DOI: 10.1002/chem.201003560

Structural Characterization of Phosphorus-Based Networks and Clusters:31P MAS NMR Spectroscopy and Magnetic Shielding Calculations on

Hittorf�s Phosphorus

Thomas Wiegand,[a] Hellmut Eckert,*[a] Stefan Grimme,*[b] Diana Hoppe,[c, d] andMichael Ruck[c]

Introduction

Almost 350 years after the discovery of phosphorus in itswhite form by the pharmacist and alchemist HenningBrand,[1] this element has experienced an incomparable sci-entific renaissance within recent years. In 2005 Ruck and co-workers[2] elucidated the structure of a novel phosphorus al-lotrope called red fibrous phosphorus. This allotrope had al-ready been postulated in 1969 by Thurn,[3] who described indetail the structure of Hittorf�s phosphorus (or violet phos-phorus). Both structures consist of phosphorus strands inthe form of pentagonal tubes constructed from three struc-tural motifs, that is, P8 and P9 cages and P2 dumbbells (seeFigure 1 for a representation of Hittorf�s phosphorus). Theprominent difference between these two structures lies inthe different connectivity of the covalently linked tubes; inHittorf�s phosphorus the tubes are arranged perpendicularto each other, whereas in the red fibrous form the strandsare parallel so that double tubes are formed. Theoreticalstudies revealed that both structures are energetically equiv-alent,[3a,4] and both modifications can be obtained by similarsynthetic routes, although the growth mechanism is still un-clear. Comparable phosphorus-based architectures havebeen found in low-charged polyanions and phosphorus chal-

[a] T. Wiegand, Prof. Dr. H. EckertInstitut f�r Physikalische ChemieGraduate School of ChemistryWWU M�nsterCorrensstraße 3048149 M�nster (Germany)Fax: (+49) 251-83-29159E-mail : eckerth@uni-muenster.de

[b] Prof. Dr. S. GrimmeOrganisch-Chemisches InstitutWWU M�nsterCorrensstraße 4048149 M�nster (Germany)Fax: +49-251-83-36515E-mail : grimmes@uni-muenster.de

[c] Dr. D. Hoppe, Prof. Dr. M. RuckFachrichtung Chemie und LebensmittelchemieTechnische Universit�t DresdenHelmholtzstraße 1001069 Dresden (Germany)

[d] Dr. D. HoppeCurrent address: Generalverwaltung der Max-Planck-GesellschaftHofgartenstr. 8, 80539 M�nchen

Supporting information for this article is available on the WWWunder http://dx.doi.org/10.1002/chem.201003560.

Abstract: The 31P MAS NMR spectrumof Hittorf�s phosphorus has been mea-sured and assigned to the 21 crystallo-graphically distinct phosphorus atomsbased on two-dimensional dipolar cor-relation spectroscopies. Application ofsuch 2D techniques to phosphorus-based networks is particularly challeng-ing owing to the wide chemical shiftdispersions, rapid irreversible decay oftransverse magnetization, and extreme-ly slow spin-lattice relaxation in thesesystems. Nevertheless, a complete as-signment was possible by using thecombination of correlated spectroscopy(COSY) and radiofrequency-driven di-polar recoupling (RFDR). The assign-ment is supported further by DFT-

based ab initio chemical shift calcula-tions using a cluster-model approach,which gives good agreement betweenexperimental and calculated chemicalshift values. The 31P chemical shiftsappear to be strongly correlated withthe average P�P bond lengths withinthe PACHTUNGTRENNUNG(P1/3)3 coordination environments,whereas no clear dependence on aver-age P-P-P bond angles can be detected.

Calculations of localized Kohn–Sham orbitals reveal that this bond-

length dependence is reflected inenergy variations in the correspondinglocalized p-p-s orbitals influencing theparamagnetic deshielding contributionin Ramsey�s equation. In contrast, thecontributions of the lone pairs toshielding differences are small and/ordo not vary in a systematic manner forthe different crystallographically dis-tinct phosphorus sites. The combinedspectroscopic and quantum chemicalapproach applied here and the in-creased theoretical understanding of31P chemical shifts will facilitate thestructural elucidation of other phos-phorus-based clusters and networks.

