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BLW method & HuLiS program

To the Tutors

Sason remarks and prospective 2 hours talk +

Philippe's remark on the initially proposed tutorial. are included in bold.

Qualitative

• ?...

Computational

Proposal from Yirong

1. benzene and formamide - focus is on the structural and energetic impact from conjugation, and how to correlate the results with experimental evidences;
2. butadiene - focus is on the conjugation in the planar structure and the hyperconjugation in the staggered structure, and their impact on the rotational barrier;
3. acid-base and H-bonding systems: BLW energy decomposition analyses.
4. visualize the results. I have been using GaussView and ChemDraw, but other graphical software should be fine with me as well.
5. Questions from any participant can be discussed and tested on site.

BLW within GAMESS (Version: MAR-25-2010 R2)

BLW is provided by 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.

INPUT (for new file roblw.src)

The BLW input is that of Gamess supplemented by two groups to define the localization of the electrons.

$BLW group

BLW refers to the Block-Localized Wave function (BLW) method, which is a variant of the ab initio Valence Bond (VB) theory. This code can perform RBLW calculations for close-shell systems and ROBLW calculations for open-shell systems. It can also be combined with the grid-DFT calculations. The algorithm to derive self-consistent BLW is based on:

• 1) E. Gianinetti; M. Raimondi; E. Tornaghi, Int. J. Quant. Chem. 60, 157-166(1996).
• 2) A. Famulari, E. Gianinetti, M. Raimondi, M. Sironi, I. Vandoni, Theor. Chem. Acc. 99, 358-365(1998).
• 3) Y. Mo, S. D. Peyerimhoff, J. Chem. Phys. 109, 1687-1697 (1998).
• 4) Y. Mo, J. Gao, S. D. Peyerimhoff, J. Chem. Phys. 112, 5530-5538 (2000).
• 5) L. Song, Y. Lin, Y. Mo, J. Phys. Chem. A, 111, 8291-8301 (2007).

NBLOCK = number of blocks, the definition of each block shall be listed in $BLWDAT group. If nblock=1, it’s just a regular RHF/ROHF calculation.

ITER = maximum number of BLW cycles (default=50)

SCFCOV = NONE, do not take any actions during the SCF iterations DAMP, use damping of the Fock matrix if energy rises DIIS , selects Pulay's DIIS interpolation (based on FOCK matrix) DDIIS, selects Pulay's DIIS interpolation (based on density matrix) (default=DIIS)

IFZB(1) = an array that lists the blocks to be frozen (orbitals kept unchanged) during the optimization. This is useful to examine individual polarization effects, for example.

To switch DFT calculation to full accuracy since the very first step (for the guess orbitals), de-activate coarse grid and SCF pre-optimization. GAMESS always starts an SCF (Hartree-Fock) and a DFT with coarse grid to accelerate the calculation. But if one needs to obtain the polarized energy, the energy of the first iteration shall be exact. To do so, add the following $DFT group. to the .inp file.

 $DFT NRAD0=96 NLEB0=302 NTHE0=12 NPHI0=24  SWOFF=0.0 $END

$BLWDAT group (required by $BLW)

For each block: NE NBF IFLAG

List of basis functions

NE is the number of electrons of that block. NBF is the number of basis functions of that block. IFLAG is an input control. IFLAG = 0, all the basis functions shall be specified; =1, the basis functions are sequential, and only the first one and the last one need be specified; =-1, this block has all the rest basis functions, thus no further specification.

The initial guess can be setup after the definitions of all blocks. It can be useful if the program fails to obtain convergence or one needs to derive the polarized energy term for the BLW-ED (energy decomposition) analysis. Note that the coefficients of MOs correspond to the list of basis functions in the definition lines of blocks. An blank line separates each blocks.

