O Quadrupole Coupling in - American Chemical Society

Article pubs.acs.org/JPCA

Unusual Electron Charge Density in Carboxylic Acid. 17O Quadrupole Coupling in cis-Cyclobutane-1,2-dicarboxylic Acid Janez Seliger*,†,‡,§ and Veselko Ž agar† †

Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia § EN-FIST Centre of Excellence, Dunajska 156, 1000 Ljubljana, Slovenia ‡

ABSTRACT: The 17O NQR frequencies have been measured in ciscyclobutane-1,2-dicarboxylic acid and the quadrupole coupling tensors have been determined at various temperatures. Two O···H oxygen positions and two O−H oxygen positions are observed, showing the presence of two different types of O−H···O hydrogen bonds in the unit cell. The quadrupole coupling constants at the O−H oxygen positions are approximately 30% lower than the lowest quadrupole coupling constants experimentally observed at the C−O−H positions in other carboxylic acids with either ordered or disordered hydrogen bonds. The O−H distances have been calculated from the 17O−1H dipole−dipole interaction at the O−H oxygen positions. The obtained values are longer than the O−H distances usually found in O−H···O hydrogen bonds with comparable O···O distance, in agreement with the proposed proton exchange O−H···O ↔ O···H−O, which partially averages the dipole− dipole interaction. The energy difference of the two proton configurations, O−H···O and O···H−O, is calculated from the O−H distances determined by NQR. The temperature dependence of the 17O quadrupole coupling tensors at the 17O···H−O oxygen positions is analyzed in the model of proton exchange and the energy differences of the two proton configurations obtained by this analysis agree with the values obtained from the O−H distances. The quadrupole coupling tensors are analyzed in a model based on the Townes and Dailey model. The model shows that the population of an oxygen lone pair orbital is at this oxygen position reduced from 2 to approximately 1.3. The electron electric charge is most probably transferred to the oxygen σ and π electron orbitals. This may be associated with the structure of the cyclobutane ring, where the X-ray data show the presence of two unusually short C−C bonds.

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INTRODUCTION A cis-cyclobutane-1,2-dicarboxylic acid molecule is in the solid state bound to two other molecules by two centrosymmetric pairs of O−H···O hydrogen bonds. Each pair of bonds is formed by two carboxylic groups (Figure 1).1 The hydrogen

The centrosymmetric pairs of O−H···O hydrogen bonds are found in a number of carboxylic acids that form dimers in the solid state. A significant degree of the proton disorder has been observed in some carboxylic acid dimers. The proton disorder has been interpreted in two ways. Furić5 has proposed a model in which the eight-membered hydrogen-bonded ring performs a 180° reorientation about the C−C axis, whereas Meier and coworkers6,7 and Nagaoka and co-workers8 proposed a model in which the two protons of an eight-membered hydrogen-bonded ring perform concerted jumps OH···O ↔ O···HO. A study of isotope effect in mixed isotope samples (1H and 2H) of benzoic acid dimers by 1H NMR relaxometry and quasielastic neutron scattering proves the model of two-proton transfer.9 Van der Helm and co-workers1 concluded on the basis of the CO and CO distances that a certain degree of proton disorder is presented also in the title compound. Nuclear quadrupole resonance (NQR) is a radio-frequency spectroscopic method that is sensitive to the electric charge distribution in the vicinity of the observed atomic nucleus. In the case of an O−H···O hydrogen bond the 17O NQR spectrum reflects the electron distribution at the hydrogen bond donor and acceptor positions. The 17O NQR parameters

Figure 1. Hydrogen bonding motif in cis-cyclobutane-1,2-dicarboxylic acid.

bonding motif is different than in similar compounds, transcyclobutane-1,2-dicarboxylic acid2 and cyclobutene-1,2-dicarboxylic acid.3 In trans-cyclobutane-1,2-dicarboxylic acid each molecule is bound to two neighboring molecules by two equivalent centrosymmertic pairs of hydrogen bonds whereas in cyclobutene-1,2-dicarboxylic acid the intramolecular and intermolecular O−H···O hydrogen bonds alternately connect the carboxylic groups forming linear chains. The later compound is an organic ferroelectric with the ferroelectric phase persisting until the thermal decomposition.4 © 2012 American Chemical Society

Received: February 23, 2012 Revised: June 8, 2012 Published: June 8, 2012 7139

dx.doi.org/10.1021/jp301802v | J. Phys. Chem. A 2012, 116, 7139−7146

The Journal of Physical Chemistry A

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are related to the position of the hydrogen nucleus (proton) within the bond and reflect the proton disorder. Gough and co-workers10 analyzed the 17O NQR data from various carboxylic acid dimers11 and related compounds. They proved the validity of the two-proton jump model. They also showed that the hydrogen bonds are indeed strongly disordered. A 17O NQR study of substituted benzoic acid dimers12,13 proved the model of concerted proton jumps. The energy difference of the two proton configurations has also been determined. The microscopic details of the electron distribution and proton disorder in a pair of the O−H···O hydrogen bonds formed by two carboxylic acids are not yet completely understood. To contribute to the understanding of some of these details, we performed a 17O NQR study of ciscyclobutane-1,2-dicarboxylic acid. During our study we observed unusually low 17O quadrupole coupling constants at the O−H oxygen positions which we relate to an unusual electron distribution at the oxygen atom.

