Vibrational spectra, conformational equilibrium and ab initio calculations of 1,2-diphenylethane

Vibrational spectra, conformational equilibrium and ab initio

calculations of 1,2-diphenylethane

Anne Horna, Peter Klaeboea,*, Bojidar Jordanovb, Claus J. Nielsena, Valdemaras Aleksaa,1

aDepartment of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo 0315, NorwaybInstitute of Organic Chemistry, Bulgarian Academy of Sciences, BG-1113 Sofia, Bulgaria

Received 16 September 2003; accepted 4 November 2003

Dedicated to Professor Manfred Winnewisser and Dr Brenda Winnewisser for their outstanding contributions to Molecular Spectroscopy

Abstract

The infrared spectra of 1,2-diphenylethane were recorded as a melt and crystalline solid in capillary films and as a pellet in KBr and

polyethylene in the 4000–50 cm21 range. Moreover, the sample was isolated in an argon matrix at ca. 5 K, and the spectra recorded in the

range 3100–450 cm21, before and after annealing. Raman spectra of the melt were recorded between 295 (supercooled) and 357 K, and

spectra of the crystalline solid were obtained at ambient temperature.

A number of infrared and Raman bands in the melt vanish in spectra of the crystal, and the compound undoubtedly exists as a mixture of

two conformers in the melt, probably anti and gauche. Various non-coincidences between the infrared and Raman bands of the crystals agree

with C2h symmetry of the anti conformer. The intensity variations with temperature of two band pairs in the liquid phase Raman spectra were

used for van’t Hoff plots, giving a value of 2.4 ^ 0.5 kJ mol21 for DH (gauche–anti). The anti conformer had the lower energy and was also

present in the crystal. Very small intensity changes were detected when the matrix spectra were annealed to 36 K (argon) revealing that the

conformational barrier was too high to allow significant conversion from gauche to the anti conformer even at the highest annealing

temperature of 36 K.

Ab initio calculations were carried out with the GAUSSIAN 98 program at the RHF/6-311G* level and the vibrational frequencies for the

anti and gauche conformers including infrared and Raman intensities were calculated. After appropriate scaling, a reasonably good

agreement was obtained between the experimental and calculated wavenumbers for both conformers. Nearly all of the 78 fundamentals of the

anti and 24 of the gauche conformers were tentatively assigned. However, strong overlap between the anti and gauche conformer bands was

observed in most of the spectral region, and additional accidental degeneracy in the spectra prevented reliable assignments for all the

vibrational bands.

q 2003 Elsevier B.V. All rights reserved.

Keywords: 1,2-Diphenylethane; Conformational stability; Infrared and Raman spectra; Ab initio calculations

1. Introduction

1,2-Diphenylethane (dibenzyl), later to be abbreviated

DPE, is an example of a 1,2-disubstituted ethane, and this

group of molecules has been a classical field for

conformational investigations. In their pioneering studies

of 1,2-dihaloethanes by means of infrared and Raman

spectroscopy, Mizushima [1] and co-workers laid the

foundation for these investigations more than 50 years

ago. Unlike, the simple 1,2-dihaloethanes with 18 funda-

mental modes of each conformer, DPE has complex infrared

and Raman spectra with 78 vibrational modes due to the

bulky benzene substituents. Because of the complexity of

this molecule, only few spectroscopic investigations have

been published for DPE.

A number of X-ray studies of DPE have been reported

[2–6] revealing the anti conformer to be present in the

crystal. The central C–C bond was found to be considerably

shorter than usual [4–6]. This result was tentatively

interpreted [4] as an average of a 1:1 mixture of two

conformers in the crystal, which were interconverted by the

torsional vibration of the benzene rings as previously

0022-2860/$ - see front matter q 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.molstruc.2003.11.042

Journal of Molecular Structure 695–696 (2004) 77–94

www.elsevier.com/locate/molstruc

1 Permanent address: Department of General Physics and Spectroscopy,

Vilnius University, 2734 Vilnius, Lithuania.

* Corresponding author. Tel.: þ47-22-85-5678; fax: þ47-22-85-5441.

E-mail address: [email protected] (P. Klaeboe).

http://www.elsevier.com/locate/molstruc

assumed for stilbene [7]. However, the C–C distance

increases in DPE at lower temperatures [5] and the short

distance was interpreted as an artifact [6] caused by the

torsional vibrations of the C–Ph bonds in the crystal [5].

The IR and Raman spectra of crystalline DPE [8] were

studied more than 30 years ago, and although nearly all

the IR bands coincided with those observed in Raman, the

spectra were interpreted in terms of an anti conformer. The

vibrational spectra of DPE and some related molecules in

the neat solids and saturated solutions (CCl4) by Chiu et al.

[9] revealed additional bands in solution of some of the

derivatives, suggesting additional conformers. In their

spectroscopic investigation of DPE and some derivatives,

North et al. [10] also suggested an additional conformer in

CCl4 and C6H12 solution, but no additional bands were

observed, except for the band at 217 cm21 (see below).

When heated above the melting point, the spectra became

slightly richer [10] and these non-identified bands were

attributed to a probable gauche conformer, in addition to the

anti conformer in the solid.

Lately, DPE has been investigated by means of gaseous

electron diffraction technique at 373 K [11], and a

predominance of the anti conformer was reported. Various

theoretical calculations on DPE with different basis sets

[12–15] have been reported, but the enthalpy difference

[16] between the anti and gauche conformers gave

inconclusive results [16,17].

Since the infrared and Raman spectra of DPE were

reported approximately 30 years ago and these results were

quite incomplete after present day standards, we decided to

carry out a comprehensive study of this molecule. We

discovered that DPE was easy to work with and gave

favourable results. The sample, which melts at 325 K forms

easily a supercooled melt, which is metastable for weeks in

an ampoule at room temperature. The sample can be studied

as a capillary melt between KBr (MIR) or polyethylene

plates (FIR) and the IR spectra recorded. Another

alternative is to prepare pellets of DPE in KBr or

polyethylene matrices. These pellets can be investigated at

room temperature, giving spectra of the solid, and may be

heated above 325 K, resulting in melt spectra. Also, the

Raman spectra of a melt above 325 K, of a supercooled melt

at room temperature and of a crystalline solid were all easily

recorded. The Raman spectra showed no fluorescence even

at a higher temperature of approximately 360 K, and the

signal to noise ratio was quite high. It was found highly

advantageous to study the IR and Raman spectra of DPE as

a melt rather than in saturated solution. Finally, a number of

IR and Raman bands present in the melt spectra vanished in

those of the crystal, interpreted as a conversion to the more

stable conformer.

In the present investigation we have assumed that the anti

conformer has parallel benzene rings, situated at right angle

to the plane defined by the central CCCC bonds. This was

reported from X-ray studies of the crystal [5], and gives rise

to point group C2h with mutual exclusion between the IR

and Raman modes. The gauche conformer has been

interpreted in terms of C2 symmetry, although no definite

structural results are available to verify this assumption.

2. Experimental

2.1. Sample preparation

The sample of DPE was a commercial product from

E. Merck, Darmstadt, with the quality for synthesis (zur

Synthese). The sample was additionally purified by

sublimation for the purpose of spectral measurements. The

melting point was found to be the same as the literature

value, 325 K.

2.2. Infrared spectral measurements

The infrared spectra were recorded on various Fourier

transform spectrometers; Bruker models IFS-88 and IFS-66

(4000–400 cm21) and a Perkin–Elmer model 2000 (4000–

400 cm21) were employed in the middle infrared region

(MIR). Two different vacuum benches of Bruker IFS-113v

(600–50 cm21) were used in the far infrared region (FIR).

All the spectrometers had DTGS detectors. Beam splitters

of Ge/KBr were employed in MIR, Mylar beam splitters of

thickness 6 and 12 mm and a metal mesh beam splitter were

used in FIR. No vapour spectra could be investigated,

because of the low vapour pressure of DPE (less than

0.1 Torr at ambient temperature).

The melt and the crystalline solid were recorded by

various techniques. The powdered solid was deposited

between two KBr (MIR) or two polyethylene plates (FIR)

and heated to temperatures around 330 K. The sample

formed a capillary melt, which was immediately placed in the

spectrometers. Because of the tendency of DPE to supercool,

the capillary layer could be investigated for an extended time,

although the temperature fell below 300 K. The next day the

recordings were repeated, and now the sample formed a

crystalline layer, and the IR spectra revealed that various

bands in the melt had vanished. When the capillaries were

kept in a refrigerator at ca. 280 K, the spectra were identical

to those of the crystal obtained previously.

