Spectroscopic and Quantum Mechanical Calculation Study of the

Article pubs.acs.org/JPCA

Spectroscopic and Quantum Mechanical Calculation Study of the Effect of Isotopic Substitution on NIR Spectra of Methanol Justyna Grabska,*,† Mirosław A. Czarnecki,*,‡ Krzysztof B. Beć,† and Yukihiro Ozaki† †

Department of Chemistry, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan Faculty of Chemistry, University of Wrocław, F. Joliot-Curie 14, 50-383 Wrocław, Poland

‡

S Supporting Information *

ABSTRACT: In this work, we studied methanol and its deuterated derivatives (CH3OH, CH3OD, CD3OH, CD3OD) by NIR spectroscopy and anharmonic quantum chemical calculations. Vibrational bands corresponding to up to three quanta transitions (first and second overtones, binary and ternary combination modes) were predicted by the use of the VPT2 route. The accuracy of prediction of NIR modes was evaluated through density functional theory (DFT) with selected density functionals and basis sets. On the basis of the theoretical NIR spectra, detailed band assignments for all studied molecules were proposed. It was found that the pattern of bands in NIR spectra of deuterated methanols can be used for identification of isotopically equalized forms. Calculations of NIR spectra of all possible forms of CXXXOX (X = H, D) molecules demonstrated that the isotopic contamination can be identified due to a coexistence of bands specific to OH and OD groups. Also, bands from partially deuterated methyl groups can be distinguished in NIR spectra. Since the VPT2 framework is known to be sensitive to inaccuracy in the case of highly anharmonic modes, we obtained an independent insight by numerical solving of the time-independent Schrödinger equation corresponding to the O−X stretching mode scanned within −0.4 to 2.0 Å over a dense grid of 0.005 Å. This way the energies of vibrational levels of the CX1X2X3OX4 (X = H, D) isotopomers and the corresponding transition frequencies were obtained with high accuracy (99%, Sigma-Aldrich Chemical Co, Germany) were distilled and dried under freshly activated molecular sieves (4 Å), while samples of methanol-d1 (CH 3 OD), methanol-d 3 (CD 3 OH), and methanol-d 4 (CD3OD) (>99.5%, Sigma-Aldrich Chemical Co, Germany) were used as received. All spectra were recorded on a Nicolet Magna 860 spectrometer with DTGS detector, and 256 scans were accumulated. NIR spectra from 10000 to 4000 cm−1 were measured in CCl4 (≈0.005−0.2 M) in a temperature-controlled quartz (Suprasil, Hellma) cell of 1−20 mm thickness at a resolution of 4 cm−1. In addition, we used CH3OD sample, which was found to contain significant contamination evidenced by the presence of OH bands in the NIR spectrum. The sample was purchased from a global manufacturer and dried by freshly activated molecular sieves (Wako Pure Chemical Industries Japan, 4 Å pore size). The NIR spectrum of this sample was measured in the range 10000−4000 cm−1 on a PerkinElmer Spectrum One NTS FT-NIR spectrometer operating in a transmittance mode. The solution of 0.005 M CCl4 (Infinity Pure, min. 99.9%; Wako Pure Chemical Industries Japan; dried similar as the CH3OD sample) was placed in rectangular quartz cell with an optical path of 10 mm. Spectral measurements were performed at a resolution of 4 cm−1, resulting in an interpolated data spacing of 1 cm−1, and 128 scans were accumulated. Each measurement was repeated three times, preceded with a B

