On the energetics of P – P bond dissociation of sterically strained tetraamino-diphosphanes †

The homolytic P–P bond fission in a series of sterically congested tetraaminodiphosphanes (R2N)2P–P(NR2)2 ({4}2–{9}2, two of which were newly synthesized and fully characterized) into diaminophosphanyl radicals (R2N)2P • (4–9) was monitored by VT EPR spectroscopy. Determination of the radical concentration from the EPR spectra permitted to calculate free dissociation energies ΔG Diss as well as dissociation enthalpies ΔHDiss and entropies ΔSDiss, respectively. Large positive values of ΔG Diss indicate that the degree of dissociation is in most cases low, and the concentration of persistent radicals – even if they are spectroscopically observable at ambient temperature – remains small. Appreciable dissociation was established only for the sterically highly congested acyclic derivative {9}2. Analysis of the trends in experimental data in connection with DFT studies indicate that radical formation is favoured by large entropy contributions and the energetic effect of structural relaxation (geometrical distortions and conformational changes in acyclic derivatives) in the radicals, and disfavoured by attractive dispersion forces. Comparison of the energetics of formation for CC-saturated N-heterocyclic diphosphanes and the 7π-radical 3c indicates that the effect of energetic stabilization by π-electron delocalization in the latter is visible, but stands back behind those of steric and entropic contributions. Evaluation of spectroscopic and computational data indicates that diaminophosphanyl radicals exhibit, in contrast to aminophosphenium cations, no strong energetic preference for a planar arrangement of the (R2N)2P unit.


Introduction
Kinetic stabilisation by sterically demanding substituents is an immensely useful concept which has played a key role in the advancement of modern organometallic and molecular inorganic chemistry and permitted the preparation of many new classes of isolable or persistent compounds. 1 A distinct example of previously unknown, kinetically stabilised species in main-group element chemistry are long-lived neutral pnictyl radicals R 2 E • (E = P, As). 2 The first specimens, 1 and 2 (Scheme 1), were generated in 1976 by Lappert et al. via reduction of chlorophosphane or chloroarsane precursors and identified as persistent radicals with half-lives t 1/2 > 1 month at 20°C by EPR spectroscopy. 3 Building on this pioneering work, to date arsanyl and phosphanyl radicals with a wider selection of bulky alkyl, aryl or amino substituents have been characterized. 4,5 Apart from some recent reports on stable phosphanyl radicals that were isolated and fully characterized in the crystalline state, 4f,h,i the monomers exist generally only in the gas phase or in solution but are dimerized when solid. 4c,d,g,j,l,6 In several cases, temperature dependent equilibria between phosphanyl radicals and their dimers (Scheme 1) were detected spectroscopically in solution, and the observed prevalence of diphosphanes at low temperatures was interpreted as reflecting the gain in enthalpy and the loss in entropy associated with the dimerization under P-P bond formation. 4c,e,g,j-l Detailed studies on the structural aspects of the dimerization of persistent pnictyl radicals were performed on 1 and the N-heterocyclic phosphanyl radical 3c. Comparison of the molecular geometries of 1P, 1As (as determined by gas phase electron diffraction) and their dimers {(Me 3 Si) 2 CH} 2 E-E{CH-(SiMe 3 ) 2 } 2 ({1P} 2 , E = P and {1As} 2 , E = As) revealed that the dimerization is accompanied by bond angle distortions in the alkyl groups and a reorientation of the CH(SiMe 3 ) 2 substituents in a R 2 E unit from a syn,syn-conformation in the radicals to a syn,anti-conformation in the dimers. Backed by computational studies, 6,7 these changes were interpreted as indicating that the dimers in the crystal are loaded with a substantial amount of steric strain energy. The possibility to discharge the strain upon release of the molecule from the crystal lattice was seen as a strong driving force for the formation of monomers in solution or the gas phase, and led to a description of 1 as "Jack-in-the-box molecules". 6 In a recent computational analysis 8 of the dimerization of 1 it was emphasized that a realistic description of the energetics of this process requires also the consideration of dispersion forces: neglecting dispersion, the energy required for P-P bond homolysis was predicted insufficient to offset the stabilizing effect of structural relaxation in the radicals, and it is only due to the dispersive attraction between the radicals that dimer formation is energetically favoured.
