MAS NMR Study of

J. Phys. Chem. B 1997, 101, 6359-6366

A

31P

Spin Diffusion and

31P-113Cd

6359

CP/MAS NMR Study of Polycrystalline Cd3(PO4)2

Stephan Dusold,† Jo1 rg Ku1 mmerlen,‡ Torsten Schaller, and Angelika Sebald* Bayerisches Geoinstitut, UniVersita¨ t Bayreuth, D-95440 Bayreuth, Germany

Wayne A. Dollase Department of Earth and Space Sciences, UniVersity of California, Los Angeles, California 90095-1567 ReceiVed: March 19, 1997; In Final Form: June 11, 1997X

Two-dimensional 31P spin diffusion MAS NMR experiments on polycrystalline Cd3(PO4)2, using a broadbanded dipolar recoupling scheme, are reported. Quantitative analysis of the 31P spin diffusion experiments as a function of mixing times yields unambiguous assignment of the six 31P resonances to the six independent crystallographic P sites in the asymmetric unit of solid Cd3(PO4)2. Internuclear P-P connectivities determined from these 31P spin diffusion MAS NMR experiments quantitatively agree with the P-P distance connectivities as determined by single-crystal X-ray diffraction. On the basis of the known assignment of all 31P resonances for Cd3(PO4)2, all 113Cd resonances can be unambiguously assigned to the respective nine independent crystallographic Cd sites, using one-dimensional selective 31P f 113Cd CP/MAS NMR techniques where a 31 P chemical shift filter is used as a preparation step for selective 31P f 113Cd cross-polarization.

Introduction The power of homonuclear dipolar recoupling methods under MAS conditions for purposes of structure elucidation by highresolution solid state NMR techniques has led to the development of a number of pulse schemes, designed to reintroduce homonuclear dipolar coupling effects while maintaining high spectral resolution under MAS conditions. Homonuclear dipolar recoupling schemes, such as rotational resonance (RR),1 RFDR,2 DRAMA,3 HORROR,4 SEDRA,5 MELODRAMA,6 C7,7 and RIL,8 have strongly differing properties with respect to efficiency and dependence on isotropic and anisotropic chemical shifts. The individually most suitable recoupling scheme can thus be chosen for a wide range of different application situations. Suppose an application situation where the homonuclear spin system at hand leads to multiple resonances over a large range of chemical shifts (with both small and large isotropic chemical shift differences present); further suppose that the task to be solved is to characterize the spin system in terms of distance connectivities. Under these conditions, the recoupling scheme employed needs to be broad-banded. Two homonuclear recoupling schemes, fulfilling this requirement of independence on chemical shifts over a sufficiently large spectral range, are C77 and RIL.8 A natural target area for the application of 31P homonuclear dipolar recoupling experiments under MAS conditions is solid inorganic phosphates; recently several reports have appeared in the literature where connectivities, or the assignment of 31P resonances to specific crystallographic P sites in polycrystalline inorganic phosphates,9-11 have been the center of attention. The weakly dipolar coupled 31P spin systems in many solid inorganic phosphates have NMR properties such that both qualitative and quantitative investigations of the 31P dipolar coupling network require broad-banded homonuclear dipolar recoupling schemes. Within the class of solid inorganic phosphates, orthophosphates are a special case: the minor distortions of the PO43- anions * Corresponding author. Fax: ++49-921-553769. E-mail: angelika. [email protected]. † E-mail: [email protected]. ‡ E-mail: [email protected]. X Abstract published in AdVance ACS Abstracts, August 1, 1997.

