J. Phys. Chem. 1993,97, 7201-7207
7201
pH, Temperature, and Concentration Dependence of the Chemical Shift and Scalar Coupling Constants in NazPH03 and NazPF03 T. C. Farrar,' J. L. Schwartz, and S. Rodriguez Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 Received: April 6, 1993
The isotropic spin coupling constants and chemical shifts have been measured for solutions of Na2PH03 and NazPF03 as a function of pH, temperature, concentration, and solvent. The isotropic phosphorus-hydrogen spin coupling constant, JPH,and the isotropic proton chemical shift,, : a for the PHOsZ-anion follow typical titration curves as a function of the solution pH. For the pH ranges 7.5-14, 2.0-5.0, and 0.1-0.3, the values for JPHare +567.5, +628.5, and about +683 Hz, respectively. The isotropic phosphorus chemical shift, , : 6 exhibits an anomalous behavior in that the value for: 6 in the pH range 2.0-7.0 is less than that in either the ranges pH 1 7.0 or pH I2. Experimental values for: 6 and are in agreement with the results of ab initio calculations. H3PH03+was prepared in a solution of HzS04; the values for JPH, : 6 and: 6 for this species are 804.1 Hz, 6.49 ppm, and 17.41 ppm, respectively. Similar results are obtained for the PF03Z-anion. For PFOsZ-, JPF values are -867 and -912 Hz in the pH ranges 6.0-1 1.0 and 2.0-4.0, respectively. JPF, and all show typical p H titration curves. Graphical representations of the temperature, concentration, and solvent dependence of the N M R parameters for PH032-and PF032-are given. Solution and solid-state N M R data, infrared data, neutron diffraction results, and ab initio calculations all indicate that changes in the pH and temperature cause changes in the PF, P H , and PO bond distances which in turn lead to changes in the N M R and infrared spectral parameters.
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1. Introduction We have been interested for some time in learning more about phosphate ions and phosphate ion derivatives because of the important role they play in chemistry and biochemistry. In particular, we are interested in understanding how the molecular and electronic structure and the molecular dynamics change as a function of environmentalconditions such as pH, solvent,cation, temperature, and concentration. The direct dipolar, indirect dipolar, quadrupolar coupling, and chemical shift tensors, which can all be obtained from nuclear magnetic resonance (NMR) experiments, offer, in principle, a means of monitoring changes in the molecular and electronic structure. This assumes that one has a reasonably clear understanding of how molecular parameters, such as bond distances, bond angles, electronic charge distribution, and others, are related to these NMR tensors. For relativelysimple,stable solid compoundsit is nowadays reasonably straightforward to measure chemical shift and quadrupole coupling tensors using FT-NMR spectrometers designed for obtaining NMR spectra of solid compounds. NMR relaxation time measurements provide a way to obtain much of this same structural information and also information about molecular dynamics for solution-state samples. The phosphite and fluorophosphateanions and their more acidic derivatives are useful model systems for a study of how the scalar coupling and chemical shift parameters change as a function of molecular and electronic structure. The ions are small enough that they are amenable to ab initio calculations of the phosphorus and proton chemical shift tensors and thus afford an important test of the accuracy of such calculations. Knowledgeof all of the components of these tensors is desirable since this provides more detailed structural information and affords one a more complete test of agreement between experimental results and theoretical calculations. Unfortunately, knowledge of all of the components of the tensors is sometimes not obtainable, especially for large and/or complex molecular systems or for systems of low symmetry. However, even for large ~
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Author to whom correspondence should be sent.
