Spectra-Structure Correlations in Isotopomers of Ethanol (CX3CX2OX; X = H, D): Combined Near-Infrared and Anharmonic Computational Study.

The effect of isotopic substitution on near-infrared (NIR) spectra has not been studied in detail. With an exception of few major bands, it is difficult to follow the spectral changes due to complexity of NIR spectra. Recent progress in anharmonic quantum mechanical calculations allows for accurate reconstruction of NIR spectra. Taking this opportunity, we carried out a systematic study of NIR spectra of six isotopomers of ethanol (CX3CX2OX; X = H, D). Besides, we calculated the theoretical spectra of two other isotopomers (CH3CD2OD and CD3CH2OD) for which the experimental spectra are not available. The anharmonic calculations were based on generalized vibrational second-order perturbation theory (GVPT2) at DFT and MP2 levels with several basis sets. We compared the accuracy and efficiency of various computational methods. It appears that the best results were obtained with B2PLYP-GD3BJ/def2-TZVP//CPCM approach. Our simulations included the first and second overtones, as well as binary and ternary combinations bands. This way, we reliably reproduced even minor bands in the spectra of diluted samples (0.1 M in CCl4). On this basis, the effect of isotopic substitution on NIR spectra of ethanol was accurately reproduced and comprehensively explained.

1. Introduction

Near-infrared (NIR) spectra are appreciably more complex and difficult for interpretation than IR or Raman spectra [1,2,3,4,5,6]. This results from a large number of strongly overlapping overtones and combination bands, numerous resonances between different modes and anharmonicity of vibrations [1,2,3,4,5,6]. Interpretation of vibrational bands has been aided by studies of a series of similar compounds (including isotopomers), or by reconstruction of the spectra by using quantum mechanical calculations [5]. The former way may provide highly speculative assignments, while the latter method has limitations that prevent their common use in NIR spectroscopy. From the point of view of applied spectroscopy, there exists an essential difference in the applicability of quantum mechanical calculation of mid-infrared (MIR) [7,8,9] and NIR spectra. A simplistic and computationally inexpensive harmonic approximation fails to predict the overtones and combination modes [10]. Because of a considerable computational cost of anharmonic calculations, simulations of NIR spectra are rare. Nevertheless, in the literature one can find examples of application of different approaches used for calculation of overtones and combination bands, including variational approaches, which are expensive but useful in selected cases [11,12]. However, the studies using a vibrational self-consistent field (VSCF) approach [13,14] and its refined variants—e.g., PT2-VSCF—are more common [15,16,17]. Recently, a number of theoretical reconstructions of NIR spectra by means of efficient vibrational second-order perturbation (VPT2) method have been reported [18]; e.g., carboxylic acids [19], fatty acids [20,21,22], aminoacids [23], nucleobases [24], nitriles [25], azines [26], phenols [27,28], and alcohols [29,30]. Considerable efforts have been undertaken in order to develop anharmonic approaches applicable to even larger molecular systems [31,32,33,34]. On the other hand, meticulous probing of vibrational potential capable of yielding nearly-exact results is also available [35,36,37,38]. Recent advances in this field include the development of multi-dimensional approaches that provide complete information on mode couplings in linear triatomic molecules [39].

The isotopic effect appears to be helpful for the analysis of NIR spectra [10]. By shifting a part of overlapped contributions, one can reduce their complexity and reveal individual bands. Time-resolved NIR spectroscopy of deuterated alcohols has also been successfully used for elucidating the diffusion coefficients [40]. In our previous work, the effect of isotopic substitution on NIR spectra of methanol has been accurately reproduced by anharmonic calculations [41]. In particular, we were able to predict the vibrational contributions from non-uniformly substituted CX3OX (X = H, D) species, which are not available from the experiment [41]. Further studies on molecules more complex than methanol are still necessary. A reasonable progress in this field is expected by examination of ethanol and all its isotopomers [42,43]. Ethanol has eight major isotopomers resulting from deuteration (CX3CX2OX; X = H, D), as compared to four in methanol. Moreover, the internal rotation around C-O(H) bond leads to rotational isomerism (gauche, trans) in molecules of ethanol, which adds additional origin of spectral variability in NIR spectra [42,43].

To enable detailed examination of the impact of various effects on NIR spectra of ethanol isotopomers, at first it is necessary to perform reliable theoretical reproduction of NIR spectra for eight isotopomers of ethanol (CX3CX2OX; X = H, D). We are interested in accurate reproduction of subtle effects observed in NIR spectra. Therefore, a combination of several electronic methods underlying VPT2 vibrational analysis will be useful for establishing the best approach capable of reproducing fine features in NIR spectra. The determination of electronic structure underlying the geometry optimization and harmonic analysis will be based on Møller–Plesset second-order perturbation (MP2) and density functional (DFT) theories. The efficiency and accuracy of reproduction of NIR bands by MP2 and DFT with single-hybrid B3LYP and double-hybrid B2PLYP density functionals will be overviewed. MP2 and DFT calculations included basis sets of increasing quality (6-31G(d,p), SNST, def2-TZVP, and aug-cc-pVTZ). Moreover, the impact of solvent cavity model will be evaluated. The anharmonic vibrational analysis will be carried out by means of generalized VPT2 (GVPT2). In our previous studies on methanol, it has been demonstrated that the relative contributions from the second overtones and ternary combinations are different for various isotopomers [41]. This work will provide detailed information on contributions from different vibrational modes and the trends observed with increasing of the alkyl chain length in going from methanol to ethanol. In addition, we will elucidate the accuracy of prediction of the three quanta transitions in NIR spectra.

2. Results and Discussion

2.1. Accuracy of Reproduction of NIR Spectra by Selected Approaches

Anharmonic calculations are significantly more challenging compared to harmonic approximation [1,2,3,4]. This holds even for efficient anharmonic approaches based on VPT2 method. At the same time, the higher quanta transitions are more prone to inaccuracies than the fundamental ones [44]. An insufficient accuracy of the ground state geometry and potential energy surface may easily propagate into inaccuracy of prediction in VPT2 calculation step. Thus, the theoretical prediction of NIR spectra is usually a compromise between the cost and accuracy. Effects like isotopic substitution [41] and conformational isomerism [29,30] may further complicate the vibrational analysis of NIR spectra.