DOI: 10.1021/acs.jpca.7b08693 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Gaussian software. The solution of the corresponding Schrö dinger equation was performed by means of the generalized Numerov method, with seven-point stencil size (seven-point numerical differentiation).36 The generalized Numerov matrix procedure and eigendecomposition of the vibrational Hamiltonian were carried out using code developed in MATLAB.40

background collection (the spectrum of the solvent). The spectra were acquired at a controlled temperature of 298 K. The baseline correction was performed in MATLAB by using the PLS Toolbox function (“baseline”). To ease comparison of the spectra, they were normalized by using the peak height of the 2νOH band as the reference. 2.2. Computational Details. All quantum mechanical calculations were carried out using Gaussian 16 rev. A.03 software.37 To simulate NIR spectra of methanols, we applied fully anharmonic vibrational analysis by means of generalized vibrational second-order perturbation theory with inclusion of vibrational transitions up to three quanta. This way, we obtained the information on the first and second overtones along with binary and ternary combinations. The vibrational analysis was preceded by geometry optimization. The determination of the ground state electronic properties and resulting molecular geometry was based on density functional theory (DFT). For calculations, we used single-hybrid B3LYP and double-hybrid B2PLYP density functionals coupled with SNST and correlation-consistent (aug-cc-pVTZ and aug-ccpVQZ) basis sets. Superfine grids for integration and solving of CPHF equations and very tight convergence of geometry optimization were selected. The calculations were carried out with the CPCM solvent model of CCl4. The obtained vibrational frequencies and intensities were used for reconstruction of NIR bands for particular model structures. The spectral profiles were approximated by a fourparameter Cauchy−Gauss product function (eq 1) a1 A (ν ) = exp( −a4 2(ν − a3)2 ) 2 1 + a 2 (ν − a3)2 (1)

3. RESULTS AND DISCUSSION 3.1. Theoretical NIR Spectra of CH3OH, CH3OD, CD3OH, and CD3OD. As will be explained in detail (section 3.2), the best quality of simulation of NIR spectra was achieved at the B2PLYP/SNST level. Hence, the theoretical spectra with the use of this method will form the basis for the following discussion. NIR experimental spectra of CH3OH, CD3OH, CH3OD, and CD3OD in CCl4 (C = 0.005 M) are shown in Figure S1 (Supporting Information). The spectra are rich in structural information, which can be elucidated in detail by comparing with the simulated spectra. Figure 1 compares the experimental NIR spectrum of CH3OH in CCl4 (C = 0.005 M) with the theoretical one. On

where a1 and a3 are the calculated intensity and band position, respectively. The band shape parameters, a2 and a3, were chosen arbitrarily for the best fitting of the experimental spectra. The band assignments were performed with the aid of potential distribution analysis carried out in Gar2Ped software,38 after defining a nonredundant set of internal coordinates in accordance with Pulay et al.39 To study in detail the anharmonicity of O−X stretching vibration and its dependence on the isotope substitutions and to ensure highly accurate data on vibrational energies, an independent approach of numerical solving of the timeindependent Schrödinger equation (eq 2) was employed

Figure 1. Comparison of experimental and calculated NIR spectra of CH3OH in CCl4 (0.005 M).

(2)

this basis, one can establish detailed assignments of the first and second overtones, as well as the binary and ternary combination bands contributing to the NIR spectrum of CH3OH. Similarly, a high level of agreement with the experimental spectra was achieved for CH3OD (Figure 2), CD3OH (Figure 3), and CD3OD (Figure 4) molecules. This way, a detailed crossanalysis of NIR spectra of methanol and its deuterated derivatives as well as the establishment of spectra−structure

where Ψ is the wave function and μ is the reduced mass corresponding to normal coordinate Q, V(Q) is the potential energy curve along the given normal coordinate, and E are the associated energy eigenvalues. The scan of the potential energy over the O−X stretching normal coordinate was performed from −0.4 to 2.0 Å with steps of 0.005 Å. The harmonic analysis to determine the normal coordinate and the grid-based energies were obtained at the B3LYP/6-311++G(3df,3pd) level, with preliminary geometry optimization using very tight convergence criteria, 10−12 SCF convergence level, superfine integration and CPHF grids. The calculations were carried out in the SMD solvent model of CCl4. This approach has been recently recommended for providing a high accuracy of the νOX potential curve.36 Ground state geometries and normal coordinates have been obtained from formatted checkpoint files with the highest precision available from the standard code of

Figure 2. Comparison of experimental and calculated NIR spectra of CH3OD in CCl4 (0.005 M).