0022-3654/93/2097-7201$04.00/0
molecules it is usually possible to obtain accurate values for the isotropic chemical shift, ,i6 and the isotropic scalar coupling constant, J h (the isotropicvalue of a tensor is one-third the sum of the diagonal values of the tensor). Such data is useful since it provides substantial information about systematic changes in the molecular structure via changes in the NMR parameters. In recent studies we have been able to obtain information about all of the components of the phosphorus, proton, and fluorine chemical shift tensors of sodium phosphite and sodium fluorophosphate using solid-state methods,' solution relaxation time measurements," and ab initio calculations.5 The work reported here, measurements of the values of the isotropic chemical shifts, ai,, and the isotropic scalar coupling constants, J h , for the compounds Na2PH03 and Na2PFO3 as a function of pH, temperature, concentration, and solvent,complementsthis earlier work and serves as a check on thevalues obtained for the chemical shift and spin coupling tensors obtained from NMR relaxation time measurements and theoretical calculations. As seen below, these parameters are quite sensitive to pH, but less sensitive to temperature, concentration, and choice of solvent. The Kal and Kaz values for phosphorous acid cited in the literature vary substantially and range from 5.0 X and 2.5 X 10-7, respectively,9to 1.6 X 10-2 and 7 X 10-7.10 The values given by Skoog and West7J for phosphorous acid are Kal = 1.0 X 10-2 and Ka2 = 2.6 X le7, assuming unit activities. Using these values, one would conclude that at pH values greater than 7.5, more than 99% of the sample exists as P H O P . At pH values between 2 and 5 pH units, 99% of the sample exists as H P H O j . At pH values less than 0.3 the predominant speciesis phosphorous acid.* The H3PH03+cation was generated by making a 0.8 M solution of phosphorous acid in concentrated HzS04.11 The presence of this species is apparent from the very large changes in the values of JPH,6L, and &.
2. Experimental Section The NaZPHOp and Na2PFO3 salts were purchased from Pfaltz and Bauer and Johnson Matthey Electronics, respectively. The ethylene glycol was purchased from Aldrich Chemical Company. 0 1993 American Chemical Society
Farrar et al.
7202 The Journal of Physical Chemistry, Vol. 97, No. 28, I993 All water used in solution preparation was deionized via ion exchange columns. The “pH” values of the different samples were adjusted by adding appropriate amounts of HCl or NaOH. All chemicals were used as obtained from the manufacturer without further purification. A Fisher Accumet Model 925 pH meter and buffered reference solutions were used for the pH measurements. See the discussion section for more details on the “pH” measurements. The H2SO4 was purchased from EM Science. The NMR spectra were obtained with a Bruker AM-360-WB, a Varian Unity 300, and a modified Bruker WP-200 spectrometer operating at fieldstrengths(BO)of 8.5,7.0, and 4.7 T, respectively. As anticipated, the values for the isotropic scalar coupling constants and the isotropic chemical shifts, expressed in Hz and ppm, respectively, are independent of magnetic field strength. The phosphorus chemical shift values are reported relative to phosphoric acid (85% aqueous solution of H3P04), the proton chemical shifts are relative to TMS (tetramethylsilane), and the fluorinechemicalshifts are relative to CF3COOH (trifluoroacetic acid), The solutions were pipetted into 10-mm NMR tubes with a centered 5-mm NMR tube which contained the reference compound. None of the solutions was degassed. Before use, the inner and outer walls of the NMR sample tubes were carefully cleaned by soaking them in deionized water, and then flushing five times with fresh deionized water. They were then dried in a stream of pure, clean, dry nitrogen gas. The pH of several solutions was measured both before and after the NMR experiments in order to check any possible contamination from adsorbed species on the sample walls. The largest pH change observed over time for a given sample (0.017 pH units) was for a Na2PHO3 sample at a pH value of 9.4. The “pH” values used are only approximate since the solutions were relatively concentrated and the ionic strength was not held constant during the titration. In both the aqueous and 60% ethylene glycol (EG)-40% water solutions the salt concentration was 0.8 M. Four sets of experiments were carried out to obtain information about the pH, temperature,concentration, and solvent dependence of the NMR parameters. For the pH dependence experiments, a group of Na2PH03 samples and a group of Na2PF03 samples were prepared with a series of pH values ranging from 0.1 to 9.5 for the PH032-samples and from 1.0 to 8.0 for the PFOJ2- samples. The temperature and concentration were held constant for both groups at values of 25 OC and 0.8 M, respectively. For the concentration-dependentexperiments, samples were prepared for which the concentration varied from 0.5 to 4.0 M for PHO3>and from 0.5 to 1.5 M for PF032-(the fluorophosphate is lesssoluble than the phosphite). In bothgroups the temperature was held constant at 25 OC. For the phosphite samples the pH was held constant at a value of 9.6, and for the fluorophosphate samples the pH was held constant at 9.7. For the third set of experiments the temperature was varied from -40 to +40 OC for both the phosphite and fluorophosphate samples. For PH032- the pH and concentration were constant at 9.2 and 0.8 M, respectively. For PF032- the pH and concentrationwere 8.0 and 0.8 M, respectively. For the pH- and temperature-dependent work, experiments were carried out in solutions of pure H20 and in 60% ethylene glycol (EG)-40% H2O mixtures.