S1089-5647(97)00992-9 CCC: $14.00

from regular tetrahedral coordination lead to usually much smaller 31P chemical shielding anisotropies than is the case for pyro-, meta-, or ultraphosphates. Here we report on the quantitative analysis of the 31P zeroquantum polarization transfer dynamics of Cd3(PO4)2, 1. It will be shown that these 31P spin diffusion experiments yield unambiguous assignment of all 31P resonances to the respective crystallographic P sites in the known12 structure of 1 and that internuclear P-P connectivities determined by NMR are in quantitative agreement with P-P distances obtained from singlecrystal X-ray diffraction. The concept of polarization transfer dynamics as a means to establish distance connectivities for 1 is further extended to include heteronuclear polarization transfer dynamics 31P f 113Cd, and unambiguous assignment of all 113Cd resonances to the nine crystallographically independent Cd sites in the asymmetric unit of 1 is achieved. Experimental Section The synthesis of our sample of Cd3(PO4)2, 1, has been described elsewhere.11 31P and 113Cd MAS NMR spectra of 1 have been obtained on Bruker MSL 100, MSL 200, and MSL 300 NMR spectrometers, corresponding to Larmor frequencies of 40.5, 81.0, and 121.5 MHz (31P), and 22.2, 44.4, and 66.6 MHz (113Cd), respectively. Isotropic chemical shifts δiso(31P) are given with respect to external 85% H3PO4, isotropic chemical shifts δiso(113Cd) are given relative to δiso (113Cd) of solid Cd(NO3)2‚ 4H2O ) -100.0 ppm.13 All two-dimensional 31P RIL8 spin diffusion experiments were run on the MSL 300, under conditions of actively controlled stability of the spinning frequency to within (1 Hz, using homebuilt equipment. Amplitudes and phases of the 31P radio frequency transmitter were adjusted on the 31P resonance of a saturated CHCl3 solution of trans-(nBu3P)2PdCl2. The 31P π/2 pulse duration was 3.5 µs, and the spinning frequency was 5000 Hz. Recycle delays had to be 15 s; eight transients per increment were accumulated. The TPPI method14 was used to obtain phase sensitive spectra in both dimensions. All 31P-113Cd double-resonance MAS NMR experiments were run on the MSL 100, using a 7 mm triple-resonance 1H© 1997 American Chemical Society

6360 J. Phys. Chem. B, Vol. 101, No. 33, 1997

Dusold et al. TABLE 1: Internuclear P-P Distances (pm) between P1-P6, Determined by Single-Crystal X-ray Diffraction,12 within a Radius of 900 pm in 1, Cd3(PO4)2a P1 P1

P2

P3 Figure 1. (a) Partial view of the three-dimensional structure 12 of solid Cd3(PO4)2, 1, where shaded tetrahedra symbolize PO43- anions and larger spheres represent Cd2+ cations. (b) 121.5 MHz 31P MAS NMR spectrum of 1, ωr/2π ) 9 kHz; isotropic 31P chemical shifts δiso (ppm): 22.0 (A), 21.5 (B), 19.5 (C), 12.0 (D), 10.6 (E), 7.9 (F).11 31P-113Cd

CP/MAS probe and an experimental setup as described elsewhere.15 Using a triple-resonance CP/MAS probe is a convenient way to refine step-by-step the 31P-113Cd Hartmann-Hahn matching condition: in a first step, with a 1H π/2 pulse duration of 6 µs preset, 1H-31P and 1H-113Cd Hartmann-Hahn matching conditions are separately set on CaHPO4‚2H2O and on Cd(NO3)2‚4H2O, respectively. With these settings, it is straightforward in a second step to further optimize the 31P-113Cd matching condition on a sample of CdSiP2 as has been proposed in the literature.16 The 31P-113Cd matching condition on a spinning sample of CdSiP2 is broader than for Cd3(PO4)2, 1, so that in a last refinement step the 31P113Cd matching condition for 1 has to be directly optimized on 1, spinning at a MAS frequency ωr/2π ) 2.5 kHz. All 31P113Cd double-resonance MAS NMR experiments on 1 were run at a MAS frequency ωr/2π ) 2.5 kHz. At a Larmor frequency ω0/2π ) 22.2 MHz for 113Cd, a MAS frequency ωr/2π ) 2.5 kHz yields 113Cd MAS NMR spectra of 1 virtually free of spinning side bands. Recycle delays for all 31P-113Cd CP/MAS NMR spectra were 15 s; selective 31P f 113Cd CP/MAS NMR spectra required the accumulation of 15000-20000 transients. Simulation of the 31P RIL spectra of 1 as a function of mixing times is based on eq 2; spin diffusion rate constants were obtained by a nonlinear least-mean-squares fit (MATLAB17 Simplex routine). Results and Discussion Two-Dimensional 31P MAS Spin Diffusion Experiments on 1. Cd3(PO4)2, 1, crystallizes in space group P21/c;12 there are six crystallographically independent P sites and nine independent Cd sites in the asymmetric unit. The threedimensional structure, together with the 31P MAS NMR spectrum of 1 (ω0/2π ) 121.5 MHz, ωr/2π ) 9 kHz), is shown in Figure 1. Table 1 lists the mutual P-P distances (within a radius of 900 pm) as determined by single-crystal X-ray diffraction.12 Recently, we have shown for Cd3(PO4)2, 1, that a twodimensional single-quantum double-quantum (1q-2q) 31P MAS correlation experiment, where the C7 sequence7 has been used for homonuclear dipolar recoupling, allows one to unambigu-