For example:
--------------------------------
$BLW  NBLOCK=2 $END
$BLWDAT
4 4 0       ← block 1 has 4 electrons and 4 basis functions
1 2 3 4    ← bfs of block 1
4 6 1    ← block 2 has 4 electrons and 6 basis functions
5 10     ← bfs of block 2 is from 5 to 10
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0                ← initial guess for the 2 occupied orbitals(4/2) of block 1 
                             ← a blanck line at the end of the block
1.0 0.0 0.0 0.0 0.0 0.0   
0.0 1.0 0.0 0.0 0.0 0.0    ← initial guess for the 2 occupied orbitals(4/2) of block 2
$END
---------------------------------

Note: Eigenvalues and compositions of BLW-MOs are stored in $SCR/*.blw.

HuLiS : a Huckel based code

Huckel - Lewis

HuLiS is provided by Stephane Humbel (Aix-Marseille Université - France).

This is a "Click-Click" java applet that deals with HuckeL and LewiS concepts. It provides coefficients and weights of mesomeric structures through two different approaches: the energy related approach is a simulated CI (HL-CI); the wave function approach is a projection of Lewis structures onto a Huckel derived wave function(HL-P). This second approach is better.

Written exercices

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.

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 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.

To do

1/ Vertical Resonance Energy - at the geometry of benzene:

 $DATA
 B3LYP/6-311+G*
 C1  
 C     6.0     0.000000     0.000000     1.395201
 C     6.0     1.208097     0.000000     0.697641
 C     6.0     1.208090     0.000000     -0.697641
 C     6.0     0.000000     0.000000     -1.395201
 C     6.0     -1.208090     0.000000     -0.697639
 C     6.0     -1.208090     0.000000     0.697639
 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

2/ Adiabatic Resonance Energy - relax the Lewis structure geometry

3/ Evaluate the space spanned by lewis structures as compared to that of delocalized wave functions

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.

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. [value to get]

3 – With the hulis program: - Draw the benzene and create then the two kékulés structures - Add to the wave function the 3 covalent Dewar structures

Stéphane could you complete this part to add questions about the completude de base.

Access to files :

.inp

Exercice 2 (allyl)

butadiene.xmi

Exercice 3 (title)

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.

1/ Make orbitals of BH3 alone (then NH3) in the geometry of the complex

 $DATA
 BLW-ED Analysis
 C1  
 N   7.0        0.000000    0.000000    0.728869
 H   1.0        0.000000    0.951707    1.095972
 H   1.0        0.824202   -0.475853    1.095972
 H   1.0       -0.824202   -0.475853    1.095972
 B   5.0        0.000000    0.000000   -0.934793
 H   1.0        0.000000   -1.170908   -1.238679
 H   1.0       -1.014036    0.585454   -1.238679
 H   1.0        1.014036    0.585454   -1.238679 
 $END

2/ Let fragment orbitals to polarize in the full complex.

3/ Let delocalize. This is just a standard DFT calculation. (TO CHECK with Yirong)

Preliminary Remarks : B3LYP calculation in Gamess is specified in $CONTRL :

 $CONTRL SCFTYP=RHF DFTTYP=B3LYP runtyp=energy maxit=200 icharg=0 $END

And 6-31G(d) basis set is requested with

  $BASIS  GBASIS=N31 NGAUSS=6 NDFUNC=1 $END

Step by step help :

1/ Perform a NH3 BLW calculation of the fragment alone in the geometry of the complexe with $BLW NBLOCK=1 and keep the .blw file for next step (same for BH3).

We obtain

nh3.log: FINAL R-B3LYP ENERGY IS -56.5111505350

bh3.log: FINAL R-B3LYP ENERGY IS -26.5644674370

= > summ = -83.07561797

2/ Do the complex in a NBLOCK=2 BLW calculation and see 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.

At this stage, we can want to do the calculation at full accuracy from the very first step. The following line avoid initial SCF cycles (SWOFF=0.0), and initial coarse grid DFT steps :

 $DFT SWOFF=0.0 NRAD0=96 NLEB0=302 NTHE0=12 NPHI0=24 $END

We obtain

ITER 1 E(RBLW) = -83.05921870

FINAL R-B3LYP ENERGY IS -83.0932178520

3/ We let not only the doublet to delocalize but all electrons. TO CHECK with Yirong

We obtain

FINAL R-B3LYP ENERGY IS -83.1480131227 AFTER 12 ITERATIONS

all input files are there