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General Diatomic and Polyatomic Molecular Ions and Molecules
479
essentially given by 1/2 the differences in vibrational energies per bond. Using Eq. (13.211), Eqs. (13.212-13.214), and the experimental D 16OD vibrational energy of Evib 2787.92 cm1 0.345661 eV [25], the corresponding Eosc D 16OD is
1 Eosc D 16OD 2 0.630041 eV 0.345661 eV 0.914421 eV 2
(13.215)
TOTAL AND BOND ENERGIES OF H 16OH AND D 16OD
ET osc H 2 16O , the total energy of the H 16OH including the Doppler term, is given by the sum of ET H 2O (Eq. (13.181)) and Eosc H 16OH given Eqs. (13.207-13.214):
ET osc H 2 16O Ve T Vm V p E O 2 p Eosc H 16OH ET H 2O Eosc H 16OH
2 e 16 ET osc H 2 O 4 0 c ' 2 1 2
3 e2 2 4 0b3 2 me 3 3 a0 a c ' 1 13.6181 eV 1 2 ln 2 2 8 ' a a c m c e k
(13.216)
(13.217)
1 k 49.652637 eV 2 0.630041 eV 2 From Eqs. (13.214) and (13.216-13.217), the total energy of H 16OH is ET osc H 2 16O 49.652637 eV Eosc H 16OH (13.218) 1 49.652637 eV 2 0.630041 eV 0.465680 eV 50.447039 eV 2 k term. ET osc D2 16O , the total energy of D 16OD including the where the experimental vibrational energy was used for the
Doppler term is given by the sum of ET D2O ET H 2O (Eq. (13.181)) and Eosc D 16OD given by Eq. (13.215): ET osc D2 16O 49.652637 eV Eosc D 16OD
(13.219) 1 49.652637 eV 2 0.630041 eV 0.345661 eV 50.567058 eV 2 k term. As in the case of the hydroxyl radical, the dissociation where the experimental vibrational energy was used for the
of the bond of the water molecule forms a free hydrogen atom and a hydroxyl radical, with one unpaired electron each. The lowering of the energy of the reactants due to the magnetic dipoles decreases the bond energy. Thus, the total energy of oxygen is reduced by the energy in the field of the two magnetic dipoles given by Eq. (13.152). The corresponding bond dissociation energy, ED , is given by the sum of the total energies of the corresponding hydroxyl radical and hydrogen atom minus the total
energy of water, ET osc H 16OH , and E (magnetic) . Thus, ED of H 16OH is given by:
ED H 16OH E ( H ) E ( 16OH ) ET osc H 16OH E (magnetic) 16
(13.220)
16
where ET ( OH ) is given by the sum of the experimental energies of O (Eq. (13.171)), H (Eq. (13.154)), and the negative of the bond energy of 16OH (Eq. (13.157)): E ( 16OH ) 13.59844 eV 13.6181 eV 4.41174 eV 31.62828 eV From Eqs. (13.154), (13.218), and (13.220-13.221), E
D
16
H OH is
ED ( H OH ) E ( H ) E ( OH ) E ( magnetic) ET osc H 16OH 16
16
(13.221)
13.59844 eV 31.62828 eV 0.114411 eV 50.447039 eV 5.1059 eV
The experimental H 16OH bond dissociation energy is [26] ED ( H 16OH ) 5.0991 eV
(13.222)
(13.223)