RETRACTED ARTICLE: RAMAN SPECTROSCOPY OF STRONG HYDROGEN BONDS O–H⋯O

Abstract

The work presents general ideas about the mechanisms determining the frequency and intensity of the scattering band of proton vibrations in the hydrogen bond O–H⋯O as it evolves from a weak bond to an extremely strong one. The Raman spectra of glycine phosphate and protonated dimethylformamide crystals containing strong and extremely strong hydrogen bonds are obtained in the temperature range of 5-300 K. It is shown that strong bonding is realized only for certain chemical states of donor and acceptor atoms and that low temperatures or high pressures are required to register proton vibrations. Schematic dependence between the frequency of proton vibrations and the rigidity of hydrogen bond O–H⋯O is discussed.

INTRODUCTION

It is commonly assumed that the frequency of O–H vibrations in the O–H⋯O hydrogen bond should decrease monotonically with increasing bond rigidity [1]. Indeed, for d _O⋯O distances in the range of 2.9-2.6 Å (weak and intermediate bonds), ν_O–H decreases from 3500 cm^–1 to ~2500 cm^–1, as is confirmed by numerous experimental data accumulated so far. However, in the region of strong bonds (d _O⋯O < 2.6 Å), the behavior of ν_O–H has been much less studied since the scattering band of O–H vibrations is either completely absent in the Raman spectra or requires special conditions (low temperatures, high pressures) to be registered. Registering this band by IR spectroscopy is also complicated due to strong broadening of this band. Besides, there is only a is limited number of bonds with strong hydrogen bonding O–H⋯O.

In recent years, significant progress in the understanding of the nature of hydrogen bonding has been achieved using the concept of quantum uncertainty of the proton coordinate. First of all, it is the work by Wang et al [2]. Benoit and Marx showed in [3] how the hydrogen bond potential and the proton position in this bond change in the series from weak to extremely strong bonds. A theoretical study of strong hydrogen bonds was also reported in [4-12].

The purpose of this work is to reveal the main mechanisms determining the frequency of proton vibrations and the scattering intensity in a wide rigidity range of O–H⋯O hydrogen bonds. The experimental data were taken from numerous reported data and supplemented by Raman spectra measured in the present work for compounds with strong hydrogen bonding O–H⋯O at 5-300 K.

EXPERIMENTAL

Glycine phosphate and protonated dimethylformamide were chosen as the studied compounds with strong hydrogen bonding O–H⋯O. The crystals of glycine phosphate NH₃CH₂COOH H₂PO₃ were prepared by N. Bogdanov (NSU) and (DMF)₂H compounds were prepared by R. Abramov (NIIC SB RAS). The synthesis and structure of this compound were discussed in [13].

The spectra were recorded on a LabRAM Horiba HR spectrometer equipped with a CCD Symphony detector (Jobin Yvon) with horizontal pixels 2048. The laser power (633 nm line of He–Ne laser) on the surface of the sample did not exceed 0.1 mW. The spectra at all temperatures were measured with a Raman microscope in the backscattering collection geometry. To collect Raman spectra at different temperatures, the sample was wrapped in an indium foil for better thermal contact and placed on the cold finger of a closed-cycle helium cryostat. All measurements were performed with a spectral resolution of 0.3-0.7 cm^–1.

RESULTS AND DISCUSSION

The potential function of hydrogen bonding is represented by a curve with two wells: a deep one near the bond donor and a shallow one near the bond acceptor (Fig. 1). According to [2, 3], hydrogen bonding is formed due to the propagation of the proton density distribution function (having a finite width comparable with the proton potential space) into the neighboring potential well near the acceptor (Fig. 1) so that a part of the proton density occurs near the acceptor oxygen and interacts with it by the same scheme as with the donor oxygen.

On the one hand, this effect is responsible for the fact that the hydrogen bond increases as the donor and the acceptor approach each other; on the other hand, the vibrational frequency ν_O–H decreases, since the bonding between both oxygen atoms is provided by the electronic density of the same hydrogen atom.

Fig. 2 shows the proton potential function for O–H⋯O bonds of various rigidities [3].