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Figure 1. Isotropic scalar coupling, JPH,as a function of pH for Na2PHOs in a H20 solution. Bo 2: 4.7 T.
here is not to provide a new analyticalmethod for the measurement of pH values or to obtain pK, values for phosphorous or fluorophosphoricacid. The measurement of the approximate pH values is simply an independent method to monitor the relative concentrations of the species present. In the work reported here we have measured only the isotropic values of the chemical shift tensors and the spin-coupling tensors. The isotropic chemical shift, 8h, is one-third the trace of the chemical shift tensor, 8 h = I/gTr 8 = ‘/3(611 + 822 + 633), and although it does not contain as much detailed information as the full chemical shift tensor, it provides useful information and is relatively easy to measure. In a similarfashion the scalar coupling constant, JPH,is one-third the trace of the spin-spin coupling tensor, JPH. Experimentally,one measures the chemical shifr, 6, defined as follows: ~obscrv~a - ”reference
8=
”reference
x lo6
(1)
The delta scale then gives the frequency shift from a reference compound, normalized by the resonance frequency of the reference compound.14 The chemical shielding scale is based on
=w BOd(1 - a) (2) where B,,bwd is the field at the nucleus, BOis the applied field, and u is the chemical shielding. For a bare nucleus, u = 0, and B-d = Bo. The u scale is convenientfor theoretical calculations but impractical for experimental work since it is not possible to observe a bare nucleus in the lab. To compare the experimental values to the theoretical values requires a relation between 8 and u. This relation is given by ~
o
6=
~
(arcfcrence - a)
(3) 1 - urefercncc where urcfemnais the chemical shielding of the reference compound relative to the bare nucleus. Usually, umfefcrena is very small compared to unity and it can be neglected in the denominator. Equation 3 then becomes
3. Results and Discussion
As mentioned above, the “pH” values measured here are only approximate values. The solutions used in these experiments were relatively concentrated; 0.8 M in sodium phosphite or in sodium fluorophosphate. This was done in order to compare the results here with those of earlier NMR relaxation time studies. In addition, no attempt was made to keep the ionic strength constant during thecourseofthetitration. Thegoalof the research
i
6
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The chemical shielding, then, is the negative of the chemical shift with an offset of umfcrcnco.See ref 14 for more details. Figure 1 shows the dependence of the isotropic 3lP-1H spin coupling constant, JPH,on the pH of a solution of Na2PHO3 in pure water. The solid line in this figure is a “theoretical” curve based on the literature dissociation constants Kal = 1.0 X 10-2 and Ka2 = 2.6 X lo-’ and literature values for the JPHcoupling ‘p8
Na2PHO3 and Na2PF03 680
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The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7203
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Figure 4. Isotropic 31Pchemical shift, bL, as a function of pH for Na2PHO3. The triangles represent the solute in a H20 solution, and the squares represent the solute in a 60% ethylene glycol+% H2O solution. Note the rather anomalous behavior (see text). EO 8.5 T.
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"PH" Isotropic *Hchemical shift, #, as a function of pH for Na2-
PHO3. The triangles represent the solute in a H20 solution, and the squares represent the solute in a 60%ethylene glyco1-40%H20 solution. Bo = 8.5 T. constants12 for each species: JPH= 669,629,and 567 Hz for H2PHO3, HPHO3-, and PH032-, respectively. The dashed line represents a best fit curve to the data points (squares) using the same algorithm as was used to generate the solid line. The values obtained from this fit are Kal = 2 X lO-l, Ka2 = 5 X lo-', and JPH= 683.0,628.5,and 567.5Hz for H2PH03, HPH03-, and PH032-, respectively. We have not taken data much below pH values of 0.0 since it is not clear to us that such values have much meaning. We have not shown the data for the H3PHO3+ solution in Figure 1 since, again, there is some question, in our view, about how to measure the 'pH" for such a solution. A number of measurements of the coupling constant and the phosphorus and proton chemical shifts were made as a function of the sulfuric acid concentration. The fact that JPHis constant for H2S04 concentrations above about 90% indicates that the value of 804.1 Hz is a limiting value for JPH and that the H3PHO3+ cation is the predominant phosphite species in 90% or greater solutions of sulfuric acid.llJ2 Our experimental measurements of a 0.8 M H2PHO3-98% H2S04 solution gave values of JPH= 804.1 Hz, 6k = 6.49ppm relative to TMS, and 6k = 17.41 ppm relative to an 85% aqueous solution of H3P04. Our values for JPHare in excellent agreement with earlier literature values.11.12 Values for: 6 and 6k were not reported in these earlier studies. For the phosphite ion it is interesting to note that although the isotropicproton chemical shift (Figure 3) and the isotropic scalar coupling (Figures 1 and 2)show titration-typecurves as a function
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TEMPERATURE
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Figure 5. Isotropic 'H chemical shift, as a function of temperature for 0.8 M Na2PHO3 at pH 9.2. The triangles represent the solute in a H20 solution, and the squares represent the solute in a 60% ethylene
glycol-40% H2O solution. EO = 7.0 T.
