J. Phys. Chem. 1990, 94, 7395-7401
7395
Temperature-Dependent NMR Relaxation Studies of Na,PHO, in Solution Thomas C. Farrar* and John D. Decatur Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 (Received: March 1, 1990)
The longitudinal relaxation of the coupled two-spin system PH03” has been studied as a function of temperature and pH. The analysis of this relaxation data provides temperature-dependent information about all components of the phosphorus and proton chemical shift tensors, the P-H dipolar parameter, and the molecular correlation time. The phosphorus isotropic chemical shift, ap(iso), the phosphorus chemical shift anisotropy (CSA), the phosphorus-hydrogen spin coupling constant, J p H , and H-P bond distance all show little change with temperature. Values for the P-H internuclear distance (corrected for vibrational averaging), the phosphorus CSA, and the proton CSA are 146.0 f 0.5 pm, -128 f 5 ppm, and 5.5 i 0.4 ppm, respectively. The sign of J p H is positive. The value of J P H and up(iso) were measured as a function of solution pH. for the species PHO?-, HPH03-, and H2PH03are +567, +625, and +680 Hz, respectively, and values The values of JPH of crp(iso) are 5.19, 4.62, and 7.29 ppm, respectively, relative to an 85% solution of phosphoric acid. It is shown that the CSA-dipolar cross-correlation relaxation effects due to multiple relaxation processes observed in coupled spin systems are suppressed in decoupled experiments. The results of the proton-decoupledexperiments agree well with the coupled experiments validating the simple approximations used to describe relaxation under decoupling. The measured value for the phosphorus CSA value agrees well with that obtained from ab initio calculations, but not with the value of -150 ppm measured for an anhydrous solid-state sample. The values for the P-H bond distance obtained from solution-state NMR experiments (corrected for vibrational averaging), solid-state NMR experiments, neutron diffraction experiments, and ab initio calculations are all in excellent agreement. It is shown that, in multiparameter NMR fitting processes, the accuracy of the results for simultaneously fit parameters is closely related to the absence of statistical correlation between the parameters fit.
Introduction Measurement of NMR relaxation times in coupled spin systems can provide a wealth of information about the structure and dynamics of molecules in solution. Spin-lattice, or longitudinal, relaxation for a given nucleus is often assumed to be single exponential and characterized by a single time constant, T I . At the high fields commonly used today, this may not be a correct assumption.’-’ If the contribution to relaxation by the chemical shift anisotropy (CSA) mechanism, which increases as the square of the magnetic field strength, is significant (i-e., more than 5-10% of the dipolar contribution), then the longitudinal relaxation may become multiexponential. In this event, the observed relaxation cannot be described as the sum of the relaxation rates of the contributing mechanisms, Le., Rtotal# Rdipola, + RCSA. For PH03*-, at fields as low as 4.8 T (200 MHz proton) where the CSA contribution is only a small part (5-10% or more) of the total relaxation, the CSA-dipolar cross-correlation terms, which give rise to significant differential transverse and longitudinal relaxation, must be considered. Each of the four lines in this coupled two-spin I = 1/2 system have different line widths requiring four separate T2values; longitudinal recovery curves for each of the four lines are described by four different triple exponentials. Previous work in this laboratory has demonstrated that these effects can be exploited to yield a simultaneous determination, at a single field and temperature, of all molecular parameters responsible for nuclear spin relaxati~n.I-~*~ For P H 0 2 - these are the chemical shift anisotropy of the proton and the phosphorus, the H-P bond distance, and the molecular correlation time. This independent determination of molecular parameters at each temperature presents the opportunity of measuring their temperature dependence, a situation which is not possible when relaxation is due to a single relaxation mechanism6 or when one of the two spins is decoupled. Additionally, the validity of the simple approximations describing the effect of decoupling upon relaxation behavior can be tested by comparing results from the coupled and decoupled experiments. It has recently been recognized that the presence of differential line broadening can affect the results observed in two-dimensional Fourier transform NMR (2D-FT-NMR) experiments.’ Mueller et al. were the first to report on coherence transfer via relaxation processes.’ These processes give rise to anomalous peaks in 2D
* Author to whom correspondence should be addressed.