One of the aims of this work was assessment of the efficiency of several combinations of the electronic theory methods and basis sets (Table 1). In addition, we examined the effect of the solvent model on the anharmonic vibrational energies. An efficient single-hybrid B3LYP functional is commonly used tool for spectroscopic studies [10]. Empirical correction for dispersion has been introduced to overcome one of the major weaknesses of DFT method [45]. In some cases, this approach markedly improves the robustness of calculation of primary parameters (i.e., energy). Therefore, recent literature suggests employing empirical correction for dispersion in DFT calculations [46]. Our previous studies have shown that, even for small and isolated molecules, this correction is advantageous in spectra modeling [29]. For molecules in solution an approximation of the solvent cavity often improves the quality of the simulated NIR spectra [28]. However, in the present work this advantage is less important (Table 1). We observed an improvement of RMSE from 45 to 35 cm−1 for CH3CH2OH, and from 27 to 24 cm−1 for CH3CH2OD. However, considering small additional cost of CPCM (ca. 10% of total CPU time in the case of GVPT2//B3LYP-GD3BJ/6-31G(d,p) calculations), it is advisable to include this correction step in the calculations.

Table 1

Positions of selected NIR bands (in cm−1) from GVPT2 anharmonic vibrational analysis in CH3CH2OH and CH3CH2OD at different levels of electronic theory and corresponding RMSE values.

Assignment	Exp.	Calculated
		MP2/aVTZ + CPCM	Diff.	B2PLYP-GD3BJ/def2-TZVP + CPCM	Diff.	B2PLYP-GD3BJ/SNST + CPCM	Diff.	MP2/6-31G(d,p) + CPCM	Diff.	B2PLYP-GD3BJ/6-31G(d,p) + CPCM	Diff.	B3LYP-GD3BJ/6-31G(d,p) + CPCM	Diff.	B3LYP-GD3BJ/6-31G(d,p)	Diff.
	CH3CH2OH
2νOH	7099	7157	58	7125	26	7081	−18	7243	144	7134	35	7061	−38	7096	−3
νsCH2 + νOH	6520.4	6578	57.6	6513	−7.4	6536	15.6	6654	133.6	6576	55.6	6477	-43.4	6472	−48.4
2δas’CH3 + νOH	5886.1	5980	93.9	5889	2.9	5922	35.9	6111	224.9	5970	83.9	5871	−15.1	5892	5.9
2νasCH2	5765.7	5897	131.3	5790	24.3	5864	98.3	5957	191.3	5898	132.3	5797	31.3	5812	46.3
2νsCH2; 2νsCH3 + δsCH3	5665.1	5759	93.9	5681	15.9	5708	42.9	5812	146.9	5722	56.9	5611	−54.1	5768	102.9
[δwaggCH2, δsCH3] + νOH	5013.8	5026	12.2	5029	15.2	5012	−1.8	5114	100.2	5049	35.2	5040	26.2	5019	5.2
[δtwistCH2, δipCOH, δwaggCH2] + νOH	4954.2	4978	23.8	4979	24.8	4959	4.8	5003	48.8	5009	54.8	5008	53.8	5003	48.8
δipCOH + νOH	4873	4881	8	4868	−5	4877	4	4958	85	4926	53	4874	1	4883	10
δsCH3 + νas’CH3	4394.8	4448	53.2	4366	−28.8	4443	48.2	4592	197.2	4473	78.2	4424	29.2	4436	41.2
[δoopCOH, τCC] + νOH	4333.5	4395	61.5	4331	−2.5	4364	30.5	4502	168.5	4416	82.5	4353	19.5	4357	23.5
		RMSE	70.0	RMSE	18.1	RMSE	40.8	RMSE	153.1	RMSE	72.2	RMSE	35.0	RMSE	44.6
	CH3CH2OD
2νasCH3	5885.2	5978	92.8	5895	9.8	5921	35.8	6114	228.8	5967	81.8	5871	−14.2	5894	8.8
2νasCH2	5765.6	5917	151.4	5788	22.4	5862	96.4	6007	241.4	5896	130.4	5799	33.4	5815	49.4
2νOD	5277.1	5312	34.9	5289	11.9	5265	−12.1	5378	100.9	5306	28.9	5250	−27.1	5255	−22.1
δscissCH2 + νasCH2	4393.7	4445	51.3	4397	3.3	4439	45.3	4592	198.3	4493	99.3	4422	28.3	4424	30.3
[δsCH3, δwaggCH2] + νasCH3	4331.8	4392	60.2	4364	32.2	4364	32.2	4500	168.2	4415	83.2	4349	17.2	4355	23.2
[δrockCH2, δrockCH3] + νsCH2	4054.1	4057	2.9	4037	−17.1	4020	−34.1	4122	67.9	4036	−18.1	4068	13.9	4058	3.9
		RMSE	80.6	RMSE	18.6	RMSE	50.0	RMSE	179.4	RMSE	83.3	RMSE	23.6	RMSE	27.3

Switching from B3LYP to B2PLYP density functional with a small basis set (6-31G(d,p)) leads to an increase in the RMSE value (Table 1). However, B2PLYP method overestimated the band positions in a systematic manner. In contrast, B3LYP approach provides irregular results. Some of the band positions (δCH) are blue-shifted, while the others (νOX and νCX; X = H, D) are red-shifted. Thus, more uniform band shift from B2PLYP method (Figure 1 and Figure 2) resulted in better interpretability of NIR spectra as compared with B3LYP results. It has a peculiar effect in NIR spectra of aliphatic alcohols, as it reduces RMSE of NIR band positions, particularly for the νOX + δCH, and νCX + δCH combination bands. However, this apparent gain does not improve the true interpretability of the spectra. It is likely that simulated NIR spectra of larger molecules may suffer even more due to binary combinations involving the stretching and deformation of the C-H and O-H vibrations. Similar inconsistency of B3LYP as compared to B2PLYP has been noted before [29,41]. Due to electron correlation being computed effectively at the MP2 level, it is commonly accepted that B2PLYP functional requires larger basis sets. B2PLYP coupled with large def2-TZVP basis set noticeably improves the quality of simulated NIR spectra (Figure 1 and Figure 2). This improvement is particularly evident in the reproduction of minor bands originating from the three quanta transitions (Figure 3 and Figure 4). This effect is nicely illustrated by reduction of RMSE from 72–83 cm−1 for B2PLYP/6-31G(d,p) to 18–19 cm−1 for B2PLYP/def2-TZVP. SNST basis set, less complex than def2-TZVP but still of triple-ζ quality, leads to worse results. An exception was observed for the prominent doublet from the νCH combination bands (at ca. 4400 cm−1), where B2PLYP/SNST calculations reproduced the peak shapes more resembling the experimental ones. However, the position of this doublet was also overestimated by this method. Hence, B2PLYP/def2-TZVP method appears to be the better tool for reliable reconstruction of NIR spectra. A similar conclusion was obtained for butyl alcohols [30].

Figure 1

NIR spectra of CH3CH2OH calculated with GVPT2 method at different levels of electronic theory; (a) B3LYP-GD3BJ/6-31G(d,p); (b) B3LYP-GD3BJ/6-31G(d,p)//CPCM; (c) B2PLYP-GD3BJ/6-31G(d,p)//CPCM; (d) MP2/6-31G(d,p)//CPCM; (e) B3LYP-GD3BJ/SNST//CPCM; (f) B2PLYP-GD3BJ/def2-TZVP//CPCM; (g) MP2/aug-cc-pVTZ//CPCM; (exp.) Experimental spectrum of CH3CH2OH in CCl4 (0.1 M).

