3086
J . Phys. Chem. 1985,89, 3086-3091
Rotational Motions of Tetrahedral Oxo Anlons in Aqueous and Methanol Solutions Yuichi Masuda, Mitsuru Sane,+ and Hideo Yamatera* Department of Chemistry, Faculty of Science, Nagoya University, Chikusa- ku, Nagoya 464 Japan (Received: January 16, 1985)
Spin-lattice relaxation rates of 170NMR of the X04"-type ions, perchlorate, sulfate, and phosphate ions, in D20 and CD30D solutions have been measured at various concentrations and temperatures. The 170relaxation rates for the X04"- ions at infinite dilution were determined by extrapolating the relaxation rates at various concentrations to zero concentration at each temperature. The electric field gradients at the oxygen site of isolated XO," ions have been calculated by using the ab initio molecular-orbital method. This gave field gradients of 2.37, 1.52, and 0.875 atomic unit for perchlorate, sulfate, and phosphate ions, respectively. The field gradient at the oxygen site for each XO," ion with a nearby single positive charge was also calculated in order to estimate the effect of surrounding solvent molecules on the field gradient. These calculations show that the fluctuation of the field gradient caused by the movement of the surrounding solvent molecules is of secondary importance in the effect on the 1 7 0 relaxation rates of the X04" ions. With the field gradient for "isolated" XO,", the rotational correlation time of each X04" ion, T,, at infinite dilution has been obtained from the relaxation rates observed for solutions of several concentrations at various temperatures. The obtained rotational correlation times at 28 OC were in D20, and 0.73 (C104-) and 1.1 ps (SO4') in CD30D. The temperature 0.80 (C104-), 2.8 and 14-16 ps (Po4'-) dependence of the rotational correlation times of the X04" ions has been analyzed on the basis of the hydrodynamic model and an Arrhenius-type model. A plot of the rotational correlation time at infinite dilution against the ratio of viscosity to ) a good linear relationship for the phosphate ion in aqueous solution. Similar plots for the perchlorate temperature ( ~ / 7 'showed and the sulfate ion in aqueous solution curved downward, the deviation from the linear relationship being larger for the former. The temperature dependence of the rotational correlation times of the XO," ions in aqueous solution at infinite dilution was well represented by the Arrhenius relation except for the phosphate ion. The activation energies for the rotational motion in aqueous solution at 28 OC were 9.3, 13, and 19 kJ/mol for the perchlorate, sulfate, and phosphate ions, respectively. The temperature dependences of the rotational correlation times of the sulfate and perchlorate ions in CD,OD at infinite dilution showed a tendency similar to that in aqueous solutions. The activation energies for the rotational motion of the sulfate and the perchlorate ion in methanol solutions, 4.5 kJ/mol (C10,) and 11 kJ/mol (Sot-), were smaller than those in the corresponding aqueous solutions.
1. Introduction
Motions of ions in solutions give useful information for investigating the dynamic feature of the ion-solvent and ion-ion interactions. The translational motion in solution has been investigated for various ions by measuring diffusion coefficients' and electric conductivities.2,3 Several theoretical approaches to the translational motion of ions have also been p r o p o ~ e d . ~ , ~ In contrast to the translational motion, rotational motion of ions has been studied less extensively; studies of the rotational motion of common inorganic ions are limited to a few cases, Le., those of the nitrate6-8 and t h i ~ c y a n a t e ions ~ , ~ by depolarized RamanG8 and Rayleigh light scattering9 Nevertheless, the rotational motion of ion is one of the important dynamic properties of the electrolyte solution, reflecting the dynamic feature of the ion-solvent and ion-ion interactions at the molecular level. Previously we have shown that the rotational motions of several complex ions are strongly affected by the formation of ion pairs when they have a certain structure of sufficiently long lifetime,I0 and that the rotational correlation time of the sulfate ion in aqueous solutions containing various univalent cations are correlated with the mobility of the water molecules around the sulfate ion." This paper is concerned with the rotational motion of common XO,"-type ions, Le., perchlorate, sulfate, and phosphate ions, in water and methanol. These X04"-type ions are nearly spherical and have similar ionic radii. If there were no specific interactions between these ions and the solvent molecules, the rotational correlation times of these ions would be approximately the same. Therefore, the rotational motion of these ions can be a good probe for the dynamic feature of the interaction between these ions and solvent molecules. The measurement of the I7O nuclear relaxation is a useful technique for investigating the rotational motion of the X04w ions in solution, since the rotational correlation times of the X04" ions can be obtained from the I7Ospin-lattice relaxation times of the 'Present address: Laboratory of Inorganic Chemistry, College of General Education, Nagoya University.
