J. Phys. Chem. 1990, 94, 7391-7394 other under the assumption C = 1 in (9). Conclusions The microwave cavity technique is a very good method to measure relaxation time with accuracy better than 3% and consequently the transition probability for the molecular collisions in the condensed phase. In addition to the temperature variation, measurements can be made in a broader range of frequencies within the microwave region by changing the oscillators driving the cavity. The C o l d o l e type behavior as used by other workersg2-” must be used to get the true picture of the dipole relaxation mechanism in water. It has been found that Debye’s single relaxation time considerations5 give reasonably good results12 with a = 0.014. For (32) Johri, G.K. J . Phys. SOC.Jpn. 1984, 53, 802. (33) Johri, G.K.;Srivastava, S. K. J . Phys. Soc. Jpn. 1980, 49, 1863. (34) Hill, N. E.;Vaughan, W. E.;Price, A. H.; Davies, M. Dielectric Properfies and Molecular Behavior; Van Nostrand: London, 1972; 289.
7391
a broader range of frequencies a value of a = 0.987 was estimated35and three dispersions have been proposedg6 in the farinfrared regions. The nonlinearity of the observed parameters is due to the associative behavior of dipoles and hydrogen bonding of dipolar molecules. The discontinuities experimentally found in the observed parameters by changing temperature in steps of 1-2 OC and those indicated theoretically in the variation of the correlation factor are a sufficient reason to suspect higher order transitions in water as was pointed out earlier by Johri et aL3’
Acknowledgment. This was work supported in part by Grant B-0842 of the Robert A. Welch Foundation, Houston, TX. (35) Bottreau, A. M.; Morean, J. M.; Laurent, J. M.; Maryat, C. J. Chem. Phys. 1975, 92, 360. (36) Zafar, M. S.;Hasted, J. B.; Chamberlain, J. Nature (London) 1973. 243, 106. (37)Johri, G.K.; Malaroda, R.; Iernetti, G.; Ciuti, P.; Carpenedo, L.; Sandri, L. Phys. Chem. Liq. 1987, 17, 153.
NMR Spin-Lattice Relaxation Studies of Methyl Isocyanide in Solution John D. Decatur and Thomas C. Farrar* Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 (Received: January 9, 1990; In Final Form: May 21, 1990)
The nitrogen quadrupole coupling constant, xN,in methyl isocyanide has been measured in solution by NMR spin-lattice (TI) relaxation measurements. The value of xN, 67 kHz, is the smallest yet measured and is the result of solventsolute interactions. Rotating frame spin-lattice relaxation times, TI,, for nitrogen were also measured. They are in agreement with the spin-lattice relaxation time results.
1. Introduction
A number of spectroscopic studies have been carried out during the past two decades to measure accurately the quadrupole coupling constant, xN, for the nitrogen nucleus in the molecule methyl isocyanide, H g C I 4 N W H . These values vary greatly, depending on the physical state of the molecules and, for those measurements done in solution, the solvent chosen. The measurement of N M R spin-lattice relaxation times is a powerful method for determining structure and dynamics in solution. For nuclei with a spin quantum number, I > relaxation is usually dominated by the quadrupole interaction. The quadrupole coupling constant, x, is a measure of the strength of this interaction. x is the product of the nuclear quadrupole moment, eQ, and the electric field gradient, V,,, at the nucleus. In nonviscous liquids where molecular reorientation is rapid, the observed spin-lattice relaxation rate, R , , is proportional to the product of the square of x and the correlation time for molecular reorientation, 7,. If the value of x is known, and if it is constant, then a measurement of TI will give an accurate value of the molecular correlation time, 7c.Conversely, if the correlation time is known, the quadrupole coupling constant can be measured and one can thus monitor changes in the electronic structure of the molecule. In general, values of x measured in the liquid phase are often different from the gas-phase values. The deuterium quadrupole coupling constant, xD,of deuterated benzene in the gas phase is 225 kHz while the liquid-state value may be 186 kHz1s2or smaller. Values for xD in methylene (CD,) groups vary from 88 to 170 kHz.’ The nitrogen (I4N) quadrupole coupling constant, xN,in methyl isocyanide changes greatly between liquid and gas phases. The gas-phase value is +489.4 f 0.4 kHz? while in the nematic Author to whom correspondence should be addressed.