The sample was ground with KBr (MIR) or with

polyethylene (FIR) and pellets were pressed. The samples

of the crystal were very similar to those of the solid

capillary. When heated to ca. 330 K the pellets became quite

transparent because of melting. However, the sample

crystallized shortly after the temperature reached 300 K,

indicating only low supercooling in the pellets. Apparently,

the KBr or polyethylene matrix initiated crystallization of

DPE just below the melting point. Successful MIR spectra

were recorded within 15 min from melting the sample, but

in FIR some samples turned partly crystalline during the

recording, since longer time in the vacuum spectrometer

was required to record the spectra. Independently, pellets of

A. Horn et al. / Journal of Molecular Structure 695–696 (2004) 77–9478

Table 1

Infrared and Raman spectral data for 1,2-diphenylethane (DPE)

Infrared Raman Interpretation

Ar-matrix Melt Solid Melt Solid Anti Gauchea

Pellet Capillary Capillary Pellet36 Kb, 5 Kc 330 Kc 330 Kc 295 Kc 295 Kc 330 Kc 295 Kc

3211 w 3211 vw, P 3219 w3164 vw 3162 vvw 3162 vvw 3173 w, P 3173 w

3114 w 3104 w 3104 w 3104 w 3102 w 3104 vvw3090 s 3085 s 3085 s 3083 s 3082 m

3072 m, P 3071 vs Ag n1

3070 s 3063 s 3061 s 3058 s 3057 s 3063 s, P 3067 vs Bg n23

3059 w, sh 3054 vs, P 3052 s Ag n2

3045 vw, sh 3043 m, br 3043 m3034 vs 3027 vs 3027 vs 3027 vs 3026 vs 3030 w, br, D 3030 w, sh Au n40 Bu n58

3009 m 3003 w 3002 m 3002 m 3003 w, P 3003 w Au n41 Bu n59

2990 w 2987 w Ag n3

2980 w 2978 w Bg n24

2951 m Bu n60

2939 vw 2939 s 2944 vs 2943 s 2939 w, sh 2937 m Au n42

2932 m 2930 m 2924 m, sh2916 vw, sh 2925 s 2924 s 2919 m 2918 s 2917 w2896 vw, br 2896 m 2896 m, br Bg n25

2866 s 2858 s 2856 s 2856 m 2855 s 2864 m 2859 m Ag n4 Bu n61

2630 w 2630 w2604 w 2603 w 2603 w 2612 vw2582 w 2582 w 2589 w

1962 vw 1960 w, sh 1958 w, sh 1964 w1946 vw 1943 m 1943 m 1947 m1885 vw 1882 w, sh 1883 w, sh 1889 w1871 vw 1868 m 1868 m 1875 m1810 vw 1802 m 1802 m 1808 m

1745 w 1746 w 1751 m1636 vw 1635 vw

1625 m1619 m 1620 w 1619 w Bg n26

1604 s 1602 s 1602 s 1600 s 1599 s 1604 s 1604 s Ag n5 Bu n62

1593 w " 1585 m 1584 m 1583 m 1583 m 1582 m 1583 m Au n43

1576 m1539 w 1543 w 1555 w,br 1538 vw

1527 vw 1528 w 1528 w 1529 vw1496 vs 1495 vs 1495 vs 1493 vs 1490 vs 1496 vw 1495 vw Ag n6 Bu n63

1455 vs 1453 vs 1453 vs 1451 s 1450 vs 1452 w, D? 1454 w? Ag n7 Au n44 Bu n64

1449 w # 1443 m, sh p p B n52

1441 m, D 1435 m Bg n27

1394 vw 1396 w, P 1402 vw?1380 w, br 1384 w 1385 w 1383 m 1383 w 1384 w 1389 vw

1344 s, P 1347 m Ag n8

1345 m " 1343 m 1343 m p p A n13

1333 w 1332 w 1332 w, sh 1332 vw 1331 vw 1334 vw 1334 m Bg n28 Au n45

1319 vw 1319 vw 1320 vw, br 1312 w, sh, P 1320 w, sh A n14

1300 vw 1300 w Bg n29

1293 vw p 1291 w1271 vw? 1268 vw 1268 vw 1262 vw 1266 vw? 1268 w Bu n65

1246 vw 1243 vw 1246 vw 1245 vw 1246 vw 1245 vw A n15

1221 vw 1225 vw, br 1230 vw? Au n46

1216 w 1216 w 1216 w p p B n55

1194 w 1198 vw 1198 w 1201 w 1201 w 1200 s, P 1204 s Bg n30 A n16

1193 w, sh 1196 vw, sh Ag n9

1182 w " 1181 m 1180 m 1180 w 1179 m 1183 w, D 1180 m Bu n66

1173 vw1157 w " 1155 m 1155 m 1145 m 1145 s 1159 m, D? 1156 m Ag n10

1140 w " 1146 m 1145 w 1141 w, sh 1142 m Au n47 Bu n67

1107 vw, br 1107 w 1108 w p p 1110 vvw Bg n31 A n19

1083 s 1080 m, sh 1079 m p p 1084 vw, P? 1078 vw B n59

1073 vw Bg n32

1068 s 1068 s 1068 s 1063 s 1063 s Au n48

1049 w "1031 s 1030 s 1030 s 1027 s 1028 s 1028 s, P 1028 s Au n49

(continued on next page)

A. Horn et al. / Journal of Molecular Structure 695–696 (2004) 77–94 79

DPE in polyethylene were prepared by soaking polyethy-

lene powder in a saturated solution of DPE in chloroform.

After the solvent was evaporated, the pellet was pressed.

These spectra revealed that DPE probably formed a

crystalline powder in the pellet.

The vapour pressure of DPE was too low to allow the

conventional mixing of the vapour with that of the inert gas

(argon) before being deposited on the cold window. Instead

the sample was placed in a quartz capillary which could be

heated electrically, ca. 7 cm from the cold CsI window.

Table 1 (continued)

Infrared Raman Interpretation

Ar-matrix Melt Solid Melt Solid Anti Gauchea

Pellet Capillary Capillary Pellet36 Kb, 5 Kc 330 Kc 330 Kc 295 Kc 295 Kc 330 Kc 295 Kc

1015 s Ag n11

1003 vs, P 1003 vs Ag n12

1004 vw 1003 vw 1003 vw 1004 vw 1003 vw Bu n68

983 w, br " 982 w 983 w 985 w 983 w 986 vw 992 vw, sh Au n50 Bu n69

983 vw, sh Ag n13

965 vw 964 w 964 w 969 m 966 m 972 w 968 vw Ag n14 Bg n33 Bu n70

966 w 956 vw 954 vvw Bg n34

941 m 938 m 938 m p p 940 m, P p B n65

904 m, P 906 w Ag n15

908 m " 906 m 906 m 906 w 909 m Bu n71

890 vw 888 vw p ? 890 vw 890 vw p B n66

853 w 853 vvw 853 vvw Au n51

842 m 842 m 841 w 842 w 846 vs,P 849 vs Ag n16 Bg n35

805 vw, P 809 vw Ag n17

771 m 790 w, sh 788 w, sh 791 vw 790 vw 786 w, D p768 m 765 s, sh 765 s, sh 767 s 763 s Bu n72

760 s, P p A n29

757 vs 753 vs 753 vs 752 vs 752 vs Au n52 Bu n73

742 w 738 s p p B n69

740 s, P 737 m Ag n17

718 vw 721 m p A n30

700 vs 697 vs 698 vs, br 700 vs 698 vs 699 vw, P 696 vw Ag n18 Bu n74

695 s, sh 695 w, sh A n31

678 m, sh 678 w B n70

622 vw 621 vw 622 w 622 w 621 w 619 s, D 621 m Bg n36 Au n53

613 vw 612 vw 611 w p p 612 w, D? 612 w, sh Ag n19 B n71

582 m 580 s 580 m p 580 w 576 w p B n72

578 w538 w537 w 537 m 534 w, sh 527 m 527 m 532 w, P p Bu n75 A n33

526 vs 519 vs 520 vs, br 517 vs 517 m 520 w, sh Bu n76

523 s504 s 503 s 503 s p p 503 w, D? p B n73

502 m 483 w 482 w 480 w473 w 471 vw p p 478 w p Ag n20

472 w 468 w 468 w p 468 vw 469 m, D 464 m A n34

426 w 428 vw p B n74

412 vvw 409 vvw 405 vw 405 vw, P? 404 vw Bg n37 Au n54

402 w 403 vvw 403 vvw 401 vw Au n55

380 m 380 m 379 w 371 w p B n75

364 w p B n76

325 vw 325 vw 327 vw p Bg n38

290 w, sh 287 s 291 m 309 vw Bu n77

284 m242 vw, br 234 s, P 243 s Ag n21

157 w 152 vw 152 vw B n77

131 m, br, D? 142 s Ag n22

105 w, sh93 w 91 m, sh Bu n78

75 vs Bg n39

35 s

pSpectral bands disappearing in the crystal, # " denote diminishing and increasing intensities after annealing, respectively. The anti conformer with C2h

symmetry has the symmetry species: Ag, Bg, Au, Bu, the gauche conformer with C2 symmetry has the species A and B; for numbering of fundamental modes,

see Table 4.a Gauche modes not listed, presumably coincide with anti fundamentals.b Annealing temperature.c Recording temperature.


