return to home page

IV.A.4. (XIV.F.)

Relative enthalpies of isomers - Comparison of 0K enthalpies (kJ mol-1)

Isomers of C3H6

index Species CAS number Name Relative experimental enthalpy (kJ mol-1) sketch
a C3H6 75194 Cyclopropane 35.7 sketch of Cyclopropane
b CH2CHCH3 115071 Propene 0.0 sketch of Propene
The calculated enthalpies include the calculated and scaled vibrational zero-point energy.
Methods with predefined basis sets
composite G1 44.3 a
0.0 b
G2MP2 40.8 a
0.0 b
G2 41.4 a
0.0 b
G3 43.0 a
0.0 b
G3B3 42.5 a
0.0 b
G3MP2 45.1 a
0.0 b
CBS-Q 40.8 a
0.0 b

Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ cc-pV(T+d)Z
hartree fock HF -9.2 a
0.0 b
63.8 a
0.0 b
63.8 a
0.0 b
58.5 a
0.0 b
  37.8 a
0.0 b
42.5 a
0.0 b
44.3 a
0.0 b
43.6 a
0.0 b
38.9 a
0.0 b
45.0 a
0.0 b
45.1 a
0.0 b
46.5 a
0.0 b
43.9 a
0.0 b
45.0 a
0.0 b
45.1 a
0.0 b
44.6 a
0.0 b
45.9 a
0.0 b
45.0 a
0.0 b
density functional LSDA -15.1 a
0.0 b
33.0 a
0.0 b
33.0 a
0.0 b
26.6 a
0.0 b
8.6 a
0.0 b
9.0 a
0.0 b
10.6 a
0.0 b
13.5 a
0.0 b
13.0 a
0.0 b
8.4 a
0.0 b
12.3 a
0.0 b
12.3 a
0.0 b
14.5 a
0.0 b
11.6 a
0.0 b
12.3 a
0.0 b
  9.7 a
0.0 b
12.8 a
0.0 b
12.3 a
0.0 b
SVWN -15.1 a
0.0 b
33.0 a
0.0 b
33.0 a
0.0 b
26.6 a
0.0 b
8.6 a
0.0 b
9.0 a
0.0 b
10.6 a
0.0 b
13.5 a
0.0 b
13.0 a
0.0 b
8.4 a
0.0 b
12.3 a
0.0 b
12.3 a
0.0 b
14.5 a
0.0 b
11.5 a
0.0 b
12.3 a
0.0 b
  9.6 a
0.0 b
12.8 a
0.0 b
 
BLYP 18.3 a
0.0 b
64.4 a
0.0 b
64.4 a
0.0 b
60.4 a
0.0 b
45.0 a
0.0 b
45.1 a
0.0 b
47.6 a
0.0 b
49.7 a
0.0 b
48.8 a
0.0 b
45.3 a
0.0 b
49.3 a
0.0 b
49.2 a
0.0 b
51.3 a
0.0 b
47.6 a
0.0 b
49.1 a
0.0 b
  45.1 a
0.0 b
49.8 a
0.0 b
49.1 a
0.0 b
B1B95 -7.6 a
0.0 b
41.3 a
0.0 b
41.3 a
0.0 b
35.0 a
0.0 b
15.4 a
0.0 b
16.4 a
0.0 b
18.7 a
0.0 b
21.2 a
0.0 b
20.5 a
0.0 b
16.0 a
0.0 b
19.2 a
0.0 b
19.2 a
0.0 b
22.3 a
0.0 b
19.5 a
0.0 b
19.3 a
0.0 b
  17.4 a
0.0 b
19.8 a
0.0 b
19.3 a
0.0 b
B3LYP 7.9 a
0.0 b
58.3 a
0.0 b
58.3 a
0.0 b
53.5 a
0.0 b
36.8 a
0.0 b
36.8 a
0.0 b
39.7 a
0.0 b
42.2 a
0.0 b
41.4 a
0.0 b
37.4 a
0.0 b
41.8 a
0.0 b
41.8 a
0.0 b
43.8 a
0.0 b
40.1 a
0.0 b
41.8 a
0.0 b
  38.7 a
0.0 b
42.4 a
0.0 b
41.8 a
0.0 b
B3LYPultrafine 7.9 a
0.0 b
58.3 a
0.0 b
58.3 a
0.0 b
53.6 a
0.0 b
36.8 a
0.0 b
36.9 a
0.0 b
39.7 a
0.0 b
42.2 a
0.0 b
41.4 a
0.0 b
37.5 a
0.0 b
41.9 a
0.0 b
41.8 a
0.0 b
44.0 a
0.0 b
40.1 a
0.0 b
41.8 a
0.0 b
  38.7 a
0.0 b
42.5 a
0.0 b
 
