# Infrared Optical Constants and Computational Studies of Neat Liquidn-Butylethylether

Authors: K. B. Beć; J. P. Hawranek
Journal: Journal of Spectroscopy
 (2013)

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## Abstract

Aliphatic ethers are of interest to researchers due to their wide application in the fuel, chemical, and pharmaceutical industry. In this paper we studied vibrational properties of neat liquidn-butylethylether (NBEE), including the determination of complex refractive index in the NIR and MIR range (11700–560 cm−1). The high absorption of neat liquid in the MIR range required the use of thin-film transmission recordings. The spectra analysis was based on conformational analysis and anharmonic calculations on B2PLYP/N07D level of theory. Final band assignments procedure was based on potential energy distributions. The theoretical investigation revealed that although 26 conformers of NBEE can be expected to exist in the liquid phase at 298 K, only few of them are essential for the forming of the spectrum. This study is important for the proper understanding of vibrational properties of other aliphatic ethers.


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## Body

## 1. Introduction

Aliphatic ethers have widespread industrial applications, ranging from solvents [1] and catalysts components [2] to fuel additives [3]. The utilization of n-butylethylether (NBEE) in fuel industry also lead to an increasing interest in the environmental studies of n-butylethylether in the last years [4–6]. Surprisingly the infrared properties of liquid n-butylethylether were never deeply investigated. In this paper, we aimed to obtain an insight into vibrational properties of the studied ether through a broad spectral range complex refractive index measurements and a detailed vibrational analysis, with the hope to fully understand factors determining the vibrational spectra of NBEE in the neat liquid phase. The determination of these data required the use of thin-film quantitative techniques in the MIR region due to strong absorption in the studied region. Experimental data are supported by a conformational analysis and subsequently a detailed anharmonic vibrational analysis. The final band assignments procedure is based on modelled on B2PLYP/N07D level vibrational spectra of all resolved NBEE conformers.The results of studies reported here are indispensable for the determination of high frequency dielectric properties ofn-butylethylether in the liquid phase.


## 2. Experimental

The NBEE sample was of the highest purity available from Aldrich, additionally dried and stored over molecular sieves under nitrogen.NIR and MIR spectra were recorded on a Nicolett Magna 860 FT-IR/Raman spectrometer. To minimize the effect of possible drift, the empty chamber was measured as a reference spectrum before and after the sample measurement. All measurements were carried out at the controlled temperature 298 K.Due to strong absorption bands, the MIR spectra were recorded in thin-film cells assembled for the purpose of this work from KBr windows polished to high flatness, monitored in sodium light on a glass optical flat. The spacers were prepared out of aluminum foils. The geometrical parameters of the cell cavity were determined by fitting the experimental interference spectrum of the empty cell with the theoretical ones, using the procedure based on the earlier derived algorithm. Several KBr cells were used with thickness ranging from 4 to 8μm. The resolution was set at 0.5 cm−1 and a scan number of 512 was chosen to ensure good signal to noise ratio.Spectra in the NIR range were measured on the same instrument. A CaF2 beamsplitter with the MCT-A detector (in the region 11700–8000 cm−1) and DTGS detector (in the 8000–4000 cm−1 region). The resolution was maintained on a 0.5 cm−1 level. Thermostated quartz cells (Hellma) of 5 and 10 mm thickness were used in the upper NIR region (11700–8000 cm−1); in the lower region cells of 0.1 and 0.5 mm thickness were used. The absorbance spectrum of the liquid was obtained by subtraction of the empty-cell spectrum from the spectrum of the cell filled with the liquid. Subsequently, the absorbance spectrum was recalculated to yield the spectrum of the absorption index k(ν).FT-Raman spectra were measured on a Nicolet Magna 860 FTIR spectrometer interfaced with a FT-Raman accessory. The samples were illuminated by a Nd:YVO4 laser line at 1.064 nm with a power of 0.2–0.3 W. A CaF2 beamsplitter was used in combination with an InGaAs detector. The interferograms were averaged over 1024 scans. The resolution of the spectra was 2 cm−1.


## 3. Data Processing

From the transmission spectra in the entire measured region, the spectrum of both components of the complex refractive index:(1)n^(ν)=n(ν)+ik(ν),
where i=-1  and ν denotes wavenumbers (cm−1) throughout this work.The real and imaginary parts of the complex refractive index are often called customarily optical constants, although they depend on frequency, temperature, and pressure for a given liquid. These dimensionless spectra fully describe optical properties of any isotropic system. Usually the interest of spectroscopists is focused on the spectrum of the absorption index,k(ν). Unfortunately, it is not easy to obtain the optical constants; what is more, an exact procedure usually requires a simultaneous determination of both components. Various methods for determination of optical constants were reviewed by Bertie [7]. In our studies, we use the transmission method [8, 9] with later enhancements [10, 11]. The method is based on transmission measurements in the MIR and NIR ranges and refractive indices determined in the visible. A serious difficulty in this method is connected with measurements of spectra in  MIR region. Due to strong absorption in this range, a very thin layers have to be used for quantitative measurements and this causes serious dispersion distorsion of the measured spectra [8]. From these data, both component spectra of the complex refractive index are obtained by the use of the procedure combining an iterative correction of the dispersion distortion [8] with the modified Kramers-Krönig procedure [11]. The spectrum was processed as a whole from 11700 to 560 cm−1.The spectra of the complex refractive index are required for the determination of high frequency dielectric properties of studied liquid, which are in progress. Moreover, the accurate determination of the absorptive properties of the liquid can be based only on the absorption index spectrumk(ν) because of the discussed above strong distortion of thin layers transmission spectra [8].


## 4. Results and Discussion

### 4.1. Complex Refractive Index in the NIR Range (11700–4000 cm−1)

The complete spectrum of the complex refractive index in the measured range (11700–4000cm−1), covering the first and second overtone regions, is presented in Figure 1.Figure 1
Spectrum of the complex refractive index of NBEE in the NIR range (11700–4000cm−1).As can be seen for the studied ether, the NIR bands are very weak except for bands in the region 6000–4000cm−1. In general, the range between 6000–5600cm−1 reflects well the doubled 3000–2800cm−1 region. The analysis of the overtones for the studied molecule was not the aim of this work and will not be presented here. However, the n^(ν)  spectrum had to be determined in the NIR region, since its knowledge is essential for an accurate determination of the n^(ν)  spectrum in the MIR region [11].