The sample evaporated in a stream of pure argon gas and

the mixture was deposited on the window of a Displex

cryostat from APD (model HS-4) with a three stage cooling

system at 5 K. Independent experiments were carried out, in

which the sample was heated to 300 K or left unheated (ca.

285 K) in an argon stream for 1–2 h.

IR spectra of the matrix isolated sample were recorded

between 3500 and 400 cm21, subsequently the matrix was

heated to 20 K in order to remove site effects. Then, the

matrix was annealed in steps of 3–5 K in periods of

15 min to a maximum of 36 K. At still higher tempera-

tures the inert gases have a pressure higher than 1023

Torr, which is not feasible in the cryostat. After each

annealing the window was recooled to 5 K and the spectra

were recorded.

2.3. Raman spectral measurements

The Raman spectra were obtained using a Dilor RTI-30

spectrometer (triple monochromator) and recorded digitally.

An argon ion laser from Spectra Physics (model 2000) was

employed using the 514.5 nm line for excitation. The melt

was studied between 298 and 357 K in a capillary tube of

2 mm inner diameter. It was heated with hot air and the

temperature controlled with a calibrated iron-constantan

thermocouple. Semiquantitative polarization measurements

were carried out. The variable temperature spectra were

employed for calculating the enthalpy difference DconfH

between the conformers in the liquid. The melt in a glass

tube might be kept at room temperature for months before

crystallization, or it could happen after a few hours. In a

refrigerator the sample crystallized readily at 278 K. The

crystal spectra were recorded at room temperature, employ-

ing both 90 and 1808 excitation.

3. Results

3.1. Infrared spectral results

MIR spectra of DPE as a capillary between two KBr

plates were recorded both as a melt above 325 K and as a

supercooled melt at room temperature. Corresponding

spectra were recorded of the crystalline solid, and these

data are listed in Table 1. Independent IR spectra were

recorded of the heated and unheated KBr pellets, and both

spectra were quite similar to those of the melt and the solid

in the capillary films. The pellet spectra are shown in Figs. 1

and 2 (1250–800 cm21 and 860–400 cm21, respectively),

in which the spectra of the heated pellet are represented by a

dashed curve, the spectra of the solid state are drawn with a

solid curve. It can be seen from the curves that several bands

of the melt vanished in the spectra of the crystal; 1443,

1343, 1293, 1216, 1108, 1079, 938, 738, 721, 611, 580, 503,

471, 468 and 364 cm21. These disappearing bands are

marked with asterisks in Table 1.

FIR spectra were recorded of DPE as a melted and

solidified capillary between two polyethylene plates as

demonstrated in Fig. 3 (650–200 cm21). An additional

spectrum of DPE in a polyethylene pellet at high

concentration is presented in Fig. 4 (450–80 cm21). The

IR spectra agreed reasonably well with the results of the

older studies [9,10], which were restricted to pellets, but

most of our weak bands had not been reported earlier. Bands

at 1340, 580 and 503 cm21 reported in a KBr pellet [9] were

not detected in our spectra of the solid, but were present in

the melt spectra. In the earlier investigations employing

dispersive spectrometers [9,10], the higher temperature in

the sample compartment compared to modern FT spec-

trometers, probably favoured a partly melting of the samples.

Infrared spectra of DPE in argon matrices, deposited at

5 K were recorded. The mixing ratio between the sample

and the inert gas is not known, due to the experimental

technique employed (see above). Apart from a small

amount of water giving rise to a broad band at

Fig. 1. Middle infrared (MIR) spectra of 1,2-diphenylethane (DPE) as a

KBr pellet in the range 1250–800 cm1; solid line, solid state spectrum;

dashed line, melt spectrum.

Fig. 2. MIR spectra of DPE as a KBr pellet in the range 860–400 cm21;

solid line, solid state spectrum; dashed line, melt spectrum.


3400 cm21, the matrix spectra had good quality and a

number of sharp bands were observed in the MIR region.

Spectra were recorded of the unannealed matrix and after

heating the matrix to 20, 23, 26, 29, 32, 34 and 36 K with

cooling to 5 K before each recording. Only small spectral

changes were observed after annealing. Matrix spectra of

the unannealed sample and after annealing to 36 K are

presented in Figs. 5 and 6 in two spectral regions. The

conformational equilibrium of the vapour phase is suppo-

sedly maintained when the gas mixture is quickly frozen on

the CsI window, provided that the conformational barrier is

not extremely low. At approximately 20 K reorientations in

the matrix are expected, while at higher annealing

temperatures a displacement of the conformational equili-

brium might occur. However, as is apparent from Figs. 5

and 6, very small intensity variations were observed after

annealing to 36 K. Negligible intensity increases were

detected at 1539, 1345, 1182, 1157, 1140, 1049, 983 and

908 cm21. The band at 1449 cm21 seemed to decrease

slightly in intensity. The conformational barrier was

apparently too high to allow a significant conversion.

From the curves of Barnes [18] the barrier should then be

above 10–12 kJ mol21. Alternatively, many of the bands

observed in the matrix are due to overlapping bands of the

anti and gauche conformers, which might explain the lack

of intensity changes.

3.2. Raman spectral results

Raman spectra of DPE, in the regions 3100–2800 and

1500–100 cm21, are presented as a liquid at ambient

temperature in two directions of polarization in Figs. 7 and

8, respectively. As is apparent, the large majority of

the Raman bands were polarized, suggesting that they

belonged to species Ag in the anti or species A of the gauche

conformer. In Figs. 9 and 10 (1630–970 cm21 and 970–

80 cm21, respectively), the Raman spectra of the super-

cooled melt are presented together with spectra of the

crystalline powder, both recorded at room temperature.

Fig. 6. MIR spectra of DPE (1100–450 cm21) in an argon matrix at 5 K,

lower curve, unannealed sample, upper curve, sample annealed to 36 K.

Fig. 5. MIR spectra of DPE (1800–1000 cm21) in an argon matrix at 5 K;

lower curve, unannealed sample, upper curve, sample annealed to 36 K.

Fig. 4. FIR spectra of DPE of a solid state sample in a polyethylene pellet

(8 mg) in the range 450–80 cm21.

Fig. 3. Far infrared (FIR) spectra of DPE as a capillary between

polyethylene plates in the range 650–200 cm21; lower curve, melt

spectrum; upper curve, solid state spectrum.


The most intense Raman bands were observed at 3063, 1028

and 1003 cm21, all being strongly polarized. As clearly

shown in the spectra, several bands, which were present in

the melt vanished in the spectra of the crystal in agreement

with the findings in the IR spectra.

Many of the weaker Raman bands of the solid, listed in

Table 1, were not reported in the earlier studies, and many of

the melt bands were not detected earlier in solution, in

which the spectra were recorded with He–Ne lasers or Hg

excitation [8–10]. The bands previously observed in CCl4or in C6H12 solution were all present [10] in their spectra of

the solid, with the exception of a band at 217 cm21 in

C6H12. However, this band was observed neither in the

Raman nor the IR spectra of the solid or the melt (Table 1)

and may be an artifact. Therefore from these spectra, only

uncertain conclusions could be drawn regarding a second

conformer present in solution. Since the solubility of DPE in

these solvents is limited, spectra of the melt are much better

suited to detect low concentrations of a second conformer,

which is absent in the solid state.

Raman spectra of the liquid were recorded at 9

temperatures between 298 and 357 K. The intensity

variations observed with temperature of certain bands

relative to neighbouring bands, were interpreted as a

displacement of the conformational equilibrium. Particu-

larly, the attention was focused upon the Raman bands,

which vanished upon crystallization. These bands were

found to increase in intensities at higher temperatures and

belonged to the high energy conformer. They were paired

with other bands (often neighbours), which remained in the

crystal. However, it is always uncertain if the correspond-

ing bands of the liquid are characteristic of only one

conformer, or if they belong to overlapping bands of both

conformers.

The intensities of each band pair were fitted to the van’t

Hoff equation: ln{IgaucheðTÞ=IantiðTÞ} ¼ 2DconfH=RT þ

constant; where Igauch=Ianti is the ratio in peak heights or

integrated areas and it is assumed that DconfH is constant

with temperature. Calculations of DconfH were carried

out from the band pairs: 760/740 and 940/904 cm21.

