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17O quadrupole coupling in C–O–H⋯OC hydrogen bonds
Chemical Physics 231 Ž1998. 81–86
17
O quadrupole coupling in C–O–H PPP O5C hydrogen bonds Janez Seliger
Department of Physics, Faculty of Mathematics and Physics and ‘‘ Jozef ˇ Stefan’’ Institute, UniÕersity of Ljubljana, Ljubljana, SloÕenia Received 18 November 1996; in final form 30 January 1998
Abstract 17
O NQR data of various organic solids containing C–O–H PPP O5C hydrogen bonds are analyzed in a simple model, where the strength of the hydrogen bond is reflected by the principal value V33 of the electric field gradient ŽEFG. tensor along the principal axis which is, at the C–O–H oxygen sites, nearly perpendicular to the plane of the C–O–H group and, at the C5O PPP H oxygen sites, nearly perpendicular to the plane of the C5O PPP H group. A nearly linear correlation between the other two principal values of the EFG tensor and V33 is obtained for both the C–O–H and C5O oxygen sites in carbonyl, carboxyl and hydroxyl groups in organic compounds. A linear correlation between V33 at the C–O–H oxygen site and V33 at the C5O PPP H oxygen site in a C–O–H PPP O5C hydrogen bond is observed, giving a possibility of assigning complex 17O NQR spectra. A correlation between V33 and the length R O PPP O of the hydrogen bond, giving the possibility of extracting structural data from the 17O NQR spectra, is observed for both oxygen sites. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Nuclear quadrupole resonance ŽNQR. is often used to obtain structural data of solids. The NQR frequencies of a nucleus namely depend on its electric quadrupole moment eQ and on the electric field gradient ŽEFG. tensor V at its site. The EFG tensor ŽV. i j s E 2 VrE x i E x j consists of the second derivatives of the electrostatic potential V with respect to the coordinates. The electric quadrupole moment eQ is a characteristic of a nucleus in its nuclear ground state, whereas the EFG tensor depends on the distribution of the electric charges in the neighborhood of the observed nucleus and thus indirectly probes the structure of the solid. The tree principal values of the traceless EFG tensor are usually labeled as VX X , VY Y and VZZ Ž< VX X < F < V Y Y < F < VZZ <.. The NQR frequencies actually depend on two parameters: the quadrupole cou-
pling constant e 2 qQrh s eQVZZrh with h being the Planck constant and on the asymmetry parameter h , h s Ž VX X y VY Y .rVZZ , of the EFG tensor. Crystallographically nonequivalent positions of a given atom result generally in different NQR frequencies of its nucleus. When exploring the details of the crystal structure of a given solid by NQR it is necessary to assign the NQR frequencies to the atomic positions in the unit cell and to relate the NQR frequencies to the arrangement of the neighboring atoms Žcrystal point symmetry, local symmetry, inter atomic distances, etc... This paper represents an attempt to correlate — from the point of view of an experimentalist — the NQR parameters from the C– 17O–H oxygen site to the NQR parameters from the C517O PPP H oxygen site in a C–O–H PPP O5C hydrogen bond and to correlate both sets of the 17O NQR parameters to the hydrogen bond length R O PPP O .
0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 7 9 - 2
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J. Seligerr Chemical Physics 231 (1998) 81–86
2. 17O NQR in carbonyl, carboxyl and hydroxyl groups A 17O nucleus has a spin I s 5r2 and thus in zero magnetic field three NQR frequencies n 5r2 – 1r2 ) n 5r2 – 3r2 G n 3r2 – 1r2 . The 17O NQR frequencies are typically a few MHz. From the 17O NQR frequencies it is possible to calculate the absolute value of the quadrupole coupling constant eQVZZrh and the asymmetry parameter h of the EFG tensor. In an 17 O–H group as well as in a short 17O PPP H hydrogen bond the rather strong proton–oxygen magnetic dipole–dipole interaction produces a fine structure of the 17O NQR lines which may be used for the determination of the O–H distance, the orientation of the O–H bond in the principal-axis frame of the EFG tensor and also the sign of the quadrupole coupling constant w1,2x. The available 17O NQR data for the C–O–H oxygen sites w3–16x, as measured by the double w1,17x and triple w4x resonance techniques, show that the quadrupole coupling constant varies from around 6 MHz in short hydrogen bonds to around 9 MHz when the interaction of the O–H group with the environment is weak. The asymmetry parameter h is in very short hydrogen bonds equal to ; 0.6. On increasing e 2 qQrh the asymmetry parameter h first