# A Quantum Chemical Study on Structures and Electronic (Hyper)polarizabilities of 2,2′-Biselenophene Rotamers

Authors: Andrea Alparone
Journal: ISRN Physical Chemistry
 (2013)

---

## Abstract

Geometries, IR and Raman spectra, nucleus independent chemical shifts, and static electronic (hyper)polarizabilities of the equilibrium conformations of 2,2′-biselenophene were determined in vacuum using density functional theory (DFT) computations. At the DFT-PBE0/6-31G+pdd′ level theantigauche structure characterized by the Se-C2-C2′-Se dihedral angle of 157° is the global minimum, whereas the syngauche rotamer (Se-C2-C2′-Se = 40°) lies ca. 0.7 kcal·mol−1 above the antigauche form. The structural and spectroscopic properties as well as the electronic polarizability of the antigauche are similar to those of the syngauche structure. On the other hand, the dipole moments and first-order hyperpolarizabilities are strongly influenced by the conformational characteristics, increasing by ca. a factor of five when passing from the antigauche to the syngauche form.


---

## Body

## 1. Introduction

Oligomers and polymers based on five-membered heterocycles have received great attention as promising conductive and nonlinear optical (NLO) materials [1–3]. Although the major efforts have been principally directed towards polyfurans, polypyrroles, and especially polythiophenes, recent studies have been also dedicated to the properties of polyselenophenes [4, 5]. Selenophene, owing to the intrinsic effects of the heavy atom, is considered an interesting building-block for the design of NLO devices [6–10]. Physicochemical properties of π-conjugated oligomers and polymers are usually influenced by the twisting degree of the backbone as well as by the extension of the electron delocalization [11, 12]. However, structural and electronic properties of large oligomers and polymers can be extrapolated by using data of smaller oligomers [11, 12].Differently from the monomer, little is known about the physicochemical properties of the smallest oligoselenophenes. Structures and torsional potentials of 2,2′-biselenophene, 2,2′:5′,2′′-terselenophene, and 2,2′:5′,2′′:5′′,2′′′-quaterselenophene have been previously investigated by usingab initio and density functional theory (DFT) methods [13, 14]. On the basis of the most recent theoretical results obtained in vacuum, 2,2′-biselenophene is predicted to exist in two nonplanar minimum-energy conformations, characterized by Se-C2-C2′-Se dihedral angles of ca. 150° (antigauche) and 40° (syngauche) [14]. The antigauche is the lowest-energy conformer, with the syngauche being predicted to lie above the antigauche structure by less than 1 kcal/mol [13, 14]. The torsional potentials of 2,2′-biselenophene for the 0°–360° rotation around the C2–C2′ bond are described by flat four-well potentials, showing a high degree of conformational flexibility [13].The present work reports important physicochemical properties of the most stable rotamers of 2,2′-biselenophene by using computational methods. The structures of the investigated conformations are displayed in Figure1. Specifically, we determined the geometries, vibrational spectra, nucleus independent chemical shifts, dipole moments, and static electronic polarizabilities and first-order hyperpolarizabilities in the gas phase. To the best of our knowledge experimental and theoretical hyperpolarizabilities of 2,2′-biselenophenes are not available so far, whereas there are a number of studies available for the monomer selenophene [6–10]. Electronic first-order hyperpolarizabilities and the related NLO properties are often affected by conformational characteristics and could be helpful tools for isomeric identification [15–20].Figure 1
Equilibrium structures of 2,2′-biselenophene in gas. Bond lengths in Å, angles in degrees.βμ(syngauche) = 263.5 a.u., βμ(antigauche) = 52.6 a.u. Colors: white (hydrogen), grey (carbon), and yellow (selenium).


## 2. Computational Details

The calculations were performed using the GAUSSIAN 03 program [21]. The geometries of the antigauche and syngauche forms of 2,2′-selenophene (Figure 1) were optimized using the PBE0 DFT method [22], together with the basis set previously developed by Kamada et al. [23] for structural and (hyper)polarizability computations. It consists of 6-31G basis set for hydrogen atoms, 6-31G+pdd for carbon atoms (ζp=0.0438, ζd1=0.18719, and ζd2=0.0438), and LANL1DZ+pdd for selenium atoms (ζp=0.0367, ζd1=0.11558, and  ζd2=0.0367), which also includes effective core-potential functions. This basis is here denoted as 6-31+pdd′. The vibrational analysis performed at the PBE0/6-31+pdd′ level under the harmonic approximation shows that all the studied structures are equilibrium geometries (no imaginary frequencies). The static electronic polarizabilities (α) and first-order hyperpolarizabilities (β) were computed at the PBE0/6-31G+pdd′ level through the coupled-perturbed HF (CP-HF) theory [24]. The following orientationally invariant quantities were employed:
(1)〈α〉=13(αxx+αyy+αzz),βμ=∑i=x,y,zβiμi|μ|,βi=13∑j=x,y,z(βijj+βjij+βjji).


