3.1. Molecular Geometry
The optimized molecular structure at the highest level of our study i.e., at b3lyp /6–311 + + g** level along with numbering scheme is given in Figs. 1(a) and 1(b). The optimized molecular structure of BTF possesses Cs point group symmetry. The symmetry plane passes through the atoms H9, C4, C1, C12 and F13 with the F14 and F15 atoms symmetrically on either side of this plane.
Figures1 (a) and 1(b).
The optimized geometrical parameters, namely, bond lengths, bond angles and dihedral angles at the rhf /6–31 + g*, b3lyp /6–31 + + g** and b3lyp /6–311 + + g** levels are collected in Table 1.
Table 1
Geometrical parameters of BTF (distances in Å and angles in degrees)
parameters | rhf/31 + + g** | b3lyp /31 + + g** | b3lyp /311 + + g** |
r (C1, C2) | 1.387 | 1.399 | 1.396 |
r(C1, C6) | 1.387 | 1.399 | 1.396 |
r(C1, C12) | 1.505 | 1.506 | 1.504 |
r (C2, C3) | 1.386 | 1.396 | 1.392 |
r (C2, H7) | 1.074 | 1.085 | 1.083 |
r (C3, C4) | 1.387 | 1.398 | 1.394 |
r (C3, H8) | 1.075 | 1.086 | 1.084 |
r (C4, C5) | 1.387 | 1.398 | 1.394 |
r (C4, H9) | 1.076 | 1.086 | 1.084 |
r (C5, C6) | 1.386 | 1.396 | 1.392 |
r (C5, H10) | 1.075 | 1.086 | 1.084 |
r (C6, H11) | 1.074 | 1.085 | 1.083 |
r (C12, F13) | 1.329 | 1.362 | 1.359 |
r (C12, F14) | 1.325 | 1.357 | 1.353 |
r (C12, F15) | 1.325 | 1.357 | 1.353 |
r (H7… F13) | 3.272 | 3.301 | 3.295 |
r (H7… F14) | 3.906 | 3.952 | 3.942 |
r (H7… F15) | 2.480 | 2.495 | 2.489 |
r (H11…F13) | 3.272 | 3.301 | 3.295 |
r (H11…F14) | 2.480 | 2.495 | 2.489 |
r (H11… F15) | 3.906 | 3.952 | 3.942 |
r (F13…F14) | 2.128 | 2.177 | 2.172 |
r (F14…F15) | 2.134 | 2.183 | 2.176 |
r (F13…F15) | 2.128 | 2.177 | 2.172 |
α(C1,C12, F13) | 111.9 | 111.8 | 111.8 |
α(C1,C12, F14) | 112.1 | 112.4 | 112.3 |
α(C1,C12, F15) | 112.1 | 112.4 | 112.3 |
α(F13,C12, 14) | 106.6 | 106.4 | 106.4 |
α(F13,C12,F15) | 106.6 | 106.4 | 106.4 |
α(F14,C12,F15) | 107.2 | 107.1 | 107.1 |
δ(C12, C1, C2, C3) | 177.9 | 177.7 | 177.7 |
δ(C12, C1, C2, H7) | -2.4 | -2.7 | -2.9 |
δ(C12, C1, C6, C5) | -177.9 | -177.7 | -177.7 |
δ(C12, C1, C6, H11) | 2.4 | 2.7 | 2.9 |
δ(C2, C1, C12, F13) | -88.9 | -88.8 | -88.7 |
δ(C2, C1, C12, F14) | 151.4 | 151.7 | 151.7 |
δ(C2, C1, C12, F15) | 30.7 | 30.8 | 30.9 |
δ(C6, C1, C12, F13) | 88.9 | 88.8 | 88.7 |
δ(C6, C1, C12, F14) | -30.7 | -30.8 | -30.9 |
δ(C6, C1, C12, 15) | -151.4 | -151.7 | -151.7 |
Optimized structure yields identical bond length pairs for the bonds C1 – C2 and C1 – C6, C2 – C3 and C5 – C6, and C3 – C4 and C4 – C5 at all the three levels of calculations rhf /6–31 + g*, b3lyp /6–31 + + g** and b3lyp /6–311 + + g**. The magnitudes of all the 6-ring C – C bond lengths are in the range of partial double bond and have same magnitudes up to 2nd place of decimal indicating extensive involvement of these bonds in conjugation. The calculated bond length of C1 – C12 at all the levels of calculations are almost same and in the range of single C – C bond length (1.504 A°). The C12 – F13 bond length has been calculated to be slightly higher than the other two C–F bonds (C12 – F14 and C12 – F15) at all the levels of the calculations. The magnitudes of all the three C–F bond lengths increase from rhf /6–31 + + g** to b3lyp /6–31 + + g** and decrease from b3lyp /6–31 + + g**to b3lyp /6–311 + + g** level.
