Theoretical Chemistry Accounts

, 131:1183

Modelization of vibrational spectra beyond the harmonic approximation from an iterative variation–perturbation scheme: the four conformers of the glycolaldehyde

Authors

    • Groupe Chimie Théorique et Réactivité, ECP, IPREM UMR CNRS 5254Université de Pau et des Pays de l’Adour 2
    • Groupe Chimie Théorique et Réactivité, ECP, IPREM UMR CNRS 5254Université de Pau et des Pays de l’Adour 2
Regular Article

DOI: 10.1007/s00214-012-1183-1

Cite this article as:
Carbonniere, P. & Pouchan, C. Theor Chem Acc (2012) 131: 1183. doi:10.1007/s00214-012-1183-1
Part of the following topical collections:
  1. Barone Festschrift Collection

Abstract

This paper presents the computed anharmonic frequencies and IR intensities in the mid-infrared region for the four conformers of glycolaldehyde (Cis cis, Trans trans, Trans gauche and Cis trans forms). The fundamental transitions and their connected overtones and combination bands through strong anharmonic couplings (Fermi resonances) are provided. The results are stemmed from an iterative variational–perturbational resolution of the vibrational problem implemented in the VCI-P code. The four potential electronic surfaces are built as a Taylor series truncated to the fourth order around each minimum geometry. The second derivatives with respect to the normal coordinates were computed at the CCSD(T)/cc-pVTZ level, while the third and fourth derivatives were estimated with the B3LYP/6-31 + G(d,p) model chemistry. For the most stable Cc form, an average deviation of about 10 cm−1 is obtained with respect to the unambiguous experimental values. Furthermore, some of the transitions observed in the CH stretchings region were reassigned. The theoretical values calculated for the Tt and Tg forms are compared to the experimental data obtained from the irradiation of the Cc conformer isolated in Ar matrix with an IR source.

Keywords

Ab initioDFTAnharmonic vibrational spectraGlycolaldehydeIR intensities

1 Introduction

The vibrational fingerprint of a molecular system that infrared (IR) or Raman spectroscopy allows to observe is a widely used information for substance recognition and for the understanding of its behavior within a chemical environment. Thus, it is also used for applications such as structural and conformational analysis [13] reactivity monitoring [4, 5] and molecular design [6].

The subtle interplay between the different effects that induce the experimental picture of such fingerprint makes the identification task non-trivial, particularly when the molecular system presents strong anharmonic couplings giving rise to IR (or Raman)-active overtones and combination bands. From a theoretical point of view, the need to go beyond the harmonic approximation for an accurate modelization of a vibrational spectrum requires to face the computational cost that makes the treatment impracticable in its most complete formalism.

In the framework of the time independent formalism, several models have been developed and implemented to explicitly take into account anharmonicity. For small molecules (3–5 atoms), converged rovibrational levels can be obtained by fully variational methods, that is, the discrete variable representation (DVR) [7] or the vibrational configuration interaction (VCI) [8] methods. For larger molecules, four approximate schemes have been proposed. The vibrational self-consistent field (VSCF) approach represents the total vibrational wave function by a separable product of single-mode wave functions optimized separately using an effective mean field potential [9]. For a better accuracy, the correlation between modes is commonly treated by (i) the vibrational Moller–Plesset perturbation theory (VMP) [10] that is computationally cheap but overestimates the strong anharmonic complings, (ii) a vibrational configuration interaction (VCI) [8] that treats properly the strongest interactions but proves much more time consuming, (iii) the vibrational mean field configuration interaction (VMFCI) [11] that plays on the partitioning of the vibrational modes and encompasses both VSCF and VCI as particular case and (iv) the vibrational coupled cluster (VCC) [12] level of theory. Several strategies to strongly reduce the computational cost of such treatment were proposed in the literature [1316] (see Ref. [16] for a more detailed description). A possible way which is used in the present study is to take advantage of both perturbative and variational approaches [17]. This variational–perturbational scheme in its most advanced version has been implemented in the VCI-P code [16] that uses small VCI matrices to treat the strongest interactions while the myriads of the weakest interactions are treated perturbationally (see the section computational details and method). Such a recipe was used to investigate the vibrational properties of the four conformers of glycolaldehyde (CH2OHCHO).