Keywords: density functional calcu-lations · Hittorf�s phosphorus · mag-netic shielding · NMR spectroscopy ·phosphorus

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cogenide cage molecules.[5] In some cases a separation of thepure phosphorus strands from copper halide matrices hasalso been observed.[6]

Besides the discovery of new structures, phosphorus andits compounds are also interesting from a materials sciencepoint of view. One current example is the application ofblack phosphorus, the most thermodynamically stable modi-fication at standard conditions, as an anode material in lithi-um-ion batteries, which is a promising line of research dueto the high charge capacity and energy density.[7] Additional-ly in the field of electrochemistry, investigations have beenconcentrated on solid ionic conductors based on inorganicmetal phosphides.[8]

The extremely large structural diversity of the different el-emental phosphorus modifications and the ability to adoptvarious structural motifs in polyphosphide-based compoundsexplain the high potential regarding technological applica-tions and help to understand why solid-state chemists havebeen intrigued by these compounds for many decades.[9] Adeeper understanding of the structure–property relationshipis a fundamental requirement for constructing novel materi-als that take the versatile properties of phosphorus-basedmaterials into account. Therefore, an improved knowledgeof local environments, structural characteristics, bondingconnectivities, and bonding situations in these compounds isessential. Herein we discuss one representative model com-pound, Hittorf�s phosphorus, in which 21 crystallographicallydistinct phosphorus positions constitute a threefold coordi-nated network making this compound one of the most com-plex phosphorus-based architectures known so far.

In recent years the utility of solid-state NMR for elucidat-ing information on various structural and dynamic aspectsof compounds containing phosphorus clusters and networkshas come into focus.[6,10] High-resolution magic-angle-spin-ning (MAS) NMR spectroscopy offers a sensitive differen-tiation between distinct phosphorus environments based onthe extremely wide 31P chemical shift range (d=300 to�550 ppm in the case of crystalline phosphides).[6,10d,11] De-spite this sensitivity, to date only a few promising correla-tions of 31P chemical shifts with structural characteristics

have been shown. Fyfe and co-workers describe a reason-ACHTUNGTRENNUNGable correlation of the 31P shielding with Fe-P-Fe bondangle in a series of phosphide-bridged di-iron complexes[12]

and Eichele and co-workers demonstrated correlations be-tween chemical shifts and Ru-P-Ru bond angles in rutheni-um carbonyl compounds that contain a phosphido ligand.[11b]

In general, however, the simple assignment of chemicalshifts to crystallographically distinct phosphorus sites re-mains a big challenge. One solution to this problem is theuse of modern sophisticated 2D solid-state NMR spectro-scopic pulse sequences, which allow a direct assignmentthrough correlations between resonances of phosphorus po-sitions in spatial proximity.

Two distinct types of experiments important in this con-text are used herein. Experiments such as COSY[10a] and R-TOBSY[13] utilize one- or two-bond connectivities to corre-late resonances based on indirect dipole–dipole interactions(J couplings), and there are numerous sequences in whichsuch correlations are based on through-space dipolar inter-actions. A powerful sequence of the latter type is the radio-frequency-driven recoupling[14] (RFDR) experiment, inwhich the homonuclear dipolar interaction, principally elim-inated under MAS conditions, is reintroduced by a series ofp pulses during the rotor cycle. As a consequence, this se-quence achieves zero quantum coherence transfer betweendipolar-coupled nuclei.

Although RFDR and many other dipolar recoupling tech-niques have provided useful insights into structural proper-ties in a great variety of chemical systems, applications ofsuch techniques to phosphorus-based clusters and networkshave been rather scarce. Previous work on the ionic conduc-tor Cu2P3I2, the structure of which is also based on phospho-rus strands, illustrates the possibility of assigning resonancesin a 31P MAS NMR spectrum to distinct phosphorussites[10a,13a] by conducting RFDR and COSY experiments.Nevertheless, owing to the large spectral dispersion (chemi-cal-shift differences and anisotropies), short spin–spin relax-ation times (due to strong dipolar couplings between direct-ly bonded P atoms) and extremely long spin-lattice relaxa-tion times of the 31P nuclei in many phosphorus cluster com-pounds (e.g., about 850 s for Hittorf�s phosphorus), thechoice and optimization of such techniques remains a con-siderable challenge in this field. Especially in case of com-plex structures, such as Hittorf�s phosphorus, theoreticalmagnetic shielding calculations are essential to support ex-perimental resonance assignments, and to obtain reasonablestarting information for the analysis of experimental 2DNMR spectra. For phosphorus-based networks, such shield-ing calculations are difficult because of the need to includeelectron correlation effects for an accurate description ofthe local electronic structure of the phosphorus atoms and,in the case of complex systems, the conflicting demands ofhigh accuracy and computational costs have to be answeredsatisfactorily. The latter point often leads to the conclusionthat calculations by using a simplified cluster model of thecrystal structure can already produce an acceptable accuracyin comparison with the often resource-consuming ap-

Figure 1. Repetition unit of the tubes in Hittorf�s phosphorus (atom num-bering according to Thurn and co-workers[3a]). The different tubes areconnected through atom P21. The bond lengths vary from 2.299 to2.178 �, the averaged P�P length is given as 2.2194 �.

