Différences entre les versions de « VBTutorial3 »
Ligne 31 : | Ligne 31 : | ||
## 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 (''$frag'' section) ? You will find the answer for this case is in the [ | + | # How would you define your different fragment orbitals for this calculation (''$frag'' section) ? You will find the answer for this case is in the [[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: |
Version du 18 juillet 2012 à 18:24
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.
Note:How to perform a VBPCM calculation |
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A VBPCM calculation is performed in the similar way as the VB calculations in vacuum. One should prepare a GAMESS input file with solvent assigned such as: The details of PCM calculation in the GAMESS can be found in GAMESS manual. Keyword "VBTYP=XMVB" in CONTRL section is also essential. After the GAMESS input file is prepared, an XMI file with keyword "VBPCM" should be prepared with the same file name as GAMESS input file. In the current XMVB package, VBSCF/PCM and BOVB/PCM calculations are both supported. |
Basic part |
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1. Compute the Energies and Wavefunctions at Reactant and Transition State with Different Sets of VB StructuresWe 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.
2. Analysis: Wavefunctions and Energies
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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:
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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>> general guidelines for BOVB calculations
Optional exercises - Homework | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Exercise 2 : computation of H—H + H. -> H. + H—H radical exchange VBSCD diagram1/ Paper exercise :a/ Considering the following radical exchange process: <math> X^{\bullet} + A-Y \rightarrow X-A + ^{\bullet}Y </math> (X = A = Y = hydrogen atom) Write the HL wave functions for R and R* and derive the value of G using semiempirical VB theory. Hints : 1) write the wave functions of R and R* so that their overlap is positive; 2) neglect the overlap beween the external atoms X and Y, and neglect the overlap between two different determinants. b/ Considering the following reaction:
<math>
X^{\bullet} + H-X \rightarrow X-H +^{\bullet}X
</math> <math>RE = [H_{12}-E_{ind}S_{12}]/(1+S_{12}) </math> where <math> E_{ind} </math> is the energy of an individual VB structure, and <math> S_{12} </math> and <math> H_{12} </math> are respectively the overlap and Hamiltonian matrix element between R and R*. c/ It is known that for strong binders, at any given bonding distance the singlet-triplet transition energy is larger than twice the bonding energy of the dimer at equilibrium distance, so that one can write the approximate expression <math>\Delta E_{ST} </math>' <math> = 2 BDE </math>, where <math> BDE </math> is the bonding energy of the dimer at equilibrium distance. Using the latter expression, express the avoided crossing term <math> B </math> as a function of the bonding energy of <math> H_{2}</math>.
2/ Computer exerciseVBSCD for H—H + H. -> H. + H—H at VBSCF then VBCISD level. In this exercise the VBSCD for H—H + H. -> H. + H—H at VBSCF then VBCISD level will be computed with 6-31G**. Computations for reactant and transition state are requested and other points are optional for advanced users.
Compute the Energies and Wavefunctions at Reactant and Transition State with Different Sets of VB Structures
Exercise 3 (paper exercise) : Conical intersection in H3• radical(for further reading, see S. Shaik and P.C. Hiberty, "The Chemist's Guide to VB theory", Wiley, Hoboken, New Jersey, 2008, pp. 157-161, exercises 6.11-6.14 pp. 174-176, and answers to the exercises pp. 188-192. Consider three hydrogen atoms Ha, Hb, Hc, with respective atomic orbitals a, b and c, and the two VB structures ] and ] . The Ha-Hb and Hb-Hc distances are equal.
Appendix : Thumb rules for the calculations of effective Hamiltonian matrix elements between determinants.
<math> <D|H|D'>=<|...i\overline{j}...||H||...\overline{i}j...|>= -2 \beta_{ij} S_{ij}</math> (for <math>D</math>, <math>D'</math> differing by spin inversion of two spin-orbitals)
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