The glycolaldehyde is the first monosaccharide detected in the interstellar medium which has increased the interest in the study of isomerism in interstellar chemistry (see Ref. [18] and therein). Among its four conformers [18, 19] so-called Cc, Tt, Tg and Ct (see Fig. 1), only the Cc conformer was detected from IR/Raman spectroscopy in gas phase [2023] or in matrix isolation [24, 25], while the Tt form is observed from IR-induced conformer interconversion process in low-temperature matrices.
https://static-content.springer.com/image/art%3A10.1007%2Fs00214-012-1183-1/MediaObjects/214_2012_1183_Fig1_HTML.gif
Fig. 1

The four conformers of glycolaldehyde and their corresponding relative energy (in kJ·mol−1) computed at the aCCSD(T)/cc-pVTZ level of theory (our work) and bMP4(SDTQ)/cc-pVQZ (see Ref. [18])

In the present study, we report the computed anharmonic fundamental transitions and their connected overtones or combination transitions through Fermi resonances of the four conformers of glycolaldehyde at least for two reasons (i) because of the presence of strong anharmonic couplings in the CH stretching region in which the assignment of the vibrational transitions appears non-univocal for the Cc and Tt conformers and (ii) because no experimental data are reported for the Tg and Ct forms.

2 Computational details and method

Computations at the CCSD(T) [26] level of theory were performed with the CFOUR [27] program, while Gaussian 09 [28] was used for the DFT computations. The anharmonic vibrational treatment relies on a hybrid [29] quartic force field in which the second derivatives are computed at the CCSD(T)/cc-pVTZ [30] level of theory, while the third and fourth derivatives are computed at the DFT level using the B3LYP functional [31, 32] with a valence double zeta Pople basis set including diffuse and polarization functions, 6–31+G(d,p) [33]. This model chemistry was chosen since it has been previously shown [34, 35] that for the prediction of harmonic and anharmonic force constants and in the case of small organic systems, it is able to approach the results obtained using the more expensive CCSD(T)/cc-pVTZ level of theory by an average value of 10 cm−1 on the fundamental transitions.

The analytic model of the potential functions is determined as follows [36]: from a minimum energy structure of a given system, a quartic force field is built in which the third and fourth derivatives are computed by 6 N–11 (N = number of atoms) numerical differentiation of analytical second derivatives. In the quartic approximation, the potential provided by the Gaussian code is a Taylor series in normal coordinates limited to the 3-mode interactions. From a technical point of view, it can be shown [36] that the best setup is obtained using a step size of 0.01 Å for the numerical differentiation of harmonic frequencies, tight convergence criteria for structural optimizations and fine grids for integral evaluation (that is, at least 99 radial and 590 angular points).

The Hamiltonian used is the pure vibrational Hamiltonian as detailed in Ref. [37]:
$$ \hat{H} = \frac{1}{2}\sum\limits_{i} {\omega_{i} p_{i}^{2} } + V_{{(q_{1} , \ldots ,q_{M} )}} + \sum\limits_{\alpha } {B_{\alpha } \left( {\sum\limits_{i,j \ne i,k,l \ne k} {\zeta_{ij}^{\alpha } \zeta_{kl}^{\alpha } q_{i} p_{j} q_{k} p_{l} \sqrt {\tfrac{{\omega_{j} \omega_{l} }}{{\omega_{i} \omega_{k} }}} } } \right)} $$
(1)
where qi and pi are, respectively, the dimensionless normal coordinates and their conjugate momenta. V (q1,…, qM) is a polynomial expansion of the PES in terms of normal coordinates qi truncated to the fourth order The last term represents the major component of the rotational contribution to the anharmonicity in which Bα is the rotational constant of the system with respect to the Cartesian axis α, and \( \zeta_{ij}^{\alpha } \) is the Coriolis constant that couples qi and qj through the rotation about the α axis.

The anharmonic vibrational treatment is based on an iterative variational–perturbational scheme implemented in the VCI-P code [16]. This code computes the anharmonic wavenumbers and the anharmonic IR intensities of the fundamental transitions, overtones and combination bands which are IR (or Raman) actives through strong anharmonic couplings (Fermi or Darling Dennisson resonances).