Figure 2

NIR spectra of CH3CH2OD calculated with GVPT2 method at different levels of electronic theory; (a) B3LYP-GD3BJ/6-31G(d,p); (b) B3LYP-GD3BJ/6-31G(d,p)//CPCM; (c) B2PLYP-GD3BJ/6-31G(d,p)//CPCM; (d) MP2/6-31G(d,p)//CPCM; (e) B3LYP-GD3BJ/SNST//CPCM; (f) B2PLYP-GD3BJ/def2-TZVP//CPCM; (g) MP2/aug-cc-pVTZ//CPCM; (exp.) Experimental spectrum of CH3CH2OD in CCl4 (0.1 M).

Figure 3

Contributions from minor bands in NIR spectra of CH3CH2OH calculated with GVPT2 method at different levels of electronic theory; (a) B3LYP-GD3BJ/6-31G(d,p); (b) B3LYP-GD3BJ/6-31G(d,p)//CPCM; (c) B2PLYP-GD3BJ/6-31G(d,p)//CPCM; (d) MP2/6-31G(d,p)//CPCM; (e) B3LYP-GD3BJ/SNST//CPCM; (f) B2PLYP-GD3BJ/def2-TZVP//CPCM; (g) MP2/aug-cc-pVTZ//CPCM; (exp.) Experimental spectrum of CH3CH2OH in CCl4 (0.1 M).

Figure 4

Contributions from minor bands in NIR spectra of CH3CH2OD calculated with GVPT2 method at different levels of electronic theory; (a) B3LYP-GD3BJ/6-31G(d,p); (b) B3LYP-GD3BJ/6-31G(d,p)//CPCM; (c) B2PLYP-GD3BJ/6-31G(d,p)//CPCM; (d) MP2/6-31G(d,p)//CPCM; (e) B3LYP-GD3BJ/SNST//CPCM; (f) B2PLYP-GD3BJ/def2-TZVP//CPCM; (g) MP2/aug-cc-pVTZ//CPCM; (exp.) Experimental spectrum of CH3CH2OD in CCl4 (0.1 M).

In contrast, MP2 method does not appear to be particularly useful for anharmonic calculations of NIR spectra of ethanol isotopomers due to significant redshift of the νCX frequencies (Figure 1 and Figure 2). It is an interesting observation, as the tendency of MP2 to describe incorrectly repulsive forces is known in the literature [47]. In this work, however, an insufficient basis set (6-31G(d,p)) may strongly deviate the results. Here, MP2 method seems to be more sensitive to the effect of a small basis set than DFT-B2PLYP method. As expected, an application of a larger basis set, e.g., aug-cc-pVTZ, improves the accuracy of calculations. However, these results are not as good as those obtained from B2PLYP/def2-TZVP method. Moreover, this improvement is accompanied by a substantial increase of computing time (by ca. 4 times). Nevertheless, selected spectral ranges (νOH + δCH ≈ 5050–4800 cm−1 and νCH + δCH doublet ≈ 4400 cm−1) were better reproduced by MP2/aug-cc-pVTZ computations. Therefore, MP2 approach may be recommended as a reference method in selected cases. Our results demonstrate that different computational methods achieve different accuracy for particular regions of NIR spectra, and these regions do not overlap. Thus, comparison of the spectra simulated by different methods (e.g., resulting from VPT2 calculations at DFT or MP2 levels) appears to be the best way for reliable interpretation of the experimental spectra.

Particular attention should be paid to 2νOH/OD band, which is the most characteristic peak for alcohols and the other important compounds like, e.g., phenols [27], terpenes [28], and polyphenols [48]. This peak is very sensitive to the chemical environment and inter- and intra-molecular interactions, and is frequently used for studies of the structure and physicochemical properties [49,50,51,52,53]. Hence, its proper theoretical reproduction is of essential importance. As shown in Figure 1, Figure 2, Figure 3 and Figure 4, and Figures S1–S6 in SM, most of the methods did not reproduce correctly the shape of this band. The experimental band from 2νOH/OD vibration reveals a slight asymmetry. This asymmetry is a result of convolution of two components due to trans and gauche conformers. The lower-frequency gauche component has also the lower intensity. Among isotopomers of ethanol, this feature was reproduced correctly only by B2PLYP/def2-TZVP method. MP2/6-31G(d,p) and MP2/aug-cc-pVTZ methods predicted correct shape of the 2νOH/OD peak only for CH3CD2OH and CD3CD2OD. As can be seen (Table 1), the peak position was overestimated by all used methods, but B2PLYP calculations give the best agreement.

In comparison with other modes, large amplitude motions (LAMs)—e.g., torsion modes and hindered rotations—are more difficult for accurate description in harmonic approximation and also by anharmonic approaches that probe the potential curve relatively shallow (e.g., VPT2) [54]. We did not find any evidence that these low-frequency modes influence NIR bands directly (i.e., their overtone and combination modes do not appear in NIR region). However, a NIR spectrum provides some insights on LAMs as well. In our case, the shape of the 2νOH/OD band is an indirect probe of the accuracy of prediction of the low-frequency modes. The shape of this band results from two components due to gauche and trans rotational conformers. Unreliable theoretical abundances of these forms would result in biased relative intensities of the 2νOH/OD components (Table S1). Gibbs free energies may be affected by erroneous LAMs, which would propagate into incorrect relative abundances of gauche and trans conformers. Because it is an isolated band of strong intensity, the simulated 2νOH/OD may be used to assess the reliability of prediction of LAMs and the related Gibbs free energies. This kind of error would manifest itself as a distorted shape of simulated 2νOH/OD band. Above effect can be seen for some of the methods used in this study, e.g., for B3LYP (B3LYP-GD3BJ/6-31G(d,p); B3LYP-GD3BJ/6-31G(d,p)//CPCM; B3LYP-GD3BJ/SNST//CPCM;) and B2PLYP coupled with an insufficient basis set (B2PLYP-GD3BJ/6-31G(d,p)//CPCM;). However, the methods which yielded the most accurate spectra in the other regions (B2PLYP/def2-TZVP; MP2/6-31G(d,p); MP2/aug-cc-pVTZ) also reproduced 2νOH/OD peak accurately (Figure 1 and Figure 2). Therefore, we conclude that the LAMs of ethanol and its derivatives were determined adequately by MP2 method. B2PLYP method also provides correct results, but it is more sensitive to the selection of a basis set. On the other hand, B3LYP tends to falsify the Gibbs free energies corrected by anharmonic ZPE. Further studies are needed to determine, whether this effect occurs because of an unreliable description of LAMs. On the other hand, inaccuracy of the 2νOH/OD frequencies prediction by VPT2 may also be considered as another contributing factor, as we have evidenced such occurrence in the case of the conformers of cyclohexanol [27]. Note that B3LYP functional coupled with a relatively simple basis set yields reasonable reproduction of NIR spectra and correctly predicts the effects of isotopic substitution at a relatively modest computational expense (Figure 1, Figure 2, Figure 3 and Figure 4 and Figures S1–S6 in SM). However, a tendency to over- and underestimate the position and intensity of some bands may be unfavorable for the reliable interpretation of theoretical NIR spectra. For exploration of more subtle effects, B2PLYP functional seems to be more suitable. In the present study of isotopic substitution and the other effects (e.g., rotational isomerism) on NIR spectra of ethanol, we used B2PLYP/def2-TZVP method with additions of GD3BJ and CPCM.

