao'' specification and automatic guess (''guess=auto'') ;
 
## second using the ''frgtyp=atom'' specification and providing HF MOs as guess orbital through an extra $Gus section in the xmvb input
 
# D-BOVB level :
 
## Compute a L-BOVB wave function using VBSCF orbitals as guess orbitals ;
 
## Starting from the previous solution, compute a D-BOVB solution, by allowing only the inactive orbitals to delocalize onto the two atoms, while the active orbitals are kept frozen. Compare total energy with the previous level.
 
# π-D-BOVB level :
 
## Recompute a π-D-BOVB solution for the F<math>{}_2</math> molecule (see : [[General_guidelines_for_BOVB_calculations#High_symmetry_case:| >> see "high symmetry case" in the "general guidelines for BOVB calculations"]].
 
## Compare the total energy and weights with the previous level.
 
# We want to calculate the charge-shift resonance energy (RE_<sub>CS</sub>) for the F<math>{}_2</math> molecule. For that, we have to compute a VB wave-function corresponding to a single covalent structure, and take the energy difference with the full (covalent+ionic) wave-function.
 
## Compute a purely covalent wave function for F<math>{}_2</math> at the VBSCF level. What would be the L-BOVB solution ?
 
## Compute a purely covalent wave function for F<math>{}_2</math> at the D-BOVB level.
 
## Deduce the RE_<sub>CS</sub> at the VBSCF, L-BOVB and D-BOVB. Compare it with the estimated exact bond energy : 39.0 kcal/mol).
 
 
 
 
 
<big><font color=red>'''***** If you have not finished these first three exercises by the end of tutorial session 1, we recommend that you move directly to [[VBTutorial2|tutorial 2]] *****'''</font></big>
 
 
 
  
== Exercice 4 '''(optional)''' : Solvent effect on C(Me)<math>{}_3</math>-Cl weights ==
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For the first question below, you can use the ''hf-scf.xmi'' input file from the previous exercise as a template.
  
# C(Me)<math>{}_3</math>-Cl at equilibrium geometry :
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# Compute a L-VBSCF wave function for the F<math>{}_2</math> molecule (all inactive orbitals localized on the fluorine atoms), using:
## Compute a VBSCF wave function using ''frgtyp=atom'' and a $Gus section to specify guess orbitals. The active electron pair will be the C-Cl bond, and all inactive orbitals should be localized either on Cl or on the C(Me3) fragment. Which structures should be kept in further BOVB calculations ?
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#* the ''frgtyp=sao'' specification ;
## Redo the VBSCF calculation reading the orbital file obtained at the previous step as guess file, and now requesting a boys localization (keyword : ''boys''). Compare the VBSCF orbitals obtained with and without the ''boys'' keyword (you can use the ''moldendat'' utility and them ''molden'' to display them).
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#* the ''boys'' keyword in the ''$ctrl'' section ;
## Compute a L-BOVB wave function.
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#* automatic guess (''guess=auto'' option) ;
## Compute a D-BOVB wave function, by freezing the active orbitals, and delocalizing all inactive orbitals onto the whole molecule (see also : [[General_guidelines_for_BOVB_calculations| >> general guidelines for BOVB calculations]]).
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# BOVB level :
# Starting from guess orbitals obtained at equilibrium geometry, redo the D-BOVB calculation for the large inter fragment distance. How does the weights of the different structures evolve when the molecule is stretched ?
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## First, compute a π-D-VBSCF wave function using previous VBSCF orbitals as guess orbitals. To do that, you should allow the π inactive orbitals of fluorine to delocalize onto the two atoms, while keeping all <math>\sigma</math> (active and inactive) orbitals localized (see also : [[General_guidelines_for_BOVB_calculations#High_symmetry_case:| >> see "high symmetry case" in the "general guidelines for BOVB calculations"]])
# Redo the D-BOVB calculations at equilibrium geometry and large distance using VBPCM for water. How does the weights change with solvation effects ?
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## Compute then a π-D-BOVB solution for the F<math>{}_2</math> molecule, starting from previous orbitals as guess.
 +
# VBCI : compute a VBCI(D,S) wave function (''vbcids'' keyword in the ''$ctrl'' section, see pp. 11 and 44 of [http://wiki.lct.jussieu.fr/workshop/images/7/71/XMVB_Manual_V20.pdf XMVB Manual]), freezing the core orbitals of fluorine in the calculation.
 +
# Deduce F<math>{}_2</math> bond energies at both the π-D-BOVB and VBCI(D,S) levels.
 +
# Recompute the same L-VBSCF wave-function, this time specifying converged RHF MOs as guess orbitals, through the ''guess=mo'' option in the $ctrl section together with an extra ''$gus'' section in the input (see ''hints'' below, [http://wiki.lct.jussieu.fr/workshop/images/7/71/XMVB_Manual_V20.pdf XMVB Manual], and/or [http://wiki.lct.jussieu.fr/workshop/images/8/85/Practical_guide_for_VB_calculations.pdf Peifeng Su's lecture slides]). This option is not necessary for this exercise, but it will prove useful for Exercise 1 of tutorial 3, and in the general case.
  