A different source of energetic stabilization was discussed for the N-heterocyclic radicals 3: based on a comparison of EPR hyperfine couplings to the 31 P and 14 N nuclei and computational evidence, Wright et al. 4g concluded that the spin density is not mainly phosphorus-based as in other phosphanyl radicals, but rather delocalized over the heterocycle. They described these species consequently as 7π-radicals and postulated that their creation from the corresponding dimers should be facilitated by a combination of steric effects (repulsion between bulky substituents) and electronic stabilization by π-delocalization. In accord with this hypothesis, formation of persistent radicals 3c from dissociation of the isolable dimer {3c} 2 was observed at exceedingly mild conditions (room temperature) in solution, 4g and an experimental evaluation of the energetics of the P-P bond homolysis of the dimer {3c} 2 gave a dissociation enthalpy ΔH Diss of 79 kJ mol −1 , 4k well below the average P-P bond enthalpy of 201 kJ mol −1 . 9 Computationally, the dissociation energies were greatly underestimated when dispersion forces were neglected (cf. an unrealistically low calculated dissociation energy of ≈3 kJ mol −1 for a N-Me substituted model dimer {3d} 2 ), 4g and overestimated when dispersion effects were included (cf. ΔH diss,calc = 95.8 kJ mol −1 for {3d} 2 and 129.9 kJ mol −1 for {3c} 2 at the ωB97X-D/cc-pVDZ level of theory). 4k Summarizing the available knowledge on persistent phosphanyl (and arsanyl) radicals, it becomes clear that their common property is the stabilization against dimer formation or further reaction 4k by sterically crowded substituents. The factors controlling this stabilization have been extensively studied for a few representatives (mainly 1), but there are still many open questions which address, e.g., the interplay of steric and electronic stabilizing effects in 3 and related cyclic or open diaminophosphanyl radicals. Improving our understanding of these factors is needed in order make better use of the still underdeveloped potential of the persistent radicals in synthesis, but also to deepen our insight into the reactivity and thermal stability of E-E-bonded frameworks, and the tuning of these qualities by steric strain. Furthermore, considering that the results of computational studies seem to depend strongly on the computational model applied, 4g,k,8 an experiment based research approach seems highly desirable in order to provide an unbiased reference point. We report here on the extension of a previous experimental study on the dissociation energetics of the diphosphane {3c} 2 4k to include compounds featuring both N-heterocyclic ({4} 2 , {5} 2 , Scheme 2) and acyclic ({6} 2 -{9} 2 ) molecular frameworks, and a discussion of the results in the light of computational studies.

Results and discussion
Synthesis and characterization of sterically crowded tetraaminodiphosphanes and diaminophosphanyl radicals Diphosphanes {4} 2 -{6} 2 were prepared by reductive coupling of appropriate chlorophosphane precursors using previously published procedures. 4j,k,10 In case of {7} 2 , the reported protocol 4c was modified by using sodium naphthalenide instead of potassium graphite as reducing agent. Finally, {8} 2 and {9} 2 were obtained analogously by reduction of the chlorophosphane precursors with magnesium or sodium (Scheme 3). Both new compounds were characterized by elemental analyses, spectral data, and single-crystal X-ray diffraction studies. ‡ The individual molecules in crystalline {8} 2 ( Fig. 1) display crystallographic C i -symmetry and exhibit therefore a staggered conformation in which both the two R 2 P moieties as a whole and the two pairs of Et 2 N and TMP substituents are mutually trans to each other. The nitrogen atoms adopt planar or near planar coordination geometries (sum of bond angles 360.0(4)°a t N8 and 353.5(4)°at N2), and the coordination planes around these atoms are strongly twisted with respect to the Scheme 2 Diphosphanes included in this study. ‡ Crystallographic data of the chlorophosphane 9_Cl (the precursor of {9} 2 ) are found in the ESI. † central NPN plane (skew angles § 62°for the TMP and 80°for the Et 2 N substituent). The molecules in crystalline {9} 2 feature a pseudo-ecliptic alignment of the R 2 P units ( Fig. 2) in which the P-N bonds to the TMP substituents lie nearly in one plane (dihedral angle N(2)-P(1)-P(1′)-N(2′) 1.2(3)°) and the piperidine rings are adjacent to each other. The resulting arrangement comes close to C 2 -symmetry. As in {8} 2 , the coordination geometry at the nitrogen atoms is quasi-planar (sum of bond angles 357.0(9)-359.2(9)°). The skew angles between the NPN unit and the iPr 2 N-substituent of ca. 83°a re similar as in {8} 2 whereas the skew of the TMP ring is less pronounced (skew angles ca. 53°).