Here, we recall [16] that the VCI-P method consists in 3 N–5 independent VCI computations (one for the fundamental state and one for each mono-excitation). For each VCI computation, an automated procedure builds iteratively an active space by selecting, through the second-order perturbational formula, the vibrational configurations that lead to the strongest couplings with the states of interest. Each active space gathers from some dozens to some hundreds of configurations while the weakest interactions, up to several hundred of thousands, are discarded from the variational process and contribute perturbationally to the anharmonicity:
$$ E_{i,L}^{VCI - P} = E_{i,L}^{VCI} + \sum\limits_{{j_{weak} }}^{{N_{weak} }} {\frac{{\left\langle {\Uppsi_{i,L - 1}^{{n_{i} }} } \right|\hat{H}\left| {\Upphi_{{j_{weak} ,L}}^{{n_{j} }} } \right\rangle^{2} }}{{E_{i}^{0} - E_{{j_{weak} ,L}}^{0} }}} $$
(2)

The process is ended at the Lth iteration when the convergence on the VCI-P energy of the state i is reached. It has been set to 0.2 cm−1 in the present study. Note that in the above expression, \( E_{i,n}^{VCI} \) corresponds to the VCI energy obtained by the diagonalization of an active space containing the Nstrong configurations \( \Upphi_{k}^{{n_{k} }} \),\( \Upphi_{k}^{{n_{k} }} \) being the nkth excitations of the configuration i. The second term represents the perturbational contribution of the weakest configurations \( \Upphi_{j}^{{n_{j} }} \)interacting with the state \( \Uppsi_{i}^{{n_{i} }} \)determined variationally at the iteration L-1.

Thus, any state of interest \( \Uppsi_{i}^{{n_{i} }} \) appears as a linear combination of the most pertinent configurations \( \Upphi_{k}^{{n_{k} }} \)that belong to the final active space:
$$ \Uppsi_{i}^{{n_{i} }} = \sum\limits_{k}^{Nstrong} {c_{ik} } \Upphi_{k}^{{n_{k} }} $$
(3)

Note that any configuration \( \Upphi_{k}^{{n_{k} }} \) for which \( c_{ik}^{2} \) is greater than a threshold (4% in the present study) is considered as a strong resonant configuration. As consequence, their multiexcitations are generated from the procedure detailed above up to the convergence of their VCI-P energy. This ensures for each CI matrix the orthogonality between the state \( \Uppsi_{i}^{{n_{i} }} \) and its connected states through Fermi resonances for which the corresponding anharmonic intensities can be determined more safely.

Furthermore, this program allows the computation of anharmonic intensities [16]: starting from the quadratic expansion of the dipole surface, the second derivatives of dipole moment, dij (where α is a Cartesian component of the dipole moment vector dj referred to the Eckart axes) are calculated in a manner analogous to the cubic and quartic force constants detailed above:
$$ D_{\alpha } = D_{\alpha } (0) + \sum\limits_{i} {d_{{\alpha_{i} }} q_{i} } + \tfrac{1}{2}d_{{\alpha_{ij} }} q_{i} q_{j} $$
(4)
The anharmonic intensity between an initial state i and a final state j is then evaluated as follows:
$$ I_{i,j} = \tfrac{{8\pi^{3} N_{A} }}{{3hc(4\pi \varepsilon_{0} )}}\nu_{i,j} \sum\limits_{\alpha } {\left\langle {\Uppsi_{i,L} } \right|D_{\alpha } \left| {\Uppsi_{{j,L^{'} }} } \right\rangle^{2} } (N_{i} - N_{j} ). $$
(5)

3 Results and discussion

Table 1 reports the vibrational transitions in the mid-infrared region of the glycolaldehyde in its Cc form. The first column corresponds to the description of the modes in terms of functional groups involved in the vibrational transition as reported in Ref. [25]. In the column 3, are reported data stemmed from a gas phase IR spectrum recorded at 300 K [23], while the data in columns 4 and 5 are issuing from low-temperature experiments in Ar matrix [24, 25]. These are compared to our theoretical results comprising the anharmonic wavenumbers, their corresponding anharmonic intensities and their theoretical descriptions. In the last columns are reported the second-order perturbative results available in the literature from a MP2/6-311++G(d,p) quartic force field [25].
Table 1

Calculated wavenumbers (cm−1) for the glycolaldehyde in its Cc form with the VCI-P method from a CCSD(T)/cc-pVTZ//B3LYP/6-31G(d,p) hybrid quartic force field

Description

Mode

Experimental

Calculations

Gas phasea

Arb

Arc

νVMP2d

νVCI–Pd

Iνd

Descriptiond

νe

OH stretch

ν18

3,549

3,541

3,542

3,542

3,570

54

81% ω18 + 7% 2ω18

3,624

as. CH2 stretch

ν17

2,881

2,895

2,855

2,876

2,898

13

74% ω17 + 16% ω16 + ω17

2,921

ν9 + ν12

   