P4

475 772 778 778 784 792 816 822 865 482 626 641 806 814 817 866 470 494 629 634 834 900

P2

P3

P4

P5

P6

475 772 778 784 792 816 822 865

482 626 641 806 814 817 866

470 494 629 634 834 900

408 476 628 656 893

510 524 671 817 883

367 455 745 777 830 850 868 897

408 540 640 810 891

488 514 611 663 897

485 504 610 645 844

480 522 639 663

484 531 645 823 834 895

407 489 615 637 883 890

367 455 745 777 830 850 868 897 408 540 640 810 891

480 522 639 644

P5

408 476 628 656 893

408 476 628 656 893

484 531 645 823 834 895

P6

510 524 671 817 883

485 504 610 645 844

407 489 615 637 883 890

547 552 574 782 833 867 872 883 547 552 574 782 833 867 872 883 491 544 767 846 849 856 869 881

491 544 767 846 849 856 869 881 489 566 599 802 807 860 863

489 566 599 802 807 860 863

a

The numbering scheme of crystallographic positions is identical to the numbering scheme in ref. 12.

ously assign the six 31P resonances A-F to the six crystallographic P sites P1-P6 as follows:11 31P

resonance: crystallographic P site:

A 3

B 2

C 1

D 4

E 6

F 5

For a 31P spin system describable within a spin-pair approximation, it would be possible to quantitatively analyze C7based 1q-2q 31P MAS correlation experiments in terms of internuclear 31P-31P distances. The three-dimensional solid state structure of Cd3(PO4)2, 1 (see Figure 1 and Table 1) with multiple and quite similar P-P connectivities, however, is such that the 31P spin system in 1 cannot be treated within a spin-pair approximation. If quantitative information about the P-P distance connectivities in 1 (and independent confirmation of the assignment from 1q-2q 31P

MAS NMR Study of Polycrystalline Cd3(PO4)2

J. Phys. Chem. B, Vol. 101, No. 33, 1997 6361

Figure 2. RIL pulse sequence for used 0q homonuclear 31P polarization transfer 8 (τr ) rotor period) experiments on 1. Note that the originally proposed, optimised version of the RIL sequence8 in addition employs amplitude switching during the first half of the rotor period for improved offset compensation. For 1, this feature of the RIL sequence turns out to be unnecessary, given sufficiently high B1 rf field strengths are used.

MAS experiments) is to be derived from 31P MAS NMR, it is preferable to employ a broad-banded dipolar recoupling scheme in conjunction with zero-quantum (0q) polarization transfer. The evolution of magnetization in a two-dimensional π/2-t1-τmixt2 exchange experiment in the presence of chemical exchange and/or cross-relaxation has been treated extensively in the literature.18,19 For the description of the 31P spin diffusion dynamics in 1, neither chemical exchange nor T1 effects need to be taken into account, and the time-domain signal is given by

s(t1, τmix, t2)) -

∑k ∑l exp(iΩkt2)[exp(Sτmix)]kl exp(iΩlt1)Ml0

(1)

where τmix is the mixing time, Ml0 denotes the equilibrium magnetization weighted by the number of equivalent spins, and S represents the matrix describing the multisite 31P spin exchange. After two-dimensional Fourier transformation, the integrated intensity Ikl of a peak with frequency coordinates (ω1,ω2) ) (Ωl,Ωk) is obtained18

Ikl ) akl(τmix)Ml0, akl(τmix) ) [exp(Sτmix)]kl

(2)

The formalism is perfectly adequate to quantitatively describe multisite 31P spin diffusion in 1 as a function of mixing time τmix under MAS conditions. Extremely slow spin diffusion in the laboratory frame under these conditions necessitates driving the spin diffusion by a suitable rf-sequence, such as the 0qRIL experiment8 (see Figure 2). The rotor-synchronized mixing sequence suspends averaging of the dipolar interaction by switching between laboratory and rotating frame each half rotor period; the train of π pulses during the second half of the rotor period serves to refocus chemical shifts. To within a very good approximation, the effective Hamiltonian during τmix is purely dipolar,8,20 and the spin diffusion rate constants sij between spins i and j are proportional to (Dij)2 (where D is the magnitude of the respective dipolar coupling constant); hence sij ) const.‚rij-6. A 0q-RIL 31P two-dimensional exchange experiment on 1, with τmix ) 80 ms, is depicted in Figure 3. A series of 15 0qRIL experiments, with τmix varied between 2 and 100 ms, has been performed. The experimentally determined integrated intensities of all diagonal and off-diagonal peaks as a function of mixing time are shown in Figure 4, in comparison to the best fit based on eq 2. For the fit procedure, the total intensity of each 2D spectrum was taken as 1000, corresponding to an initial condition for Ml0 ) 166.7 for the six diagonal peaks. These and the spin