decreases and reaches the value of zero at e 2 qQrh f 7 MHz. On a further increase of e 2 qQrh the asymmetry parameter h increases and reaches a value close to 1 at e 2 qQrh f 9 MHz. The available analyses of the dipole fine structures of the 17O NQR lines w1,8,9,11–16x show that it is the X-principal axis which is at a low quadrupole coupling constant perpendicular to the O–H bond. On the other hand at a large quadrupole coupling constant the Y-principal axis points perpendicular to the O–H bond. The sign of the quadrupole coupling constant is negative. Also in some papers of our group w13–16x where it is stated that the quadrupole coupling constant is positive we did not take into account the negative value of the 17O gyromagnetic ratio g . At the C5O sites w3–15x the quadrupole coupling constant is in short hydrogen bonds around 6 MHz and the asymmetry parameter is around 0.6. On increasing the length of the hydrogen bond the quadrupole coupling constant decreases and the
asymmetry parameter h increases. At approximately e 2 qQrh f 5.8 MHz the asymmetry parameter h reaches the value of one. Then the quadrupole coupling constant increases and the asymmetry parameter decreases until at e 2 qQrh f 8 MHz the asymmetry parameter becomes equal to 0. At still higher quadrupole coupling constants the asymmetry parameter h again increases. The highest quadrupole coupling constant and the corresponding h at a C517O site observed in solids are around 11.5 MHz and 0.45, respectively, whereas in gaseous formaldehyde the values of e 2 qQrh s q12.37 MHz and h s 0.694 are observed by microwave spectroscopy w18x. The analyses of the dipole fine structures of the 17 O NQR lines from the C517O PPP H sites show that in a short hydrogen bond the X-principal axis of the EFG tensor at the 17O site points perpendicular to the O PPP H bond. On the basis of the proton disorder model w13,19x it may be concluded that also at larger quadrupole coupling constants Žup to around 8 MHz. in some planar compounds the X-principal axis of the EFG tensor at the 17O PPP H site points perpendicular to the plane of the C–O–H PPP O5C group. The quadrupole coupling constant of the 17 O PPP H oxygen is in very short hydrogen bonds negative and in longer hydrogen bonds positive. On the basis of the above data we may suppose that the 17O quadrupole coupling constant in solids ranges from ; y9 MHz for a ‘pure’ C–O–H site to ; q11.5 MHz for a ‘pure’ C5O site. The out-ofplane principal value of the EFG tensor Ž V33 in later discussion. ranges from ; q9 MHz for a ‘pure’ C–O–H site to ; y8 MHz for a ‘pure’ C5O site. These suppositions are in agreement with the theoretical predictions Žw20,21x and references cited therein. of the signs of the principal values and the orientations of the principal axes of the 17O quadrupole coupling tensor in carbonyl, carboxyl and hydroxyl groups in organic compounds. Gready w20x also observed an approximate correlation between the oxygen p p population and the out-of-plane EFG magnitude Ž V33 . which agrees with the predictions of the Townes and Dailey theory. A correlation of e 2 qQrh vs. h has been observed for both the C–O–H and C5O oxygen sites w6,9,10x. A correlation of e 2 q ŽC517O. Qrh vs. e 2 q ŽC– 17O– H. Qrh has been observed in hydrogen bonded sys-
J. Seligerr Chemical Physics 231 (1998) 81–86
tems w10x. These correlations show that the parameters of the EFG tensor at the oxygen site depend mainly on the electron distribution in the chemical bonds formed by oxygen. The influence of the neighboring electric charges is small. Only violent thermal motions may strongly influence the EFG tensor. Since the EFG tensor at the oxygen site is mainly of the local origin, one of its principal axes points nearly perpendicular to the plane of either the C–O– H or the C5O PPP H group. We name the principal value of the EFG tensor along this out-of-plane principal axis V33 . The other two principal values of the EFG tensor along the two in-plane principal axes we name V11 and V22 . The out-of-plane principal axis of the EFG tensor is a unique axis which does not change its direction on the rearrangement of the electron distribution in the chemical bonds formed by oxygen. On the basis of the above experimental and theoretical evidence we suppose that the principal value V33 of the EFG tensor along the out-of-plane principal axis adequately reflects the local electric charge distribution at both the C5O and C–O–H oxygen sites. We also suppose that both V33 at the C–O–H site and V33 at the C5O PPP H site in a C–O–H PPP O5C hydrogen bond reflect the strength of the hydrogen bond.