B3PW91 -2.7 a
0.0 b
44.8 a
0.0 b
44.8 a
0.0 b
39.5 a
0.0 b
21.5 a
0.0 b
21.6 a
0.0 b
23.8 a
0.0 b
26.7 a
0.0 b
26.0 a
0.0 b
22.1 a
0.0 b
25.7 a
0.0 b
25.7 a
0.0 b
28.3 a
0.0 b
25.1 a
0.0 b
26.0 a
0.0 b
  23.8 a
0.0 b
26.5 a
0.0 b
26.0 a
0.0 b
mPW1PW91 -6.4 a
0.0 b
41.9 a
0.0 b
41.7 a
0.0 b
36.5 a
0.0 b
18.3 a
0.0 b
18.4 a
0.0 b
20.9 a
0.0 b
23.7 a
0.0 b
23.1 a
0.0 b
19.0 a
0.0 b
22.9 a
0.0 b
22.9 a
0.0 b
25.5 a
0.0 b
22.3 a
0.0 b
23.1 a
0.0 b
  21.2 a
0.0 b
23.7 a
0.0 b
23.1 a
0.0 b
M06-2X -10.4 a
0.0 b
43.4 a
0.0 b
43.4 a
0.0 b
35.8 a
0.0 b
16.2 a
0.0 b
16.2 a
0.0 b
18.3 a
0.0 b
20.6 a
0.0 b
20.0 a
0.0 b
15.8 a
0.0 b
19.8 a
0.0 b
19.9 a
0.0 b
22.5 a
0.0 b
18.3 a
0.0 b
20.5 a
0.0 b
  16.9 a
0.0 b
21.1 a
0.0 b
 
PBEPBE 1.5 a
0.0 b
45.1 a
0.0 b
45.0 a
0.0 b
40.7 a
0.0 b
23.2 a
0.0 b
23.3 a
0.0 b
25.4 a
0.0 b
27.6 a
0.0 b
27.0 a
0.0 b
23.1 a
0.0 b
26.6 a
0.0 b
26.6 a
0.0 b
29.4 a
0.0 b
26.1 a
0.0 b
26.8 a
0.0 b
  24.2 a
0.0 b
27.3 a
0.0 b
26.8 a
0.0 b
PBEPBEultrafine 1.5 a
0.0 b
45.0 a
0.0 b
45.0 a
0.0 b
40.7 a
0.0 b
23.2 a
0.0 b
23.3 a
0.0 b
25.5 a
0.0 b
27.7 a
0.0 b
27.1 a
0.0 b
23.1 a
0.0 b
26.7 a
0.0 b
26.7 a
0.0 b
29.5 a
0.0 b
26.2 a
0.0 b
26.8 a
0.0 b
  24.2 a
0.0 b
27.4 a
0.0 b
 
PBE1PBE -9.2 a
0.0 b
39.7 a
0.0 b
39.7 a
0.0 b
34.6 a
0.0 b
15.6 a
0.0 b
15.7 a
0.0 b
18.2 a
0.0 b
20.8 a
0.0 b
20.2 a
0.0 b
16.0 a
0.0 b
20.0 a
0.0 b
20.0 a
0.0 b
22.7 a
0.0 b
19.5 a
0.0 b
20.2 a
0.0 b
  18.4 a
0.0 b
20.8 a
0.0 b
 
HSEh1PBE -7.8 a
0.0 b
41.4 a
0.0 b
41.4 a
0.0 b
36.2 a
0.0 b
17.3 a
0.0 b
17.3 a
0.0 b
19.8 a
0.0 b
22.5 a
0.0 b
21.9 a
0.0 b
17.7 a
0.0 b
21.7 a
0.0 b
21.7 a
0.0 b
24.5 a
0.0 b
21.1 a
0.0 b
22.0 a
0.0 b
  19.9 a
0.0 b
22.5 a
0.0 b
 