Figure 3. 121.5 MHz 31P 0q-RIL spectrum of 1; obtained with a mixing time τmix ) 80 ms, ωr/2π ) 5000 Hz.

diffusion rate constants sij (i, j ) A, B, ...; i * j) represent the fit parameters. Only the build-up curves between the two 31P resonances A and B had to be excluded from this procedure: our 121.5 MHz 31P 2D exchange experiments suffer from incomplete resolution in this spectral region. The AB/BA offdiagonal peaks are not sufficiently well separated from the diagonal peaks AA, BB and hence would produce systematic errors in the data analysis. The best fit, as depicted in Figure 4, yields the following spin diffusion matrix SNMR for the six 31P resonances A-F:

(

SNMR ) CNMR ‚ -0.0659 0.0292 0.0292 -0.0705 0.0108 0.0031 0.0056 0.0166 0.0153 0.0096 0.0050 0.0121

0.0108 0.0031 -0.0424 0.0099 0.0038 0.0149

0.0056 0.0166 0.0099 -0.0512 0.0108 0.0084

0.0153 0.0096 0.0038 0.0108 -0.0512 0.0117

0.0050 0.0121 0.0149 0.0084 0.0117 -0.0520

)

The known structure of 1 permits calculation of a spin diffusion matrix SX-ray according to

sij ) CX-ray

-6 ∑n rij,n

(3)

where summation over n indicates the need to define a radius over which mutual Pi-Pj distances have to be taken into account. Given the rij-6 dependence, a radius of 900 pm is sufficient to calculate SX-ray; the diagonal elements of SX-ray are obtained as

sii ) C

(-sij) ∑ i*j

(4)

Equations 3 and 4, and the mutual P-P distances listed in Table 1 yield SX-ray for the six crystallographic P sites P1-P6:

(

SX-ray ) CX-ray ‚ -0.8295 0.1179 0.1179 -1.2558 0.1238 0.5245 0.1971 0.2780 0.3326 0.1614 0.1212 0.1741

0.1238 0.5245 -1.2811 0.1577 0.1442 0.3309

0.1971 0.2780 0.1577 -0.8743 0.1146 0.1270

0.3326 0.1614 0.1442 0.1146 -0.8896 0.1369

0.1212 0.1741 0.3309 0.1270 0.1369 -0.8900

)

In order to be able to directly compare SNMR to SX-ray, it is necessary to define a scaling factor C ) CNMR/CX-ray. Choosing


Dusold et al.

Figure 4. Comparison of experimental (O) 31P spin diffusion build-up curves and best fit (solid curve). The arrangement of curves is such that top left curve ) diagonal peak AA, bottom right curve ) diagonal peak FF. On the x-axis in each curve the mixing time is given in ms; the y-axis gives the integrated intensities of the respective peaks, with the y-axes defined such that the total integrated spectral intensity is 1000.

C such that sX-ray max 17.96CX-ray and

(

SNMR ) CX-ray ‚ -1.1832 0.5245 0.5245 -1.2664 0.1935 0.0551 0.1004 0.2980 0.2748 0.1720 0.0900 0.2167

)

sNMR max ,

0.1935 0.0551 -0.7618 0.1772 0.0688 0.2672

we

0.1004 0.2980 0.1772 -0.9203 0.1938 0.1509

obtain

0.2748 0.1720 0.0688 0.1938 -0.9188 0.2094

CNMR

)

0.0900 0.2167 0.2672 0.1509 0.2094 -0.9342

)

By far the best agreement between SNMR and SX-ray is found for the assignment permutation 31P

resonance: crystallographic P site:

A 3

B 2

C 1

D 4

E 6

F 5

This assignment from analysis of the 31P spin diffusion dynamics in 1 is identical to the assignment previously derived from a 31P MAS 1q-2q correlation experiment on 1.11 Rearranging SNMR according to this assignment gives (SNMR)′:

(

(SNMR)′ ) CX-ray ‚ -0.7618 0.0551 0.0551 -1.2664 0.1935 0.5245 0.1772 0.2980 0.2672 0.2167 0.0688 0.1720

0.1935 0.5245 -1.1832‘ 0.1004 0.0900 0.2748

0.1772 0.2980 0.1004 -0.9203 0.1509 0.1938

0.2672 0.2167 0.0900 0.1509 -0.9342 0.2094

0.0688 0.1720 0.2748 0.1938 0.2094 -0.9188

)