0022-3654/90/2094-739 1$02.50/0
phase of Merck’s ZLI 1167 liquid crystal solvent, xNexhibits a temperature dependence and ranges from 170 kHz (5 “C) to 205 kHz (55 0C).5 In this paper NMR spin-lattice relaxation times are used to determine a value for xN in methyl isocyanide in the liquid state where hydrogen-bonding interactions may be important. We also compare the accuracy of results from T I measurements with results from T I ,measurements, where T I ,is the spin-lattice relaxation time in the rotating frame. 2. Theory For quadrupole relaxation of spin I = 1 nuclei, the spin-lattice relaxation is a single exponential described by6 R l = l / T l = (3/40)x2{J(w)
+ 4J(2w))
(1)
where x = eQ(d2V/dz2)/his the quadrupole coupling constant expressed in rad/s, J ( w ) = ~ ~ / ( 1a%:), eQ is the electric quadrupole moment, V,, = dzV/dz2is the electric field gradient at the nucleus, w is the nuclear Larmor frequency in rad/s, and 7c is the molecular correlation time for isotropic reorientation. It has been shown by Blicharski’ that the spinspin relaxation time, T2,and the spin-lattice relaxation in the rotating frame, TI,,are
+
(1) Zijl, P.C. van; MacLean, C.; Skoglund, C. M.; Bothner-By, A. A. J . Magn. Reson. 1985, 65, 316. (2)Oldani, M.; Ha, T. K.; Bauder, A. Chem. Phys. Lett. 1985, 115,317. (3) Hertz, H. G. Prog. N M R Spectrosc. 1983, 16, 115. (41 Kukolich, S.G. J . Chem. Phys. 1972, 57, 869. ( 5 ) Barbara, T. M. Mol. Phys. 1985, 54 (3), 651. (6) Abragam, A. The Principles of Nuclear Magnetism; Oxford University: New York, 1961;Chapter 8. (7) Blicharski, J. S.A c f a Phys. Pol. 1972, A41, 223.
0 1990 American Chemical Society
7392 The Journal of Physical Chemistry, Vol. 94, No. 19, 19'90 equal for spin I = 1 and are given by l/Tl,, = 1/T2 = (3/80)x2{3J(0) + 5J(w) + 2J(2w)) (2)
For isotropic Brownian diffusional motions J ( 0 ) = 7, J(w) = J(2w) =
7,
1
+ w27:
1
+ 4w27:
75
Equation 2 is valid under the extreme narrowing condition
w17,
w - wo, where w is the frequency of the observed resonance and wo is the applied rf frequency. In the experiments done here the yB1/27rvalue was 3125 Hz. This easily meets the condition that yB1/2.rr >> w - w, since the transmitter was placed directly on resonance and the J coupling to the methyl protons is 6 Hz. The intensity immediately after the spin-locking pulse is measured as a function of spin-locking time, t , which is then fit to the equation The TI, measurements were performed on the Bruker AM 360 instrument with a Bruker IO-" probe. Since the spin-locking pulse must be applied for a relatively long time (up to several seconds), the high power normally used for short pulses cannot be used because of large heating effects on the sample and probe. A pulse voltage of 60 uw (%ohm load, 9.2-w peak power) was chosen because this was the maximum voltage in which heating effects were minimal. The heating effects were estimated by observing the control temperature of the Bruker VT controller when a several-second spin-locking pulse was applied. Above 60 V a rise in temperature of more than a degree was observed. Most spin-locking pulse times were on the order of 10-100 ms, and thus heating effects were minimal. This pulse voltage, used for all TI, experiments, corresponded to a 90° pulse time of 80 ps and thus a yBI of 3125 Hz. The appropriate test to determine whether the TI, experiment is being performed properly is to compare TI, with TI when they are known to be equal. Thus, at room temperature where W ~ > Aw). For measurements of TI, the standard inversion recovery sequence, 18Oo-~-9O0,was used. The 90° pulse time was 35 ps, and inversion pulses were composite: 90,-180,-90,. At least 15 different T values in the TI experiment or 15 different spin-locking times in the TI, experiment were used to sample the recovery curves. The TI intensity data were fit to the three-parameter equation
