Nuclear Quadrupole Resonance Study of Proton and Deuteron

Article pubs.acs.org/JPCC

Nuclear Quadrupole Resonance Study of Proton and Deuteron Migration in Short Strong Hydrogen Bonds Formed in Molecular Complex 3,5-Dinitrobenzoic Acid−Nicotinic Acid and in Deuterated 3,5-Pyridinedicarboxylic Acid T. Apih,† A. Gregorovič,† V. Ž agar,† and J. Seliger*,†,‡ †

“Jožef Stefan” Institute, Jamova 39, 1000 Ljubljana, Slovenia Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia

‡

ABSTRACT: Temperature dependences of the 14N nuclear quadrupole resonance (NQR) frequencies have been measured in molecular complex 3,5-dinitrobenzoic acid−nicotinic acid (35DBNA) and in deuterated 3,5pyridinedicarboxylic acid (DPDA). In deuterated DPDA, the temperature dependences of the deuterium quadrupole coupling constants and asymmetry parameters η have also been measured. In 35DBNA, the magnitude of the quadrupole coupling constant of the pyridine nitrogen agrees with the experimentally observed proton transfer. No proton exchange (O−H···N ↔ O−···H−N+) is observed. The temperature dependence of the 14N quadrupole coupling constant is analyzed in a model of a resonance hybrid of two extreme electron configurations of the molecules. The energy difference of the two extreme electron configurations is determined. In the same model, we analyzed previously published 14N NQR data of the NHO hydrogen bond in nondeuterated 3,5-pyridinedicarboxylic acid. The 14N NQR data in DPDA show the presence of a quasi-continuous isosymmetric phase transition at around 210 K. No mixture of the high-temperature phase and the low-temperature phase has been observed below this temperature. We analyzed the temperature dependence of the 14N quadrupole coupling constant in DPDA in the model of a resonance hybrid of two extreme electron configurations and determined the temperature dependences of their contributions to the electronic state of the molecule.

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INTRODUCTION Hydrogen bonding is an important chemical interaction that occurs in a variety of organic and inorganic materials. These bonds, which are largely electrostatic in nature, are weaker than covalent and ionic bonds but stronger than ordinary dipole− dipole and dispersion forces. Hydrogen bonding plays a crucial role in many biological processes. It is further connected to some interesting physical properties including ferroelectricity, pyroelectricity, nonlinear optical properties, among others. Short strong hydrogen bonds (SSHB) possess a strongly covalent character. An interesting phenomena occurring in SSHB is temperature-dependent proton migration that has been observed by inelastic neutron scattering in 3,5pyridinedicarboxylic acid (PDA),1,2 urea phosphoric acid,3,4 a 1:2 cocrystal of benzene-1,2,4,5-tetracarboxylic acid and 4,4bipyridyl,5 a 1:1 crystal of 2-methylpyridine and pentachlorophenol,6 pyridinium 2,4-dinitrobenzoate,7 3,5-dinitrobenzoic acid−3,5-dimethylpyridine complex,8 dimethylurea−oxalic acid complex,9 and in molecular complex 3,5-dinitrobenzoic acid− nicotinic acid (35DBNA).10 The variable-temperature X-ray and neutron diffraction study of 35DBNA indicates a significant degree of proton transfer in the short NHO hydrogen bond. Complementary ab initio MD simulations at 400 K show the key proton hopping across the © 2016 American Chemical Society

NHO short strong hydrogen bond, spending short periods along the trajectory (8% of the simulation time) bonded to the O atom.10 Deuteration of a strong hydrogen bond is known to strongly change its properties.11 Well-known effects are large isotope shifts of phase transition temperatures in hydrogen-bonded ferroelectrics and the occurrence of polymorphism in deuterated hydrogen bonded compounds. Very little is known about the effect of isotopic H/D substitution on proton migration in SSHBs. A deuterated form of PDA, DPDA, was found to be isomorphous with the protonated form. Both forms exhibit H/ D migration in the NHO SSHB. The proton in PDA moves away from the N donor and toward the center of the hydrogen bond by 0.095(7) Å when the temperature is increased from 15K to 296 K. In the same temperature interval, the deuteron displacement in DPDA is considerably larger, equal to 0.306(5) Å.2,12 The deuteron displacement is associated with a phase transition at approximately 175 K. This displacement is also Received: March 14, 2016 Revised: April 21, 2016 Published: April 22, 2016 9992