The change of the ν_O–H vibration as a function of the hydrogen bond strength can be monotonic only until both vibrational states (the ground one (0) and the first excited one (1)) occur in the same potential well near the donor (Fig. 2a), which is fulfilled for rigidities ranging from weak to intermediate bonds. However, as d _O⋯O decreases, the proton potential becomes significantly anharmonic and no more relates to known solutions of the harmonic oscillator problem. Finally, at d _O⋯O ~ 2.6 Å the excited state is “pushed” out of the narrow well to the region of a wide potential well formed by a sum of two potential minima (Fig. 2b). The wave function of the first excited state of a particle in a harmonic oscillator is one period of the de Broglie wave λ with energy

$$E=\frac{{{p}^{2}}}{2m}=\frac{{{h}^{2}}}{2m{{\lambda }^{2}}}\sim \frac{1}{{{\lambda }^{2}}}.$$

(1)

The wavelength λ is determined by the oscillator size. Therefore, as the excited vibrational state goes to the wide minimum where the oscillator increases by 1.5-2 times, its energy decreases by 2-4 times compared to its expected value in the absence of the wavelength jump. At the same time, its ground vibrational state remains within the narrow minimum and the size of its potential space and energy remain almost unchanged. For this reason, the vibrational frequency ν_OH = E(1) — E(0) also decreases significantly while the dependence of ν_OH on distance d _O⋯O should decrease sharply at d _O⋯O ~ 2.6 Å. This is the most dramatic moment in the evolution of hydrogen bonding. Proton positions turn out to be different in ground and excited vibrational states: the non-excited proton is located in the narrow minimum next to one oxygen atom while the excited proton occurs in the center of the bond. Therefore, proton is to be shifted along the bond to make excitement of the vibration possible. However, incident electromagnetic radiation in Raman spectroscopy interacts with the electronic shells of atoms rather than with their nuclei, since the frequency of the incident radiation (~2·10⁴ cm^–1) is an order of magnitude higher than that of nuclear displacements (~2·10³ cm^–1). For this reason, the processes accompanied by atomic displacements are not manifested in Raman spectra but can be active in IR absorption. (It is well known that the intensity of the O–H band in Raman spectra almost vanishes for O–H⋯O hydrogen bond frequencies below 2700 cm^–1, while the band becomes highly uninformative and consists of several peaks with intensities at the level of the spectrum noise.) Finally, many compounds with intermediate bonding show no O–H bands at all.

Fig. 1

Proton potential function (solid curve) and assumed proton density distribution (dashed curve) on the hydrogen bond. The region of proton density penetration into the neighboring well is dashed.

Fig. 2

Proton potential function as a function of d _O⋯O: weak bond, d _O⋯O > 2.7 Å (a), intermediate bond d _O⋯O = 2.6-2.7 Å (b), strong bond (deep tunneling regime), transition to the single-well potential, d _O⋯O = 2.4-2.6 Å (c), extremely strong bond (ultrashort, centered HB), d _O⋯O < 2.4 Å (d) [3].

As mentioned above, some intermediate hydrogen bonding may lead to the situation presented in Fig. 2b when the excited vibrational state is pushed into a the wide single-well minimum while the ground vibrational state remains in the narrow minimum. The proton positions in excited and ground vibrational states turn out to be different: the excited proton occurs in the center of the bond whereas the non-excited one occupies the narrow minimum next to one of the oxygen atoms. Therefore, a proton displacement along the bond is required for the excitation. Incident electromagnetic radiation in Raman spectroscopy interacts with the electronic shells of atoms rather than with their nuclei, since the frequency of the incident radiation (~2·10⁴ cm^–1) is an order of magnitude higher than that of nuclear displacements (~2·10³ cm^–1). (In IR spectroscopy, a vibrational quantum is excited if the frequency of incident electromagnetic radiation is equal to the frequency of normal mechanical vibrations of the molecule. In Raman spectroscopy, the frequency of the incident radiation is high and greatly exceeds the frequencies of mechanical atomic vibrations; therefore, the field of the incident electromagnetic wave affects only the electronic shells of the atoms rather than the atoms as such. However, the reaction of electron density to the external field depends on the polarizability of chemical bonding modulated by mechanical vibrations which are slow compared to the frequency of the incident field. It is this modulation of the system′s polarizability during vibrations that causes Raman scattering at the frequency of molecular or crystal vibrations). In other words, in the situation shown in Fig. 2b, the intensity of scattering on O–H vibrations should vanish to zero. Indeed, many compounds with intermediate hydrogen bonding O–H⋯O exhibit no scattering band of O–H vibrations in their Raman spectra. To show experimentally the moment when the vibrational band disappears in the Raman spectrum, distance d _O⋯O should be monotonously decreased in the same compound, which can be achieved by changing the temperature or the external pressure. Thus, the position of proton vibrational states in the potential of intermediate hydrogen bonding (when the ground state remains in the narrow minimum at the donor oxygen while the first excited state falls within the broad minimum (Fig. 2b)) is the reason of radical changes in the Raman spectra, namely, abrupt and substantial decrease of the O–H vibration frequency and the vanishing of the scattering intensity.