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proaches based on periodic boundary conditions. Herein, wereport quantum-chemical calculations based on density func-tional theory (DFT) of Hittorf�s phosphorus within the clus-ter model approach and illustrate their benefit in obtaininga deeper understanding of the origin of 31P chemical shiftsin threefold-coordinated phosphorus species. For a generaloverview of such calculations, see reference [15].

Results and Discussion

One- and two-dimensional 31P NMR spectra of Hittorf�sphosphorus : Figure 2 shows the 31P MAS NMR spectrum

obtained at 11.7 T by using a spinning rate of 30 kHz. Basedon spinning-speed-dependent measurements (see Figure S1,Supporting Information) the resonances of all 21 distinctphosphorus sites present in the crystal structure can be iden-tified. Although fast MAS also considerably reduces the ho-monuclear magnetic 31P–31P dipole–dipole interactions, theresidual linewidths are still too broad to resolve any peakmultiplicities due to J coupling effects. Figure 2 indicates arather wide chemical shift range between d= 171 and�85 ppm. Comparison with reference data (white phospho-rus, d=�527 ppm;[16] black phosphorus, d= 22 ppm[17]) illus-trates the remarkable sensitivity of the 31P magnetic shield-ing to local distortions of the pyramidal PACHTUNGTRENNUNG(P1/3)3 environ-ments. Peak pattern integration (including the correspond-ing spinning sidebands) revealed an intensity ratio of2:1:3:1:1:1:2:2:2:1:1:1:1:1:1. The resonances at d=171.3 and�84.5 ppm are of particular interest because their isolatedpositions in the spectra suggest some unique structural fea-tures that set them apart from the other phosphorus sites.Based on this consideration we assign the isolated resonanceat d=�84.5 ppm to the tube-connecting atom P21 (see

Figure 1). As confirmed further below by the magneticshielding calculations, the strong shielding effect can be re-lated to the shortest observed P�P bond lengths and thelargest P-P-P bond angles compared with all of the other Penvironments. These structural specifics are known to be theresult of the pressure the above-lying tubes develop throughthe sum of their van der Waals interactions; the bondlengths are shortened and atoms P17 and P18 are pushedapart.[3a] The consequences of these non-covalent interac-tions, namely, the distortion of the coordination sphere ofphosphorus atom P21, can be correlated with the remark-able low-frequency displacement of the 31P resonance, allow-ing a preliminary peak assignment. Based on the same argu-ment, the signal at d= 171.3 ppm is assigned to the P atomswith the largest average P�P bond lengths and the smallestaverage P-P-P bond angles. These are the bridging atoms ofthe P8 cage (P19 and P20).

Further analysis and discussion of the 31P MAS NMRspectrum requires peak assignments based on 2D NMRmethods combined with ab initio calculations of magneticshieldings. Examination of numerous different 2D NMRtechniques led us to the conclusion that a combination ofCOSY and RFDR provides a powerful complementary ex-perimental approach for the NMR peak assignment in Hit-torf�s phosphorus. In COSY experiments the observed crosspeaks arise from coherence transfer between covalentlybonded phosphorus species, whereas RFDR experimentsdemonstrate spatial proximity through re-coupling of directhomonuclear dipolar interactions.

First impressions for the peak assignment are obtainedfrom the 31P–31P TPPI-COSY spectrum in which cross peaksare observed for most of the directly bonded phosphoruspairs (see Figure 3). For the resonance at highest frequency(d=171.3 ppm), assigned to the phosphorus species P19/P20, a very intense correlation peak to the resonance at d=

135.2 ppm is observed. This high intensity results from thecoupling of the two “roof” positions P19/P20 to four directlybonded phosphorus sites (namely the base of the P8 cage).The resonance at the lowest frequency (d=�84.5 ppm)shows only two strong correlations to the signals at d= 21.6and 26.9 ppm. The observation of only two cross peaks isconsistent with our assignment to the tube-connecting atomP21, which is connected to itself and to two other crystallo-graphically distinct P atoms (P17, P18). Based on thesestarting points, the peak assignment can be carried outthrough connectivity mapping to give the result summarizedin Table 1.