### 4.2. Complex Refractive Index in the MIR Range (4000–560 cm−1)

Spectra of complex refractive index of NBEE separated into upper MIR region (4000–2000 cm−1) and lower MIR region (2000–560 cm−1) can be found in Figures 2 and 3, respectively. The detailed discussion of the MIR range will be presented later in this paper. Raman spectrum is presented in Figure 4.Figure 2
Spectrum of the complex refractive index of NBEE in the upper MIR range (4000–2000 cm−1).Figure 3
Spectrum of the complex refractive index of NBEE in the lower MIR range (2000–560 cm−1).Figure 4
Raman spectrum of liquid NBEE.


### 4.3. Anharmonic Vibrational Analysis

In our theoretical research, we possibly seek most accurate reproduction of experimental spectra, as it is a step needed for the following studies of dielectric properties of examined liquids. To achieve that in case of aliphatic ethers, the analysis of theoretical spectra of various conformers is needed [12]. Also the use of anharmonic calculations on relatively high level is inevitable. In our previous studies [13], we found the hybrid DFT functional B2PLYP with the N07D basis set as exeptionally valuable, considering the accuracy of calculated frequencies and computational cost. Our findings confirm the reported in the literature advantages of discussed computational method [14].We based the conformational analysis of NBEE on results of previous studies ofn-butylmethylether (NBME) [15]. We combined 11 stable conformations of the butyl chain found earlier [15] with three possible conformations of the ethyl chain. As a result we obtained 33 initial conformations of NBEE. Eventually 7 of them were found redundant and excluded due to symmetry operations-resulting in a total of 26 NBEE conformations, which were subsequently optimized on a B2PLYP/N07D level of theory.We assumed the following name scheme for NBEE conformers:xyza, where x denotes conformation (“trans”, “gauche+” or “gauche−”; T, G+ or G-, resp.) on a O–Cα bond, y on a Cα–Cβ bond, and z on a Cβ–Cγ bond in the butyl chain, and similarly adenotes the conformation on  Cα′–O bond in the ethyl chain. This corresponds to our notation scheme used earlier.The detailed data on resulting NBEE conformer population is presented in Table1. The “TG–T T” conformer is clearly dominant, with a 39% concentration, followed by “TG+G+ T” and “TTT T” conformers both with 13% contributions. As it can be noticed, only few conformers have concentrations high enough to manifest itself in the experimental vibrational spectrum. Nevertheless, the modelled theoretical spectrum involves all investigated forms. The calculated abundances are Boltzmann based.Table 1
Relative B2PLYP/N07D energiesΔE, relative B2PLYP/N07D energies with zero-point correction ΔEZPE, relative free Gibbs energies (298.15 K), and abundances of NBEE conformers.
Conformer
Δ
E (kcal/mol)
Δ
E
ZPE (kcal/mol)
Δ
G (kcal/mol)
Symmetry
Rel. abundance (%)
TG−T  T
0
0
0
C1
38.8
TG+G+  T
0.80
0.70
0.63
C1
13.4
TTT  T
0.08
0.29
0.23
Cs
13.1
TTG−  T
1.04
1.16
1.04
C1
6.7
TG−G+  T
1.72
1.45
1.33
C1
4.1
TG−T  G+
1.60
1.57
1.38
C1
3.8
TG−T  G−
1.61
1.57
1.41
C1
3.6
G+G+T  G−
1.70
1.62
1.42
C1
3.5
G+TT  T
1.68
1.83
1.56
C1
2.8
G+TT  G−
1.68
1.87
1.68
C1
2.3
TG+G+  G−
2.37
2.26
1.95
C1
1.4
TG+G+  G+
2.41
2.29
2.12
C1
1.1
G−G−G−  T
2.41
2.29
2.24
C1
0.9
G−TG+  T
2.73
2.80
2.38
C1
0.7
G−TG−  G+
2.69
2.74
2.37
C1
0.7
TG−G+  G+
3.34
3.00
2.51
C1
0.6
TTG−  G+
2.65
2.77
2.47
C1
0.6
TTG−  G−
2.59
2.73
2.63
C1
0.5
TG−G+  G−
3.28
2.95
2.68
C1
0.4
G−G−G+  T
3.32
3.00
2.89
C1
0.3
G+G+T  G+
3.10
2.99
2.91
C1
0.3
G+TT  G+
3.07
3.19
3.11
C1
0.2
G−G−G−  G−
3.90
3.70
3.39
C1
0.1
G−G−G+  G−
4.70
4.37
4.18
C1
0.0
G−TG+  G−
4.07
4.11
4.00
C1
0.0
G−TG−  G−
4.05
4.12
3.97
C1
0.0


