Biomedical Engineering Reference
In-Depth Information
Thermal correction to Gibbs Free Energy=
0.164839
Sum of electronic and zero-point Energies=
-551.349677
Sum of electronic and thermal Energies=
-551.339131
Sum of electronic and thermal Enthalpies=
-551.338187
Sum of electronic and thermal Free Energies=
-551.387798
E (Thermal)
CV
S
KCal/Mol
Cal/Mol-Kelvin Cal/Mol-Kelvin
Total
133.977
38.971
104.416
Electronic
0.000
0.000
0.000
Translational
0.889
2.981
41.212
Rotational
0.889
2.981
30.713
Vibrational
132.200
33.010
32.490
Vibration 1
0.594
1.983
5.556
Vibration 2
0.595
1.980
5.100
Vibration 3
0.597
1.973
4.445
...
...etc
The partition functions are also printed.
17.8 Excited States
Electronic ground states are all well and good, but there is a wealth of experimental spec-
troscopic data that relates to the excited states of molecules. One of the simplest and most
widely studied sequences of organic molecules to be investigated by spectrophotometry is
afforded by the set of monocyclic azines, of which pyridine forms the first member. It is
instructive to compare this series with benzene.
All the molecules have 42 electrons, 21 electron pairs, and I can write their ground state
electronic configurations
Ψ
0
: (ψ
1
)
2
(ψ
2
)
2
...(ψ
21
)
2
We refer to Ψ
0
as the
reference state
. Single excitations can be produced by promoting an
electron from one of the occupied orbitals to an unoccupied (virtual) one, just as we did in
Chapter 15 for dihydrogen, so the first few single excitations have configurations
Ψ
1
: ψ
1
ψ
2
...ψ
21
ψ
22
Ψ
2
: ψ
1
ψ
2
...ψ
21
ψ
23
Ψ
3
: ψ
1
ψ
2
...ψ
20
ψ
21
ψ
22
Ψ
4
: ψ
1
ψ
2
...ψ
20
ψ
21
ψ
23
Electron spin has to be taken into account, and proper Slater determinants constructed.
The ground-state wavefunction will be a single Slater determinant but there are four pos-
sibilities (say, (a), (b), (c) and (d)) for each of the four excited states. In our dihydrogen
calculation, I grouped the determinants together so that they were spin eigenfunc-
tions. In modern configuration interaction (CI) calculations, we work directly with the
