Tensor, orbital hardness

Different practical procedures for computing r) have been proposed, that range from the computation of the difference between the energy values of the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals [8,9], to the atom in molecules based models [10, 11], to the charge sensitivity analysis [12, 13], to the use of Slater transition state theory [14], to the Janak s extension of DFT for fractional occupancies [15, 16]. Recently, Neshev and Mineva have proposed a scheme for the construction of the internally resolved hardness tensor in... 

Applications presented here include the computation of total hardness values of a selected number of atoms and molecules, orbital Fukui indices and orbital softness tensor (polarization) for test systems. In addition, the change of the hardness along the isomerization paths of HCN and 03H+ is reported. 

The Janak s theorem (eq.17) and the hardness tensor definition (eq. 20) allows the calculations of Tiij as the first derivative of the Kohn-Sham orbital eigenvalues with respect to the orbital occupation numbers [17] ... 

By using the elements of the hardness tensor, calculated through eq. (23) for k valence orbitals, as the coefficients of the equations (31) for a system with AN=0 is obtained the following matrix ... 

The derivatives (40) define the shell hardness tensor, i)s, while the potentials (39) define the generalized shell (orbital) energies, g. 

The effect of the orbital relaxation on the hardness tensor can be estimated via the finite difference approach [52, 53]. 

TABLE 3.9 The Hartree-Fock, B3LYP, SVWN, and BP86/6-31G Chemical Hardness Computations for the [CHjO]" Molecule by Using Orbital Energies and Vertical Total Energies for Ionization Potential and Electron Affinity Calculation, Respectively IRHT=intemaUy resolved hardness tensor, H/L=HOMO/LUMO (Putz et al., 2004)... 

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