0022-3654/85/2089-3086$01 .50/0
170-enriched X04" ions. The magnetic relaxation of a nucleus is usually caused by the interaction of its electric with I > quadrupole moment with the electric field gradient at the nuclear site. The spin-lattice relaxation time ( T I )of the 1 7 0 nucleus of an isolated X04" ion at the extreme narrowing limit is expressed byI2
R1 = ( l / T l ) =
-%( 21 + 3 10
P ( 2 1 - 1)
)t
--j-)( 1 e2qQ
+ :)T,
(1)
where I , cy, and e2qQ/hare the spin of 170( I = 2 / 5 ) , asymmetry parameter, and so-called quadrupole coupling constant, respectively. The parameter eQ is the quadrupole moment of the 170 nucleus ( Q = -0.0265 X cm2),I3 eq is the electric field gradient at the 170nucleus along the 0-X direction, and T, is the rotational correlation time of the 0-X vector which coincides with that of the XO," ion. The water and the methanol molecules (1) Robinson, R. A,; Stokes, R. H. "Electrolyte Solutions"; Butterworths: London, 1959. (2) Kay, R. L. "Water, A Comprehensive Treatise"; Franks, F., Ed.; Plenum Press: New York, 1973; Vol. 3, Chapter 7. (3) Takisawa, N.; Osugi, J.; Nakahara, M. J . Phys. Chem. 1981, 85, 3582; J . Chem. Phys. 1982, 77, 4717. Nakahara, M.; Torok, T.; Takisawa, N.; Osugi, J. J . Chem. Phys. 1982, 76, 5145. (4) Boyd, R. H. J . Chem. Phys. 1961, 35, 1281. Zwanzig, R. J . Chem. Phys. 1963, 38, 1603; 1970, 52, 3625. (5) Hubbard, J.; Onsager, J. J . Chem. Phys. 1977, 67, 4850. Hubbard, J. J . Chem. Phys. 1978, 68, 1649. (6) James, D.; Forst, R. L. Discuss. Faraday SOC.1977, 64, 48. (7) Kato, T.; Umemura, J.; Takenaka, T. Mol. Phys. 1978, 36, 621. (8) Whittle, M.; Clarke, J. H. R. Mol. Phys. 1981, 44, 1435. (9) Kato, T.; Takenaka, T. Mol. Phys. 1982, 46, 257. (10) Masuda, Y.; Yamatera, H. J . Phys. Chem. 1983, 87, 5339; 1984.88, 3425. (11) Masuda, Y.; Yamatera, H. J . Chem. SOC.,Faraday Trans 1 1985, 81, 127. (1 2) Abragam, A. "The Principles of Nuclear Magnetism"; Oxford: London, 1961; Chapter 8. (13) Harrey, J. S. M. Proc. R. SOC.London, Ser. A 1965, 285, 581.
0 1985 American Chemical Society
Tetrahedral Oxo Anions surrounding the X04" ion in solution cause an additional field gradient a t the I7O nuclear site of the ion. This effect was estimated by an ab initio molecular orbital calculation, in the same manner as applied to the estimation of the field gradient at the oxygen nucleus of the sulfate ion in aqueous solution."