 
{| class="collapsible collapsed wikitable"
 
{| class="collapsible collapsed wikitable"
 
|-
 
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!''Hints and remarks''
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!'''Hints and remarks'''
 
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|-
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* It is strongly advisable to use the ''boys'' keyword at the VBSCF step, as it will provide more physically meaningful orbitals for the next BOVB calculations (the same remark would hold with VBCI)
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To prepare a ''$gus'' section for reading RHF MOs as a guess (''guess=mo'' option)  :
* To reperform D-BOVB at large interatomic distances (question n°2), you have to proceed in two steps :
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# first compute gamess RHF solution only (remove : ''vbtyp=xmvb'' in the $control section of Gamess input ''my_file.inp'')
** starting from the orbitals converged at equilibrium distances (question n°1.3) as a guess : reperform a L-BOVB first at large interatomic distances ;
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# read the RHF orbitals in Gamess output (''my_file.out'') and identify those who could be good guess orbitals for your different VB orbitals. For instance :
** then, starting from the orbitals just obtained as a guess do a D-BOVB calculation.
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#* MO n°1 is a symmetry combination for 1s cores of the two Fluorine, so this same MO n°1 could be used as a guess orbital for the two localized VB orbitals corresponding to the fluorine cores (MO n°2 is the corresponding antisymmetric combination, so it bears the same information) ;
* Same remark for solvent calculations : you can start from converged gas phase L-BOVB orbitals as guess, but you'll have first to reperform L-BOVB and then D-BOVB.
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#* MO n°3 (or alternatively MO n°4) could be used as guess orbital for the two VB orbitals describing the 2s lone pairs of the fluorine atoms ;
|}
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#* MO n°5 and 7 (or alternatively 6 and 8) could be used as guess for the <math>\pi_x</math> and <math>\pi_y</math>  lone pairs ;
 +
#* last, MO n°8 describe the <math>\sigma</math> bond, and could be used as guess for the two active orbitals
 +
# Then build the ''$gus'' section in XMVB input accordingly, and start your calculation (don't forget to restore ''vbtyp=xmvb'' in the $control section of Gamess input)
 +
 
 +
Note that using automatic guess works fine in a simple case like this one, using ''guess=mo'' simply accelerates convergence. However, for larger molecules, specifying a good orbital guess through ''guess=mo'' and an extra $gus section will often be useful.
  
|}
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For VBCI(D,S) calculation on difluorine : don't forget to add ''NCOR=2'' and ''ctol=0.01'' options in the ''$Ctrl'' section.
  
 +
To compute the bond energies :
 +
* at the BOVB level, you can simply use the ROHF energies computed with Gamess for the separate fragments (F atoms here), because the L- and D-BOVB wave functions (like the VBSCF one) dissociate to uncorrelated separate fragments
 +
* at the VBCI(D,S) level, you have to compute the separate fragments at this level of theory, and the ''Davidson corrected energy'' should be used. Don't forget to add ''nmul=2'' in the ''$Ctrl'' section to specify doublet spin state for the fluorine atom.
  
