BSSE

Calculation of Basis Set Superposition Error

Instruction

In this lesson we are going to study the effect of computational chemistry method and size of basis set on the basis set superposition error for a simple water model and discuss about the comparison on size of model system. We will create monomer and dimer water models and do optimize the molecule to find out the most stable structure for those by using various methods; with two basis set used; 3-21G and aug-cc-pvtZ. All of computational probably may be calculated with Gaussian and visualized by Gaussview programs. Then we would calculate and compare the total energy as well as error between with and without using BSSE correction on our studied dimer of water model. The counterpoise parameter of this model will be also approximated.

Keywords: Dispersion correction, Effect of basis set, BSSE

∆E(AB) = E(AB|AB) − E(AB|A) − E(AB|B)    BSSE correction

∆E(AB) = E(AB|AB) − E(A|A)  − E(B|B)     No BSSE correction

Counterpoise BSSE = ∆E(BSSE) - ∆E(Non-BSSE)

where E(a|b) denote Energy of optimized geometry of b calculated using basis set a. [1]

Model system and computational details

Method: HF, MP2, and DFT

Functional (for DFT): B3LYP with and without dispersion correction [2]

Basis set: - 3-21G (small) and aug-cc-PVTz (big)

Ex. of Gaussian's input file for BSSE calculation

%chk=dimer-water-b3lyp-bigbasis-bsse.chk

%mem=800MW

%nproc=2

#p Opt Freq SCF(tight) B3LYP/aug-cc-PVTz  gfinput counterpoise=2    ! Input calculation setting deck

BSSE Correction: water dimer

0 1 0 1 0 1                                                         ! Charge and Multiplicity for whole system,

O       -0.006859   -1.448901    0.000000,1                         ! fragment, 1 and fragment 2, respectively.

H       -0.411233   -1.840395    0.754906,1

H       -0.411233   -1.840395   -0.754906,1

O       -0.006859    1.588958    0.000000,2

H        0.056868    0.646169    0.000000,2

H        0.875345    1.914160    0.000000,2

Ex. Comparison water molecule for before and after optimization.

Before (left) and after (right) optimization using Density Functional Theory (DFT) calculation for single water molecule. The O--H bond distance for these two structures are

Ex. 3D Optimized structure of dimer water system calculated at B3LYP/aug-cc-pvtz

This dimer water molecule was carried out using DFT calculation at level of B3LYP/aug-cc-PVTZ. The selected structural parameter of interest are the bond distance between oxygen atom and hydrogen on an adjacent molecule which is of about 0.9 angstroms. The interaction between those is hydrogen bond.

Computational results

The data below is the calculated total energies and different energies as well as comparison of counterpoise BSSE in A.U. and kcal/mol.

Example of an analyzed BSSE calculation using my home-made script to extract computed energy.

Run by nutt at black.localdomain on Wed Jul  5 18:49:35 +07 2017

--------------------------------------------------------------------------------------------------------------

File Name: ./hf-small/dimer-hf-small-bsse.log    Standard basis: 3-21G (6D, 7F)

E(AB|AB)  =  -151.189403605  A.U.

 E(AB|A)  =  -75.5930128444  A.U.

 E(AB|B)  =  -75.5867354514  A.U.

 E(A|A)   =  -75.5859247853  A.U.

 E(B|B)   =  -75.5859153974  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0096553092  A.U.  =  -6.0587354889276  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0175634223  A.U.  =  -11.0211001835169  kcal/mol

Counterpoise BSSE = .0079081131  A.U.  =  4.9623646945893  kcal/mol

--------------------------------------------------------------------------------------------------------------

File Name: ./hf-big/dimer-hf-big-bsse.log    Standard basis: Aug-CC-pVTZ (5D, 7F)

E(AB|AB)  =  -152.128367980  A.U.

 E(AB|A)  =  -76.0612614459  A.U.

 E(AB|B)  =  -76.0612241877  A.U.

 E(A|A)   =  -76.0612000125  A.U.