The C12 – F14 and C12 – F15 bond lengths are exactly equal (1.353 A°) however, their magnitudes are smaller than C12 – F13 bond length (1.359 A° ). All these C–F bond lengths are slightly smaller than C –F bond length (1.37 A° ) for the Fluorine atom directly attached to the benzene ring suggesting stronger bonding between the C and F atoms in the CF3 group as compared to the aromatic ring carbon- fluorine bond. Non - bonded distance H7…..F13 is longer than H7…..F15 and H11…..F13 is longer than H11.…..F14. The calculated distances F13 …..F14 and F13…..F15 are found to have the same magnitudes ( 2.172 A°) but these are slightly smaller than the distance F14…..F15 ( 2.176 A°). The bond angle C1 – C12 – F13 decreases from rhf to b3lyp level of calculations and its magnitude is found to be (111.80). The bond angles C1 – C12 – F14 and C1 – C12 – F15 are equal in magnitudes (112.30). Their values increase from rhf /6–31 + + g** to b3lyp /6–31 + + g** and decrease from b3lyp /6–31 + + g** to b3lyp /6–311 + + g** level. The magnitudes of the angles F13 – C12 – F14 and F13 – C12 – F15 are identical (106.40). Their magnitudes decrease from the rhf to the b3lyp level of calculations. The angle F14 – C12 – F15 (107.10) is higher than the angles F13 – C12 – F14 and F13 – C12 – F15 which is in conformity with larger non–bonded distance between F14 and F15 as compared to the non-bonded distances F13 … F14 and F13 … F15 discussed above. The dihedral angles C12– C1 – C2 – C3 and C12 – C1 – C6 –C5 decrease from the rhf to the b3lyp /6–31 + + g** to theb3lyp /6–311 + + g** levels and are calculated to be 177.70. Thus, the C12 atom is found to be slightly out of phenyl ring–plane. The dihedral angles C12 – C1 – C2 – H7 and C12 – C1 – C6 – H11 increase from the rhf to the b3lyp /6–31 + + g** to the b3lyp /6–311 + + g** level and are calculated to be 2.90 which also indicates that the C12 atom is slightly out of phenyl ring–plane. The dihedral angles C2 – C1 – C12 – F13 and C6 – C1 – C12 – F13 decrease from the rhf to the b3lyp level and each one of these is found to have a magnitude of 88.70. The dihedral angles C2 – C1 – C12 – F14 and C6 – C1 – C12 – F14 increase from the rhf to the b3lyp level and their magnitudes are found to be 151.70 and − 30.90, respectively. The magnitudes of the dihedral angles C2 – C1 – C12 – F15 and C6 – C1 – C12 – F15 increase from the rhf to the b3lyp level and are calculated to be 30.90 and − 151.70, respectively. Thus, it is clear that F14 and F15 are out of plane and are situated on one side of the phenyl ring – plane whereas the F13 atom resides on the opposite side of this plane. This can be viewed from the optimized structure at the highest level of calculation shown in Fig. 1(b).
3.2 Atomic Charges
APT atomic charges at various atomic sites of the BTF molecule calculated at the rhf /6–31 + g*, b3lyp/6–31 + + g** and b3lyp/6–311 + + g** levels are collected in Table 2.