DOI: 10.1021/acs.jpcc.6b02639 J. Phys. Chem. C 2016, 120, 9992−10000

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The Journal of Physical Chemistry C significantly larger than the proton displacement found to date in any other systems. The NHO and NDO SSHB in 35DBNA, PDA, and DPDA exhibit significantly different properties as far as the proton (or deuteron) migration is concerned. In order to understand the differences, it is necessary to perform further experiments which may elucidate the basic parameters which determine the proton (or deuteron) position in a SSHB. Nuclear quadrupole resonance (NQR) has proven to be a suitable technique for the observation of proton position and motion in a hydrogen bond. 17O NQR studies of hydrogen bonded ferroelectric KH2PO4 unambiguously show the presence of proton exchange between two equivalent equilibrium positions (O−H···O ↔ O···H−O) in the paraelectric phase which freezes in the ferroelectric phase.13,14 14N NQR study of organic ferroelectric (H2-TPPZ) (Hca)215 shows the presence of proton exchange in NHN hydrogen bonds in the paraelectric phase. Phonon driven proton transfer in NHO SSHB formed in PDA has been investigated by 14N NQR.16 In cocrystal 4,4′-bipyridyl -5-chlorosalycilic acid (1:1), 14N NQR shows the presence of a NHO SSHB where the proton transfer from the hydrogen bond donor (O) to the hydrogen bond acceptor (N) occurs, and similarly to PDA, with increasing temperature, the proton displaces toward the oxygen atom.17 To investigate the proton and deuteron behavior in the NHO SSHB in 35DBNA and in NDO SSHB in DPDA, we performed the variable-temperature 14N NQR study of both compounds. In addition, we performed the variable-temperature deuteron NMR study of DPDA. The obtained results are analyzed in view of previous NQR and NMR results obtained in related hydrogen bonded systems.

ν± =

e 2qQ e 2qQ (3 ± η) ν0 = ν+ − ν− = η 4h 2h

(1)

Here, e2qQ/h is the quadrupole coupling constant (often abbreviated as qcc), and η is the asymmetry parameter of the electric field gradient (EFG) tensor. The EFG tensor Vik, Vik = ∂2V/∂xi∂xk, is a symmetric second rank traceless tensor composed of the second derivatives of the electrostatic potential V with respect to the coordinates taken at the position of the atomic nucleus. Only the electrostatic potential of the electric charges surrounding the atomic nucleus is considered. The EFG tensor has three real principal values labeled as VXX, VYY, and VZZ (|VZZ| ≥ |VYY| ≥ |VXX|). The quadrupole coupling constant is defined as e2qQ/h = |eQVZZ|/ h, were h is the Planck constant, and the asymmetry parameter η is defined as η = (VXX − VYY)/VZZ. They are calculated from the NQR frequencies in the following way: e2qQ/h = 2(ν+ + ν−)/3 and η = 2ν0/(e2qQ/h). Furthermore, it is possible to calculate the magnitudes of the principal values of the quadrupole coupling tensor qik, which is defined as qik = eQVik/h. The largest (by magnitude) principal value qZZ is equal to ± e2qQ/h. The two smaller principal values qYY and qXX are related to qZZ and η as qYY = −qZZ(1 + η)/2 and qXX = −qZZ(1− η)/2. The sign of qZZ cannot be determined by NQR. Different experimental techniques, for example, microwave spectroscopy, or quantum chemical calculations are needed to determine its sign. Experimental Techniques. The 14N NQR frequencies have been measured by 1H−14N nuclear quadrupole double resonance (NQDR). The NQDR techniques used in the present study are the solid-effect technique19 and the technique using multiple frequency sweeps and two-frequency irradiation.20,21 The details of the present experimental setup and the measuring procedure were published in a previous paper,22 where also the references to the original papers are given. Here we give only a brief description of the two techniques. Both techniques are based on pneumatic sample shuttling between a high magnetic field (0.75 T in our case) and a variable low magnetic field B, where the proton NMR frequency νH is equal to νH = γHB/2π. In the high magnetic field, the proton spin system is polarized and the proton NMR signal is measured at the end of the magnetic field cycle. In the low magnetic field, simultaneous transitions between the energy levels of 14N and 1H occur which in general reduce the proton magnetization. In the solid effect technique, we apply during the time spent in the low magnetic field B a strong rf magnetic field with the frequency ν. We may observe dips in the ν-dependence of the proton NMR signal at the end of the magnetic field cycle when ν = νQ ± νH (solid effect dips) and when ν = νQ (level crossing dip). Here νQ is a 14N NQR frequency. When the dips are weak, we use signal averaging. We typically measure four signals at the same value of ν and then change it for 10 kHz, and so on. The accuracy of the determination of a 14N NQR frequency by the solid effect technique is typically ±10 kHz. In the technique using multiple frequency sweeps, we apply during the time spent in the low magnetic field a series of linear frequency sweeps of the rf magnetic field in the frequency range between νl and νu (νl < νu). The duration of a single sweep is 10 ms and an average amplitude of the rf magnetic field is about 2 mT. The frequency limits νl and νu are chosen so that a sweep covers both higher 14N NQR frequencies ν+ and ν−. We perform the νH-scan in steps of 10 kHz and search for the dip in

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EXPERIMENTAL DETAILS Sample Preparation. The molecular structures of 3,5dinitrobenzoic acid, nicotinic acid and 3,5-pyridinedicarboxylic acid are presented in Figure 1.

Figure 1. Molecular structures of substances used in the present study.