Fig. 10. Raman spectra of DPE in the range 970–80 cm21 at 295 K; solid

line, solid state spectrum; dotted line, supercooled melt.

Fig. 9. Raman spectra of DPE in the range 1630–970 cm21 at 295 K; solid

line, solid state spectrum; dotted line, supercooled melt.

Fig. 8. Raman spectra of DPE in the range 1500–100 cm21 at 298 K in two

directions of polarization.

Fig. 7. Raman spectra of DPE in the range 3100–2800 cm21 at 298 K in

two directions of polarization.


The former Raman bands were strong and well separated,

and apparently well suited for a thermodynamic study,

while the pair 940/904 cm21 had lower intensity. The bands

in the numerator vanished in the crystal, and as will be

shown below they were attributed to the gauche conformer.

Van’t Hoff plots were constructed, employing both peak

heights and integrated areas of the proper Raman bands.

However, a large scatter of the points in the van’t Hoff plots

were observed, and considerable discrepancies were

obtained between results from the two band pairs, also

when peak heights or integrated areas were utilized.

Probably, the 740 cm21 band had contributions also from

other modes (possibly fundamentals or combination bands

of the gauche conformer) in addition to Ag n17 of the anti

conformer. As seen in Table 1, the B n69 mode (gauche)

which is both IR and Raman active, is situated very close to

the Raman band 740 cm21 and may influence the results.

The plots employing peak heights of the 760/740 and the

940/904 cm21 pairs are presented in Fig. 11, they gave the

values 1.8 and 3.2 kJ mol21, respectively. From integrated

areas of the band pair 760/740 cm21 a value of 2.2 kJ mol21

were obtained. A somewhat uncertain average value of DH

(gauche–anti) ¼ 2.4 ^ 0.5 kJ mol21 was obtained.

3.3. Calculations

Hartree Fock quantum chemical calculations were

performed using the GAUSSIAN 98 programs [19]. The 6-

311 G* basis set was employed in the RHF approximation,

which has been successfully employed in many earlier

studies in this laboratory [20]. The minima on the potential

surface were found by relaxing the geometry according to

the conventional Berny procedure. The optimized bond

distances and angles for the anti and gauche conformers

were calculated, but they have not been given for the sake

of brevity.

3.4. Normal coordinate calculations

A set of analytical H–F force constants was derived for

each of the two conformers, from the HF/6-311G*

calculations. The large number of diagonal and off-diagonal

force constants calculated have not been included for the

sake of brevity, but can be obtained from the authors on

request. The calculated ab initio force constants were

transformed from Cartesian to a set of symmetry valence

coordinates. As generally observed for ab initio calculated

vibrational modes, they were invariably at higher frequen-

cies than the experimental values. In order to make a

complete assignment of the observed IR and Raman bands,

a normal coordinate analysis with scaled force constants

was carried out.

A reasonably good agreement between the experimental

and calculated wave numbers was achieved by using scaling

factors of 0.9 for the stretching and bending modes above,

and 1.0 for the modes below 400 cm21. The same

procedure, based upon the HF/6-311G* basis set has

successfully been applied in these laboratories to a large

number of silanes [20]. In addition, infrared intensities,

Raman scattering cross-sections and Raman polarization

ratios, r; were calculated for the anti and gauche conformers

of DPE. The complete set of data for the anti conformer is

listed in the lengthy Table 2. For the sake of brevity, the

calculated wavenumbers and intensity parameters for only a

selected (see below) group of gauche fundamentals are

listed in Table 3.

The PED (potential energy distribution) was calculated

and expressed in terms of normalized symmetry coordi-

nates. The numbering of the atoms is shown in Fig. 12. The

quantitative description of the largest PED terms (1–3 are

included) for each normal vibration of the anti and some

gauche conformers have been listed in Tables 2 and 3.

The symmetry coordinates are defined in Table 4. They are

based upon a set of valence coordinates apparent from Fig.

12 and defined in accordance with the description suggested

in the monograph of Wilson et al. [21]. The fundamentals

are numbered as n1 –n22 for the modes belonging to species

Ag, as n23 –n39 for those of Bg, as n40 –n57 for Au and finally

as n58 –n78 for the Bu modes of the anti conformer. For the

gauche conformer the fundamentals are numbered as

n1 –n40 for A and as n41 –n78 for B. In the gauche conformer

24 modes (10 A and 14 B) were selected. As described

below they were calculated to lie more than 10 cm21 from

the nearest anti mode. They correspond reasonably well

with IR and Raman bands which are present in the melt

spectra and were listed in Table 3.

When the complete list of the scaled ab initio calculated

wave numbers for the anti (Table 2) and the gauche (not

listed) conformers is compared, it is found that most of the

anti modes are separated by less than 2–4 cm21 from the

gauche modes. This is not unexpected since the large

number of modes involving the aromatic skeletons are

group frequencies, which are not much influenced by

Fig. 11. Van’t Hoff plots of the band pair 760/740 (circles) and

940/904 cm21 (squares) in the temperature range 298–357 K, employing

peak heights.


Table 2

Observed and calculated fundamental modes of the anti conformer in 1,2-diphenylethane (DPE)

