Essentials of Computational Chemistry

10.4 STANDARD-STATE HEATS AND FREE ENERGIES 369
Table 10.2 Experimental H o
f,0 ,Ho f,298 ,Go f,298
(kcal mol−1 ) for the atoms
values and spin–orbit corrections
Atom H o
f,0 a H o
f,298 a G o f,298 a Spin–orbit b
H( 2 S) 51.63 ± 0.001 52.103 43.93
Li ( 2 S) 37.69 ± 0.20 38.074 28.19
Be ( 1 S) 76.48 ± 1.20 77.438 67.73
75.8 ± 0.8 c 76.75 ± 0.8 c 66.04 ± 1.2 c
B( 2 P) 136.2 ± 0.2 133.84 122.91 ± 0.2 −0.03
C( 3 P) 169.98 ± 0.10 171.29 160.03 −0.09
N( 4 S) 112.53 ± 0.02 112.97 102.05 ± 0.02
O( 3 P) 58.99 ± 0.02 59.553 48.08 −0.23
F( 2 P) 18.47 ± 0.07 18.97 7.66 −0.38
Na ( 2 S) 25.69 ± 0.17 25.645 14.70
Mg ( 1 S) 34.87 ± 0.20 35.158 24.57
Al ( 2 P) 78.23 ± 1.00 78.800 67.08 −0.21
Si ( 3 P) 106.6 ± 1.9 107.55 95.59 −0.43
108.1 ± 0.5 c 109.0 ± 0.5 c 97.1 ± 0.5 c
P( 4 S) 75.42 ± 0.20 75.619 64.00
S( 3 P) 65.66 ± 0.06 66.200 54.25 −0.56
Cl ( 2 P) 28.59 ± 0.001 28.991 17.23 −0.84
a All data, unless otherwise noted, are from the JANAF tables, see Chase, M. W., Jr. 1998. J. Phys.
Chem. Ref. Data, Monograph 9, 1, for most recent versions.
b Amount by which lower energy spin–orbit state lies below unsplit term, see Moore, C. Natl. Bur.
Stand. (US) Circ 467, 1952.
c Estimates considered to improve on experimental values, see Ochterski, J. W.; Petersson, G. A.;
Wiberg, K. B. 1995. J. Am. Chem. Soc., 117, 11299.
unlikely) that the atomic levels will overlap for the other two quantities. As a consequence,
one cannot compute, say, H o
f,298 for the molecule by overlapping the atomic levels for H0
and then taking the level of H298 as H o
f,298 . From inspection of Figure 10.1, this would be
equivalent to computing the 298 K heat of formation as
H o
f,298 (M) = E(M) + ZPVE(M) + [H298(M)
atoms
− H0(M)] −
z
atoms
E(Xz) +
z
H o
f,0 (Xz)
(10.32)
where molecule M is composed of constituent atoms X. This is not valid. The correct procedure
is instead to overlap the theoretical and experimental atomic H298 values and then read
off the molecular 298 K heat of formation, as detailed in the caption to Figure 10.1. This
procedure is expressed mathematically as
H o
f,298 (M) = E(M) + ZPVE(M) + [H298(M) − H0(M)]
{E(Xz) + [H298(Xz) − H0(Xz)]}+
atoms
−
z
atoms
z
H o
f,298 (Xz) (10.33)
The reason the former procedure fails is that the theoretical reference state is taken
to be a constant temperature (0 K, by virtue of particles being taken to be at rest), but