83
3. The correlation diagrams In order to check the above suppositions we first plot the correlation diagram of V11 and V22 vs. V33 . The experimental data are taken from Refs. w1,3– 16,18x. The assignment of the out-of-plane principal axis and the sign of the quadrupole coupling constant are made on the basis of the experimental w1,8,9,11– 16x and theoretical w20,21x arguments. The correlation diagram is shown in Fig. 1. A nearly linear correlation of V11 vs. V33 and also a nearly linear correlation of V22 vs. V33 are observed in the whole range of V33 covering both the C–O–H and C5O sites. The principal value V22 is negative whereas the principal value V11 is positive in the range of available experimental data. At the C– 17O–H oxygen sites the quadrupole coupling constant is negative and equal to eQV22 rh whereas at the C517O oxygen sites the quadrupole coupling constant is in the range 0 MHz - eQV33 rh - 1 MHz negative and equal to eQV22 rh whereas below eQV33rh f 0 MHz the quadrupole coupling constant changes sign and becomes equal to eQV11 rh. In symmetric hydrogen bonds eQV33 rh is observed as being equal to ; 1 MHz. The correlation diagram given in Fig. 1 is simpler than the previously published correlation
Fig. 1. The correlation diagram of the principal values V11 and V22 of the 17O EFG tensor along the two in-plane principal axes vs. the third principal value V33 for the C517O and C– 17O–H groups. The broken line indicates the transition from the C5O sites to the C–O–H sites.
J. Seligerr Chemical Physics 231 (1998) 81–86
84
The two out-of-plane principal values of the EFG tensor seem to be linearly correlated as eQV33 Ž C5O . h
s 2.9 MHz y 1.5
eQV33 Ž C–O–H . h
.
Ž 2.
Fig. 2. The correlation diagram of eQV33 r h at the C5O PPP H site vs. eQV33 r h at the C–O–H site in a C–O–H PPP O5C hydrogen bond.
This correlation is useful in determining which pair of oxygen atoms participates in the same hydrogen bond. The data are of course conclusive only when the EFG tensors are not partially averaged out due to thermal motions. A motion which often strongly influences the EFG tensor at both oxygen sites in a O–H PPP O hydrogen bond is the proton exchange O–H PPP O l O PPP H–O. This exchange occurs in carboxylic acid dimers and in some other systems Žsquaric acid, diglycine nitrate, KH 2 PO4-type systems, etc.. undergoing structural phase transitions associated with the ordering of protons in the O– H PPP O hydrogen bonds. If p 1 denotes the probability of occupation of the more probable proton site and p 2 denotes the probability of occupation of the less probable proton site in a disordered O–H PPP O hydrogen bond we may express the two out-of-plane principal values of the 17O EFG tensor in terms of the order parameter S, S s p 1 y p 2 , as
² V33 Ž C5O. : s² V33 :q 2
diagrams of e qQrh vs. h and it covers both the C– 17O–H and the C517O oxygen sites. The correlation of eQV11 rh vs. eQV33rh and the correlation of eQV22 rh vs. eQV33rh can be expressed as
h eQV22 h
s 5.8 MHz y 0.63
eQV33
s y5.8 MHz y 0.37
h
,
eQV33 h
.
2
V33 Ž C5O . y V33 Ž C–O–H . ,
Ž 3a .
² V33 Ž C–O–H. : s² V33 :y
eQV11
S
S 2
V33 Ž C5O . y V33 Ž C–O–H . .
Ž 1a .
Ž 3b .
Ž 1b .
Here ² V33 : s w V33 ŽC5O. q V33 ŽC–O–H.xr2. We assumed that the two out-of-plane principal axes of the EFG tensor coincide. The two motionally averaged principal values of the EFG tensor are correlated as
If some 17O NQR data do not fit to this correlation diagram there is a strong indication of a thermal motion which partially averages out the EFG tensor. The correlation of V33 ŽC5O. vs. V33 ŽC–O–H. in C–O–H PPP O5C hydrogen bonds is shown in Fig. 2. The data are taken from Refs. w1,6–9,11,13,15x.
eQV33 Ž C5O .
¦
h
;
s 2.9 MHz y
2h
eQV33 Ž C–O–H .
¦
y
eQV33 Ž C–O–H .
h
;
Ž 4.