∂ 2Ψ(Q ) = ∂Q 2

{

2μ (V (Q ) − E) Ψ(Q ) ℏ2

}

C


Article


+ νb type combinations) to the total calculated integral intensity. These results confirm our previous conclusions,30 that, in the case of unsubstituted molecules, the higher order overtones and combinations are much less important for determining their NIR spectrum, as demonstrated in Figure 5 and in Figures S2−S17 (Supporting Information). However, there are some exceptions; e.g., a ternary combination mode at 4400 cm−1 in the spectrum of CD3OH is clearly observed (Figure S13 in the Supporting Information). As can be seen from Table 5, for CH3OH, the first overtones contribute to the spectrum in 10,000−4000 cm−1 by 32%, while the second overtones, by 1%. The difference between binary and ternary combinations is less significant, 49 and 18% (including 9% contribution of 2νa + νb modes), respectively. One can expect that the deuteration of the OH or methyl group increases the contribution from the higher overtones and combinations at the expense of those from the first overtones and the binary combinations. Indeed, for CH3OD, the contributions from the first overtones are reduced to 25%, while those of the second overtones increase to 2%. The contributions from the binary and ternary combinations are slightly biased toward binary ones (with 54% contribution). However, for a fully substituted methyl group, the frequencies of combination modes involving the CD3 group are strongly red-shifted and as a result they no longer appear in the NIR region. Therefore, the contribution from the first overtones is more significant (60% for CD3OH and CD3OD) than that from the binary combinations (26 and 16%, respectively). It is of particular note that, for all studied molecules, the contributions of the second overtones (0.5−3%) and ternary combinations (14−21%) remain significantly lower than those of the lesser order modes. With increasing degree of deuterization, the contribution from the first overtones increases at the expense of the binary combinations. This effect is evident in the NIR region from 7500 to 4000 cm−1 (Table 5). However, when focusing on the higher wavenumber NIR region (from 10,000 to 7500 cm−1), the second overtones and binary combinations completely disappear from the spectra regardless of the level of deuterization (Table 5). The contributions from the other modes vary among the different isotopomers; however, an increasing level of deuterization enhances the significance of the higher order modes as well. As a consequence, in the spectra of CD3OH and CD3OD from 10000 to 7500 cm−1 only the ternary combinations and the second overtones appear. For CD3OH, the major contribution comes from 2νa + νb modes (81%) (Table 5). In conclusion, an adequate reproduction of the experimental NIR spectra in the region 7500−4000 cm−1 is feasible even with calculations limited to the first overtones and binary combinations. In the case of methanol and its deuterated derivatives, the estimated loss of the relevant information is about 20%. However, the ignored bands are of very low intensity. Moreover, it is expected that with the increasing complexity of the molecule this loss may become smaller due to higher contributions from the binary combinations.23,25,30 3.2. The Evaluation of Accuracy of VPT2 Calculations in the NIR Region. As demonstrated previously, DFT method is particularly suitable for anharmonic vibrational analysis, in view of the balance between reliability and computational affordability. In Table 6 are compared the accuracies of vibrational frequencies by GVPT2 for the selected density functionals and basis sets. The double hybrid B2PLYP

Figure 3. Comparison of experimental and calculated NIR spectra of CD3OH in CCl4 (0.005 M).