The P-P distance in {8} 2 falls into the range known for other strained symmetrical diphosphanes (Table 1) whereas that in {9} 2 exceeds even the longest distances reported so far (2.320-2.321 Å in {3c} 2 and {4} 2 ) 4j,k by more than 3 pm. A reasonable explanation for the extreme bond lengthening may be seen in the pseudo-ecliptic conformation which is most likely enforced by the steric requirements of the substituents and maximizes the Pauli-repulsion between P-N bonds and lone-pairs ¶ at adjacent phosphorus atoms.
The 31 P spectra of {8} 2 display two singlets with slightly unequal intensity, and the 1 H and 13 C NMR spectra contain two sets of signals of Et 2 N and tetramethylpiperidyl (TMP) substituents. Similar features had also been observed for {7} 2 4c and indicate the presence of a mixture of meso-and rac-diastereomers with different stereochemical configuration at the phosphorus atoms in solution. A 31 P NMR spectrum of {9} 2 recorded at −80°C shows likewise two signals which coalesce, however, to a single line at higher temperature. The 1 H and 13 C NMR spectra display also intricate temperature dependent coalescence phenomena. In addition, a new, extremely broad resonance (Δν 1/2 = 7100 Hz at r.t., cf. Fig. S3 in the ESI †) grows in when the temperature is raised and reversibly disappears upon cooling. We attribute this signal to radical 9, the presence of which was independently proven by EPR spectroscopy (see below). Altogether, the observed spectral changes indicate the simultaneous occurrence of two dynamic processes, viz. reversible equilibration between {9} 2 and two radicals 9 (which enables also interconversion between rac-and meso-{9} 2 ), and freezing of the TMP ring inversion at low temperature. It should be noted that there is ample literature precedence    for the spectroscopic observation of equilibration between persistent phosphanyl radicals and their dimers, 4c,e,j-l but {9} 2 is to the best of our knowledge the first example where the coexistence of both reactants has been established by NMR spectroscopy. Direct characterization of radicals was feasible by recording EPR spectra of solutions of {4} 2 -{9} 2 in inert solvents (hexane, toluene). The signals of the radicals were readily observed at ambient (4, 9) or elevated temperature (5-8) and analysed by simulation using the EasySpin 12 program ( Table 2).
The spectral parameters of 4, 5 and 7 match previously published data. 4a,c,j,l All signals are split into multiplets due to hyperfine coupling with the nuclear spins of the 31 P (I = 1/2) and one (7)(8)(9) or two (4-6) 14 N (I = 1) nuclei. In some cases, additional couplings to remote 1 H or 29 Si nuclei are resolved. The hyperfine couplings to phosphorus (60-84 G) are larger than in 3c (a( 31 P) = 42 G 4k ) and cover roughly the lower half of the range of couplings (63-108 G 2a ) in known phosphanyl radicals. The absence of resolved hyperfine coupling to one 14 N nucleus in 7 had been previously noted and was attributed to the fact that couplings to nitrogen atoms in silylaminogroups are usually unobservable, 4a,c presumably since their steric bulk prevents a coplanar orientation of the phosphorus and nitrogen coordination planes. 2a The spectra of 8, 9 reveal, however, that unequal a( 14 N) couplings are also observable in dialkylamino-substituted phosphanyl radicals and the absence of resolved coupling to 14 N is thus not specific for silylamino groups.