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17

qZZ =

e 2qQ h

1+η 2 1−η = −qZZ 2

qYY = −qZZ qXX

(2) 17

ii. Proton Exchange. When the EFG tensor at the O position varies in time, as for example in the case of a proton exchange between two sites in an O−H···O hydrogen bond, the NQR spectrum depends on the characteristic frequency of the time variation. The characteristic frequency of the proton exchange is mainly much higher than the 17O NQR frequencies. In this case, the 17O NQR spectrum depends on the timeaveraged EFG tensor. We assume that the O−H···O hydrogen bond is asymmetric and proton exchanges between two nonequivalent positions with the probability P for the O−H···O proton position and (1 − P) for the O···H−O proton position (P > 0.5) as shown in Figure 2. In the 17O NQR spectrum we observe two oxygen

O NQR

i. NQR Frequencies. 17O, the only magnetically active stable oxygen isotope, has a natural abundance of 0.037%. The spin of 17O is I = 5/2. In zero magnetic field a 17O nucleus exhibits three doubly degenerate nuclear quadrupole energy levels. Their energies depend on the 17O nuclear quadrupole moment eQ and on the electric-field-gradient (EFG) tensor Vik = ∂2V/∂xi∂xk, composed of the second derivatives of the electrostatic potential V at the position of the 17O nucleus with respect to the coordinates. The symmetric traceless second rank EFG tensor has three real principal values: VZZ = eq, VYY, and VXX (|VZZ| ≥ |VYY| ≥ |VXX|). The energies of the nuclear quadrupole energy levels as well as the transition (NQR) frequencies depend on the quadrupole coupling constant eQVZZ/h = e2qQ/h and on the asymmetry parameter η, η = (VXX − VYY)/VZZ, of the EFG tensor. Here h is Planck constant. The energies E of the three doubly degenerate nuclear quadrupole energy levels are calculated from the secular equation:14 x 3 − 7(3 + η2)x − 20(1 − η2) = 0

Figure 2. Proton exchange in a pair of hydrogen bonds.

positions 17O−H and H···17O and the NQR frequencies depend on four 17O EFG tensors: V(17O−H···O), V(17O···H− O), V(O−H···17O), and V(O···H−17O). The time-averaged EFG tensors at the 17O−H and H···17O oxygen positions are expressed as V(17O−H) = P V(17O−H···O) + (1 − P)V(17O···H−O) V(H···17O) = P V(O−H···17O) + (1 − P)V(O···H−17O)

(3)

The probability P depends on temperature. It is related to the equilibrium constant K, K = exp(−G/RT), as

P = 1/(K + 1)

(4)

Here G/NA is the energy difference ΔE of the two proton configurations of a centrosymmetric pair of hydrogen bonds. iii. Dipolar Structure of 17O NQR Lines. We assume that 17 a O nucleus interacts with the nearest hydrogen nucleus in zero external magnetic field. The Hamiltonian reads

(1)

Here an energy E is expressed as E = (e2qQ/20)x, where x is a solution of the secular equation. The three 17O NQR frequencies are usually designated as ν5/2−1/2 > ν5/2−3/2 ≥ ν3/2−1/2. They uniquely depend on the quadrupole coupling constant e2qQ/h and the asymmetry parameter η. The asymmetry parameter η is calculated from the ratio R = ν3/2−1/2/ν5/2−3/2, which monotonously changes from R = 0.5 at η = 0 to R = 1 at η = 1. When η is known, the quadrupole coupling constant can be calculated from any 17O NQR frequency. The EFG tensor Vik cannot be measured directly. The NMR experiment in a single crystals gives the quadrupole coupling tensor qik, qik = eQVik/h. The NMR and NQR experiments in powder samples give only the principal values of the quadrupole coupling tensor. The principal values of the quadrupole coupling tensor are calculated from e2qQ/h and η as

H = HQ (17O) + HD(17O−1H) HQ (17O) =

e 2qQ ⎛ 2 ⎜3I Z − I (I + 1) 4I(2I − 1) ⎝ ⎞ η + (I+2 + I −2)⎟ ⎠ 2

HD(17O−1H) =

μ0 ℏ2γHγO 4πr 3

(I S⃗ ⃗ − 3(I n⃗ ⃗)(Sn⃗ ⃗))

(5) 17

Here eQ is the nuclear electric quadrupole moment of O, eq is the largest principal value, and η is the asymmetry parameter of the EFG tensor at the position of 17O, I ⃗ is the spin of 17O, S⃗ is the spin of 1H, n⃗ is the unit vector along the O−H bond, and γO 7140



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and γH are the gyromagnetic ratios of 17O and 1H, respectively. The dipolar contribution HD(17O−1H) may be treated as a perturbation. The energy levels of the main contribution HQ(17O) are calculated according to expression 1 and the six eigenstates |±m⟩ (m = 5/2, 3/2, 1/2) may be generally written in the form14 m m |±m⟩ = C5/2 (η)|±5/2⟩ + C1/2 (η)|± 1/2⟩ m + C3/2 (η)|∓3/2⟩

(5a)