I(r) = Io exp(-r/T,)
+ Iq(l
- exp(-r/T,))
(8)
using the Bruker supplied fitting routine which estimates the initial magnetization, Io, the equilibrium magnetization, IW, and TI. Low-power proton composite pulse decoupling was employed during acquisition for both T I and T1,measurements. Temperature control was provided by the commercial Bruker VT controller and was stable to *0.20 "C. The temperature was measured by a platinum resistance thermometer before and after each experiment, and the two values were averaged. In the infrequent event that these two temperatures differed by more than 0.4 "C, the data were rejected and the experiment was repeated. The methyl isocyanide sample was prepared by standard methods.1° The final methyl isocyanide product (bp = 59-60 19) Vold, R. L.; Vold, R. R.; Simon, H. E. J . Magn. Reson. 1973, 1 1 , 283.
T
~
N M R Studies of Methyl Isocyanide in Solution
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7393
TABLE I: TI, T,, and Line-Width Data as a Function of TemPerature
204.01 193.78 189.40 188.65 184.60 179.04 177.41 173.73 170.30 168.30
0.0945 0.0570 0.0270 0.0257 0.0182 0.0124 0.0113 0.0095 0.0087 0.0085
0.055 0.026
0.022
0.0162 0.0096 0.0078 0.0054 0.0038 0.0028
0.0146 0.090 0.0066 0.0048 0.0036 0.0026
z J
2
-4.0
Z
-J
-
-5.0
I
I, The three high-temperature values for ( 7 ~ u ~ / ~are ) - l not listed since they contain substantial systematic errors due to residual inhomogeneities in the Bo magnetic field. TABLE 11: Best-Fit Parameter Values" method Y .. kHz rn. s
,.
TI T;/Tl
"I
67.0i IO 64.2 20
*
(2.4 0.9) X (5 i 6) X lO-I7
accessible because the sample froze below this temperature. The data were fit by using both T Idata alone to eqs 5 and 1 and the ratio T 2 / T Ito eqs 5 and 6. The best-fit curves from the two methods are displayed in Figures 1 and 2. The best-fit values for the parameters E,, T ~ and , xN from the two methods are displayed in Table 11. It is apparent from Figure 1 that both sets of data, TI and TI,, do not both fit equally well the theoretical model, Le., eqs 1 and 6. The upper smooth curve in Figure 1 is the least-squares best fit for the experimental T Idata. The lower smooth curve for TI, in Figure 1 was obtained from the experimental TI data and the correlation time calculated from eq 1. This correlation time was then used with eq 2 to obtain the lower TI, curve. As can be seen, the experimental TI, data do not fit well at the lower temperatures. This was done rather than do a best fit to the experimental T I , data, since it was known that the TI, data contained systematic errors at the lower temperatures. The TI data in our experiments here are more accurate for several reasons. First, there is much less scatter in the TI intensity values. Second, there are, to the best of our knowledge, no systematic errors associated with the TI measurements reported here. Third, at the lower temperatures, the time for the entire preparation pulse train is a smaller fraction of the relaxation time in the TI experiment. Although the time for the composite inversion pulse is 140 ps in the TI determination and the 90' pulse in the TI, determination is 80 /IS, TI, is 3 times shorter than TIat the
.eo
.
.
.
.
.
.
,
.
.
. .