Table-2. APT atomic charges at various atoms of the BTF molecule
S.No.
|
Atoms
|
rhf /6-31++g**
|
b3lyp /6-31++g**
|
b3lyp /6-311++g**
|
1
|
C1
|
-0.140
|
-0.165
|
-0.164
|
2
|
C2
|
-0.023
|
-0.017
|
-0.023
|
3
|
C3
|
-0.069
|
-0.043
|
-0.045
|
4
|
C4
|
0.029
|
0.009
|
0.004
|
5
|
C5
|
-0.069
|
-0.043
|
-0.045
|
6
|
C6
|
-0.023
|
-0.017
|
-0.023
|
7
|
H7
|
0.069
|
0.064
|
0.067
|
8
|
H8
|
0.044
|
0.038
|
0.041
|
9
|
H9
|
0.044
|
0.038
|
0.043
|
10
|
H10
|
0.044
|
0.038
|
0.041
|
11
|
H11
|
0.069
|
0.064
|
0.067
|
12
|
C12
|
1.873
|
1.771
|
1.805
|
13
|
F13
|
-0.638
|
-0.599
|
-0.610
|
14
|
F14
|
-0.605
|
-0.569
|
-0.579
|
15
|
F15
|
-0.605
|
-0.569
|
-0.579
|
APT charges at the atomic sites C2 and C6 are equal and similarly those at the atomic sites C3 and C5 are equal. These values are found to be − 0.023 and − 0.045, respectively. The magnitudes of the atomic charges decrease from the rhf /6–31 + + g** to the b3lyp /6–31 + + g** and increases from the b3lyp /6–31 + + g** to the b3lyp /6–311 + + g** level. The atomic charge at the site C1 increases from the rhf to the b3lyp level of calculation and possesses the value − 0.164 whereas the magnitude of atomic charge at the site C4 decreases from the rhf /6–31 + + g** to the b3lyp /6–31 + + g** to the b3lyp /6–311 + + g** and found to have the value 0.004. Thus, all the carbon atoms in the phenyl ring possess –ve charges except the carbon atom C4. The order of magnitude of the negative charge on the ring carbon atoms are as C1 > (C3 / C5) > (C2 / C6). The carbon atom C12 possesses the highest positive charge (1.805). The magnitude of charge on C12 decreases from the rhf /6–31 + + g** to the b3lyp /6–31 + + g**and increases from the b3lyp /6–31 + + g**to the b3lyp /6–311 + + g**level. Amongst the three fluorine atoms F13 possesses the highest negative charge (–0.610) than the other two fluorine atoms which possess equal negative charges (–0.579). Since C12 is attached with highly electronegative fluorine atoms, it is expected to possess the highest + ve charge and therefore, it would exhibit electron withdrawing inductive effect on the benzene ring nucleus. Due to this withdrawing inductive effect of the CF3 group the highest electron charge accumulation takes place at the C1 carbon atom of the ring (–0.164). The charge density decreases at the ortho (C2, C6) and the para (C4) positions due to electromeric effect of the electron withdrawing CF3 group. Consequently, C3 and C5 meta position carbon atoms of the ring possess more –ve charge than all the ring carbon atoms except C1. It is to be noted that the electron withdrawing effect is most prominent at the para position, resulting in positive charge (0.004) the site C4.
3.3 Vibrational Frequencies and their Assignments
Optimized structure at the b3lyp /6–311 + + g** level shown in the Figs. 1(a) and 1(b) of the BTF molecule shows that it is a non-planar molecule having Cs molecular symmetry. Its 39 normal modes of vibrations are distributed between the two symmetry species of the Cs point group as:
Phenyl ring: 17 a′ + 13 a″ CF3 group : 5 a′ + 4 a″
Under the Cs point group symmetry all the modes are Raman and IR active. The fundamental frequencies calculated at the rhf /6–31 + g*, b3lyp /6–31 + + g** and b3lyp /6–311 + + g** levels are collected in Table 3.
Table-3 Calculated and observed fundamental frequencies (cm-1) of BTF
S.
No.
|
Calculated
|
Observed#
|
Mode assignments
|
rhf
|
b3lyp
|
IR
|
Raman
|
6-31+g*
|
6-31++g**
|
6-311++g**
|
cm-1
rel. int.
|
cm-1
rel. int.