Substituting (SNMR)′ and SX-ray, respectively, in eq 2 yields the build-up curves shown in Figure 5, comparing the best fit

TABLE 2: Ratio of Spin Diffusion Rate Constants (sNMR )′/ ij for the Six P Sites P1-P6 sX-ray ij P1 P2 P3 P4 P5 P6

P1

P2

P3

P4

P5

P6

0.85 0.46 1.56 0.89 0.8 0.56

0.46 1 1 1.07 1.34 0.98

1.56 1 0.92 0.63 0.62 0.83

0.89 1.07 0.63 1.05 1.31 1.52

0.8 1.34 0.62 1.31 1.05 1.53

0.56 0.98 0.83 1.52 1.53 1.03

build-up curves obtained from the experimental NMR data to the build-up curves calculated from the X-ray structure. The agreement between calculated and experimentally determined build-up curves is fairly good. For a closer consideration of the quality of agreement, we have to inspect Table 2, listing the ratio of spin diffusion rate constants (SNMR )′/ ij SX-ray for the six P sites P1-P6. Agreement is generally best ij for the largest rates, with a maximum deviation by 8% for the five largest and a deviation by 15% for the smallest diagonal rate. The four largest off-diagonal values agree within 20%; the average difference between experimental and calculated rate constants is 26.3%. This seemingly large error in terms of spin diffusion rate constants in fact translates into a fairly small error in terms of distances, as follows: suppose we had a two-spin system, and spin diffusion rate constants determined for this two-spin system in two different experiments would differ by 26.3%. The r-6 relationship between distances and rate constants in that case would correspond to a difference in r for this two-spin system of only 3.8% as determined from these two different experiments. For solid 1, we cannot directly recast spin diffusion rate constants into individual mutual P-P distances as each spin diffusion rate constant is composed of contributions from several P-P distances. In principle, however, the fairly small errors found in terms of distances should



Figure 5. Comparison of 31P spin diffusion build-up curves for 1: solid curve, best fit from 31P NMR experiments; dotted curve, calculated from the single-crystal X-ray structure.12

make it possible to numerically simulate internuclear distances also for cases of multisite spin exchange such as in 1, as long as one internuclear distance in such a multisite system is either known or can be determined by other independent means.27 Nonselective and Selective 31P f 113Cd CP/MAS NMR Experiments on 1. On the basis of the known assignment of all six 31P resonances A-F in solid 1 to the respective crystallographic P sites P1-P6, an attempt may be made to also achieve unique assignment of all 113Cd resonances A-H to the respective nine different Cd sites 1-9 in the asymmetric unit of 1. Neither consideration of isotropic chemical shifts δiso(113Cd) alone nor additional consideration of the principal components of the 113Cd chemical shielding tensors (as determined by a 113Cd 2D PASS experiment on 111) warrants such unique assignment. A strategy for the unique assignment of the 113Cd resonances to the respective crystallographic Cd sites in 1, again has to rely on distance information encoded in magnitudes of dipolar coupling constants, in this case heteronuclear 31P-113Cd dipolar coupling. All nine independent Cd sites in the asymmetric unit of 1 are characterized by specific mutual distance patterns, relating them to the crystallographic P sites P1-P6 (see Table 3), and corresponding to individual patterns of heteronuclear 31P-113Cd dipolar coupling for each 113Cd resonance. Heteronuclear polarization transfer 31P f 113Cd under MAS conditions then provides the method of choice to translate spectrally resolved NMR information, depending on magnitudes of dipolar coupling constants, into the crystallographic Cd-P distance pattern. A 44.4 MHz 113Cd MAS NMR spectrum of 1 (ωr/2π ) 5.0 kHz) is shown in Figure 6 a. Eight of the nine possible 113Cd resonances are resolved, with nearly equal integrated intensities; only the resonance at δiso ) 10.1 ppm (labeled B, B′) has double relative integrated intensity due to accidental spectral overlap. A 22.2 MHz 113Cd MAS NMR spectrum of 1 (ωr/2π ) 2.5 kHz) obtained by 31P f 113Cd crosspolarization (CP) with a CP contact time τCP ) 15 ms, is shown

TABLE 3: Internuclear Cd-P Distances (pm) in 1, within a Radius of 700 pm, As Determined by Single-Crystal X-ray Diffraction (ref 12)a Cd1