3087
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 R1/S-
'
h
2. Experimental Section 2.1. Materials. Perchlorate enriched in 1 7 0 was prepared by electrolyzing a solution of lithium chloride in I70-enriched water according to the literature method.14 The solution of 5.6 mg of anhydrous lithium chloride in 0.33 cm3 of 170-enriched water (50 atom %, Prochem Co. Ltd) was electrolyzed at 4.5-5.0 V in a microelectrolysis cell (ca. 1 cm3capacity) with platinum electrodes (ca. 0.04 cm2). The solution in the cell was kept at 20-22 "C with constant stirring. The electrolysis was continued over 20 h. After the resulting solution was concentrated, the I70-enriched potassium perchlorate was obtained by adding potassium chloride to the s o l ~ t i o n . ' ~The yield of KC1I7o4was about 70%. The conversion of the potassium salt into the ammonium salt was carried out by an ion-exchange technique with a 30 cm X 1 cm (diameter) column of Bio-Rad AG 50W-X8 (200-400 mesh) cation exchanger. l70-enriched sulfuric acid was prepared by oxidizing sulfur with bromine in I70-enriched water (50 atom %).15 The resulting I70-enriched sulfuric acid was diluted with a small amount of normal water with cooling and neutralized with 2 M potassium hydroxide. The solution was dried up to give I70-enriched potassium sulfate, which was recrystallized from water. The yield was ca. 55%. To another portion of the I70-enriched potassium sulfate solution, silver nitrate was added in excess to result in the formation of 170-enriched silver sulfate, from which tetraethylammonium sulfate was obtained by double decomposition with tetraethylammonium chloride. For the preparation of 170-enriched potassium phosphate, phosphorus trichloride was hydrolyzed in I70-enriched water (50 atom %) to obtain phosphorous acid (H3P1703),'5which was then oxidized by slowly adding bromine at 60 "C until a slight color of bromine remained.16 After the solution was diluted with a small amount of normal water with cooling, 2 M lithium hydroxide was added until pH 14. From the basic solution, lithium phosphate (Li3PI7O4)was precipitated with 4 M lithium chloride. The yield was ca. 60%. The lithium phosphate obtained was converted into potassium salt (K3PI7o4)by an ion-exchange technique. Each 170-enriched salt was used for N M R measurements after recrystallization. For preparation of the sample solutions, each salt was dissolved in a small amount of D 2 0 and was dried under reduced pressure at room temperature. After these procedures were repeated, the salt was dissolved in D 2 0 (99.75%). The CD30D solutions were similarly prepared with C D 3 0 D (99.5%) in place of D 2 0 . 2.2. 170N M R Measurement. The 1 7 0 N M R spectra were obtained on a Jeol FX-60 Fourier-transform spectrometer equipped with a special probe for multinucleus measurements operating at 8.1 MHz. The spin-lattice relaxation time (TI)of the I7Onucleus was obtained by the inversion-recovery methodI7 with the pulse sequence of [ 180" pulse-t-90" pulse-T-I,. The T, value for each sample solution was determined by a series of measurements with more than 12 different time intervals ( t ) and with the waiting time (7') more than 10Tl;the area of the signal for each time interval ( t ) was measured and its variation with t was analyzed by the use of an exponential fit based on the method of Kowalewski et a1.18 For several samples, the measurements of TIwere repeated 5 times or more (at 28 "C); consistent results (within 3%) were obtained for TI of each sample. The measurements were performed using
3. Results and Discussion 3.1. Determination of Rotational Correlation Times of the X04" Ions at Infinite Dilution. Figure 1 shows concentration dependences of the 1 7 0 relaxation rate, R , (= Tl-l),of X1704" in the D 2 0 and CD30D solutions at 28 "C. In all the cases, the R 1 values were not largely dependent on the concentration. The concentration dependences of the R I values were also measured at other temperatures. The results were similar to those in Figure 1. 170relaxation rates for each Xl7o4- ion at infinite dilution were determined by extrapolation at each temperature.22 The 1 7 0 relaxation rates obtained for the sulfate ion in aqueous solution at various temperatures showed a reasonable agreement with ~) based previous results from I7O line-width ( v ~ , measurements on the relationship, R l = ~ v ~ , ~ . ~ ~ The I7Orelaxation rates were related to the rotational correlation times of the X04"- ions. Nuclear quadrupole interaction is the dominant mechanism in the relaxation of the I7O nucleus ( I = 5 / 2 ) . At the extreme narrowing limit, the relaxation rate of the 170nucleus of the "isolated" X04" ion is expressed by eq 1. The electric field gradient at the oxygen nucleus (the eq value in eq 1) was calculated for the isolated phosphate and perchlorate ions by an ab initio molecular-orbital method similar to that previously reported for the sulfate ion." The calculated electric field gradients along the 0-C1 and 0-P directions of the perchlorate and phosphate ions were 2.37 and 0.875 au, respectively.
