Article pubs.acs.org/JPCA
Doubly Hydrogen Bonded Dimer of δ‑Valerolactam: Infrared Spectrum and Intermode Coupling Prasenjit Pandey* and Tapas Chakraborty Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India S Supporting Information *
ABSTRACT: We report here the vibrational analysis of the infrared spectrum of doubly hydrogen bonded dimer of δ-valerolactam measured in CCl4 solution at room temperature (22 °C). The compound shows an equilibrium of population distributed over the monomer and doubly hydrogen bonded dimer, which is manifested by the isosbestic point in the normalized spectra for solutions of different concentrations. Dimerization induced changes in transition frequencies and intensities have been measured and compared with the computed results. Our results suggest doubling of the intensity of the amide-I (predominantly νCO) band by double hydrogen bonding at the amide (−C(O)−N(H)−) interface. The amide-A (νN−H) spectral region appears broad and is featured with quite a few numbers of substructures. These substructures are theoretically reproduced by incorporating electrical anharmonicity to the vibrational states. Computational results at the MP2/6-311++G(d,p) level of theory are seen to nicely agree with the measured spectral data.
1. INTRODUCTION Doubly hydrogen bonded dimers (DHBD) are extensively studied by various spectroscopic and photophysical means.1−36 Main interests of such studies are to investigate the effect of hydrogen bonding on complex spectral structure, particularly near νX−H (X = N, O) transition, and the shortening of life times of the vibrationally excited states. Anharmonic couplings of νX−H with low-frequency intermolecular vibrations or with overtone/combination transitions of fingerprint modes (Fermi resonance) play significant roles behind such spectral and dynamical manifestations. DHBD of δ-valerolactam is a model system that closely mimics the base pairing in nucleic acids. It also mimics hydrogen bonding interactions between two peptide linkages (−C(O)−N(H)−). Still, there is hardly any report on spectral analysis of this dimeric system. Reasons behind this scarcity of spectroscopic study on the dimer are obvious. The compound lacks any efficient UV-chromophoric group and thus is not suitable to be treated by any UV-resonance based technique for gas phase study. However, spectral assignments of the DHBD bands in solution are difficult because of the coexistence of monomer and other possible polymeric structures in equilibrium. Also, the number and identity of possible candidates in solution phase, even at the dimeric level, are not established. Although there is no direct report on the determination of the degree of association of the title compound, a relevant study was reported for its lower analogue, γ-butyrolactam, by Smet et al.37 They used nonlinear dielectric spectroscopy in benzene using concentrations up to 0.9 M and derived a value of 2.3 D for dipole moment of dimer. Obviously, the value differs markedly from the nonexistent dipole moment of a symmetric DHBD. The authors explained © 2012 American Chemical Society
the discrepancy by invoking structural interconversion between singly and doubly hydrogen bonded forms of the dimer in solution. Pandey et al. trapped the singly hydrogen bonded dimer (SHBD) of the compound in solid matrix of nitrogen, but its signatures were absent in the infrared spectrum recorded for CCl4 solution of the compound.38,39 In the present article, we show that monomer and DHBD are the only components that remain in measurable quantities, detected through conventional infrared measurement, in sufficiently dilute CCl4 solution at room temperature (22 °C), and the infrared bands of DHBD can be sorted out and distinctly identified by applying some simple scaling techniques. Prior to this report, many studies with CCl4 solution of δvalerolactam were performed, mainly to determine the dimerization constant,40−45 but spectral analysis of the DHBD covering the fingerprint, amide-I (mainly νCO), as well as the complex structures near amide-A (νN−H) transitions was never attempted. The present study is meant to fill that gap. Here, we report the infrared spectral analysis of DHBD of δ-valerolactam over a large spectral region. We complement our spectral assignments with quantum chemistry computations at the MP2/6-311++G(d,p) level of theory.