The two eigenstates |+m⟩ and |−m⟩ are degenerate. The label m = 5/2 stands for the highest energy level and the level m = 1/2 stands for the lowest energy level when e2qQ/h > 0. It denotes the magnetic quantum numbers of the eigenstates in the case of η = 0 (Cnm(0) = δmn). Each doubly degenerate nuclear quadrupole energy levels splits due to the dipolar interaction with the nearest proton (S = 1/2) into a quartet of energy levels. Their energies can be calculated analytically when the O−H bond is in the X−Y, X−Z, or Y−Z plane of the principal coordinate system of the EFG tensor. In the case of a C−O−H group one of the principal axes of the 17O EFG tensor (usually X or Y15) is expected to point perpendicular to the C−O−H plane. For this situation the shifts of the four dipolar energy levels δE from the energy of the nuclear quadrupole energy level |±m⟩ are given as16

Figure 3. Dependences of the widths of the 17O NQR lines on the angle between the principal axis Z of the EFG tensor and the direction of the O−H bond for the O−H bond lying in the X−Z plane (full lines) and in the Y−Z plane (broken lines).

assumed that the O−H bond lies either in the X−Z plane or in the Y−Z plane of the EFG tensor. It should be noted that the proton two-site exchange produces an apparent increases the O−H distance. The distance R determined from the widths of the 17O NQR lines is given by the expression17,18

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O−H⊥Y

δE3,4 = b ±

(2c − a)2 + 3(a 2 − c 2) sin 2 θ

O−H⊥X (2c + b)2 + 3(b2 − c 2) sin 2 θ

δE1,2 = −a ± δE3,4 = a ±

(2c − b)2 + 3(b2 − c 2) sin 2 θ

(6)

Here the parameters a, b, and c are expressed as a = 2K ⟨−m|IX |m⟩ b = 2iK ⟨−m|IY |m⟩ c = 2K ⟨m|IZ|m⟩ K=

μ0 ℏ2γHγO 16πr

3

=h

4.08 kHz r 3(0.1 nm)

(8)

EXPERIMENTAL SECTION cis-Cyclobutane-1,2-dicarboxylic acid was purchased at Sigma Aldrich and used as obtained. For the measurement of the 17O NQR spectra we used several 1H−17O NQDR techniques based on magnetic field cycling between a high magnetic field B0 and zero magnetic field. A pneumatic shuttle of the sample between two magnets with B0 = 0.75 T and B < 50 μT has been used. The distance between the two magnets is 35 cm. The transfer time between the two magnets is 0.1 s. A magnetic field cycle starts with the proton polarization in the high magnetic field B0. The sample is then adiabatically transferred into zero magnetic field where it stays for a time τ. This period is called the relaxation period. The sample is at the end of the relaxation period transferred back into the high magnetic field B0 and the proton NMR signal S is measured immediately after the sample stops in the high magnetic field. During the adiabatic transfer from B = B0 to B = 0 the spin temperature of the proton spin system drops in a solid sample for about 3 orders of magnitude and the Zeeman order transfers to dipolar order. In zero magnetic field the spin temperature of the proton dipolar spin reservoir, which is initially low, exponentially approaches the sample temperature with the spin−lattice relaxation time T1(B=0). When at the end of the relaxation period, the magnetic field at the sample position adiabatically increases from B = 0 to a magnetic field that is larger than the local dipolar magnetic field a proton magnetization M establishes. The proton magnetization M is proportional to the inverse spin temperature of the proton dipolar system. The intensity of the proton NMR signal S at the end of the magnetic field cycle, when the sample reaches the high magnetic field B0, is proportional to M. It exponentially decays on increasing τ as S = S0 exp(−τ/T1(B=0)). In a NQDR experiment τ is fixed at a value approximately equal to T1(B=0). One or more radio-frequency (rf) magnetic fields are applied during the relaxation period.

(2c + a)2 + 3(a 2 − c 2) sin 2 θ

δE1,2 = −b ±

R−3 = PR−3(17O−H···O) + (1 − P)R−3(17O···H−O)

(7)

The transition between two 17O nuclear quadrupole energy levels consists in fact of 4 × 4 = 16 transitions between the dipolar energy levels with slightly different frequencies. The NQR line is broadened and structured. From the dipolar structure of the three 17O NQR lines it is in principle possible to determine the O−H distance, the orientation of the O−H bond in the eigenframe of the EFG tensor and the sign of the quadrupole coupling constant. All this is possible when the dipolar structure is well resolved, i.e., in the case of a strong 17 O−1H dipolar interaction and a weak 1H−1H dipolar interaction. The O−H distance can also be determined from the 17O NQR line-widths. In Figure 3 we show the dependence of the widths of the three 17O NQR lines 5/2−1/2, 5/2−3/2, and 3/2−1/2 on the angle between the O−H bond and the principal axis Z of the EFG tensor in the case of η = 0.7. It is 7141