To further prove the spatial proximities and resolve morecross peaks (especially those close to the diagonal), RFDRmeasurements were carried out. By choosing very shortmixing times, couplings between directly bonded phosphorusspecies can be selected. A mixing time of 444 ms was foundto be a good compromise for the conflicting demands ofcross-peak intensity and spectral selectivity. The 31P–31PRFDR spectrum obtained with this mixing time is displayedin Figure 4a. Almost all the correlations, including thoseclose to the diagonal, are visible, which confirms the peak

Figure 2. a) Experimental 31P MAS NMR spectrum of Hittorf�s phospho-rus carried out at 11.7 T (202.5 MHz) with a spinning frequency of30 kHz. b) Simulated spectrum and c) individual peak contributions tothe simulations. Spinning sidebands are marked by * and resonancesmarked with + are attributed to impurities.

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FULL PAPERPhosphorus-Based Networks and Clusters

assignment discussed above. However, correlations betweensignals with very different chemical shifts show reduced in-tensity in this experiment (e.g., P10/P2, P10/P9 and P10/P11) or are even absent (P21/P18 and P21/P17). Special at-tention should be paid to the cross peaks between the bridg-ing atoms of the P9 cage (P17 and P18) and the base atomsP9 and P11, which clearly confirms the arrangement of theneighboring phosphorus atoms in the base plane discussedbelow. Figure 4b shows the RFDR spectrum with twice the

mixing time used in the first experiment (888 ms). Longer-range correlations marked by asterisks have appeared andthe intensities of the cross peaks are strongly enhanced, insome cases almost obscuring the diagonal peaks (e.g., P6and P14, which show strong dipolar couplings to four baseatoms of the P8 cage). In this spectrum the correlations ofthe bridging atom P21 to the adjacent peaks at about d=

25 ppm are again clearly visible because the longer mixingtime compensates for the reduced recoupling efficiency inthe case of large chemical shift differences.

Altogether, a clear ordering of NMR resonances to thedifferent structural motifs is visible in the 31P NMR spec-trum due to the different local environments of the crystal-lographically distinct phosphorus sites. The atoms of the P8

cage are completely assigned to the resonances at high fre-quencies within a chemical shift range of d=171.3 to96.1 ppm, whereas most of the sites of the P9 cage resonateat lower frequencies in the spectral region from d= 65.7 to�84.5 ppm. One striking exception is the basal P10 atom ofthe P9 cage, which shows a remarkably high chemical shiftof d=129 ppm that can be explained as follows: the P2

dumbbells, which act as the linkers between the structuralmotifs of the P8 and P9 units, resonate at d=77.0 (P12 andP16) and 68.7 ppm (P4 and P8). The behavior of identicalchemical shifts parallel to the tube axis may be explained bythe inclination of the basis plane of the tubes (atoms P2, P4,P6, P8, P10, P12, P14 and P16) of about 458 relative to thea–b plane, which means that the free bonds of the atom P21poke out of this plane nearly perpendicularly. The tube-con-necting atom of the directly covalently linked tube is, there-fore, oriented towards atoms P1, P3, P5, P7, P2, P4, P6 andP8, which leads to a cancellation of the pair symmetry per-

Figure 3. 31P–31P TPPI-COSY spectrum acquired at 7.0 T (121.5 MHz) with a spinning frequency of 25 kHz. The features parallel to the diagonal resultfrom spinning sidebands. N : Correlations that are expected but not seen in this experiment, mainly because of overlap with diagonal peaks.

Table 1. Comparison of experimentally assigned and theoretically deter-mined chemical shift values (referenced to 85 % H3PO4). The latter weredetermined by using the cluster model shown in Figure 6a by using BP86GGA-functional and TZVP basis set.