2,649

2,650

1

83% ω9 + ω12 + 4% ω17

 

ν9 + ν10

   

2,503

2,496

1

83% ω9 + ω10 + 4% ω17

 

13

   

2,798

2,913

14

58% 2ω13 + 15% ω16

 

ν12 + ν13

   

2,882

2,883

9

54% ω12 + ω13 + 16% 2ω4 + ω12 + 10% ω16

2,836

4 + ν13

    

2,874

11

32% 2ω4 + ω13 + 27% ω12 + ω13 + 13% ω16

 

s. CH2 stretch

ν16

2,840

2,845

2,895

2,999

   

2,967

4 + ν11

    

2,794

6

55% 2ω4 + ω11 + 16% 4ω4 + 4% ω16

 

ν10 + ν12

   

2,689

2,681

2

76% ω10 + ω12 + 10% ω10 + ω11 + 4% ω16

 

CH stretch

ν15

2,820

2,907

2,845

2,822

2,854

19

49% ω15 + 26% ω11 + ω12

2,870

12

   

2,831

2,816

14

43% 2ω12 + 33% ω11 + ω13 + 4% ω15 + 7% ω16

 

ν11 + ν12

   

2,775

2,767

5

62% ω11 + ω12 + 16% ω15

 

11

2,710

2,712

2,713

2,720

2,707

6

78% 2ω11 + 10% ω15

2,718

C=O stretch

ν14

1,754

1,747

1,747

1,770

1,761

108

64% ω14 + 25% 2ω6

1,753

6

1,706

1,697

1,707

1,702

1,716

33

58% 2ω6 + 27% ω14

1,711

4

   

1,441

1,412

10

73% 2ω4 + 12% ω13 + 9% ω11

 

CH2 scissor

ν13

1,456

1,425

1,443

1,429

1,421

1,430

1,424

1,460

1,454

11

81% ω13 + 13% 2ω4

1,462

CH2 wag, ip OH bend

ν12

1,378

1,399

1,400

1,426

1,421

27

92% ω12

1,420

ip CH bend

ν11

1,356

1,367

1,366

1,367

1,363

31

94% ω11

1,378

ip OH bend, CH2 wag,

ν10

1,275

1,267

1,268

1,279

1,273

41

94% ω10

1,265

CH2 twist

ν9

 

1,229

1,229

1,225

3

95% ω9

1,235

8

  

2,209

2,229

2,233

1

86% 2ω8 + 1% ω8

2,222

C–O stretch

ν8

1,112

1,110

1,110

1,120

1,120

80

93% ω8

1,116

CH2 twist, op CH bend

ν7

 

1,130

1,087

1,081

0

95% ω7

1,090

CC stretch

ν6

859

858

856

865

865

49

91% ω6

867

O=CC bend, CCO bend

ν5

752

749

751

757

758

9

95% ω5

740

CH2 rock, op CH bend

ν4

 

722

713

0

96% ω4

715

Comparison with the experimental values obtained in gas phase and in Ar matrix and VPT2 results from a MP2/6-311++G(d,p) quartic force field [24]. Calculated intensities are in km·mol−1

aTaken from Ref. [23], taken from Ref. [24], taken from Ref. [25], our work, taken from Ref. [24]

Globally, the VCI-P results achieve an average convergence of 11 cm−1 with the overall of the non-ambiguous experimental values (values reported in Table 1 excepted ν7, ν13, ν15, ν16, as discussed). This mean absolute deviation (M.A.D) is confronted to the VPT2 results [25] stemmed from a MP2/6-311G(d,p) quartic force field for which a mean deviation of about 17 cm−1 is observed on the same set.

The experimental values in the 1,800–700 cm−1 region are particularly well reproduced by the VCI-P approach, namely for the remarkable case of Fermi resonance that occurs between the C=O stretching and the first overtone of the C–C stretching mode. Indeed, a gap of 45–50 cm−1 is observed between the two transitions both experimentally and theoretically with an intensity ratio \( I_{{\nu_{C = O} }} :I_{{2\nu_{C - C} }} \) of about 5:1 in gas phase [23], 2:1 in Ar matrix [24] and 3:1 from our calculations.

