Table 3 Global Chemical Reactivity Descriptors(GCRD)

The energy gap (ΔE_gap)

ΔE_gap = (E_LUMO – E_HOMO)

Ionization potential (I_P)

I_P =−E_HOMO

Electron affinity (E_A)

E_A =−E_LUMO

Hardness (η)

\(\eta =\frac{{I}_{P}- {E}_{A}}{2}\)

Softness (\({\varvec{\sigma}}\))

\(\sigma =\frac{1}{\eta }\)

Electronegativity (χ)

\(\chi =\frac{{I}_{P }+{ E}_{A}}{2}\)

Chemical potentials (µ)

µ = −\(\chi \)

The fraction of electron transferred (ΔN)

(ΔN)\(=\frac{{\upchi }_{\mathrm{Ce }}-{\upchi }_{\mathrm{Ligand}}}{{2(\upeta }_{\mathrm{Ce }}+{\upeta }_{\mathrm{Ligand}})}\)

Electrophilicity index (ω)

(ω) = \(\frac{{\upmu }^{2}}{2\eta }\)

The back donation

(ΔE_{back-donation})\(=-\frac{\upeta }{4}\)