2.2. Origins of NIR Bands of CX3CX2OX (X = H, D)

The simulations of NIR spectra of ethanol isotopomers in CCl4 solutions by GVPT2 anharmonic method at B2PLYP-GD3BJ/def2-TZVP//CPCM level accurately reproduced most of the experimental bands (Figure 5 and Figure 6). On this basis, we performed detailed and reliable band assignments (Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8 and Table 9). The consistency of these assignments was positively verified by comparison with the experimental spectra of six isotopomers. High accuracy of simulations allows to analyze the theoretical spectra of CH3CD2OD and CD3CH2OD (Figure 6C,D and Table 8 and Table 9) which are not available commercially. All assignments were supported by an analysis of the potential energy distributions (PEDs; Tables S2–S9).

Figure 5

Band assignments in NIR spectra of deuterated ethanols based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. (A) CH3CH2OH; (B) CH3CH2OD; (C) CH3CD2OH; (D) CD3CH2OH. Band numbering corresponds to that presented in Table 2, Table 3, Table 4 and Table 5.

Figure 6

Band assignments in NIR spectra of deuterated ethanols based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. (A) CD3CD2OH; (B) CD3CD2OD; (C) CH3CD2OD; (D) CD3CH2OD. Band numbering corresponds to that presented in Table 6, Table 7, Table 8 and Table 9.

Table 2

Band assignments in NIR spectra of CH3CH2OH based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented in Figure 5A.

Peak Number	ν Exp	ν Calc	Assignment (Major Contribution)
1	8718.0	8739	2νasCH2 + νasCH3
2	8430.0	8526	3νasCH2
3	8329.0	8416	3νsCH2
4	8131.0	8329	2νsCH2 + νasCH2
5	7400–7300	7400–7300	δsCH3 + νasCH3 + νas’CH3[δas’CH3, δasCH3] + νasCH3 + νas’CH3δscissCH2 + νasCH2 + νas’CH3[δrockCH2, δrockCH3] + νasCH2 + νOH
6	7300–7200	7300–7200	δtwistCH2 + νasCH3 + νas’CH3δsCH3 + νsCH3 + νas’CH3[δasCH3, δas’CH3] + νsCH3 + νasCH3[δasCH3, δas’CH3] + νsCH3 + νas’CH3
7	7099.0	7125	2νOH
8	6610.0	6609	νsCH3 + νOH
9	6565.0	6540	2δasCH3 + νOH
10	6520.4	6513	νsCH2 + νOH
11	6331.0	6314	2δtwistCH2 + νOH
12	6271.8	6275	δipCOH + δwaggCH2 + νOH
13	6193.0	6178	[τCC, δoopCOH] + νasCH3 + νas’CH3
14	6063.0	6085	2δipCOH + νOH
15	6051.0	6021	[νCC, δipCOH] + δtwistCH2 + νOH
16	5936.0	5948	2νas’CH3, νasCH3 + νas’CH3
17	5886.1	5889	2δas’CH3 + νOH
18	5809.0	5846	[δasCH3, δas’CH3] + δscissCH2 + νasCH2
19	5765.7	5790	2νasCH2
20	5665.1	5681	2νsCH2; 2νsCH3 + δsCH3
21	5634.0	5632	δipCOH + δwaggCH2 + νsCH3
22	5287.6	5277	δipOH + δCCO +νOH
23	5111.0	5128	δscissCH2+ νOH
24	5071.0	5118	[δasCH3, δas’CH3] + νOH
25	5013.8	5029	[δwaggCH2, δsCH3] + νOH
26	4996.2
27	4954.2	4979	[δtwistCH2, δipCOH, δwaggCH2] + νOH
28	4873.0	4868	δipCOH + νOH
29	4724.3	4763	δsCH3 + 2[δasCH3, δas’CH3]
30	4677.0	4726	[νCO, δrock’CH3] + νOH
31	4582.9	4648	[δoopCOH, τCC] + δas’CH3 + νsCH3
32	4454.0	4450	3δscissCH2
33	4409.0	4396	δscissCH2 + νasCH2
34	4394.8	4366	δsCH3 + νas’CH3
35	4333.5	4331	[δoopCOH, τCC] + νOH
36	4232.6	4269	δtwistCH2 + νas’CH3
37	4162.0	4177	δipCOH + νsCH2
38	4131.7	4137	δtwistCH2 + νsCH2
39	4057.4	4020	[δrockCH2, δrockCH3] + νsCH2
40	4024.0	3997	[νCO, δrock’CH3] + νasCH2

Table 3

Band assignments in NIR spectra of CH3CH2OD based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented in Figure 5B.

Peak Number	ν exp	ν calc	Assignment (Major Contribution)
1	8428.0	8334	2νsCH2 + νasCH2
2	7777.5	7796	3νOD
3	7260.0	7227	δtwistCH2 + νasCH3 + νas’CH3
4	7099.1	7112	δas’CH3 + νsCH2 + νasCH2
5	6133.4	6200	τCC + νasCH3 + νas’CH3
6	5935.0	5946	2νas’CH3
7	5885.2	5895	2νasCH3
8	5850.0	5847	[δasCH3, δas’CH3] + δscissCH2 + νasCH2
9	5765.6	5788	2νasCH2
10	5665.7	5669	2δwaggCH2 + νsCH2
11	5564.3	5559	νOD + νsCH2
12	5494.3	5498	νasCH2 + δtwistCH2 + δwaggCH2
13	5277.1	5289	2νOD
14	4947.0	4963	[δrockCH2, δrockCH3] + δtwistCH2 + νsCH2
15	4873.0	4846	[δrockCH2, δrockCH3] + [δrockCH2, δrockCH3] + νsCH2
16	4720.8	4717	[νCO, δrock’CH3, δipCOD] + [δrock’CH3, δipCOD, δscissCH2CO] +νOD
17	4393.7	4397	δscissCH2 + νasCH2
18	4331.8	4364	[δsCH3, δwaggCH2] +νasCH3
19	4253.4	4275	δtwistCH2 + νas’CH3
20	4155.1	4127	[δrock’CH3, δipCOD, δscissCH2CO] +νasCH3
21	4105.0	4063	[δrock’CH3, δipCOD, δscissCH2CO] + νsCH3
22	4054.1	4037	[δrockCH2, δrockCH3] + δsCH2

Table 4

Band assignments in NIR spectra of CH3CD2OH based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented in Figure 5C.