multiple quantum filtered correlation spectra of macromolecules (where correlation times are long). Differential relaxation can also affect two-dimensional correlation (COSY) experiment^.**^ The experiments described here are also of interest because they are the one-dimensional equivalent of the 2D-FT-NMR NOESY experiment and provide some insight into the accuracy and precision of the results of such experiments. A number of questions have been raised recently about the accuracy of the NOESY experiments.I0 Since most 2D-FT-NMR experiments involve a time period during which the coupled spins evolve, the relaxation behavior during the evolution times is important, especially if the evolution times are long enough for significant longitudinal or transverse relaxation to occur. This will generally be the case for large molecules with long correlation times and short relaxation times (Le., when W ~ T ,N 1). An appreciation of these complex relaxation interactions is necessary for the correct interpretation of many of the common multidimensional experiments. In this paper we describe the experimental conditions and the data analysis considerations needed to obtain accurate, simultaneous values for molecular parameters for a system of two coupled spins. We report the temperature dependence of these values and compare the results of the coupled experiments with those when proton decoupling is employed. These experiments are part of a series which are designed to provide more information about basic relaxation processes in coupled spin systems in which multiple relaxation processes are present. We are interested in learning what factors determine the magnitude of the components of the chemical shift tensor, the spin-coupling tensor, and the quadrupole coupling tensor, how accurately these parameters can be measured, and to what extent the components of these tensors may be considered constant for a given molecule or ion in solution. We (1) Farrar, T. C.; Locker, I. C. J. Chem. Phys. 1987,87,3281. See also: Z . Phys. Chem. 1987,lS1. 24. (2) Shimizu, H. J . Chem. Phys. 1964,40(11), 3357. (3) Mackor, E. L.; MacLean, C. Prog. N M R Specrrosc. 1967,3, 129. (4) Farrar, T. C.; Quintero, R. A. Chem. Phys. Lerr. 1985, 122,41. (5) Farrar, T. C.; Quintero, R. A. J . Phys. Chem. 1987,91,3224. (6)Hertz, H. G. Prog. N M R Spectrosc. 1983,16, 115. (7) Mueller, N.; Bodenhausen, G.; Wuethrich, K.; Ernst, R. R. J . Magn. Reson. 1985,65,531. (8) Wimperis, S.;Bodenhausen, G. Chem. Phys. Lerf. 1987, 140, 41. (9) Wimperis, S.;Bodenhausen, G. Mol. Phys. 1989,66,897. (10) Clore, G. M.; Gronenbom, A. M. J. Magn.Reson. 1989,84,398. See also: Gronenborn, A. M.; Clore, G. M. Anal. Chem. 1989,62,2.
0022-3654 f 9012094-7395%02.50/0 0 1990 American Chemical Society
7396 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 are also interested in discovering what correlations exist between these three tensors and the molecular and electronic structure of molecules. Experimental Section Na2PH03.5H20was obtained from Reidel Chemical Co. Two samples were prepared, utilizing different solvent systems. For the ethylene glycol/D20 solvent system, the water of hydration was removed by heating to 90 'C under vacuum at l C 3 Torr. The sample was then dissolved in 99.96% gold label D 2 0 (obtained from the Aldrich Chemical Co.) to make a 3.0 M solution. The pH of the solution was adjusted to about 12 by adding NaOD, prepared by adding sodium metal to DzO. A 1-5-mL volume of this solution was added to 3.2 mL of ethylenad, glycol (obtained from MSD Isotopes). This afforded a 32 68 mixture of D 2 0 / ethylene-d6 glycol that was 1 M in P H 0 3 . For the methanold6/D20 system, the dried Na2PH03 was dissolved in DzO and redried in order to exchange any residual waters of hydration. This Na2PH03was then dissolved in a 40/60 mixture (by volume) of methanoi-d6/D20 to make a 0.88 M solution. NaOD was added to adjust the pH to 12.4. The residual HDO in both samples was checked by proton N M R measurements; the HDO peak intensity was less than that of either of the proton resonance lines in the PH032- spectrum. These two samples are hereafter referred to as sample E (for ethylene glycol) and sample M (for methanol). For the measurements of JPHand up(iso) at different solution pH values (monitored with a pH