5.40 1x10-31
6.00
1
*40/,, .20
, I
,
4.80
,
,
,
,
,
, , ,
,
,
, , , ,
,
,
5.40
\,I 6.00
IXIO.31
UTEMPERATURE Figure 2. TI,/T, as a function of inverse temperature. Crosses are experimental data.
lowest temperatures. The smallest spin-locking time in the T!, experiment, ideally on the order of 100 ps when T = 3 ms, 1s then barely longer than the preparation pulse, an! thus those measured intensities are probably incorrect due to relaxation during the 90' pulse. We should point out that this problem is not inherent in the TI, method but rather was a limitation of the particular commercial spectrometer with which we were working. The best-fit curve to the T1,/TI ratio data is displayed in Figure 2. The best-fit parameters from this data are different from those derived from the TI data and give somewhat different correlation times than those obtained from the TI data. Thus, one should interpret TI,/T1data with caution unless the 90' pulse times are short compared to TI, and to the spin-locking times. This analysis neglects possible chemical shift anisotropy (CSA) contributions to the relaxation. An estimate of the CSA contribution can be made assuming the value of 360 ppm for nitrogen in methyl isocyanide reported by Yannonill is correct. In the extreme narrowing limit the CSA contribution to TI is given by RCsA
=(~/~~)(Y&AU)~T~
(9)
where in the above equation yBo is expressed in units of hertz. The ratio of the CSA to the quadrupolar spin-lattice rates in the extreme narrowing limit is given by
If one uses the value of 67 kHz for xN,360 ppm for Au, and 26.0 MHz for yBo, RaA/R, = 0.0069 and thus the CSA contribution can be safely neglected. Dipolar contributions to the I4N relaxation time are equally small (less than 1%) and are also neglected. ~~
(IO) Schuster, R. E.;Scott, J. E.; Casanova, J., Jr. Org. Syn. 1973.5, 772.
.
I " " " " " " " " " " " " ' 1
a x value for T 2 / T Itaken at the temperature of the TI minimum.
4. Results and Discussion TI and TI, were measured at various temperatures; the results are shown in Table 1. Temperatures below 168 K were not
.
Figure 1. In T I and In T I , as a function of inverse temperature with best-fit curves from TI data. Crosses are T Idata and circles are T I ,data.
E..- kca I ,/mol 6.37 0.15 6.32 i 0.4
"C) was collected in a cold trap and redistilled to afford a colorless liquid that was greater than 99% pure as determined by IH NMR. The choice of solvent mixture was made for its properties at low temperatures. The solutions should become very viscous but remain unfrozen such that the molecular motions are slow enough to access the region Wo7, = 1. The mixture chosen was 66% methanol-d, and 33% ethylene-d6 glycol. Samples were made in 10 mm N M R tubes that were cleaned to remove any trace of paramagnetic ion contaminants. An equal volume of both methyl cyanide and methyl isocyanide was then transferred via vacuum line to tubes containing the solvent mixture. The samples were then degassed by several freeze-pump-thaw cycles to remove dissolved oxygen and sealed under high vacuum. The final volume concentrations were as follows: methyl cyanide, 5%; methyl isocyanide, 5%; eth~1ene-d~ glycol, 3 1%; methanold,, 59%.
.
4.80
~
( 1 1 ) Yannoni, C.
S.J . Chem. Phys. 1970, 52 (4). 2005.