Peak Number	ν exp	ν calc	Assignment (Major Contribution)
1	8717.0	8788	3νasCH3
2	8434.1	8728	νsCH3 + νasCH3 + νas’CH3
3	8337.0	8665	2νsCH3 + νasCH3
4	7345.0	7324	[δrockCD2, δtwist CD2] + νas’CH3 + νOH
5	7251.0	7255	[δasCH3, δas’CH3] + νsCH3 + νasCH3
6	7098.2	7126	2νOH
7	6590.4	6618	νas’CH3 + νOH
8	6205.8	6257	2δipCOH + νOH
9	6158.0	6198	2δipCOH + νOH
10	5929.9	5943	2νasCH3
11	5895.4	5892	2νas’CH3
12	5828.0	5844	νsCH3 + νas’CH3
13	5763.8	5744	νsCD2 + νOH
14	5669.1	5595	νsCH3 + 2νasCH3
15	5449.0	5496	δrockCH3 + δsCH3 + νas’CH3
16	5439.4	5449	δscissCD2CO + 2νasCH3
17	5282.0	5309	νasCD2 + 2[δasCH3, δas’CH3]
18	5070.1	5094	νsCD2 + νasCH3
19	5017.0	5018	[τCC, δoop COH] + 2[δasCH3, δas’CH3]
20	4927.0	4954	δipCOH + νOH
21	4898.3	4930	δipCOH + νOH
22	4792.1	4806	[νCO, δwaggCD2] + νOH
23	4737.2	4744	δscissCD2 + νOH
24	4650.2	4641	[νCC, δrock’CH3] + νOH
25	4591.7	4600	[νCO, δwaggCD2] + νOH
26	4513.3	4525	δipCOH + νOH
27	4404.6	4437	[δasCH3, δas’CH3] + νas’CH3
28	4338.0	4373	δsCH3 + νas’CH3
29	4275.7	4285	δipCOH + νasCH3
30	4238.1	4218	νsCD2 + νasCD2
31	4129.6	4147	[νCO, δwaggCD2] + νas’CH3
32	4079.7	4117	δrockCH3 + νasCH3
33	4056.2	4052	δrockCH3 + νsCH3, δscissCD2CO + νOH

Table 5

Band assignments in NIR spectra of CD3CH2OH based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented in Figure 5D.

Peak Number	ν exp	ν calc	Assignment (Major Contribution)
1	8405.0	8511	3νasCH2
2	8307.6	8323	2νsCH2 + νasCH2
3	7098.5	7124 (t)7100 (g)	2νOH
4	6841.1	6897	[νCO, δas’CD3] + νsCH2 + νasCH2
5	6517.6	6510	νsCH2 + νOH
6	6324.0	6261	[δipCOH, δtwistCH2] + δwaggCH2 + νOH
7	6268.0	6111	[δrock’CD3, νCC] + νas’CD3 + νOH
8	6070.4	6059	2[δipCOH, δtwistCH2] + νOH
9	5966.3	5966	[δsCD3, νCC] + δwaggCH2 + νOH
10	5839.1	5825	2νasCH2
11	5772.1	5793	2νasCH2
12	5628.0	5686	2νsCH2
13	5533.0	5641	2νsCH2
14	5427.9	5419	2δtwistCH2 + νasCH2
15	5358.0	5367	[νCO, δas’CD3] + νsCD3 + νas’CD3
16	5286.8	5287	δsCD3 + δtwistCH2 + νasCH2
17	5190.0	5188	2[δsCD3, νCC] + νsCH2
18	5102.7	5084	δoopCOH + 2δwaggCH2
19	5007.1	5028	δwaggCH2 + νOH
20	4955.8	4987	[δtwistCH2, δipCOH, δwaggCH2] + νOH
21	4853.8	4853	[δipCOH, δtwistCH2] + νOH
22	4764.7	4768	[δsCD3, νCC] + νOH
23	4676.7	4676	νCO + νOH
24	4558.4	4511	δas’CD3 + [δtwistCH2, δipCOH] + νas’CD3
25	4443.0	4429	δscissCH2 + νasCH2
26	4390.5	4390	δscissCH2 + νasCH2
27	4329.0	4356	δscissCH2 + νsCH2
28	4263.8	4332	δscissCH2 + νsCH2
29	4174.6	4180	2[δtwistCH2, δipCOH, δwaggCH2] + δscissCH2
30	4100.0	4107	τCC + δoopCOH + νOH

Table 6

Band assignments in NIR spectra of CD3CD2OH based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented in Figure 6A.

Peak Number	ν exp	ν calc	Assignment (Major Contribution)
1	7099.0	7126 (t)7102 (g)	2νOH
2	6444.0	6495	νsCD2 + [νasCD2, νasCD3] + [νas’CD3, νasCD2]
3	6232.1	6244	2δipCOH +νOH
4	6162.9	6224	2[νCC, δwaggCD2] + νOH
5	6063.0	6059	[δscissCD2, νCO] + [νCC, δwaggCD2] + νOH
6	5838.3	5861	[νasCD2, νasCD3] + νOH
7	5732.3	5746	[δrockCD2, δrockCD3] + [δsCD3, δwaggCD2] + νOH
8	5478.7	5488	[νCC, δwaggCD2] + νsCD3 + [νasCD2, νasCD3]
9	5285.8	5247	νsCD3 + νasCD2 + νCO
10	5160.0	5103	[δtwistCD2, δrockCD3, δrockCD2] + 2[νCC, δwaggCD2]
11	4903.7	4947	δipCOH + νOH
12	4769.2	4766	[δscissCD2, νCO] + νOH
13	4701.4	4714	[δas’CD3, δasCD3] + νOH
14	4598.4	4604	[νCO, δwaggCD2] + νOH
15	4525.0	4539	[δtwistCD2, δrockCD3, δrockCD2] + δipCOH + [νas’CD3, νasCD2]
16	4506.9	4499	2δscissCD2CO + νasCD3
17	4430.0	4447	[νasCD2, νasCD3] +νasCD3, 2[νas’CD3, νasCD2]
18	4409.6	4420	[νasCD2, νasCD3] + [νas’CD3, νasCD2]
19	4332.0	4334	2νasCD2
20	4267.4	4235	[νsCD2, νsCD3] + νasCD2
21	4156.8	4140	2δoopCOH +νOH
22	4013.0	4012	δscissCD2CO +νOH

Table 7

Band assignments in NIR spectra of CD3CD2OD based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented in Figure 6B.