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In Slusher and Hahn’s technique,19 we apply during the relaxation period a strong (several millitesla) phase modulated rf magnetic field with the frequency ν. A square 180° phase modulation of the rf magnetic field with the modulation frequency about 1 kHz is normally used. A frequency scan is performed in the range where the 17O NQR frequencies are expected to be found in steps of 10 kHz. Several magnetic field cycles are repeated at a fixed value of ν and the proton NMR signal is averaged. When the frequency ν matches a 17O NQR frequency νQ, the interaction between the “hot” 17O spin system quantized in the quadrupole rotating frame and the “cold” proton dipolar spin system produces a relaxation of the proton spin temperature toward infinity and consequently a lower proton magnetization at the end of the magnetic field cycle. In the ν dependence of the proton NMR signal S, we observe a dip when the frequency ν matches a 17O NQR frequency. When the proton−17O magnetic dipolar interaction is strong, as in an O−H group, it produces in zero magnetic field a splitting of the 17O nuclear quadrupole energy levels into dipolar quartets. The width of a quartet is approximately 50 kHz when the proton−oxygen distance is 0.10 nm. The 17O NQR lines are in this case about 100 kHz broad. The structure and width of a 17O NQR line can be measured by a twofrequency20 or by a three-frequency technique.21 In the twofrequency technique that has been used in the present study we apply during the relaxation period two rf magnetic fields with the frequencies ν1 and ν2. The basic of this technique is as follows. The dipolar energy levels of each quartet are coupled to the dipolar energy reservoir of the rest of protons. So the proton dipolar system establishes within each quartet the Boltzmann distribution over the energy levels with the temperature equal to the spin temperature of the proton dipolar system. When one of the two frequencies, e.g., ν1, lies within a dipolar broadened 17O NQR line, the rf irradiation equalizes the population of the two dipolar energy levels separated by ν1 in frequency. This produces a number of flipflop transitions in both quartets hit by the rf irradiation on one side and in the proton dipolar energy reservoir on the other side. These transitions reestablish the Boltzmann population over the energy levels in the two quartets. These flip-flop transitions produce a small increase of the proton dipolar spin temperature, which usually cannot be observed. When the two nonequal frequencies ν1 and ν2 lie within a dipolar broadened 17 O NQR line, the Boltzmann distribution over the energy levels in the two quartets hit by the irradiations cannot be established and a continuous flow of energy from the quartets to the proton dipolar system takes place. This causes an increase of the proton dipolar spin temperature at the end of the relaxation period and consequently a decrease of the proton NMR signal S at the end of the magnetic field cycle. In an actual experiment the 17O NQR lines are first located by the Slusher and Hahn’s technique. After the 17O NQR lines are located, the two-frequency technique is used so that one of the two frequencies, e.g., ν1, is fixed close to one edge of the NQR line and a scan is performed by the frequency ν2. A lower proton NMR signal S is observed when the frequencies ν1 and ν2 are not equal and when the frequency ν2 remains within the same 17O NQR line as ν1. So the other edge of the 17O NQR line is determined. Then the frequency ν1 is fixed at the other edge of the 17O NQR line and the scan is repeated. Both scans give the structure and the width of the NQR line. The two-

frequency technique can also be used to resolve overlapping O NQR lines.

17

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EXPERIMENTAL RESULTS AND DISCUSSION i. Experimental Results. The 1H−17O NQDR spectrum of cis-cyclobutane-1,2-dicarboxylic acid at T = 163 K as measured by Slusher and Hahn’s technique is presented in Figure 4a. Two

Figure 4. 1H−17O NQDR spectrum of cis-cyclobutane-1,2-dicarboxylic acid at T = 163 K measured by the Slusher and Hahn’s technique (a) and two-frequency analysis of two overlapping 17O NQR lines centered at 850 kHz (b). The arrows indicate the fixed frequency ν1 in the three ν2-scans.

strong broad lines centered at 850 and 1070 kHz are observed. Four additional narrower and weaker lines are observed at 1245, 1355, 1650, and 1840 kHz. The four narrower and weaker lines are the 3/2−1/2 and 5/2−3/2 transition lines from the 17O···H oxygen positions in two different hydrogen bonds. The NQDR lines at 1245 and 1840 kHz are somewhat narrower than the lines at 1355 and 1650 kHz. The pair of lines observed at 1245 and 1840 kHz thus corresponds to the hydrogen bond where the O···H distance is larger than in the other bond. The two broad and strong NQDR lines correspond to the C−O−H oxygen positions. We actually expect four lines. The reason for observing only two lines is that the NQR lines overlap. The lines are resolved by the two-frequency technique. Figure 4b shows how the two NQDR lines forming the broad NQDR line centered at 850 kHz are resolved and the widths of the individual lines are determined. First the frequency ν1 is fixed in the center of the line (ν1 = 850 kHz) and the scan by the frequency ν2 is performed over the complete line. In such a way the lower edge of the 17O NQR line with the lower frequency and the upper edge of the 17O NQR line with the higher frequency are determined as being equal 780 and 925 kHz. Then the frequency ν1 was fixed close to the lower edge obtained by the first scan (790 kHz) and the scan by the frequency ν2 is repeated. A lower proton signal is observed until the frequency ν2 remains within the 17O NQR line starting at 780 kHz. This line ends at 870 kHz. Then the frequency ν1 was fixed close to the upper edge of the overlapping lines (910 kHz) and the scan by the frequency ν2 gives the lower edge of the 17O NQR line at 825 kHz. So the two lines corresponding to the 1/2 − 3/2 transition are centered at 825 and 875 kHz and have the widths 90 and 100 kHz, respectively. In the same way we resolved also the two NQR lines from the 17O−H oxygen positions corresponding to the transition 5/ 2−3/2. They are centered at 1030 and 1105 kHz and have the 7142