Cd2

Cd3

Cd4

Cd5

Cd6

Cd7

Cd8

Cd9

P1

311 339 648

301 516 617

500 656

577 595

343 347

622 648 655

521 605

351 684 699

304 339

342 571 639 647

509 532 606

301 616 641

329 535 620 663 320 653

330 615

P2

510 578 600 649 319 573 596

P3

579 592 598 649 353 696

336 529

352 506 599 699 578 629

305 533 584

345 656

302 665

325 541 627

608 619 625

500 632 695 341

324 342 675 336 637 681

510 624 686 331 586 587

3421 683

333 459 331 347

327 353 682

516

358 612

466 619 635 696 334 337

P4 P5

341 488 670

333 353 586 617 642 665

P6

329 650

505 582

357 516 331 587 666 693

593 631 684

544 620 639 658 671 309 636 637 335 625 653 350 687 699 341 433 695

a The numbering scheme of crystallographic sites is identical to the numbering scheme in ref 12.

in Figure 6 b. Obviously, for relatively long contact times τCP, all Cd sites in 1 experience polarization from 31P to approximately the same extent. For a rigid solid, the rate of the heteronuclear polarization transfer is strongly dependent on the respective internuclear distance(s) involved,18,21,22 and the dynamics of the polarization transfer may hence be used for purposes of site discrimination. The intensities of the 113Cd resonances A-H as a function of 31P f 113Cd CP contact time


Figure 6. 113Cd MAS NMR spectra of 1. (a) 44.4 MHz 113Cd singlepulse MAS NMR spectrum; ωr/2π ) 5 kHz, recycle delay 30 s, pulse duration 2 µs ()flip angle of 36°), 856 transients. (b) 22.2.MHz 113Cd MAS NMR spectrum, obtained after nonselective 31P-113Cd crosspolarization with a CP contact time τCP ) 15 ms, ωr/2π ) 2.5 kHz. Isotropic 113Cd chemical shifts δiso (ppm): 64.5 (A), 10.1 (B,B'), 3.8 (C), -6.8 (D), -9.1 (E), -27.9 (F), -30.5 (G), -35.1 (H).11

Figure 7. Relative intensities of 113Cd resonances A-H as a function of contact time τCP after nonselective 31P-113Cd cross-polarization.

τCP are depicted in Figure 7. Within experimental error, the build-up curves of 113Cd polarization for 1 are identical for all Cd sites, and no conclusions about specific assignment may be reached from this experiment. This experimental finding is not surprising if we inspect the crystallographic Cd-P distance patterns (see Table 3), and keep in mind that the 113Cd polarization as a function of τCP, as shown in Figure 7, represents the sum of polarization, acquired by each Cd site from essentially the entire 31P spin system. Clearly, 31P f 113Cd CP/MAS NMR experiments on 1, where the entire 31P spin system contributes to the polarization transfer, are not sufficiently selective to allow unique assignment of the various 113Cd resonances to specific crystallographic Cd sites. To achieve sufficient selectivity in 31P f 113Cd CP/MAS NMR experiments, two options exist. We could either use twodimensional 31P-113Cd heteronuclear correlation methods (HETCOR)23,24 to establish the Cd-P connectivities, or we could employ selective 31P excitation schemes in conjunction with onedimensional 31P f 113Cd CP/MAS where then only a preselected 31P resonance represents the source of 113Cd polarization. While two-dimensional correlation experiments may appear as the more elegant approach, performance of only few, selective onedimensional experiments has practical advantages with respect to the total necessary amount of spectrometer time. For many

Dusold et al.

Figure 8. Chemical shift filter for (a) selective direct 31P observation, (b) selective 31P f 113Cd cross-polarization.