of pH, the isotropic phosphorus chemical shift exhibits a rather anomalous behavior as shown in Figure 4. The value for 6% is less in the pH range of 2.0 to 7.0than it is for pH values greater than 7.0. This anomalous behavior is in accord with ab initio calculation^.^ Note that in ref 5 the parameter plotted in the lower part of Figure 5 was the experimental chemical shift converted to chemicalshieldingusing the equation u = 6 + udmm (from eq 4 in that reference). This equation is not correct, but should be u = ureferenw - 6 (refer to eq 4 in this paper). When the correct equation is used, the trend in the theoretical data matches the trend in the experimental data with both the theoretical and experimental chemical shieldingversus pH curves going through a maximum and, hence, the chemical shvr versus pH curves going through a minimum. In Figure 3, the fit to the water solution data points (triangles and solid line) was performed with the best fit K,, and Ka2values (2 X 10-1 and 5 X 10-7,respectively) obtained from the fit in Figure 1. The proton chemical shift values used for each species were 6k = 6.19.6.10,and 5.96ppm for HzPHOp, HPHO3-, and PH032-, respectively. Again, the same best fit Kal and K.2values were used to fit the water solution data in Figure 4 (triangles and solid line). The fit to the isotropic phosphorus chemical shift data was quite accurate even with the anomaly mentioned earlier. The phosphorus chemical shift values used for each species were 6k = 5.90,3.42,and 3.80 ppm for H2PHO3, HPHO3-, and PH032-, respectively.
7204 The Journal of Physical Chemistry, Vol. 97, No. 28, 1993
Farrar et al.
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TEMPERATURE
(OC) Figure 6. Isotropic 3lP chemical shift, &,as a function of temperature for 0.8 M NazPHO, at pH 9.2. The triangles represent the solute in a H20 solution, and the squares represent the solute in a 60% ethylene glycol40% H2O solution. BO = 7.0 T.
Earlier theoretical calculations5 and solid-state N M R experiments' from this laboratory indicate that the PH and PO bond distances in PH032-and the PF and PO bond distances in PFOQ change as a function of pH and/or the extent of hydration of the anion. Moedritzer" has derived an equation from general theory which relates the change in chemical shift to the change in the effective electronegativity of the oxygens, the change in the total number of electrons in the d, orbitals produced by variations in the ?r character of the PO bond, and the increase in the OPO bond angle, all of which are caused by the association of the oxygens with hydrogen(s). Both theory and experiment show that rpH in the acid phosphite, HPHO3-, is about 5 pm shorter than that in the doubly charged phosphite anion, PH032-,and rpH in the free acid, HzPHO3, is about 9 pm shorter than that in the doubly charged phosphite anion. Similarly, rpH in a sample of MgPHOp.SH20 isabout 5 pmshorter than that inananhydrous sample of MgPH03. Thus direct protonation of either the oxygen atoms in the phosphite anion or the solvent molecules hydrogen bonded to those oxygen atoms influences the direct phosphorushydrogen bond length. Theoretical calculations and X-ray diffraction results show that the PO bond lengths become shorter as the pH is decreased (i.e., as one goes from the doubly charged anion to the singly charged anion and finally to the free acid). This shortening of the PH and PO bond distances leads to corresponding changes in the chemical shift, spin-coupling, and quadrupole coupling tensors. In some of our previous work concerning N M R relaxation time measurements of phosphorous acid and fluorophosphoric acid and their derivatives, it was necessary to use solutions whose viscosity could be varied over a wide range. This is required in order to reach sample conditions in which WOT, N 1, where wo is the precessional frequency of the nuclei and T~ is the molecular correlation time. For this reason the solvent used was usually a mixture of 60% ethylene glycol (EG) and 40% water. To determine the effect of solvent on the N M R parameters and to complement data obtained from earlier relaxation time experiments we have here obtained data for solutions using only water and for solutions using the 60% E G 4 0 % water mixture. As can be seen in Figure 2, the value of JPHis essentially the same in both solutions. The values for the proton chemical shift (Figure 3) and those of the phosphorus chemical shift (Figure 4), however, are different in the two solutions. In the present case, the difference in the solvents changes the extent of the hydrogen bonding to water molecules and, consequently, changes the molecular bond distances. The temperature dependencies of the proton and phosphorus chemical shifts and the scalar coupling of the phosphite anion in both water and EG/H20 solutions are shown in Figures 5 , 6 , and
0
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TEMPERATURE (OC) Figure 7. Isotropicscalar coupling,JPH,as a function of temperature for 0.8 M Na2PHO3 at pH 9.2. The triangles represent the solute in a H20 solution, and the squares represent the solute in a 60% ethylene glycol40% H20 solution. BO = 7.0 T.