{| class="collapsible collapsed wikitable"
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Note that a more accurate BOVB bond energy could be obtained by pushing to [[The_SD_BOVB_method|higher SD-BOVB level]], and with VBCISD by using a larger basis set.
|-
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|}
!<big><big><big>'''Paper exercise (optional - homework)'''</big></big></big>
 
|-
 
|
 
  
==Exercise 5 : '''The lone pairs of H<sub>2</sub>O'''==
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==Exercise 3 : '''The lone pairs of H<sub>2</sub>O'''==
  
 
(for further reading, see S. Shaik and P.C. Hiberty, '''"The Chemist's Guide to VB theory"''', Wiley, Hoboken, New Jersey, 2008, pp. 107-109)
 
(for further reading, see S. Shaik and P.C. Hiberty, '''"The Chemist's Guide to VB theory"''', Wiley, Hoboken, New Jersey, 2008, pp. 107-109)
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# Focusing on the lone pairs only, write the four-electron single-determinants <math>\Psi_{\textrm{MO}} </math> and <math>\Psi_{\textrm{VB}} </math> .
 
# Focusing on the lone pairs only, write the four-electron single-determinants <math>\Psi_{\textrm{MO}} </math> and <math>\Psi_{\textrm{VB}} </math> .
 
# Expand <math>\Psi_{\textrm{VB}} </math> into elementary determinants containing only <math>n</math> and <math>p</math> orbitals, eliminate determinants having two identical spinorbitals, and show the equivalence between <math>\Psi_{\textrm{VB}}</math> and <math>\Psi_{\textrm{MO}}</math>.
 
# Expand <math>\Psi_{\textrm{VB}} </math> into elementary determinants containing only <math>n</math> and <math>p</math> orbitals, eliminate determinants having two identical spinorbitals, and show the equivalence between <math>\Psi_{\textrm{VB}}</math> and <math>\Psi_{\textrm{MO}}</math>.
# We now remove one electron from H<math>{}_2</math>O. Write the two possible VB structures <math>\Phi_1</math> and <math>\Phi_2</math> in the VB framework.  
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# We now remove one electron from H<math>{}_2</math>O. Write the two possible VB structures <math>\Phi_1</math> and <math>\Phi_2</math> in the VB framework. By convention, one may write the doubly occupied lone pair first, then the singly occupied one.  
 
# The two ionized states are the symmetry-adapted combinations [[File:ion-neg.png|90px]] and [[File:ion-pos.png|90px]]. From the sign of the hamiltonian matrix element <math>\langle \Phi_1 \vert \hat{H} \vert \Phi_2 \rangle</math>, give the energy ordering of the two ionized states.
 
# The two ionized states are the symmetry-adapted combinations [[File:ion-neg.png|90px]] and [[File:ion-pos.png|90px]]. From the sign of the hamiltonian matrix element <math>\langle \Phi_1 \vert \hat{H} \vert \Phi_2 \rangle</math>, give the energy ordering of the two ionized states.
 
# By expanding the two ionized states into elementary determinants (dropping the normalization constants), show that they are equivalent, respectively, to the MO configurations <math>\vert nn\bar{p}\vert</math>  and <math>\vert pp\bar{n}\vert</math>.
 
# By expanding the two ionized states into elementary determinants (dropping the normalization constants), show that they are equivalent, respectively, to the MO configurations <math>\vert nn\bar{p}\vert</math>  and <math>\vert pp\bar{n}\vert</math>.
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Dernière version du 18 janvier 2013 à 15:56

<<< VB tutorials main page


Basics of VB theory and XMVB program

Exercise 1 : HF molecule weights

The Gamess and XMVB input files for the HF molecule are provided in the Exercise folder on the tutorial machines. These are VBSCF calculations with the 6-31G(d,p) basis set, with the fragment specification in terms of symmetry-adapted orbitals (frgtyp=sao). Then these input files could serve you as templates for the next exercises.