(14) Anbar, M.; Guttmann, S.; Lewitus, Z . In?. J . Appl. Radiar. Isor. 1959, 7, 87. (15) Anbar, M.; Dostrovsky, I. J . Chem. SOC.1954, 1094. (16) Anbar, M.; Guttmann, S. Int. J . Appl. Radiat. Isot. 1959, 4 , 233. (17) Farrar, T. C.; Becker, E. D. "Pulse and Fourier Transform NMR"; Academic Press: New York, 1971; Chapter 2. (18) Kowalewski, J.; Levy, G. C.; Johnson, L. F.; Palmer, L. J. J . Magn. Reson. 1977, 26, 5 3 3 .
(19) Tatewaki, H.; Huzinaga, S . J. Comput. Chem. 1980, I , 205. Sakai, Y.; Tatawaki, T.; Huzinaga, S . J . Comput. Chem. 1981,2, 100; 1981, 2, 108. (20) Johansen, H. Theoret. Chim. Acta 1974, 32, 273. (21) Kashiwagi, H.; Takada, T.; Miyoshi, E.; Obara, S. "Program JAMOL 3"; Program Library, Institute for Molecular Science Computer Center, Okazaki, Japan. (22) The effect of the formation of HP042-on the R1value was shown to be negligible by measuring the R I values at different pH's.
130
c
0
I
0.1
0.2
0.3 "1.0
2.0
mol/kg
Figure 1. Concentration dependences of the 170relaxation rates of the X04" ions at 28 OC: m, NH4C10, in D,O; 0,NH4C10, in CD,OD; 0 , K2S04in D20; 0,(Et4N)*S04in CD30D; A, K3POpin D20.
5-mm (0.d.) cylindrical tubes (sample height, ca. 11 mm) and the temperature was controlled within 0.5 OC. The sample solutions were degassed under vacuum twice with freeze-pumpthaw cycles and torch sealed. 2.3. Ab Initio Molecular-Orbital Calculation. Calculations of the LCAO M O S C F type for perchlorate and phosphate ions were performed using the MID 1 Gaussian-type function sets given by Huzinaga et aI.l9 (For sulfate, see ref 11.) To the basis sets for chlorine and phosphorus, 3d orbitals with an orbital exponent of 0.46 were added. The electric field gradient at the oxygen nucleus was calculated for isolated perchlorate and phosphate ions (Cl-0 = 1.46 A and P-0 = 1.55 A)2oand also for these anions with a nearby single positive charge by using the program package JAMOL 3 given by Kashiwagi et al.21
Masuda et al.
g+ SO,2- > C104-, which reflects the order in the magnitude of the interaction between the solvent molecules and the negatively charged oxygen atoms of XO.,". The value of the activation energy for the sulfate ion, rather than that for the perchlorate ion, corresponds to that reported for the rotation of the nitrate ion in aqueous solution about an axis perpendicular to the C, axis (about 14 kJ/mo18), in spite of the fact that the perchlorate ion resembles the nitrate ion in its charge and its "structure-breaking" property in aqueous solution. The difference in the activation energy between the perchlorate and the nitrate ion can be attributed to the difference in the effect of the rotational motion on the solvent; the rotation of the nitrate ion about an axis perpendicular to the C, axis is accompanied by displacement of the solvent molecules, while such
3090 The Journal of Physical Chemistry, Vola89, No. 14, 1985 In T = -26
-25
-26
-27
- 28
in C D ~ Q D 8 O C
\ 5
3.0
3.5
4.0
T- IO K Figure 6. Plots of the natural logarithm of the rotational correlation times of the X04" ions at infinite dilution against 1/T. The solid lines O : - correindicate the tangent at 28 OC. The symbols 0 and X for P spond to those in Figure 5 .