TPSSh             23.4 a
0.0 b
                       
Moller Plesset perturbation MP2 28.5 a
0.0 b
66.5 a
0.0 b
66.5 a
0.0 b
59.2 a
0.0 b
24.3 a
0.0 b
24.0 a
0.0 b
  26.1 a
0.0 b
25.0 a
0.0 b
21.9 a
0.0 b
25.8 a
0.0 b
25.7 a
0.0 b
29.9 a
0.0 b
29.0 a
0.0 b
26.1 a
0.0 b
  30.5 a
0.0 b
27.0 a
0.0 b
26.1 a
0.0 b
MP2=FULL 28.3 a
0.0 b
66.4 a
0.0 b
66.4 a
0.0 b
59.0 a
0.0 b
23.9 a
0.0 b
23.4 a
0.0 b
26.1 a
0.0 b
25.0 a
0.0 b
23.8 a
0.0 b
17.5 a
0.0 b
23.8 a
0.0 b
24.0 a
0.0 b
29.5 a
0.0 b
28.7 a
0.0 b
24.5 a
0.0 b
  29.2 a
0.0 b
25.4 a
0.0 b
 
MP3 28.8 a
0.0 b
66.2 a
0.0 b
66.2 a
0.0 b
59.0 a
0.0 b
29.0 a
0.0 b
28.6 a
0.0 b
31.4 a
0.0 b
31.1 a
0.0 b
29.9 a
0.0 b
28.0 a
0.0 b
31.9 a
0.0 b
31.8 a
0.0 b
35.0 a
0.0 b
34.4 a
0.0 b
32.5 a
0.0 b
  36.2 a
0.0 b
33.1 a
0.0 b
 
MP3=FULL         28.6 a
0.0 b
                           
MP4 33.2 a
0.0 b
72.6 a
0.0 b
72.6 a
0.0 b
66.0 a
0.0 b
34.4 a
0.0 b
33.7 a
0.0 b
35.8 a
0.0 b
35.0 a
0.0 b
33.5 a
0.0 b
31.4 a
0.0 b
34.4 a
0.0 b
34.4 a
0.0 b
38.5 a
0.0 b
38.4 a
0.0 b
35.2 a
0.0 b
    35.5 a
0.0 b
 
MP4=FULL 33.0 a
0.0 b
72.5 a
0.0 b
72.5 a
0.0 b
65.9 a
0.0 b
34.1 a
0.0 b
33.3 a
0.0 b
35.5 a
0.0 b
34.1 a
0.0 b
32.4 a
0.0 b
26.9 a
0.0 b
32.7 a
0.0 b
32.8 a
0.0 b
37.8 a
0.0 b
38.1 a
0.0 b
33.7 a
0.0 b
  37.1 a
0.0 b
34.1 a
0.0 b
 
B2PLYP         34.0 a
0.0 b
                           
Configuration interaction CID 24.4 a
0.0 b
65.1 a
0.0 b
65.1 a
0.0 b
58.0 a
0.0 b
27.6 a
0.0 b
26.9 a
0.0 b
29.9 a
0.0 b
30.3 a
0.0 b
28.9 a
0.0 b
25.9 a
0.0 b
29.6 a
0.0 b
29.5 a
0.0 b
33.7 a
0.0 b
32.5 a
0.0 b
30.3 a
0.0 b
  33.4 a
0.0 b
30.7 a
0.0 b
 
CISD 24.5 a
0.0 b
  66.3 a
0.0 b
59.5 a
0.0 b
29.0 a
0.0 b
  31.1 a
0.0 b
31.5 a
0.0 b
30.0 a
0.0 b
26.9 a
0.0 b
30.4 a
0.0 b
30.3 a
0.0 b
34.7 a
0.0 b
33.6 a
0.0 b
31.2 a
0.0 b
  34.1 a
0.0 b
31.5 a
0.0 b
 