1394
The Journal of Physical Chemistry, Vol. 94, No. 19, 199(3
Other studies of methyl isocyanide in liquid crystal have raised questions about significant distortions in molecular geometry, anisotropic motions, and magnetic field dependent effects. An advantage of relaxation time studies in normal liquids is the fact that such complications, as these which arise in liquid-crystal studies, are absent. Although most of the work reported here was done in a magnetic field of 8.3 T (360-MHz proton frequency), some measurements were also made at 2.3 and 5.0 T. The results for all of the molecular parameters were independent of magnetic field strength. The fit of the data to an Arrhenius plot is excellent. We know of no experimental evidence here or in previous studies to indicate that the motion is not isotropic in normal (not liquid crystal) solvents. Temperaturedependent proton relaxation time measurements were made for both methyl cyanide and methyl isocyanide. Here, again, there was an excellent fit of the data to Arrhenius plots. The value of xN determined from this T I study, 67 kHz, is substantially smaller than previously reported values. Microwave gas-phase studies yield a value of 489 kHz! Several NMR studies have been reported on the neat liquid. Reported values of xN for the neat liquid are 270,12 approximately 500," and 300 kHz.14 Yannoni has studied methyl isocyanide while partially oriented in a nematic liquid-crystal solvent and found xN to be 272 f 2 kHz." The most recent study, which was also conducted in a liquid-crystal solvent (ZLI 1167), showed xN to be temperature dependent and cover a range of 170-205 kHz over the temperature range 0-55 0C.5 It has been noted that, in general, values of x in the solid phase are 10-1 5% smaller than that of the gas.I2 The difference in values of x for methyl isocyanide between the gas and liquid phase are, however, much greater than this. Reaction field theory has recently been invoked in an attempt to explain the apparent solvent dependence of x in methyl isocyanide.Is In this theory, the molecule polarizes its surroundings and generates its own "reaction" field. The reaction field rotates with the molecule, and if this field is inhomogeneous, an extra contribution to the field gradient is generated, which may add or subtract from the molecular values, thus modifying x. Additionally, the reaction field can polarize the bonds, an effect which is also capable of changing x. We attribute the extremely small (12) Moniz, W. B.; Poranski, C. F., Jr. J . Phys. Chem. 1969, 73, 4145. (13) Kemp, M. K.; Pochan, J. M.; Flygare, W. H. J . Phys. Chem. 1967, 71, 765.
(14) Lowenstein, A.; Margalit, Y. J . Phys. Chem. 1965, 69, 4152. (1 5) Huis, L.; Bulthuis, J.; van der Zwan, G.; MacLean, C. J . Phys. Chem. 1987, 91, 3430.
Decatur and Farrar value of xN determined in this study to solute interactions with a solvent known for strong hydrogen bonding. Ideally, such temperature-dependent measurements of T I or the ratio T 2 / T Icould be extended to several solvent systems to investigate the effect of different local environments on the electronic structure of 14N. The requirement of slowing down molecular motion such that UT, i= 1, however, restricts the possible solvent systems to those that become very viscous without freezing at low temperature. This is particularly troublesome for I4N because the Larmor frequency is very low. Other solvents (toluene, pure methanol) were investigated, but the region of the T I minimum was not accessible. The large range of possible xN values for methyl isocyanide, as shown by this and previous studies, demonstrates that calculation of correlation times from TI measurements based on literature values of xN for isocyanides should be carried out with caution. Ab initio calculations in this laboratoryI6 of nitrogen quadrupole coupling constants in small molecules show clearly that solvent-solute interactions can change the value of xN by several hundred kilohertz in cyanides and isocyanides. Since typical values of xN in cyanides are about 4 MHz, the percentage change for these compounds as a function of solvent is much less than that for the isocyanides which, by chance, happen to have smaller xN values. Since T I is proportional to the square of xN, a factor of 2 error in xN,which is well within the range of possible values for methyl isocyanide, results in a factor of 4 error in the correlation time. In principle, either T, or a combination of T I and T I ,measurements, as a function of the temperature in the vicinity of the T I minimum, provide information about molecular correlation times and quadrupole coupling constants. In the present case for methyl isocyanide, both experiments provide a reasonably accurate measurement, 67.0 f 10 kHz, for the value of xN, in a solution of ethylene glycol and methanol. The T I , experiments indicate that xN is essentially independent of temperature over the range studied.
Acknowledgment. We gratefully acknowledge the support of the National Science Foundation for the support of this research (NSF Grant CHE-8802373). We thank both referees for a number of helpful comments and suggestions. (16) Trudeau, J. D.; Farrar, T. C. To be published. (17) Hiltunen, Y.; Jokisaari, J.; Lounila, J.; Pulkkinen, A. Chem. Phys. Lett. 1988, 148, 353. (18) Plomp, A. C.; Loman, A. C.; Bulthuis, J. J . Chem. Phys. 1986, 84, 6591.