Peak Number	νExp	νCalc	Assignment (Major Contribution)
1	7771.0	7799	3νOD
2	6468.0	6525	νsCD3 + [νas’CD3, νasCD2] + νasCD3
3	6450.0	6447	3νasCD2
4	6290.1	6267	2νsCD2 + νasCD2
5	5276.0	5289	2νOD
6	4948.0	5020	[νCO, δtwistCD2] + 2[δscissCD2, νCO]
7	4902.2	4929	[δtwistCD2, δrockCD2] + 2[δscissCD2, νCO]
8	4779.2	4795	νsCD2 + νOD
9	4509.0	4510	[δasCD3, δas’CD3] + [νCC, δwaggCD2] +νasCD3
10	4437.4	4465	2νas’CD3, νasCD3 + νas’CD3
11	4409.3	4434	2νasCD3, νasCD2 + νas’CD3
12	4325.2	4381	2[δscissCD2, νCO] + νsCD3
13	4269.5	4337	2νasCD2
14	4170.2	4241	[νsCD2, νsCD3] + νasCD2

Table 8

Band assignments in NIR spectra of CH3CD2OD based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented Figure 6C.

Peak Number	νCalc	Assignment (Major Contribution)
1	8781	3νas’CH3
2	8722	νsCH3 + νasCH3 + νas’CH3
3	8666	2νsCH3 + νasCH3, 2νsCH3 + νas’CH3
4	7802	3νOD
5	7257	[δasCH3, δas’CH3] + νsCH3 + νasCH3
6	6445	3νasCD2
7	6188	τCC + νasCH3 + νas’CH3
8	5943	2νasCH3, νasCH3 + νas’CH3
9	5890	2[δas’CH3, δasCH3] + νas’CH3, 2νas’CH3
10	5845	νsCH3 + νasCH3
11	5728	2δsCH3 + νasCH3
12	5288	2νOD
13	5182	νasCD2 + νas’CH3
14	5120	νasCD2 + νsCH3
15	5097	νsCD2 + νasCH3
16	5046	τCC + 2[δasCH3,δas’CH3]
17	4796	δoopCOD + 2[δas’CH3,δasCH3]
18	4434	τCC + [δwaggCD2,νCC] + νas’CH3
19	4372	δsCH3 +νasCH3, δsCH3 +νas’CH3
20	4341	2νasCD2
21	4289	τCC + δscissCD2 + [δscissCD2,νCO]
22	4233	νsCD2 + νasCD2
23	4190	2νsCD2, [δwaggCD2, νCC] + νasCH3
24	4149	[δscissCD2, νCO] + νasCH3, [δscissCD2, νCO] +νas’CH3
25	4113	δrockCH3 + νas’CH3
26	4089	[δscissCD2, νCO] + νsCH3
27	4056	δrockCH3 + νsCH3

Table 9

Band assignments in NIR spectra of CD3CH2OD based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. Band numbering corresponds to that presented Figure 6D.

Peak Number	ν calc	Assignment (Major Contribution)
1	8560	3νasCH2, 2νsCH2 + νasCH2
2	8508	3νasCH2
3	8305	2νsCH2 + νasCH2
4	7802	3νOD
5	7088	δscissCH2 + νsCH2 + νasCH2
6	6736	δrockCH2 + νsCH2 + νasCH2
7	6706	[νCO, δas’CD3] + νsCH2 + νasCH2
8	6614	3νas’CD3
9	6505	νsCD3 +νasCD3 +νas’CD3
10	6382	2νsCD3 + νasCD3, 2νsCD3 + νas’CD3
11	5821	[δoopCOD, τCC] + νasCH2 + νsCH2
12	5785	2νasCH2, δwaggCH2 + δscissCH2 + νasCH2
13	5638	2νsCH2, νsCH2 + νasCH2
14	5547	νOD + νsCH2
15	5473	δrockCH2 + δscissCH2 + νasCH2
16	5288	2νOD
17	5106	[τCC, δoopCOD] + 2δwaggCH2
18	4986	2[νCC, δsCD3] + νOD
19	4585	δrock’CD3 + 2δwaggCH2
20	4503	[τCC, δoopCOD] + δwaggCH2 + νasCH2
21	4459	2νasCD3
22	4431	[δas’CD3, νCO] + [νCC, δsCD3] + νas’CD3
23	4385	δscissCH2 + νasCH2
24	4324	2νas’CD3, δscissCH2 + νsCH2
25	4237	δwaggCH2 + νsCH2
26	4167	δtwistCH2 + νasCH2
27	4112	δtwistCH2 + νsCH2
28	4015	[δrockCD3, δrockCH2] + δrockCH2 + νas’CD3

NIR spectra of ethanol isotopomers mainly consist of the combinations of stretching and bending OX and CX (X = H, D) modes (Figure 1, Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6 and Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8 and Table 9). The region below 5500 cm−1 for CH3CH2OH is almost entirely contributed by the combination bands, while absorption from the overtones dominates above 5500 cm−1. NIR spectrum of ethanol may be roughly divided into four regions, but only two of them contain meaningful contributions from overtones. These regions are contributed mainly by vibrations from: (1) 2νOX; (2) 2νCX and νCX + νCX; (3) νOX + δCX; (4) νCX + δCX; (X = H, D). The other combination bands like νOX + νCX, and 2δCX + νCX have low intensity. Isotopic substitution introduces significant band shift, strongly affecting the appearance of NIR spectra (Figure 5 and Figure 6 and Figures S1–S6). It should be noted, that the region of 5700–5400 cm−1 for ethanols containing CH3 and CH2 groups is strongly affected by the anharmonic effects. This effect is well seen for CH3CH2OH (Figure 1) and CH3CH2OD (Figure 2). The most meaningful contributions in this region originate from νCH + νCH (νasCH2 + νsCH2), 2δCH + νCH, and 2νasCH2 vibrations as well.

One can notice the overestimated intensities of the 2νCH and νCH + νCH bands appearing in the 6000–5500 cm−1 region (Figure 5 and Figure 6 and Figures S1–S6). The magnitude of this effect varies between the different methods; however, it is present in all cases. A similar overestimation we have observed for butyl alcohols [30]. At present, we are unable to explain the reasons for these overestimations. Unexpectedly, B2PLYP functional (regardless of basis set; 6-31G(d,p), SNST, and def2-TZVP yielded similar results) significantly overestimates the frequencies of 2δCH + δCH transitions, shifting them to the 5500 cm−1 region. In contrast, the most of other transitions in NIR region is accurately reproduced by this approach. In the case of the 2δCH + δCH modes, large positive anharmonic constants appeared in GVPT2 vibrational analysis. Consequently, positions of the corresponding bands were predicted far from a simple combination of the harmonic frequencies. This shift has not been observed for the remaining approaches. Presently, the reason of this behavior is not clear. Because of very low intensity of 2δCH + δCH bands, these erroneous predictions do not provide meaningful contributions to NIR spectra. However, this occurrence demonstrates the need for using more than one method during examination of the fine spectral effects.

