Table 3: Calculated vibrational frequencies for S1 state of benzoic acid dimer at the CIS/6-311++G(d,p) level ( 𝜈 , stretching; 𝛿 , in-plane bending; 𝛾 , out-of-plane bending; 𝜏 , torsion).

No.Sym.Freq. 𝜈 (cm−1)Approximate description

1A′′16“Butterfly” monomers twisting
2A′′30Oop. monomers twisting
3A45Ip. monomers twisting (“cogwheel”)
4A′′52Oop. monomers rocking
5A′′71 𝜏 (COOH)
6A′′80 𝜏 (COOH)
7A87Ip monomers rocking (H-bond shearing)
8A96H-Bonds stretching
9A′′103 𝜏 (COOH)
10A′′172 𝛾 (–COOH) (A)
11A214 𝛿 (–COOH) (B)
12A′′215 𝛾 (–COOH) (B)
13A249 𝛿 (–COOH) (A)
14A′′306Oop. ring deform. (B)
15A307Ip. ring deform. (B)
16A′′327Oop. asym. rings deform.
17A380Ip. ring deform. (A)
18A402Ip. ring deform. (B)
19A′′409Oop. ring deform. (A)
20A′′437Oop. ring deform. (A)
21A497 𝛿 (C–COOH) (A)
22A525 𝛿 (C–COOH) (B)
23A592 𝛿 (COOH) sciss. + ip. ring deform. (B)
24A606Ip. ring deform. (A)
25A′′624 𝛾 (CH) (B)
26A646 𝛿 (COOH) sciss. + ip. ring deform. (A)
27A′′673Oop. ring deform. (A)
28A′′700 𝛾 (COOH) + 𝛾 (CH) (B)
29A′′718 𝛾 (CH) (A)
30A740 𝛿 (COOH) sciss. + ring breath. (B)
31A′′746 𝛾 (OH) + 𝛾 (CH) (B)
32A′′755 𝛾 (OH) + 𝛾 (CH) (B)
33A777 𝛿 (COOH) sciss. + ring breath. (A)
34A′′780 𝛾 (C–COOH) + 𝛾 (OH) + 𝛾 (CH) (B)
35A′′816 𝛾 (C–COOH) + 𝛾 (OH) + 𝛾 (CH) (A)
36A′′836 𝛾 (CC) + 𝛾 (CH) (B)
37A′′860 𝛾 (CC) + 𝛾 (CH) (A)
38A′′877 𝛾 (OH) (A)
39A′′901 𝛾 (OH) (B)
40A903 𝜈 (CC)ring (B)
41A944Ring breath. (B)
42A965 𝜈 (CC)ring (B)
43A′′965 𝛾 (CH)
44A976Ring breath. (A)
45A1003Ring breath. (A)
46A′′1004 𝛾 A(CH) (A)
47A′′1009 𝛾 A(CH) (A)
48A1021 𝜈 (CC)ring (B)
49A1050 𝜈 (CC)ring (A)
50A1089 𝜈 (CC)ring + 𝛿 (CH) (A)
51A1099 𝛿 (CC)ring + 𝛿 (CH) (B)
52A1111 𝜈 (CC)ring + 𝛿 (CH) (A)
53A1133 𝛿 (CH) (B)
54A1155 𝛿 (CH) (A)
55A1201 𝜈 (CC)ring + 𝛿 (CH) (A)
56A1205 𝜈 (CC)ring + 𝛿 (CH) (B)
57A1254 𝛿 (OH) (B)
58A1282 𝛿 (OH) (A)
59A1309 𝛿 (CH) (B)
60A1312 𝛿 (CH) (A)
61A1385 𝛿 (CH) (B)
62A1392 𝛿 (CH) ( A + B )
63A1417 𝛿 (CH) ( A + B )
64A1437 𝜈 (CC)ring + 𝛿 (CH) (A)
65A1445 𝜈 (CC)ring + 𝛿 (CH) (B)
66A1485 𝜈 (CC)ring + 𝛿 (CH) (A)
67A1533 𝜈 (CC)ring + 𝛿 (CH) (B)
68A1586 𝜈 (CC)ring (B)
69A1587 𝜈 (CC)ring (A)
70A1609 𝜈 (CC)ring (A)
71A1653 𝜈 (C=O) (B)
72A1723 𝜈 (C=O) (A)
73A2990 𝜈 (CH) (A)
74A3004 𝜈 (CH) (A)
75A3013 𝜈 (CH) (A)
76A3015 𝜈 (CH) (B)
77A3020 𝜈 (CH) (B)
78A3034 𝜈 (CH) (A)
79A3038 𝜈 (CH) (A)
80A3039 𝜈 (CH) (B)
81A3047 𝜈 (CH) (B)
82A3051 𝜈 (CH) (B)
83A3367 𝜈 (OH) (A)
84A3473 𝜈 (OH) (B)

The calculated frequencies were uniformly scaled by a factor of 0.9. (A) and (B) label the molecule of the dimer, which is necessary for proper mode description.