J. Seligerr Chemical Physics 231 (1998) 81–86
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Fig. 3. The plot of eQV33 rh at the C– 17O–H and C517O PPP H oxygen sites vs. the hydrogen bond length R O PPP O . The full lines are calculated after expressions Ž6..
and the corresponding point in the correlation diagram does not lie on the line Ž2.. The correlation of V33 ŽC5O PPP H. and V33 ŽC– O–H. vs. the hydrogen bond length R O PPP O is shown in Fig. 3. The data are taken from Refs. w7,9,11,13x. The out-of-plane principal values V33 ŽC–O–H. and V33 ŽC5O PPP H. are indeed correlated to R O PPP O what gives us a possibility to extract the hydrogen bond length R O PPP O from the 17O NQR data. In order to write a mathematical expression for this correlation we use a model of interacting ‘soft’ electric dipoles where 2 y6 V33 s V330 q V331 Ry3 O PPP O q V33 R O PPP O q . . . .
Ž 5.
A similar correlation of deuterium quadrupole coupling constant vs. Ry3 O PPP O has already been observed in some hydrogen-bonded carboxylic acids w9,10x. The best fit of the experimental data to expression Ž5. is given as: V33 Ž C–O–H . s 9.5 MHz y 27 MHz Ry3 O PPP O y 1290 MHz Ry6 O PPP O ,
Ž 6a .
V33 Ž C5O. s y10.2 MHz q 56 MHz Ry3 O PPP O q 1400 MHz Ry6 O PPP O ,
Ž 6b .
where the hydrogen bond distance R O PPP O is given in 0.1 nm. The expressions Ž6. are nothing else but two empirical expressions which seem to give a reason-
able description of the correlation V33 vs. R O PPP O in the range 0.24 nm - R O PPP O - 0.3 nm. 4. Conclusions 17
O NQR data of organic solids containing C–O– H PPP O5C hydrogen bonds are analyzed in a simple model where it is assumed that Ž1. the electric field gradient tensor at the C–O–H oxygen site as well as at the C5O PPP H oxygen site is mainly of the local nature and Ž2. that the electron distribution around the oxygen nucleus is reflected on the principal value V33 of the EFG tensor along the out-of-plane principal direction which is perpendicular to the direction of the oxygen–hydrogen bond. The correlation diagram of the other two principal values, V11 and V22 , of the EFG tensor vs. V33 is plotted. The choice of the principal value V33 is made on the basis of experimental data and theoretical arguments. A nearly linear correlation of V11 vs. V33 as well as a nearly linear correlation of V22 vs. V33 is observed continuously through the whole range of V33 belonging to the C–O–H and to the C5O oxygen sites. A nearly linear correlation of V33 at the C–O–H oxygen site vs. V33 at the C5O PPP H oxygen site in a C–O–H PPP O5C hydrogen bond is as well ob-
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J. Seligerr Chemical Physics 231 (1998) 81–86
served. This correlation may in solids containing various oxygen sites and hydrogen bonds give an indication which oxygen sites belong to the same hydrogen bond. A correlation of V33 at both oxygen sites in a C–O–H PPP O5C hydrogen bond vs. the hydrogen bond length R O PPP O is observed and expressed in form of two empirical expressions Ž6.. This correlation may be useful when estimating the hydrogen bond length by 17O NQR. The above correlation relations give conclusive results only when some violent thermal motions influencing the 17O EFG tensor Žlibrations, reorientation, hydrogen exchange, etc.. are either not present in the sample or they are slow on the NQR time scale. In an opposite case the EFG tensor is partially averaged out due to the thermal motion and the above correlation relations do not hold any more. In general the frequency of a thermal motion decreases with decreasing temperature and at a low enough temperature it may become slow on the NQR time scale.
References w1x S.G.P. Brosnan, D.T. Edmonds, J. Magn. Reson. 38 Ž1980. 47.