The deuteration of the OH group leads to a noticeable shift of the νOD + δCH band. In contrast, the other bands do not shift meaningfully, as can be easily seen from comparison of CH3CH2OH and CH3CH2OD spectra (Figure 5A,B). In particular, the absorption from the νCH + δCH in the 4600–4000 cm−1 region remains unaffected. This region can be used to monitor the isotopic substitutions of the CH3 and CH2 groups, as it leads to highly specific spectral changes. Obviously, simultaneous deuteration of both groups implies more significant changes. However, the most interesting effects result from the selective substitution of one of these groups. The presence of the CH3 group gives rise to a prominent doublet near 4395 and 4330 cm−1. This doublet has a complex structure resulting from overlapping of the contributions from the CH2 (Figure S7 in Supplementary Material), leading to a broadening of the high-frequency wing of the doublet. As expected, this contribution is not present in the spectrum of CH3CD2OH (Figure S7B). On the other hand, the isotopic substitution of the CH3 reveals a part of the overlapping contributions, as observed more clearly in the second derivative spectrum of CD3CH2OH (Figure S7C). This effect is well seen in the calculated spectra (Figure S7C).

The higher frequency NIR region (>7000 cm−1) is also very sensitive to the isotopic effect. A weak absorption from the higher order overtones and combination bands creates difficulties in the analysis of this region. The deuteration of the OH group significantly reduces the number of the bands as a result of red-shift of the combination bands. The simulated spectra confirmed the high isotopic purity of the samples, except of CD3CD2OD which shows the 2νOH peak near 7100 cm−1 in the experimental spectrum (Figure 6B). This is in contrast to previously studied methanol, in which various non-uniform substitutions have been identified [41]. Contrary to -CX bonds, the H or D atoms in -OX bonds are labile, therefore, the OD group tends to exchange into the OH even by exposition of the deuterated alcohol to air. Since this band has a high absorptivity, therefore even small impurities due to the OH appear in NIR spectrum as a clear band at 7100 cm−1. In contrast, no -CH bands are observed in the spectrum of CD3CD2OD (Figure 6B). NIR spectroscopy is particularly sensitive and selective for the isotopic effect, although the theoretical calculations are necessary for proper spectra interpretation. The spectral manifestations of the OH group in OD derivatives are obscured by ternary combinations from the CH vibrations that appear in the same region. For example, the δas’CH3 + νsCH2 + νasCH2 bands in CH3CH2OD (Figure 5B), and δscissCH2 + νsCH2 + νasCH2 bands in CD3CH2OD (Figure 6D) are observed.

One can speculate that the isotopic substitution and conformational isomerism lead to convoluted spectral changes. This phenomenon will be a subject of our next paper (in preparation).

Another insight, which becomes possible only through theoretical simulation of NIR spectra, is estimation of the relative contributions from different kinds of vibrational transitions (Table 10). As compared with methanol [41], ethanol offers better opportunity to analyze these contributions, because of higher number of isotopomers and more complex NIR spectra. The effect of various kinds of isotopic substitution of the CH3, CH2, and OH groups on NIR spectra may be elucidated. In the 10,000–4000 cm−1 region two quanta transitions, first overtones (2νx) and binary combinations (νx + νy), are the most meaningful components of the spectra. In particular, binary combinations from the CH3 group have significant contribution—e.g., for CH3CH2OH they are responsible for 47% of NIR intensity—while upon deuteration of the CH3 group this contribution decreases to 32.6%. An even more pronounced effect is observed for OD derivatives, the analogous values for CH3CH2OD and CD3CH2OD are 51.2% and 35.5%, respectively. Simultaneously, the isotopic substitution of the methyl group increases the relative intensity of the first overtones, while the intensity of the second overtones remains insignificant. As expected, the importance of the second overtones increases in the upper NIR region (10,000–7500 cm−1). Interestingly, this trend is not observed for the ternary combinations (νx + νy + νz and 2νx + νy), although for OD derivatives the 2νx + νy contribution increases and the νx + νy + νz contribution decreases upon deuteration of the CH3 group. The isotopic substitution of the CH2 group provides similar changes, but is noticeably less significant.

Table 10

Contributions (in %) from the first and second overtones as well as binary and ternary combinations into NIR spectra of ethanol isotopomers based on GVPT2//B2PLYP-GD3BJ/def2-TZVP//CPCM calculations. a

	10,000–4000 cm−1
	2νx	3νx	νx + νy	νx + νy + νz	2νx + νy
CH3CH2OH	26.1	1.7	47.0	14.3	10.9
CH3CH2OD	18.0	2.2	51.2	17.4	11.1
CH3CD2OH	35.8	1.7	41.5	11.8	9.2
CD3CH2OH	40.9	1.2	32.6	15.1	10.1
CD3CD2OH	46.0	0.3	23.7	15.8	14.2
CD3CD2OD	43.1	2.0	19.2	17.8	17.9
CH3CD2OD	27.9	3.2	44.7	15.0	9.2
CD3CH2OD	36.0	2.5	35.5	10.8	15.2
	10,000–7500 cm−1
	2νx	3νx	νx + νy	νx + νy + νz	2νx + νy
CH3CH2OH	0.0	39.7	0.0	22.3	38.0
CH3CH2OD	0.0	55.5	0.0	15.4	29.1
CH3CD2OH	0.0	43.9	0.0	30.5	25.6
CD3CH2OH	0.0	66.9	0.0	1.4	31.7
CD3CD2OH	0.0	0.0	0.0	43.0	57.0
CD3CD2OD	0.0	100.0	0.0	0.0	0.0
CH3CD2OD	0.0	69.9	0.0	16.7	13.4
CD3CH2OD	0.0	76.3	0.0	0.5	23.2
	7500–4000 cm−1
	2νx	3νx	νx + νy	νx + νy + νz	2νx + νy
CH3CH2OH	26.5	1.2	47.6	14.2	10.5
CH3CH2OD	18.4	1.0	52.4	17.5	10.7
CH3CD2OH	36.0	1.4	41.8	11.7	9.1
CD3CH2OH	41.4	0.4	33.0	15.3	9.9
CD3CD2OH	46.0	0.3	23.7	15.8	14.2
CD3CD2OD	43.7	0.5	19.5	18.0	18.2
CH3CD2OD	28.4	2.0	45.5	15.0	9.1
CD3CH2OD	37.0	0.5	36.4	11.1	15.0

a The comparison is based on integrated intensity (cm−1) summed over simulated bands, convoluted with the use of Cauchy−Gauss product function (details in the text) in relation to the total integrated intensity.