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squares represent. :6 The Na2PFO3 solutions are unstable at low pH, and as a result, solutions at low pH had decomposed before 19F measurementscould be made. BO = 8.5 T for 3lP data and 7.0 for 19F data.
7, respectively. As was previously mentioned, there is a clear correlation between the bond distances and the chemical shifts and coupling constants. From Figures 1-4, we see that and JPHincrease with decreasing bond length for the entire pH range while & initially decreases as the pH is lowered and then a t much lower pH levels increases dramatically. Since the average values of the bond distances decrease as the sample temperatures decrease, one might predict that for the phosphite anion, 6$ and JPHwill both increase with decreasing temperature. One might also predict that 6k would decrease with decreasing temperature since the temperature studies were performed on the phosphite anion (pH = 9.2) in the high pH region, where 6k decreases with decreasing bond length. In fact, this is what is observed for all three parameters. For the fluorophosphate anion the dominant species a t pH values greater than 6 and less than 1 are PF032-and H2PFO3, respectively. For pH values between 2 and 4 the dominant species is HPF03-. The sodium fluorophosphate solutions are unstable at low pH values; for pH values below 1.O the sample decomposes before accurate measurements can be made. Figure 8 shows the pH dependence of 6k and 6L in a water solution. Figure 9 shows the pH dependence of JpF for the PFOQ anion in a water solution and in a solution of the EG-H20 mixture. Theoretical ab initio calculations in this lab have shown that the PF bond distance in fluorophosphate decreases with protonation just as the PH bond distance decreases with protonation in ph0~phite.l~Here, on the basis of the pH (or bond distance) dependent data, one predicts that 6k and 6k will decrease with
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The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7205
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"PH" Figure 9. Isotropic scalar coupling, Jpp, as a function of pH for NazPFO3. The triangles represent the solute in a H2O solution, and the squares represent the solute in a 60% ethylene glycol-40%H20 solution. Bo 8.5 T.
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Figure 10. Isotropic 19F and 3lP chemical shifts (Sk and S& respectively)as a function of temperature for 0.8 M NazPFO3 in a water solution at pH 8.0. The triangles represent Sk,and the squares represent &.BO = 8.5 T for 31Pdata and 7.0 for I9F data.
Figure 13. Isotropic scalar coupling, JPH,as a function of concentration for Na2PHO3 at 25 ' C and pH 9.6. BO = 8.5 T.