meter), dilute solutions of H2PH03were titrated with different amounts of standardized 0.05 M NaOH. The N M R spectrum was recorded at several places along the titration including the equivalence points. Literature values of the dissociation constants for phosphorus acid, K l = 1 .OO X and K2 = 2.6 X lo-', allow the calculation of the amount of each species present as a function of pH. The phosphorus chemical shift was measured relative to 85% phosphoric acid. The samples were degassed by at least eight freeze-pumpthaw cycles on a high-vacuum line and sealed under high vacuum. The N M R tubes were carefully cleaned before use and treated with sodium EDTA solutions to remove any trace of paramagnetic ion contaminants. Measurements made over a period of 36 months show no change in the relaxation times for a given set of experimental conditions, and they show no exchange of the proton directly bonded to the phosphorus atom. This sample, contained in an 8-mm tube, is held concentric in a IO-" tube filled with acetone-d6 which allows field frequency locking at temperatures where the sample eth~1ene-d~ glycol/D20 resonances become too broad. In the relaxation experiments performed here temperature stability is of paramount importance. For this reason we have designed and built a temperature controller which is capable of holding the temperature constant to better than d~0.035OC for periods up to 36 h or longer. This device has been described elsewhere.' Typical phosphorus 90' pulse widths were 25-30 ps; proton 90° pulse widths were approximately 20 ps. All spin inversions were accomplished with composite pulses designed to compensate for R F inhomogeneity (90, - 18OY - 90,).'2 Relaxation delays of 10 times the relaxation time for the most slowly relaxing of the four spectral lines were used. A spectral width of about IO00 Hz was used (the value of JPHvaries with pH from 567 to 680 Hz). Free induction decays (fid) were zero filled prior to Fourier transformation to provide at least 15 data points above the half-height for each peak. As shown in an earlier paper," in order to obtain reliable values for the CSA's, the dipolar parameter, and the correlation time, it is necessary to execute the following experiments: (1) broadband (nonselective) inversion recovery of 31P, followed by observation of 3 1 P( 2 ) broad-band inversion of the 'H lines followed by observation of 3 1 Pand (3) simultaneous broad-band inversion of the 'Hlines and the 31P lines followed by observation of 3iP.
b
'
(1 I ) Farrar, T. C.; Sidky, E. Y.; Decatur, J. D. J . Magn. Reson., in press. (12) Levitt, M. H. J . Magn. Reson. 1982, 48, 234. (13) Decatur, J. D.; Farrar, T.C. J . Phys. Chem., in press.
Farrar and Decatur Twenty-five 7 values for each experiment were collected, two or three of which were at least 10 times greater than Ti; these were used to check the long-term stability of the system and the reproducibility of the data. Between 12 and 24 h are required to collect the data for the experiments described above. To minimize the effects of spectrometer instability, the program cycles through the three experiments in the following manner:
where n indicates one of the 25 T values and EXPI, EXPI, and EXP, are experiments with the three different boundary conditions. Eight scans are collected for each value of n and then the entire sequence is repeated m times to give the required signal to noise ratio. This cycling reduces the stability required of the spectrometer to only the few minutes necessary to collect eight scans for each of 75 fids instead of the many hours required for the entire experiment. Peak heights were used for magnetization intensities. These were then scaled to account for the differences in height that result from the differential line broadening. Reproducibility between equilibrium values was 0.5% (standard deviation) or better. In the proton-decoupled experiments, broad-band decoupling was achieved by a hard-wired WALTZ-16 box driven by a clock asynchronous to signal a q u i s i t i ~ n . ' ~Low power (yBo = 1.1 kHz) provided sharp lines (T2limited at 5 2 Hz) and minimal decoupling sidebands (3%). The sample heating effects of decoupling were estimated by placing a platinum resistance thermometer (PRT) in an NMR tube and solvent identical with the sample. This