1 2
Spectra-structure correlations in NIR region:
3
spectroscopic and anharmonic DFT study of
4
n-hexanol, cyclohexanol and phenol
5 6
Krzysztof B. Bed*1, Justyna Grabska1 and Mirosław A. Czarnecki2
7 8 9 10
1
Department of Chemistry, School of Science and Technology, Kwansei Gakuin University,
11
Sanda, Hyogo 669-1337, Japan
12 13
2
Faculty of Chemistry, University of Wrocław, F. Joliot-Curie 14, 50-383 Wrocław, Poland
14 15 16 17 18 19 20 21 22 23 24 25
Corresponding Author.
26
Email:
[email protected] 1
27
Abstract
28
We investigated near-infrared (7500-4000 cm-1) spectra of n-hexanol, cyclohexanol and
29
phenol in CCl4 (0.2 M), by using anharmonic quantum calculations. The investigated
30
molecules represent three major kinds of alcohols, linear and cyclic aliphatic and
31
aromatic ones. Vibrational second-order perturbation theory (VPT2) was employed to
32
calculate the first overtones and binary combination modes and to reproduce the
33
experimental NIR spectra. The level of conformational flexibility of these three alcohols
34
varies from one stable conformer of phenol through four conformers for cyclohexanol to
35
few hundreds conformers in the case of n-hexanol. To take into account the most relevant
36
conformational population of n-hexanol, a systematic conformational search was
37
performed. Accurate reproduction of the experimental NIR spectra was achieved and
38
detailed spectra-structure correlations were obtained for these three alcohols. VPT2
39
approach provides less reliable description of highly anharmonic modes, i.e. OH
40
stretching. In the present work this limitation was manifested in erroneous results yielded
41
by VPT2 for 2OH mode of cyclohexanol. To study the anharmonicity of this mode we
42
solved the corresponding time-independent Schrödinger equation based on a dense-grid
43
probing of the relevant vibrational potential. These results allowed for significant
44
improvement of the agreement between the calculated and experimental 2 OH band of
45
cyclohexanol. These studies are of great meaning since numerous important
46
biomolecules include similar structural units. A detailed knowledge on spectral properties
47
of these three types of alcohols is therefore essential to advance our understanding of
48
NIR spectroscopy of important constituents of biomolecules.
49 50
Keywords: near-infrared spectroscopy, alcohols, phenols, quantum chemical calculation,
51
overtones, combination modes, time-independent vibrational Schrödinger equation,
52
spectra-structure correlation, anharmonic spectra.
53
2
54
Introduction *
55
Near-infrared (NIR) spectroscopy (12,500-4000 cm-1; 800-2500 nm) is growing in
56
importance in science and technology over the last two decades. 1,2,3 In relation to other
57
vibrational spectroscopies (mid-IR or Raman), NIR spectroscopy (NIRS) offers advantages
58
like simpler instrumentation and general versatility.1,4 Numerous physicochemical studies,
59
including the anharmonicity of molecular vibrations, 3,
60
intermolecular interactions,3,7,8 and hydrogen-bonding,3,9,10,11,12,13 solution chemistry14
61
and microheterogeneity,15 solvent effects,16,17 etc., provide a good basis for applications
62
of NIRS in analytical chemistry. NIRS appears to be very useful for qualitative and,
63
quantitative analysis of natural products,
64
samples21 and medical tools.22 Therefore, NIRS is now one of the most important tools
65
in scientific and industrial laboratories.
18
food,
19
5
molecular structure,3, 6
pharmaceuticals, 20 medical
66
Unfortunately, NIR spectra remain difficult for direct interpretation. The spectral
67
information is intrinsically complex as a result of significant overlapping of overtones and
68
numerous combination bands. 23 Therefore, applications of NIRS strongly rely on
69
statistical data analysis.3 As a result, NIRS is often used as a black-box tool. However, the
70
ways of application of NIRS extend well beyond the plain correlations between the
71
molecular properties of the sample and its NIR spectrum.
72
Quantum mechanical calculations are routinely one of the most important sources of
73
independent insights in the case of IR and Raman spectroscopies. The analysis of the
74
fundamental bands can be successfully carried out by ordinary harmonic calculations.24
75
On the other hand, in the case of NIR spectra an anharmonic approach is required. This
76
imposes considerable requirements on the accuracy and computational affordability.2,25
77
Hence, for a long time only the simplest molecules could be satisfactorily treated with
78
fully anharmonic calculations. Therefore, our understanding of NIR spectra is still
79
insufficient.1,2,3,26 Advances in the theory of anharmonic methods and a rapid growth of
*
This article is dedicated to Professor Yukihiro Ozaki from Kwansei Gakuin University on the occasion of his retirement, to honour his work which significantly advanced our knowledge on near infrared spectroscopy.