### 4.4. Modelled Spectra of NBEE Conformers

Gaussian 09 [16] was used to calculate the spectra of each conformer. The potential energy distribution was calculated using the gar2ped package [17], and the normal coordinates were constructed in accordance to Pulay et al. [18]. The selection of modes was based on the dominant PED values. The definitions of internal coordinates for NBEE molecule are shown in Table 2. The atom numbering in the NBEE molecule can be found in Figure 5.Table 2
Definitions of internal coordinates for NBEE molecule.
Coord.
Definition
Description
1
O1–C2 stretch.
C–O stretch.
2
O1–C5 stretch.
C–O stretch.
3
C2–H3 stretch.
C(H2)–H stretch.
4
C2–H4 stretch.
C(H2)–H stretch.
5
C2–C18 stretch.
C–C stretch.
6
C5–H6 stretch.
C(H2)–H stretch.
7
C5–H7 stretch.
C(H2)–H stretch.
8
C5–C8 stretch.
C–C stretch.
9
C8–H9 stretch.
C(H2)–H stretch.
10
C8–H10 stretch.
C(H2)–H stretch.
11
C8–C11 stretch.
C–C stretch.
12
C11–H12 stretch.
C(H2)–H stretch.
13
C11–H13 stretch.
C(H2)–H stretch.
14
C11–C14 stretch.
C–C stretch.
15
C14–H15 stretch.
C(H3)–H stretch.
16
C14–H16 stretch.
C(H3)–H stretch.
17
C14–H17 stretch.
C(H3)–H stretch.
18
C18–H19 stretch.
C(H3)–H stretch.
19
C18–H20 stretch.
C(H3)–H stretch.
20
C18–H21 stretch.
C(H3)–H stretch.
21
C(18)H3 sym.  def.
CH3 sym.  def.
22
C(18)H3 asym. def.
CH3 asym. def.
23
C(18)H3 asym. def.'
CH3 asym. def.'
24
C(18)H3 rock.
CH3 rock.
25
CH3rock.'
CH3rock.'
26
C(14)H3 sym.  def.
CH3 sym.  def.
27
C(14)H3 asym. def.
CH3 asym. def.
28
C(14)H3 asym. def.'
CH3 asym. def.'
29
C(14)H3 rock.
CH3 rock.
30
C(14)H3 rock.'
CH3 rock.'
31
C(2)H2 sciss.
CH2 sciss.
32
C(2)H2 sciss.
CH2 sciss.
33
C(2)H2 rock.
CH2 rock.
34
C(2)H2 wagg.
CH2 wagg.
35
C(2)H2 twist.
CH2 twist.
36
C(5)H2 sciss.
CH2 sciss.
37
C(5)H2 sciss.
CH2 sciss.
38
C(5)H2 rock.
CH2 rock.
39
C(5)H2 wagg.
CH2 wagg.
40
C(5)H2 twist.
CH2 twist.
41
C(8)H2 sciss.
CH2 sciss.
42
C(8)H2 sciss.
CH2 sciss.
43
C(8)H2 rock.
CH2 rock.
44
C(8)H2 wagg.
CH2 wagg.
45
C(8)H2 twist.
CH2 twist.
46
C(11)H2 sciss.
CH2 sciss.
47
C(11)H2 sciss.
CH2 sciss.
48
C(11)H2 rock.
CH2 rock.
49
C(11)H2 wagg.
CH2 wagg.
50
C(11)H2 twist.
CH2 twist.
51
C2–C8 tors.
C–C tors.
52
C2–O1 tors
C–O tors
53
C5–O1 tors
C–O tors
54
C5–C8 tors.
C–C tors.
55
C8–C11 tors.
C–C tors.
56
C11–C14 tors.
C–C tors.
57
C2–O1–C5 bend.
C–O–C bend.Figure 5
Atom numbering in the NBEE molecule.Table3 presents PED values for the most abundant (39%) DNBE conformer(“TG–T T”). Due to the high volume of data, PED tables for other conformers are not shown, but are available from authors upon request. The theoretical spectra of 8 most abundant NBEE conformers are presented in Figure 6.Table 3
PED table for the major conformer (“TG−T T”) of NBEE.
Calculated frequency (cm−1)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Harmonic
Anharmonic
1
72.2
59.4
52
(48)
54
(22)
53
(10)
2
73.9
80.2
55
(59)
54
(13)
52
(6)
37
(6)
3
78.3
68.1
53
(71)
42
(10)
4
140.5
134.1
52
(35)
−54
(28)
−53
(7)
37
(6)
42
(6)
5
210.4
210.8
57
(29)
−32
(20)
−54
(15)
−37
(13)
55
(9)
6
244.1
229.1
51
(69)
−56
(11)
−42
(6)
7
249.9
245.2
56
(68)
51
(16)
−54
(6)
8
272.3
273.9
47
(38)
−42
(33)
−54
(6)
53
(5)
9
329.5
327.9
47
(27)
37
(18)
57
(12)
8
(10)
42
(9)
10
442.7
440.6
32
(50)
−37
(12)
−24
(11)
57
(11)
11
540.1
535.0
37
(23)
−42
(18)
−47
(11)
57
(9)
43
(8)
12
747.7
750.9
48
(45)
43
(26)
30
(10)
13
830.9
823.1
25
(41)
−33
(37)
−35
(13)
14
842.1
828.1
30
(20)
−43
(17)
48
(10)
2
(9)
1
(8)
−50
(7)
24
(6)
15
859.5
843.9
11
(32)
29
(16)
14
(9)
−38
(8)
8
(8)
16
922.2
906.0
24
(24)
1
(15)
−30
(11)
5
(10)
50
(8)
43
(8)
−37
(6)
17
987.9
972.6
38
(30)
29
(28)
−44
(9)
−49
(8)
−40
(6)
18
995.3
975.1
5
(16)
−2
(15)
−8
(14)
45
(13)
30
(10)
−50
(9)
19
1054.7
1028.9
14
(52)
−5
(11)
2
(9)
−8
(8)
−11
(7)
20
1087.1
1062.8
5
(23)
8
(17)
−1
(15)
14
(13)
−11
(12)
21
1129.6
1100.4
24
(19)
−5
(14)
−11
(13)
8
(11)
32
(8)
−2
(6)
29
(6)
22
1165.1
1126.7
1
(41)
−2
(40)
23
1167.1
1141.0
38
(20)
−29
(16)
11
(13)
24
(7)
−42
(7)
−47
(6)
24
1190.0
1162.4
33
(18)
25
(11)
−43
(9)
24
(8)
48
(7)
−1
(6)
−30
(5)
25
1203.9
1177.6
33
(30)
25
(16)
38
(11)
43
(8)
−48
(6)
26
1268.7
1237.6
40
(41)
45
(14)
−30
(11)
48
(8)
−50
(8)
27
1293.1
1258.7
40
(24)
−45
(21)
50
(14)
44
(9)
30
(6)
28
1309.9
1277.9
35
(84)
25
(10)
29
1339.9
1306.7
50
(40)
−49
(16)
45
(16)
−44
(11)
40
(6)
30
1345.9
1313.2
49
(30)
45
(16)
44
(16)
−40
(13)
50
(12)
31
1395.6
1364.2
34
(46)
39
(31)
21
(13)
32
1419.5
1382.6
44
(26)
−21
(23)
−49
(21)
39
(9)
11
(9)
33
1424.1
1389.6
21
(42)
44
(14)
−39
(12)
−49
(8)
−8
(7)
34
1430.5
1413.7
26
(82)
14
(10)
35
1462.3
1443.9
34
(35)
−39
(29)
−21
(9)
−5
(9)
−8
(5)
36
1491.4
1459.7
41
(88)
46
(5)
37
1498.7
1469.1
22
(69)
−23
(22)
−25
(8)
38
1510.0
1479.3
46
(48)
−28
(36)
−27
(7)
39
1515.1
1498.0
27
(75)
−28
(16)
−30
(8)
40
1516.5
1484.8
23
(55)
22
(18)
−31
(14)
−24
(6)
41
1523.3
1495.1
46
(45)
28
(33)
27
(7)
42
1526.4
1481.3
36
(64)
−31
(21)
43
1544.4
1502.1
31
(61)
36
(25)
44
2985.8
2863.6
6
(54)
7
(28)
−4
(8)
−3
(8)
45
2999.3
2828.0
4
(42)
3
(41)
6
(12)
46
3022.6
2877.3
7
(59)
−6
(31)
47
3029.5
2884.4
3
(48)
−4
(46)
48
3050.8
2944.8
10
(34)
13
(28)
9
(25)
12
(5)
49
3055.5
2919.9
13
(57)
−10
(24)
12
(6)
50
3058.4
2956.9
17
(36)
16
(29)
15
(24)
10
(7)
51
3074.6
3006.3
18
(40)
20
(30)
19
(30)
52
3094.0
2949.3
9
(56)
−10
(25)
−12
(17)
53
3113.3
2969.0
12
(43)
17
(20)
−16
(15)
9
(7)
−13
(7)
−10
(6)
54
3134.3
2988.8
16
(35)
−17
(29)
12
(25)
−13
(7)
55
3136.7
2993.0
15
(72)
−16
(14)
−17
(11)
56
3152.2
3005.6
18
(60)
−20
(21)
−19
(19)
57
3160.9
3011.5
19
(51)
−20
(48)Figure 6
Experimentalk(ν) spectrum of liquid NBEE and simulated B2PLYP/N07D vibrational spectra of most abundant NBEE conformers (abundance larger than 3%).