PRT was then placed into the probe, the decoupler was switched on, and the sample was allowed to come to thermal equilibrium. To avoid the direct interference of the decoupler with the measurement of the PRT, the temperature was recorded immediately after the decoupler was turned off. The increase in the equilibrium temperature upon decoupling was less than 0.20 O C . The temperature dependence of the 3iPisotropic chemical shift of PH032-was measured a t 4.8 T (200 MHz 'H)and at 8.6 T (360 MHz IH).These measurements were made without deuterium lock to avoid convoluting the temperature dependence of the deuterium chemical shift with the phosphorus shift. The temperature was independently measured with a PRT inserted into the probe before and after the measurements. The phosphorus relaxation experiments, both coupled and proton decoupled, were performed at 4.8 T using the home-built temperature controller. Theory The theory of spin-lattice relaxation in coupled spin systems has been treated in detail by a number of a u t h ~ r s . ' J J ~ - 'The ~ populations of the energy levels are represented by the diagonal elements of the density matrix, uii, and the spin-lattice relaxation is described by the following differential equation:
-du*ii - - CRiijj(u*jj dt
rJ*jj( a))
J
The elements of the relaxation matrix, for the case of two spin 1 / 2 nuclei relaxed by the dipolar and CSA interaction, are calculated by the theory developed by Redfield" and are given in Table I. Two isotropic random field terms, A and B (for 31Pand IH,respectively), were included in the analysis to account for the (14) Shaka, A. J.; Keller, J.; Freeman, R. J . Magn. Reson. 1983,53,313. (15) Werbelow, L. G.; Grant, D. M. Ado. Mag. Reson. 1977, 9, 189. (16) Vold. R. L.; Vold, R. R. Prog. N M R Specrrosc. 1978, 12, 79. (17) Redfield, A. G . Advances in Magnetic Resonance; Waugh, J. S., Ed.; Academic: New York, 1965; Vol. 1 . (18) Blicharski, J. S. Z . Narurforsch. 1972, A27, 1355. (19) Koenigsberger, E.; Sterk, H. J . Chem. Phys. 1985, 83, 2723. (20) Huis, L.; Bulthuis, J.; van der Zwan; MacLean, C. J . Phys. Chem. 1987, 91, 3430. (21) Collins, K. D.; Washabaugh, M. W. Q.Reu. Eiophys. 1985.18.323. (22) Nishida, B. C.; Vold, R. L.; Vold, R. R. J . Phys. Chem. 1986, 90, 4465.
N M R Relaxation Studies of Na2PH03
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7397
TABLE I: Elements of the Relaxation Matrix Relating to Spin-Lattice Relaxation for P H O g Where the Principal Axis Frames of the Dipolar and Chemical Shift Interactions Are Coincident
[
1
Rl122 = j A u -~ 2pAU, ~ 1 R1133 = I j A u x 2 - 2pAux
3p2]J,
+ A/2
1
+ 3p2 Jx + B/2
dI2 dt = -2R3344(433 - 044) + R1133(~11- u33) R2244(‘22 - u44) + R1144(u44 - all) + R2233(622 - c 3 3 ) (4) where the R , are given in Table I. As a result of the decoupling field, u l l - uj3 = u22and eqs 3 and 4 simplify to dI1 dt
R114 = 12p2J+
-(2Rl122 + R1144 + R2233)z1
(5)
dt = -(2R3344 + R1144 + R2233)12
(6)
dI2
R2233 = 2p2J-
[ [: 1
R2244 = jAux2 + 2pAux
1 1
+ 3p2 Jx + B/2
R334 = -hA2 + 2 p A u ~ 3p2 JA
+ A/2
=0
Although it appears that the two lines relax with different rates, the decoupling field causes rapid exchange of the proton spin states and the observed rate then equals the average of the rates for the two lines:
where Au, = Y ~ B ~ -( Uul),, , ~ p = YAYXh/2rAX3, and
(7) Thus, the effect of the decoupling field is to eliminate the CSA-dipolar cross-relaxation terms. The recovery is described by a single exponential and the rate of recovery is just the sum of the contributions from each mechanism: Rtot
=
= R1122 + R3344
TI
R1144
+ R2233
= RCSA + Rdipolar + Rrandom = [(2/3)Au2 Jo =
(9)
+ 6p2]JA+ 12p2J++ 2p2J- + A
where Auig, and the spectral density functions, JA, J x , etc. are as defined in Table I. The temperature dependence of the correlation time may be described by an Arrhenius relationship
7,
5
residual intermolecular dipolar interactions with solvent deuterium and cations, as well as the spin-rotation interactional6 The random terms A and B, which allow for noncorrelated intermolecular relaxation (primarily with the deuterons in the solvent), are of the form y?B,%,, where Bi is the randomly fluctuating field produced by spins external to PH032-. These random terms depend upon temperature because of the implicit dependence on TC.