ˇ w2x J. Seliger, V. Zagar, R. Blinc, A. Novak, J. Chem. Phys. 84 Ž1986. 5857. w3x Y. Hsieh, J.C. Koo, E.L. Hahn, Chem. Phys. Lett. 13 Ž1972. 563. w4x R. Kado, Y. Takanada, J. Magn. Reson. 32 Ž1978. 89. w5x C.P. Cheng, T.L. Brown, J. Am. Chem. Soc. 101 Ž1979. 2327. w6x I.J.F. Poplett, J.A.S. Smith, J. Chem. Soc., Faraday Trans. 2 75 Ž1979. 1703. w7x L.G. Butler, C.P. Cheng, T.L. Brown, J. Phys. Chem. 85 Ž1981. 2738. w8x S.G. Brosnan, D.T. Edmonds, I.J.F. Poplett, J. Magn. Reson. 45 Ž1981. 451. w9x I.J.F. Poplett, M. Sabir, J.A.S. Smith, J. Chem. Soc., Faraday Trans. 2 77 Ž1981. 1651. w10x I.J.F. Poplett, J.A.S. Smith, J. Chem. Soc., Faraday Trans. 2 77 Ž1981. 1473. w11x M. Suhara, J.A.S. Smith, J. Magn. Reson. 50 Ž1982. 237. w12x C.R. Brett, D.T. Edmonds, J. Magn. Reson. 49 Ž1982. 304. ˇ w13x J. Seliger, V. Zagar, R. Blinc, J. Magn. Reson. 58 Ž1984. 359. ˇ w14x J. Seliger, V. Zagar, R. Blinc, A. Novak, S. Rodin, Ferroelectr. Lett. 6 Ž1986. 93. ˇ w15x J. Seliger, V. Zagar, R. Blinc, Chem. Phys. Lett. 164 Ž1989. 405. ˇ w16x J. Seliger, V. Zagar, R. Blinc, E. Hadjoudis, F. Milia, Chem. Phys. 142 Ž1990. 237. w17x R.E. Slusher, E.L. Hahn, Phys. Rev. 166 Ž1968. 332. w18x W.H. Flygare, J.T. Lowe, J. Chem. Phys. 43 Ž1965. 3645. w19x A. Gough, M.M.I. Haq, J.A.S. Smith, Chem. Phys. Lett. 117 Ž1985. 389. w20x J.E. Gready, J. Phys. Chem. 88 Ž1984. 3497. w21x M.H. Palmer, Z. Naturforsch. 51a Ž1996. 442.
17
O quadrupole coupling in C–O–H PPP O5C hydrogen bonds Janez Seliger
Department of Physics, Faculty of Mathematics and Physics and ‘‘ Jozef ˇ Stefan’’ Institute, UniÕersity of Ljubljana, Ljubljana, SloÕenia Received 18 November 1996; in final form 30 January 1998
Abstract 17
O NQR data of various organic solids containing C–O–H PPP O5C hydrogen bonds are analyzed in a simple model, where the strength of the hydrogen bond is reflected by the principal value V33 of the electric field gradient ŽEFG. tensor along the principal axis which is, at the C–O–H oxygen sites, nearly perpendicular to the plane of the C–O–H group and, at the C5O PPP H oxygen sites, nearly perpendicular to the plane of the C5O PPP H group. A nearly linear correlation between the other two principal values of the EFG tensor and V33 is obtained for both the C–O–H and C5O oxygen sites in carbonyl, carboxyl and hydroxyl groups in organic compounds. A linear correlation between V33 at the C–O–H oxygen site and V33 at the C5O PPP H oxygen site in a C–O–H PPP O5C hydrogen bond is observed, giving a possibility of assigning complex 17O NQR spectra. A correlation between V33 and the length R O PPP O of the hydrogen bond, giving the possibility of extracting structural data from the 17O NQR spectra, is observed for both oxygen sites. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Nuclear quadrupole resonance ŽNQR. is often used to obtain structural data of solids. The NQR frequencies of a nucleus namely depend on its electric quadrupole moment eQ and on the electric field gradient ŽEFG. tensor V at its site. The EFG tensor ŽV. i j s E 2 VrE x i E x j consists of the second derivatives of the electrostatic potential V with respect to the coordinates. The electric quadrupole moment eQ is a characteristic of a nucleus in its nuclear ground state, whereas the EFG tensor depends on the distribution of the electric charges in the neighborhood of the observed nucleus and thus indirectly probes the structure of the solid. The tree principal values of the traceless EFG tensor are usually labeled as VX X , VY Y and VZZ Ž< VX X < F < V Y Y < F < VZZ <.. The NQR frequencies actually depend on two parameters: the quadrupole cou-
pling constant e 2 qQrh s eQVZZrh with h being the Planck constant and on the asymmetry parameter h , h s Ž VX X y VY Y .rVZZ , of the EFG tensor. Crystallographically nonequivalent positions of a given atom result generally in different NQR frequencies of its nucleus. When exploring the details of the crystal structure of a given solid by NQR it is necessary to assign the NQR frequencies to the atomic positions in the unit cell and to relate the NQR frequencies to the arrangement of the neighboring atoms Žcrystal point symmetry, local symmetry, inter atomic distances, etc... This paper represents an attempt to correlate — from the point of view of an experimentalist — the NQR parameters from the C– 17O–H oxygen site to the NQR parameters from the C517O PPP H oxygen site in a C–O–H PPP O5C hydrogen bond and to correlate both sets of the 17O NQR parameters to the hydrogen bond length R O PPP O .
