20
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
LUMO 3.217 eV
(a)
(b)
HOMO-1 -18.787 eV
LUMO+1 4.810 eV
HOMO -10.566 eV
Fig. 2.20 Several CMO patterns of methane molecule with orbital symmetry and energies calculated by DFT/B3LYP/6-31G** after the structural optimization. a Occupied and b unoccupied
MO’s. Note that there is a node of wavefunction inside the lowest unoccupied MO (LUMO) in (b)
Table 2.3 NBO representation of water molecule (starting from the CMO’s obtained by
DFT/B3LYP/6-31G**) a
NBO No.
Occupancy
Orbital energy (in eV)
Characteristics
1
1.99903
−19.286
σ(O–H)
Ψ = 0.8588(sp 3.47 ) O + 0.5123s H
2
1.99903
−19.286
σ(O–H)
Ψ = 0.8588(sp 3.47 ) O + 0.5123s H
3
1.99710
−16.705
σ(lone pair at O)
Ψ = (sp 0.80 ) O
4
1.99790
−7.868
π(lone pair at O)
Ψ = p O
5
0.00003
12.866
σ*(O–H)
Ψ = 0.5123(sp 3.47 ) O − 0.8588s H
6
0.00003
12.866
σ*(O–H)
Ψ = 0.5123(sp 3.47 ) O − 0.8588s H
a Those representing the core (2s) of the O atom and the Rydberg state are omitted
2.2.3 Bond Energy
The bond-energy value provides the information as to bond strength of each molecule.
These values are often given by experimental technique such as mass spectrometric
measurement as well as by theoretical estimations. Considerable numbers of bondenergy values are tabulated in the experimental handbook as the bond dissociation
energy or dissociation enthalpies (Rumble 2018). For polyatomic molecules having