Experimentally, one observes not populations of energy levels but population differences, or line intensities. In order to use the line intensities directly in the analysis, the relaxation matrix was transformed to the line intensity basis. The solution to this set of differential equations is
+
(8)
+
+
+
I = cleAlfvl c2eAzrv2 c3eA~fv3c4eA4fv4 I ( m ) (2) In the analysis program the relaxation matrix is calculated based on estimated values of Pup,AuH,p, T,, A, and B which are defined in Table 1. This is then numerically diagonalized to give eigenvalues XI through X4 and eigenvectors vl through v4. Note that since the number of nuclei is constant, one of the eigenvalues is zero and the relaxation is described by a triple exponential. From the initial conditions (which depend upon the pulse experiment) and the equilibrium line intensities, the constants cI to c4 are obtained and then the predicted line intensities are calculated as a function of time. Nonlinear least-squares methods are used to find the set of best fit parameters. In order to accurately describe the results of experiments employing proton decoupling it is necessary to solve the equations of evolution of the density matrix with a Hamiltonian which includes a term 7 4 to account for the presence of the decoupling rf field. The solution to these equations is difficult. A reasonable approximation to the answer can be obtained by observing that the decoupling field maintains equal spin populations on levels 1 and 3, and on levels 2 and 4. The recovery of the coupled phosphorus lines is given by
7c
=
TO
exP(Ea/RT)
(10)
where E, is the activation energy for isotropic reorientation and T is the temperature. As the correlation time becomes longer, each of the above spectral densities, e.g., JA, passes through a maximum leading to a minimum value for T I . Measuring TI over a temperature range that includes the minimum allows the determination of p, E,, and r0. Equation 8 states that, in the decoupled experiment, the total rate of relaxation is the sum of the dipolar, the CSA, and the intermolecular (random) relaxation rates. Since in a single experiment these contributions cannot be separated, the decoupling results in a loss of information relative to the coupled case. Field-dependent relaxation studies can be used to provide information on the magnitude of the CSA interaction. By carrying our measurements on several samples of varying proton to deuteron ratios for the solvent molecules, we can obtain information about the magnitude of the intermolecular dipolar interaction (the random field interaction). That is, the CSA and intermolecular contributions cannot be estimated in a decoupled experiment with data from a single field and single sample. For correlation times down to the T , minimum (Wo?, N l), eq 10 is an accurate representation of the temperature dependence of rC(or r L ) . Note that rlI,in the present case, does not contribute to the relaxation. At temperatures below the T I minimum, the solution becomes glassy, the behavior is no longer Arrhenius, and the data is no longer accurately described by eq 10. The data may be fit over a very wide temperature range, extending well below the T Iminimum, by using a Cole-Davidson function which gives an accurate representation of the data. The coupled relaxation time measurements give information about the chemical shift anisotropy, Pa = ull - uLr and the high-resolution experiment gives the isotropic chemical shift, up(iso) = (1/3)(uxx uyy + uzz) = (1/3)(2aL + all). Simple algebra then gives the components of the chemical shift tensor in terms of these two measured quantities: uL = 3up(iso) - Au
+
uli =
(2/3)Au
+ ap(iso)
(1 1)
Farrar and Decatur
7398 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 TABLE 11: Best Fit Parameters and Their Uncertainties for SamDle E temp, 7c X noH, nop, A, B, no. of OC lolo. s Dom DDm 'b;" rad/s rad/s trials 34.97 30 37 23.49 14.55 5.63 1.18 -4.1 1 -7.66 -15.82 -21.36 -30.88 % uncb
1.072' 1.276' 1.650' 2.40 3.56 4.62 5.72 7.07 10.6 14.04 18.1 3.8
4.79 4.78 4.74 5.2 5.37 5.16 5.55 5.66 5.80 5.12 4.15 4.9
-109.1 -106.2 -109.1 -113.9 -1 19.2 -122.7 -127.4 -131.0 -135.2 -138.6 -125.4
1.569 1.570 1.555 1.545 1.523 1.516 1.504 1.500 1.503 1.540 1.676
2.2 0.32
0.027 0.021 0.028 0.05 1 0.064 0.092 0.13 0.181 0.297 0.46 0.526 12
0.076 0.080 0.098 0.128 0.173 0.19 0.193 0.204 0.224 0.233 0.227
180
4
1
3 3 2 3 3
IS0
-
I20 -
1
3 1
.....................