Figure 4. Comparison of experimental and calculated NIR spectra of CD3OD in CCl4 (0.005 M).

correlations become possible. The width of simulated bands shown in Figures 1−4 was intentionally reduced for better resolving of contributing peaks. The assignments of major vibrational modes for the studied molecules are presented in Tables 1−4. The band numbers in the tables correspond to those in Figures 1−4. Comparison of the experimental and theoretical spectra allows for observation of the contaminant bands due to isotope equilibration in the spectra of deuterated samples. Obtaining an adequate purity of deuterated samples is often a challenging problem, particularly in the case of low molecular weight alcohols.41 This results from difficulties in the synthesis process and also from spontaneous isotope equilibration enhanced by the hydrogen-bonding interaction occurring in the neat-liquid alcohol sample as well as an effect of water contamination.41 In our case, the bands originating from this kind of impurities could be evidenced in all deuterated methanols (Figures 2−4) with a varying level of contamination. This will be further discussed in detail in section 3.3. In Figure 5 are displayed the contributions from the bands due to first and second overtones, as well as binary and ternary combination bands in the NIR spectrum of CH3OH. The ternary combinations involving the fundamental and first overtone transitions (2νa + νb) are presented separately as well. The band widths were optimized to obtain the best fit of the theoretical spectra to the experimental ones. The corresponding spectra for the remaining methanols are presented in the Supporting Information (Figures S2−S17). In Table 5 are collected the relative contributions of the bands due to particular kinds of NIR modes (first and second overtones; binary and ternary combinations with separated 2νa D


Article

The Journal of Physical Chemistry A Table 1. Band Assignments in the NIR Spectrum of CH3OHa wavenumber (cm−1)

a

band number

experimental

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

8421 8136 7364 7279 7119 6888 6817 6585 6555 6475 6271 6011 5961 5930 5892 5832 5814 5772 5089 4961 4857 4708 4666 4482

25 26 27 28

4241 4178 4135 4006

calculated 8527 8116 7298 7193 7137 6891 6679 6662 6614 6550 6303 5960 5924 5876 5854 5798 5784 5747 5107 4982 4907 4729 4656 4460, 4424, 4413, 4350, 4301 4239 4136 4113 4022

difference −106 20 66 86 −18 −3 138 −77 −59 −75 −32 51 37 54 38 34 30 25 −18 −21 −50 −21 10

2 42 22 −16

band assignments 2νas′CH3 + νsCH3 (δasCH3, δas′CH3) + νasCH3 + νOH 2νas′CH3 + (δas′CH3, δasCH3) δsCH3 + 2(δas′CH3, δasCH3) 2νOH νas′CH3 + δrock′CH3 + νsCH3 τCO + νsCH3 + νOH νasCH3 + νOH νas′CH3 + νOH νsCH3 + νOH 2(δCOH, δrockCH3) + νOH νas′CH3 + νOH 2νasCH3 (δasCH3, δas′CH3) + 2νas′CH3 + δsCH3 2νas′CH3 (δasCH3, δas′CH3) + (δas′CH3, δasCH3) + νsCH3 (δCOH, δrockCH3) + δsCH3 + νasCH3 νas′CH3 + νsCH3 δsCH3 + νOH (δCOH, δrockCH3) + νOH (δrockCH3, δCOH) + 2(δCOH, δrockCH3) (δrockCH3, δCOH) + νOH (νCO, δCOH) + νOH δsCH3 + νasCH3, (δasCH3, δas′CH3) + νas′CH3, νas′CH3 + δsCH3, (δas′CH3, δasCH3) + νsCH3, 3νsCH3 (δCOH, δrockCH3) + νsCH3 (νCO, δCOH) + 2(δrockCH3, δCOH) δrock′CH3 + νas′CH3 (νCO, δCOH) + νasCH3

Band numbers correspond to those in Figure 1.

case of νOH/OD + δCH3 modes, this effect results in a compensation of the error due to the overestimation of δCH3 frequencies.28 Having compared the accuracy levels of the overviewed methods, a short note about the resource efficiency of anharmonic calculations can be made. Here, the utilization of B2PLYP functional involves about 2 times increase of the total calculation time vs B3LYP functional (geometry optimization, harmonic analysis, GVPT2 calculations), with all other factors being equal. The extension of GVPT2 calculations onto three quanta modes involves only a minor increase in computation time against a standard two-quanta calculation at the B2PLYP/ SNST level, at least for the case of small molecules. Extension to three quantas increases the demand for memory; however, for the molecules of methanol size, it still remains moderate when using DFT methods. The above statements should be considered as rough estimates, as various factors influence the resource consumption and in general these estimates may not be transferrable between different computational environments. The absolute RMSE values for NIR modes are mostly larger than those for MIR modes, since NIR modes are located at higher wavenumbers. On the other hand, significant overlap of NIR modes23,31,32 makes the accuracy of the reproduction of individual modes more important for the overall agreement between the calculated and experimental NIR spectra. 3.3. Qualitative Analysis of Isotope Contaminations by NIR Spectroscopy. Estimation of the accuracy of the