0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 7 9 - 2
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J. Seligerr Chemical Physics 231 (1998) 81–86
2. 17O NQR in carbonyl, carboxyl and hydroxyl groups A 17O nucleus has a spin I s 5r2 and thus in zero magnetic field three NQR frequencies n 5r2 – 1r2 ) n 5r2 – 3r2 G n 3r2 – 1r2 . The 17O NQR frequencies are typically a few MHz. From the 17O NQR frequencies it is possible to calculate the absolute value of the quadrupole coupling constant eQVZZrh and the asymmetry parameter h of the EFG tensor. In an 17 O–H group as well as in a short 17O PPP H hydrogen bond the rather strong proton–oxygen magnetic dipole–dipole interaction produces a fine structure of the 17O NQR lines which may be used for the determination of the O–H distance, the orientation of the O–H bond in the principal-axis frame of the EFG tensor and also the sign of the quadrupole coupling constant w1,2x. The available 17O NQR data for the C–O–H oxygen sites w3–16x, as measured by the double w1,17x and triple w4x resonance techniques, show that the quadrupole coupling constant varies from around 6 MHz in short hydrogen bonds to around 9 MHz when the interaction of the O–H group with the environment is weak. The asymmetry parameter h is in very short hydrogen bonds equal to ; 0.6. On increasing e 2 qQrh the asymmetry parameter h first decreases and reaches the value of zero at e 2 qQrh f 7 MHz. On a further increase of e 2 qQrh the asymmetry parameter h increases and reaches a value close to 1 at e 2 qQrh f 9 MHz. The available analyses of the dipole fine structures of the 17O NQR lines w1,8,9,11–16x show that it is the X-principal axis which is at a low quadrupole coupling constant perpendicular to the O–H bond. On the other hand at a large quadrupole coupling constant the Y-principal axis points perpendicular to the O–H bond. The sign of the quadrupole coupling constant is negative. Also in some papers of our group w13–16x where it is stated that the quadrupole coupling constant is positive we did not take into account the negative value of the 17O gyromagnetic ratio g . At the C5O sites w3–15x the quadrupole coupling constant is in short hydrogen bonds around 6 MHz and the asymmetry parameter is around 0.6. On increasing the length of the hydrogen bond the quadrupole coupling constant decreases and the
asymmetry parameter h increases. At approximately e 2 qQrh f 5.8 MHz the asymmetry parameter h reaches the value of one. Then the quadrupole coupling constant increases and the asymmetry parameter decreases until at e 2 qQrh f 8 MHz the asymmetry parameter becomes equal to 0. At still higher quadrupole coupling constants the asymmetry parameter h again increases. The highest quadrupole coupling constant and the corresponding h at a C517O site observed in solids are around 11.5 MHz and 0.45, respectively, whereas in gaseous formaldehyde the values of e 2 qQrh s q12.37 MHz and h s 0.694 are observed by microwave spectroscopy w18x. The analyses of the dipole fine structures of the 17 O NQR lines from the C517O PPP H sites show that in a short hydrogen bond the X-principal axis of the EFG tensor at the 17O site points perpendicular to the O PPP H bond. On the basis of the proton disorder model w13,19x it may be concluded that also at larger quadrupole coupling constants Žup to around 8 MHz. in some planar compounds the X-principal axis of the EFG tensor at the 17O PPP H site points perpendicular to the plane of the C–O–H PPP O5C group. The quadrupole coupling constant of the 17 O PPP H oxygen is in very short hydrogen bonds negative and in longer hydrogen bonds positive. On the basis of the above data we may suppose that the 17O quadrupole coupling constant in solids ranges from ; y9 MHz for a ‘pure’ C–O–H site to ; q11.5 MHz for a ‘pure’ C5O site. The out-ofplane principal value of the EFG tensor Ž V33 in later discussion. ranges from ; q9 MHz for a ‘pure’ C–O–H site to ; y8 MHz for a ‘pure’ C5O site. These suppositions are in agreement with the theoretical predictions Žw20,21x and references cited therein. of the signs of the principal values and the orientations of the principal axes of the 17O quadrupole coupling tensor in carbonyl, carboxyl and hydroxyl groups in organic compounds. Gready w20x also observed an approximate correlation between the oxygen p p population and the out-of-plane EFG magnitude Ž V33 . which agrees with the predictions of the Townes and Dailey theory. A correlation of e 2 qQrh vs. h has been observed for both the C–O–H and C5O oxygen sites w6,9,10x. A correlation of e 2 q ŽC517O. Qrh vs. e 2 q ŽC– 17O– H. Qrh has been observed in hydrogen bonded sys-
J. Seligerr Chemical Physics 231 (1998) 81–86
tems w10x. These correlations show that the parameters of the EFG tensor at the oxygen site depend mainly on the electron distribution in the chemical bonds formed by oxygen. The influence of the neighboring electric charges is small. Only violent thermal motions may strongly influence the EFG tensor. Since the EFG tensor at the oxygen site is mainly of the local origin, one of its principal axes points nearly perpendicular to the plane of either the C–O– H or the C5O PPP H group. We name the principal value of the EFG tensor along this out-of-plane principal axis V33 . The other two principal values of the EFG tensor along the two in-plane principal axes we name V11 and V22 . The out-of-plane principal axis of the EFG tensor is a unique axis which does not change its direction on the rearrangement of the electron distribution in the chemical bonds formed by oxygen. On the basis of the above experimental and theoretical evidence we suppose that the principal value V33 of the EFG tensor along the out-of-plane principal axis adequately reflects the local electric charge distribution at both the C5O and C–O–H oxygen sites. We also suppose that both V33 at the C–O–H site and V33 at the C5O PPP H site in a C–O–H PPP O5C hydrogen bond reflect the strength of the hydrogen bond.