3
80
available computational power over the years have allowed to push the limits in
81
theoretical NIRS. Recent development of deperturbed and generalized VPT2 schemes,27
82
combining good accuracy with relatively modest computational complexity and versatility
83
should be noted. As a result, growing number of NIR spectroscopic studies aided by VPT2
84
calculations is observed over the last two or three years.10,18,28,29,30,31 Nowadays, the
85
theoretical NIR spectra of fairly complex molecules, i.e. rosmarinic acid18 or
86
medium-chain fatty acids,32 can be successfully obtained.
87
The OH group strongly affects physicochemical properties of alcohols. The OH group
88
can be attached to various types of molecular structures, i.e. normal or cyclic aliphatic
89
chains or aromatic rings. The properties of the OH group, in particular its vibrational
90
frequencies, strongly depend on the environment. For this reason, it is of high interest to
91
establish detailed correlations between the structural factors of the three types of
92
alcohols and their specific NIR spectral features. The first overtones of the free or weakly
93
bonded OH are very pronounced in NIR spectra; therefore their spectral parameters
94
(intensity, position, half-width) are a rich source of information on self-association and
95
interactions with other molecules. It is relatively easy to study the OH stretching of the
96
first overtone bands and so far many works focused on these bands.1,3,6,8-11,13 In contrast,
97
the other bands appearing in the NIR region have not been used so often, despite
98
carrying rich information on the structure and properties of these molecules 3,7 The
99
complexity of NIR spectra has been the major obstacle in such studies. To overcome this
100
problem it is necessary to establish detailed band assignments and obtain comprehensive
101
spectra-structure correlations in a broad range of NIR (7500 – 3800 cm-1). Here, we
102
attempt to extend our knowledge to medium-size alcohols of great importance. The OH
103
group appears in numerous molecules, including carbohydrates, nucleic acids, aliphatic
104
OH groups playing role in the adsorption of proteins or nucleic acids,33,34 cyclic alcohols
105
appearing in metabolic paths,35,36 polyphenols in natural products or acting as radical
106
scavengers,18 etc. The aim of the present work is elucidation of the differences between
107
the NIR spectra for three major kinds of alcohols represented by n-hexanol, cyclohexanol 4
108
and phenol, on the basis of fully anharmonic calculations. To achieve this aim we
109
employed two different approaches. Firstly, the second-order vibrational theory (VPT2)
110
computations were used to simulate NIR spectra from 7500 to 4000 cm-1 and to enable
111
detailed reproduction of the experimental bands. An analysis of the contributions from
112
overtone and combination bands in various spectral subregions provided reliable band
113
assignments. The limitations of VPT2 in describing highly anharmonic modes, such as OH
114
stretching mode, clearly appears in the case of cyclohexanol. Secondly, in this particular
115
case we perform a detailed study of the vibrational potential, vibrational levels and
116
corresponding transition frequencies based on numerical solving of the related
117
time-independent Schrödinger equation.
118 119
1. Materials and methods
120
1.1.
Experimental
121
The samples were purchased from Wako Pure Chemical Industries Japan (n-hexanol,
122
min. 97%; cyclohexanol, min. 98%; phenol, min. 99%) and dried by freshly activated
123
molecular sieves (Wako Pure Chemical Industries Japan, 4Å pore size). The NIR spectra
124
were measured in 10000 – 3700 cm-1 range on a Perkin Elmer Spectrum One NTS FT-NIR
125
spectrometer operating in a transmittance mode. The solutions of 0.2 M in CCl4 (Infinity
126
Pure, min. 99.9%; Wako Pure Chemical Industries Japan; dried similar as above) were
127
placed in rectangular quartz cell of optical path of 10 mm. Spectral measurements were
128
performed at resolution of 4 cm-1, resulting in an interpolated data spacing of 1 cm -1 and
129
64 scans were accumulated. Each spectrum was recorded 3 times, preceded with a
130
background collection (the spectrum of the solvent). The spectra were measured at a
131
controlled temperature of 298 K. A baseline correction was performed by using the
132
software operating the spectrometer. No other spectral pre-treatment was applied.
133
1.2.
Computational details
134
All quantum mechanical calculations were carried out using Gaussian 09 Rev. E.01
135
software. 37 Conformational search (refer to Section 2.1 for detailed explanation), 5
136
geometry optimization and anharmonic vibrational analysis were carried out at Density
137
Functional Theory (DFT) level. Single-hybrid B3LYP density functional coupled with
138
6-31G(d,p) basis set for conformational searches, and SNST basis set for the subsequent
139
computations were employed. This method has been reported to be very efficient and
140
accurate in similar studies.10,25,28,30-32 With the exception of conformational searches,
141
superfine grids for integration and solving CPHF equations, and very tight convergence of
142
geometry optimization were applied. The calculations were carried out with
143
conductor-like polarizable continuum model (CPCM)38 of CCl4 solvent and with the use of
144
third formulation of Grimme’s empirical correction for dispersion with Becke-Johnson
145
damping (GD3BJ).39 To simulate NIR spectra of studied alcohols we performed fully
146
anharmonic vibrational analysis by means of deperturbed/generalized vibrational
147
second-order perturbation theory (DVPT2/GVPT2);27 in this case the tightly coupled
148
modes were not subjected to variational treatment. Applied computational procedure
149
enabled us to obtain information on the first overtones and binary combinations. As
150
previously shown,28,30-32 this approach is sufficient to capture the major features of NIR
151
spectra without extensive calculations.