functional coupled with the triple-ζ SNST basis set provided the best and most consistent results with RMSE (root mean squared error) of 24.4−29.7 cm−1 for all studied molecules and total (averaged) RMSE of 27.6 cm−1. The switch to correlationconsistent basis sets of triple-ζ (aug-cc-pVTZ) and even quadruple-ζ (aug-cc-pVQZ) decreases the quality of results. The single-hybrid B3LYP functional favored the SNST basis set as well, and provided results with 45.2 cm−1 of total RMSE. However, the results obtained with B3LYP functional were considerably less consistent than those of B2PLYP, regardless of the basis set used. The results for B3LYP/SNST provided RMSE as low as 14.0 cm−1 in the case of CD3OH and as high as 77.8 cm−1 for CH3OH. Hence, one can conclude that the B2PLYP functional should be preferred for NIR studies of small molecular systems. In general, B3LYP better reproduces the frequencies of the OH/OD vibrations as compared with B2PLYP with the same basis set. It is valid for both overtones of OH/OD and the combinations of OH/OD with the CH/CD; in every case, B2PLYP overestimates more significantly the experimental values. In contrast, the vibrations of CH/CD are better reproduced by B2PLYP. These trends are well seen when the aug-cc-pVTZ basis set is used (Table 6). In this case, B3LYP/ aug-cc-pVTZ yields the combinations of OH/OD stretching and CH3 deformation modes within a few cm−1 of the experimental values. It confirms the tendency of B3LYP for underestimating of the OH/OD stretching frequency.28 In the E


Article

The Journal of Physical Chemistry A Table 2. Band Assignments in the NIR Spectrum of CH3ODa wavenumber (cm−1)

a

band number

experimental

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

8368 7796 7375 7286 7117 6995 6801 6477 6142 5925 5879 5787 5677 5628 5521 5408 5288 5044 4759 4704 4398

22 23 24 25 26

4273 4200 4133 4054 4016

calculated 8524 7820 7297 7181 7042 6889 6758 6454 6131 5922 5850 5743 5669 5625 5591 5389 5303 5019 4779 4634 4480, 4461, 4422, 4346 4233 4182 4120 4053 4024

difference −156 −24 78 105 75 106 43 23 11 3 29 44 8 3 −70 19 −15 25 −20 70

40 18 13 1 −8

band assignments 2νas′CH3 + νsCH3 3νOD 2νas′CH3 + (δas′CH3, δasCH3) νas′CH3 + (δas′CH3, δasCH3) + νsCH3 (δasCH3, δas′CH3) + 2(δas′CH3, δasCH3) ? νasCH3 + νCO + νsCH3 νas′CH3 + νCO + νsCH3 τCO + 2(δas′CH3, δasCH3) τCO + νas′CH3 + νasCH3 2νasCH3, νas′CH3 + νasCH3 2νas′CH3 νas′CH3 + νsCH3 δrockCH3 + δsCH3 + νasCH3 νas′CH3 + δrockCH3 + δsCH3 νOD + νsCH3 δrockCH3 + (δas′CH3, δasCH3) + νOD 2νOD 2νCO + νasCH3 (δCOD, δrockCH3) + δrockCH3 + νOD νsCH3 + 2(δasCH3, δas′CH3) (δas′CH3, δasCH3) + νasCH3, (δasCH3, δas′CH3) + νasCH3, (δasCH3, δas′CH3) + νas′CH3, δrock′CH3 + νOD, νOD + νsCH3 2(δCOD, δrockCH3) + νOD νas′CH3 + δrockCH3 δrockCH3 + νsCH3 δrock′CH3 + νsCH3 νCO + νasCH3