No. Observeda IIR IR r Calculatedb Scaledc IIR IR r PEDd Description

Ag n1 3072 m P 3363 3027 0 592 0.14 99S7 (y)C–H stretch

n2 3003 w P 3338 3004 0 215 0.57 86S8 þ 11s8 (y)C–H stretch

n3 2990 w P 3322 2990 0 18 0.25 91S9 (y)C–H stretch

n4 2864 m P 3193 2874 0 119 0.07 99S3 sCH2 sym. stretch

n5 1604 s P 1800 1620 0 74 0.57 64S5 þ 22S20 þ 10S17 CyC stretch

n6 1496 vw 1660 1494 0 1 0.74 60S19 þ 34S6 CyC–H bend

n7 1452 w,sh 1623 1461 0 25 0.62 93S14 sCH2 scissor

n8 1344 s P 1516 1365 0 35 0.36 77S15 þ 10S2 sCH2 deformation

n9 1193 w D? 1313 1182 0 21 0.11 35S2 þ 15S4 (y)C–C stretch

n10 1159 m D? 1293 1164 0 5 0.72 71S20 þ 25S5 CyC–H bend

n11 1015e s 1123 1011 0 20 0.08 49S6 þ 19S19 þ 15S4 þ 14S18 CyC stretch

n12 1003 vs P 1108 998 0 13 0.38 59S12 þ 13S1 þ 12S21 (y)C–H out-of-plane bend

n13 983e vw,sh 1101 991 0 12 0.30 34S11 þ 32S12 þ 19S1 (y)C–H out-of-plane bend

n14 972 w 1085 977 0 0 0.10 58S18 þ 41S4 Ring bend

n15 904 m P 1016 914 0 3 0.54 56S11 þ 14S12 þ 11S1 (y)C–H out-of-plane bend

n16 805 vw P 928 835 0 19 0.10 20S13 þ 18S4 þ 14S2 C6H5–C–C bend

n17 740 s P 821 738 0 12 0.06 47S10 þ 20S21 (y)C–H out-of-plane bend

n18 699 vw P 775 697 0 1 0.31 60S21 þ 14S10 Ring torsion

n19 612 w D? 672 605 0 4 0.70 43S17 þ 19S21 þ 13S13 Ring bend

n20 478 w 522 470 0 5 0.34 49S22 þ 26S16 Ring torsion

n21 234 s P 255 255 0 7 0.52 43S22 þ 11S13 þ 11S2 þ 10S11 Ring torsion

n22 131 m D? 131 131 0 8 0.71 38S16 þ 27S13 þ 12S22 yC–C out-of-plane bend

Bg n23 3063 s P 3349 3014 0 79 0.75 89S27 þ 11S28 (y)C–H stretch

n24 2980 w P? 3324 2992 0 176 0.75 88S28 þ 11S27 (y)C–H stretch

n25 2896 m P 3218 2896 0 75 0.75 99S23 sCH2 antisym. stretch

n26 1620 w 1772 1595 0 14 0.75 68S25 þ 10S35 CyC stretch

n27 1441 m D 1609 1448 0 1 0.75 29S24 þ 27S35 þ 27S37 Mixed

n28 1334 vw 1483 1335 0 0 0.75 65S35 þ 21S32 CyC–H bend

n29 1300 vw 1425 1282 0 8 0.75 62S32 þ 11S33 sCH2 wag

n30 1200 s P 1331 1198 0 1 0.75 34S37 þ 21S26 þ 19S35 CyC–H bend

n31 1110e vvw 1220 1098 0 10 0.75 27S24 þ 22S35 þ 18S26 þ 13S32 Mixed

n32 1073 vw 1169 1052 0 1 0.75 64S26 þ 27S37 CyC stretch

n33 972 w 1086 977 0 0 0.75 92S30 (y)C–H out-of-plane bend

n34 956 vw 1074 967 0 0 0.75 50S31 þ 28S24 sCH2 twist

n35 846 vs P 946 852 0 0 0.75 99S29 (y)C–H out-of-plane bend

n36 619 s D 680 612 0 10 0.75 87S33 Ring bend

n37 405 vw P? 454 408 0 0 0.75 82S39 þ 18S30 Ring torsion

n38 327 vw 339 339 0 0 0.75 78S34 C6H5–C–C bend

n39 75e vs 59 59 0 3 0.75 87S38 C6H5–CH2 torsion

Au n40 3027 vs 3349 3014 126 0 89S44 þ 10S45 (y)C–H stretch

n41 3003 w 3325 2993 12 0 89S45 þ 10S44 (y)C–H stretch

n42 2939 s 3244 2920 38 0 99S40 sCH2 antisym. stretch

n43 1585 m 1772 1595 5 0 68S43 þ 10S53 CyC stretch

n44 1453 vs 1609 1448 15 0 29S42 þ 27S53 þ 27S55 CyC stretch

n45 1332 w 1478 1330 0 0 73S54 þ 10S53 CyC–H bend

n46 1221f vw 1355 1220 0 0 35S55 þ 24S41 þ 20S49 þ 12S53 Mixed

n47 1146 m 1269 1142 1 0 36S49 þ 27S53 þ 16S43 þ 14S54 sCH2 twist

n48 1068 s 1170 1053 6 0 78S41 þ 17S55 CyC stretch

n49 1030 s 1167 1050 3 0 57S42 þ 16S49 þ 10S53 CyC stretch

n50 983 w 1085 977 0 0 92S47 (y)C–H out-of-plane bend

n51 853 vvw 946 852 0 0 100S46 (y)C–H out-of-plane bend

n52 753 vs 826 743 0 0 83S48 þ 11S49 sCH2 wag

n53 621 vw 681 613 0 0 86S51 Ring bend

n54 412 vvw 454 408 0 0 82S57 þ 18S47 Ring torsion

n55 402 w 400 400 0 0 74S52 þ 10S50 C6H5–C–C bend

n56 40 40 0 0 77S50 þ 13S52 (–)CH2–CH2 torsion

n57 23 23 0 0 89S56 C6H5–CH2 torsion

Bu n58 3027 vs 3363 3027 67 0 99S63 (y)C–H stretch

n59 3003 w 3338 3004 29 0 86S64 þ 11S63 (y)C–H stretch



Table 2 (continued)


n60 2951f m 3322 2990 28 0 91S65 (y)C–H stretch

n61 2858 s 3200 2880 72 0 100S59 sCH2 sym. stretch

n62 1602 s 1799 1619 22 0 64S61 þ 22S76 þ 10S73 CyC stretch

n63 1495 vs 1660 1494 35 0 59S57 þ 34S62 Ring torsion

n64 1453 vs 1641 1476 6 0 97S70 sCH2 scissor

n65 1271f vw 1419 1277 1 0 81S71 þ 10S58 sCH2 rock

n66 1181 m 1314 1182 0 0 35S58 þ 15S60 þ 14S74 þ 14S75 Mixed

n67 1146 m 1293 1163 0 0 72S76 þ 24S61 CyC–H bend

n68 1003 vw 1122 1010 6 0 49S62 þ 19S75 þ 16S74 þ 15S60 CyC stretch

n69 983 w 1105 995 0 0 67S68 þ 23S67 (y)C–H out-of-plane bend

n70 964 w 1085 977 0 0 57S74 þ 42S60 Ring bend

n71 906 m 1022 920 4 0 64S67 þ 15S68 (y)C–H out-of-plane bend

n72 765 s,sh 853 768 0 0 31S58 þ 22S73 þ 21S60 þ 11S74 Mixed

n73 753 vs 845 761 86 0 43S66 þ 30S78 þ 14S72 (y)C–H out-of-plane bend

n74 697 vs 775 698 82 0 60S78 þ 17S66 Ring torsion

n75 537 m 582 523 34 0 34S77 þ 25S72 þ 13S68 þ 11S78 Mixed

n76 519 vs 567 510 4 0 71S73 þ 14S58 Ring bend

n77 287 s 319 319 2 0 59S77 þ 19S69 þ 13S66 Ring torsion

n78 67 67 0 0 49S69 þ 36S72 C6H5–C–C bend

a Raman and IR frequencies from melt spectra, except when noted.b Calculated from RHF/6-311G**.c Scaled with 0.9 above 400 cm21 and 1.0 below 400 cm21.d Meaning of symmetry coordinates, see Table 4, only four terms or less are included in PED.e Raman spectra from solid.f Infrared spectra from argon matrix.

Table 3

Observed and calculated fundamentals of select modes of the gauche conformer in 1,2-diphenylethane (DPE)


A n13 1343 m s P 1499 1349 2 12 0.37 37S1522S5421S49 sCH2 deform

n14 1319 vw w P 1470 1323 0 8 0.28 44S5426S15 CyC–H bend

n15 1246 vw vw 1372 1235 1 3 0.61 41S4919S1516S55 sCH2 twist

n16 1198 w w P 1322 1190 1 7 0.34 18S5514S212S53 Mixed

n19 1107 w vw 1215 1093 2 8 0.45 29S4219S5318S41 CyC stretch

n29 760 s P 846 761 10 2 0.03 36S1027S2113S16 (y)C–H out-of-plane

n30 721 m 807 726 3 18 0.01 23S1719S1016S2 Ring torsion

n31 695 s 775 697 11 0 0.59 61S2114S10 Ring torsion

n33 537 m w P 590 531 4 2 0.34 22S2219S1715S16 Mixed

n34 468 w m D? 520 468 0 4 0.13 37S2220S1716S16 Ring torsion

B n52 1443 m m D 1609 1448 14 0 0.75 29S2428S3727S35 Mixed

n55 1216 w 1355 1220 0 1 0.75 35S3722S2621S32 CyC–H bend

n59 1080 m vw P 1176 1058 2 0 0.75 45S2419S2614S32 CyC stretch

n65 938 m m P 1050 945 7 1 0.75 39S6711S31 (y)C–H out-of-plane

n66 890 vw vw 991 892 0 0 0.75 40S6730S31 (y)C–H out-of-plane

n69 738 s 832 749 3 18 0.03 23S1719S1016S2 Ring bend

n70 678 m 774 696 73 0 0.75 59S7816S66 Ring torsion

n71 612 vw w D? 680 612 0 8 0.75 86S33 Ring bend

n72 580 s w 635 572 18 1 0.75 18S7817S6913S68 Mixed

n73 503 s w D 549 495 13 4 0.75 36S7321S7716S72 Ring bend

n74 426 w vw 454 408 0 0 0.75 82S5718S30 Ring torsion

n75 380 m 394 394 0 0 0.75 50S7717S69 Ring torsion

n76 364 w 354 354 1 0 0.75 68S3411S77 C6H5–C–C bend

n77 157 w 134 134 1 4 0.75 38S7725S69 Ring torsion

Gauche fundamentals not listed, presumably overlap with anti fundamentals in Tables 1 and 2.a IR data from melt spectra, except when noted.b Calculated from RHF/6-311G**.c Scaled with 0.9 above 400 cm21 and 1.0 below 400 cm21.d Meaning of symmetry coordinates, see Table 4, only four terms or less are included in PED.


the C–C–C–C dihedral angles of the anti (1808) and

gauche conformers (608). It is expected that most of these

bands from one conformer will overlap those of the other.

Moreover, because of the weak interaction across the ring

system, many Ag and Bu and Bg and Au modes of anti will

be accidentally degenerate and so will many A and B modes

of the gauche conformer, resulting in a still higher overlap.

An accurate inspection of the scaled ab initio calculated

wavenumbers for the anti (Table 2) and gauche modes (not

listed), reveals that the following seven anti modes are

separated more than 10 cm21 from the closest neighbouring

gauche modes: 1282 (47, 41), 1277 (42, 46), 835 (17, 74),

738 (11, 12), 510 (21, 15), 339 (15, 21), 255 (10, 99) cm21,

in which the two numbers in the parentheses are the

wavenumber shifts from an anti mode to the two

neighbouring gauche modes, one lying at higher and one

at lower frequencies than the anti mode. All these modes are

correlated with observed bands and assigned to anti

fundamentals in Tables 1 and 2. Correspondingly, the

following eight of the 78 scaled gauche modes (not listed)

are situated more than 10 cm21 from the two nearest

neighbouring anti modes: 1349 (16, 16), 1235 (15, 42), 945

(25, 22), 892 (22, 40), 726 (12, 28), 572 (33, 49), 495 (15,

25), 354 (46, 15). It is highly significant that all eight of

these modes correspond to observed melt bands, which

vanish in the solid state and are equipped with asterisks in

Table 1. As seen from Table 3, these modes are assigned as

the following observed gauche fundamentals: 1343, A n13;

1246, A n15; 938, B n65; 890, B n66; 721, A n30; 580, B n72;

503, B n73 and 364, B n76: None of them coincide with the

anti fundamentals listed in Table 1. These findings therefore

support the conclusion that the anti conformer alone is

present in the solid.