A polycrystalline sample of 35DBNA was obtained from the reaction of 3,5-dinitrobenzoic acid and nicotinic acid in a 1:1 molar ratio, as described in ref 10. Both reagents were purchased from Sigma-Aldrich and used as obtained. A polycrystalline sample of DPDA with deuterated carboxylate groups only was prepared by hydrothermal treatment of PDA in D2O, as described in ref 12. PDA was purchased from Sigma-Aldrich and used as obtained. 14 N NQR. The nucleus of the nitrogen isotope 14N has in its ground state a spin of I = 1 and a nonzero electric quadrupole moment eQ. Its three NQR frequencies ν+ ≥ ν− ≥ ν0 are expressed as18 9993


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The Journal of Physical Chemistry C the νH-dependence of the proton NMR signal at the end of the magnetic field cycle occurring at νH = ν0. When the dip is found we fix νH in the center of the dip and perform separate νl and νu scans. When νl passes the 14N NQR frequency ν− from below the proton NMR signal at the end of the magnetic field cycle increases. Similarly the proton NMR signal increases when the sweep frequency limit νu passes the 14N NQR frequency ν+ from above. After the frequencies ν+ and ν− are located by the above technique, we apply two-frequency irradiation to determine these two frequencies with a typical accuracy of ±5 kHz. Deuteron quadrupole perturbed NMR line shapes were measured at the deuteron NMR frequency equal to 56.3364 MHz on a homemade NMR spectrometer. Quadrupole coupling constant and asymmetry parameter for two deuterons were estimated from fitting the quadrupole perturbed NMR powder line shape. Temperature was in both spectrometers measured with a platinum resistance thermometer. The temperature uncertainty due to different positions of the sample and thermometer in the transfer tube or in the NMR probe is less than 1 K.

Figure 3. Temperature dependences of the principal values qXX, qYY, and qZZ of the quadrupole coupling tensor. Here |qZZ| = e2qQ/h is the quadrupole coupling constant.

decreasing temperature, they decrease in size gradually and reach the values of 1280, 1900, and −3180 kHz at T = 214 K. Below this temperature, we observe a steep decrease of the magnitudes of the three principal values. They reach at 145 K the values of 1063, 1134, and −2197 kHz. As shown in our previous studies, the principal values of the quadrupole coupling tensor for the hydrogen bonded pyridine nitrogen correlate.23,24 Figure 4 shows that also in DPDA we observe the

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EXPERIMENTAL RESULTS I. DPDA. The 14N NQR frequencies in DPDA have been measured at various temperatures by the two-frequency irradiation technique. At each temperature, the three NQR frequencies ν + , ν −, and ν 0 have been unambiguously determined. The temperature dependences of the higher 14N NQR frequencies ν+ and ν− are presented in Figure 2.

Figure 4. Correlation between the principal values of the 14N quadrupole coupling tensor in DPDA as measured at various temperatures.

Figure 2. Temperature dependences of the 14N NQR frequencies ν+ and ν− in DPDA.

correlation between the principal values of the 14N quadrupole coupling tensor as measured at different temperatures. This correlation matches the previously observed correlation for hydrogen bonded pyridine nitrogen. The deuterium NQR parameters e2qQ/h and η have been deduced from the frequency distribution of the quadrupole perturbed 2H NMR line as measured in a polycrystalline sample. There are two distinct deuterium positions in the sample: one in the “normal” ODO hydrogen bond and the other in the NDO SSHB. Two deuterium positions have been indeed deduced from the 2H NMR spectra. The measured and simulated deuterium NMR spectra are presented in Figure 5. The temperature dependence of the deuterium quadrupole coupling constants and asymmetry parameters is presented in Figure 6 and Figure 7, respectively. For one deuterium position (ODO), the quadrupole coupling constant is at 340 K equal to e2qQ/h = 180 kHz and the asymmetry parameter is equal to η = 0.075. With decreasing temperature, e2qQ/h gradually decreases to about

At the highest temperature, 337 K, the 14N NQR frequencies are equal to 2695, 2340, and 355 kHz. With decreasing temperature, the 14N NQR frequencies gradually decrease, and at 214 K, reach the values of 2540, 2230, and 310 kHz. Below this temperature, we observe a steep decrease of the 14N NQR frequencies. They reach at 145 K the values of 1665, 1630, and 35 kHz. At around 160 K, the frequency ν+ becomes equal to ν− (η = 0). The results of a NQR measurements are usually interpreted in terms of the quadrupole coupling constant e2qQ/h and the asymmetry parameter η. Here we interpret them in terms of the principal values of the quadrupole coupling tensor instead. The largest principal value by size qZZ, |qZZ| = e2qQ/h, is in the case of a pyridine nitrogen negative, as shown in our previous studies.23 The temperature dependences of qXX, qYY, and qZZ are presented in Figure 3. The three principal values are at 337 K equal to 1325, 2035, and −3360 kHz, respectively. With 9994


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K, e2qQ/h strongly decreases and reaches the value of 48 kHz at T = 160 K and below. The asymmetry parameter η increases to about 0.46. II. 35DBNA. In 35DBNA, there are three distinct nitrogen positions: the pyridine nitrogen position in the nicotinic acid molecule and two nitro groups in 3,5-dinitrobenzoic acid molecule. The high-frequency part of the 1H−14N NQDR spectrum of the pyridine nitrogen at 223 K is presented in Figure 8.

