Computational Chemistry

parabolicE/qrelationship (Fig5.32), i.e. to a steeper curve than the real one, and
thus to stiffer bonds. Stiffer bonds need more energy to stretch them (or bend them,
for bending force constants), and thus absorb higher-frequency infrared light.
Harmonic frequencies thus derived from experimental IR spectra are higher than
theobserved(the “raw”) experimental frequencies, and are closer to ab initio
frequencies than are the observed frequencies [ 237 ]. Since both theoretically
calculated (e.g. by ab initio methods) frequencies and experimentally-derived
harmonic frequencies are based on a parabolicE/qrelationship, it is sometimes
considered better to compare calculated frequencies with harmonic frequencies
rather than observed experimental frequencies [ 238 ]. Because both ab initio- and
experimentally-derived harmonic frequencies rest on second derivatives, we might
expect ab initio frequencies to converge not toward the observed experimental, but
rather toward the experiment-derived harmonic frequencies, as correlation level/
basis set are increased. This is indeed the case, as has been shown by calculations on
water with high correlation levels (CCSD(T);Section 5.4.3) and large basis sets
(polarization functions and triply- or quadruply- split valence shells (Section 5.3.3).
Theobservedwater frequencies are 3,756, 3,657, and 1,595 cm#^1. For these three
fundamental frequencies, the deviations fell from 269, 282, and 127 cm#^1 at the
Hartree–Fock level to only 9, 13 and 10 cm#^1 higher than the experiment-derived
harmonic values of 3,943, 3,832 and 1,649 cm#^1 [ 239 ]. Such harmonic frequencies
are typically about 5% higher, and ab initio calculated frequencies about 5–10%

∆ r

E

energy idealized

actual

curve

E vs. ∆ r

(^0) extension of bond
(amount of stretching)
E vs. ∆ r curve (a parabola)
Fig. 5.32 The actual curve for potential energy vs. stretch for a bond is not really a parabola, i.e.
not reallyE¼(Dr)^2 , but near the equilibrium bond length (Dr¼0) the parabola fits the actual
curve fairly well
334 5 Ab initio Calculations