A Theoretical Study of Spectroscopic Properties of a Hemiacetal by TDDFT Method

Introduction

The formation of acetals as a result of reaction between aldehydes and alcohols is known to proceed through the formation of the corresponding hemiacetals (structure I, Figure 1). These hemiacetals are highly unstable and difficult to isolate and therefore it is not possible to record the spectra of pure hemiacetals. Their existence in reasonable concentration in solutions, however, has been postulated in a number of cases ^1-3 and spectroscopic data of some of such compounds in reaction medium have been reported.^{2, 3} The proposed hemiacetal structure and the reported spectra in reaction mixture can only be justified by theoretical calculation. The density functional theory (DFT) ^{4, 5} is currently being applied for carrying out a variety of quantum chemical calculations ranging from geometry optimization of large clusters⁶ to the study of reaction rates.^{7, 8} For theoretical prediction of spectroscopic properties (transition energy, oscillator strength etc.), the time dependent density functional theory (TDDFT) has been developed ^{9- 11} and is now being widely used.^{12- 13} The objective of the present work is to calculate the infrared absorption frequencies, UV-vis absorption maxima and NMR chemical shifts of the unstable molecule, 1-methoxy ethanol (Structure II, Figure 1) by applying the computational method of TDDFT and comparing them with available experimental data.^{2, 3} Effect of change in solvent polarity on the UV-vis spectrum has also been studied theoretically and the results are expected to have some predictive value for spectroscopic investigations of similar compounds which may be formed in situ during chemical reactions.

Computational details

All computations were performed on a Pentium computer with Gaussian 03 Revision D.01 suite of programmes.¹⁴ DFT calculations were done by using the Becke’s three parameter hybrid¹⁵ exchange potential with the correlation function of Lee, Yang and Parr ¹⁶ (B3LYP). The basis sets 6-31+G(d), 6-31++G(d,p) and 6-311+G(d,p) were used. Optimization of the ground state geometry of the molecule at B3LYP level was carried out in vacuum and also in Tetrahydrofuran (THF), Chloroform (CHCl₃), acetonitrile (CH₃CN), dimethylsulfoxide (DMSO) and methanol (MeOH) solutions by the polarizable continuum model ^{17, 18} (PCM). Using the ground state optimized geometry, the vibrational frequencies, ¹H and ¹³C NMR chemical shifts and electronic transition energies were calculated. Similarly by using the TDDFT method under the PCM formalism the electronic transition energies in THF, CHCl₃, CH₃CN, DMSO and MeOH medium were calculated. In the PCM, the solute is placed in the solvent reaction field cavity created by a series of overlapping spheres initially devised by Tomasi et. al. ^{17, 18} and implemented by Barone et. al. ^{19- 20} also by Tomasi and co-workers ^{21, 22}.

Results and Discussions

Optimized Geometry

The optimized geometry of the hemiacetal of acetaldehyde (compound II, Figure 1) computed at B3LYP/6-31++G(d,p) level in vacuo and in dimethyl sulfoxide (DMSO) is shown in Figure 2 along with the necessary atom labels. The calculated structural details are summarized in Table 1. Such optimization has also been carried out in four other solvents of varying polarity and also using the 6-31+G(d) basis set; these results are given as supplementary material.

Results of thermo-chemical calculation, as given in Table 2, indicate that in going from vacuum to solution phase the stability of the hemiacetal increases and that too, with increase in solvent polarity (dielectric constant, ε). This suggests that the hemiacetal molecule should be polar, and this is substantiated by the calculated dipole moment of about 3.2 D (Table 1 and also in supplementary material). It is also to be noted that change of basis set from 6-31+G(d) to 6-31++G(d,p) brings about an increase in stabilization energy of about 9.5 kcal mol^-1 (Table – 2).

Figure 1:  Formation of (I) hemiacetal by reaction between an aldehyde (RCHO) and an alcohol  (R1OH); hemiacetal (II) formation by reaction between acetaldehyde and methanol. Click here to View figure

Figure 2: The optimized geometry of the hemiacetal of acetaldehyde (compound II, Figure 1) computed at B3LYP/6-31++G(d,p) level in vacuum. Click here to View figure

 

Table 1:  Main structural features (bond length, bond angle, dipole moment) of the optimized   geometries in vacuum and in DMSO solvent calculated with 6-31+G(d) and 6-31++G(d,p) basis set. Atom labels refer to Fig. 2.

