© 2011 BlackLight Power, Inc. All rights reserved.
More Polyatomic Molecules and Hydrocarbons
659
From Eqs. (14.620-14.622), the total energy of each 12CH 2 is
EalkaneT osc 12CH 2 49.66493 eV Ealkane osc 12CH 2 (14.623)
1 49.66493 eV 2 0.25017 eV 0.35532 eV 49.80996 eV 2 k where e given by Eq. (13.458) was used for the term.
The derivation of the total CH 2 bond dissociation energy, EDalkane 12CH 2 follows from that of the bond dissociation
energy of dihydrogen carbide radical, ED 12CH 2 , given by Eqs. (13.524-13.527). EDalkane 12CH 2 is given by the sum of the initial C 2 sp 3 HO energy, E C , 2 sp 3 (Eq. (14.146)), and two times the energy of the hydrogen atom, E H (Eq. (13.154)),
minus the sum of EalkaneT osc 12CH 2 (Eq. (14.623)) and E (magnetic) (Eq. (13.524)): EDalkane 12CH 2 E C , 2sp 3 2 E ( H ) EalkaneT osc 12CH 2 E magnetic
Thus, the total CH 2 bond dissociation energy, EDalkane CH 2 is
(14.624)
12
12
EDalkane 12CH 2 14.63489 eV 2 13.59844 eV EalkaneT osc 12CH 2 E magnetic
41.83177 eV 49.80996 eV 0.14803 eV 7.83016 eV
(14.625)
SUM OF THE ENERGIES OF THE C C MOs AND THE HOs OF CONTINUOUSCHAIN ALKANES
The energy components of Ve , V p , T , Vm , and ET of the C C -bond MOs are the same as those of the CH MO except that energy of the Calkane 2 sp 3 HO is used. The energies of each C C -bond MO are given by the substitution of the semiprincipal axes (Eqs. (14.523-14.524) and (14.528)) into the energy equations of the CH MO (Eqs. (13.449-13.453)), with the exception that E Calkane , 2 sp 3 (Eq. (14.512)) replaces E C , 2 sp 3 in Eq. (13.453). The total number of C C bonds of Cn H 2 n 2 is n 1 .
Thus, the energies of the n 1 bonds is given by Ve n 1 0.91771 Vp
n 1 e2 8 0 a 2 b 2
2e2
8 0 a 2 b 2
a a 2 b2 a a 2 b2
n 1 28.79214 eV
n 1 9.33352 eV
T n 1 0.91771
2
2me a a 2 b 2
Vm n 1 0.91771
ln
2
4me a a 2 b 2
a a 2 b2 a a 2 b2
ln
a a 2 b2 a a 2 b2
(14.626) (14.627)
n 1 6.77464 eV n 1 3.38732 eV
(14.628) (14.629)
n 1 e2
1 a0 a c ' (14.630) 0.91771 2 2 a ln a c ' 1 15.56407 eV n 1 31.63537 eV is the total energy of the C C MOs given by Eq. (14.520) which is reiteratively matched to Eq.
ETalkane C C ,
where ETalkane C C ,
ln
8 0 c '
(13.75) within five-significant-figure round off error. Since there are two carbon atoms per bond, the number of C C bonds is n 1 , and the energy change of each C 2 sp 3
shell due to the decrease in radius with the formation of each C C -bond MO is ETalkane C C , 2 sp 3 (Eq. (14.517)), the total energy of the C C -bond MOs, ETalkane C C , is given by the sum of 2 n 1 ETalkane C C , 2 sp3 and ETalkane C C , , the
MO contribution given by Eq. (14.630):