inorganic solids devoid of protons, the absence of 1H lifts the necessity to use additional 1H high-power decoupling, but X f Y double-resonance NMR experiments, such as 31P f 113Cd CP/MAS NMR experiments on 1, then have to be performed under conditions of T1 relaxation times of X (where X is a spin1/ nucleus other than 1H), which will often be considerably 2 longer than 1H T1 relaxation times in, for instance, organic solids. With this constraint, a full two-dimensional X-Y correlation experiment may require prohibitively long times to acquire the necessary data set. From this purely practical point of view, application of selective one-dimensional X f Y doubleresonance NMR techniques can be advantageous for inorganic solids. For the study of 1, we have adopted the selective onedimensional 31P f 113Cd CP/MAS approach. In principle, either selective 31P excitation using a DANTE pulse sequence,25 or nonselective 31P excitation followed by a chemical shift filter may serve as the preparation step for selective one-dimensional 31P f 113Cd CP/MAS NMR experiments on 1. Selective 31P f 29Si CP/MAS NMR experiments on silicon phosphide SiP, where a 31P DANTE sequence was used as the CP preparation step, have been reported in the literature.16 We have employed a chemical shift filter as is shown in Figure 8; for the successive application of appropriate filters for the elimination of more than one resonance, the otherwise inconveniently long 31P T1 relaxation times turn into an advantage. If one 31P resonance is to be selected in the presence of more than one further 31P resonance, then in n successive steps the ∆CS/4 chemical shift filter has to be applied repeatedly, with appropriately adjusted durations of τsel ) ∆CS/4 for each of the n different isotropic chemical shift differences ∆CS present; after a delay τrel to allow for transverse relaxation, the third π/2 pulse may either be used as a read pulse for direct 31P observation (see Figure 8a) or as a preparation pulse for subsequent selective 31P f 113Cd cross-polarization (see Figure 8b). For selective 31P f 113Cd CP/MAS NMR experiments on 1, relaxation delays n‚τrel ) n‚50 ms lead to a loss of magnetization of the selected 31P resonance of less than 25%. The results of selective one-dimensional 31P f 113Cd CP/ MAS NMR experiments on 1 are shown in Figure 9, where column a displays the respective selected 31P resonance and column b the corresponding 113Cd MAS NMR spectrum, obtained after 31P f 113Cd cross-polarization from this selected 31P resonance. Only the two 31P resonances A, B have a chemical shift difference too small to select them separately;



Figure 9. Selective observation of 31P (column a) and corresponding selective 31P f 113Cd CP/MAS NMR spectra (column b). All CP/MAS NMR spectra were obtained with a contact time τCP ) 2 ms. For comparison, the top row shows the nonselective 40.5 MHz 31P MAS NMR spectrum (a) and the corresponding 22.2 MHz nonselective 31P113Cd CP/MAS NMR spectrum (b), also obtained with τ CP ) 2 ms. Note that the 113Cd MAS NMR spectrum in the bottom row of column b is the result of cross-polarization from 31P(A) + 31P(B).

the 113Cd MAS NMR spectrum shown in the bottom row of Figure 9b thus corresponds to cross-polarization from 31P(A) + 31P(B). The five 113Cd CP/MAS NMR spectra resulting from the five different 31P preparation/selection procedures show distinct differences in relative intensities of the various 113Cd resonances A-H. All selective 31P f 113Cd CP/MAS NMR spectra of 1, as shown in Figure 9b, are the result of a CP contact time τCP ) 2 ms. A contact time as short as τCP ) 2 ms (see Figure 7 for comparison) is well within an initial rate regime,18,21 where we may consider the relative intensities in each of the different 113Cd CP/MAS NMR spectra as a characteristic pattern of the various short-range Cd-P distances of the respective P sites/31P resonances. In an approximation for this short contact time regime (that is, neglecting rotating frame relaxation T1F), we may simply take the cross-relaxation rate constants TIS-1, describing the polarization transfer 31P f 113Cd, as proportional to the second moment of the respective heteronuclear I-S dipolar interaction, and hence proportional to rIS-6 (where rIS is the internuclear I-S distance).21 On the basis of known Cd-P distances in 1 we may then calculate expected relative intensities Intrel for each of the 113Cd resonances of the nine independent Cd sites for each of the selective 31P f 113Cd CP/MAS NMR experiments as Intrel ) C‚(rCdx-Py 6)-1 for all Cdx-Py combinations, where C is a constant for a given, short CP contact time τCP. The expected relative intensities of the 113Cd resonances of the nine crystallographic Cd sites Cd1-Cd9 (calculated for a radius of 700 pm around each of the six P sites P1-P6, and considering all Cd sites within this radius) are given in Table 4. Since the assignment of the six 31P resonances A-F to the crystallographic P sites P1-P6 is already known, comparison of the experimentally determined relative intensities in the selective 31P f 113Cd CP/MAS NMR spectra with the calculated

Figure 10. Comparison of experimental selective 31P f 113Cd CP/ MAS NMR spectra of 1 (left column) to calculated expected relative intensities Intrel (right column). Top row in left column: nonselective 31 P-113Cd CP/MAS NMR spectrum (as in Figure 9) for comparison. (a) CP from 31P(F) ) P5, (b) CP from 31P(E) ) P6, (c) CP from 31P(D) ) P4, (d) CP from 31P(C) ) P1, (e) CP from 31P(A) + 31P(B) ) P3 + P2.

expected relative intensities straightforwardly yields the following assignment of the 113Cd resonances A-H to the crystallographic Cd sites: 113Cd resonance: crystallographic Cd site:

A 8

B, B′ 5, 4

D 1

E 6

F 7

G 9

H 2

The assignment of the 113Cd resonances to the nine crystallographic Cd sites in 1 is further illustrated in Figure 10 where the five selective 31P f 113Cd CP/MAS NMR spectra are shown together with stick plot representations of the expected relative intensities for the assignment given above. Given the approximations made to calculate expected relative intensities, some minor imperfections in selecting the respective 31P resonances (see Figure 9a), and the practical compromise necessary in choosing a CP contact time τCP, which simultaneously has to be (i) short enough so that only short-range effects are being monitored, and (ii) long enough to obtain acceptable signal-to-noise ratios in reasonable amounts of time, the agreement between experimental data and calculated relative intensities is very good; no other assignment permutation yields similarly good agreement. Our assignment of the 113Cd resonances in 1 is in complete disagreement with a previous assignment attempt reported in the literature.26 This previously given assignment is based on consideration of small differences in the asymmetry parameters of the 113Cd chemical shielding tensors of 1 that had been derived from 113Cd MAS NMR spectra with only very few and low-intensity spinning side bands. We have recently shown11 that these data reported on 1 in the literature26 are highly inaccurate; furthermore, there is no reason to expect any useful correlation between 113Cd chemical shielding tensor asymmetry parameters and CdO5 group inertial tensor asymmetry parameters. Conclusions We have not used any qualitative considerations of specific structural features in solid 1 for assigning either 31P or 113Cd

TABLE 4: Relative Intensities Intrel (au), Calculated within a 700 pm Radius, for Selective 31P f

P1 ) 31P C P2/3 ) 31P B/A P4 ) 31P D P5 ) 31P F P6 ) 31P E

C 3

113Cd

Cd1 ) 113Cd D

Cd2 ) 113Cd H

Cd3 ) 113Cd C

Cd4 ) 113Cd B′

Cd5 ) 113Cd B

Cd6 ) 113Cd E

Cd7 ) 113Cd F

17.7 1.6 5.3 7.2 8.0

14.1 12.7 12.7 0.4 0.9

0.8 25.3 0.4 5.3 8.1

0.5 19.9 0.9 6.4 13.4

1.2 16.0 15.1 7.2 0.5

11.8 14.6 0.8 8.1 4.9

0.5 22.9 6.3 1.4 14.1

Cross-Polarization in 1 Cd8 ) A

113Cd

8.7 10.0 8.5 13.4 0.5

Cd9 ) G

113Cd

7.9 12.7 7.4 5.6 7.9

6366 J. Phys. Chem. B, Vol. 101, No. 33, 1997 resonances to specific crystallographic sites. The assignment procedures are solely based on distance connectivities as measured by X-ray diffraction and by polarization transfer dynamics in NMR. It is important that these assignment procedures are free of all, potentially misleading, bias from local symmetry arguments or other model assumptions. With the assignments of all 31P and 113Cd resonances in 1 now objectively determined, the structural properties of 1 may be closely inspected for direct relationships between structure and isotropic or anisotropic NMR parameters of 1.27 In principle, 2q and 0q polarization transfer experiments under MAS conditions do carry identical information about mutual internuclear distance connectivities. 1q-2q correlation methods have advantages with respect to assignment of resonances to specific crystallographic sites, as also “self-connectivities” are directly displayed. 0q methods are more broadly applicable for purposes of quantitative characterization of distance connectivities, as also spin systems that cannot be approximated by a spin-pair model can be treated in a quantitative manner. Regardless of whether 2q or 0q polarization transfer techniques are being employed, for cases of multiple sites with a correspondingly large range of multiple isotropic and anisotropic chemical shifts, it is important that the pulse sequence used is sufficiently broad-banded to ensure a purely dipolar transfer mechanism. Naturally, this consideration becomes increasingly important for experiments carried out at high external magnetic field strengths. It is an advantage that amongst the various homonuclear dipolar recoupling schemes also extremely narrowbanded versions, such as rotational resonance (RR)1, exist. We have pointed out above that for a multiple-site case such as Cd3(PO4)2, 1, it is basically sufficient if only one (of many) internuclear P-P distances can be determined independently in order to provide the necessary scaling factor for the conversion of spin diffusion rate constants into geometric distances, also in the absence of X-ray diffraction information. For instance, rotational resonance recoupling is in principle sufficiently selective to provide such information even in the presence of multiple resonances. Further work along these lines is in progress and will be reported elsewhere.27 Acknowledgment. Support of this work by Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie is gratefully acknowledged. We thank H. Eckert, Mu¨nster, for the donation of a sample of CdSiP2.

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MAS NMR Study of

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