As can be seen (Table 10), the region above 7500 cm−1 is contributed only by three and higher quanta transitions. Therefore, in this region the effect of isotopic substitution is even more visible. The deuteration of the CH3 group increases the contributions from the second overtones at the expense of νx + νy + νz combinations, while the contributions from 2νx + νy remain similar. Interestingly, NIR spectrum of CD3CD2OD above 7500 cm−1 includes the second overtones only.

These observations remain in agreement with our previous findings on methanol isotopomers [41]. However, the contributions from the three quanta transitions are more important for ethanol. For CH3CH2OH these transitions involve 25.9% of total intensity (10,000–4000 cm−1), while for CH3OH this value was found to be 19.2%. The difference between CD3OD and CD3CD2OD is even larger (23.5% vs. 36.7%).

3. Experimental and Computational Methods

3.1. Materials and Spectroscopic Measurements

In Table 11 are collected the details on the samples used in this work. The experimental spectrum of CH3CH2OH was taken from our previous work [29]. All samples were used as received, while solvent (CCl4) was distilled and additionally dried using freshly activated molecular sieves (Aldrich, 4A). All ethanols were measured in CCl4 solution (0.1 mol dm−3). NIR spectra were recorded on Thermo Scientific Nicolet iS50 spectrometer using InGaAs detector, with a resolution of 2 cm−1 (128 scans), in a quartz cells (Hellma QX, Hellma Optik GmbH, Jena, Germany) of 100 mm thicknesses at 298 K (25 °C).

Table 11

Samples used in this study

	Sample	Purity	D Atom Content	Other Remarks
1	CH3CH2OD	99%	≥99.5%
2	CH3CD2OH	99%	98%
3	CD3CH2OH	99%	99%
4	CD3CD2OH	99%	99.5%
5	CD3CD2OD	>99%	≥99.5%	anhydrous
6	CCl4	>99%	-

Samples were purchased from Sigma-Aldrich Chemie GmbH (Taufkirchen, Germany).

3.2. Computational Procedures

Our calculations were based on density functional theory (DFT) with double-hybrid B2PLYP density functional [55] (unfrozen core) coupled with Karlsruhe triple-ζ valence with polarization (def2-TZVP) [56] basis set. Grimme’s third formulation of empirical correction for dispersion with Becke-Johnson damping (GD3BJ) was applied [57]. To better reflect solvation of molecules, CCl4 cavity in solvent reaction field (SCRF) [58] was included at conductor-like polarizable continuum (CPCM) [59] level. Very tight criteria for geometry optimization and 10−10 convergence criterion in SCF procedure were set. Electron integrals and solving coupled perturbed Hartree-Fock (CPHF) equations were calculated over a superfine grid. The selected method provided good reproduction of NIR spectra of various molecules in CCl4 solution [19,29,30].

We carried out the anharmonic vibrational analysis at generalized vibrational second-order perturbation theory (GVPT2) [60,61] level. In this approach, the anharmonic frequencies and intensities of the vibrational transitions up to three quanta were obtained. This allows to simulate fundamental, first and second overtones, as well as binary and ternary combination bands. Quantum mechanical calculations were carried out with Gaussian 16 (A.03) [62]. One of the major features implemented in GVPT2 approach is the automatic treatment of tight vibrational degenerations, i.e., resonances [63]. In this work the search for resonances included Fermi (i.e., 1-2) of type I (ωi ≈ 2ωj) and type II (ωi ≈ ωj + ωk), and Darling–Dennison (i.e., 2-2, 1-1, and 1-3) resonances. All possible resonant terms within search thresholds were included in the variational treatment. The resonance search thresholds (respectively, maximum frequency difference and minimum difference PT2 vs. variational treatment; in (cm−1)) were: 200 and 1 (for the search of 1–2 resonances), 100 and 10 (for 2-2, 1-1, and 1-3).

To display the simulated spectra we applied a four-parameter Cauchy–Gauss (Lorentz–Gauss) product function [20]. The theoretical bands were modelled with a2 and a4 parameters equal to 0.055 and 0.015, resulting with full-width at half-height (FWHH) of 25 cm−1. Exception was made for better agreement with the weaker and broader experimental bands, which are presented in Figure 3 and Figure 4. In this case the values were 0.075, 0.015, and 35 cm−1, respectively. The final theoretical spectra were obtained by combining the spectra of trans and gauche conformers, mixed in accordance with the calculated abundances of each form [64]. The relative abundances of the gauche (ng) and trans (nt) conformers were determined as following equation [65]. where Gibbs free energy (ΔG) corresponds to the value calculated at 298 K corrected by anharmonic (VPT2) zero-point energy (ZPE); A and A are the degeneracy prefactors of the Boltzmann term for the gauche (1) and trans (2) conformers.

The band assignments were aided by calculations of potential energy distributions (PEDs). PEDs were obtained with Gar2Ped software [66], using natural internal coordinate system defined in accordance with Pulay [67]. The numerical analysis of the theoretical results and the processing of the experimental spectra were performed with MATLAB R2016b (The Math Works Inc.) [68].

4. Conclusions

Isotopic substitution leads to much higher variability in NIR spectra as compared with IR spectra, due to significant contribution from the combination bands. The pattern of OH/OD, CH3/CD3, and CH2/CD2 groups in ethanol often leads to fine spectral changes, which may be monitored and explained in detail by anharmonic quantum mechanical simulations. Our studies were devoted to NIR spectra of eight isotopomers of ethanol (CX3CX2OX (X = H, D)) by using anharmonic GVPT2 vibrational analysis. The calculations were performed at several levels of electronic theory, including DFT and MP2 to find accurate and efficient theoretical approach for studies of isotopic effect in NIR spectra. Our results indicate that DFT approach using double-hybrid B2PLYP functional, coupled with def2-TZVP basis set, and supported by GD3BJ correction with CPCM solvent model yielded the best results. The theoretical spectra obtained by this approach enabled us to assign most of NIR bands, including two (2νx and νx + νy) and three quanta (3νx, νx + νy + νz, and 2νx + νy) transitions. Accuracy of these calculations permitted us to analyze theoretical NIR spectra of CH3CD2OD and CD3CH2OD for which the experimental spectra are not available. The effect of the isotopic substitution of the OH, CH3, and CH2 groups was satisfactory reproduced and explained. Moreover, the relative contributions of selected groups and kinds of transitions were elucidated and discussed. The contributions from the CH3 group appear to be more important than those from the CH2 group. The isotopic substitution in the CH3 group leads to the most prominent intensity changes in NIR spectra as compared to the changes due to the substitution of the other groups. The bands from the three quanta transitions are more important for isotopomers of ethanol than for derivatives of methanol.