## 3. Results and Discussion

Theantigauche form is the global minimum-energy structure, characterized by the Se-C2-C2′-Se dihedral angle of 157°. The syngauche form (Se-C2-C2′-Se = 40°) lies above the antigauche conformation by 0.68 kcal·mol−1, in good agreement with previous ab initio and DFT results [13, 14], especially with the B3LYP/6-311++G** computations (ΔE = 0.73 kcal·mol−1) [14]. Thus on the basis of the present results, in the gas phase the antigauche is the prevailing structure (ca. 76%), with the syngauche being however an important conformation (ca. 24%). Note that, as can be appreciated from the data reported in Figure 1, the geometries of the gauche rotamers are very similar to each other. In particular, the bond lengths and angles of the antigauche differ, respectively, by no more than 0.003 Å (C2′-C2) and 1.3° (C2′-C2-C3) from the corresponding values of the syngauche form. The structural similarity is also confirmed by the spectroscopic results. For both the rotamers we determined the nucleus independent chemical shift perpendicular to the plane of the selenophene ring at the distance of 1 Å [NICS(1)⊥] [25, 26]. This parameter is closely connected to aromaticity, a negative NICS(1)⊥ value denoting an aromatic ring [25, 26]. The PBE0/6-31+pdd′  NICS(1)⊥ values for the antigauche and syngauche 2,2′-biselenophenes are very close to each other, being calculated to be −17.6 and −17.3 ppm, respectively. Note that, when passing from the monomer to the dimer, the ring aromaticity decreases by ca. 20%.The above results on the calculated geometries are also corroborated by the IR and Raman spectra obtained at the PBE0/6-31+pdd′ level under the harmonic approximation. The simulated vibrational spectra in the 500–1800 cm−1 range are displayed in Figure 2. The complete sets of wavenumber values (ω), IR intensities (IIR), and Raman activities (ARaman) of the antigauche and syngauche forms of 2,2′-biselenophene are given in Tables 1 and 2. The most active Raman peak of the antigauche form placed at 1526 cm−1 (ARaman=1594 Å4/amu) is principally attributed to the C=C + C–C bonds stretching vibration with the nonnegligible contribution of in-plane C–H bending deformations (mode no. 9, Table 1). A graphical representation of the atom vector displacements involved in this mode is given in Figure 2(a). The corresponding transition for the syngauche conformation is blue-shifted by only 1 cm−1 (Table 2). Additionally, the IR spectrum of both rotamers is dominated by an isolated band located at 673 cm−1 for the antigauche (IIR=126.5 km/mol, mode no. 28) and at 682 cm−1 for the syngauche(IIR=118.4 km/mol, mode no. 27). As can be seen in Figure 2(b), this transition is assigned to a pure out-of-plane bending deformation.Table 1
Vibrational wavenumbers,ω (cm−1), infrared intensities, IIR (km/mol), and Raman activities, ARaman (Å4/amu), of the antigauche form of 2,2′-biselenophene.
Mode no.
ω
I
IR
A
Raman
1
3280
0.0
378.7
2
3280
1.3
0.8
3
3227
0.2
322.4
4
3226
8.9
14.9
5
3206
17.7
5.4
6
3206
0.0
98.0
7
1631
0.2
940.4
8
1573
4.7
0.1
9
1526
1.2
1593.9
10
1515
29.4
1.3
11
1390
0.0
26.9
12
1352
4.0
0.4
13
1288
0.3
17.9
14
1241
27.9
0.6
15
1230
1.6
20.3
16
1110
1.1
0.5
17
1097
0.0
60.2
18
1072
0.4
29.2
19
1072
11.5
0.3
20
892
0.1
3.4
21
889
0.1
0.4
22
874
0.7
0.1
23
838
0.7
0.8
24
829
31.9
1.6
25
817
3.7
44.1
26
765
65.2
0.2
27
679
4.5
1.6
28
673
126.5
1.5
29
658
0.3
8.3
30
628
0.6
0.4
31
581
0.1
45.2
32
565
0.8
1.2
33
550
2.0
5.8
34
514
1.3
0.7
35
461
0.4
0.7
36
412
7.6
3.6
37
320
0.1
0.7
38
246
0.0
3.1
39