4. Discussion

4.1. Conformers

As is apparent from Table 1, 14 infrared bands around

1443, 1343, 1293, 1216, 1107, 1080, 938, 890, 738, 721,

612, 580, 503 and 473 cm21 vanish during crystallization.

Correspondingly, 10 Raman bands at 940, 890, 786, 760,

576, 532, 503, 478, 428 and 364 cm21 also disappear after

crystallization. Some of these modes are observed in both

spectra. Undoubtedly, these bands belong to the conformer,

which disappears in the crystal, and some are also enhanced

in intensity with increasing temperatures as observed in the

Raman spectra of the liquid.

Earlier studies of DPE by infrared and Raman spec-

troscopy [8–10] suggested that the anti conformer was

present in the solid. It was suggested [9,10] that an

additional conformer was present in solution and in the

melt. However, no spectra or new bands from the solution or

melt were presented (concerning the Raman band at

217 cm21 (w) in C6H12, see above) in support of this

conclusion [10]. In the vapour phase anti is the more

abundant conformer at 373 K, as observed from gaseous

electron diffraction [11].

Quantum chemical HF and DFT calculations [16] reveal

that anti had lower energy (3.6 kJ mol21 with RHF/6-

311G** and 3.1 kJ mol21 with B3LYP/6-311G**), but by

employing MP2 calculations the energies were reversed. In

a more recent study [17], the DFT results with a larger basis

set (6-311þþG) gave a preference of 0.3 kJ mol21 for the

anti conformer. Corrections for electron correlation ener-

gies at the MP4SDQ level, however, resulted in

1.0 kJ mol21 lower energy for the gauche conformer [17].

Thus, the quantum chemical calculations favour anti as the

more stable conformer, but these calculations are not quite

conclusive.

Studies by X-ray crystallography [5,6] reveal that the

crystal contained molecules in the anti conformer with an

apparent short central C–C distance, which increased at

lower temperatures. In order to explain the short central C–

C bond, it was suggested by Harada et al. [5] that the

molecular structure is a 1:1 mixture of two conformers, as

suggested earlier for stilbene [7]. This assumption is not in

accordance with the present results, which clearly reveal

that while two conformers are present in the melt and in the

argon matrix, only one conformer, apparently anti, was

found in the solid.

Applied to the present spectra, the anti conformer with

C2h symmetry should give rise to Raman active Ag and Bg

and IR active Au and Bu modes, all of these bands should be

present both in the melt and in the solid state spectra. On the

other hand, the gauche conformer with C2 symmetry and

species A and B, should have bands active both in the

infrared and the Raman spectra of the melt, but all of these

should vanish in the crystal. It is immediately seen from

Table 1 that many bands do not follow these criteria, and

reliable assignments into anti and gauche bands from the IR

and Raman spectra alone are not feasible. The obvious

reason for this uncertainty is that the large majority of the

anti and gauche bands overlap, making a clear distinction

between the presence or absence of bands in the crystal

spectra uncertain.

It was reported above that among the 78 fundamental

modes, calculated for each conformer, seven modes of the

anti and eight of the gauche conformer were separated more

than 10 cm21 (some bands much more) from the nearest

Fig. 12. The anti conformer of DPE with numbering of atoms.


Table 4

Definition of internal symmetry coordinates in 1,2-diphenylethane (DPE) (anti)

Description Definitiona

Ag C–C stretch S1 ¼ DT

(y)C–C stretch S2 ¼ 1ffiffi

2p ðDD1 þ DD2Þ

sCH2 sym. stretch S3 ¼ 12ðDd15 þ Dd16 þ Dd18 þ Dd17Þ

CyC stretch S4 ¼ 1ffiffiffi

12p ðDR3;10 þ DR3;14 þ DR10;11 þ DR13;14 þ DR11;12 þ DR12;13 þ DR4;9

þ DR4;5 þ DR8;9 þ DR5;6 þ DR7;8 þ DR6;7Þ


24p ðDR3;10 þ DR3;14 2 2DR10;11

2 2DR13;14 þ DR11;12 þ DR12;13

þ DR4;9 þ DR4;5 2 2DR8;9 2 2DR5;6

þ DR7;8 þ DR6;7Þ

CyC stretch S6 ¼ 1ffiffi

8p ðDR3;10 þ DR3;14 2 DR11;12 2 DR12;13 þ DR4;9 þ DR4;5

2 DR7;8 2 DR6;7Þ

(y)C–H stretch S7 ¼ 1ffiffiffi

10p ðDs24 þ Ds28 þ Ds25 þ Ds27 þ Ds26 þ Ds23 þ Ds19 þ Ds22

þ Ds20 þ Ds21Þ

(y)C–H stretch S8 ¼ 14ðDs24 þ Ds28 þ Ds25 þ Ds27 2 2Ds26 þ Ds23 þ Ds19 þ Ds22

þ Ds20 2 2Ds21Þ


10p ðDs24 þ Ds28 2 Ds25 2 Ds27 þ Ds26 þ Ds23 þ Ds19 2 Ds22

2 Ds20 þ Ds21Þ

(y)C–H out-of-plane S10 ¼ 1ffiffiffi

10p ðDp24 þ Dp28 þ Dp25 þ Dr27 þ Dp26 þ Dp23 þ Dp19

þ Dp22 þ Dp20 þ Dp21Þ

(y)C–H out-of-plane S11 ¼ 14ðDp24 þ Dp28 þ Dp25 þ Dr27 2 2Dp26 þ Dp23 þ Dp19

þ Dp22 þ Dp20 2 2Dp21Þ


10p ðDp24 þ Dp28 2 Dp25 2 Dr27 þ Dp26 þ Dp23 þ Dp19

2 Dp22 2 Dp20 þ Dp21Þ

C6H5–C–C bend S13 ¼ 1ffiffi

2p ðDv1 þ Dv2Þ

sCH2 scissor S14 ¼ 1ffiffi

2p ðD11 þ D12Þ

sCH2 deformation S15 ¼ 1ffiffi

8p ðDa3;1;16 þ Da3;1;15 þ Da4;2;17 þ Da4;2;18 2 Da2;1;16 2 Da2;1;15

2 a1;2;17 2 a1;2;18Þ

yC–C out-of-plane S16 ¼ 1ffiffi

2p ðDp1 þ Dp2Þ



Table 4 (continued)