152
The vibrational frequencies and intensities were used for reconstruction of NIR bands
153
for particular model structures in the same way as previously described.30,45 The final
154
theoretical NIR spectra were constructed as weighted-sum of calculated spectra of
155
different conformational isomers (ref. Section 2.1) with respect to the calculated
156
Boltzmann coefficients. The Boltzmann coefficients were derived from Gibbs free
157
energies (B3LYP/SNST) corresponding to 298 K, additionally corrected by anharmonic
158
zero-point energy (ZPE) values. This approach worked well with the exception of
159
cyclohexanol case, which will be discussed in detail in Section 2.6.
160
The band assignments were performed with an aid of potential distribution analysis
161
carried out in Gar2Ped software,40 after defining a non-redundant set of natural internal
162
coordinates in accordance with Pulay et al. 41
6
163
To enable accurate calculation of anharmonicity of OH stretching vibration, in cases
164
where VPT2 calculation scheme gave erroneous results (cyclohexanol), an independent
165
approach of numerical solving of time-independent Schrödinger equation (Eq. 1) was
166
employed: 𝜕2 𝛹 ( 𝑄 )
167
𝜕𝑄 2
2𝜇
= { ℏ2 (𝑉(𝑄) − 𝐸 )}𝛹 (𝑄)
(1)
168
In Eq. 1 Q denotes the respective normal coordinate, Ψ the wave function, the reduced
169
mass of the corresponding oscillator, V the potential energy, and E the energy eigenvalue.
170
The scan of the potential energy over the OH stretching normal coordinate was
171
performed from -0.4 to 2.0 Å with 0.005 Å/step. The harmonic analysis to determine the
172
normal coordinate was carried out at B3LYP/6-311++G(3df,3pd) level, with preliminary
173
geometry optimization using very tight convergence criteria, 10 -12 SCF convergence level,
174
superfine integration and CPHF grids and CPCM solvent model of CCl4. The following
175
grid-based energies were obtained with the use of 6-311G(d,p) basis set, all other
176
parameters being equal to those listed above. The solution of the corresponding
177
Schrödinger equation was performed by means of generalized Numerov’s method, with
178
seven-point numerical differentiation.42
179 180
2. Results and discussion
181
2.1 The conformational flexibility of alcohols
182
The studied alcohols (Figure 1a-c) differ notably in levels of conformational flexibility.
183
Phenol is the simplest case as it has only one stable conformer, with O-H bond parallel
184
and in plane of the aromatic ring (Fig. S1 in Supplementary Material). Six-membered
185
saturated ring of cyclohexanol takes four stable conformational isomers, in which the OH
186
group is either in gauche or trans position (with the respective the values of OHCH
187
torsional angle: 64 and 180 degrees). All conformers of cyclohexanol were included in the
188
computations of NIR spectrum, although the axial conformers are in minority (with total
189
abundance of around 5%). The energetic relations between equatorial gauche and trans
190
conformers appears to be highly dependent on the used computational method (see 7
191
Section 2.6 and Tables S2-S3 in Supplementary Material).
192
n-Hexanol required a different approach as it has a significant level of conformational
193
flexibility. Because of 5 possible rotations (one about C-O and four about C-C bonds) the
194
total number of stable conformations of n-hexanol (assuming two gauche and one trans
195
configurations, and regarding the symmetry properties) is 243. For this reason we
196
performed a six-dimensional rigid scan of potential energy surface (PES) of n-hexanol
197
molecule at B3LYP/6-31G(d,p) level. Afterwards, we selected the representative
198
population of the most stable conformers, by considering those within 2 kcal/mol of the
199
relative B3LYP/6-31G(d,p) single point energy as resulted from the PES scan. At this step
200
the structures redundant due to symmetry operations were excluded. The selected 46
201
non-redundant conformers were subjected to geometry optimization (B3LYP/SNST) which
202
reduced the number of unique, spectroscopically distinguishable conformers of n-hexanol
203
to 32 (for detailed information refer to Table S1 in Supplementary Materials) which were
204
the basis for the subsequent spectroscopic computations, as described in Section 1.2.
205 206
Figure 1. Molecular structure of major conformers of (A) n-hexanol, (B) cyclohexanol, (C) phenol.
207 208
2.2 Analysis of NIR spectrum of n-hexanol.
209
In the NIR spectrum of n-hexanol (Figure 2, Table 1) four major spectral subregions
210
can be noticed. In the range of 7150-7000 cm-1 moderately intense first overtone band of
211
OH stretching mode appears, with Amax value at 7103 cm-1. Between 6000-5500 cm-1
212
occur a number of overlapped bands due to stretching modes of the CH2 and CH3 groups.