  1. Just inspect these inputs, run the gamess-xmvb program (using : vbrun hf-scf), and analyze the outputs. Which structure(s) should be kept in further BOVB calculations ?
  2. Using VBSCF orbitals as guess orbitals :
    1. Compute a L-BOVB wave function on a selected subset of structures ;
    2. Compute a VBCISD wave function, freezing the 1s core orbital of fluorine in the VBCI calculation (NCOR=1 option), and printing only structures which have a coefficient superior to 0.01 (ctol=0.01 option) ;
    3. Compare structure weights at the VBSCF, L-BOVB and VBCI levels


>> general guidelines for BOVB calculations

Exercise 2 : F<math>{}_2</math> molecule and bond energy

To answer the first two questions below, we strongly recommend you to comment your input files as extensively as what was done in the input files of the previous exercise. This will allow you to clearly see if you understand all components of an XMVB input.

For the first question below, you can use the hf-scf.xmi input file from the previous exercise as a template.

  1. Compute a L-VBSCF wave function for the F<math>{}_2</math> molecule (all inactive orbitals localized on the fluorine atoms), using:
    • the frgtyp=sao specification ;
    • the boys keyword in the $ctrl section ;
    • automatic guess (guess=auto option) ;
  2. BOVB level :
    1. First, compute a π-D-VBSCF wave function using previous VBSCF orbitals as guess orbitals. To do that, you should allow the π inactive orbitals of fluorine to delocalize onto the two atoms, while keeping all <math>\sigma</math> (active and inactive) orbitals localized (see also : >> see "high symmetry case" in the "general guidelines for BOVB calculations")
    2. Compute then a π-D-BOVB solution for the F<math>{}_2</math> molecule, starting from previous orbitals as guess.
  3. VBCI : compute a VBCI(D,S) wave function (vbcids keyword in the $ctrl section, see pp. 11 and 44 of XMVB Manual), freezing the core orbitals of fluorine in the calculation.
  4. Deduce F<math>{}_2</math> bond energies at both the π-D-BOVB and VBCI(D,S) levels.
  5. Recompute the same L-VBSCF wave-function, this time specifying converged RHF MOs as guess orbitals, through the guess=mo option in the $ctrl section together with an extra $gus section in the input (see hints below, XMVB Manual, and/or Peifeng Su's lecture slides). This option is not necessary for this exercise, but it will prove useful for Exercise 1 of tutorial 3, and in the general case.

Exercise 3 : The lone pairs of H2O

(for further reading, see S. Shaik and P.C. Hiberty, "The Chemist's Guide to VB theory", Wiley, Hoboken, New Jersey, 2008, pp. 107-109)

This exercise aims at comparing two descriptions of the lone pairs of H<math>{}_2</math>O : (i) the MO description in terms of non-equivalent canonical MOs and (ii) the « rabbit-ear » VB description in terms of two equivalent hybrid orbitals.

H2o ex1.png
<math>\Psi_{\textrm{MO}}</math>   <math>\Psi_{\textrm{VB}}</math>


  1. Focusing on the lone pairs only, write the four-electron single-determinants <math>\Psi_{\textrm{MO}} </math> and <math>\Psi_{\textrm{VB}} </math> .
  2. Expand <math>\Psi_{\textrm{VB}} </math> into elementary determinants containing only <math>n</math> and <math>p</math> orbitals, eliminate determinants having two identical spinorbitals, and show the equivalence between <math>\Psi_{\textrm{VB}}</math> and <math>\Psi_{\textrm{MO}}</math>.
  3. We now remove one electron from H<math>{}_2</math>O. Write the two possible VB structures <math>\Phi_1</math> and <math>\Phi_2</math> in the VB framework. By convention, one may write the doubly occupied lone pair first, then the singly occupied one.
  4. The two ionized states are the symmetry-adapted combinations Ion-neg.png and Ion-pos.png. From the sign of the hamiltonian matrix element <math>\langle \Phi_1 \vert \hat{H} \vert \Phi_2 \rangle</math>, give the energy ordering of the two ionized states.
  5. By expanding the two ionized states into elementary determinants (dropping the normalization constants), show that they are equivalent, respectively, to the MO configurations <math>\vert nn\bar{p}\vert</math> and <math>\vert pp\bar{n}\vert</math>.