Ring bend S17 ¼ 1ffiffiffi

24p ð2Df14;3;10 2 Df3;10;11 2 Df3;14;13 2 Df10;11;12 2 Df12;13;14

þ 2Df11;12;13 þ 2Df5;4;9 2 Df4;9;8 2 Df4;5;6 2 Df7;8;9 2 Df5;6;7

þ 2Df6;7;8Þ


12p ðDf14;3;10 2 Df3;10;11 2 Df3;14;13 þ Df10;11;12 þ Df12;13;14

2 Df11;12;13 þ Df5;4;9 2 Df4;9;8 2 Df4;5;6 þ Df7;8;9

þ Df5;6;7 2 Df6;7;8Þ

CyC–H bend S19 ¼ 14ðDb3;10;24 þ Db3;14;28 2 Db11;10;24 2 Db13;14;28 þ Db10;11;25

þDb14;13;27 2 Db12;11;25 2 Db12;13;27 þ Db4;9;23 þ Db4;5;19 2 Db8;9;23

2 Db6;5;19 þ Db9;8;22 þ Db5;6;20 2 Db7;8;22 2 Db7;6;20Þ

CyC–H bend S20 ¼ 14ðDb3;10;24 þ Db3;14;28 2 Db11;10;24 2 Db13;14;28 2 Db10;11;25

2Db14;13;27 þ Db12;11;25 þ Db12;13;27 þ Db4;9;23 þ Db4;5;19 2 Db8;9;23

2 Db6;5;19 2 Db9;8;22 2 Db5;6;20 þ Db7;8;22 þ Db7;6;20Þ

Ring torsion S21 ¼ 1ffiffiffi

24p ðDt3;10 2 Dt14;3 2 2Dt10;11 þ 2Dt13;14 þ Dt11;12

2 Dt12;13 2 Dt4;9 þ Dt5;4 þ 2Dt9;8 2 2Dt6;5 2 Dt8;7 þ Dt7;6Þ

Ring torsion S22 ¼ 1ffiffi

8p ðDt3;10 2 Dt14;3 2 Dt11;12 þ Dt12;13 2 Dt4;9 þ Dt5;4 þ Dt8;7

2 Dt7;6Þ

Bg sCH2 antisym. stretch S23 ¼ 12ðDd15 2 Dd16 þ Dd18 2 Dd17Þ


12p ðDR3;10 2 DR3;14 þ DR10;11 2 DR13;14 þ DR11;12 2 DR12;13

þ DR4;9 2 DR4;5 þ DR8;9 2 DR5;6 þ DR7;8 2 DR6;7Þ


8p ðDR3;10 2 DR3;14 2 DR11;12 þ DR12;13 þ DR4;9 2 DR4;5 2 DR7;8

þ DR6;7Þ


24p ðDR3;10 2 DR3;14 2 2DR10;11 þ 2DR13;14 þ DR11;12 2 DR12;13

þ DR4;9 2 DR4;5 2 2DR8;9 þ 2DR5;6 þ DR7;8 2 DR6;7Þ

(y)C–H stretch S27 ¼ 1ffiffi

8p ðDs24 2 Ds28 þ Ds25 2 Ds27 þ Ds23 2 Ds19 þ Ds22 2 Ds20Þ


8p ðDs24 2 Ds28 2 Ds25 þ Ds27 þ Ds23 2 Ds19 2 Ds22 þ Ds20Þ

(y)C–H out-of-plane S29 ¼ 1ffiffi

8p ðDp24 2 Dp28 þ Dp25 2 Dr27 þ Dp23 2 Dp19 þ Dp22 2 Dp20Þ


8p ðDp24 2 Dp28 2 Dp25 þ Dr27 þ Dp23 2 Dp19 2 Dp22 þ Dp20Þ



Table 4 (continued)


sCH2 twist S31 ¼ 1ffiffi

8p ðDa3;1;16 2 Da3;1;15 þ Da4;2;17 2 Da4;2;18 þ Da2;1;16 2 Da2;1;15

þ a1;2;17 2 a1;2;18Þ

sCH2 wag S32 ¼ 1ffiffi

8p ðDa3;1;16 2 Da3;1;15 þ Da4;2;17 2 Da4;2;18 2 Da2;1;16 þ Da2;1;15

2 a1;2;17 þ a1;2;18Þ

Ring bend S33 ¼ 1ffiffi

8p ðDf3;10;11 2 Df3;14;13 2 Df10;11;12 þ Df12;13;14 þ Df4;9;8

2 Df4;5;6 2 Df7;8;9 þ Df5;6;7Þ

C6H5–C–C bend S34 ¼ 12ðDb1;3;10 2 Db1;3;14 þ Db2;4;9 2 Db2;4;5Þ

CyC–H bend S35 ¼ 12ðDb11;12;26 2 Db13;12;26 þ Db8;7;21 2 Db6;7;21Þ

CyC–H bend S36 ¼ 14ðDb3;10;24 2 Db3;14;28 2 Db11;10;24 þ Db13;14;28 þ Db10;11;25

2Db14;13;27 2 Db12;11;25 þ Db12;13;27 þ Db4;9;23 2 Db4;5;19 2 Db8;9;23

þ Db6;5;19 þ Db9;8;22 2 Db5;6;20 2 Db7;8;22 þ Db7;6;20Þ

CyC–H bend S37 ¼ 14ðDb3;10;24 2 Db3;14;28 2 Db11;10;24 þ Db13;14;28 2 Db10;11;25

þ Db14;13;27 þ Db12;11;25 2 Db12;13;27 þ Db4;9;23 2 Db4;5;19

2 Db8;9;23 þ Db6;5;19 2 Db9;8;22 þ Db5;6;20 þ Db7;8;22 2 Db7;6;20Þ

C6H5–CH2–torsion S38 ¼ 1ffiffi

2p ðDt1 þ Dt2Þ


24p ðDt3;10 þ Dt14;3 2 2Dt10;11 2 2Dt13;14 þ Dt11;12 þ Dt12;13

2 Dt4;9 2 Dt5;4 þ 2Dt9;8 þ 2Dt6;5 2 Dt8;7 2 Dt7;6Þ

Au sCH2 antisym. stretch S40 ¼ 12ðDd15 2 Dd16 2 Dd18 þ Dd17Þ


24p ðDR3;10 2 DR3;14 2 2DR10;11 þ 2DR13;14 þ DR11;12 2 DR12;13

2 DR4;9 þ DR4;5 þ 2DR8;9 2 2DR5;6 2 DR7;8 þ DR6;7Þ


12p ðDR3;10 2 DR3;14 þ DR10;11 2 DR13;14 þ DR11;12 2 DR12;13

2 DR4;9 þ DR4;5 2 DR8;9 þ DR5;6 2 DR7;8 þ DR6;7Þ


8p ðDR3;10 2 DR3;14 2 DR11;12 þ DR12;13 2 DR4;9 þ DR4;5 þ DR7;8

2 DR6;7Þ


8p ðDs24 2 Ds28 þ Ds25 2 Ds27 2 Ds23 þ Ds19 2 Ds22 þ Ds20Þ


8p ðDs24 2 Ds28 2 Ds25 þ Ds27 2 Ds23 þ Ds19 þ Ds22 2 Ds20Þ


8p ðDp24 2 Dp28 þ Dp25 2 Dr27 2 Dp23 þ Dp19 2 Dp22 þ Dp20Þ



Table 4 (continued)



8p ðDp24 2 Dp28 2 Dp25 þ Dr27 2 Dp23 þ Dp19 þ Dp22 2 Dp20Þ

sCH2 wag S48 ¼ 1ffiffi

8p ðDa3;1;16 2 Da3;1;15 2 Da4;2;17 þ Da4;2;18 þ Da2;1;16 2 Da2;1;15

2 a1;2;17 þ a1;2;18Þ

sCH2 twist S49 ¼ 1ffiffi

8p ðDa3;1;16 2 Da3;1;15 2 Da4;2;17 þ Da4;2;18 2 Da2;1;16 þ Da2;1;15

þ a1;2;17 2 a1;2;18Þ

(–)CH2–CH2–torsion S50 ¼ Dt1;2

Ring bend S51 ¼ 1ffiffi

8p ðDf3;10;11 2 Df3;14;13 2 Df10;11;12 þ Df12;13;14 2 Df4;9;8 þ Df4;5;6

þ Df7;8;9 2 Df5;6;7Þ

C6H5–C–C bend S52 ¼ 12ðDb1;3;10 2 Db1;3;14 2 Db2;4;9 þ Db2;4;5Þ

CyC–H bend S53 ¼ 12ðDb11;12;26 2 Db13;12;26 2 Db8;7;21 þ Db6;7;21Þ

CyC–H bend S54 ¼ 14ðDb3;10;24 2 Db3;14;28 2 Db11;10;24 þ Db13;14;28 þ Db10;11;25

2Db14;13;27 2 Db12;11;25 þ Db12;13;27 2 Db4;9;23 þ Db4;5;19 þ Db8;9;23

2 Db6;5;19 2 Db9;8;22 þ Db5;6;20 þ Db7;8;22 2 Db7;6;20Þ

CyC–H bend S55 ¼ 14ðDb3;10;24 2 Db3;14;28 2 Db11;10;24 þ Db13;14;28 2 Db10;11;25

þDb14;13;27 þ Db12;11;25 2 Db12;13;27 2 Db4;9;23 þ Db4;5;19 þ Db8;9;23

2 Db6;5;19 þ Db9;8;22 2 Db5;6;20 2 Db7;8;22 þ Db7;6;20Þ


2p ðDt1 2 Dt2Þ


24p ðDt3;10 þ Dt14;3 2 2Dt10;11 2 2Dt13;14 þ Dt11;12 þ Dt12;13

þ Dt4;9 þ Dt5;4 2 2Dt9;8 2 2Dt6;5 þ Dt8;7 þ Dt7;6Þ

Bu (y)C–C stretch S58 ¼ 1ffiffi

2p ðDD1 2 DD2Þ

sCH2 sym. stretch S59 ¼ 12ðDd15 þ Dd16 2 Dd18 2 Dd17Þ


12p ðDR3;10 þ DR3;14 þ DR10;11 þ DR13;14 þ DR11;12 þ DR12;13

2 DR4;9 2 DR4;5 2 DR8;9 2 DR5;6 2 DR7;8 2 DR6;7Þ


24p ðDR3;10 þ DR3;14 2 2DR10;11 2 2DR13;14 þ DR11;12 þ DR12;13

2 DR4;9 2 DR4;5 þ 2DR8;9 þ 2DR5;6 2 DR7;8 2 DR6;7Þ



Table 4 (continued)