|
1
|
6(0.03,3).75
|
4(0.04, 3).75
16(0.0, 3.4) .75161
|
16(0.04, 3).75
|
|
|
t (CF3) (a²)
|
2
|
144(0.01,4).75
|
131(0.01, 4).75
|
131(0.01, 4) .75
|
140(vw)
|
139(s,p)
|
g(C-CF3) (a¢)
|
3
|
214(1,0.04).75
|
195(1, 0.04).75
|
196(0.5,0.1) .75
|
203(w)
|
199(vvw)
|
b(C-CF3) (a²)
|
4
|
349(3,1)29
|
319(2,1).36
|
320(2,1).34
|
317(vvw)
|
321(vw,dp)
|
rII(CF3) (a¢)
|
5
|
366(3,3).23
|
339(3, 3).23
|
340(3,3).24
|
336(s)
|
339(m,p)
|
ds(CF3) (a¢)
|
6
|
431(1,0.4).75
|
390(1, 1).75
|
394(1, 1).75
|
393(m)
|
|
r^ (CF3) (a²)
|
7
|
451(0.01,0.01).75
|
412(0.001,0.01).75
|
409(0.02, 0.03).75
|
403(m)
|
400(w,dp)
|
f (ring) (a²)
|
8
|
534(1,0.4).62
|
480(1, 1).64
|
483(1, 1).66
|
485(m)
|
485(vvwd,dp)
|
das (CF3) (a¢)
|
9
|
626(0.4,1).75
|
563(0.03, 1).75
|
568(0.1, 1).75
|
585
|
583(vvwb)
|
das (CF3) (a²)
|
10
|
652(11,0.2).53
|
590(7, 0.3).60
|
591(6, 0.3).67
|
596(s)
|
|
f (ring) (a¢)
|
11
|
675(0.1,5) .75
|
630(0.1, 5).75
|
632(0.1, 5).75
|
616(w sh)
|
618(m,dp)
|
a (ring) (a²)
|
12
|
715(24, 1)54
|
657(18, 1).74
|
662(18, 1).75
|
657(s)
|
658(w,p)
|
a (ring) (a¢)
|
13
|
771(59,0.03).44
|
707(44, 0.005).33
|
702(45, 0.02).32
|
695(s)
|
|
f (ring) (a¢)
|
14
|
841(1, 12).02
|
766(0.5, 13).02
|
768(1, 13).03
|
763
|
770(s,p)
|
ns(CF3) (a¢)
|
15
|
863(58, 1).30
|
781(49, 1).07
|
780(52, 1).05
|
770(s)
|
|
g(CH) (a¢)
|
16
|
956(0.1, 1).75
|
860(0.1, 0.1).75
|
857(0.2, 0.1).75
|
843(w)
|
844(vwd,dp)
|
g(CH) (a²)
|
17
|
1057(7, 0.4).42
|
944(7, 0.2).49
|
941(8, 0.2).45
|
923(m)
|
925(vwd,dp)
|
g(CH) (a¢)
|
18
|
1088(0.01, 44).03
|
1016(3, 30).04
|
1018(1, 34).04
|
1004(w)
|
1004(vs,p)
|
a (ring) (a¢)
|
19
|
1113(0.04, 0.01).75
|
990(0.1, 0.1).75
|
985(0.1, 0.01).75
|
970(vw)
|
972(vwd,p)
|
g(CH) (a²)
|
20
|
1118(26, 14).08
|
1043(49,22).03
|
1042(52, 16).04
|
1028(s)
|
1027(m,p)
|
n (ring) (a¢)
|
21
|
1132(0.1, 0.01).68
|
1010(0.1, 0.01).74
|
996(0.2, 0.01).72
|
990(vvw)
|
991(w)
|
g(CH) (a¢)
|
22
|
1176(8, 0.1).75
|
1095(68, 1).75
|
1089(91, 1).75
|
1067
|
|
b(CH) (a²)
|
23
|
1177(82, 3).09
|
1081(73, 1).62
|
1078(84, 2).69
|
1031
|
|
b(CH) (a¢)
|
24
|
1215(29, 2).75
|
1188(0.1, 3).75
|
1187(0.1, 3).75
|
1156
|
1164(wd,dp)
|
b(CH) (a²)
|
25
|
1296(5, 3).73
|
1207(4, 5).71
|
1205(4, 4).69
|
1180(vs)
|
1187(wd,p)
|
b(CH) (a¢)
|
26
|
1313(309, 3).68
|
1121(274, 4).45
|
1104(277, 4).41
|
1072(vs)
|
1080(w,p)
|
n as(CF3) (a¢)
|
27
|
1320(117, 0.3).75
|
1166(162, 1).75
|
1153(150, 1).75
|
1152(vs)
|
1164(wd,dp)
|
n as(CF3) (a²)
|
28
|
1369(95, 1).75
|
1363(0.4, 0.1).75
|
1339(1, 0.1).75
|
1303(vw)
|
|
n (ring) (a²)
|
29
|
1468(378, 6).75
|
1325(328,19).13
|
1318(338, 20).14
|
1328(vs)
|
1324(m, p)
|
n (C-CF3) (a¢)
|
30
|
1471(9, 0.3).75
|
1348(3,0.3).75
|
1355(2, 0.2).75
|
1362(m)
|
1365(vvvw)
|
b(CH) (a²)
|
31
|
1608(28, 0.2).75
|
1487(17,0.4).75
|
1483(18, 0.3).75
|
1459(vs)
|
1458(vvw,dp)
|
n (ring) (a²)
|
32
|
1667(0.2,1).65
|
1535(0.1,0.1).73
|
1530(0.03, 0.1).75
|
1502(vvw)
|