Here, the most ambiguous assignment concerns the fundamental transition of the CH2 scissoring mode for which two bands of about the same intensity [23, 24] were observed. From the experiment in gas phase [23], the two values (1,425 and 1,456 cm−1) were assigned to the fundamental transition even though it was pointed out that one of the two positions could correspond to the first overtone of ν4 (CH2 rocking mode). From low-temperature experiments in Ar matrix, a triplet is reported in Ref. [24] (1,421–1,429–1,443 cm−1) invoking possible site effects in this material, while the Ref. [25] mentions only a doublet (1,424–1,430 cm−1). These observations are consistent with our calculations concerning both the positions and the intensity ratio. Thus, the values around 1,430 and 1,450 cm−1 are assigned to the 2ν4 and ν13 (CH2 scissoring), respectively.

More problems are encountered in the region above 2,600 cm−1 since the symmetric CH2 and CH stretching modes are affected by strong anharmonic couplings, giving rise to several IR-active overtones and combination bands. Starting from the CH stretching mode region, the presence of a Fermi resonance between this mode (ν15) and the first overtone of the op CH bending mode (2ν11) was observed in the three experiments [2325], but different values of ν15 were reported (2,820, 2,907 and 2,845 cm−1), while the value of 2ν11 is determined around 2,710 cm−1. The theoretical description reveals a more subtle interplay involving four transitions, in particular between the 2ν12 and the ν15, calculated at 2,816 and 2,854 cm−1, respectively, for which the intensities are of the same magnitude. Thus, the experimental value of 2,820 cm−1 corresponds probably to the 2ν12 transition. Note, therefore, that the deviation between theory and experiment on the 2ν11, ν15 and 2ν12 are of 9, 4 and 3–5 cm−1, respectively.

The assignment of the CH2 stretching mode (ν16) is not straightforward. According to our theoretical description, the harmonic character ω16 is widely spread within the states 2ν13, ν12 + ν13 and 2ν4 + ν13 and no major component of ω16 appears, according to the form of the PES used. However, Fig. 2a that displays the anharmonic spectrum of the Cc form shows a multiplet shape in the CH stretching region very close to the pictures reported in Ref. [20, 23].
https://static-content.springer.com/image/art%3A10.1007%2Fs00214-012-1183-1/MediaObjects/214_2012_1183_Fig2_HTML.gif
Fig. 2

anharmonic spectra of the four conformers of glycolaldehyde in the 3,800–2,600 cm−1 region and the 1,800–700 cm−1 region with the VCI-P method from a CCSD(T)/cc-pVTZ//B3LYP/6-31G(d,p) quartic force field. a Cc form, b Tt form, c Tg form, d Ct form

If we turn our attention on the asymmetric CH2 and OH stretching modes, the observed deviation is about 3–17 cm−1 and 21–29 cm−1 with the VCI-P results, respectively, while it is about 5–19 cm−1 and 0–7 cm−1 with the VMP2 results. Here again [38], in the absence of Fermi resonance, the VMP2 treatment is closer to the experimental counterpart for a mode having a well-defined Morse potential even though the analytical form of the PES used has no Morse behavior far from the local minimum (quartic force field). Nevertheless, the VCI-P wavenumber, based on such a force field, is closer to the experimental value than its VCI counterpart (see Eq. 2) that yields some discrepancies of 20–34 cm−1 and 39–50 cm−1 for the asymmetric CH2 stretching mode and OH stretching mode, respectively.

Table 2 reports the anharmonic frequencies and activities calculated in the mid-infrared region for the glycolaldehyde in its Tt form. These results are compared with the experimental data obtained when irradiating the Cc conformer isolated in matrix with an IR source [24]. In the region below 1,800 cm−1, the very strong absorptions (νC–C, νC–O, ip OH bending) are in good agreement with the theoretical computations, while the very weak absorption (op CH bending) is too far from its theoretical counterpart. In the region above 2,600 cm−1, the experimental transition observed at 2,935 cm−1 probably does not correspond to νa,CH2 since it appears 72 cm−1 higher than the corresponding theoretical value and the observed νOH mode at 3,668 cm−1 is overestimated by 72 cm−1 by our computations. According to Table 3, it should be noted that the experimental values pointed out here (2,935 and 3,668 cm−1) are closer to their theoretical counterpart belonging to the Tg form which is expected very close in energy to the Tt form.
Table 2