Figure 5. Experimentally determined (a,c) and simulated (b,d) deuterium NMR spectra in DPDA at two temperatures.

Figure 8. High-frequency part of the 1H−14N NQDR spectrum of pyridine nitrogen in 35DBNA as measured by the solid effect (circles, νH = 100 kHz) and by the two-frequency irradiation technique (squares, νH = 40 kHz).

At the proton NMR frequency νH = 100 kHz, we observe by the solid effect technique two broad dips centered at 1530 kHz and at 1625 kHz. The position of the first dip is νHindependent, whereas the second dip shifts toward higher frequencies when νH increases. So the first dip is the level crossing dip which occurs at ν = νQ, and the second dip is the solid effect dip which occurs at ν = νQ + νH. Multiple frequency sweeps covering the region 1500−2000 kHz show a significant decrease of the proton NMR signal at νH = 40 kHz. So we fixed νH at this value and used the two-frequency irradiation which gave two narrower dips at 1500 kHz and 1540 kHz. These two lines are not resolved in the solid effect spectrum. The 14N NQR frequencies of the pyridine nitrogen are thus at 223 K equal to 1540, 1500, and 40 kHz. In the frequency range characteristic for the nitro groups, we observe only three 14N NQR frequencies: 940, 740, and 200 kHz. So the two nitro groups are either equivalent or the frequency splitting of the doublets (if the groups are slightly nonequivalent) is smaller than the resolution (10 kHz) of the two-frequency irradiation technique. The temperature dependences of the 14N NQR frequencies from the nitro groups were measured by the two-frequency irradiation technique. We were not able to use the same technique for the pyridine nitrogen because of the short proton T1 in the low frequency region (νH < 50 kHz) at room temperature and above. So we used the solid effect technique a n d m e a s u r e d t h e a v e r a g e f r e q u e n c y ν̅ , ν ̅ = (ν+ + ν−)/2 = 3e 2qQ /4h. The temperature dependences of the average 14N NQR frequency ν̅ from the pyridine nitrogen position and the 14N NQR frequencies from the nitrate groups is presented in Figure 9. The NQR frequencies from the two nitro groups are within the experimental accuracy (±10 kHz) temperature independent. On the other hand, the average 14N NQR frequency νfrom ̅ the pyridine nitrogen position gradually increases with increasing temperature from 1515 kHz at 158 K to 1635 kHz at 403 K.

Figure 6. Temperature dependences of the 2H quadrupole coupling constants in DPDA.

Figure 7. Temperature dependence of the asymmetry parameter η at the two deuterium positions in DPDA.

175 kHz at 210 K. In the same temperature interval η does not change within the experimental accuracy. Below this temperature, we observe a larger decrease of e2qQ/h and a larger increase of η. At 100 K, they reach the values of 150 kHz and 0.13, respectively. At the other deuterium position (NDO) the quadrupole coupling constant is significantly lower, equal to 68 kHz at T = 340 K. The asymmetry parameter η is at this temperature equal to 0.3. Until about 210 K, e2qQ/h gradually decreases to about 62 kHz. The asymmetry parameter η is in this temperature interval constant within the experimental accuracy. Below 210 9995


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coupling tensor time dependent. The NQR frequencies depend on the time-averaged quadrupole coupling tensor and are usually lower than in the case of no motion. With increasing temperature, the intensities of the thermal motions increase, and as a consequence, we observe a decrease of the quadrupole coupling constant. There can be different reasons for the increase of the 14N quadrupole coupling constant with increasing temperature. The N···O distance varies with temperature from 2.58 Å at 30 K to 2.50 Å at 300 K.10 The temperature variation of the SSHB length may influence proton position within the bond and consequently the 14N quadrupole coupling constant. The proton potential well within the hydrogen bond may be asymmetric, steeper at the nitrogen side and less steep at the oxygen site. Proton thermal motion within this potential well would in time average increase the N+−H distance and consequently increase the 14N quadrupole coupling constant. As the third possibility we consider an exchange of the SSHB between two nonequivalent electron configurations. This can be for example the effect of proton two-site exchange (N+−H··· O ↔ N···H−O), as suggested in ref 10 on the basis of MD calculations. This can be also an exchange between proton ground state and proton first excited state in the hydrogen bond potential well. In case of a fast exchange between a lower energy configuration 1 and a higher energy configuration 2, the principal value ZZ of the time-averaged quadrupole tensor reads

Figure 9. Temperature dependences of 14N NQR frequencies from the pyridine nitrogen position (squares) and from the nitro groups (circles) in 35DBNA.

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DISCUSSION The quadrupole coupling tensor of the pyridine nitrogen is strongly influenced by hydrogen bonding and proton transfer. In case of a weakly interacting pyridine nitrogen in solids, its largest (by size) principal value qZZ is approximately equal to −4.6 MHz. In the gas phase, it is even larger, equal to −4.908 MHz.25 The principal axis Z is directed along the lone pair orbital, the principal axis Y is directed perpendicular to the plane of the pyridine ring and the principal value X is perpendicular to the principal axes Y and Z. On increasing hydrogen bond strength, qZZ decreases by size and reaches the minimum value of about −0.6 MHz in case of a complete proton transfer (N+H) with negligible hydrogen bonding.26 In the whole range, the three principal values qXX, qYY, and qZZ correlate.23 The temperature dependence of the 14N quadrupole coupling constant e2qQ/h = |qZZ| of the pyridine nitrogen in 35DBNA is presented in Figure 10.

