THE EVALUATION OF PROTONATION ENERGY OF MOLECULES IN TERMS OF QUANTUM THEORETICAL DESCRIPTORS - Theoretical and Computational Research in the 21st Century - page 220

χ , the global softness, S , and the global electrophilicity index, ω , respec-
tively, of the molecules are computed by invoking the Koopmans' theorem
and Eqs. (15), (17), (19), and (20).
An MLR [97] is performed using Minitab15 to compute the correlation
coeffi cients C, C 1 , C 2 , C 3 , and C 4 by plotting experimental PA along the
abscissa and the values of the quantum mechanical descriptors along the
ordinate. The computed correlation coeffi cients C, C 1 , C 2 , C 3 and C 4 , for
all the sets are tabulated in Table (10.1).

TABLE 10.1 Correlation coefficients and R 2 value for the Set 1, Set 2, Set 3, Set 4, Set5,

and Set 6
Sets C C 1 C 2 C 3 C 4 R 2

1 450 18.0 24100 −40539 8019 0.992

2 −113 −4.66 −1810 3561 −705 0.818

3 17.1 0.666 −0.1 −0.1 −0.15 0.995

4 −129 −7.94 147 167 −11.1 0.916

5 31.7 1.08 −31.4 −39.5 4.19 0.911

6 2.3 −0.308 89.1 −44.1 4.06 0.88

Thereafter, invoking the suggested ansatz, Eq (14), and putting the
quantum mechanical descriptors and the correlation coeffi cients in the
Eq (14), we have computed the PAs of six sets of carbon compounds.
The comparative study of theoretically evaluated and experimentally de-
termined PAs of the Set 1-Set 6 is performed in the Tables (10.2-10.7),
respectively.

TABLE 10.2 Experimental PA (eV), calculated PA (eV), and R 2 for the Set 1

Molecule Experimental PA Calculated PA R 2

Methane 5.63294 6.01418 0.99

Ethane 6.17932 6.56332

Propane 6.48286 6.83883

Butane* 6.83237 7.07331

Isobutane 7.02491 7.34303