Since the de Broglie wavelength is determined by the width of the potential well and the position of the vibrational state in the well, the frequency of proton vibrations should decrease already in the case of weak bonding, since the interaction potential between the proton and the donor atom is deformed from the side of the acceptor (Fig. 2a) and becomes substantially anharmonic while the potential well broadens. This is another reason why the proton vibrational frequency decreases together with the d _O⋯O distance.

The next stage in the evolution of hydrogen bond O–H⋯O is the formation of a two-well potential (Fig. 2c) whose symmetry is determined by the formation of hydrogen bonding between two identical molecules. The energy of the ground vibrational state in the symmetric potential can be lower or higher than the barrier U ₀ between the minima. In the harmonic approximation (when U = kq ², where U is the energy of the particle; k is the force constant; q is the deviation from the equilibrium), barrier U ₀ is written as

$${{U}_{0}}=\text{k}{{\left( \frac{\Delta }{2} \right)}^{2}},$$

(2)

where Δ is the distance between the minima. The force constant depends on the electronegativity of oxygen atoms and takes specific value for each given compound. Distance Δ depends on the external pressure or the crystal temperature which determines the population of thermal vibrations. In other words, barrier U ₀ decreases with increasing external pressure or decreasing temperature; therefore, it is easy to reproduce the situation in Fig. 2c when both vibrational states occur within the broad minimum and Raman scattering becomes active. Further decreasing the distance between oxygen atoms will lead to the formation of extremely strong hydrogen bonding whose proton potential becomes similar to the ordinary harmonic oscillator potential (Fig. 2d). The conditions for the formation of an extremely strong hydrogen bonding are total identity of the donor and the acceptor (i.e., oxygen atoms should belong to two identical molecules) and high electronegativity of them both.

Glycine phosphate. Fig. 3 shows a fragment of glycine phosphate structure and the Raman spectrum of the crystal in the region of proton vibrations on the O–H⋯O bond.

As temperature decreases, a broad structureless band (dashed line in Fig. 3) appears in the spectrum at 930-980 cm^–1. The shape of the band is utterly unusual: the peak of the band is located at its low-frequency edge (~930 cm^–1) and the minimum is located at the high-frequency edge (~980 cm^–1).

The glycine phosphate crystal contains two short hydrogen bonds O–H⋯O at 2.48 Å and 2.52 Å ([14-17], Fig. 3a) with totally identical oxygen atoms in both bonds, while the proton potential has a symmetrical two-well shape at room temperature. In this case, the protons in each pair should occupy positions near both atoms with equal probabilities. At room temperature, the equiprobable distribution is achieved due to proton jumps over the potential barrier.

The appearance of a broad band at 930-980 cm^–1 with decreasing temperature and, correspondingly, decreasing barrier means that the energy of zero-point proton vibrations exceeds the potential barrier so that the transition from the ground state to the first excited vibrational state becomes active in the Raman spectrum. Thus, the band at 930-980 cm^–1 should be assigned to proton vibrations in the broad potential of hydrogen bonding.

Fig. 3

Fragment of the structure of the glycine phosphate crystal (a); Raman spectrum of glycine phosphate in the region of proton vibrations on the hydrogen bond O–H⋯O (b).

Fig. 4

Schematic formation of the contour of the scattering band on proton vibrations: distribution of O⋯O distances due to quantum uncertainty of the oxygen atom coordinate (a); positions of zero-point energies relative to the barrier for short (1), intermediate (2), and long (3) distances O⋯O (b).