Quadratic configuration interaction QCISD 39.0 a
0.0 b
74.2 a
0.0 b
74.2 a
0.0 b
67.6 a
0.0 b
34.8 a
0.0 b
34.3 a
0.0 b
36.4 a
0.0 b
36.0 a
0.0 b
34.6 a
0.0 b
32.2 a
0.0 b
35.3 a
0.0 b
35.3 a
0.0 b
39.5 a
0.0 b
39.0 a
0.0 b
36.2 a
0.0 b
  39.2 a
0.0 b
36.4 a
0.0 b
 
QCISD(T) 38.5 a
0.0 b
75.6 a
0.0 b
75.6 a
0.0 b
  36.8 a
0.0 b
36.2 a
0.0 b
38.2 a
0.0 b
37.4 a
0.0 b
35.9 a
0.0 b
33.7 a
0.0 b
36.6 a
0.0 b
36.5 a
0.0 b
40.8 a
0.0 b
40.9 a
0.0 b
37.3 a
0.0 b
  40.8 a
0.0 b
37.6 a
0.0 b
 
QCISD(TQ) 38.8 a
0.0 b
75.3 a
0.0 b
75.3 a
0.0 b
69.0 a
0.0 b
36.8 a
0.0 b
36.2 a
0.0 b
38.2 a
0.0 b
37.5 a
0.0 b
36.1 a
0.0 b
      40.9 a
0.0 b
41.1 a
0.0 b
         
Coupled Cluster CCD 38.8 a
0.0 b
71.8 a
0.0 b
71.8 a
0.0 b
64.5 a
0.0 b
31.6 a
0.0 b
30.9 a
0.0 b
33.3 a
0.0 b
33.1 a
0.0 b
31.7 a
0.0 b
29.5 a
0.0 b
32.8 a
0.0 b
32.8 a
0.0 b
37.0 a
0.0 b
36.1 a
0.0 b
33.7 a
0.0 b
  37.3 a
0.0 b
34.1 a
0.0 b
 
CCSD 38.9 a
0.0 b
73.8 a
0.0 b
73.8 a
0.0 b
67.1 a
0.0 b
34.4 a
0.0 b
33.6 a
0.0 b
35.8 a
0.0 b
35.5 a
0.0 b
34.1 a
0.0 b
31.7 a
0.0 b
34.9 a
0.0 b
34.9 a
0.0 b
39.0 a
0.0 b
38.5 a
0.0 b
35.8 a
0.0 b
  39.0 a
0.0 b
36.0 a
0.0 b
 
CCSD=FULL 38.7 a
0.0 b
73.7 a
0.0 b
73.7 a
0.0 b
67.0 a
0.0 b
33.8 a
0.0 b
33.1 a
0.0 b
35.4 a
0.0 b
34.5 a
0.0 b
33.1 a
0.0 b
27.1 a
0.0 b
33.1 a
0.0 b
  38.3 a
0.0 b
38.2 a
0.0 b
    37.7 a
0.0 b
   
CCSD(T) 38.5 a
0.0 b
75.5 a
0.0 b
75.5 a
0.0 b
69.1 a
0.0 b
36.6 a
0.0 b
36.0 a
0.0 b
38.0 a
0.0 b
37.3 a
0.0 b
35.8 a
0.0 b
33.5 a
0.0 b
36.5 a
0.0 b
36.4 a
0.0 b
40.7 a
0.0 b
40.8 a
0.0 b
37.2 a
0.0 b
  40.8 a
0.0 b
37.5 a
0.0 b
 
CCSD(T)=FULL 38.3 a
0.0 b
75.4 a
0.0 b
75.4 a
0.0 b
69.0 a
0.0 b
36.3 a
0.0 b
35.5 a
0.0 b
37.7 a
0.0 b
36.3 a
0.0 b
34.8 a
0.0 b
28.9 a
0.0 b
34.7 a
0.0 b
34.8 a
0.0 b
40.0 a
0.0 b
40.5 a
0.0 b
35.7 a
0.0 b
  39.5 a
0.0 b
   

Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 51.6 a
0.0 b
34.0 a
0.0 b
56.4 a
0.0 b
43.8 a
0.0 b
60.4 a
0.0 b
60.1 a
0.0 b
density functional LSDA 18.0 a
0.0 b
2.0 a
0.0 b
27.0 a
0.0 b
12.7 a
0.0 b
24.8 a
0.0 b
24.9 a
0.0 b
SVWN 18.0 a
0.0 b
2.0 a
0.0 b
27.0 a
0.0 b
12.7 a
0.0 b
24.8 a
0.0 b
24.9 a
0.0 b
BLYP 50.3 a
0.0 b
38.2 a
0.0 b
58.8 a
0.0 b
48.8 a
0.0 b
58.0 a
0.0 b
57.9 a
0.0 b
B1B95 20.6 a
0.0 b
3.9 a
0.0 b
28.2 a
0.0 b
13.9 a
0.0 b
33.2 a
0.0 b
33.2 a
0.0 b
B3LYP 44.4 a
0.0 b
30.7 a
0.0 b
52.5 a
0.0 b
41.4 a
0.0 b
52.1 a
0.0 b
52.1 a
0.0 b
B3LYPultrafine 44.5 a
0.0 b
30.8 a
0.0 b
52.5 a
0.0 b
41.4 a
0.0 b
52.2 a
0.0 b
52.1 a
0.0 b
B3PW91 29.3 a
0.0 b
13.9 a
0.0 b
37.4 a
0.0 b
24.3 a
0.0 b
38.4 a
0.0 b
38.4 a
0.0 b
mPW1PW91 26.7 a
0.0 b
10.8 a
0.0 b
34.6 a
0.0 b
21.3 a
0.0 b
36.0 a
0.0 b
35.9 a
0.0 b
M06-2X 17.1 a
0.0 b
-0.2 a
0.0 b
26.1 a
0.0 b
11.2 a
0.0 b
33.7 a
0.0 b
33.7 a
0.0 b
PBEPBE 29.4 a
0.0 b
14.5 a
0.0 b
38.1 a
0.0 b
25.0 a
0.0 b
38.9 a
0.0 b
38.8 a
0.0 b
PBEPBEultrafine 29.4 a
0.0 b
14.5 a
0.0 b
38.2 a
0.0 b
25.1 a
0.0 b
38.9 a
0.0 b
38.8 a
0.0 b
PBE1PBE 24.4 a
0.0 b
7.9 a
0.0 b
32.3 a
0.0 b
18.2 a
0.0 b
34.0 a
0.0 b
34.0 a
0.0 b
HSEh1PBE 26.1 a
0.0 b
9.4 a
0.0 b
33.8 a
0.0 b
19.6 a
0.0 b
35.7 a
0.0 b
35.7 a
0.0 b
Moller Plesset perturbation MP2 48.5 a
0.0 b
17.3 a
0.0 b
53.2 a
0.0 b
26.3 a
0.0 b
58.9 a
0.0 b
58.9 a
0.0 b
MP2=FULL 48.5 a
0.0 b
17.3 a
0.0 b
53.2 a
0.0 b
26.3 a
0.0 b
58.7 a
0.0 b
58.7 a
0.0 b
MP3 48.9 a
0.0 b
22.4 a
0.0 b
53.4 a
0.0 b
31.3 a
0.0 b
58.4 a
0.0 b
58.3 a
0.0 b
MP4 53.7 a
0.0 b
25.9 a
0.0 b
58.0 a
0.0 b
34.5 a
0.0 b
63.7 a
0.0 b
63.6 a
0.0 b
MP4=FULL 53.7 a
0.0 b
25.9 a
0.0 b
58.0 a
0.0 b
34.5 a
0.0 b
63.5 a
0.0 b
63.4 a
0.0 b
Configuration interaction CID 49.0 a
0.0 b
21.6 a
0.0 b
53.1 a
0.0 b
30.5 a
0.0 b
58.5 a
0.0 b
58.4 a
0.0 b
CISD 50.3 a
0.0 b
22.9 a
0.0 b
54.0 a
0.0 b
31.6 a
0.0 b
59.8 a
0.0 b
59.6 a
0.0 b
Quadratic configuration interaction QCISD 56.8 a
0.0 b
27.7 a
0.0 b
60.6 a
0.0 b
36.1 a
0.0 b
66.4 a
0.0 b
66.2 a
0.0 b
QCISD(T) 57.9 a
0.0 b
29.0 a
0.0 b
61.5 a
0.0 b
37.1 a
0.0 b
67.1 a
0.0 b
67.0 a
0.0 b
QCISD(TQ) 58.0 a
0.0 b
29.3 a
0.0 b
61.6 a
0.0 b
37.3 a
0.0 b
67.1 a
0.0 b
67.0 a
0.0 b
Coupled Cluster CCD 53.8 a
0.0 b
24.5 a
0.0 b
58.3 a
0.0 b
33.4 a
0.0 b
63.5 a
0.0 b
63.4 a
0.0 b
CCSD 56.5 a
0.0 b
27.2 a
0.0 b
60.3 a
0.0 b
35.6 a
0.0 b
66.0 a
0.0 b
65.8 a
0.0 b
CCSD=FULL 56.5 a
0.0 b
27.2 a
0.0 b
60.3 a
0.0 b
35.6 a
0.0 b
65.8 a
0.0 b
65.6 a
0.0 b
CCSD(T) 57.9 a
0.0 b
28.9 a
0.0 b
61.5 a
0.0 b
37.0 a
0.0 b
67.1 a
0.0 b
67.0 a
0.0 b
CCSD(T)=FULL 57.9 a
0.0 b
28.9 a
0.0 b
61.5 a
0.0 b
36.9 a
0.0 b
67.0 a
0.0 b
66.8 a
0.0 b