### 4.5. Simulation of Experimental Spectra

The final calculated spectrum ofn-butylethylether was obtained as a linear combination of calculated spectra of all conformers with regard to their calculated abundances. The number of conformers taken into account is 26; however, as can be concluded from Table 1 only few of them are abundant enough to impact vibrational spectrum. Theoretical spectra compared with experimental ones are presented in Figures 7 and 8. Amplified segments of spectra are presented for a better view of details. We have chosen the Cauchy-Gauss product function [19] as the band model, with a constant Cauchy-Gauss ratio and a constant half-width of the bands. Parameters a2=0.15 and a4=0.03 were used in the product function, resulting in the full-width at half height of 14 cm−1.Figure 7
Calculated and experimental spectra of NBEE in the upper MIR range (3300–2500 cm−1).Figure 8
Calculated and experimental spectra of NBEE in the lower MIR range (1800–560 cm−1).There are no proton donor groups in the studied molecule, therefore no association due to hydrogen-bonding is expected. Although a weak proton donor behavior of Cα–H bonds was demonstrated for H-bonded n-propanol [20], the screening by the alkyl groups prevents any interaction with the oxygen atom in a neighboring ether molecule. No evidence was also found in the literature for other types of structure-making forces in liquid ethers, for example,  due to dipole-dipole interactions, since the dipole moment of NBEE amounts only to 1.24 D [21]. Thus, the existence of dimers or higher polymers, which could influence vibrational spectra by concentration effects can be safely excluded.Comparing the results with previous harmonic studies of di-n-propylether [12], it can be noticed that the quality of spectra reproduction is noticeably higher when unscaled B2PLYP/N07D anharmonic calculations are employed. The agreement between the calculated and experimental frequencies as well as the overall shape of the resulting theoretical spectrum is much better than the similar results yielded with harmonic B3LYP calculations even with application of scaling. It is also worth noticing that the agreement with experimental spectra in the lower range (1800–560 cm−1) is still better than in upper range (stretching modes), both in raw frequencies and overall shape of resulting spectra, similarly as for previously studied dipropyl ether [12, 22].