Table 3. Band Assignments in the NIR Spectrum of CD3OHa wavenumber (cm−1)

a

band number

experimental

calculated

difference

band assignments

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

7118 6430 6384 6184 6031 5961 5883 5770 5713 5611 5105 4921 4763 4721 4624 4497 4420 4380 4308 4011

7137 6404 6386 6212 6050 5975 5909 5812 5754 5691 5141 4937 4773 4725 4618 4520 4469 4401 4271 4009

−19 26 −2 −28 −19 −14 −26 −42 −41 −80 −36 −16 −10 −4 6 −23 −49 −21 37 2

2νOH 2νas′CD3 + νsCD3 νas′CD3 + 2νCO 2δCOH + νOH (δsCD3, νCO) + δCOH + νOH τCO + νsCD3 + νOH νasCD3 + νOH δrockCD3 + δCOH νsCD3 + νOH (δasCD3, δas′CD3) + 2νas′CD3 τCO + 2δCOH δCOH + νOH (δsCD3, νCO) + νOH (δas′CD3, δasCD3) + νOH νCO + νOH δrockCD3 + νOH 2νasCD3 2νas′CD3 νas′CD3 + νsCD3 νCO + 2(δsCD3, νCO)


trace of isotope contamination. In the case of CH3OD, a 2νOH band appears at 7119 cm−1, while a 2νOD band is located at 5288 cm−1 in the spectrum of CD3OH. These two samples

simulated NIR spectra allows for identification of the contaminant bands in the experimental spectra. For CH3OD (Figure 2) and CD3OH (Figure 3), one can observe a clear F


Article

The Journal of Physical Chemistry A Table 4. Band Assignments in the NIR Spectrum of CD3ODa wavenumber (cm−1)

a

band number

experimental

calculated

difference

band assignment

1 2 3 4 5 6 7 8 9 10 11

7797 ∼6651 ∼6550 ∼6475 ∼6385 5496 5288 4435 4389 4345 4268

7819 6642 6545 6495 6403 5603, 5530 5303 4472 4403 4340 4275

−22 ∼9 ∼5 ∼ −20 ∼ −18

3νOD 3νasCD3, νasCD3 + 2νas′CD3 3νas′CD3 νas′CD3 + νsCD3 + νasCD3 2νas′CD3 + νsCD3 νas′CD3 + (2δas′CD3, 2δasCD3) 2νOD 2νasCD3, νas′CD3 + νasCD3 2νas′CD3 νsCD3 + νasCD3 νas′CD3 + νsCD3

−15 −37 −14 5 −7


Amax(2νΟD) was 0.14 and 0.55 for samples no. 1 and no. 2, respectively. Evidently, sample no. 2 is significantly more contaminated by the presence of the molecules with a OH group. An inspection of Figure S18 (Supporting Information) reveals that the first overtones of OH and OD stretching vibrations are single and symmetric bands, in agreement with an earlier report.9 3.3.1. The Theoretical NIR Spectra of Isotope Substitutions CXXXOX (X = H, D). To qualitatively estimate the possible contamination due to isotope equilibration or not perfect synthesis, we simulated NIR spectra of all possible deuterated compositions of methanol. The numbering of the atoms in CX1X2X3OX4 (X = H, D) molecule is shown in Figure 7. In principle, for methanol, one can expect 16 different structures; however, due to symmetry properties, the X2 and X3 atoms are indistinguishable and finally we obtain 12 vibrationally distinguishable structures (including CH3 OH, CH 3OD, CD3OH, and CD3OD molecules). The simulated NIR spectra of these 12 structures (Figure 8) were the basis for the following analysis of contaminant bands observed in the experimental spectra. Figure 8 compares the theoretical VPT2 NIR spectra of all CH3OH isotopomers. It is clear that the spectra differ significantly from each other, and that the isotopic substitution of the methyl group develops highly specific bands in the spectra of isotopically contaminated samples. The results of