213
This region was not reproduced satisfactorily by the theoretical calculations due to 8
214
overestimation of the intensities of the overtone bands (Figure 1). The region between
215
5000 and 4600 cm-1 show a broad envelope of weak intensity due to the combination
216
bands of the OH stretching and CH2 deformation modes. The band intensities in vicinity of
217
the low frequency range of this envelope (~4700 cm-1) were underestimated in the
218
calculated spectrum. Probably this results from contribution of the minor conformers
219
(Section 2.1) and the higher order modes (i.e. second overtones, ternary combinations).
220
The dominant region of NIR spectrum of n-hexanol appears between 4350-4000 cm-1,
221
with the major peak at 4336 cm -1. It is the most complex region, in which multiple
222
combination bands overlap. The most important contributions are due to combinations
223
of deformation and stretching modes of the methylene groups. The NIR spectrum of
224
n-hexanol systematically deviates from the spectra of lower weight aliphatic alcohols due
225
to an increased contribution of the bands involving CH 2 group vibrations (Figure 2, Table
226
1).28,45,43
227 228 229
Figure 2. Experimental (0.2 M, CCl4) and calculated NIR spectra of n-hexanol together with proposed
230
refer to Fig. S1 in Supplementary Material.
band assignments. Band numbers correspond to those presented in Table 1. For better view of details
9
231 232
Table 1. Experimental and calculated NIR bands of n-hexanol and proposed band assignments.
Band
Wavenumber / cm-1
Band assignment
number
Experimental
Calculated
Diff.
1
7103
7077
-26
2OH
2
6514
6472
-42
as CH2 + OH
3
5912
5855
-57
as’CH3 + as CH3
4
5865
5827, 5806
-
as CH2 + as’CH3 2 as’CH3
5
5807
5777
-30
as CH2
78
s CH2 as CH2 + as CH2
6
5682
5760
as CH2 + s CH2 7
5620-5400
-
5740-5500
as CH2 + as CH2 as CH2 + s CH2 as CH2
8 9
5010 4962
-20
4990 4951
-11
waggCH2 + OH twistCH2, COH] + OH waggCH2 + OH, twistCH2, COH] + OH
10
4900-4700
-
4900-4700
twistCH2, rockCH2] + OH rockCH2, CC] + OH twistCH2, rockCH2, rock’CH2 ] + OH
11
4401
4385
-16
as CH2, as’CH2] + as’CH3
12
4336
4333
-3
sciss CH2, as’CH3] + as CH2 sciss CH2 + s CH2
13
4265
4281
16
s CH3, waggCH2] + s CH3 twistCH2 + as CH2 waggCH2 + s CH2
14
4200-4100
-
4200-4100
[ rockCH2, rock’CH2] + as CH2 [ rockCH2, rock’CH2] + s CH2 twistCH2 + s CH2
15
4068
-14
4054
twistCH2, COH] + as CH2
233 234
2.2 Analysis of NIR spectrum of cyclohexanol.
235
In comparison to n-hexanol, the NIR spectrum of cyclohexanol reveals similar four
236
spectral subregions with comparable relative peak intensities (Figure 3, Table 2). In the
237
experimental spectrum the 2 OH peak appears at 7073 cm -1, while VPT2 calculations 10
238
failed to predict this value correctly as will be discussed in Section 2.6. The region of
239
6000-5500 cm-1 is populated by overtone and combination bands of CH 2 stretching
240
modes. Between 5000 and 4500 cm -1 appears a number of peaks from combinations of
241
the OH stretching and CH2 deformations. The 4400-4000 cm-1 region is populated by
242
intense peaks due to combinations of CH2 stretching and deformation (scissoring,
243
wagging and twisting) modes. Since modelling of the NIR spectrum of cyclohexanol
244
involved its entire conformational population, instead of selected representation as in the
245
case of n-hexanol, the agreement with experimental spectrum is higher than that in the
246
previous case (except the mentioned 2 OH band). Besides, n-hexanol has also CH3 group
247
in its structure what significantly increases a number of the binary combinations in the
248
relevant region.
249 250
Figure 3. Experimental and calculated NIR spectra of c yclohexanol (0.2 M, CCl 4) and proposed band
251
assignments. Band numbers correspond to those presented in Table 2. For better view of details refer
252
to Fig. S2 in Supplementary Material.
253 11
254 255
Table 2. Experimental and calculated NIR bands of cyclohexanol and proposed band assignments.