chemical shifts due to the increased number of electrons and the limitations of our present computer. Figure 12 shows, for the phosphite anion, the concentration dependencies of: 6 (triangles) and (squares) in a H2O solution; Figure 13 shows the concentration dependence of JPH. These results are similar to those of the pH-dependent studies and suggest that as the concentration decreases, the PH bond distance decreases (the PO bond distances are probably also decreasing). This is probably due to the fact that the anion becomes more completely hydrated as the concentrationdecreases and, as seen above, increasing hydration and/or oxygen protonation leads to shorter PH and PO bond distances. This interpretation is in accord with the pH and temperature dependence results. Again, since the pH of these solutions was held constant at 9.6, the solutions here are in the high pH region of the versus pH curve and would be expected to produce a curve with a positive slope for 6L versus I ~ H .This is the trend seen in Figure 12. For the fluorophosphate anion the concentration dependencies for 6L and JPFare consistent with the temperature-dependent results; lower concentration leads to greater hydration, shorter bond distances, a decrease in and an increase in the magnitude of Jpp. The value of 6L, however, is, within experimental error (f0.5 Hz), independent of the anion concentration. Further evidence for the close correspondencebetween the PH bond distance in the phosphite anion and the solution pH is given by studies of the pH dependence of the PH infrared stretch frequency.21 The infrared data also show typical titration-type plots and show clearly that the force constant for the PH bond increases with decreasing pH. However, because the time scale in infrared spectroscopy is small compared to the time scale of
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TEMPERATURE (OC) Figure 11. Isotropic scalar coupling, Jpp, as a function of temperature for 0.8 M NazPFO3 at pH 8.0. The triangles represent the solute in a H20 solution, and the squares represent the solute in a 60% ethylene glycol-40% H2O solution. BO = 8.5 T.
decreasing temperature and that the magnitudeof Jpp will increase with decreasing temperature. The temperature dependenciesof 6% and JPFfor solutions of NazPFO3 in water are shown in Figures 10 and 11. As is seen, the slopes for all of these curves are positive, in agreement with our predictions and those of Chesnut.16 Although ab initio calculations were performed to determine PF bond distances in P F 0 3 s as a function of pH (or bond distance), ab initio chemical shift calculations could not be performed with a large basis set for comparison with experimental
6k,
4.0
3.0
CONCENTRATION (Molarity) Figure 12. Isotropic IH and 3lP chemical shifts (Sgand SL, respectively) as a function of concentration for NazPHO3 at 25 O C and pH 9.6. The triangles represent Sg,and the squares represent 6L. BO = 8.5 T.
6L,
Farrar et al.
7206 The Journal of Physical Chemistry, Vol. 97, No. 28, 1993
the exchange between species, one sees two data points at the equivalence points representing the individual species in equilibrium as contrasted to the smooth transition in the N M R data where the time scale is large compared to the time scale of the exchange and, hence, the species average determines the data points. Dissociation constants obtained from the IR titration data are in agreement with dissociation constants obtained from the NMR data. We have also carried out neutron and X-ray diffraction studies of sodium phosphite. A comparison of the results of the NMR, neutron, X-ray, IR, and ab initio work is interesting. The ab initio calculations are usually performed for isolated molecules in the gas phase in the absence of molecular vibrations and rotations. For this reason it is not surprising that one seldom sees absolute agreement between the calculated and observed values. One does expect, however, that trends will be accurately predicted, and this is the case here. If one makes reasonable corrections for the changes in molecular structure due to molecular motions and solvent-solute interactions the agreement between theory and experiment is much better. The results reported here and in other recent theoretical work1620 show the importance of solvent-solute interactions in making accurate calculations of chemical shift tensors. Solid-state NMR studied show clearly that the PH bond distance for anhydrous sodium phosphite samples is longer than that for hydrated samples. Data from both solution- and solidstate NMR experimentsand from neutron diffraction experiments show that in MgPHOySHZO and Na1PH03.5Hz0 there are three waters of hydration for each oxygen on the phosphite anion, that is, a total of nine waters of hydration for the overall anion. The structural changes occurring in the anion are similar for either direct protonation of an oxygen (a covalent OH bond) by changing the pH of the solutionor for hydrogen bonding between the oxygen on the phosphite and a proton on a water of hydration. The changes caused by a single hydrogen bond are smaller than those caused by a direct covalent bond with a proton, but for the phosphite anion there are nine hydrogen bonds, three for each oxygen. The overall changes are, consequently, significant. Theoretical calculations also indicate that for most compounds studied the first derivative of the chemical shielding with respect to the equilibrium bond distance, (C~U/&),=,~, is negative.17J8 It is difficult to make a direct comparison between this derivative and the experimentally observed temperature dependence, since changing the temperature changes the average bond distance of the PH bond and all of the PO bonds. for example, in the phosphite and fluorophosphate anions the primary changes H in uiso and u k , respectively, and u;, for both molecules are due to the changes in the PH and PF bond distances, then we might expect that the values for (au/dr)r=,owill be negative. Since experimentally we observe the chemical shift, 6, which is related to the chemical shielding by eq 4, we would expect that (d6/ would be positive. Experimentally, we find that (Xi/&),., is positive for ur and u;, for the PF032-anion (see Figure 10) and positive for uiso t for the PH032-anion (see Figure 6). These, then, are all in accord with theoretical trends. We find that (t36/6r),=, is negative for ULfor the PHO+- anion (see Figure 5 ) . At this point, a clear explanation has not been proposed. In addition, ( ~ 3 6 / 8 r ) ~is= , ~ positive for the phosphorus chemical shift at high pH values, near zero at mid pH values, and negative for low pH values. From the calculated values of the shielding tensor, one is tempted to plot the individual components u11, UZZ, and u33 as a function of phosphite species in order to more clearly see which component may be responsible for the anomaly. But the principal axis system of the chemical shift tensor has an angular dependence with the molecular axis system and the angle between these also changes as a function of the phosphite species, making comparison of the individual components difficult. If the angle between these was nearly zero for all of the species, one could confidently draw
u,
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750
100
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rPH (pml Figure 14. Isotropic scalar coupling, JPH,(squares and solid line) and
, and dashed line) as the infrared PH stretching frequency, V ~ H (triangles a function of the PH bond distance (picometers).