ZZ = P(1)qZZ (1) + P(2)qZZ (2)

(2)

Here P(1) is the probability of finding the system in the configuration 1, and qZZ(1) is the largest principal value of the quadrupole coupling tensor in this configuration. P(2), P(2) = 1 − P(1), is the probability of finding the system in the higher energy configuration 2 with the corresponding quadrupole coupling tensor element qZZ(2) along the Z direction. If we assume that the energy difference ΔE of the configurations 1 and 2 does not vary with temperature we may express the probability P(1) as P(1) = 1/(1 + exp(−ΔE/kBT)). The solid line in Figure 9 is obtained by fitting the experimental data to Expression 2 with the parameters qZZ(1) = −2024 kHz, qZZ(2) = −5200 kHz, and ΔE = kB1230 K = 106 meV = 10.2 kJ/mol. The value of qZZ(2) seems to be too large for the proposed model of proton exchange, where qZZ(2) = qZZ(N···H−O). Hydrogen bonding generally reduces the 14N quadrupole coupling constant of the pyridine nitrogen. For the N···H−O configuration of a short hydrogen bond, we expect the 14N quadrupole coupling constant in the range between 3 and 4 MHz, but the value of |qZZ(2)| is even larger than the quadrupole coupling constant of a noninteracting pyridine nitrogen. However, the possibility of proton transfer N+−H···O → N···H−O cannot be completely eliminated because its influence on the electron charge distribution in the SSHB and consequently on the 14N quadrupole coupling tensor has not yet been determined. A reduction of the population of the nitrogen π electron orbital would produce a positive change Δq of qYY and a negative change − Δq/2 of (negative) qZZ. A value of Δq of approximately 3 MHz would reasonably explain the large value of qZZ(2). This is about 1/3 of the contribution of one electron in the nitrogen 2p orbital,27 so the population of the nitrogen π electron orbital is in this model reduced for 1/3. In the model of proton exchange, we obtain the probability P(2) of occupying the higher energy state at 400 K as being

Figure 10. Temperature dependence of the quadrupole coupling constant of the pyridine nitrogen in 35DBNA. The experimental accuracy is ±10 kHz. The solid line is the fit to the model of a resonance hybrid of two extreme electron configurations of the complex.

The quadrupole coupling constant is around 2 MHz, which is much lower than 4.6 MHz, and therefore, the proton transfer occurred. This is in agreement with the neutron diffraction study which shows that the NH distance (1.119 Å at room temperature) is indeed shorter than the HO distance (1.383 Å at room temperature).10 The increase of e2qQ/h with increasing temperature is somehow peculiar. Usually we observe a nearly linear decrease of e2qQ/h with increasing temperature. This is the effect of thermal motions which make the quadrupole 9996


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identical. Quasi continuous isosymmetric phase transitions have indeed been observed,29,30 so the continuous phase transition in DPDA as observed within the experimental resolution of NQDR is not a surprise. At the phase transition, some structural changes occur. The lengths of the ODO and NDO hydrogen bonds change and deuteron in the NDO SSHB displaces from the nitrogen atom in the low temperature phase to the oxygen atom in the high temperature phase.2 14N NQR shows that also the electron distribution within the SSHB strongly changes. The deuterium NMR shows the presence of two deuterium positions in hydrogen bonds with significantly different quadrupole coupling constants: the ODO and NDO deuterium positions. At both positions e2qQ/h gradually decreases with decreasing temperature in the high temperature phase until 210 K. Below this temperature until about 170 K, we observe a steep decrease and below 170 K only a slight variation of e2qQ/ h. For the ODO hydrogen bond it is known that the deuterium e2qQ/h correlates with the O···O distance ROO. The relationship proposed by Soda and Chiba31 and modified by Poplett and Smith32 reads

equal to 4.4%, which is not far from the value 8% obtained in the MD simulation. A more reasonable explanation of the experimental data is the existence of a resonance hybrid of two extreme electron configurations of the complex. In this case, the parameters P(1) and P(2) in Expression 2 are the temperature-dependent contributions of the two extreme electron configurations to the electronic state of the complex. The temperature dependence of the contributions P(1) and P(2) seem to be well described by the expression P(2)/P(1) = exp( −ΔE /kBT )

We may in the model of a resonance hybrid of two extreme electron configurations analyze also the 14N NQR data in PDA.16 A fit of these data to Expression 2 is presented as the solid line in Figure 11.

e 2qQ 4.882 kHz (nm)3 = 442.7 kHz − 3 h R OO

(3)