Wavenumber / cm-1
Band
Band assignment
number
Experimental
Calculated
Difference
1
7073
7045,67831)
-
2OH
2
5873
5838
-35
as CH2
3
5803
5776
-27
4
5710
5721
11
5
5674
5690
16
as CH2 as CH2 + as CH2 as CH2 CH + as CH2 as CH2 + as CH2 as CH2 as CH2 + as CH2
6
5650-5380
-
5660-5500
as CH2 + s CH2 as CH2 s CH2 CH
7
5011
4919
-92
CH + OH
8 9
4951 4884
4855 4794
-96 -90
CH + OH waggCH2 + OH
10
4849
4763
-86
twistCH2 + OH
11 12
4752 4691
4668 4583
-84 -108
COH, rockCH2, twistCH2] + OH rockCH2, COH] + OH
13
4361
4343
-18
as CH2 + sciss CH2
14 15
4338 4267
4314 4255
-24 -12
as CH2 + sciss CH2 as CH2 + sciss CH2
16
4199
4197
-2
waggCH2 + CH
17 18
4175 4112
4163 4130
-12 18
twistCH2, COH] + CH twistCH2, COH] + as CH2
19
4069
4070
1
twistCH2 + s CH2
256
1)
257
As can be seen from Table 2, the calculated combinations involving stretching OH mode
258
have considerably lower agreement with the experimental wavenumbers. The relatively
259
poor accuracy of prediction of highly anharmonic modes, such as OH stretching, is known
260
limitation of VPT2 approach and it will be discussed in Section 2.6. It is noteworthy, that
261
this effect propagates onto combination modes involving OH vibration as well.
This discrepancy will be discussed in detail in Section 2.6.
262 12
263 264
2.3 Analysis of NIR spectrum of phenol.
265
NIR spectrum of phenol (Figure 4 and Table 3) can be roughly divided into three
266
subregions. The bands appearing in 6100-5900 cm-1 range arise mainly from the CH
267
stretching modes. The lower frequency NIR region, 5200-4000 cm-1, also is highly
268
characteristic with numerous sharp and intense peaks. These peaks originate mainly from
269
the combinations of ring deformation and CH stretching modes (Figure 4, Table 3). Note,
270
that due to lower symmetry compared to benzene molecule, the normal modes of phenol
271
ring are different (refer to Supplementary Material for animated presentation of all
272
normal vibrations of phenol molecule). The differences between NIR spectra of aliphatic
273
and aromatic alcohols will be discussed in detail in Section 2.7. Like in the case of
274
cyclohexanol the accuracy of calculated wavenumbers of the combinations involving OH
275
mode is relatively lower than that from the CH modes (Figure 4, Table 3).
276
A lower agreement between the simulated and experimental spectra in the
277
vicinity of 6000 cm -1 region, particularly noticeable in the case of alcohol molecules, is
278
related to lower accuracy of prediction of the first overtones of C-H stretching vibrations.
279
Although further studies would be needed to bring full explanation of this discrepancy, it
280
can be expected that inter-mode anharmonicity is the key factor standing behind it. The
281
fundamental C-H stretching vibrational levels have similar energy to the combinations of
282
the stretching and bending modes of the same groups; this effect can be followed by
283
comparing the spectra of the three alcohols (Figs. 2-4 and Tables 1-3), for which the
284
positions of CH modes clearly differ. The resulting degeneracy affects the involved states,
285
as illustrated by us before [44]. The reproduction of these degeneracies is more
286
challenging, particularly for VPT2 computational scheme, thus resulting in relatively lower
287
accuracy of the simulated spectra in the region around 6000 cm-1.
13
288 289 290 291 292 293
Figure 4. Experimental and calculated NIR spectra of phenol (0.2 M, CCl 4) and proposed band assignments. Band numbers correspond to those presented in Table 3. For better view of details refer to Fig. S3 in Supplementary Material.
Table 3. Experimental and calculated NIR bands of phenol and proposed band assignments.
Wavenumber / cm-1
Band
Band assignment
number
Experimental
Calculated
Difference
1
7052
6970
-82
2
5999
6073,6041
-
3
5940
5906
-34
2CH
4
5208
5164
-44
CC, CH] + OH
5
5079
5038
-41
CH, CC] + OH
6
4948
4844
-104
CH, COH] + OH
7
4782
4726
-56
COH,CC ] + OH
8
4677
4663
-14
[CC, CH] + CH
9
4645
4639
-6
[CC, CH] + CH
10
4617
4598
-19
[CC] + CH
11
4551
4546
-5
CH, CC] + CH(ip)1)
12
4384
4391
7
CC + CH
14
2OH 2CH CH + CH
294 295
1)
13
4309
4288
-21
CO, ring trigonal ] + CH
14
4226
4244
18
CO, ring trigonal ] + CH
15
4131
4088
-43
CC + CH(ip)1)
16
4061
4064
3
ring trigonal ,CC] + CH
17
4050
4044
-6
ring trigonal ,CC] + CH
CH(ip) denotes in-phase CH stretching mode; for the clarity all other CH modes in the table refer to
opposite-phase stretching;
296 297
2.4 Spectral contributions of overtones, binary combinations and conformational
298
isomers
299
An analysis of the simulated peaks makes possible to obtain insight into the origin of
300
NIR spectra (Figure 5A-C and Figures S5-S7 in Supplementary Material). The origin of NIR
301
peaks appearing in the spectra of studied alcohols is in general similar to that determined
302
for simpler alcohols.28,45 The relative influence of the overtone bands rapidly decreases
303
upon going to lower wavenumber region of NIR spectrum. In the 6100-5500 cm-1 region
304
occur comparable contributions from the first overtones and binary combinations.