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quadrupole coupling constant at the COH oxygen position.12,13 This is the effect of increasing proton disorder. In the present compound the 17O quadrupole coupling constants at the CO oxygen positions indeed decrease on increasing temperature whereas the 17O quadrupole coupling constants at the COH oxygen positions increase on increasing temperature. This cannot be solely the effect of increasing proton disorder. The structures and widths of the 17O NQR lines at the C− O−H oxygen positions have been precisely measured at 161 K and the O−H distances R(O−H) have been calculated from expressions 6 and 7 as being equal R(O(1)−H) = 0.111 ± 0.003 nm and R(O(10)−H) = 0.108 ± 0.003 nm. A larger O− H distance is assumed to correspond to a shorter C−O distance as determined by the X-ray diffraction.1 In both cases the O−H bond lies in the Y−Z plane of the EFG tensor and forms an angle of 55° ± 5° with the Z axis. The sign of the quadrupole coupling constant seems to be at both oxygen positions negative, but the poorly resolved dipolar structure of the 17O NQR lines, which is the consequence of relatively broad proton dipolar line in zero magnetic field, makes this conclusion questionable. ii. Proton Exchange and the O−H Dipole Interaction. The lengths of the two hydrogen bonds in cis-cyclobutane-1,2dicarboxylic acid are equal R(O(1)−O(2)) = 0.264 nm and R(O(10)−O(9)) = 0.265 nm.1 The O−H distance is in ordered hydrogen bonds with comparable hydrogen bond length between 0.101 and 0.102 nm.23 An apparently larger O− H distance observed in the present case is the effect of the proton disorder O−H···O ↔ O···H−O. This disorder partially averages the 1H−17O magnetic dipole interaction. This is of course not the only motion producing an apparently longer O− H distance and the temperature variation of the NQR frequencies in hydrogen bonded systems. The inclusion of fluctuations and disorder in terms of atomic motion of the surrounding molecules turns out to be important to obtain the correct magnitude of the temperature effect.26 Anyhow a large difference between the expected and experimentally observed O−H distances suggests that the proton exchange is the dominant mechanism. We calculate the probability P of the more probable proton configuration of the hydrogen bond according to expression 8. For the O−H distance we use an average value R(O−H) = 0.1015 nm. The O···H distance we calculate from the O···O distance assuming that the O−H···O angle is close to 180°. For the hydrogen bond O(1)−H···O(2) we obtain P = 0.69. This corresponds to the energy difference ΔE1,2 equal ΔE1,2 = kB 130 K = 11 meV. In a similar way we obtain for the O(10)− H···O(9) hydrogen bond the probability P equal 0.78 corresponding to ΔE10,9 = kB 200 K = 17 meV. These energy differences are of the same order of magnitude as the energy differences observed in substituted benzoic acid dimers.12,13 iii. Quadrupole Coupling Tensors. To understand the unusually low quadrupole coupling constants observed at the COH oxygen positions, we propose a model in which the electron electric charge is from the oxygen lone-pair orbitals partially transferred to the σ and π orbitals. We calculate the change in the quadrupole coupling tensor in a simple model based on the Townes and Dailey model.27 The basic supposition is that a nonbonding lone electron pair produces an axially symmetric contribution to the quadrupole coupling tensor with the magnitude q1 directed in the direction of the lone pair orbital. A bonding electron in either the σ- or π-bond

widths 90 and 80 kHz, respectively. The widths and positions of the 17O NQR lines are determined with an accuracy of ±10 kHz. To investigate the changes of the 17O NQR parameters produced by the proton disorder, we measured the 17O NQR frequencies at three temperatures: 163, 201, and 241 K. The 17 O NQR frequencies, quadrupole coupling constant, and asymmetry parameter η at various oxygen positions are presented in Table 1. The CO and COH oxygen Table 1. 17O NQR Frequencies, Quadrupole Coupling Constant e2qQ/h, and Asymmetry Parameter η at Various Oxygen Positions in cis-Cyclobutane-1,2-dicarboxylic Acid T (K) 163

201

241

oxygen position

ν5/2−3/2 (kHz)

ν3/2−1/2 (kHz)

e2qQ/h (kHz)

η

C−O(1)H C−O(10)H CO(2) CO(9) CO(1)H CO(10)H CO(2) CO(9) CO(1)H CO(10)H CO(2) CO(9)