Figure 5. Contributions from the bands due to first and second overtones, as well as binary and ternary combination bands into the NIR spectrum of CH3OH (high resolution figure and magnified spectral regions are available in the Supporting Information).

have good quality, and as a result, the amount of contamination is reasonably low. However, the quality of commercial samples with isotope substitutions is not always satisfactory. We acquired a number of low quality CH3OD samples, as evidenced by the presence of a strong 2νOH band (Figure 6). In this case, the first overtone of the OH stretching band is stronger than that from the OD group. This indicates that the population of the molecules with OH and OD groups is of the same order. The peak heights ratio (Figure 6) Amax(2νOH)/

Table 5. Percentage Contribution of the First and Second Overtones as Well as Binary and Ternary Combinations into NIR Spectra of Methanolsa 7500−4000 cm−1 CH3OH CH3OD CD3OH CD3OD

CH3OH CH3OD CD3OH CD3OD

10000−7500 cm−1

2ν

3ν

νa + νb

νa + νb + νc

2νa + vb

32.6 25.4 60.2 61.4

0.3 0.4 0.5 1.0

49.6 55.2 25.8 16.5

9.1 11.1 4.7 8.0

8.4 7.9 8.8 13.1

2ν

3ν

0.0 48.1 0.0 60.3 0.0 0.0 0.0 100.0 10000−4000 cm−1

νa + νb

νa + νb + νc

2νa + νb

0.0 0.0 0.0 0.0

20.4 13.0 19.2 0.0

31.5 26.7 80.8 0.0

2ν

3ν

νa + νb

νa + νb + νc

2νa + νb

32.0 24.7 60.2 60.3

1.1 2.1 0.5 2.7

48.8 53.8 25.8 16.2

9.3 11.1 4.7 7.9

8.8 8.3 8.8 12.9

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

G


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Table 6. Experimental and Calculated Frequencies (in cm−1) of selected overtones and combination modes of CH3OH, CH3OD, CD3OD, and CD3OH calculated B2PLYP/SNST

a

B2PLYP/aVTZ

a

B2PLYP/aVQZa

B3LYP/SNST

B3LYP/aVTZa

B3LYP/aVQZa

Exp.

7100 5842 5764 5665 5078 4954 4698

7122 5834 5782 5653 5090 4964 4707

7139 5831 5777 5644 5101 4975 4718

7119 5961 5892 5772 5089 4961 4708

47.5 CH3OD 5925 5334 4405

78.0

77.8

82.2

5846 5276 4361

5838 5290 4343

5835 5299 4345

37.8 CD3OD 5334 4470 4399

29.5

39.6

40.3

5277 4415 4339

5290 4408 4333

5300 4407 4330

31.7

35.9

38.3

7100 5863 5711 4910 4744 4489 4410

7123 5868 5711 4917 4753 4499 4404

7140 5879 5720 4932 4768 4510 4404

CH3OH 7183 5921 5834 5740 5133 5005 4751

2νOH 2νasCH3 2νas′CH3 νas′CH3 + νsCH3 δsCH3 + νOH (δCOH, δrockCH3) + νOH (δrockCH3, δCOH) + νOH

7137 5924 5854 5747 5107 4982 4729

7169 5918 5831 5741 5124 4996 4743

RMSE

26.6

42.6

2νas′CH3 2νOD (δasCH3, δas′CH3) + νas′CH3

5922 5303 4422

5922 5325 4402

RMSE

29.7

32.8

2νOD 2νasCD3, νas′CD3 + νasCD3 2νas′CD3

5303 4472 4403

5325 4466 4396

RMSE

24.4

28.2

2νOH νasCD3 + νOH νsCD3 + νOH δCOH + νOH (δsCD3, νCO) + νOH δrockCD3 + νOH 2νasCD3

7137 5909 5754 4937 4773 4520 4469

7169 5921 5771 4951 4789 4534 4462

33.9 CD3OH 7185 5931 5766 4957 4799 4544 4467

RMSE

29.3

41.6

48.7

14.0

9.5

12.6

Total RMSE

27.6

41.4

38.0

45.2

47.5

53.4

5879 5288 4398

5288 4435 4389

7118 5883 5713 4921 4763 4497 4420

Abbreviations used: aVTZ for aug-cc-pVTZ; aVQZ for aug-cc-pVQZ.