TABLE I: Experimental and Theoretical Parameten aa a Function of Phosphite Species
PHO32HPH03HzPHO3 H3PHO3+
147.1 141.6 138.8 137.3
567.5 628.5 683.0 804.1
2322.29 2387.67 2435.33
3.81 3.81 -34.02 3.45 -15.06 6.09 2.97 17.41 a Fromref5whichuseda4-31GSbasisset. Fromref21. cReferenced to 85%phosphoricacid (H3PO4,aqueous solution). Thetheoreticalvalues value were convertedfrom the u scale to the S scale (eq 4) using a udof 494.45 ppm for 85%&Pod; this allowsan easier comparison between theoretical and experimental numbers. conclusions as to which component plays the major role in determining the trend of the chemical shielding or chemical shift versus pH from a plot of the aforementioned. Although these axes systems are coincident for H3PH03+and PH032-,they are not coincident for HzPH03 and HPHOS-. For the PFO,Z- anion (a6/&),.,, is positive for both the phosphorus and the fluorine chemical shifts throughout the pH scale, in agreement with theoreticalcalculations.More theoretical work on these two systems is in progress in this laboratory and will be reported a t a later date. Figure 14 shows plots of the value of JPHversus the PH bond distance and the PH infrared stretching frequency versus the bond distance; both are linear. The ab initio PH bond distance calculations give a value of 137.3 pm for the H3PHO3+ cation. This is only 1.5 pm shorter than the free acid PH bond distance. If we assume that the linear plot of JpH versus PH bond distance is valid, and given the fact that JPHfor the cation is 804.1 Hz, we predict a PH bond distance in H3PHO3+ of 129.4 pm. This difference in the experimentally predicted values and the value from ab initio calculations is rather surprising since the experimental values for the PH bond distances for the other three species agree quite well with Gaussian 92 ab initio calculations. If the 129.4-pm bond distance is correct, we anticipate a PH stretching frequency for the cation (based on the least squares fit to the HzPH03, HPH03-, and PHOpZ-Y P H values) of 2558 cm-1. Work to obtain other independent experimental values for the bond distance as well as the PH stretching frequency is in progress in this laboratory. Table I gives the ab initio bond distance and isotropic 3IP chemical shift values as well as the experimental isotropic 31P chemical shift, scalar coupling, and infrared stretching frequencies for each of the phosphite species. Notice that although there is a difference between the experimental and theoretical values of the isotropic 31Pchemical shifts, the trends are the same. 4. Summary and Conclusions
For the PH032-anion and its more acidic derivatives, both the phosphorus-proton spin-coupling constant, JPH, and the isotropic
Na2PH03 and Na2PF03 proton chemical shift, 6ro, show a linear dependence on the PH bond distance. JPHchanges by approximately -13.5 Hz/pm and by about -0.0274 ppm/pm. There is a similar correlation between the PF bond distance and the values for JPF,6k, and &. There is also a linear relation between the PH stretching frequency and the bond distance, -13.4 cm-l/pm. The behavior of the phosphorus isotropic chemical shift with respect to the bond distance is not linear as is the isotropic scalar coupling and the isotropic proton chemical shift. There is insufficient data to provide a clear physical explanation for this behavior. Clearly, caution should be used in making correlations between isotropic values and molecular structure, especially if the behavior of the components of the chemical shift tensor are not known. The N M R solvent-, pH-, and temperature-dependent solution data along with the