Geometrical Parameter	B3LYP/6-31+G(d)		B3LYP/6-31++G(d,p)
	Vacuum	DMSO	Vacuum	DMSO
R(C1-O5) /  Å	1.426	1.433	1.426	1.434
R(O5-C10) /  Å	1.419	1.425	1.419	1.426
R(O3-H4) /  Å	0.972	0.988	0.968	0.984
A(O3-C1-O5) / deg	107.1	107.3	107.1	107.3
A(O3-C1-C6) / deg	107.7	108.1	107.7	108.1
A(O5-C1-C6) / deg	113.0	112.1	113.0	112.0
A(C1-O3-H4) / deg	107.7	108.6	107.7	108.7
A(C1-O5-C10) / deg	114.9	114.5	114.9	114.4
Dipole moment / Debye	2.3164	3.2535	2.2908	3.2386

Table 2: Variation of ground state energy of the hemiacetal with solvent polarity calculated at DFT /B3LYP level using two basis sets; the absolute energies include zero-point correction.

Medium	Dielectric constant of solvent	Absolute energy / Ha		Energy relative to vacuum (kcal mol-1)
		6-31+G(d)	6-31++G(d,p)	6-31+G(d)	6-31++G(d,p)
Vacuum	–	-269.465167	-269.480562	0.00	0.00
CHCl3	4.9	-269.475150	-269.490404	-6.26443	-6.17595
THF	7.58	-269.476783	-269.492023	-7.28915	-7.19189
MeOH	32.63	-269.479858	-269.495075	-9.21874	-9.10705
CH3CN	36.64	-269.479918	-269.495133	-9.25640	-9.14344
DMSO	46.70	-269.480087	-269.495292	-9.36244	-9.34222

UV-vis spectra

The electronic transitions were calculated by the TDDFT method in vacuum and in five different solvents, namely, tetrahydrofuran (THF), chloroform (CHCl₃), acetonitrile (CH₃CN), methanol (MeOH) and dimethylsulfoxide (DMSO) at the B3LYP level of theory with basis sets 6-31+G(d) and 6-31++G(d,p), using 30 singlet states in each case. The PCM formalism was used for calculation in solution phase and the respective optimized ground state geometries in the above mentioned solvents were used as input. Five absorption bands were found to have reasonable oscillator strength within the region of 150 nm. Some more absorption bands with strong oscillator strength were observed below 150 nm, but such bands fall deep within the vacuum UV region and were discarded as they might not be observed experimentally. Changing the medium from vacuum to different solvents causes a blue shift for all the calculated absorption bands. Some important transitions are shown in Table 3. A representative UV-vis spectrum of 1-Methoxy ethanol in CHCl₃ medium calculated at TDDFT/B3LYP/6-31++G(d,p) level is given in Figure 3.

Electronic transitions in the long wavelength region (above 150 nm) with the maximum oscillator strengths are found to follow a certain trend with change in solvent polarity. For example, the transition energies shown in Table 4 increase with two important solvent polarity indices, namely,  E_T(30) and Z-value of the solvents (introduced by Reichardt  ²³ and Kosower ²⁴ respectively) with an exception in case of chloroform. The variation of electronic transition energy (Kcal mol^-1)with two solvent polarity indices, E_T(30) and Z is shown in Figure 4. This indicates a specific type of interaction between molecule II and chloroform. However, the slow overall increase of transition energy with solvent polarity hints at an uneven distribution of electronic charge in the ground state which gives rise to an appreciable dipole moment of the hemiacetal molecule.

Table 3: Transition energies (eV), wave lengths of absorption maxima (nm) and oscillator strengths (f) of electronic transitions of 1-Methoxy ethanol in different media calculated by TDDFT method using two basis sets.