|
n (ring) (a¢)
|
33
|
1781(1,12).75
|
1638(0.3,9).75
|
1630(0.2, 8).75
|
1614(w)
|
1610(m, dp)
|
n (ring) (a²)
|
34
|
1809(10,21).75
|
1657(6,25).71
|
1648(6, 24).71
|
1614(w)
|
1593(w, p)
|
n (ring) (a¢)
|
35
|
3349(0.3,45).75
|
3187(0.3,52).75
|
3170(0.2, 48).75
|
|
2995(w,p)
|
n (CH) (a¢)
|
36
|
3362(8,100).75
|
3198(8,111).75
|
3181(7, 104).75
|
3049(m )
|
|
n(CH) (a²)
|
37
|
3372(16,53).33
|
3207(13, 75).26
|
3190(11, 67).27
|
|
3022(w,p )
|
n(CH) (a¢)
|
38
|
3383(11,6) .75
|
3218(7, 8).75
|
3201(6, 6).75
|
|
|
n(CH) (a²)
|
39
|
3386(2,268).15
|
3220(2, 296).14
|
3203(2, 297).13
|
3076(m)
|
3076(s,p)
|
n(CH)(a¢)
|
# taken from Refs.2 and 4; rel. int.= relative intensity. The numbers left to the brackets under the columns 2, 3 and 4
correspond to the frequencies and those right to the brackets correspond to the values of depolarisation ratios.
The first numbers in the brackets correspond to the IR intensities and the second numbers to the Raman intensities.
s = strong, m = medium, v=very, w = weak, sh = shoulder, s = strong, b= broad, d= diffused, p= polarized, dp = depolarized.
3.3.1 C–H Modes:
The 5 C–H bonds give rise to the 15 normal modes which are distributed under the Cs symmetry as: a’ − 3 ν(CH) + 2 β(CH) + 3γ (CH); a” – 2 ν(CH) + 3β(CH) + 2γ (C–H). Pictorial view of the normal modes shows that all the five ν(CH) modes are pure ν(CH) modes. It is to be noted that the calculated frequencies 3203, 3190 and 3170 cm− 1 belong to the symmetric species a′ and the frequencies 3201 and 3181 cm–1 to the anti-symmetric species a″. The five β(CH) modes are identified as the calculated frequencies 1355, 1205, 1187, 1089 and 1078 cm− 1. Out of these the frequencies 1205 and 1078 cm− 1 belong to the species a′ and the remaining three frequencies to the species a″. It could be seen from the GaussView that the frequency 1205 cm− 1 is a pure CH planar bending mode whereas the frequency 1078 cm− 1 arises due to the mixing of the CH planar bending mode with the ring stretching and the symmetric CF3 stretching modes. Out of the three β(CH) frequencies under the species a″ the frequency 1187 cm− 1 appears to arise due to pure CH planar bending mode. However, the frequency 1355 cm− 1 arises due to the mixing of the CH planar bending mode with the ring stretching mode and the frequency 1089 cm− 1 originates due to the coupling of the CH planar bending mode with the ring stretching and the anti-symmetric CF3 (a″) stretching modes.
Out of the 5 γ(CH) frequencies calculated as 996, 985, 941, 857 and 780 cm− 1, the frequencies 996, 941 and 780 cm− 1 belong to the species a′ and the frequencies 985 and 857 to the species a″. The two higher frequencies under the symmetric species and the two frequencies under the anti–symmetric species appear to be pure γ(CH) modes while the lowest frequency of the symmetric species appear to mix with the non-planar ring deformation mode slightly.