3 3
.o
I .a
determined from best fit line of In 7c vs 1 / T and then fixed during fitting procedure. Uncertainties for an individual determination, as A / x X loo%, determined from replicate measurements. These are the maximum experimental uncertainties. The phosphorus isotropic shift is referenced to 85% phosphoric acid. Results and Discussion
Proton-decoupled 31P spin-lattice relaxation rates for sample E (Na2PH03dissolved in a 32/68 by volume mixture of D 2 0 / ethylene-d, glycol) were measured at 4.8 T as a function of temperature. The data, shown in Table IV, were then fit to eqs 8 and 10 with the assumption (justified below) that Aup and rHP are independent of temperature. The best fit curve of In T , vs 1 / T is displayed in Figure 3. Since it is not possible to simultaneously fit all the parameters appearing in eq 8, a value of Aup = -1 28 ppm was chosen and the values of the random field term, A, were taken from the results of the coupled experiments (Table 11). Fitting the temperature-dependent T,'s to eqs 8 and 10 yielded values of rHp, E,, and T~ which are 15 1 .O f 2 pm, 7.82 f 0.31 kcal/mol, and (3.56 f 1 ) X respectively. These values are not sensitive to the values of Aup or A because Aup and A contribute little to the total relaxation, as discussed below. Comparison of values of T, in Tables I1 and IV reveals that values calculated on the basis of these decoupled experiments agree extremely well with correlation times obtained from the coupled experiments. The value obtained for the P-H bond distance is also in excellent agreement with the results from the coupled experiments. Since the decoupled 31Pspin-lattice relaxation rate is simply the sum of contributions from each relaxation mechanism, the 31PTl's can be corrected for the small relaxation contribution from the CSA and random interactions. Because Aup and p are multiplied by different spectral densities, Ji, the fractional contributions depend upon the correlation time and, consequently, the temperature. From -35.3 to 32.5 OC at up = 80.9 MHz, the contributions are % Rdi& = 80-89, % RcsA = 15-7, and % R b = 10-1. Here we see clearly that the dipolar contribution is, in all cases, at least 6 times greater than the CSA contribution at 4.8 T. Even at the highest field available today, 14.4 T (wH = 600 MHz), the dipolar contribution for PHO$- would still be twice the CSA contribution. This is in sharp contrast to the field, 8.6 T (wH = 360 MHz), that produces the largest differential effect in the coupled system. This occurs when the parameters p and Aup/3 are equal (see, e.g., R1122in Table I). The relative insignificance of the CSA to the overall decoupled rate is due to the large dipolar contribution from the elements R2233 and Although the CSA contributes a minor amount to the total relaxation, in the coupled system it still gives rise to significant differential transverse and longitudinal relaxation. Typical phosphorus recovery curves of the coupled system resulting from one of the pulse experiments (number 2 in Experimental Section) are shown in Figure 1. The best fits to eq 2 are displayed as smooth lines. The parameters that are fit by the nonlinear least-squares routine are p (which yield a value for rHP
3.0
TIME
4.4
a7c
2.0
-1
Figure 1. Typical phosphorus recovery curves of the coupled system resulting from pulse sequence 2 (see Experimental Section). Low-frequency line (A),high-frequency line (0). TABLE 111: Best Fit Parameters from the Coupled Experiments for SamDle M no. of B, A, temp, 7C X A ~ H , Aup, OC rad/s rad/s trials IOIO, s ppm PPm
'%'
12.97 1.438 5.91 1.684 -1.15 2.685 -8.21 3.096 -15.39 4.646 -24.5 6.401 9.807 -28.20 -3 1.45 11.85
4.044 4.56 4.51 5.54 5.46 5.65 5.42 5.40
-88.7 -100.8 -98.5 -1 19.5 -122.7 -142.5 -129.7 -128.2
1.632 1.588 1.600 1.537 1.519 1.510 1.500 1.505
0.0124 0.0263 0.0339 0.083 0.094 0.34 0.204 0.191
0.0381 0.0665 0.0886 0.14 0.164 0.208 0.186 0.167
1 1
2
TABLE I V Proton-Decoupled Tl's and Cdcukted Correlation Times for Sample A temp, "C Ti, s 72 x 1010, s 32.55 23.97 15.08 0.63 -8.92 -15.13 -2 1.90 -26.70 -30.90 -35.33
1.055 0.873 0.645 0.397 0.282 0.24 0.228 0.24 0.263 0.346
1.09 1.56 2.32 4.65 7.66 10.8 16.1 21.6 28.2 37.8
OCalculated from eq IO using E, = 7.54 kcal/mol and
70
= 4.5
X
10-16 s.