Medium	B3LYP/6-31+G(d)	B3LYP/6-31++G(d,p)
Vacuum	eV          nm          f  6.901     179.66   0.0137 7.2611   170.75   0.0326 7.4144   167.22   0.0424	eV          nm          f  6.6189   187.32   0.0136 6.9064   179.52   0.0305 7.041     176.09   0.0416
CHCl3	eV          nm          f  7.0542   175.76    0.0144 7.3004   169.83    0.0536 7.5102   165.09    0.0247	eV          nm          f 6.7551   183.54   0.0139 6.9499   178.4     0.0434 7.1042   174.52   0.0405
THF	eV          nm          f 7.0787   175.15   0.0142 7.3027   169.78   0.055 7.5365   164.51   0.0228	eV          nm          f 6.7781   182.92   0.0136 6.9537   178.3     0.0438 7.1117   174.34   0.0382
MeOH	eV          nm          f 7.1276   173.95   0.0141 7.3164   169.46   0.0559 7.5945   163.25   0.0228	eV          nm          f 6.8265   181.62   0.0132 6.9729   177.81   0.0437 7.1326   173.83   0.0339
CH3CN	eV          nm          f 7.1292   173.91   0.0145 7.3142   169.51   0.0565 7.596     163.22   0.0227	eV          nm          f 6.8271   181.61   0.0134 6.9719   177.84   0.0441 7.1319   173.84   0.0338
DMSO	eV          nm          f 7.128     173.94   0.0149 7.3124   169.55   0.0593 7.594     163.27   0.0245	eV          nm          f  6.8277   181.59   0.0139 6.971     177.86   0.0463 7.1312   173.86   0.035

Figure 3: UV-vis spectrum of 1-Methoxy ethanol in CHCl3 medium calculated by TDDFT method at B3LYP/6-31++G(d,p) level. Click here to View figure

 

Table 4: Variation of transition energy of UV absorption maximum of 1-methoxy ethanol with solvent polarity.

Solvent	ET(30) / kcal-mol-1	Z / kcal-mol-1	E / kcal-mol-1
THF	37.4	–	160.35
CHCl3	39.1	63.2	160.26
DMSO	45.1	71.1	160.74
CH3CN	45.6	71.3	160.76
MeOH	55.4	83.6	160.79

 

Figure 4: Variation of electronic transition energy with two solvent polarity indices, ET(30) and Z. Click here to View figure

 

Infrared spectra

With the optimized geometries obtained at B3LYP level in vacuum, THF, CHCl₃, CH₃CN, DMSO and MeOH the vibrational frequencies were calculated with 6-31+G(d) and at 6-31++G(d,p) basis sets and compared with the reported experimental results of the IR absorption bands of the hemiacetal of acetaldehyde. Anharmonicity effects were also taken into account at five different temperatures and the thermochemical results are given in the supplementary materials. Both harmonic and anharmonic frequencies are given in Table 5 along with reported experimental values ^{5, 6} in methanol medium. The theoretical calculated frequencies are in good agreement with the experimentally observed values, particularly if anharmonicity effect is considered.

The absorption around the region of 345 cm^-1 is due to various bending vibrations present in the molecule, the absorption within the region between 1150 cm^-1 to 1000 cm^-1 is due to different O-C stretching and bending of the ether linkage present in the molecule, the absorption region around 3100 cm^-1 is due to C-H stretching vibrations, and the absorption region in between 3800 cm^-1 and 3300 cm^-1 is due to O-H stretching. Table 5 lists the important vibrations observed in the hemiacetal molecule in different media. One calculated IR spectrum of 1-methoxy ethanol is also shown in Figure 5. The displacement vectors corresponding to the predicted vibrational mode at 1104 cm^-1 in CHCl₃ medium, calculated at TDDFT/B3LYP/6-31++G(d,p) level, is represented in Figure 6.