305
However, the binary combinations are the most important features below 5500 cm-1. As
306
can be seen, in this region appear a large number of overlapped combination modes. As a
307
result, the 5500-4000 cm-1 region is very characteristic and sensitive to structural
308
differences; hence it resembles a “fingerprint” region known in IR spectroscopy.
309
The influence of conformational flexibility on the NIR spectrum is shown in Figures
310
6a-b. In the spectrum of n-hexanol (Figure 6a) occurs broad bands resulting from heavy
311
overlap of the contributions due to various conformational isomers. In the case of
312
cyclohexanol, where there is one major conformer (Figure 6b), the band separation is
313
much higher. This fact remains consistent with a higher band separation in the case of
314
phenol (Fig. 4), which only has one stable conformational isomer. The general trend, as
315
one would expect, is that the increase in conformational flexibility increases the
316
experimental bandwidths and decreases the overall “sharpness” of the peaks. Larger
317
number of contributing modes due to larger number of the isomers is the key factor here,
318
although their relative abundances should also be considered. The spectral regions in 15
319
which larger number of contributions appears are affected stronger. For studying the
320
subtle effects the most informative cases are cyclohexanol and phenol, as the difference
321
in the number of their relevant conformers. The lower NIR region (4500 – 4000 cm-1) is
322
affected the most, as evidenced by the calculated spectra (Fig. 3-4). The case of n-hexanol
323
demonstrates that large level of conformational flexibility leads to the broadening of the
324
bands in the entire NIR region (Fig. 2).
16
325 326 327 328 329
Figure 5. Contributions of the first overtone and binary combination bands to NIR spectra of (A) n-hexanol, (B) c yclohexanol, (C) phenol according to the results of GVPT2//B3LYP/SNST calculations. The intensities of calculated bands are in common scale with the final theoretical spectra . For better view of details refer to Figs. S4-S6 in Supplementary Material.
17
330
331 332 333
Figure 6. Contributions of the conformational isomers (narrow lines) into NIR spectra of (A) n-hexanol,
334
details refer to Figs. S8-S9 in Supplementary Material.
(B) c yclohexanol, according to the results of GVPT2//B3LYP/SNST calculations. For better view of
335 336
2.5 Analysis of the 2 OH band
337
The first overtone band of the OH stretching mode is highly specific in NIR spectra and
338
has been rich source of information about the structure and interactions of alcohols. The
339
position of this band is different for each of the three alcohols. For n-hexanol this band is
340
located at 7103 cm -1, for cyclohexanol at 7073 cm -1 and for phenol at 7052 cm -1. The
341
neighbouring of the cyclic structure and particularly an aromatic ring shifts the peak
342
position to lower wavenumbers as a result of lower electron density located at the
343
oxygen due to the ring effect. As it has been demonstrated, the shape of this peak is
344
influenced by the contributions from different conformational isomers.45 In the case
345
when only one conformer exist, i.e. methanol 28 or tert-butanol30,45 the shape of the 2 OH
346
is symmetric, if the associated forms do not contribute. A possible broadening of the
347
red-tail should be accounted for the higher order overtone and the combination bands of
348
weak intensity. 45 Figure 7 compares the envelopes of the 2 OH band for all studied
349
alcohols. Clearly, the molecule of phenol has only one conformer. The broadening of the
350
band for n-hexanol (Figure 7) is due to presence of two major components located at
351
7109 and 7081 cm-1 ( =28 cm-1), as evidenced in the second derivative spectrum. This
18
352
splitting was assumed to originate from frequency grouping of gauche and trans
353
conformers with respect to C-O bond (OH group).46
354
The 2 OH bandshape of cyclohexanol reveals similar splitting, but the relative
355
intensity of both rotational conformers is significantly higher (Figure 7). Again, this
356
observation remains consistent with the previous work.46 The major component appears
357
at 7074 cm-1, while and the minor one at 7047cm-1 of 27 cm-1). The presence of two
358
significant equatorial conformers (and two axial ones with negligible contribution) was
359
predicted by the calculations discussed in Sections 2.1 and 2.2. However, VPT2
360
calculations at B3LYP/SNST level provided a completely wrong picture of the 2 OH band,
361
by predicting a unrealistic position of the leading conformer (Figure 3).
362 363
Figure 7. NIR and second derivative spectra of studied alcohols (0.2 M; CCl4) in the region of the first
364
overtone of the OH stretching band.
365 366
2.6 Anharmonicity of the OH stretching mode and conformational analysis of
367
cyclohexanol
368
As shown a VPT2 calculation at B3LYP/SNST level does not provide reliable position of
369
the 2 OH band. To get more reliable insight into the conformational contributions to the
370
NIR spectrum and to improve the agreement with the experimental spectrum we 19
371
employed a detailed study on the anharmonic potential of the OH stretching vibration of
372
the two major conformational isomers of cyclohexanol. A scan of the potential energy
373
over a dense grid along with the OH stretching coordinate and subsequent solving of the
374
time-independent Schrödinger equation gives an accuracy of vibrational levels of the
375
order of less than 0.1 cm-1. Therefore, the only factor affecting the agreement with
376
experimental frequencies results from the accuracy of energy determination over the grid
377
points (Figure 8). This approach yields higher amount of anharmonicity compared to
378
VPT2 calculations at the expense of longer computational time.