### 4.6. Identification of Bands in MIR Region

The identification of bands observed in liquid phase spectra, based on a PED analysis and thorough comparison of the experimentalk(v) spectrum with modelled IR spectrum are presented in Table 4. The calculated wavenumbers in the table refer to band positions in the modelled spectrum incorporating a number of calculated spectra of conformers. Therefore they differ from the calculated wavenumbers for individual conformers.Table 4
MIR and Raman band identification for liquid NBEE.
ν
exp(cm−1)
ν
calc   (cm−1)
Vibrational modes contributions
IR
Raman
1
2975.5
2975.7
3003
CH3 str. asym.
2
2961.5
2962.5
2991
CH3 str. asym.',  CH2 str. asym.
3
2934.6
2934.1
2955
CH3 str. asym.',  CH2 str. asym.
4
~2913
2913.4
2919
CH2 str. sym.
5
~2874
2873.4
2884
CH2 str. asym.
6
2864.4
2868.9
2861
CH2 str. asym.
7
2799.3
2799.2
—
—
8
1488.4
1487.0
1495
CH2 sciss., CH3 asym. def.'
9
1466.0
—
1469
CH3 asym. def.
9
1458.7
~1457
—
—
10
1412.5
—
1414
CH3 sym. def.
11
1376.3
—
1390
CH3 sym. def.
12
1333.5
—
1364
CH2 wagg.
13
1300.2
1299.0
1307
CH2 twist.
14
1262.2
~1257
1259
CH2 twist.
15
1231.4
1230.8
1237
CH2 twist.
16
1123.2
1119.9
1126
C–O stretch.
17
1099.0
1099.2
1100
CH3 rock., C–C stretch.
18
1067.9
~1066
1062
C–C stretch.
19
1026.5
1027.7
1028
C–C stretch.
20
972.4
~972
975
C–C stretch.
21
901.5
901.9
905
CH3 rock.
22
870.7
—
871
C–C stretch., CH3 rock.
23
826.7
~828
828
CH3rock.', CH2 rock.As stated before, the quality of experimental spectra reproduction is lower in the C–H stretching region—in terms of band positions and relative intensities as well, resulting in overall different spectrum shape. Moreover, in this region, the differences of modes frequencies between conformers are highest; therefore we can see a significant level of band overlapping here. Nevertheless main bands can still be clearly identified. The CH3 stretching asymmetric and CH2 stretching asymmetric, as well as stretching symmetric modes for those groups, have been identified (Table 4). Unexpectedly, the 2864.4 cm−1 band was found to be a CH2 (ethyl chain) stretching asymmetric band, strongly shifted towards lower wavenumber.Aliphatic ethers and thioethers exhibit several weak bands at 2800–2700 cm−1 range which are absent in alkanes. In the NBEE spectrum, we can observe such bands too, with the most prominent one at 2799 cm−1 wavenumber. We are not exactly sure about the origin of those bands; however, our calculations suggest at least a contribution of fundamental bands. According to collected data, a few of investigated NBEE conformers contain a significantly shifted symmetric stretching band of α-CH2 groups, including the third most abundant “TTT T” conformer with the band at a calculated frequency 2766 cm−1. Such a high shift of α-CH2 symmetric stretching band has been observed for all previously studied aliphatic ethers.The lower MIR region is dominated by CH3 asymmetric deformation, CH2 scissoring, and CH2 wagging modes (in the 1500–1300 cm−1 range), and by CH2 twisting, C–O stretching, and C–C stretching modes (in the 1300–1000 cm−1 range). The broadening of C–O stretching band due to overlapping bands of conformers can be easily observed. Due to this effect also the relative intensity of C–O band is slightly lower than expected; it is; however, still the most intense band in the spectrum. Also a considerable contribution of C–C stretching bands into the broadened C–O stretching band in studied spectra is probable.Summarizing, the influence of oxygen atom can be pointed out in the spectrum of investigated ether. According to the analyzed data, both CH2(-O) groups in NBEE differ from other methylene groups. The presence of multiple relevant conformers to band broadening and overlapping which is mostly noticeable in case of C–H stretching range and C–O stretching band.


## 4.1. Complex Refractive Index in the NIR Range (11700–4000 cm−1)

The complete spectrum of the complex refractive index in the measured range (11700–4000cm−1), covering the first and second overtone regions, is presented in Figure 1.Figure 1
Spectrum of the complex refractive index of NBEE in the NIR range (11700–4000cm−1).As can be seen for the studied ether, the NIR bands are very weak except for bands in the region 6000–4000cm−1. In general, the range between 6000–5600cm−1 reflects well the doubled 3000–2800cm−1 region. The analysis of the overtones for the studied molecule was not the aim of this work and will not be presented here. However, the n^(ν)  spectrum had to be determined in the NIR region, since its knowledge is essential for an accurate determination of the n^(ν)  spectrum in the MIR region [11].


## 4.2. Complex Refractive Index in the MIR Range (4000–560 cm−1)

Spectra of complex refractive index of NBEE separated into upper MIR region (4000–2000 cm−1) and lower MIR region (2000–560 cm−1) can be found in Figures 2 and 3, respectively. The detailed discussion of the MIR range will be presented later in this paper. Raman spectrum is presented in Figure 4.Figure 2
Spectrum of the complex refractive index of NBEE in the upper MIR range (4000–2000 cm−1).Figure 3
Spectrum of the complex refractive index of NBEE in the lower MIR range (2000–560 cm−1).Figure 4
Raman spectrum of liquid NBEE.


## 4.3. Anharmonic Vibrational Analysis

In our theoretical research, we possibly seek most accurate reproduction of experimental spectra, as it is a step needed for the following studies of dielectric properties of examined liquids. To achieve that in case of aliphatic ethers, the analysis of theoretical spectra of various conformers is needed [12]. Also the use of anharmonic calculations on relatively high level is inevitable. In our previous studies [13], we found the hybrid DFT functional B2PLYP with the N07D basis set as exeptionally valuable, considering the accuracy of calculated frequencies and computational cost. Our findings confirm the reported in the literature advantages of discussed computational method [14].We based the conformational analysis of NBEE on results of previous studies ofn-butylmethylether (NBME) [15]. We combined 11 stable conformations of the butyl chain found earlier [15] with three possible conformations of the ethyl chain. As a result we obtained 33 initial conformations of NBEE. Eventually 7 of them were found redundant and excluded due to symmetry operations-resulting in a total of 26 NBEE conformations, which were subsequently optimized on a B2PLYP/N07D level of theory.We assumed the following name scheme for NBEE conformers:xyza, where x denotes conformation (“trans”, “gauche+” or “gauche−”; T, G+ or G-, resp.) on a O–Cα bond, y on a Cα–Cβ bond, and z on a Cβ–Cγ bond in the butyl chain, and similarly adenotes the conformation on  Cα′–O bond in the ethyl chain. This corresponds to our notation scheme used earlier.The detailed data on resulting NBEE conformer population is presented in Table1. The “TG–T T” conformer is clearly dominant, with a 39% concentration, followed by “TG+G+ T” and “TTT T” conformers both with 13% contributions. As it can be noticed, only few conformers have concentrations high enough to manifest itself in the experimental vibrational spectrum. Nevertheless, the modelled theoretical spectrum involves all investigated forms. The calculated abundances are Boltzmann based.Table 1
Relative B2PLYP/N07D energiesΔE, relative B2PLYP/N07D energies with zero-point correction ΔEZPE, relative free Gibbs energies (298.15 K), and abundances of NBEE conformers.
Conformer
Δ
E (kcal/mol)
Δ
E
ZPE (kcal/mol)
Δ
G (kcal/mol)
Symmetry
Rel. abundance (%)
TG−T  T
0
0
0
C1
38.8
TG+G+  T
0.80
0.70
0.63
C1
13.4
TTT  T
0.08
0.29
0.23
Cs
13.1
TTG−  T
1.04
1.16
1.04
C1
6.7
TG−G+  T
1.72
1.45
1.33
C1
4.1
TG−T  G+
1.60
1.57
1.38
C1
3.8
TG−T  G−
1.61
1.57
1.41
C1
3.6
G+G+T  G−
1.70
1.62
1.42
C1
3.5
G+TT  T
1.68
1.83
1.56
C1
2.8
G+TT  G−
1.68
1.87
1.68
C1
2.3
TG+G+  G−
2.37
2.26
1.95
C1
1.4
TG+G+  G+
2.41
2.29
2.12
C1
1.1
G−G−G−  T
2.41
2.29
2.24
C1
0.9
G−TG+  T
2.73
2.80
2.38
C1
0.7
G−TG−  G+
2.69
2.74
2.37
C1
0.7
TG−G+  G+
3.34
3.00
2.51
C1
0.6
TTG−  G+
2.65
2.77
2.47
C1
0.6
TTG−  G−
2.59
2.73
2.63
C1
0.5
TG−G+  G−
3.28
2.95
2.68
C1
0.4
G−G−G+  T
3.32
3.00
2.89
C1
0.3
G+G+T  G+
3.10
2.99
2.91
C1
0.3
G+TT  G+
3.07
3.19
3.11
C1
0.2
G−G−G−  G−
3.90
3.70
3.39
C1
0.1
G−G−G+  G−
4.70
4.37
4.18
C1
0.0
G−TG+  G−
4.07
4.11
4.00
C1
0.0
G−TG−  G−
4.05
4.12
3.97
C1
0.0