solid-state N M R data of anhydrous and hydrated phosphite salts are all consistent with the interpretation that either protonation of or hydrogen bonding to the oxygen atoms causes a significant change in the molecular and electronic structure of phosphite salts. For H2PH03, HPHO3-, and PHOs2- ab initio calculations indicate that the direct PH bond distances are 147.1, 141.6, and 138.8 pm, respectively; these results are in excellent agreement with experimental values obtained from solid-state and solutionstate NMR experiments and X-ray diffraction, neutron diffraction, and infrared data. If we assume that the isotropic scalar coupling, JPH,is a good measure of the PH bond distance, i.e., linear with bond distance, it is a bit surprising that the theoretical calculations predict that the PH bond distance in H2PHO3 is only 1.5 pm longer than that in H3PH03+. Given the very large differences in JPHvalues for these two species and the linear dependence seen in the three related species, it is most probable that the P H bond distance in the cation is substantially shorter (by about 10 pm) than that in the neutral acid. More N M R and infrared experiments are being carried out in order to obtain additional experimental values of the P H bond distance in the H3PH03+cation. The Kal and Ka2values obtained from fits to the JPH, , :a and 6h titration curves agree reasonably well with
6L
The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7207 the literature values and indicate that the “pH” values used here are reasonably accurate in spite of the fact that relatively concentrated solutions were used.
Acknowledgment. We gratefully acknowledge a number of very helpful discussions with Mr. Jon D. Trudeau and help with a computer program written by Mr. Thomas C. Stringfellow, and we acknowledge the support of the National Science Foundation for the support of this research (NSF Grant CHEM9102674); S.Rodriguez was supported under a summer NSFREU supplement CHE-9247325. References and Notes Farrar, T. C.; Smith, S.K. Manuscript in preparation. Farrar, T. C.; Locker, I. C. J. Chem. Phys. 1987, 87, 3281. Decatur, J. D.; Farrar, T. C. J . Phys. Chem. 1990, 94, 7391. Farrar, T. C.; Decatur, J. D. J. Phys. Chem. 1990, 94, 7395. ( 5 ) Farrar, T. C.; Trudeau, J. D. J . Phys. Chem. 1990,946277-6282. (6) Chesnut, D. B. Annu. Rep. NMR Spectrosc. 1989, 21, 51-97. (7) Lide, D. R., Ed. CRCHandbookof ChemistryandPhysics, 71st 4.; CRC Press: Bcca Raton, FL, 1990. (8) Skoog, A. D.; West, D. M. Fundamentals of Analytical Chemistry, 4th ed.; CBS College Publishing: New York, 1982. (9) Petrucci, R. H.General Chemistry, 4th 4.; Macmillan Publishing Company: New York, 1985. (10) Ebbing,D. D.; Wright0n.M.S. GeneralChemistry,Znded.;Houghton Mifflin Company: Dallas, TX, 1987. (11) Sheldrick, G. M. Trans. Faraday SOC.1967, 63, 1077-1082. (12) Haas, T. E.; Gillman, H.D. Inorg. Chem. 1968, 7, 2051-2054. (13) Moedritzer, K. Znorg. Chem. 1967, 6, 936-939. (14) Duncan, T. M. A Compilation of Chemical Shvt Anisotropies; Farragut Press: Chicago, 1990. (15) J. D. Trudeau, unpublished results. (16) Chesnut, D. B.; Phung, C. G. Chem. Phys. 1990, 147, 91-97. (17) Jameson, C. J. A Specialist Periodic Report on NMR, Royal Society of Chemistry: London, 1991; Vol. 21. (18) Jameson, C. J.; de Dios, A. C.; Jameson, A. K. J. Chem. Phys. 1991, 95, 9042. (19) Rohlfing, C. M.; Allen, L. C.; Ditchfield, R. Chem. Phys. Lett. 1982, 86, 380. (20) Giessner-Prettre, C.; Pullman, A. Chem. Phys. Lett. 1985,114,258. (21) Stringfellow, T. C.; Trudeau, J. D.; Farrar, T. C. J . Phys. Chem. 1993, 97, 3985-3989. (1) (2) (3) (4)