379
In order to obtain highly accurate OH normal coordinate, the harmonic analysis was
380
performed at B3LYP/6-311++G(3df,3pd) level of theory. These calculations also resulted in
381
corrected order of the conformational stability (Table S2-S3 in Supplementary Material).
382
The inaccuracy of vibrational frequencies at B3LYP/SNST with anharmonic ZPE corrections
383
was propagated into inaccurate Gibbs free energies and thus Boltzmann coefficients.
384
By applying these two improvements we obtained much better agreement between
385
the calculated and experimental frequencies of the 2OH of cyclohexanol. First of all, the
386
band due to the major conformer (equatorial-gauche) appears at higher wavenumber
387
(7092 cm-1) than the following one (equatorial-trans, 7062 cm-1), which fully corresponds
388
to the conclusion drawn from the second derivative spectrum (Figure 7). Moreover, the
389
calculated splitting ( =30 cm-1) of both conformers is similar to the experimental value
390
( =27 cm-1), while VPT2 calculations completely failed in this case ( =260 cm-1), as
391
evidenced in Table 4. The 2 OH frequencies obtained by solving Schrödinger equation
392
were overestimated by 18 cm -1 and 15 cm-1 for gauche and trans conformers, respectively.
393
However, these values correspond only to 0.25% and 0.21% of the relative error (Table 4).
20
394 395
Figure 8. Vibrational potential and vibrational states [B3LYP/6-311 G(d,p)] of the OH stretching mode of
396
the main (equatorial-gauche) conformer of cyclohexanol.
397 398 399
Table 4. The comparison of 2 OH vibrational frequencies in [cm -1] of two main conformers of
400
equation based on scanning of the potential energy along the 2 OH normal coordinate.
cyclohexanol determined with the use of VPT2 approach and numerical solving of Schr ödinger
exp.
calc. (VPT2//B3LYP/SNST)
calc. (V(Q) probing//
B3LYP/6-311G(d,p))
equat. gauche
7074
7043
7092
equat. trans
7047
6783
7062
27
260
30
401 402
2.7 Generalized spectra-structure correlations in n-hexanol, cyclohexanol and phenol
403
NIR spectra of three types of alcohols, open-chain and cyclic aliphatic and aromatic
404
ones, reflect structural features of these molecules. The 2 OH band (7150 – 7000 cm-1)
405
was analysed in detail in Section 2.5 and its spectral parameters are strongly connected to
406
the molecular structure. At first, we elucidate the similarities and differences between 21
407
n-hexanol and cyclohexanol and afterwards we discuss the major features that distinct
408
the aliphatic alcohols from the aromatic ones.
409
The regions of 5900-5500 cm-1 and 5100-4400 cm-1 of n-hexanol and cyclohexanol
410
look similar (Figure 2-3). The spectrum of open-chain alcohol shows enhanced band
411
broadening due to significant conformational flexibility and the existence of additional
412
combination bands involving the methyl group vibrations. Apart of that, the origin of the
413
respective bands of these two alcohols is similar. The differences in the 4500-4000 cm-1
414
region are more pronounced, with much higher band separation in the case of
415
cyclohexanol. Linear hexanol reveals a single major peak at 4336 cm -1 (combination of the
416
stretching and bending modes of CH 2 and CH3) followed by a weaker one at 4265 cm -1.
417
This observation is consistent with that reported for butyl alcohols.30 It seems that
418
uniformity of the ~4336 cm-1 peak is enhanced by the conformational flexibility, as the
419
molecules having lower number of isomers tend to exhibit a separation of the major band
420
into two peaks.30 In the cyclic hexanol these two bands (4338 and 4267 cm -1) are more
421
separated and the latter one is the more intense. The 4200-4000 cm-1 region for
422
n-hexanol reveals heavy broadening, while in the spectrum of cyclohexanol are observed
423
two separated peaks. This results from significantly lower number of conformational
424
isomers and relatively higher separation of the fundamentals of in-ring CH2 deformation
425
modes in cyclohexanol.