## 4.4. Modelled Spectra of NBEE Conformers

Gaussian 09 [16] was used to calculate the spectra of each conformer. The potential energy distribution was calculated using the gar2ped package [17], and the normal coordinates were constructed in accordance to Pulay et al. [18]. The selection of modes was based on the dominant PED values. The definitions of internal coordinates for NBEE molecule are shown in Table 2. The atom numbering in the NBEE molecule can be found in Figure 5.Table 2
Definitions of internal coordinates for NBEE molecule.
Coord.
Definition
Description
1
O1–C2 stretch.
C–O stretch.
2
O1–C5 stretch.
C–O stretch.
3
C2–H3 stretch.
C(H2)–H stretch.
4
C2–H4 stretch.
C(H2)–H stretch.
5
C2–C18 stretch.
C–C stretch.
6
C5–H6 stretch.
C(H2)–H stretch.
7
C5–H7 stretch.
C(H2)–H stretch.
8
C5–C8 stretch.
C–C stretch.
9
C8–H9 stretch.
C(H2)–H stretch.
10
C8–H10 stretch.
C(H2)–H stretch.
11
C8–C11 stretch.
C–C stretch.
12
C11–H12 stretch.
C(H2)–H stretch.
13
C11–H13 stretch.
C(H2)–H stretch.
14
C11–C14 stretch.
C–C stretch.
15
C14–H15 stretch.
C(H3)–H stretch.
16
C14–H16 stretch.
C(H3)–H stretch.
17
C14–H17 stretch.
C(H3)–H stretch.
18
C18–H19 stretch.
C(H3)–H stretch.
19
C18–H20 stretch.
C(H3)–H stretch.
20
C18–H21 stretch.
C(H3)–H stretch.
21
C(18)H3 sym.  def.
CH3 sym.  def.
22
C(18)H3 asym. def.
CH3 asym. def.
23
C(18)H3 asym. def.'
CH3 asym. def.'
24
C(18)H3 rock.
CH3 rock.
25
CH3rock.'
CH3rock.'
26
C(14)H3 sym.  def.
CH3 sym.  def.
27
C(14)H3 asym. def.
CH3 asym. def.
28
C(14)H3 asym. def.'
CH3 asym. def.'
29
C(14)H3 rock.
CH3 rock.
30
C(14)H3 rock.'
CH3 rock.'
31
C(2)H2 sciss.
CH2 sciss.
32
C(2)H2 sciss.
CH2 sciss.
33
C(2)H2 rock.
CH2 rock.
34
C(2)H2 wagg.
CH2 wagg.
35
C(2)H2 twist.
CH2 twist.
36
C(5)H2 sciss.
CH2 sciss.
37
C(5)H2 sciss.
CH2 sciss.
38
C(5)H2 rock.
CH2 rock.
39
C(5)H2 wagg.
CH2 wagg.
40
C(5)H2 twist.
CH2 twist.
41
C(8)H2 sciss.
CH2 sciss.
42
C(8)H2 sciss.
CH2 sciss.
43
C(8)H2 rock.
CH2 rock.
44
C(8)H2 wagg.
CH2 wagg.
45
C(8)H2 twist.
CH2 twist.
46
C(11)H2 sciss.
CH2 sciss.
47
C(11)H2 sciss.
CH2 sciss.
48
C(11)H2 rock.
CH2 rock.
49
C(11)H2 wagg.
CH2 wagg.
50
C(11)H2 twist.
CH2 twist.
51
C2–C8 tors.
C–C tors.
52
C2–O1 tors
C–O tors
53
C5–O1 tors
C–O tors
54
C5–C8 tors.
C–C tors.
55
C8–C11 tors.
C–C tors.
56
C11–C14 tors.
C–C tors.
57
C2–O1–C5 bend.
C–O–C bend.Figure 5
Atom numbering in the NBEE molecule.Table3 presents PED values for the most abundant (39%) DNBE conformer(“TG–T T”). Due to the high volume of data, PED tables for other conformers are not shown, but are available from authors upon request. The theoretical spectra of 8 most abundant NBEE conformers are presented in Figure 6.Table 3
PED table for the major conformer (“TG−T T”) of NBEE.
Calculated frequency (cm−1)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Mode
(%)
Harmonic
Anharmonic
1
72.2
59.4
52