Table 5:  Vibrational frequency data of 1-Methoxy ethanol calculated at 6-31+G(d) and 6-31++G(d,p) basis sets with and without connection for anharmonicity

Medium	Frequency (cm-1)
	B3LYP/6-31+G(d)		B3LYP/6-31++G(d,p)		Experimental  (in MeOH)
	Harmonic	Anharmonic	Harmonic	Anharmonic
Vacuum	939 1119 1125 1169 1233 3734	921 1093 1140 1157 1204 3556	935 1112 1121 1164 1227 3810	917 1087 1150 1136 1250 3637	920,1100 – 1150 (with a peak at 1140), 1210
CHCl3	840 1105 1111 1155 1280 3508	943 972 1042 1038 1061 3244	929 1028 1100 1104 1149 3569	978 1080 1117 1147 1254 3321
THF	931 1103 1153 1230 3464	931 1160 1133 1198 3146	927 1148 1173 1223 3531	911 1173 1200 1232 3220
MeOH	1098 1106 1118 1149 1276 3382	931 999 1229 1082 1235 3019	1030 1110 1143 1174 1265 3447	917 953 1222 1178 1216 3083
CH3CN	928 1099 1105 1148 1228 3380	985 1077 1149 1139 1206 3016	1030 1095 1096 1143 1222 3444	1010 1110 1033 952 1167 3092
DMSO	838 1036 1098 1103 1149 3374	937 947 916 1017 1047 3194	924 1094 1143 1173 1222 3439	1040 1052 1120 1140 1215 3293

 

Figure 5: Theoretically predicted infra red spectrum of 1-Methoxy ethanol in CHCl3 medium calculated at B3LYP/6-31++G(d,p) level. Click here to View table

Figure 6: Displacement vectors of the vibrational mode at 1104 cm-1 of 1-Methoxy ethanol in CHCl3 medium calculated at B3LYP/PCM/ 6-31++G(d,p) level   Click here to View figure

 

¹H and ¹³C NMR spectra

For calculation of NMR chemical shifts the structure was optimized at B3LYP/6-311G(2d,p) level in CHCl₃ medium by the PCM formalism ^{16- 18} and the optimized geometry was subjected to NMR calculations by the guage-independent atomic orbital method. Results are given in Table 6 where the atom labels refer to Fig.1. The ¹³C NMR spectrum is represented in Figure 7. The calculated ¹³C NMR spectrum shows three distinct signals (Fig. 7), corresponding to three different carbon environments in the hemiacetal molecule as evident from the optimized structure (Figure 2); the theoretically obtained chemical shifts are in accordance with the electronic charge distribution obtained by natural population analysis. The calculated chemical shifts for ¹H NMR are clustered in the region 0.8 – 5.02 δ as shown in Table 6. The reported experimental values ² are also in this range. Moreover, it is noteworthy (from Table 6) that the ¹H NMR shifts vary in accordance with the natural charges on the H-atoms – higher electronic charge resulting in upfield resonance.

Table 6: ¹H and ¹³C NMR chemical shifts (δ, ppm) and electronic charge distribution of 1-methoxy   ethanol calculated at DFT/B3LYP/6-311+G(2d,p) level in CHCl₃ solvent.Atom labels are in accordance with Figure 2.

Atom type	GIAO NMR Isotropic shielding with respect to TMS (δ, ppm)	Electronic Charge distribution
H2	5.02	0.13943
H4	2.29	0.49775
H7	1.35	0.20429
H8	1.19	0.21238
H9	0.80	0.21024
H11	3.29	0.16282
H12	3.60	0.18792
H13	3.21	0.16274
C1	103.40	0.43955
C6	18.21	-0.61136
C10	55.16	-0.20759

Figure 7: 1H NMR spectrum of 1-Methoxy ethanol in CHCl3 medium calculated at TDDFT/B3LYP/6-31++G(d,p) level. Click here to View figure

 

Summary

Attempts have been made to circumvent the difficulty in experimental detection and characterization of unstable hemiacetals by DFT- and TDDFT-based computational predictions. One such hemiacetal of interest, namely, 1-methoxy ethanol has been considered. Its structural and spectroscopic properties (UV-vis, IR, ¹H and ¹³C NMR) in vacuum and in a series of solvents with varying solvent polarity have been calculated. The computed results are in good agreement with reported experimental data. In case of IR, consideration of anharmonicity effect yields better agreement with experiment. The UV-vis spectra are predicted to show somewhat regular blue shift with increase in solvent polarity.

Acknowledgement

P. D. thanks the UGC, New Delhi for the financial assistance extended through a minor research project (Project No. F.PSW-006/09-10).

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