1105 1030 1650 1840 1125 1050 1620 1800 1140 1065 1585 1760

825 875 1355 1245 830 880 1360 1290 840 890 1370 1335

3950 3770 6005 6455 4010 3835 5920 6385 4065 3890 5825 6310

0.661 0.807 0.768 0.549 0.648 0.791 0.793 0.615 0.646 0.788 0.827 0.677

positions are assigned according to the CO bond lengths.1 A shorter CO bond length corresponds to a more asymmetric OH···O hydrogen bond and to narrower C17O NQR lines and broader C17OH NQR lines. The 17O quadrupole coupling constants and asymmetry parameters η at the CO oxygen positions fall in the range observed in other carboxylic acids whereas the 17O quadrupole coupling constants at the COH oxygen positions (∼4 MHz) are significantly lower than the lowest 17O quadrupole coupling constants (∼6 MHz) observed at this position in carboxylic acids with either asymmetric or symmetric hydrogen bonds.11−13,22−25 A lower quadrupole coupling constant can be in principle the effect of a strong molecular disorder, as for example, the 180° reorientation around the CC axis proposed by Furić,5 which causes an averaging of the quadrupole coupling tensor. The characteristic frequency of this motion must be higher than the 17O NQR frequencies to observe averaging. Such a violent motion, in which protons are involved, usually produces a high proton spin−lattice relaxation rate T1−1, which increases on decreasing temperature as the reorientations slow down. The magnetic field cycling experiments did not show any exceptionally short proton T1 in the frequency range between ∼20 kHz and 32 MHz and in the temperature range between 160 K and room temperature. Moreover, the proton spin−lattice relaxation rate decreases on decreasing temperature. These observations make the reorientations highly improbable. The second unusual feature is the temperature dependence of the 17O quadrupole coupling constants. In several carboxylic acid dimers we observe the decrease of the 17O quadrupole coupling constant at the COH oxygen position on increasing temperature. On the other side, at the CO···H oxygen position, the 17O quadrupole coupling constant first decreases and then increases and approaches the 17O 7143



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produces an axially symmetric contribution to the quadrupole coupling tensor with the magnitude q2 directed along the bond. Both q1 and q2 are positive. The EFG tensor produced by a negative electron has a negative principal value along the symmetry axis and the17O nuclear electric quadrupole moment is negative, so their product is positive. We first consider an ideal noninteracting CO group and an ideal noninteracting COH group. The electron distribution in both groups is presented in Figure 5 together with the principal directions of

qOH

⎡q − q 0 0 ⎤ ⎡−9.5 0 0 ⎤ 1 ⎢ 2 ⎥ ⎢ ⎥ = ⎢0 ⎥ = ⎢0 0 0 0 0 ⎥ MHz ⎢0 0 q1 − q2 ⎥⎦ ⎢⎣ 0 0 9.5⎥⎦ ⎣ (11)

An analysis of the experimentally available 17O NQR data15 indeed shows that the quadrupole coupling tensor at the C− O−H oxygen position approaches the form given by expression 11. The analysis further shows a linear correlation of the principal values of the quadrupole coupling tensor covering the whole range from the CO oxygen position to the C−O−H oxygen position which may be by the present assignment of the principal axes a, b, and c expressed as qaa = −5.8 MHz − 0.37qcc qbb = 5.8 MHz − 0.63qcc

Figure 5. Distribution of bonding (full circles) and nonbonding (open circles) electrons around an oxygen atom in a CO and in a CO H group. The approximate principal directions a and b of the quadrupole coupling tensor are shown for both cases. The principal axis c is perpendicular to the plane of the figure.

The two limiting quadrupole coupling tensors (expressions 10 and 11) obtained under simplified conditions agree well with eqs 12. The symmetric hydrogen bonds are observed at qcc ≈ 1 MHz. Figure 6 presents the 17O NQR data for the present compound on the correlation diagram of −qaa and qbb versus

the quadrupole coupling tensor which are determined on the basis of symmetry arguments. The principal directions of the quadrupole coupling tensor we label as a, b, and c. First we consider the CO group. In this simple model we assume that the three in-plane contributions to the quadrupole coupling tensor (the σ-bond and two lone-pair orbitals) are arranged symmetrically around the oxygen atom with the angle between them equal 120°. The π-bond contribution points along the c direction perpendicular to the plane. The 17O quadrupole coupling tensor qO is in this simplified situation equal ⎡1 1 ⎢ q2 − q1 2 4 ⎢ ⎢ qO = ⎢ 0 ⎢ ⎢ ⎢⎣ 0

0 5 q − q2 4 1 0

⎤ ⎥ ⎥ ⎥ 0 ⎥ ⎥ ⎥ 1 q2 − q1⎥ ⎦ 2

Figure 6. Principal values qaa and qbb versus the principal value qcc of the quadrupole coupling tensor in cis-cyclobutane-1,2-dicarboxylic acid at various temperatures. The arrows indicate the increasing temperature. The full lines are given by eqs 12.

0

qcc. The quadrupole coupling constants at the O−H oxygen positions are assumed to be negative as suggested by the dipolar structure of the 17O NQR lines. The NQR data for the CO oxygen positions (O(9) and O(2)) agree with the eqs 12. Also the temperature variation of qaa, qbb, and qcc at these oxygen positions agrees with increasing proton disorder that changes their values in the direction of the symmetric hydrogen bond. The quadrupole coupling data for the C−O−H oxygen positions (O(10) and O(1)) are observed far from the correlation lines. Also the temperature variation of qcc is opposite to the temperature variation of qcc in “normal” hydrogen bonds. We assume that the temperature variation of qaa, qbb, and qcc is the consequence of a fast proton exchange between two nonequivalent proton positions in the hydrogen bond: O− H···O ↔ O···H−O. The principal axis c of the EFG tensor at a given oxygen position does not change when the proton jumps. The average value ⟨qcc(H···17O)⟩ observed by NQR at the O− H···17O oxygen position is under this assumption equal