(48)
54
(22)
53
(10)
2
73.9
80.2
55
(59)
54
(13)
52
(6)
37
(6)
3
78.3
68.1
53
(71)
42
(10)
4
140.5
134.1
52
(35)
−54
(28)
−53
(7)
37
(6)
42
(6)
5
210.4
210.8
57
(29)
−32
(20)
−54
(15)
−37
(13)
55
(9)
6
244.1
229.1
51
(69)
−56
(11)
−42
(6)
7
249.9
245.2
56
(68)
51
(16)
−54
(6)
8
272.3
273.9
47
(38)
−42
(33)
−54
(6)
53
(5)
9
329.5
327.9
47
(27)
37
(18)
57
(12)
8
(10)
42
(9)
10
442.7
440.6
32
(50)
−37
(12)
−24
(11)
57
(11)
11
540.1
535.0
37
(23)
−42
(18)
−47
(11)
57
(9)
43
(8)
12
747.7
750.9
48
(45)
43
(26)
30
(10)
13
830.9
823.1
25
(41)
−33
(37)
−35
(13)
14
842.1
828.1
30
(20)
−43
(17)
48
(10)
2
(9)
1
(8)
−50
(7)
24
(6)
15
859.5
843.9
11
(32)
29
(16)
14
(9)
−38
(8)
8
(8)
16
922.2
906.0
24
(24)
1
(15)
−30
(11)
5
(10)
50
(8)
43
(8)
−37
(6)
17
987.9
972.6
38
(30)
29
(28)
−44
(9)
−49
(8)
−40
(6)
18
995.3
975.1
5
(16)
−2
(15)
−8
(14)
45
(13)
30
(10)
−50
(9)
19
1054.7
1028.9
14
(52)
−5
(11)
2
(9)
−8
(8)
−11
(7)
20
1087.1
1062.8
5
(23)
8
(17)
−1
(15)
14
(13)
−11
(12)
21
1129.6
1100.4
24
(19)
−5
(14)
−11
(13)
8
(11)
32
(8)
−2
(6)
29
(6)
22
1165.1
1126.7
1
(41)
−2
(40)
23
1167.1
1141.0
38
(20)
−29
(16)
11
(13)
24
(7)
−42
(7)
−47
(6)
24
1190.0
1162.4
33
(18)
25
(11)
−43
(9)
24
(8)
48
(7)
−1
(6)
−30
(5)
25
1203.9
1177.6
33
(30)
25
(16)
38
(11)
43
(8)
−48
(6)
26
1268.7
1237.6
40
(41)
45
(14)
−30
(11)
48
(8)
−50
(8)
27
1293.1
1258.7
40
(24)
−45
(21)
50
(14)
44
(9)
30
(6)
28
1309.9
1277.9
35
(84)
25
(10)
29
1339.9
1306.7
50
(40)
−49
(16)
45
(16)
−44
(11)
40
(6)
30
1345.9
1313.2
49
(30)
45
(16)
44
(16)
−40
(13)
50
(12)
31
1395.6
1364.2
34
(46)
39
(31)
21
(13)
32
1419.5
1382.6
44
(26)
−21
(23)
−49
(21)
39
(9)
11
(9)
33
1424.1
1389.6
21
(42)
44
(14)
−39
(12)
−49
(8)
−8
(7)
34
1430.5
1413.7
26
(82)
14
(10)
35
1462.3
1443.9
34
(35)
−39
(29)
−21
(9)
−5
(9)
−8
(5)
36
1491.4
1459.7
41
(88)
46
(5)
37
1498.7
1469.1
22
(69)
−23
(22)
−25
(8)
38
1510.0
1479.3
46
(48)
−28
(36)
−27
(7)
39
1515.1
1498.0
27
(75)
−28
(16)
−30
(8)
40
1516.5
1484.8
23
(55)
22
(18)
−31
(14)
−24
(6)
41
1523.3
1495.1
46
(45)
28
(33)
27
(7)
42
1526.4
1481.3
36
(64)
−31
(21)
43
1544.4
1502.1
31
(61)
36
(25)
44
2985.8
2863.6
6
(54)
7
(28)
−4
(8)
−3
(8)
45
2999.3
2828.0
4
(42)
3
(41)
6
(12)
46
3022.6
2877.3
7
(59)
−6
(31)
47
3029.5
2884.4
3
(48)
−4
(46)
48
3050.8
2944.8
10
(34)
13
(28)
9
(25)
12
(5)
49
3055.5
2919.9
13
(57)
−10
(24)
12
(6)
50
3058.4
2956.9
17
(36)
16
(29)
15
(24)
10
(7)
51
3074.6
3006.3
18
(40)
20
(30)
19
(30)
52
3094.0
2949.3
9
(56)
−10
(25)
−12
(17)
53
3113.3
2969.0
12
(43)
17
(20)
−16
(15)
9
(7)
−13
(7)
−10
(6)
54
3134.3
2988.8
16
(35)
−17
(29)
12
(25)
−13
(7)
55
3136.7
2993.0
15
(72)
−16
(14)
−17
(11)
56
3152.2
3005.6
18
(60)
−20
(21)
−19
(19)
57
3160.9
3011.5
19
(51)
−20
(48)Figure 6
Experimentalk(ν) spectrum of liquid NBEE and simulated B2PLYP/N07D vibrational spectra of most abundant NBEE conformers (abundance larger than 3%).