assuming a negligible AJ, the spin coupling anisotropy), ACTH,Aup, T ~ A, , and B. The initial magnetizations of both nuclei as well as the phosphorus equilibrium value are also fit. The proton equilibrium value is determined by the ratio of the proton and phosphorus Larmor frequencies. Altogether, then, nine independent parameters are fit. Best fit values, for a number of different temperatures, for rc, Aup, rHP,AuH, and the random field terms A and B, are shown in Tables I1 and I11 for samples E and M, respectively (sample M is Na2PH03 dissolved in a 40/60 by volume mixture of methanol-d6/D20). These values were obtained by letting all nine parameters vary and obtaining a best fit curve for the relaxation recovery curves. The relaxation data obtained from the coupled experiments at the higher temperatures (23-35 "C) contained slightly greater scatter (1%) than at the lower temperatures (0.25-0.50%). This is the result of long-term spectrometer instability (gain, Bo homogeneity, etc..) which becomes apparent as the time required for the complete set of experiments (>24 h) increases due to the longer relaxation times at the higher temperatures. The spectral signal-to-noise ratio, (S/N), was greater than 500 in all cases and was obtained with 64 scans. Additionally, Monte Carlo simulations indicate that, at shorter correlation times, the intrinsic pa-
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7399
N M R Relaxation Studies of Na2PH03 ~
"
"
'
"
"
"
'
"
'
"
"
.x
~
t
"
-21.0
-I C
-J
://
1
TABLE V Correlation Matrix of Parameters for T~ = 8.5 X s AUH P Au~ A B AuH 1.00 P 0.34 1.00 TC 0.84 0.45 1.00 A u ~ -0.82 -0.59 -0.98 1.00 A -0.78 -0.69 -0.95 0.98 1.00 B -0.29 -0.73 -0.28 0.43 0.43 1.00
.I
+
,#X'
-23.0 3' 3.50
4.00 1x10-31
UTEMPERATURE Figure 2. Temperature dependence of the correlation time for sample E determined from the coupled experiments when the value of rHpis allowed to be fit at each temperature (+) (and the best fit -) and when fHp is fixed to 151.0pm at all temperatures ( X ) (and the best fit ---).
c -
-1.0
-1.5 4.00
3.50 1x10-3 I
Inverse Temperature Figure 3. Temperature dependence of the proton-decoupled T,'s for sample E and best fit to eqs 8 and IO. rameter uncertainties become somewhat greater." That is, for a constant amount of scatter in the data, parameter uncertainties become greater at shorter correlation times. Parameter value uncertainties are thus greater at the higher temperatures. As we have shown in ref 13, if a parameter is known with certainty and can be removed from the list of parameters to be fit, then the fitting procedures will give substantially increased precision for the remaining parameters. Since a first pass through the parameter fit procedure showed that the correlation time data follows very closely in Arrhenius relation, we obtained T, from a best fit line to the In T~ vs 1 / T data (eq 10). Only the seven temperatures between -21.36 and +14.55 OC were included in the best fit regression for the correlation time, since they were known to be more accurate and precise than the three high-temperature points. Figure 2 shows the best fit line to these data having slope E, = 7.0817 f 0.07 kcal/mol and intercept -34.526. For both samples, the apparent temperature dependence of rHp and Aapdetermined from the coupled experiments is substantial. The bond distance covers a range from 157 pm at the lowest and highest temperatures to 150 pm near -8 O C thus appearing to pass through a minimum. The value for Aap changes monotonically from -138.7 ppm at the lowest temperatures to -106.2 ppm at the higher temperatures. Although a trend in AuH may be present, enough scatter is present to question its validity. The data shown in Table I1 are averages of the results of several independent experiments taken, usually, several weeks apart. The results are highly reproducible and of high precision (less than 1% scatter in the experimental data). Data similar to sample E are observed for sample M in rHp, and Aap. Interestingly, the values of these parameters between the two samples are similar when the sample viscosities are similar (and thus the correlation
TABLE VI: Correlation Matrix of Parameters for T~ = 8.5 X IO-" s Auw P T, A u ~ A B ACTH 1.00 P -0.95 1.00 70 0.95 -0.99 1.00 POP -0.94 0.98 -0.99 1.00 A -0.90 0.92 -0.95 0.97 1.00 B -0.79 0.78 -0.82 0.87 0.91 1.00