426
The differences between the aliphatic and aromatic alcohols are more evident (Figure
427
2-4). Phenol has a strong band at 5999 cm -1, while the aliphatic alcohols possess a broad
428
band envelope from 5900 cm-1 to ~5500 cm-1. Further, the region between 5300 and 4000
429
cm-1 shows distinct differences between the aliphatic and aromatic alcohols. In the entire
430
region the band separation for phenol is notably higher. Between 5300 and 4750 cm-1
431
phenol has three strong, well separated peaks (combinations of OH+ CC, CH), while
432
aliphatic alcohols have much weaker and heavily overlapped bands ( OH+ CH2). Again,
433
better division of CC,CH fundamentals of phenol in IR region can be attributed to this
434
distinct NIR bands separation. 22
435
Further, the pattern of intensity ratio in the region of 5300-4000 cm-1 is different for
436
aliphatic and aromatic alcohols. Between 5300 and 4500 cm -1 phenol shows
437
medium-to-strong (5300-4900 cm-1) and strong bands (4900-4500 cm-1) followed by
438
significant absorbance decrease between 4500-4150 cm-1, interrupted by a sharp peak at
439
4309 cm-1 (CH+ CO, ring trigonal ). Next, the absorbance rises again developing a sharp
440
band at 4061 cm -1 ( CH+CO, ring trigonal ). Assuming arbitrary sub-regions (in cm-1) of
441
roughly a. 5300-4900; b. 4900-4500; c. 4500-4100; d. 4100-4000; the aliphatic alcohols
442
feature (a-b-c-d): w-vw-vs-m (weak, very weak, very strong, medium) bands, while
443
phenol m-s-w-vs ones. This order of relative intensities allows for very reliable distinction
444
between aliphatic and aromatic alcohols.
445 446
3. Summary
447
NIR spectra of n-hexanol, cyclohexanol and phenol were accurately reproduced by
448
anharmonic DFT calculations. By taking into account the first overtone and binary
449
combination bands originating from individual conformational isomers (a selection of the
450
most relevant population was necessary in the case of n-hexanol) it was possible to
451
achieve very good agreement between the calculated and experimental spectra. Detailed
452
assignments of all significant bands in NIR region from 7500 to 4000 cm-1 were proposed
453
and the spectra-structure correlations were estimated on that basis.
454
VPT2 calculations appear to be very useful for applied spectroscopic studies, as they
455
provide accurate reproduction of entire NIR spectra. However, this approach is somewhat
456
limited in an accurate description of vibrational modes strongly deviating from the
457
harmonic oscillator model, like the 2 OH vibration in cyclohexanol. This problem was
458
addressed by scanning of the vibrational potential over a dense-grid and subsequent
459
solving of the time-independent Schrödinger equation This way, not only the details of
460
the 2 OH band were fully elucidated, but also the predicted equilibrium between
461
different conformations were in line with those obtained from the experimental spectrum
462
of cyclohexanol. 23
463
The studied molecules are model structures for important biomolecules, in which an
464
OH group is attached to various kinds of chemical environments. Therefore, the obtained
465
correlations between the structural features and the corresponding NIR spectra should
466
provide good basis for better understanding of the spectral details for a wide range of
467
compounds.
468 469
Supplementary Material
470
This article contains Supplementary Material.
471 472
Acknowledgement
473
Calculations have been carried out in Wrocław Centre for Networking and
474
Supercomputing (http:/www.wcss.pl), under grant no. 375.
475 476
24
477
Authors
478
Krzysztof B. Beć
479 480
Krzysztof B. Bed obtained his PhD degree (2014) in Physical and Theoretical Chemistry
481
from University of Wrocław, Poland. His research involved thin-film infrared spectroscopy,
482
optical constants and computational spectroscopy. He joined Professor Yukihiro Ozaki
483
research team as a postdoctoral fellow at Kwansei Gakuin University, Japan (2015) where
484
he was involved in developing applications of anharmonic methods in simulation of
485
near-infrared spectra. He continued his work in basic and applied NIR spectroscopy in
486
Prof. Christian W. Huck team at University of Innsbruck, Austria (2016). Afterwards, he
487
re-joined Professor Yukihiro Ozaki team at Kwansei Gakuin University as an assistant
488
professor, where he is currently involved in development of ATR-FUV spectroscopy and its
489
application in studies of polymer-carbon nanostructure composites.
490 491
Justyna Grabska
492 493
Justyna Grabska obtained PhD degree (2015) in Physical and Theoretical Chemistry from
494
University of Wrocław, Poland. Her work is focused on vibrational spectroscopy,
495
high-frequency dielectric function and scientific programming. She started her research in
496
the field of near-infrared spectroscopy after joining Prof. Christian W. Huck team as a
497
postdoctoral fellow at University of Innsbruck, Austria (2016). Her current research as a 25
498
postdoctoral researcher in Professor Yukihiro Ozaki group focuses on computational NIR
499
spectroscopy.
500 501
Mirosław A. Czarnecki
502 503
Mirosław Czarnecki obtained his M. Sc. (1981) and Ph.D. (1989) degrees in Physical and
504
Theoretical Chemistry from the University of Wrocław. He was a postdoctoral fellow at
505
Kwansei Gakuin University, Japan (1992-1993) and University of Essen, Germany (1995).
506
At present, he is a professor at the Faculty of Chemistry, University of Wrocław, Poland.
507
His current research involve hydrogen bonding, molecular structure, microheterogeneity
508
in binary liquids, liquid crystals, MIR, NIR and Raman spectroscopy, computer aided
509
spectroscopy, 2D correlation analysis, chemometrics and theoretical calculations.
510
26
511
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29