(9)

To obtain the values of q1 and q2, we use the data for formaldehyde determined in the gas phase by the microwave spectroscopy.28 The 17O quadrupole coupling tensor is in this case ⎡−1.89 0 ⎤ 0 ⎢ ⎥ q0 = ⎢ 0 12.37 0 ⎥ MHz ⎢⎣ 0 0 −10.48 ⎥⎦

(12)

(10)

From expressions 9 and 10 we obtain q1 = 11.45 MHz and q2 = 1.95 MHz. A strongly bound electron in the lone-pair orbital produces approximately a 3 times larger contribution to the quadrupole coupling tensor than a valence electron. Next we consider a noninteracting C−O−H group. Here we asume that all four electron orbitals point in the tetrahedral directions with an angle 109° between two orbitals. The quadrupole coupling tensor qOH is under this assumption equal

⟨qcc(H···17O⟩ = Pqcc(O−H···17O) + (1 − P) qcc(O···H−17O) 7144

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Article

⎡−7.5 0 0 ⎤ ⎢ ⎥ qN(17O−H···O) = ⎢ 0 3.0 0 ⎥ MHz ⎢⎣ 0 0 4.5⎥⎦

Here qcc(O−H···17O) and qcc(O···H−17O) are the values of qcc at the position of 17O when the proton is at the more and less probable position, respectively. The values of qcc(O−H···17O) and qcc(O···H−17O) depend on the length of the hydrogen bond and may not be mixed with their limiting values given by expressions 10 and 11. A correlation between qcc(O−H···17O) and qcc(17O−H···O) has also been observed in hydrogen bonds of various length given as15 qcc(O−H···17O) + 1.5qcc(17O −H···O) = 2.9 MHz

⎡−4.5 0 0 ⎤ ⎢ ⎥ qN( O···H−O) = ⎢ 0 8.0 0 ⎥ MHz ⎣0 0 −3.5⎦ 17

The comparison of expressions 16 and 17 shows that in the O− H proton configuration the principal value qbb(17OH···O) is nearly equal to the principal value qNbb(17OH···O). On the other hand, the principal values qaa(17OH···O) and qcc(17O H···O) differ from qNaa(17OH···O) and qNcc(17OH···O) by ±4.2 MHz. The situation is different in the 17O···H proton configuration. Here qaa is nearly unchanged whereas qbb and qcc change in average for ±4.1 MHz. An inspection of Figure 5 and expressions 9 and 10 shows that this may be the consequence of a reduced population of the lone-pair orbitals which dominate the quadrupole coupling tensor of 17O. In a C O···H group the principal value qaa only weakly depends on the change of the population of the lone pair orbitals whereas in a COH group this is the case for the principal value qbb, as experimentally observed. The contribution of a lone pair orbital to the 17O quadrupole coupling tensor is reduced from 11.45 MHz to 11.45 MHz − 4.15 MHz = 7.3 MHz. There are two possible reasons for this reduction. Either the lone pair orbitals may deform and therefore contribute less to the quadrupole coupling tensor or some electron electric charge is transferred to a different position, most probably to the σ and π orbitals of the oxygen atom. In the latter case the amount of the electric charge transferred from the nonbonding oxygen orbitals to the bonding oxygen orbitals is equal 4 × 4.15/11.45 = 1.45 unit electric charge. The reason for the electric charge rearrangement can be guessed on the basis of the X-ray diffraction data.1 Two C−C bonds in the cyclobutane ring are unusually short. In the cyclobutane molecule the C−C bonds are 0.1556 nm long.29 Also in trans-cyclobutane-1,2-dicarboxylic acid the C−C distances are approximately of the same length.2 In the present compound the length of the bond C(4)−C(5) is 0.1526 nm and the length of the bond C(5)−C(6) is 0.1531 nm. The bond C(6)−C(7) has the same length as the bonds in cyclobutane and the bond C(4)−C(7) is only slightly shorter, 0.1546 nm. The authors of the structural study were unable to explain such a large difference in the lengths of the C−C bonds. The present NQR data suggest an explanation of this difference. Shorter C−C bonds are associated with a larger population of the π electron orbitals. It is possible that the excess electron population in the C(4)−C(5) and C(5)−C(6) bonds comes from the carboxylic groups and the rearrangement of the electron charge distribution in an oxygen atom is needed to preserve the C−O and O−H bonds.

(14)

In carboxylic acid dimers with the O···O distance 0.265 nm we experimentally obtained the values qcc(O−H···17O) = −3.5 MHz and qcc(17O−H···O) = 4.5 MHz.12,13 We use these values in the further analysis. First we consider the “normal” O(2) and O(9) oxygen positions. For the calculation of the energy difference of the two proton configurations in the two unequal pairs of hydrogen bonds we use the above values of qcc(O−H···17O) and qcc(17O− H···O) and the experimentally determined values of ⟨qcc(H···17O)⟩ at 163, 201, and 241 K. As the result we obtain ΔE1,2 = kB (115 ± 15) K = 10 ± 1.5 meV and ΔE10,9 = kB (190 ± 15) K = 16 ± 1.5 meV. These values agree within the experimental error with the values calculated from the time averaged proton−oxygen distances at the 17O−H···O oxygen positions 1 and 10. Next we consider the O(1) and O(10) oxygen positions. Here we treat the complete quadrupole coupling tensors. For the sake of simplicity we assume that the angle between the principal axis a (or b) of the 17O quadrupole coupling tensor in the O−H proton configuration and the principal axis a (or b) at the same oxygen position in the O···H proton configuration is small and may be taken as zero. This angle is in the ideal extreme case of noninteracting CO and COH groups (Figure 5) equal 35°. The linear eqs 12 suggest that this angle is indeed small in the range of strong hydrogen bonds. The time averaged quadrupole coupling tensor ⟨q(17OH)⟩ is equal q(17O−H) = P q(17O−H···O) + (1 − P)q(17O···H−O) (15)