 E(B|B)   =  -76.0611851156  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0058823464  A.U.  =  -3.6911900130392  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0059828519  A.U.  =  -3.7542575158057  kcal/mol

Counterpoise BSSE = .0001005055  A.U.  =  .0630675027665  kcal/mol

--------------------------------------------------------------------------------------------------------------

File Name: ./dft-big/dimer-dft-big-bsse.log    Standard basis: Aug-CC-pVTZ (5D, 7F)

E(AB|AB)  =  -152.939679072  A.U.

 E(AB|A)  =  -76.4662439466  A.U.

 E(AB|B)  =  -76.4661663671  A.U.

 E(A|A)   =  -76.4661927076  A.U.

 E(B|B)   =  -76.4661343916  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0072687583  A.U.  =  -4.5611676395249  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0073519728  A.U.  =  -4.6133849879184  kcal/mol

Counterpoise BSSE = .0000832145  A.U.  =  .0522173483935  kcal/mol

--------------------------------------------------------------------------------------------------------------

File Name: ./dft-big/dimer-dft-vdw-big-bsse.log    Standard basis: Aug-CC-pVTZ (5D, 7F)

E(AB|AB)  =  -152.940860116  A.U.

 E(AB|A)  =  -76.4662529092  A.U.

 E(AB|B)  =  -76.4661784556  A.U.

 E(A|A)   =  -76.4662001779  A.U.

 E(B|B)   =  -76.4661462431  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0084287512  A.U.  =  -5.2890666642536  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0085136950  A.U.  =  -5.3423691535850  kcal/mol

Counterpoise BSSE = .0000849438  A.U.  =  .0533024893314  kcal/mol

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File Name: ./dft-small/dimer-dft-small-bsse.log    Standard basis: 3-21G (6D, 7F)

E(AB|AB)  =  -151.969280289  A.U.

 E(AB|A)  =  -75.9826456042  A.U.

 E(AB|B)  =  -75.9748224415  A.U.

 E(A|A)   =  -75.9739148995  A.U.

 E(B|B)   =  -75.9738721616  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0118122433  A.U.  =  -7.4122181074799  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0214932279  A.U.  =  -13.4870649869337  kcal/mol

Counterpoise BSSE = .0096809846  A.U.  =  6.0748468794538  kcal/mol

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File Name: ./dft-small/dimer-dft-vdw-small-bsse.log    Standard basis: 3-21G (6D, 7F)

E(AB|AB)  =  -151.970535444  A.U.

 E(AB|A)  =  -75.9827298506  A.U.

 E(AB|B)  =  -75.9748530475  A.U.

 E(A|A)   =  -75.9739230221  A.U.

 E(B|B)   =  -75.9738846171  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0129525459  A.U.  =  -8.1277614098877  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0227278048  A.U.  =  -14.2617656954144  kcal/mol

Counterpoise BSSE = .0097752589  A.U.  =  6.1340042855267  kcal/mol

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File Name: ./mp2-small/dimer-mp2-small-bsse.log    Standard basis: 3-21G (6D, 7F)

E(AB|AB)  =  -151.189403605  A.U.

 E(AB|A)  =  -75.5930128444  A.U.

 E(AB|B)  =  -75.5867354515  A.U.

 E(A|A)   =  -75.5859247853  A.U.

 E(B|B)   =  -75.5859153975  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0096553091  A.U.  =  -6.0587354261773  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0175634222  A.U.  =  -11.0211001207666  kcal/mol

Counterpoise BSSE = .0079081131  A.U.  =  4.9623646945893  kcal/mol

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File Name: ./mp2-big/dimer-mp2-big-bsse.log    Standard basis: Aug-CC-pVTZ (5D, 7F)

E(AB|AB)  =  -152.128367980  A.U.

 E(AB|A)  =  -76.0612614459  A.U.

 E(AB|B)  =  -76.0612241877  A.U.

 E(A|A)   =  -76.0612000125  A.U.

 E(B|B)   =  -76.0611851156  A.U.

Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  -.0058823464  A.U.  =  -3.6911900130392  kcal/mol

Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  -.0059828519  A.U.  =  -3.7542575158057  kcal/mol

Counterpoise BSSE = .0001005055  A.U.  =  .0630675027665  kcal/mol

--------------------------------------------------------------------------------------------------------------

References.

[1] Counterpoise Correction and Basis Set Superposition Error C. David Sherrill

[2] S. Grimme, J. Antony, S. Ehrlich and H. Krieg, “A consistent and accurate ab initio parameterization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu,” J. Chem. Phys., 132 (2010) 154104. DOI: 10.1063/1.3382344

[3] g09_calc_bsse.sh : https://github.com/rangsimanketkaew/library-g09/

Code script:

#!/bin/bash

# Written by Rangsiman Ketkaew, CompChem TU, June, 2017

# Usage: $ chmod +x ./calc_bsse.sh

#      : $ ./calc_bsse.sh

read -p "Enter Your Gaussian Output: " file

who=`whoami`

node=`hostname`

now=`date`

where=`pwd`

if [ -e $file ]; then

echo "

---------------------------------------- BSSE Energy Extraction -----------------------------------------

Run by $who at $node on $now

---------------------------------------------------------------------------------------------------------

" > $where/results.BSSE.$file.txt

#echo "We are at $where"

#for f in `find ./ -name "*bsse*.log"`

bs=`grep 'Standard basis' $file|tail -1`

for f in $file

do

  echo "File Name: $f   $bs" >> $where/results.BSSE.$file.txt

  E_AB_AB=`grep 'SCF D' $f | awk '{print $5}'|tail -5|sed -n '1p'`

  E_AB_A=`grep 'SCF D' $f | awk '{print $5}'|tail -5|sed -n '2p'`

  E_AB_B=`grep 'SCF D' $f | awk '{print $5}'|tail -5|sed -n '3p'`

  E_A_A=`grep 'SCF D' $f | awk '{print $5}'|tail -5|sed -n '4p'`

  E_B_B=`grep 'SCF D' $f | awk '{print $5}'|tail -5|sed -n '5p'`

  echo -e "E(AB|AB)  =  $E_AB_AB  A.U.\n" \

   "E(AB|A)  =  $E_AB_A  A.U.\n" \

   "E(AB|B)  =  $E_AB_B  A.U.\n" \

   "E(A|A)   =  $E_A_A  A.U.\n" \

   "E(B|B)   =  $E_B_B  A.U." >> $where/results.BSSE.$file.txt

  deltaE_bsse=`echo $E_AB_AB - $E_AB_A - $E_AB_B | bc -l` ; deltaE_bsse_con=`expr $deltaE_bsse*627.503 | bc -l`

  deltaE_norm=`echo $E_AB_AB - $E_A_A - $E_B_B |bc -l` ; deltaE_norm_con=`expr $deltaE_norm*627.503 | bc -l`

  cp_bsse=`echo $deltaE_bsse - $deltaE_norm | bc -l` ; cp_bsse_con=`expr $cp_bsse*627.503 | bc -l`

  echo "Diff Energy with BSSE     =  E(AB|AB) - E(AB|A) - E(AB|B) =  $deltaE_bsse  A.U.  =  $deltaE_bsse_con  kcal/mol" \

  >> $where/results.BSSE.$file.txt

  echo "Diff Energy without BSSE  =  E(AB|AB) - E(A|A) - E(B|B)   =  $deltaE_norm  A.U.  =  $deltaE_norm_con  kcal/mol" \

  >> $where/results.BSSE.$file.txt

  echo "Counterpoise BSSE = $cp_bsse  A.U.  =  $cp_bsse_con  kcal/mol" \

  >> $where/results.BSSE.$file.txt

  #echo $E_AB_AB - $E_AB_A - $E_AB_B | bc -l

  echo -e "---------------------------------------------------------------------------------------------------------\n" \

  >> $where/results.BSSE.$file.txt

 done

 echo "Congrats !!! Please check file results.BSSE.$file.txt"

else

 echo "Error !!! File $file does not exist."

fi