8p ðDR3;10 þ DR3;14 2 DR11;12 2 DR12;13 2 DR4;9 2 DR4;5 þ DR7;8

þ DR6;7Þ


10p ðDs24 þ Ds28 þ Ds25 þ Ds27 þ Ds26 2 Ds23 2 Ds19 2 Ds22 2 Ds20

2 Ds21Þ

(y)C–H stretch S64 ¼ 14ðDs24 þ Ds28 þ Ds25 þ Ds27 2 2Ds26 2 Ds23 2 Ds19 2 Ds22 2 Ds20

þ 2Ds21Þ


10p ðDs24 þ Ds28 2 Ds25 2 Ds27 þ Ds26 2 Ds23 2 Ds19 þ Ds22 þ Ds20

2 Ds21Þ


10p ðDp24 þ Dp28 þ Dp25 þ Dr27 þ Dp26 2 Dp23 2 Dp19 2 Dp22

2 Dp20 2 Dp21Þ

(y)C–H out-of-plane S67 ¼ 14ðDp24 þ Dp28 þ Dp25 þ Dr27 2 2Dp26 2 Dp23 2 Dp19 2 Dp22

2 Dp20 þ 2Dp21Þ


10p ðDp24 þ Dp28 2 Dp25 2 Dr27 þ Dp26 2 Dp23 2 Dp19 þ Dp22

þ Dp20 2 Dp21Þ

C6H5–C–C bend S69 ¼ 1ffiffi

2p ðDv1 2 Dv2Þ

sCH2 scissor S70 ¼ 1ffiffi

2p ðD11 2 D12Þ

sCH2 rock S71 ¼ 1ffiffi

8p ðDa3;1;16 þ Da3;1;15 2 Da4;2;17 2 Da4;2;18 2 Da2;1;16 2 Da2;1;15

þ a1;2;17 þ a1;2;18Þ


2p ðDp1 2 Dp2Þ


24p ð2Df14;3;10 2 Df3;10;11 2 Df3;14;13 2 Df10;11;12 2 Df12;13;14

þ 2Df11;12;13 2 2Df5;4;9 þ Df4;9;8 þ Df4;5;6 þ Df7;8;9 þ Df5;6;7

2 2Df6;7;8Þ


12p ðDf14;3;10 2 Df3;10;11 2 Df3;14;13 þ Df10;11;12 þ Df12;13;14

2 Df11;12;13 2 Df5;4;9 þ Df4;9;8 þ Df4;5;6 2 Df7;8;9

2 Df5;6;7 þ Df6;7;8Þ



mode of the opposite conformer. It is significant that all the

eight gauche modes which were predicted from the

calculations to be far from the corresponding anti modes

were observed in the IR and/or Raman spectra of the melt

and vanished in those of the solid. They are marked with

asterisks in Table 1 and were assigned to gauche

fundamentals in Table 3. These features strongly support

the anti conformer being present in the solid while the

gauche conformer exists in the melt in a mixture with anti.

4.2. Spectral assignments

The observed enthalpy difference of the gauche and anti

conformers of 2.4 kJ mol21 leads to an estimated ratio of

anti/gauche ¼ 1.27 at the melting point of 325 K since

gauche has a statistical weight 2. This ratio agrees

reasonably well with the IR and Raman intensities of the

melt spectra. In many cases the IR and Raman bands of the

melt, remaining in the crystal spectra and attributed to anti,

had approximately the same intensity as the bands vanishing

in the crystal spectra and assigned to the gauche conformer.

Examples are the two Raman pairs 760/740 and

940/904 cm21. However, in other cases the bands belonging

to gauche were weaker than those ascribed to anti, and it has

been suggested that [9] the ratio in solutions is 1:2 at room

temperature.

The wavenumbers of the observed infrared and Raman

bands of DPE (Table 1) are tentatively assigned to a nearly

complete set of 78 fundamentals of the anti conformer. They

are numbered in the conventional order of the symmetry

species, Ag;Bg;Au and Bu and compared with the scaled ab

initio calculated wave numbers in Table 2. Obviously, no

detailed discussion of the assignments in these lengthy

tables can be presented, but a few guidelines mentioned: (1)

the assigned fundamentals relied heavily upon the calcu-

lated wave numbers (scaled) and the shifts between the

observed and calculated values were moderate. (2) The Ag

and Bg modes were preferably attributed to separate Raman

bands and the Au and Bu modes to separate IR bands. (3)

The calculated IR intensities, Raman cross-sections and

polarization ratios played a minor role. (4) Most anti and

gauche bands overlapped, particularly in the regions 1600–

1400 and 1200–950 cm21 as indicated by the calculations.

A number of observed bands were attributed to

overlapping anti bands. Particularly, the Ag –Bu and the

Bg –Au modes frequently coincided, since they represent in-

phase and out-of-phase vibrations relative to the symmetry

center. As seen in Table 1, the weak interaction across the

DPE molecule is demonstrated by the small (or non-

existent) wavenumber difference between many of these

modes, leading to accidental degeneracy.

As is apparent from Table 1, 24 fundamentals belonging

to the gauche conformer were tentatively assigned. They are

also listed in Table 3, spanning the symmetry species A and

B, which should all be active both in the IR and Raman

spectra. These fundamentals should in principle be present

both in the IR and in Raman spectra and they should vanish

in the spectra of the solid. The gauche modes, calculated

more than 10 cm21 from neighbouring anti modes (see

above), are obvious candidates, and IR and Raman bands

Table 4 (continued)


CyC–H bend S75 ¼ 14ðDb3;10;24 þ Db3;14;28 2 Db11;10;24 2 Db13;14;28 þ Db10;11;25 þ

Db14;13;27 2 Db12;11;25 2 Db12;13;27 2 Db4;9;23 2 Db4;5;19 þ Db8;9;23 þ

Db6;5;19 2 Db9;8;22 2 Db5;6;20 þ Db7;8;22 þ Db7;6;20Þ

CyC–H bend S76 ¼ 14ðDb3;10;24 þ Db3;14;28 2 Db11;10;24 2 Db13;14;28 2 Db10;11;25

2Db14;13;27 þ Db12;11;25 þ Db12;13;27 2 Db4;9;23 2 Db4;5;19 þ Db8;9;23

þ Db6;5;19 þ Db9;8;22 þ Db5;6;20 2 Db7;8;22 2 Db7;6;20Þ

Ring torsion S77 ¼ 1ffiffi

8p ðDt3;10 2 Dt14;3 2 Dt11;12 þ Dt12;13 þ Dt4;9 2 Dt5;4 2 Dt8;7

þ Dt7;6Þ


24p ðDt3;10 2 Dt14;3 2 2Dt10;11 þ 2Dt13;14 þ Dt11;12 2 Dt12;13 þ Dt4;9

2 Dt5;4 2 2Dt9;8 þ 2Dt6;5 þ Dt8;7 2 Dt7;6Þ

a See Fig. 12 for numbering of atoms. The internal coordinates for stretching (DT ; DD; DR; Dd; Ds), bending (Da; Db; D1; Dv), torsion (Dt), and out-of-

plane deformations (Dp) are defined as in Ref. [21].


which did not meet the criteria to originate from the anti

conformer were frequently chosen as gauche. However, in

some cases gauche fundamentals were attributed to bands,

which did not completely vanish in the crystal.

Various weak infrared and a few Raman bands have been

left unassigned in Table 1. Many of them are undoubtedly

combination bands or overtones from the large number of

fundamentals in DPE. It is interesting to note that in all the

four Raman bands of the pairs 760/740 and 940/904 cm21,

employed in the van’t Hoff plots (Fig. 11) (two anti and two

gauche), the largest contribution to PED comes from (y)C–

H out-of-plane bend.

In an infrared spectroscopic study combined with

molecular mechanics calculations of the closely related

molecule 1,2-di( p-bromophenyl)ethane, Stolov et al. [22]

report results more complicated than those assumed for

DPE. Thus, they found a mixture of anti and three uncertain

additional conformers in solutions. These conformers were

supposedly due to restricted rotation around the CPh –Caliph

in addition to the Caliph –Caliph; which gives rise to the anti

and gauche conformers. In the solid state they found two

crystalline modifications, one being anti. One of the crystals

was metastable (possibly containing a gauche conformer)

and converted to the stable crystal (anti) in 15–30 min at

300 K [22].

Acknowledgements

V.A. was supported by a fellowship from the Research

Council of Norway to Northwest Russia and the Baltic

Countries.

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Vibrational spectra, conformational equilibrium and ab initio calculations of 1,2-diphenylethane

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Transcript of Vibrational spectra, conformational equilibrium and ab initio calculations of 1,2-diphenylethane