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3. The correlation diagrams In order to check the above suppositions we first plot the correlation diagram of V11 and V22 vs. V33 . The experimental data are taken from Refs. w1,3– 16,18x. The assignment of the out-of-plane principal axis and the sign of the quadrupole coupling constant are made on the basis of the experimental w1,8,9,11– 16x and theoretical w20,21x arguments. The correlation diagram is shown in Fig. 1. A nearly linear correlation of V11 vs. V33 and also a nearly linear correlation of V22 vs. V33 are observed in the whole range of V33 covering both the C–O–H and C5O sites. The principal value V22 is negative whereas the principal value V11 is positive in the range of available experimental data. At the C– 17O–H oxygen sites the quadrupole coupling constant is negative and equal to eQV22 rh whereas at the C517O oxygen sites the quadrupole coupling constant is in the range 0 MHz - eQV33 rh - 1 MHz negative and equal to eQV22 rh whereas below eQV33rh f 0 MHz the quadrupole coupling constant changes sign and becomes equal to eQV11 rh. In symmetric hydrogen bonds eQV33 rh is observed as being equal to ; 1 MHz. The correlation diagram given in Fig. 1 is simpler than the previously published correlation
Fig. 1. The correlation diagram of the principal values V11 and V22 of the 17O EFG tensor along the two in-plane principal axes vs. the third principal value V33 for the C517O and C– 17O–H groups. The broken line indicates the transition from the C5O sites to the C–O–H sites.
J. Seligerr Chemical Physics 231 (1998) 81–86
84
The two out-of-plane principal values of the EFG tensor seem to be linearly correlated as eQV33 Ž C5O . h
s 2.9 MHz y 1.5
eQV33 Ž C–O–H . h
.
Ž 2.
Fig. 2. The correlation diagram of eQV33 r h at the C5O PPP H site vs. eQV33 r h at the C–O–H site in a C–O–H PPP O5C hydrogen bond.
This correlation is useful in determining which pair of oxygen atoms participates in the same hydrogen bond. The data are of course conclusive only when the EFG tensors are not partially averaged out due to thermal motions. A motion which often strongly influences the EFG tensor at both oxygen sites in a O–H PPP O hydrogen bond is the proton exchange O–H PPP O l O PPP H–O. This exchange occurs in carboxylic acid dimers and in some other systems Žsquaric acid, diglycine nitrate, KH 2 PO4-type systems, etc.. undergoing structural phase transitions associated with the ordering of protons in the O– H PPP O hydrogen bonds. If p 1 denotes the probability of occupation of the more probable proton site and p 2 denotes the probability of occupation of the less probable proton site in a disordered O–H PPP O hydrogen bond we may express the two out-of-plane principal values of the 17O EFG tensor in terms of the order parameter S, S s p 1 y p 2 , as
² V33 Ž C5O. : s² V33 :q 2
diagrams of e qQrh vs. h and it covers both the C– 17O–H and the C517O oxygen sites. The correlation of eQV11 rh vs. eQV33rh and the correlation of eQV22 rh vs. eQV33rh can be expressed as
h eQV22 h
s 5.8 MHz y 0.63
eQV33
s y5.8 MHz y 0.37
h
,
eQV33 h
.
2
V33 Ž C5O . y V33 Ž C–O–H . ,
Ž 3a .
² V33 Ž C–O–H. : s² V33 :y
eQV11
S
S 2
V33 Ž C5O . y V33 Ž C–O–H . .
Ž 1a .