For the ODO hydrogen bond, the experimental values of e2qQ/ h at 150 K and at 296 K are equal to (153 ± 2) kHz and (180 ± 2) kHz, respectively. From these values, we obtain ROO as being equal to 2.56 and 2.65 Å, respectively. The neutron diffraction studies2 give the values 2.58 and 2.64 Å, which are not much different from the calculated ones, so we may conclude that the temperature variation of the deuterium quadrupole coupling constant in the ODO hydrogen bond is mainly due to the temperature variation of the O···O distance. The data presented in Figure 5 show that the ODO hydrogen bond length continuously shortens in the phase transition temperature range between 210 and 160 K. For the NDO hydrogen bonds, no expression similar to Expression (3) has yet been proposed, and thus, the NMR data cannot be directly related to the neutron diffraction data, which show that the N···O distance changes from 2.564 Å at 296 K to 2.531 Å at 150 K. The deuterium quadrupole coupling constant may in principle depend on the length of the NDO hydrogen bond and on the position of deuteron within the bond. It is difficult to judge which contribution is dominant. In the ODO hydrogen bond, an increase of the length of 0.06 Å results in an increase of e2qQ/h of 27 kHz. On the other hand, in the NDO hydrogen bond, the increase of the bond length of 0.03 Å results in an increase of e2qQ/h of 20 kHz. The ratio Δ(e2qQ/ h)/ΔR is equal to 450 kHz/Å in the ODO hydrogen bond. In the NDO hydrogen bond, the same ratio is equal to 670 kHz/ Å. The two ratios are comparable, and therefore, we can conclude that also in the NDO hydrogen bond the change of the bond length strongly influences the change of the deuterium quadrupole coupling constant. Again the main change of the deuterium quadrupole coupling constant occurs in the phase transition region between 210 and 160 K, and thus, we may assume that also the main change of the NDO hydrogen bond length occurs in this temperature region. The temperature dependence of 14N quadrupole coupling constant in DPDA can also be analyzed in the model of a resonance hybrid of two extreme electronic configurations. The NQR parameters fitting experimental data in this model are

Figure 11. Fit of the temperature dependence of the 14N quadrupole coupling constant in PDA to the model of a resonance hybrid of two extreme electron configurations of the molecule.

The NQR parameters obtained in this fit, qZZ(1) = −2290 kHz and qZZ(2) = −5200 kHz, do not differ significantly from the parameters obtained in case of 35DBNA; however, the energy difference ΔE of the two extreme electron configurations, ΔE = kB460 K = 40 meV = 3.8 kJ/mol, is much smaller than in 35DBNA. The experimental points deviate from the fitting line for slightly more than what is the experimental uncertainty of the determination of the quadrupole coupling constant (±20 kHz). There is also an inflection point observed at about 250 K. A correction of the above simple model of the temperature variation of the contributions P(1) and P(2) in PDA is needed to get a better fit. In DPDA, the 14N NQR data show a continuous phase transition at about 210 K. Below this temperature, we do not observe a mixture of the two phases, as shown in ref 12, but a continuous temperature variation of a single set of 14N NQR frequencies. A mixture of the two phases would result in two sets of the 14N NQR frequencies, which were not observed. The phase transition is isosymmetric according to the crystallographic data.2,12 Such transitions can be related to changes in the electronic structure and/or crystalline structure.28 From the thermodynamic point of view, isosymmetric phase transition are necessarily first-order and discontinuous because in the mean-field description the Landau condition is always violated. However, the Landau theory does not determine the size of the discontinuity, and weakly discontinuous transitions could be hard to detect near the critical temperature because both structures are almost 9997


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The Journal of Physical Chemistry C qZZ(1) = −2100 kHz, qZZ(2) = −5200 kHz, and the energy difference ΔE of the two extreme electron configurations is in the high-temperature phase equal to ΔE = kB120 K = 10 meV = 1.0 kJ/mol. The NQR parameters qZZ(1) and qZZ(2) are close to the ones obtained in 35DBNA and PDA. The contributions of the two extreme electron configurations P(1) and P(2) to the electronic state of the molecule as calculated from the temperature dependence of qZZ are presented in Figure 12.

experimental values, where the neutron diffraction and NQR data (T, R, e2qQ/h) are simultaneously known: PDA (296 K, 1.308 Å, 2794 kHz; 100 K, 1.18 Å, 2430 kHz (extrapolated)), 35DBNA (300 K, 1.119 A, 2070 kHz), DPDA (295 K, 1.457 Å, 3330 kHz; 150 K, 1.192 Å, 2220 kHz). In addition, we use the “limiting” values: (i) R = ∞, e2qQ/h = 4.9 MHz and (ii) R = 1.02 Å (the sum of the hydrogen and nitrogen covalent radii), e2qQ/h = 0.6 MHz and plot e2qQ/h in dependence of R−3. The plot is presented in Figure 13.

Figure 12. Contributions of the two extreme electron configurations P(1) and P(2) to the electronic state of the DPDA molecule as functions of temperature.

Figure 13. Correlation between the 14N quadrupole coupling constant e2qQ/h and one over the NH or ND distance R to the third power.