Fig. 4 presents a qualitative explanation for the unusual proton band contour. Distance d _O⋯O is not fixed and is determined by the Gaussian distribution curve due to the quantum uncertainty of coordinates of oxygen atoms (Fig. 4a). (It can be shown that the quantum uncertainty of oxygen coordinates is about 2 times lower than that of the proton, while the sum of uncertainties of two oxygen atoms is comparable to that of the proton). Suppose that the most probable d _O⋯O distance in glycine phosphate at low temperature corresponds to potential curve (2) shown in Fig. 4b. In this case, the ground vibrational state of the proton coincides with the top of the barrier. Then the ground state at longer d _O⋯O lies below the potential barrier (curve 3 in Fig. 4b) and falls within the region where the scattering on proton vibrations is prohibited. At shorter d _O⋯O distances (curve 1 in Fig. 4b), both ground and excited states occur within the same broad potential minimum, and the scattering appears again in the spectra. This is why the scattering band in glycine phosphate has such an unusual shape (Fig. 3b). The frequency of 930 cm^–1 appearing at the edge of the scattering band and corresponding to the peak of its intensity should be assigned to the frequency of proton vibrations on the hydrogen bond O–H⋯O which corresponds to the point when zero-point vibrations become equal to the barrier height, after which both vibrational states (the ground state and the first excited state) occur within the broad minimum. Thus, the glycine phosphate crystal is a perfect example demonstrating the beginning of a new stage in the evolution of hydrogen bonding when both vibrational states (the ground one and the first excited one) occur within the same broad minimum of the two-well potential.

Fig. 5

Fragment of the (DMF)₂H structure [13] (a); Raman spectra of compound [(DMF)₂H]₂[W₆Cl₁₄] in the region of proton vibrations at various temperatures (b).

Protonated dimethylformamide. [(DMF)₂H]₂[W₆Cl₁₄] [13] is a rare compound in chemistry possessing a very short hydrogen bond O⋯H⋯O. Fig. 5a shows a fragment of its structure where oxygen atoms of DMF molecules can occupy two different positions to form O⋯H⋯O hydrogen bonds with the lengths of 2.36 Å (site occupancy 70%) and 2.46 Å (site occupancy 30%) at 140 K. The C–O bond lengths are 1.272 Å (for O⋯O = 2.36 Å) and 1.266 Å (for O⋯O = 2.46 Å). The latter two values indicate that the C–O bonds are close to single bonds and, consequently, the shells of oxygen atoms are not completely filled and their electronegativity is high. This fact along with complete identity of oxygen atoms creates conditions for the formation of an extremely strong symmetric hydrogen bond O⋯H⋯O.

Since d _O⋯O distances in (DMF)₂H are much shorter than in glycine phosphate, the proton potential must have the shape shown in Fig. 2d, and the expected frequency of proton vibrations must be significantly higher than that in glycine phosphate.

Fig. 5b shows the Raman spectra of the studied compound in the region of proton vibrations on hydrogen bonds at 5-300 K. At lower temperatures, two broad bands (1370 cm^–1 and 1450 cm^–1) appear: a low-frequency one at T ≤ 110 K and a high-frequency one at T ≤ 60 K. Also, the intensity of the band at 1422 cm^–1, which is weak at room temperature, begins to increase together with intensities of both broad bands.

The frequency of the mode at 1422 cm^–1 is close to the vibrational frequency of a single C–O bond (~1300 cm^–1) and is significantly lower than that of the C=O double bond (~1800 cm^–1), in full agreement with crystal data and with the assumption on the electronegativity of oxygen atoms participating in hydrogen bonding. The intensity of the C–O mode is the result of the resonant response on the appearance of hydrogen bonding in the spectrum.

Broad bands at 1370 cm^–1 and 1450 cm^–1 correspond to proton vibrations on a strong hydrogen bond nominally characterized by a two-well potential but with a low U ₀ barrier between the minima due to small d _O⋯O distances (Fig. 2c). For such potential, the frequency of proton vibrations is directly proportional to the rigidity of hydrogen bonding. Therefore, the modes at 1370 cm^–1 and at 1450 cm^–1 should be assigned to the vibrations of the longer and the shorter hydrogen bond, respectively. The temperature dependency of the intensity of both modes is the most interesting part of their features and requires a detailed discussion.