194
0.1
4.8
40
106
1.7
0.8
41
105
0.1
0.7
42
22
0.1
1.9
The calculations were carried out at the PBE0/6-31 + pdd′ level.Table 2
Vibrational wavenumbers,ω (cm−1), infrared intensities, IIR (km/mol), and Raman activities, ARaman (Å4/amu), of the syngauche form of 2,2′-biselenophene.
Mode no.
ω
I
IR
A
Raman
1
3279
1.0
367.3
2
3279
0.1
13.3
3
3229
6.6
238.9
4
3228
3.0
103.6
5
3212
0.0
59.3
6
3211
13.2
103.0
7
1624
0.6
755.4
8
1574
0.2
4.3
9
1527
14.9
1151.6
10
1507
6.3
15.4
11
1377
1.3
39.0
12
1373
1.0
9.9
13
1285
4.4
21.9
14
1263
45.0
8.1
15
1199
14.3
1.1
16
1109
0.2
4.6
17
1096
0.1
30.5
18
1070
2.0
0.4
19
1057
13.0
20.2
20
895
1.1
0.4
21
893
0.0
5.4
22
890
1.8
1.6
23
847
3.1
14.8
24
835
28.5
0.1
25
821
14.8
33.7
26
784
30.0
1.4
27
682
118.4
0.4
28
680
11.0
2.4
29
658
2.5
3.5
30
651
4.8
5.9
31
573
0.9
8.5
32
554
1.8
0.5
33
520
3.1
7.6
34
504
1.3
7.8
35
476
0.0
24.3
36
423
7.4
0.3
37
287
0.1
1.2
38
257
0.5
1.9
39
245
0.0
6.4
40
102
1.6
1.2
41
80
0.1
1.7
42
37
0.0
5.3
The calculations were carried out at the PBE0/6-31 + pdd′ level.Simulated gas-phase Raman (a) and IR (b) spectra of 2,2′-biselenopheneantigauche and syngauche conformations. Lorentz line shapes with half-width of 10 cm−1 are used. PBE0/6-31+pdd′ results.
(a)
(b)Beside to the structural and spectroscopic properties, now we explore the electric properties of thegauche rotamers. As a test case, we computed the electric properties also for the monomer, for which some experimental and high-level theoretical estimates are available from the literature. The experimental gas-phase dipole moment (μ) of selenophene at 0.39 D [27] is overestimated by the present calculations (μ=0.47 D), whereas the observed 〈α〉 value of 74.90 a.u. [28] is reasonably reproduced by the PBE0/6-31+pdd′ level (〈α〉=70.44 a.u., −6%). Unfortunately, the experimental first-order hyperpolarizability of selenophene is not available to date. However, the PB0/6-31G+pdd′βμ value of selenophene of 98.2 a.u. is in excellent agreement with the datum previously predicted by the CCSD(T)/6-31G+pdd′ computations at 98.4 a.u. (with a deviation of −0.2%) [7].Similarly to the monomer, both 2,2′-biselenophenes show a rather low polarity. However, due to the mutual arrangement of the selenophene moieties, when going from theantigauche  to the syngauche form, the μ value increases by ca. a factor of five (μ=0.19 D versus μ=0.88 D). A somewhat different behaviour occurs for the electronic polarizabilities, with the 〈α〉(syngauche) value of 150.76 a.u. being very close to the corresponding datum of the antigauche structure (152.74 a.u., +1%). By contrast, both the magnitude and direction of the βμ vector (see Figure 1) are strongly influenced by the conformation, in line with the results obtained for the dipole moments. Specifically, the βμ vector for the antigaucheform is directed along the z-axis, whereas for the syngauche rotamer it is aligned along the y-axis. More importantly, the present PB0/6-31G+pdd′ calculations predict βμ(syngauche) > βμ(antigauche) by ca. a factor of five.


## 4. Conclusions

The present results indicate that the calculated electronic polarizability and structural and spectroscopic properties of 2,2′-biselenophenes are little dependent on the conformation. Differently, both the magnitude and direction of the dipole moment and first-order hyperpolarizability are significantly influenced by the structural features. Therefore thegauche rotamers could be unambiguously discriminated on the basis of their rather different NLO signals.



---

*Source: 251635-2013-12-26.xml*