Assignment dexptl [ppm] dcalcd [ppm] Dd [ppm]

P1 65.7 52.5 13.2P2 10.0 7.8 2.2P3 65.7 47.7 18.0P4 68.7 88.2 �19.5P5 142.3 138.1 4.2P6 108.9 135.9 �27.0P7 135.2 144.8 �9.6P8 68.7 77.5 �8.8P9 41.2 46.0 �4.8P10 129.0 109.6 19.4P11 35.9 44.5 �8.6P12 77.0 72.8 4.2P13 135.2 167.4 �32.2P14 96.1 105.7 �9.6P15 135.2 170.6 �35.4P16 77.0 77.7 �0.7P17 26.9 �12.4 39.3P18 21.6 �7.7 29.3P19 171.3 193.6 �22.3P20 171.3 182.5 �11.2P21 �84.5 �82.4 �2.1

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H. Eckert, S. Grimme et al.

pendicular to the tube axis (see Figure 5). Therefore, it isreasonable to assume that the remarkable shielding differ-ence for atoms P2 and P10 (about d= 120 ppm) is due tothe fact that P2 is significantly oriented towards atom P21’of the above-lying tube and is probably more strongly influ-enced by the anisotropy cone of both bridging atoms P21and P21’, which leads to the observed low-frequency shift.This suggestion is also supported by ab initio calculations on

different cluster models withand without consideration ofthe effect of an anisotropy cone(details are given in the Sup-porting Information, Figure S9and Table S10).

Ab initio 31P magnetic shieldingcalculations : The cluster modelused for the magnetic shieldingcalculation is taken from thecrystal structure[3a] and is shownin Figure 6a. It consists of onelayer composed of parts ofthree tubes in one plane andthree further tubes almost per-pendicular to those. Free phos-phorus valences were saturatedwith hydrogen atoms, the posi-tions of which are optimized atthe def2-SVP[18] level by usingthe GGA functional BP86[19]

while freezing the phosphorusframework. The largest abinitio calculation conducted inthis work consists of 5304 con-tracted Gaussian basis functionsand considers all 3536 electrons(for further information, seethe Experimental Section). Allthe magnetic shielding calcula-tions were conducted within theGIAO (gauge including atomicorbitals) framework. Figure 7shows a strong correlation be-tween the experimentally as-signed chemical shifts and thecalculated values (TZVP[20]

basis set), corresponding to anadjusted R2 value of 0.94. Inparticular, the tentative startingpoints of the 2D assignments(i.e., the “roof” positions of theP8 and P9 clusters) are clearlyidentified at the highest and thelowest frequencies, respectively.Also, the chemical shift differ-ences between the base atomsof the P9 cluster underlines the

assignment of P2 to the lower and P10 to the much higherfrequency. Despite the deviations in absolute values due tolimitations of the cluster model used and/or systematicerrors resulting from the applied theoretical level, the devel-oped peak assignment is confirmed by the calculations. Fi-nally, an excellent correlation (R2 =0.91; see the SupportingInformation, Figure S8) is also found with the simpler clus-ter model of Figure 6b.

Figure 4. a) 31P–31P RFDR spectrum obtained at 7.0 T (121.5 MHz) with a spinning frequency of 27 kHz and arepetition rate of 500 s. The mixing time was set to 444 ms. b) 31P–31P RFDR spectrum obtained at 7.0 T(121.5 MHz) with a spinning frequency of 27 kHz and a repetition rate of 470 s. The mixing time was set to888 ms. Longer-range correlations are marked by N.

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FULL PAPERPhosphorus-Based Networks and Clusters

The theoretical studies also open up the possibility forgaining a deeper understanding of the origin of magneticshieldings of the three-fold coordinated phosphorus speciesby analyzing correlations of 31P chemical shifts with thelocal trigonal pyramidal PACHTUNGTRENNUNG(P1/3)3 geometries present. Indeed,Figure 8 illustrates a general trend for both the experimentaland the calculated chemical shift values with the average P�P bond lengths: smaller chemical shifts are related to short-er bond distances. However, considerable deviations are ob-served for the base atoms of the P8 cluster (i.e., atoms P5,P7, P13 and P15) and atom P2. In the first case lower chemi-

cal shift values and in the latter a higher one would be ex-pected. We attribute these deviations to special shielding ef-fects of the “roof” atoms in both cluster units. Even so, theexperimental 31P chemical shifts of P5, P7, P13 and P15 are

Figure 5. Cutout of the structure of Hittorf�s phosphorus showing the in-clination of the plane, including the base atoms P2, P4, P6, P8, P10, P12,P14 and P16 of about 458 relative to the ab plane, which is responsiblefor the observed pair symmetry parallel to the tube axis (e.g., comparablechemical shifts for P12/P16 rather than P12/P4 and P16/P8, respectively).This effect is enhanced by the cross-wise orientation of the directly con-nected tubes.

Figure 6. a) Cluster model of Hittorf�s phosphorus used in the DFT calcu-lations of magnetic shielding. The chemical shifts were determined forthe repetition unit within the middle tube in the lower layer. Free valen-ces were saturated with hydrogen atoms, the positions of which were op-timized at the BP86 level of theory. b) Simplified cluster model used inthe analysis of LMOs.