The analysis of the experimental data obtained at 161 and 241 K together with the energy differences of the two proton configurations determined from the time-averaged O−H distance and from the 17O NQR data at the O···H oxygen positions 2 and 9 gives ⎡−3.4 0 0 ⎤ ⎢ ⎥ q( O−H···O) = ⎢ 0 3.2 0 ⎥ MHz ⎣0 0 0.2 ⎦ 17

⎡−4.9 0 0 ⎤ ⎢ ⎥ q(17O···H−O) = ⎢ 0 4.1 0 ⎥ MHz ⎢⎣ 0 0 0.8 ⎥⎦

(17)

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CONCLUSIONS The 17O NQR frequencies have been measured in ciscyclobutane-1,2-dicarboxylic acid at various temperatures and the quadrupole coupling tensor has been determined. Two O···H oxygen positions and two O−H oxygen positions are clearly identified in agreement with the crystal structure showing the presence of two different types of O−H···O hydrogen bonds in the unit cell.

(16)

The “normal” quadrupole coupling tensors qN(17OH···O) and qN(17O···HO), observed in a majority of CO− H···OC hydrogen bond with the length about 0.265 nm, are12,13 7145



Article

(16) Seliger, J.; Ž agar, V.; Blinc, R.; Novak, A. J. Chem. Phys. 1986, 84, 5857−5861. (17) Brosnan, S. G. P.; Edmonds, D. T. Phys. Lett. A 1981, 81, 243− 245. (18) Seliger, J.; Ž agar, V.; Blinc, R.; Schmidt, V. H. Phys. Rev. B 1990, 42, 3881−3886. (19) Slusher, R. E.; Hahn, E. L. Phys. Rev. 1968, 166, 332−347. (20) Brosnan, S. G. P.; Edmonds, D. T. J. Magn. Reson. 1981, 45, 440−450. (21) Seliger, J.; Ž agar, V. J. Magn. Reson. 2010, 203, 220−225. (22) Wu, G. Prog. Nucl. Magn. Reson. Spectrosc. 2008, 52, 118−169. (23) Brosnan, S. G. P.; Edmonds, D. T.; Poplett, I. J. F. J. Magn. Reson. 1981, 45, 451−469. (24) Poplett, I. J. F.; Sabir, M.; Smith, J. A. S. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1651−1668. (25) Seliger, J.; Ž agar, V.; Blinc, R. Chem. Phys. Lett. 1989, 164, 405− 408. (26) Schmidt, J.; Sebastiani, D. J. Chem. Phys. 2005, 123, 074501. (27) Townes, C. H.; Dailey, B. P. J. Chem. Phys. 1949, 17, 782−796. (28) Flygare, W. H.; Lowe, J. T. J. Chem. Phys. 1965, 43, 3645−3653. (29) Wiberg, K. B. In The chemistry of cyclobutanes; Rappoport, Z., Liebman, J. F., Eds.; John Wiley & Sons, Ltd.: 2005; pp 1−15.

The shortest O−H distances have been calculated at the O− H oxygen positions from the 1 H− 17 O dipole−dipole interaction. The calculated values, 0.111 and 0.108 nm, are longer than the O−H distances usually found in O−H···O hydrogen bonds with comparable O···O distance. It is assumed that the bonds are disordered and the energy difference of the two proton configurations, O−H···O and O···H−O, is calculated as being equal 11 meV in the hydrogen bond O(1)−H···O(2) and 17 meV in the hydrogen bond O(10)− H···O(9). The 17O quadrupole coupling tensors at the 17O···H−O oxygen positions 2 and 9 are analyzed in the model of proton exchange and the energy difference of the two proton configurations is determined as being equal to 10 and 16 meV. These values agree with the values obtained from the O− H distances within the experimental accuracy. The quadrupole coupling constants at the O−H oxygen positions 1 and 10 are lower than the quadrupole coupling constants experimentally observed at the C−O−H positions in other carboxylic acids. Also the temperature variation of the quadrupole coupling tensor is unusual.. The data are analyzed in a model based on the Townes and Dailey model. The model shows that the contribution of the electrons in the lone pair oxygen orbitals to the quadrupole coupling tensor is reduced for about 2 MHz per electron. So either the lone pair orbitals deform or some electron electric charge is transferred from the nonbonding lone pair orbitals to the bonding σ and π orbitals of an oxygen atom. A possible reason for the rearrangement of the electron charge distribution of an oxygen atom at the O−H oxygen position based on the X-ray data is given.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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REFERENCES

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