## 4.5. Simulation of Experimental Spectra

The final calculated spectrum ofn-butylethylether was obtained as a linear combination of calculated spectra of all conformers with regard to their calculated abundances. The number of conformers taken into account is 26; however, as can be concluded from Table 1 only few of them are abundant enough to impact vibrational spectrum. Theoretical spectra compared with experimental ones are presented in Figures 7 and 8. Amplified segments of spectra are presented for a better view of details. We have chosen the Cauchy-Gauss product function [19] as the band model, with a constant Cauchy-Gauss ratio and a constant half-width of the bands. Parameters a2=0.15 and a4=0.03 were used in the product function, resulting in the full-width at half height of 14 cm−1.Figure 7
Calculated and experimental spectra of NBEE in the upper MIR range (3300–2500 cm−1).Figure 8
Calculated and experimental spectra of NBEE in the lower MIR range (1800–560 cm−1).There are no proton donor groups in the studied molecule, therefore no association due to hydrogen-bonding is expected. Although a weak proton donor behavior of Cα–H bonds was demonstrated for H-bonded n-propanol [20], the screening by the alkyl groups prevents any interaction with the oxygen atom in a neighboring ether molecule. No evidence was also found in the literature for other types of structure-making forces in liquid ethers, for example,  due to dipole-dipole interactions, since the dipole moment of NBEE amounts only to 1.24 D [21]. Thus, the existence of dimers or higher polymers, which could influence vibrational spectra by concentration effects can be safely excluded.Comparing the results with previous harmonic studies of di-n-propylether [12], it can be noticed that the quality of spectra reproduction is noticeably higher when unscaled B2PLYP/N07D anharmonic calculations are employed. The agreement between the calculated and experimental frequencies as well as the overall shape of the resulting theoretical spectrum is much better than the similar results yielded with harmonic B3LYP calculations even with application of scaling. It is also worth noticing that the agreement with experimental spectra in the lower range (1800–560 cm−1) is still better than in upper range (stretching modes), both in raw frequencies and overall shape of resulting spectra, similarly as for previously studied dipropyl ether [12, 22].


## 4.6. Identification of Bands in MIR Region

The identification of bands observed in liquid phase spectra, based on a PED analysis and thorough comparison of the experimentalk(v) spectrum with modelled IR spectrum are presented in Table 4. The calculated wavenumbers in the table refer to band positions in the modelled spectrum incorporating a number of calculated spectra of conformers. Therefore they differ from the calculated wavenumbers for individual conformers.Table 4
MIR and Raman band identification for liquid NBEE.
ν
exp(cm−1)
ν
calc   (cm−1)
Vibrational modes contributions
IR
Raman
1
2975.5
2975.7
3003
CH3 str. asym.
2
2961.5
2962.5
2991
CH3 str. asym.',  CH2 str. asym.
3
2934.6
2934.1
2955
CH3 str. asym.',  CH2 str. asym.
4
~2913
2913.4
2919
CH2 str. sym.
5
~2874
2873.4
2884
CH2 str. asym.
6
2864.4
2868.9
2861
CH2 str. asym.
7
2799.3
2799.2
—
—
8
1488.4
1487.0
1495
CH2 sciss., CH3 asym. def.'
9
1466.0
—
1469
CH3 asym. def.
9
1458.7
~1457
—
—
10
1412.5
—
1414
CH3 sym. def.
11
1376.3
—
1390
CH3 sym. def.
12
1333.5
—
1364
CH2 wagg.
13
1300.2
1299.0
1307
CH2 twist.
14
1262.2
~1257
1259
CH2 twist.
15
1231.4
1230.8
1237
CH2 twist.
16
1123.2
1119.9
1126
C–O stretch.
17
1099.0
1099.2
1100
CH3 rock., C–C stretch.
18
1067.9
~1066
1062
C–C stretch.
19
1026.5
1027.7
1028
C–C stretch.
20
972.4
~972
975
C–C stretch.
21
901.5
901.9
905
CH3 rock.
22
870.7
—
871
C–C stretch., CH3 rock.
23
826.7
~828
828
CH3rock.', CH2 rock.As stated before, the quality of experimental spectra reproduction is lower in the C–H stretching region—in terms of band positions and relative intensities as well, resulting in overall different spectrum shape. Moreover, in this region, the differences of modes frequencies between conformers are highest; therefore we can see a significant level of band overlapping here. Nevertheless main bands can still be clearly identified. The CH3 stretching asymmetric and CH2 stretching asymmetric, as well as stretching symmetric modes for those groups, have been identified (Table 4). Unexpectedly, the 2864.4 cm−1 band was found to be a CH2 (ethyl chain) stretching asymmetric band, strongly shifted towards lower wavenumber.Aliphatic ethers and thioethers exhibit several weak bands at 2800–2700 cm−1 range which are absent in alkanes. In the NBEE spectrum, we can observe such bands too, with the most prominent one at 2799 cm−1 wavenumber. We are not exactly sure about the origin of those bands; however, our calculations suggest at least a contribution of fundamental bands. According to collected data, a few of investigated NBEE conformers contain a significantly shifted symmetric stretching band of α-CH2 groups, including the third most abundant “TTT T” conformer with the band at a calculated frequency 2766 cm−1. Such a high shift of α-CH2 symmetric stretching band has been observed for all previously studied aliphatic ethers.The lower MIR region is dominated by CH3 asymmetric deformation, CH2 scissoring, and CH2 wagging modes (in the 1500–1300 cm−1 range), and by CH2 twisting, C–O stretching, and C–C stretching modes (in the 1300–1000 cm−1 range). The broadening of C–O stretching band due to overlapping bands of conformers can be easily observed. Due to this effect also the relative intensity of C–O band is slightly lower than expected; it is; however, still the most intense band in the spectrum. Also a considerable contribution of C–C stretching bands into the broadened C–O stretching band in studied spectra is probable.Summarizing, the influence of oxygen atom can be pointed out in the spectrum of investigated ether. According to the analyzed data, both CH2(-O) groups in NBEE differ from other methylene groups. The presence of multiple relevant conformers to band broadening and overlapping which is mostly noticeable in case of C–H stretching range and C–O stretching band.


## 5. Summary

Basing on IR studies including thin-film MIR transmission recordings, the spectrum of the complex refractive index for liquidn-butyethylether was determined in a broad spectral range. A detailed conformer population analysis and anharmonic vibrational analysis was performed on a B2PLYP/N07D level of theory. The observed spectrum of neat liquid was accurately reproduced, and a successful identification of numerous MIR bands of studied liquid was carried out.



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*Source: 705218-2012-10-14.xml*