times are similar) rather then when the temperatures are similar. As discussed below, the changes in these parameters as a function of temperature do not reflect actual changes in the molecule. The temperature dependence of the phosphorus isotropic chemical shift, ap(iso), was measured over the range -23 to +7 OC and was found to be almost independent of temperature, i.e., 0.0016 ppm/OC. This behavior contrasts with that usually found when phosphorus is situated in a nonsymmetric electronic environment. Trivalent phosphorus compounds with low symmetry typically exhibit a up(iso) temperature dependence of 0.05 ppm OC or greater.23 PF032-, which is very similar to PH032-,shows a ap(iso) temperature dependence of 0.025 ppm/OC. The changes in Aap reported here for PH032- are more than 2 orders of magnitude greater than the changes in up(iso). Since aim= 1/3(2aL + all), it can be seen that the components of the shielding tensor, uI and ail, must have nearly opposite temperature dependencies, Le., doll/dT -2do,/dT if the changes in Pap are real. Ab initio calculations of the chemical shift tensor for PHOt-, which have been performed in this l a b o r a t ~ r y indicate ,~~ that changes in Aap, resulting from bond length changes, are similar in magnitude to changes in ap(iso); Le., changes in Aup should be accompanied by changes in up(iso). Since up(iso) is experimentally temperature independent, these calculations indicate that the apparent changes in the experimental values of Pap do not reflect actual molecular changes. These calculations probe bond distance changes but ignore possible intermolecular effects. The above conclusion is valid to the extent that the dominant effect of temperature is rotational-vibrational changes in the bond distance. The spin-coupling constant, JpH, was found to be relatively temperature independent, Le., -0.050 Hz/OC, as was the P-H stretch frequency observed in temperature-dependent infrared experiment^.^^ Both observations are strong indications that little or no temperature-dependent changes occur in the P-H bond distance. Except for the fits of the NMR relaxation data, then, all measurements indicate that the P-H bond distance and the phosphorus chemical shift anisotropy are essentially temperature independent over the range of temperatures studied here. We, therefore, refit the relaxation data for sample E at all temperatures using a number of different, fixed, P-H bond distances. Fixed P-H bond distances of 150.0, 150.5, and 151.0 pm all gave excellent fits to the relaxation data. Bond distances greater or smaller than these resulted in substantially larger residuals in the leastsquares fit routine. Furthermore, when bond distances were fixed to values outside the range, 150 IrHp I151, both the correlation time and phosphorus CSA values became physically unreasonable. When a fixed bond distance of 150.5 pm is used and the remaining
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(23) Gorden, M. D.; Quin, L. D. J . Magn. Reson. 1976, 22, 149. (24) Trudeau, J. D.; Farrar, T. C., submitted for publication to J . Phys.
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7400 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
parameters are refitted, both the proton and phosphorus C$A's became temperature independent. The new values obtained for Aup and AuH were -128 f 3 and +5.5 f 0.4 ppm, respectively. The apparent temperature dependence of THp and Aup, when r H p is not fixed, is due to the fact that the parameters become statistically more highly correlated as the temperature increases. When parameters are correlated, they are partially redundant mathematically and the available data cannot separate the parameters fully; in other words, the parameters are not completely independent. For the case where all parameters are allowed to vary, Tables V and VI show the correlation coefficients for two different temperatures with their corresponding values of T ~ At . the higher temperatures, and hence, shorter correlation times, the correlation coefficients between parameter become very high and approach unity. The value of the bond distance, 150.5 pm, agrees well with the values determined over the temperature range from about 1 to -16 OC from the coupled measurements when r H p is not fixed. The values of Aap over this temperature range are also in agreement with the value of Aup of -128 ppm. This range of temperatures corresponds to correlation times ranging from about 4.0 X to 1.0 X s. The T I minimum, where T~ = 1.5 X s, occurs at about -20 OC. Thus, to obtain the most accurate parameter values from these experiments without the requirement of fixing the bond distance, the temperature should be adjusted such that the correlation time lies in the range 0.2