The points lie approximately on a line which can be expressed as

At low temperature the contributions P(1) and P(2) approach the values one and zero respectively, whereas in in the high temperature phase they are approximately equal to 0.6 and 0.4, respectively. The experimentally determined position of deuteron in the hydrogen bond (N−1.192 Å−D−1.340 Å− O in the low-temperature phase and N−1.457 Å−D−1.101 Å− O in the high-temperature phase) shows that there is no deuteron two-site exchange. In case of the two-site exchange, in the high-temperature phase, we expect deuteron to be close to the center of the hydrogen bond and not close to the oxygen atom. Also, the neutron diffraction studies of DPDA2 give a single deuteron position in the high temperature phase and not two position as for example observed in KH2AsO4.33 The 14N NQR results and the hydrogen bond parameters are summarized in Table 1. The energy difference of the two extreme electron configurations seem be related to the N···O hydrogen bond length. The shortest N···O distance of 2.500 Å corresponds to the largest energy difference of 106 meV, and the longest N···O distance of 2.564 Å corresponds to ΔE = 10 meV. There seems also to be a correlation between the 14N quadrupole coupling constant e2qQ/h = |qZZ| and the N···H/D distance. In a previous 17O NQR study of phosphates, we have shown that the principal values of the 17O quadrupole coupling tensor correlate with the PO distance.34 In the present case, we investigate a possible correlation between the 14N quadrupole coupling constant and the NH or ND distance R. We use the

e 2qQ = 4900 kHz − 4.45 kHz (nm)3 /R3 (4) h Further experiments are needed to prove the above expression. If it is correct, it can be used to find the proton or deuteron position within a hydrogen bond by 14N NQR.

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CONCLUSIONS Temperature dependences of the 14N NQR frequencies have been measured in 35DBNA and DPDA by double resonance. In DPDA, the temperature dependence of the deuterium quadrupole coupling constant and asymmetry parameter η have been measured by 2H NMR. In 35DBNA, the 14N quadrupole coupling constant of the pyridine nitrogen, which is involved in a SSHB, nonlinearly increases with increasing temperature. Its value is low, equal to approximately 2.1 MHz, and shows that the proton transfer O− H···N → O−...H−N+ occurs in the hydrogen bond. The temperature variation of the 14N quadrupole coupling constant may be an effect of the temperature variation of the length of the hydrogen bond or the proton two-site exchange, but it may be also the effect of a resonance hybrid of two extreme electron configurations of the complex, which vary with temperature. In the latter case, we obtained the 14N quadrupole coupling constants equal to 2.0 MHz in the lower-energy extreme configuration and 5.2 MHz in the higher-energy extreme

Table 1. Hydrogen Bond Parameters (N···O Distance and N···H/D Distance),2 the Largest Principal Value qZZ of the 14N Quadrupole Coupling Tensor, the Calculated Principal Value qZZ(1) for the Lower Energy Extreme Electron Configuration, and the Energy Difference ΔE of the Two Extreme Electron Configurations of a DPDA Molecule substance

T/K

N···O /Å

N···H/D /Å

qZZ /MHz

qZZ(1) /MHz

ΔE /meV

35DBNA DPDA DPDA PDA

300 150 296 296

2.500(7) 2.531(3) 2.564(3) 2.525(3)

1.119(15) 1.192(3) 1.457(4) 1.308(6)

−2.07(1) −2.20(2) −3.30(2) −2.80(2)

−2.02(1) −2.10(2) −2.10(2) −2.29(2)

106(5) 10(3) 40(5)