First of all, both bands occur at low temperatures. Nominally, this is the same behavior as the one observed in the glycine phosphate crystal. However, as mentioned above (equation (2)), barrier U ₀ between the minima is proportional to the force constant of hydrogen bonding (steepness of the potential minimum) and to the squared distance between the minima. The steepness of (DMF)₂H minima is so large that even slight lengthening of the O⋯O distance due to thermal crystal vibrations makes barrier U ₀ exceed the zero-point energy of proton vibrations at room temperature, i.e. in the position where Raman scattering on proton vibrations is prohibited. For lower temperatures, crystal vibrations are frozen, the length of hydrogen bonding decreases, the barrier becomes lower, and both vibrational states appear in the broad minimum to become Raman active states. In other words, strong hydrogen bond remains strong with increasing temperature, but the potential steepness and thermal vibrations make barrier U ₀ too high at room temperature relative to the zero-point energy.

For the same reason, the band at 1450 cm^–1 in the spectrum appears at lower temperatures than the band at 1370 cm^–1. The first mode belongs to vibrations of the stronger hydrogen bond; therefore, its appearance in the Raman spectrum requires that all crystal vibrations, including most low-frequency ones (≤ 40 cm^–1), be frozen to make the barrier low enough.

The proposed interpretation is perfectly illustrated by the temperature sequence reflecting the appearance of proton vibration bands on the bonds of different rigidities (Fig. 5b) and is additionally supported by the assumption that appearance or disappearance of proton vibrations in the Raman spectra for intermediate and strong bonds depends on the energy positions of ground and first excited vibrational states relative to the barrier between the minima.

Thus, the dependence of the frequency of proton vibrations on the O–H⋯O hydrogen bond is not monotonic: there is a gap in the region of intermediate bonds, and its minimum value corresponds to intermediate bonds rather than to strong bonds. Fig. 6 schematically shows the assumed ν_OH change as a function of distance d _O⋯O.

At low temperatures, the transition of the ground proton state from the narrow minimum at the donor to the broad minimum of combined potential (like in glycine phosphate and (DMF)₂H) has one more unexpected effect. It is well known that measuring distance O⋯O by two different methods, X-ray and neutron diffractions, gives somewhat different values. This is due to the fact that the X-rays are scattered on the electronic shells of atoms, whereas neutrons are scattered on the nuclei. In the hydrogen bond, the electronic shell of the donor oxygen is partially shifted towards the proton due to chemical interaction with it. Therefore, the position of the donor atom measured by X-ray diffraction is also shifted towards the proton and the acceptor oxygen, while the obtained d _O...O value is slightly underestimated, which is not essential in most cases. However, as mentioned above, in strong and extremely strong hydrogen bonds, the proton is located near the donor at high temperatures and between the donor and the acceptor at low temperatures. Therefore, the position of the donor oxygen measured by X-ray diffraction will be shifted relative to its true position at high temperatures and will not be shifted at low temperatures. At the same time, the registered distance d _O...O will increase with decreasing temperatures, whereas its real value can only decrease. This effect can leads to incorrect interpretations of structural data obtained by X-ray diffraction.

Fig. 6

Assumed dependence of the frequency of O–H vibration as a function of distance d _O⋯O for the hydrogen bond O–H⋯O.

CONCLUSIONS

Hydrogen bond O–H⋯O is the most common and the most diverse of chemical bonds. The diversity of bonds is due to the fact that the donor and the acceptor can have either different or similar chemical properties with respect to the hydrogen atom. In the latter case, extremely strong hydrogen bonds can be formed, which is fundamentally impossible when the donor and the acceptor are different chemical elements (e.g., oxygen and nitrogen). The study of strong and extremely strong O–H⋯O hydrogen bonds by Raman spectroscopy is complicated by the fact that proton vibrations can only be registered by lowering the temperature or by increasing the external pressure.

ACKNOWLEDGMENTS

The author expresses sincere thanks to N. Bogdanov (NSU) for preparing the glycine phosphate crystal for the study.