Biomedical Engineering Reference
In-Depth Information
This simple geometric series can be summed exactly to give
1
exp
q
vib
=
(17.22)
hc
0
ω
e
k
B
T
1
−
−
and once again it is usually written in terms of the vibrational temperature θ
vib
:
1
exp
q
vib
=
(17.23)
θ
vib
T
1
−
−
Finally we need to know the electronic partition function. This is almost always 1, unless
the electronic ground state is degenerate (in which case it is equal to the degeneracy) or
unless there is a very low-lying excited state.
17.7 Back to L-Phenylanine
Let me now return to L-phenylanine. The Gaussian 03 'frequency' calculation also gives
thermodynamic properties, calculated along the lines discussed above. Here is an abbrevi-
ated output. First we have moments of inertia and then a calculation of the rotational and
vibrational temperatures.
Principal axes and moments of inertia in atomic units:
1 2 3
EIGENVALUES - - 1026.19740 3017.84285 3333.43073
X
0.99982
0.01842
0.00491
Y
-0.01827
0.99942
-0.02889
Z
-0.00544
0.02879
0.99957
This molecule is an asymmetric top.
Rotational symmetry number 1.
Warning -- assumption of classical behavior for rotation
may cause significant error
Rotational temperatures (Kelvin) 0.08440 0.02870 0.02598
Rotational constants (GHZ): 1.75867 0.59802 0.54141
Zero-point vibrational energy 532871.0 (Joules/Mol)
127.35923 (Kcal/Mol)
Vibrational temperatures:
49.53
62.36
86.88 142.01 280.87
(Kelvin)
405.40 422.99 483.72 489.81 545.09
653.24 713.44 813.05 927.86 952.80
Next come the various contributions to the internal energy
U
(here called
E
), the heat
capacity
C
and the entropy
S
.
Zero-point correction=
0.202960 (Hartree/Particle)
Thermal correction to Energy=
0.213506
Thermal correction to Enthalpy=
0.214451