Single point energy calculations (select basis sets)
6-311+G(3df,2p) cc-pVDZ cc-pVTZ aug-cc-pVDZ aug-cc-pVTZ cc-pV(T+d)Z
Moller Plesset perturbation MP2FC// HF/6-31G* 24.8 a
0.0 b
27.2 a
0.0 b
25.0 a
0.0 b
29.1 a
0.0 b
26.4 a
0.0 b
25.0 a
0.0 b
MP2FC// B3LYP/6-31G* 14.7 a
0.0 b
27.9 a
0.0 b
25.5 a
0.0 b
29.8 a
0.0 b
26.9 a
0.0 b
25.5 a
0.0 b
MP2FC// MP2FC/6-31G* 26.8 a
0.0 b
30.2 a
0.0 b
27.0 a
0.0 b
32.2 a
0.0 b
28.4 a
0.0 b
27.0 a
0.0 b
MP4// HF/6-31G* 33.3 a
0.0 b
35.9 a
0.0 b
33.9 a
0.0 b
    33.9 a
0.0 b
MP4// B3LYP/6-31G*   37.0 a
0.0 b
34.3 a
0.0 b
    34.3 a
0.0 b
MP4// MP2/6-31G* 35.1 a
0.0 b
  36.1 a
0.0 b
    36.1 a
0.0 b
Coupled Cluster CCSD// HF/6-31G* 34.2 a
0.0 b
37.0 a
0.0 b
34.9 a
0.0 b
37.9 a
0.0 b
  34.9 a
0.0 b
CCSD(T)// HF/6-31G* 35.3 a
0.0 b
38.7 a
0.0 b
35.9 a
0.0 b
39.3 a
0.0 b
  35.9 a
0.0 b
CCSD// B3LYP/6-31G* 24.0 a
0.0 b
37.5 a
0.0 b
35.0 a
0.0 b
    35.0 a
0.0 b
CCSD(T)// B3LYP/6-31G* 24.4 a
0.0 b
39.3 a
0.0 b
36.3 a
0.0 b
    36.3 a
0.0 b
CCSD(T)//B3LYP/6-31G(2df,p)     36.0 a
0.0 b
    36.0 a
0.0 b
CCSD// MP2FC/6-31G* 35.8 a
0.0 b
39.8 a
0.0 b
36.5 a
0.0 b
40.8 a
0.0 b
37.3 a
0.0 b
36.5 a
0.0 b
CCSD(T)// MP2FC/6-31G* 37.5 a
0.0 b
41.9 a
0.0 b
38.1 a
0.0 b
42.6 a
0.0 b
38.9 a
0.0 b
38.1 a
0.0 b
NC = not calculated
For descriptions of the methods (AM1, HF, MP2, ...) and basis sets (3-21G, 3-21G*, 6-31G, ...) see the glossary in section I.C. Predefined means the basis set used is determined by the method.
gaw refers to the group additivity method implemeted in the NIST Chemistry Webbook.

See section III.C.1 List or set vibrational scaling factors to change the scale factors used here.
See section III.C.2 Calculate a vibrational scaling factor for a given set of molecules to determine the least squares best scaling factor.