displacement is not needed for the rotation of the nearly spherical perchlorate ion. 3.3. Dynamic Feature of the Rotational Motion of the XO," Ions. We first consider the rotational motion of the X04" ions in aqueous solution. Equation 2 based on the hydrodynamic model describes the temperature dependence of the rotational correlation time better for an X04" ion with a higher negative charge than for a less negative X04". The increase in the negative charge changes the hydrodynamic boundary condition for the rotational motion of the X04" ions from slipping to sticking. In the sticking boundary condition, the fluid at the surface of the rotor moves with the rotor at the same velocity. On the contrary, the velocity of the fluid is zero in the perfect slipping b ~ u n d a r y . ~The ' rotational correlation time of the water molecules in the hydration sphere of the phosphate ion (- 13 ps at 25 0C)2*is notably larger than that of bulk water (2.5 ps at 25 0C)29and is nearly as large as that of the phosphate ion. This indicates that the water molecules neighboring the phosphate ion largely follow the rotational motion of the phosphate ion because of the strong attractive interaction between the phosphate oxygen atoms and the hydrogen atoms of water. This dynamic feature of the rotation of the phosphate ion is similar to the hydrodynamic rotational motion with the sticking boundary condition. This explains the reason why the C parameter shows a value for the sticking boundary condition in spite of the size of the phosphate ion being too small in size to regard the solvent as continuum. On the contrary, the hydrodynamic boundary condition (28 "C) of the perchlorate ion in aqueous solution is nearly slipping and the temperature dependence of the rotational correlation time of the perchlorate ion is well represented by an Arrhenius-type relation (eq 3). The rotational correlation time of the water molecules in the hydration sphere of the perchlorate ion (-2.0 (28) Masuda, Y.; Yamatera, H., unpublished data. (29) Hertz, H. G. "Water, A Comprehensive Treatise"; Franks, F., Ed.; Plenum Press: New York, 1973; Vol. 3, Chapter 7.
Masuda et al. ps at 25 0C)29is slightly smaller than that of bulk water molecules (2.5 ps at 25 oC)rBbut is much larger than that of the perchlorate ion (0.75 ps at 25 "C). This means that the water molecules in the first sphere of the perchlorate ion stay practically unmoved during the rotation of the perchlorate ion, or, figuratively speaking, the perchlorate ion is rotating in a cavity of the cluster of the water molecules. Then, if the average configuration of the water molecules in the hydration sphere of the perchlorate ion does not appreciably change in the temperature mnge of the experiments, the rotation of the perchlorate ion is associated with an activation energy corresponding to the mean energy for breaking the hydrogen bonds between the perchlorate ion and the water molecules. The perchlorate and the phosphate ions are in contrast to each other in the dynamic feature of the rotational motion. The rotation of the perchlorate ion is mainly affected by the interaction with the water molecules in the first sphere of the perchlorate ion, while the effect of the rotation of the phosphate ion reaches distant water molecules due to strong electrostatic and hydrogen-bonding interactions between the phosphate oxygen atom and the hydrogen atom of water and between water molecules. The rotational motion of the phosphate ion in aqueous solution is to a certain extent accompanied by neighboring water molecules, which are also linked with outer water molecules. Consequently, rotation of a phosphate ion causes the breaking of water-water links. The rotational motion of the phosphate ion is, at least partly, affected by dynamic properties of the bulk water, such as viscous flow, or rotational and translational motion of the molecules. The activation energies for these dynamic processes increase with decreasing t e m p e r a t ~ r e . ~This ~ , ~feature ~ is consistent with the result that eq 3 does not adequately represent the temperature dependence of the rotational correlation time of the phosphate ion (Figure 6 ) . The C coefficient in eq 2 and the Eeffvalue in eq 3 obtained for the sulfate ion from the temperature dependence of its rotational correlation time indicate that the sulfate ion is intermediate between the phosphate and perchlorate ions in the dynamic feature of the rotational motion in aqueous solution. Next we compare the rotational motions of the perchlorate and sulfate ions in CD30Dwith those in D20. The activation energies for the rotation of the perchlorate and sulfate ions were found to be smaller in CD30D than in D20,respectively (Table I). This can be attributed to the