2. MATERIALS AND METHODS 2.1. Experimental Section. δ-Valerolactam (99% purity) was purchased from Sigma-Aldrich, and any trace of water impurity was removed by vacuum distillation. Spectroscopy grade CCl4 (99.9% purity) was used as solvent for all Received: July 17, 2012 Revised: August 19, 2012 Published: August 23, 2012 8972
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and overtone transitions. Thus, in the case of combination transition, where two different normal modes (say ith and jth ones) are simultaneously excited, the expression for transition moment reduces to
measurements. A commercial FTIR spectrometer (IFS/66S, Bruker Optics) equipped with a DTGS Detector and KBr Beam splitter was used to measure the FTIR spectra in the midinfrared region (400−4000 cm−1) at a resolution of 1 cm−1. The spectrometer was purged continuously with dry nitrogen gas to minimize the interference of atmospheric water and carbon dioxide. Spectra of 0.037, 0.0222, 0.0074, and 0.0037 M solutions of δ-valerolactam in CCl4 were recorded at room temperature (22 °C) using a homemade solution cell that consists of a pair of KBr windows and a Teflon spacer of 1 mm thickness. 2.2. Theoretical Section. All quantum chemistry computations have been performed using GAMESS program package.46 Optimized electronic structures and harmonic frequencies of the vibrational modes have been obtained by computations at the MP2/6-311++G(d,p) level of theory. Distributions of normal mode energies over internal coordinates have been carried out by the method of Pulay and Torok.47 Infrared band intensities have been calculated by measuring dipole moments at grid points used for displacements along normal mode coordinates and by using the harmonic nature of the potential functions. The theory behind the calculation of infrared transition-intensity is discussed in the following section. 2.2.1. Intensity Calculation. Intensity (I) of an infrared transition for a molecular vibration is given by the following expression:48,49 I=
8π 3NA ΔEv ⟨Ψfiv|μ|̂ Ψinv⟩2 3hc
⟨1i 1j |μ|̂ 0i0j⟩ =
⟨1j |Q j|0j⟩
⎛ ∂μ ⎞ 1 ∑ ⎜⎜ ⎟⎟ Q i + ∂ Q 2 i ⎠0 i ⎝
⟨2i|μ|̂ 0i⟩ =
1 ⎛ ∂ 2μ ⎞ ⎜ ⎟ ⟨2i|Q i 2|0i⟩ 2 ⎜⎝ ∂Q i 2 ⎟⎠
(5)
0
In the present work, the dipole moment derivatives have been evaluated at grid points for normal mode displacements, and the integrals for one and two quanta excitations have been solved assuming harmonic nature (mechanical) of the concerned vibrational levels.
3. RESULTS AND DISCUSSION 3.1. Molecular Geometry. Experimental results for geometrical parameters of the DHBD are not available. However, experimental data for rotational constants of the monomer were reported by Kuze et al.50 To chose acceptable level of computation for the present system, we performed electronic structure calculations at different theoretical levels and compared the computed rotational constants of monomer with the reported values (Table 1). It is clear that calculation at
(1)
Table 1. Comparison of Computed Rotational Constants of δ-Valerolactam with Experimental Data rotational constanta
measured
A B C
4590.96 2495.03 1731.06
a
⎛ ⎞ ∂ 2μ ⎟ ⎜ Q Q + ... ∑⎜ ∂Q i ∂Q j ⎟⎠ i j i,j ⎝ 0
b
HF/6311+ +G(d,p)
B3LYP/6311+ +G(d,p)
MP2/6 -31G(d)
MP2/6 -311+ +G(d,p)
4625.16 2524.57 1744.87
4577.11 2474.77 1715.66
4605.09 2485.38 1727.58
4604.11 2487.43 1729.40
Rotational constants are in MHz unit. bValues taken from ref 50.
the MP2/6-311++G(d,p) level gives the best estimations of the monomer rotational constants. We used the same level of theory for prediction of structures and harmonic normal modes of the DHBD. The structures optimized into two different geometries, one with Ci symmetry and the other, C2, and those are depicted in Figure 1. Both are isoenergetic and their calculated infrared spectra are almost identical. These happen because of the presence of two optical isomers of monomer moiety, produced through inverted ring structure at the remote part from the intermolecular interaction site (i.e., −C(O)− N(H)−). Henceforth, we would discuss only about the Ci symmetric form of DHBD, which is indistinguishable from the C2 symmetric form, for the purpose of analysis of their IR spectra. Optimized geometrical parameters of DHBD (henceforth, synonymous with the Ci form) are presented in Table 2. Comparison of these data with those of the monomer reveals that hydrogen bonding has pronounced effects on the geometry of the −C(O)−N(H)− segment of the molecule. Thus, the CO and N−H bond lengths increase to the extents of 0.016 and 0.015 Å, respectively, from monomer, and the angular
(2)
where the subscripts i and j denote the numbering of normal modes. For the intensity of a fundamental transition, the contributions from the second and higher order terms are comparatively very small and can be ignored. Thus, for a fundamental transition of the ith normal mode, the transition moment can be written approximately as ⎛ ∂μ ⎞ ⎟⎟ ⟨1i |Q i|0i⟩ ⟨1i |μ|̂ 0i⟩ = ⎜⎜ ⎝ ∂Q i ⎠0
(4)
and for overtone transition, where a normal mode is excited by two quanta, the expression for transition moment becomes
assuming that the total population before excitation is at the initial vibrational state. In this expression NA, h, c, ΔEv, and μ̂ denote Avogadro number, Planck’s constant, speed of light, vibrational transition energy, and electric dipole moment operator, respectively; and the integral ⟨Ψfiv|μ|̂ Ψinv⟩, known as transition moment, dictates the change in electric dipole moment during transition from initial vibrational state (Ψvin) to the final one (Ψvfi). Now, the change in electric dipole moment of a molecule from that in equilibrium geometry (μ0) with normal mode displacements (Q) can be represented in terms of a Taylor series as μ = μ0 +
⎧⎛ ⎞⎫ ⎛ ⎞ 2 ⎪ 1 ⎪⎜ ∂ 2μ ⎟ ⎜ ∂ μ ⎟ ⎬⟨1i |Q |0i⟩ ⎨⎜ + i ⎟ ⎜ ⎟ 2 ⎪⎝ ∂Q i ∂Q j ⎠ ⎝ ∂Q j∂Q i ⎠0 ⎪ ⎭ ⎩ 0
(3)
However, for combination and overtone transitions, the crossterms (second and higher order) in the dipole moment expression in eq 2 are to be considered (electrical anharmonicity). Here, truncation of the series up to second order terms gives reasonably accurate values for combination 8973
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Figure 1. Optimized geometries of Ci and C2 symmetric forms of doubly hydrogen bonded dimer of δ-valerolactam computed by the MP2/6-311+ +G(d,p) level of theory.