Calculated wavenumbers (cm−1) for the glycolaldehyde in its Tt form with the VCI-P method from a CCSD(T)/cc-pVTZ//B3LYP/6-31G(d,p) hybrid quartic force field

Description

Mode

expa

νVMP2b

νVCIPb

b

Descriptionb

OH stretch

ν18

3,668

3,707

3,740

36

82% ω18 + 6% 2ω18

as. CH2 stretch

ν17

2,940

2,903

2,921

15

74% ω17 + 4% ω16 + ω17

ν10 + ν12

 

2,621

2,625

1

83% ω10 + ω12 + 4% ω17

ν8 + ν13

 

2,553

2,534

1

65% ω8 + ω13 + 4% ω17

13

 

2,849

2,921

8

64% 2ω13 + 19% 2ω5 + ω13 + 13% ω16

5 + ν13

  

2,882

10

34% 2ω5 + ω13 + 14% ω16

s. CH2 stretch

ν16

2,935

2,971

2,863

10

33% ω16 + 27% 2ω13

CH stretch

ν15

2,810

2,807

2,823

35

34% ω15 + 30% 2ω12

12

 

2,795

2,783

9

52% 2ω12 + 21% ω15 + 8% ω16

ν11 + ν12

 

2,748

2,743

20

67% ω11 + ω12 + 16% ω15 + 6% ω16

11

 

2,701

2,686

9

76% 2ω11 + 15% ω15

C=O stretch

ν14

1,747

1,767

1,770

145

91% ω14

CH2 scissor

ν13

1,439

1,472

1,458

12

76% ω13 + 16% 2ω5

5

 

1,441

1,420

3

64% 2ω5 + 17% ω13

CH2 wag, ip OH bend

ν12

 

1,410

1,406

6

91% ω12

ip CH bend

ν11

1,353

1,357

1,354

4

94% ω11

CH2 twist

ν10

1,220

1,217

0

94% ω10

ip OH bend, CH2 wag,

ν9

1,203

1,214

1,203

68

93% ω9

op CH bend

ν8

1,129

1,088

1,083

2

95% ω8

C–O stretch

ν7

1,065

1,082

1,083

63

90% ω7

CC stretch

ν6

998

996

994

46

92% ω6

CH2 rock, op CH bend

ν5

728

719

0

95% ω5

O=CC bend, CCO bend

ν4

538

539

540

6

91% ω4

Comparison with the experimental values obtained in Ar matrix. Calculated intensities are in km·mol−1

aTaken from Ref. [24], b our work

Table 3

Calculated wavenumbers (cm−1) for the glycolaldehyde in its Tg and Ct forms with the VCI-P method from a CCSD(T)/cc-pVTZ//B3LYP/6-31G(d,p) hybrid quartic force field

Tg

Ct

Description

Mode

CC//B3

Mode

CC//B3

OH stretch

ν18

3,703

27

ν18

3,715

36

as. CH2 stretch

ν17

2,965

7

ν17

2,883

20

   

ν10 + ν12

2,650

1

   

ν10 + ν11

2,624

1

   

ν7 + ν13

2,531

1

s. CH2 stretch

ν16

2,918

16

ν16

2,857

29

5 + ν13

2,859

2

5 + ν13

2,884

5

ν10 + ν12

2,683

9

   

13

2,822

1

13

2,912

10

   

5

2,757

5

   

ν11 + ν12

2,830

5

CH stretch

ν15

2,794

23

ν15

2,710

62

12

2,718

12

12

2,790

49

   

11

2,763

1

ν10 + ν12

2,682

13

   

C=O stretch

ν14

1,764

137

ν14

1,790

151

   

6

1,707

10

CH2 scissor

ν13

1,446

7

ν13

1,449

16

5

1,411

5

   

CH2 wag, ip OH bend

ν12

1,372

13

ν12

1,416

7

ip CH bend

ν11

1,361

16

ν11

1,384

7

ip OH bend, CH2 wag,

ν10

1,312

3

ν10

1,233

1

CH2 twist

ν9

1,182

15

ν9

1,184

68

C–O stretch

ν8

1,079

66

ν8

1,129

26

CH2 twist, op CH bend

ν7

1,049

32

ν7

1,080

2

CC stretch

ν6

1,023

29

ν6

860

35

O=CC bend, CCO bend

ν5

712

5

ν5

718

0

CH2 rock, op CH bend

ν4

519

2

ν4

713

56

Calculated intensities are in km·mol−1

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© Springer-Verlag 2012