Computational Chemistry

GIAO B3LYP/6-311þG(d,p) shifts to be in good agreement with experiment when
appropriate calculated geometries were used [ 121 ].
Figure7.9compares with experiment [ 122 , 123 ]^13 C and^1 H NMR spectra
calculated at these levels:

1. B3LYP/6-311þþG* for the NMR calculations, using B3LYP/6-311þþG
   (2df,2p), and HF/3-21G() for the geometries and


2. B3LYP/6-31G for the geometries, using B3LYP/6-31G, B3LYP/6-311þG*,
   and B3LYP/6-311þþG* for the NMR calculations
   Thus the figure shows for each of these molecules: (1) a fairly high-level NMR
   calculation on a high-level and a low-level geometry, and (2) a medium-level
   geometry probed with a medium-, a fairly high-, and a still higher-level calculation.
   For such a very small sample the results cannot reasonably be expected to do more
   than show up gross differences in accuracy, but they do suggest that for DFT NMR
   chemical shifts, if high accuracy is not needed B3LYP/6-311+G on B3LYP/6-
   31G* geometries may be adequate.

C

(2.17, experimental room

temperature average)

• 3.26


• 6.33


• 6.38
  (– 8.7)

HHC

H

H

0.29 B3LYP / 6-31G* NMR

0.27 B3LYP / 6-311+G* NMR

0.25 B3LYP / 6-311++G** NMR

(0.23 experimental)

H 2 C CH 2

HH

0.32

0.32

0.22

(0.22)

0.48

• 1.42
  
  
  • 0.95
    (1.4)
  
  
  
  

H

7.21

7.42

7.56

(7.27)

121.1

133.4

134.3

(128.5)

O

C

C C

H

H H

H

H H

1.66

1.88

1.87

2.06

2.15

2.20

192.7

212.7

212.1

(206.7)

28.3

31.1

31.6

(30.6)

0.25 B3LYP / 6-311++G(2df, 2p) geom

0.17 HF / 3-21G(*) geom

• 6.31


• 6.94

B3LYP / 6-311++G** NMR B3LYP / 6-31G* geom

0.19

0.01

• 0.93


• 1.23

B3LYP / 6-311++G** NMR

B3LYP / 6-31G* geom

7.63

7.54

134.2

133.0

B3LYP / 6-311++G** NMR

B3LYP / 6-31G* geom 31.631.7

1.86

1.75

2.21

2.14 211.3

212.8

B3LYP / 6-311++G** NMR B3LYP / 6-31G* geom

Fig. 7.9 Calculated and experimental^1 H and^13 C NMR spectra. Chemical shifts (dvalues) are
relative to the H and C of TMS. The calculations were done with the default NMR method (GIAO)
implemented in Gaussian 03 [ 78 ]. The experimental values (in parentheses) are from [ 122 ], except
for the^13 C values for methane and cyclopropane [ 123 ] (for these [ 122 ] gave"2.3 and"2.9, which
seem suspect). The calculated values are in vacuo and the experimental are in CDCl 3 , except
for methane and cyclopropane, which are gas-phase measurements which were given relative to
benzene and have been adjusted here to be relative to TMS. The changes in going from vacuum to
CDCl 3 are likely to be fairly small (within ca.d1) for these molecules. Values to the left of the
structures are all for B3LYP/6-311þþG NMR calculations on B3LYP/6-311þþG(2df,2p)
(first line) or HF/3-21G()(second line) geometries. Values to the right of the structures are all
for B3LYP/6-31G geometries with NMR calculations at the B3LYP/6-31G, B3LYP/6-311þG,
and B3LYP/6-311þþG levels (upper,middleandlowest lines, respectively)

494 7 Density Functional Calculations