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Bonding and Molecular Orbitals in Main Group Compounds

Introduction

Gaussian modelling can be used in order to optimize a molecule and thereby collect thermodynamic information and kinetic data

Optimisation of BH3

Gaussian modelling can be used in order to optimize a molecule and thereby collect thermodynamic information and kinetic data. The molecule which has been investigated is BH3 and an image of the non-optimised form is shown below.

An image showing an non-optimised BH3 molecule

During the optimisation of a molecule, if we assume that the B and H nuclei have a given position, then we can solve the Schrodinger equation and therefore determining the electron density and energy of the nuclei in that position, known as the SCF part of the Schrodinger equation. From this, we can then determine the equation for the particular position of the nuclei and this can be achieved by moving the nuclei between different SCF's until the lowest energy geometry is found which is known as the optimised geometry. The first optimisation carried out used a B3LYP method and the optimisation data for BH3 can be found here:File:BH3 OPT.LOG. An image for the optimised molecule is shown below.


The B-H bond distance for this molecule is: 1.19349Å

The H-B-H bond angle for this molecule is: 120

The table below summaries the information gained from the optimisation of the molecule. One piece of information shown in the table is the basis set and this shows the level of accuracy of the calculation. This particular basis set, 3-21G, has a low accuracy, although this does mean that the speed of the calculations are fast, in this particular case 10 seconds.

Results summary for the Optimization
File type .log
Calculation type FOPT
Calculation method RB3 LYP
Basis Set 3-21G
Final Energy (a.u) -26.46226338
Gradient (a.u) 0.00020672
Dipole moment(D) 0.0000
Point group D3H
Length of Calculation (s) 10



 Item               Value     Threshold  Converged?
 Maximum Force            0.000413     0.000450     YES
 RMS     Force            0.000271     0.000300     YES
 Maximum Displacement     0.001610     0.001800     YES
 RMS     Displacement     0.001054     0.001200     YES
 Predicted change in Energy=-1.071764D-06
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1935         -DE/DX =    0.0004              !
 ! R2    R(1,3)                  1.1935         -DE/DX =    0.0004              !
 ! R3    R(1,4)                  1.1935         -DE/DX =    0.0004              !
 ! A1    A(2,1,3)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 -------------------------------------------------------------------------------- 


Optimisation plots of BH3

A Total Energy graph of BH3


A RMS graph of BH3



A movie depicting the position of the nuclei at each step of optimization for a BH3 molecule






































A better Gaussian model of BH3

A 6-13G optimisation of BH3 is shown here:File:BH3 OPT 6 13GJND.LOG

The B-H bond length is: 1.19143A

The H-B-H bond angle is:120

Results summary for the Optimisation
File type .log
Calculation type FOPT
Calculation method RB3 LYP
Basis Set 6-13G(d,p)
Final Energy (a.u) -26.61532252
Gradient (a.u) 0.00021672
Dipole moment(D) 0.0000
Point group D3H
Length of Calculation (s) 7

Optimisation of TIBr3

An image of the non-optimized TIBr3 molecule












An image of the optimised TIBr3 molecule

The link for the optimised TIBr3 molecule can be found here: File:Log 69180 TIbr3optimisation.log

The TI-Br bond length is: 2.65095

The Br-TI-Br angle is: 120








Results summary for the Optimization
File type .log
Calculation type FOPT
Calculation method RB3 LYP
Basis Set LanL2DZ
Final Energy (a.u) -91.21812851
Gradient (a.u) 0.00000090
Dipole moment(D) 0.0000
Point group D3H
Length of Calculation (s) 23.5


      Item               Value     Threshold  Converged?
 Maximum Force            0.000413     0.000450     YES
 RMS     Force            0.000271     0.000300     YES
 Maximum Displacement     0.001610     0.001800     YES
 RMS     Displacement     0.001054     0.001200     YES
 Predicted change in Energy=-1.071764D-06
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1935         -DE/DX =    0.0004              !
 ! R2    R(1,3)                  1.1935         -DE/DX =    0.0004              !
 ! R3    R(1,4)                  1.1935         -DE/DX =    0.0004              !
 ! A1    A(2,1,3)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------


Optimisation of BBr3

An image of the non-optimized BBr3 molecule











The link for the optimised BBr3 molecule can be found here: File:BBr3 optimistion JND.log

An image of the optimised BBr3 molecule

The B-Br bond length is: 1.93396

The Br-B-Br angle is:120







Results summary for the Optimization
File type .log
Calculation type FOPT
Calculation method RB3 LYP
Basis Set Gen
Final Energy (a.u) -64.43645296
Gradient (a.u) 0.00000382
Dipole moment(D) 0.0000
Point group D3H
Length of Calculation (s) 25.6


      Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000036     0.001800     YES
 RMS     Displacement     0.000023     0.001200     YES
 Predicted change in Energy=-4.026780D-10
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.934          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.934          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.934          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------