Table 2. Some of the Important Geometrical Parameters of the Monomer As Well As DHBD of δ-Valerolactam Optimized at the MP2/6-311++G(d,p) Level of Theory geometrical parameters
monomer
DHBD
C1−O3 (Å) C1−N4 (Å) N4−H8 (Å) O3−C1−N4 (deg) C1−N4−H8 (deg) O3−C1−N4−H8 (deg) O3−H8′ (Å) C1−O3−H8′ (deg)
1.226 1.373 1.014 121.56 112.77 −6.85
1.242 1.351 1.029 122.08 115.56 −4.45 1.853 121.48
orientations of CO and N−H also display significant changes. We have employed infrared spectroscopy for experimental investigation of these predicted changes in molecular structures owing to dimer formation. 3.2. Infrared Spectra. Midinfrared (400−4000 cm−1) spectrum of δ-valerolactam in 0.0074 M CCl4 solution is displayed in Figure 2. Major IR active transitions are seen to be clustered around three distinct regions, labeled as A, B, and C in the Figure. 3.2.1. Amide-A Region. The segment of the spectrum corresponding to this transition is denoted by A in Figure 2. Apparently, it appears as multiple substructures extended over the range of 2800 to 3500 cm−1. Expanded view of the region for solutions of different concentrations is depicted in the upper panel of Figure 3. For clear comparison of changes of the band intensities with concentration, the spectra are normalized (details of the normalization method are described in the Supporting Information), and the resultant spectra are shown in the lower panel of the same Figure. Here, normalization has been done with respect to νC−H bands, appearing in the frequency range of 2800−3000 cm−1, which are not affected noticeably upon dimerization. An isosbestic point is apparent at ∼3387 cm−1. It is well-known that normalization of overlapping bands of two components in equilibrium gives rise to isosbestic points;51−54 however, such isosbestic points are highly improbable when more than two components are in equilibrium.51−58 Thus, in the present case, we infer that only two components are present in equilibrium in the measured range of concentration of δ-valerolactam, and those are monomer and the DHBD. The intensity of the band at 3418 cm−1 deplets with an increase in solution concentration, while
Figure 2. Midinfrared (400−4000 cm−1) spectrum of δ-valerolactam in 0.0074 M CCl4 solution. Three different segments are highlighted by A, B, and C.
the bands in between 3000 and 3400 cm−1 grow with concentration increase. Thus, we assign the former band (3418 cm−1) to νN−H of the monomer and the rest, extending from 3000 to 3400 cm−1, to DHBD. It is worth mentioning that such broad and rich spectral profile is very common for doubly hydrogen bonded dimers.1,16−18 Anharmonic couplings among several vibrational modes play significant roles in development of such spectral profile. In a recent report on 7-azaindole dimer, Dreyer showed that the broad and complex spectral structure extending from 2400 to 3400 cm−1 can be reproduced to a good degree by taking into account the anharmonic couplings of the νN−H transition with several low frequency fundamentals and their combinations/overtones.36 In the present case, of course, the spectral profile is relatively simple. The fundamental for the antisymmetric combination of two N−H stretching can be distinctly identified (the most intense band at ∼3205 cm−1), and the neighboring substructures (3000−3175 cm−1) can be assigned easily as combinations of the amide-I with some of the IR active fingerprint transitions in the range of 1411 to 1498 cm−1 (a more detailed discussion is presented in the following sections). However, the band at 3305 cm−1 can be assigned either as overtone of amide-I transition or a combination between νN−H and a low-frequency vibration, but the correct 8974
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intensities of combination transitions, two normal modes are excited simultaneously, and the respective second order dipole moment derivatives are calculated. The combinations between the νN−H and low-frequency (
