122
M. M. Kabanda and K. P. Otukile
2 Computational Details
The geometry optimisations of the reactants, transition states and products were
performed with the DFT method and the MP2 method. DFT calculations were performed utilising the M06-2X and the M11-L functionals and using the 6-31+G(d,p)
and 6-311++(3df,2p) basis set. These basis sets are extensively utilised in the study of
chemical reactions and specifically in the characterisation of transition state geometries [20–35]. The reaction transition states (TSs) were located using the synchronous
transit-guided quasi-newton technique for the saddle point search (QST3 module).
Frequency calculations were performed, at the same level of calculations as the
optimised geometry procedure, on fully optimized conformers to determine the
nature of the stationary points. For ground state geometries no imaginary frequencies
were observed, whereas there was only one imaginary frequency for the transition
state geometries. Zero-point and thermal enthalpies corrections, computed at T =
298 K and pressure of 1 atm in the rigid rotor harmonic oscillator approximation,
were performed to obtain free energies. Solvent effects on geometries and relative
conformational stabilities were taken into consideration using the continuum solvation model density (SMD) [23], in which, unlike other continuum models, the full
solute electron density is used without defining partial atomic charges.
All calculations were performed with Gaussian09 [36]. The schematic representations were drawn using the ChemOffice package in the UltraChem 2010 [37] version
and conformers were drawn using GaussView5 program [38].
The Quantum Mechanics Atoms in Molecule (QMAIM) was performed using the
AIMAll [39]. The wavefunctions necessary for utilisation in the QMAIM program
were calculated on the basis of fully optimised geometries using the same level of
accuracy as in the optimisation. The number of critical points (CPs) found for all
of the analysed systems are in agreement with the Poincare-Hopf rule. The electron
density (ρ) and its Laplacian (∇
2
ρ) at the bond critical point (BCP) were calculated
in order to characterise the various structures. According to the topological analysis
of electronic charge density, in the theory of the atoms in molecules (AIM [40]),
electron density () and Laplacian of the electron density, (∇
2 ), are used to describe
the strength and the characteristic of the bond, respectively. The Laplacian (∇
2 ) is
the sum of λ 1 , λ 2 , and λ 3 , where λ i is the th eigenvalue of the Hessian matrix of the
electronic density. In general, when ∇
2 < 0 the bond is covalent, but when ∇
2 > 0
the bond belongs to the electrostatic interaction.
M. M. Kabanda and K. P. Otukile
2 Computational Details
The geometry optimisations of the reactants, transition states and products were
performed with the DFT method and the MP2 method. DFT calculations were performed utilising the M06-2X and the M11-L functionals and using the 6-31+G(d,p)
and 6-311++(3df,2p) basis set. These basis sets are extensively utilised in the study of
chemical reactions and specifically in the characterisation of transition state geometries [20–35]. The reaction transition states (TSs) were located using the synchronous
transit-guided quasi-newton technique for the saddle point search (QST3 module).
Frequency calculations were performed, at the same level of calculations as the
optimised geometry procedure, on fully optimized conformers to determine the
nature of the stationary points. For ground state geometries no imaginary frequencies
were observed, whereas there was only one imaginary frequency for the transition
state geometries. Zero-point and thermal enthalpies corrections, computed at T =
298 K and pressure of 1 atm in the rigid rotor harmonic oscillator approximation,
were performed to obtain free energies. Solvent effects on geometries and relative
conformational stabilities were taken into consideration using the continuum solvation model density (SMD) [23], in which, unlike other continuum models, the full
solute electron density is used without defining partial atomic charges.
All calculations were performed with Gaussian09 [36]. The schematic representations were drawn using the ChemOffice package in the UltraChem 2010 [37] version
and conformers were drawn using GaussView5 program [38].
The Quantum Mechanics Atoms in Molecule (QMAIM) was performed using the
AIMAll [39]. The wavefunctions necessary for utilisation in the QMAIM program
were calculated on the basis of fully optimised geometries using the same level of
accuracy as in the optimisation. The number of critical points (CPs) found for all
of the analysed systems are in agreement with the Poincare-Hopf rule. The electron
density (ρ) and its Laplacian (∇
2
ρ) at the bond critical point (BCP) were calculated
in order to characterise the various structures. According to the topological analysis
of electronic charge density, in the theory of the atoms in molecules (AIM [40]),
electron density () and Laplacian of the electron density, (∇
2 ), are used to describe
the strength and the characteristic of the bond, respectively. The Laplacian (∇
2 ) is
the sum of λ 1 , λ 2 , and λ 3 , where λ i is the th eigenvalue of the Hessian matrix of the
electronic density. In general, when ∇
2 < 0 the bond is covalent, but when ∇
2 > 0
the bond belongs to the electrostatic interaction.