Ž 3b .
Ž 1b .
Here ² V33 : s w V33 ŽC5O. q V33 ŽC–O–H.xr2. We assumed that the two out-of-plane principal axes of the EFG tensor coincide. The two motionally averaged principal values of the EFG tensor are correlated as
If some 17O NQR data do not fit to this correlation diagram there is a strong indication of a thermal motion which partially averages out the EFG tensor. The correlation of V33 ŽC5O. vs. V33 ŽC–O–H. in C–O–H PPP O5C hydrogen bonds is shown in Fig. 2. The data are taken from Refs. w1,6–9,11,13,15x.
eQV33 Ž C5O .
¦
h
;
s 2.9 MHz y
2h
eQV33 Ž C–O–H .
¦
y
eQV33 Ž C–O–H .
h
;
Ž 4.
J. Seligerr Chemical Physics 231 (1998) 81–86
85
Fig. 3. The plot of eQV33 rh at the C– 17O–H and C517O PPP H oxygen sites vs. the hydrogen bond length R O PPP O . The full lines are calculated after expressions Ž6..
and the corresponding point in the correlation diagram does not lie on the line Ž2.. The correlation of V33 ŽC5O PPP H. and V33 ŽC– O–H. vs. the hydrogen bond length R O PPP O is shown in Fig. 3. The data are taken from Refs. w7,9,11,13x. The out-of-plane principal values V33 ŽC–O–H. and V33 ŽC5O PPP H. are indeed correlated to R O PPP O what gives us a possibility to extract the hydrogen bond length R O PPP O from the 17O NQR data. In order to write a mathematical expression for this correlation we use a model of interacting ‘soft’ electric dipoles where 2 y6 V33 s V330 q V331 Ry3 O PPP O q V33 R O PPP O q . . . .
Ž 5.
A similar correlation of deuterium quadrupole coupling constant vs. Ry3 O PPP O has already been observed in some hydrogen-bonded carboxylic acids w9,10x. The best fit of the experimental data to expression Ž5. is given as: V33 Ž C–O–H . s 9.5 MHz y 27 MHz Ry3 O PPP O y 1290 MHz Ry6 O PPP O ,
Ž 6a .
V33 Ž C5O. s y10.2 MHz q 56 MHz Ry3 O PPP O q 1400 MHz Ry6 O PPP O ,
Ž 6b .
where the hydrogen bond distance R O PPP O is given in 0.1 nm. The expressions Ž6. are nothing else but two empirical expressions which seem to give a reason-
able description of the correlation V33 vs. R O PPP O in the range 0.24 nm - R O PPP O - 0.3 nm. 4. Conclusions 17
O NQR data of organic solids containing C–O– H PPP O5C hydrogen bonds are analyzed in a simple model where it is assumed that Ž1. the electric field gradient tensor at the C–O–H oxygen site as well as at the C5O PPP H oxygen site is mainly of the local nature and Ž2. that the electron distribution around the oxygen nucleus is reflected on the principal value V33 of the EFG tensor along the out-of-plane principal direction which is perpendicular to the direction of the oxygen–hydrogen bond. The correlation diagram of the other two principal values, V11 and V22 , of the EFG tensor vs. V33 is plotted. The choice of the principal value V33 is made on the basis of experimental data and theoretical arguments. A nearly linear correlation of V11 vs. V33 as well as a nearly linear correlation of V22 vs. V33 is observed continuously through the whole range of V33 belonging to the C–O–H and to the C5O oxygen sites. A nearly linear correlation of V33 at the C–O–H oxygen site vs. V33 at the C5O PPP H oxygen site in a C–O–H PPP O5C hydrogen bond is as well ob-
86
J. Seligerr Chemical Physics 231 (1998) 81–86
served. This correlation may in solids containing various oxygen sites and hydrogen bonds give an indication which oxygen sites belong to the same hydrogen bond. A correlation of V33 at both oxygen sites in a C–O–H PPP O5C hydrogen bond vs. the hydrogen bond length R O PPP O is observed and expressed in form of two empirical expressions Ž6.. This correlation may be useful when estimating the hydrogen bond length by 17O NQR. The above correlation relations give conclusive results only when some violent thermal motions influencing the 17O EFG tensor Žlibrations, reorientation, hydrogen exchange, etc.. are either not present in the sample or they are slow on the NQR time scale. In an opposite case the EFG tensor is partially averaged out due to the thermal motion and the above correlation relations do not hold any more. In general the frequency of a thermal motion decreases with decreasing temperature and at a low enough temperature it may become slow on the NQR time scale.
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