Figure 7. Atom numbering in the CX1X2X3OX4 molecule (X = H, D).

corresponding bands was not observed even for highly contaminated CH3OD (sample no. 2). It is known that VPT2 offers very good accuracy, but its reliability is not sufficient in the case of highly anharmonic modes, such as OX stretching vibration. To critically evaluate the possible differences in the anharmonicity of OX stretching vibration depending on the isotopic substitution of the methyl group, a different approach was applied. A dense grid scan of the potential energy over the OX stretching coordinate gives a very good approximation of the mode anharmonicity (Figure 9). By solving the timeindependent Schrödinger equation for each CX3OX (X = H,

Figure 6. A NIR spectrum of low contaminated CH3OD sample (sample no. 1), highly contaminated CH3OD sample (sample no. 2), and the resulting difference spectrum.

VPT2 calculations also reveal significant spectral shifts (up to 15 and 9 cm−1 for OH and OD bands, respectively) of the 2νOX band due to different substitutions of the CH3 group. However, in the experimental or second derivative spectra (Figure S18 in the Supporting Information), any splitting of the H


Article


Table 7. Comparison of the Calculated 2νOX Vibrational Frequencies in cm−1 with the Use of the VPT2 Approach and Numerical Solving of the Schrödinger Equation Based on Scanning the Potential Energy along the 2νOX Normal Coordinate CH3OH CD3OH CDHHOH CHDHOH CDDHOH CHDDOH CH3OD CD3OD CHDHOD CDHDOD CHDDOD CDHHOD

exp.

calc. (VPT2)

calc. (V(Q) probing)

7119 7119

7136.7 7137.0 7123.6 7122.8 7123.2 7122.4 5302.4 5303.0 5294.7 5295.2 5294.3 5303.1

7110.2 7109.3 7109.3 7111.9 7111.0 7110.2 5273.6 5274.0 5274.9 5275.4 5273.4 5274.1

5288 5288

perfect (CH3OH and CHDDOH, both 7110.2 cm−1) if the X2 and X3 isotopes are equal. However, in the case of different X2 and X3 isotopes, the 2νOH frequency is blue-shifted by 1.7 to 7111.9 cm−1 (Table 7). One can observe exactly the same situation in the case of molecules with X1 = D and a OH group. The frequency of 2νOH for CD3OH and CDHHOH is exactly the same, 7109.3 cm−1. Uneven substitution of X2 and X3 positions results in a blue-shift of 2νOH to 7111.0 cm−1 (Table 7). The same conclusions can be drawn from the analysis of 2νOD frequencies (Table 7). The molecules with X1 = H have almost perfectly the same 2νOD frequency when X2 and X3 isotopes are equal (CH3OD and CHDDOD, 5273.6 and 5273.4 cm−1, respectively). Uneven substitution leads to a blue-shift of the 2νOD frequency to 5274.9 cm−1 in the case of the CHDHOD molecule (1.3−1.5 cm−1 difference for CH3OD and CHDDOD). The molecules with X1 = D and OD group follow this pattern as well. The 2νOD frequencies for CD3OD and CDHHOD are 5274.0 and 5274.1 cm−1, while, for CDHDOD,

Figure 8. Calculated NIR spectra of CXXXOX (X = H, D) molecules.

D) molecule, the accuracy of resolved vibrational levels should be of the order of

Spectroscopic and Quantum Mechanical Calculation Study of the

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