3.3.2 CF3 group modes
The pictorial view suggests that out of the nine modes of the CF3 group the modes τ, ρ⊥, δas(a″) and νas(a’) are almost pure CF3 group modes and these are calculated to be 16, 394, 568 and 1104 cm− 1. The other five CF3 group modes are coupled modes. The calculated frequency 340 cm− 1 contains contribution from the δs and the planar ring bending modes. Similarly, the calculated frequency 483 cm− 1 arises due to the mode δas(a’) coupled with the non–planar ring bending mode. Assignment of the νs(CF3) mode has been controversial and has been widely discussed in the literature. It is to be noted that in the Raman spectra of benzene derivatives with CF3 group (s) one observes frequencies in the ranges 700–800 cm− 1 and 1300–1350 cm− 1 with good intensities and low depolarisation ratios. Some authors [1] have assigned the νs(CF3) mode in the range 1300–1350 cm− 1 and the δs(CF3) mode in the range 700–800 cm− 1, while some other group of workers [5] have assigned the νs(CF3) mode in the range 700–800 cm− 1 and the ν(C–CF3) mode in the range 1300–1350 cm− 1. The δs (CF3) mode has been assigned at a much lower frequency (in the range 275–350 cm− 1) by the latter group of workers. The present ab initio calculations favour the assignments of the latter group of workers and the most suitable candidate for the mode νs(CF3) is calculated to be 768 cm− 1. It may be noted here that this mode also involves planar ring deformation and slight ν(C–CF3) modes. Similarly, the modes νas(a’) and νas(a”) are identified as the calculated frequencies 1104 and 1153 cm− 1. Usually C–F stretching appears with very large IR intensity. The calculated IR intensities for the νas (a’ and a”) are found to be substantially large. The observed IR bands at 1072 and 1152 cm− 1 with very strong IR intensities are correlated to the calculated frequencies 1104 and 1153 cm− 1 respectively.
3.3.3 C – CF3 Modes
The C–CF3 bond gives arise to the three normal modes, namely, the ν(C–CF3), β(C–CF3) and γ(C–CF3) modes. As discussed earlier, the mode ν(C–CF3) has been assigned in the range 1300–1350 cm− 1 for a number of benzene derivatives containing CF3 group (s). The present calculation places this mode at 1318 cm− 1. Pictorial view suggests that this mode is coupled with β(C–H) and νs(CF3) modes. The β and γ modes are calculated to be at 196 and 131 cm− 1 with the corresponding observed band at ~ 200 and 140 cm− 1 respectively and these are found to be pure modes.
3.3.4 Phenyl Ring Modes
The six ring stretching modes are identified as 1648 1630, 1530, 1483, 1339 and 1042 cm− 1. It could be seen that the first five frequencies involve mixing of the ring stretching with the planar CH bending modes while the last one is a result of the mixing of the ring stretching and the νs(CF3) modes. It corresponds to the ring breathing mode (993 cm− 1) of benzene. Assignment for this mode has been controversial in benzene derivatives and is widely discussed in the published literature. Though it is forbidden in IR spectrum under D6h symmetry, in the present case it has good IR intensity. The observed frequency corresponding to this mode is 1028 cm− 1. Out of the three ring planar deformation modes the trigonal bending mode is one of the substituent sensitive modes, because in this mode the alternate three C atoms of the ring come closer to and the remaining three C atoms go farther from the ring center. Thus, one triangle formed by the alternate C atoms contract while the other one expands. Therefore, when one substituent is replaced for a H atom one of the triangles is loaded which makes the triangular motion of the triangle containing the substituent difficult. However, the other triangle remains unaffected. Thus, in mono substituted benzenes with a heavy substituent the trigonal ring bending remains practically unaffected. For BTF this mode is calculated to have the frequency 1018 cm− 1. The other two ring planar bending modes are identified as the frequencies 662 and 632 cm− 1 corresponding to the species a’ and a”. The torsional motions of the ring give rise to three modes in substituted benzenes. In the case of BTF the mode corresponding to the phenyl ring torsional mode 4 is calculated to be 702 cm− 1 and those corresponding to the mode 16 as 591 (a’) and 409 (a”) cm− 1.