Figure 7. Correlation between experimentally assigned and ab initio shifts(BP86, TZVP) obtained from the cluster-model approach (see Figure 6a).c : A linear regression with an adjusted R2 value of 0.94.

Figure 8. a) Experimental data and b) calculated values for the correla-tion of 31P chemical shifts with average P�P bond lengths in Hittorf�sphosphorus. c : A linear regression with an adjusted R2 value of 0.79,in which P sites P2, P5, P7, P13 and P15 were not included (see the maintext).

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H. Eckert, S. Grimme et al.

very close to each other, which corresponds well with thefact that their average P�P bond distances are very similar.An adjusted R2 value of 0.79 was determined for the corre-lation between bond lengths and chemical shifts if P2, P5,P7, P13 and P15 are excluded from this correlation based ontheir above-mentioned special structural features. In con-trast, a general correlation between averaged pyramidalbond angles and chemical shifts could not be found (seeFigure 9, the adjusted R2 was determined as 0.36). Only the

separation of the spectrum into two spectral regions, one oc-cupied by P21 and the other one by all other atoms, is signif-icant. Therefore, we conclude that the covalent bond lengthsin Hittorf�s phosphorus dominate the chemical-shift differ-entiation between the different P atoms.

Table 2 lists the separate diamagnetic and paramagneticcontributions to the 31P magnetic shielding values. Thesedata confirm the widely accepted general assumption thatshielding differences in 31P NMR spectra due to differentchemical environments result primarily from differences inthe paramagnetic shielding part whereas the diamagneticpart stays almost constant.[21] The paramagnetic contributionto nuclear shielding within the framework of DFT theory isgiven by:

sparaN;uv ¼

2c2

Xocc

k

Xvac

a

fk lO;u faj��� �

fa lN;v

�� r�3N fkj

� �

ek � eað1Þ

in which fk and fa represent occupied and virtual molecularorbitals, respectively. The numerator consists of two matrixelements: the “orbital Zeeman term” (OZ) and the “para-magnetic nuclear spin electron orbit term” (PSO).[22] Thedenominator includes the energy difference between the oc-cupied and virtual molecular orbitals.* From Equation (1), a

large contribution to the paramagnetic shielding differencescan particularly arise in cases of small energy denominators.Based on Equation (1), we qualitatively investigated theabove-mentioned correlation between d ACHTUNGTRENNUNG(31P) and averageP�P bond lengths by calculating localized molecular orbitals(LMOs) with the Foster-Boys localization scheme.[23] Theseorbitals have the advantage that they can be interpretedwithin a chemist�s view of bonding, that is, bonding, anti-bonding or lone-pair character. We further calculated theexpectation value of the Kohn–Sham–Fock operator in theLMO basis for the LMOs of the three s bonds and of thelone pairs. Neglecting off-diagonal elements in the Fockmatrix, we interpreted those values qualitatively as energiesof the LMOs and used them for a description of the energydenominator in Equation (1). All these calculations aredone by using the simpler cluster model of Figure 6b. Fig-ure 10a illustrates that the LMO energies of the three s

bonds have a significant effect on the 31P chemical shift ex-pressed in a linear correlation (adjusted R2 value of 0.69).Nevertheless, considerable scatter is observed, which indi-cates that the effects of different OZ and PSO terms alsomake significant contributions to the observed shielding dif-ferences. Nevertheless, the above correlation of shieldingwith LMO energies is not observed for the orbital energy ofthe lone pairs. We thus conclude that the contributions ofthe lone pairs to shielding differences do not vary in a sys-tematic manner for the different crystallographically distinctphosphorus sites. Nevertheless, it is known that these LMOsalso contribute to the absolute value of the magnetic shield-ing as shown by previous IGLO calculations.[24]

Having shown that the LMO energies of the bonds corre-late with the chemical shifts, the origin of this effect must beanalyzed. Figure 11 shows the influence of differing P�P

Figure 9. Absence of a clear correlation of 31P chemical shifts with aver-age P-P-P pyramidal angles. c : A linear regression with an adjusted R2

value of only 0.36.

Table 2. Calculated diamagnetic (sdia) and paramagnetic magnetic shield-ings (spara) in term of Ramsey�s equation for the different phosphorussites (BP86, TZVP, model Figure 6a).