smaller positive charge of the hydrogen atom of methanol than that of water, if the experimental activation energies practically correspond to the energies for breaking the hydrogen bond between the anion and the solvent molecule. On the other hand, the obtained Cvalues (Table I) were larger in CD30D than those in D 2 0 for the respective ions. This shows that the rotational motion of the ions is accompanied by the methanol molecules to a greater extent than by the water molecules, in spite of the weaker electrostatic (and/or hydrogenbonding) interaction between those ions and the methanol molecules. This is also consistent with the fact that the rotational motion of the solvent molecules neighboring the anions (as compared with those in the bulk) is more strongly restricted in the methanol solution than in the aqueous solution because of the weaker solventsolvent interaction in methanol than in ~ a t e r . ~ * . ~ ~
Acknowledgment. The computations were carried out on a HITAC M-200H computer at the Computer Center of the Institute for Molecular Science. 4. Appendix
Estimation of the Effect of the Field Gradient due to Solvent Molecules on the Rotational Correlation Time of the XO," Ions. We consider the ''0 relaxation rate of the XO," ion in the presence of an additional field gradient caused by solvent mole(30) Eisenberg, D.; Kauzman, W. "The Structure and Properties of Water"; Oxford University Press: London, 1969; Chapter 4. (31) Krynicki, K. Physica (Amsterdam) 1966, 32, 167. (32) Engel, G.; Hertz, H. G. Ber. Bumenges. Phys. Chem. 1968,72,808. (33) Nakamura, S.;Meiboom, S. J. Am. Chem. SOC.1967, 89, 1765. Hertz, H. G.; Tutsch, R.; Bowmann, N. S. J . Phys. Chem. 1976, 80, 417.
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3091
Tetrahedral Oxo Anions cules. In order to estimate the effect of this additional field gradient, the field gradient is divided into two parts: (i) the field gradient at the oxygen nucleus of the isolated XO," ion and (ii) that a t the same oxygen nucleus caused by surrounding solvent molecules. Here we consider two extreme cases of dynamic correlation between the XO," ion and the solvent molecules. Case 1. This is the extreme of strong interaction; the configuration of the system consisting of the X O p ion and surrounding solvent molecules is maintained for a time interval much longer than the rotational correlation time of the XO," ion. Then the field gradient due to neighboring water molecules is simply added to the field gradient within the isolated X O p ion. Assuming that the main axis of this additional field gradient coincides with the 0-X axis and neglecting the asymmetry parameter, we have the following equation for the I7O relaxation rate of the XO," ion.
R , = ( 1 2 ~ / 1 2 5 ) ( e ~ Q / h ) ~ (+e qeqs)%, o~
(A-1)
where eqox and eq, are respectively the main-axis components of the parts i and ii of the field gradient; eq, is the resultant field gradient caused by the solvent molecules. Case 2. This is the extreme of weak interaction; the motion of the solvent molecules are independent of that of the X04" ion. We further divide this extreme into two cases. (a) If the motion of the solvent molecules is much faster than the rotational motion of the XO," ion, the solvent molecules fluctuate very fast and they do not appreciably affect the 170 relaxation rate of the XO," ion. (b) If the translational and rotational motion of the solvent molecules in the first hydration sphere of the XO," ion is much slower than the rotational motion of the X O p ion, the solvent molecules can be regarded to be practically fixed. Then the 170 relaxation rate of the X04" ion is expressed by an equation similar to eq A-1 with an eq, value nearly equal to or smaller than that in eq A- 1 .34 The preceding discussion shows that the acceleration of the I7O relaxation rate is largest in case 1 , where the rate is expressed by eq A-1. For a semiquantitative estimate of the effect of solvent molecules, a b initio molecular-orbital calculations of the eq value have been made on simple models, in which a +e charge is placed at various distances from an oxygen atom of X04". Figure 2 shows the results on each X04" ion as a function of the 170-+e distance, rop, of a representative configuration with the +e charge on the 0-X axis. Calculations have also been made with the +e charge off the axis, giving the field gradients along the 0-X direction nearly equal to or smaller than the values shown in Figure 2 for respective rOp values. (34) In this case the magnitude of the fluctuation of the field gradient caused by the solvent molecules is not necessarily equal to the eq, value in eq A-1 under the condition of case 1 . The eq, value in this case is estimated to be smaller than that in case 1.