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(6) Steiner, T.; Majerz, I.; Wilson, C. C. First O-H-N Hydrogen Bond with a Centered Proton Obtained by Thermally Induced Proton Migration. Angew. Chem., Int. Ed. 2001, 40, 2651−2654. (7) Majerz, I.; Gutmann, M. J. Temperature-Dependent SingleCrystal Neutron Diffraction Study of the Strong OHN Hydrogen Bond in Pyridinium 2,4-Dinitrobenzoate. J. Phys. Chem. A 2008, 112, 9801−9806. (8) Majerz, I.; Gutmann, M. J. Mechanism of Proton Transfer in the Strong OHN Intermolecular Hydrogen Bond. RSC Adv. 2011, 1, 219− 228. (9) Jones, A. O. F.; Lemée-Cailleau, M. H.; Martins, D. M. S.; McIntyre, G. J.; Oswald, I. D. H.; Pulham, C. R.; Spanswick, C. K.; Thomas, L. H.; Wilson, C. C. Temperature Dependent Solid-State Proton Migration in Dimethylurea−Oxalic Acid Complexes. Phys. Chem. Chem. Phys. 2012, 14, 13273−13283. (10) Ford, S. J.; McIntyre, G. J.; Johnson, M. R.; Evans, I. R. Structure and Dynamics Studies of the Short Strong Hydrogen Bond in the 3,5-Dinitrobenzoic Acid−Nicotinic Acid Molecular Complex. CrystEngComm 2013, 15, 7576−7582. (11) For example: Sobczyk, L.; Obrzud, M.; Filarowski, A. H/D Isotope Effects in Hydrogen Bonded Systems. Molecules 2013, 18, 4467−4476 and the references cited therein.. (12) Ford, S. J.; Delamore, O. J.; Evans, J. S. O.; McIntyre, G. J.; Johnson, M. R.; Radosavljević Evans, I. Giant Deuteron Migration during the Isosymmetric Phase Transition in Deuterated 3,5Pyridinedicarboxylic Acid. Chem. - Eur. J. 2011, 17, 14942−14951. (13) Blinc, R.; Seliger, J.; Osredkar, R.; Mali, M. 17O Quadrupole Resonance Study of the Ferroelectric Phase Transition in KH2PO4. Phys. Lett. A 1974, 47, 131−132. (14) Brosnan, S. G. P.; Edmonds, D. T. An 17O Nuclear Quadrupole Resonance Study of Hydrogen Atom Motion in KH2PO4. Phys. Lett. A 1981, 81, 243−245. (15) Seliger, J.; Ž agar, V.; Asaji, T.; Hasegawa, Y. 14N NQR and Proton NMR Study of Ferroelectric Phase Transition and Proton Exchange in Organic Ferroelectric (H2-TPPZ) (Hca)2. Phys. Chem. Chem. Phys. 2010, 12, 3254−3259. (16) Seliger, J.; Ž agar, V. Phonon Driven Proton Transfer in 3,5Pyridinedicarboxylic Acid Studied by 2H, 14N and 17O NQR. J. Phys. Chem. A 2011, 115, 11652−11654. (17) Seliger, J.; Ž agar, V. Hydrogen Bonding and Proton Transfer in Cocrystals of 4,4′-Bipyridil and Organic Acids Studied by Nuclear Quadrupole Resonance. Phys. Chem. Chem. Phys. 2014, 16, 18141− 18147. (18) See for example: Seliger, J. Nuclear Quadrupole Resonance: Theory, in: Lindon, J. C.; Tranter, G. E.; Holmes, J. L. (Eds.), Encyclopedia of Spectroscopy and Spectrometry; Academic Press, San Diego, 2000; pp 1672−1680. (19) Seliger, J.; Ž agar, V. Measurement of the 14N Nuclear Quadrupole Resonance Frequencies by the Solid Effect. J. Magn. Reson. 2008, 193, 54−62. (20) Seliger, J.; Ž agar, V.; Blinc, R. A New Highly-Sensitive 1H-14N Nuclear-Quadrupole Double-Resonance Technique. J. Magn. Reson., Ser. A 1994, 106, 214−222. (21) Seliger, J.; Ž agar, V.; Blinc, R. 1H-14N Nuclear Quadrupole Double Resonance With Multiple Frequency Sweeps. Z. Naturforsch., A: Phys. Sci. 1994, 49, 31−34. (22) Seliger, J.; Ž agar, V. Tautomerism and Possible Polymorphism in Solid Hydroxypyridines and Pyridones Studied by 14N NQR. J. Phys. Chem. A 2013, 117, 1651−1658. (23) Seliger, J.; Ž agar, V.; Asaji, T.; Gotoh, K.; Ishida, H. A 14N Nuclear Quadrupole Resonance Study of Phase Transitions and Molecular Dynamics in Hydrogen Bonded Organic Antiferroelectrics 55DMBP−H2ca and 1,5-NPD−H2ca. Phys. Chem. Chem. Phys. 2011, 13, 9165−9172. (24) Seliger, J. Nuclear Quadrupole Resonance Study of Hydrogen Bonded Solid Materials. Acta Chim. Slov. 2011, 58, 471−477. (25) Heineking, N.; Dreizler, H.; Schwarz, R. Nitrogen and Deuterium Hyperfine Structure in the Rotational Spectra of Pyridine and [4-D] Pyridine. Z. Naturforsch., A: Phys. Sci. 1986, 41, 1210−1213.

configuration and the energy difference of the two configurations equal to 106 meV. The large quadrupole coupling constant (5.2 MHz) in the higher-energy extreme configuration rules out the possibility of the proton two-site exchange. We analyzed the previously published 14N NQR data in PDA in the model of a resonance hybrid of two extreme electron configurations of the molecule and obtained the quadrupole coupling constants in the two electron configurations equal to 2.3 and 5.2 MHz and the energy difference of the two extreme configurations equal to 40 meV. The 14N NQR data in DPDA show the presence of a quasicontinuous isosymmetric phase transition at around 210 K. No mixture of the high-temperature phase and the low-temperature phase has been observed below this temperature. We analyzed the temperature dependence of the 14N quadrupole coupling constant in DPDA also in the model of a resonance hybrid of two extreme electron configurations of the molecule and obtained the 14N quadrupole coupling constants in the two extreme electron configurations equal to 2.1 and 5.2 MHz. Far below the phase transition temperature, the contribution of the higher energy configuration is negligible, whereas above the phase transition temperature, the contribution of the higher energy configuration is approximately 40% and the energy difference of the two extreme electron configurations is equal to 10 meV. The simultaneous change of the O···O and N···O distances in the phase transition region, as observed by 2H NMR, suggests that the electron structures of the two hydrogen bonds are not independent.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +386 1 4766576. Fax: +386 1 2517281. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the Slovenian Research Agency program P1-0125.

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Nuclear Quadrupole Resonance Study of Proton and Deuteron

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