Assignment sdia [ppm] spara [ppm]

P1 963.1 �726.9P2 963.7 �682.8P3 964.1 �723.0P4 963.8 �763.3P5 963.2 �812.5P6 964.0 �811.1P7 964.3 �820.4P8 963.8 �752.6P9 963.2 �720.4P10 962.9 �783.8P11 963.2 �718.9P12 962.9 �747.0P13 962.8 �841.4P14 962.3 �779.3P15 962.7 �844.6P16 963.0 �751.9P17 964.5 �663.3P18 964.6 �668.2P19 962.3 �867.2P20 963.3 �857.1P21 965.4 �594.2

[*] According to Reference [22], lO and lN represent one-electron opera-tors that describe the angular momentum around the gauge origin ofthe external vector potential and the angular momentum around thenucleus in question, respectively; u and v denote Cartesian compo-nents; c denotes the speed of light.

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FULL PAPERPhosphorus-Based Networks and Clusters

bond lengths on the LMO energies. Indeed, shorter P�Plengths result in lower LMO energies and indicate a stron-ger chemical bond. In those cases the paramagnetic contri-bution to the magnetic shielding is smaller (the resulting

energy differences in Equation (1) are larger), which resultsin lower 31P chemical shifts. Thus the theoretical calculationssupport the semi-empirical correlations of chemical shiftswith bond lengths in Hittorf�s phosphorus, allowing for adeeper understanding of magnetic shielding in polyphos-phide networks. Nevertheless, the P-P-P pyramidal bondangles also influence 31P chemical shifts, which probably ex-plains the deviations in the correlations shown in Figure 10.Indeed, systematic ab initio calculations on white phospho-rus and PACHTUNGTRENNUNG(PH2)3, in which P�P bond lengths and P-P-P pyra-midal angles were varied, allow the separation of bondlength and bond angle effects on chemical shifts and revealthe influence of both structural parameters upon the 31Pmagnetic shielding values (see the Supporting Information,Figures S2–S7).

Conclusion

The 31P MAS NMR spectrum of Hittorf�s phosphorus wassuccessfully assigned to the 21 crystallographically distinctphosphorus atoms by using 2D NMR correlation spectrosco-py and quantum-chemical calculations within the cluster-model approach. Correlations are based on 1J couplings andhomonuclear dipolar interactions arising from direct intera-tomic connectivity. Experimentally determined chemicalshifts show a good agreement with theoretically calculatedmagnetic shieldings at the GGA DFT level. The resultshighlight a clear ordering of resonances to the various struc-tural motifs present in Hittorf�s phosphorus; the phosphorussites in the P8 cage resonate at higher frequencies and thosein the P9 unit predominantly at lower frequencies. The moststrongly shielded P atoms are the tube-connecting P21atoms, indicating the special electronic character of thislocal environment. The extremely wide chemical shift rangeillustrates the sensitivity of 31P solid-state NMR spectrosco-py towards small changes in the local environments of thephosphorus nuclei. These variations can be used for obtain-ing an improved understanding of structure and bonding instrongly covalently bonded phosphorus systems. We haveshown that in Hittorf�s phosphorus variations in the averageP�P bond lengths of the three s bonds exert the strongestinfluence on the 31P magnetic shielding: shorter P�P lengthsresult in smaller contributions to the paramagnetic shieldingcomponent, thus producing lower resonance frequencies. Inthis context quantum-chemical calculations of LMOs revealthat the P�P bond-dependent energies of the LMOs of thebonds have a large impact on chemical shift values. Theseare responsible for site-to-site variations in the excitationenergy in the paramagnetic shielding term of Ramsey�sequation. The increased understanding of the chemical shiftsin threefold coordinated phosphorus species will facilitatepeak assignments and thus contribute to the structural eluci-dation of other phosphorus-based clusters and networks.

Figure 10. a) Absence of a correlation between 31P chemical shifts andLMO energies of the lone pairs and b) the correlation between 31P chem-ical shifts and averaged LMO energies of the P-P-s bonds for the clustermodel in Figure 6b. c : A linear regression with an adjusted R2 value of0.69.

Figure 11. Linear correlation between averaged LMO energies of thebonds and average P�P bond length for each phosphorus site. c : Alinear regression with an adjusted R2 value of 0.77.

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H. Eckert, S. Grimme et al.