We only consider the change in eq caused by the positive charge at the hydrogen atom in contact with the I7O atoms of XO,"; the negative charge at the oxygen atom of the neighboring solvent molecules and the electric dipole of more distant solvent molecules make only minor contributions to the eq value at the I7Onucleus.35 When a fractional charge of +0.2e (the substitute for a hydrogen atom)36 exists at a distance of 1.7 A (=O--H distance in an ordinary hydrogen bond)37along the 0-X axis, the change in the field gradient at 170is estimated to be 0.01, 0.02, and 0.03 au r e s p e c t i ~ e l y . ~The ~ change is infor C104-, and Po43-, significant (as compared with experimental errors) for the perchlorate and sulfate ions; however, it may not be neglected for the phosphate ion, on which further discussion will be made. There may be two or more hydrogen atoms near a particular 170 atom.29 In such a case, however, the hydrogen atoms should be displaced from the 0-X axis and the resultant field gradient due to these hydrogen atoms will not largely exceed the magnitude due to one hydrogen atom on the axis. The quantum-mechanical effect of hydrogen-bond formation on the field gradient at the nucleus of the hydrogen-bonded oxygen atom has not been considered in the calculation. However, this will not seriously affect the results, since it has been shown for the chloride ion O5Cl-) that the quantum-mechanical effect is smaller in magnitude than, and opposite in sign to, the electrostatic effect at normal hydrogen-bond distances.j9 Considering the situations discussed above, we estimated eq, 50.6 au (a value twice as large as that for the phosphate-oxygen nucleus with a +0.2e charge at 1.7 A). This eq, value will result in 14% increase in Rl according to eq A-I. In calculating the 7, value from the measured relaxation rate ( R , )with eq A-1, consideration of eq, of 0.6 au makes the T, value 12% smaller than that obtained without considering the effect of the solvent on the field gradient. The 7,values thus obtained are shown by cross marks in Figures 5 and 6. They show that the disregard of the effect of the solvent does not cause any significant difference except for the slight change in the value of 7,. Registry No. CIO;, 14797-73-0; SO:-, 14808-79-8; P043-, 1426544-2; methanol, 67-56-1. (35) Hertz, H. G.; Hortz, M.; Klute, R.; Stalidis, G.; Versmold, H. Ber.
Bunsenges. Phys. Chem. 1974, 78, 24. Hertz, H. G.; Hortz, M.; Keller, G.; Versmold, H.; Yoon, C. Ber. Bunsenges. Phys. Chem. 1974, 78, 493. (36) A fractional charge of +O.kwas placed on the water hydrogen atoms
in the ST2 and BNS models (Ben-Naim, A.; Stllinger, F. H. "Water and Aqueous Solutions"; Hone, R. A., Ed.; Wiley: New York, 1971; Chapter 8. (37) Ruben, H. W.; Templeton, D. H.; Rosenstein, R. D.; Olovosson, I. J . Am. Chem. Soc. 1961,83, 821. (38) The field gradient caused by a nearby charge is assumed to be proportional to the magnitude of that charge. (Lucken, E. A. C. "Nuclear Quadrupole Coupling Constant";Academic Press: New York, 1969; Chapter 5). (39) EngstrGm, S.; Jason, B. Mol. Phys. 1981, 43, 1235. Engstrom, S.; Jbson, B.; Jbson, B. J . Magn. Reson. 1982, 50, 1 .