Experimental Section

Hittorf�s phosphorus was prepared by using known literature proce-ACHTUNGTRENNUNGdures.[2a, 3a] All the NMR experiments were performed using 2.5 mmdouble and triple resonance probes with spinning rates between 25 and34 kHz for reducing chemical shift anisotropy effects and 31P–31P homo-nuclear dipolar couplings. The sample was filled in the middle third of arotor volume to ensure optimal homogeneity of the radiofrequency am-plitude. 31P single-pulse MAS experiments were carried out at 11.7 T(n0 =202.5 MHz) by using a BRUKER Avance DSX FT-NMR spectrom-eter. The applied 908 pulse length was adjusted to 1.9 ms and the relaxa-tion delay was set to 600 or 1000 s. Chemical shifts are reported relativeto 85 % H3PO4. All line shape analysis was done by using the DMFIT[25]

software.

Spin-lattice relaxation time measurements were conducted at 7.0 T (n0 =

121.5 MHz) by using an Avance III BRUKER console by employing thesaturation recovery pulse sequence (fifteen 908 pulses of 1.65 ms length).The COSY experiment was performed at 7.0 T operating at a spinningfrequency of 25 kHz. The applied pulse sequence was based on the TPPI-COSY scheme including a pre-saturation comb. The 908 pulse width wasset to 2.0 ms and the repetition rate was 600 s. Eight transients wereadded for the direct dimension, whereas 84 increments were collected inthe indirect dimension. The spectral width in both dimensions was set to62.5 kHz. RFDR experiments were carried out at 7.0 T using a spinningfrequency of 27 kHz. Pulse lengths for 90 and 1808 pulses were set to2.65 and 5.3 ms, respectively. The mixing time with highest spectral selec-tivity and maximum cross-peak intensity was optimized to 444 ms, whichresulted in 12 applied p pulses in each experiment that are phase-cycledaccording to the XYXY YXYX XYXY scheme. The signal was detectedafter a rotor-synchronized echo with an echo time of one rotor period.Eight transients were collected for the direct dimension and 104 incre-ments in the indirect dimension by using the STATES-TPPI method forquadrature detection in the F1 dimension and a recycle delay of 500 s,following presaturation by a saturation comb. The spectral width in theindirect dimension was chosen as 66.67 kHz. The experiment was addi-tionally performed by using a longer mixing time of 888 ms that resultedin 24 applied p pulses phase-cycled according to the XY-8[26] scheme. Inthis experiment the relaxation time was set to 470 s and the saturationcomb consisted of 20 908 pulses. The applied pulse lengths were opti-mized to 2.5 and 5 ms for 90 and 1808 pulses, respectively.

Theoretical magnetic shielding calculations were performed by using theTURBOMOLE program package[27] within the cluster-model approachon different models in which at least the first coordination sphere of theconsidered repetition unit is represented correctly. The positions of thephosphorus atoms in those models were taken from crystal structures de-termined by Thurn and Krebs.[3a] Free phosphorus valences were saturat-ed with hydrogen atoms, the positions of which were optimized at theDFT BP86[19] GGA level with Ahlrich�s def2-SVP[18] basis set (conver-gence criterion 10�7 EH, integration grid m4[28]) by employing the RI ap-proximation.[29] The calculations of the chemical shifts were also per-formed with the BP86 functional and the triple-zeta plus polarization(TZVP)[20] or def2-SVP basis sets using the GIAO approach.[30] The useof the GGA functional results in a diagonal magnetic Hessian matrixthat remarkably reduces the computational effort.[31] Chemical shifts arereported relative to H3PO4 by subtracting the calculated magnetic shield-ings of the different phosphorus positions from the calculated shieldingof phosphoric acid on the discussed level of theory (sH3PO4

ACHTUNGTRENNUNG(TZVP)=

288.75 ppm, sH3PO4(def2-TZVP) =262.12 ppm, sH3PO4

ACHTUNGTRENNUNG(def2-SVP) =

361.88 ppm). LMOs were obtained by using the Foster-Boys localizationscheme[23] as implemented in an in-house program (due to technical reas-ACHTUNGTRENNUNGons, these studies were performed on a simplified model by using thedef2-SVP basis set, see Figure 6b).

Acknowledgements

This work was supported by the Sonderforschungsbereich SFB 858 (“Co-operative Systems in Chemistry”) and by DFG grant Ec168/10-1 (“Supra-molekulare Aggregationen”). T.W. thanks the NRW Graduate School ofChemistry for additional support and the Fonds der Chemischen Indus-trie for a personal fellowship.

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Received: December 10, 2010Published online: June 10, 2011

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H. Eckert, S. Grimme et al.