Computational studies on different conformers of 6-9 confirm the expectation 2a,4a that the spin density resides mainly in the phosphorus p-orbital and reveal further that its delocalization on the nitrogen atoms shows a marked conformational dependence that is largely independent of substituent type ( Fig. 3 and Table 3): maximum values of the spin density, and hence the hyperfine coupling constant (a( 14 N) 5-6 G), are found when the coordination planes at the phosphorus and nitrogen atoms are coplanar, and minimum values (|a( 14 N)| < 1 G) when they are close to perpendicular.
Based on this correlation, we can confirm the association of the large hyperfine coupling in 7 with the NiPr 2 group 4a,c and conclude further that the splittings in the spectra of 8,9 arise from interaction with the NR 2 (R = Et, iPr) groups and the coupling to the TMP substituent is unresolved. The observation that a( 14 N) in 4-6 is smaller than in 7-9 ( Table 2) may be attributable to the presence of librational motion of the R 2 N-groups in the real molecules which cannot be reproduced computationally. However, the calculations support the earlier conjecture 4g that the reduction of a( 31 P) and simultaneous increase of a( 14 N) in 3c coincides with extended delocalization of the spin density over the complete ring (Fig. 3).

Thermochemistry of diphosphane dissociation
Thermochemical parameters for the dissociation of the diphosphanes according to R 2 P-PR 2 ⇄ 2 R 2 P • may be derived from the temperature dependent variation of the equilibrium con- , and a second conformer of 9 with skewed alignment of R 2 N-groups (bottom right; skew angles 69°and 59°). The two conformers of 9 illustrate the dependence of N-centred spin density on skew angles. The drawn isodensity surfaces include 75% of the total spin density.
. The latter can be determined by measuring the radical concentration in a sample prepared by dissolution of a known amount of solid diphosphane, and then back-calculating the actual concentration of the diphosphane in solution. The radical concentration is readily obtained from the double integral of the EPR signal in relation to that of a reference sample with a known number of spins. 12 Following this approach, we determined the concentration of radicals 4-9 in solutions of {4} 2 -{9} 2 against a calibrated sample of ultramarine blue by using a previously published procedure. 4k A summary of the thermochemical parameters derived from these measurements is given in Table 4, and a detailed account is contained in the ESI. † Evaluation of the data in Table 4 reveals that although the radicals 4-9 are spectroscopically readily observable as persistent species at ambient or elevated temperature, the dissociation equilibria lie in all cases but {9} 2 extensively on the side of the diphosphanes, and the dissociation affects generally far less than 1% of the dimers even at temperatures as high as 120°C. In case of {9} 2 , the calculated degree of dissociation for a solution of 1 mM initial concentration of 0.65(5) at 295 K clearly exceeds the value of 0.063 (7) for 3c, and attests that radicals predominate under these conditions. The observation of a large variability in ΔH Diss and ΔS Diss reveals, however, that structural changes have nonetheless a significant impact on the energetics of the bond fission. Comparing the dissociation energetics of {4} 2 and {5} 2 with that of {3c} 2 shows that introduction of the CC double bond goes along with a decrease in ΔH Diss by some 23-25 kJ mol −1 . In view of the presence of identical or at least similar substituents in all species, attractive dispersion forces between the two R 2 P fragments in the dimers are not expected to change greatly, and the lower dissociation enthalpy for {3c} 2 is thus considered to reflect mainly the postulated 4g extra stabilization of radical 3c by π-delocalization effects.
It should be noted, however, that the exceptional dissociation tendency of {3c} 2 (as evidenced by the drastic decrease of ΔG 295 Diss as compared to {4} 2 and {5} 2 ) is not attributable to the enthalpy lowering alone, but is assisted by a simultaneous large increase in the entropic term. Since the translational contribution to the reaction entropy is identical in all cases, this change implies that the loss of internal conformational flexibility associated with radical dimerization must increase significantly from 5 over 4 to 3c. Without going into detail, we presume that the difference between the last two species owes to the rigidity of the unsaturated heterocyclic ring in 3c, which severely reduces the conformational freedom of the N-aryl groups. The further shift of the dissociation equilibrium to the side of the dimer in case of {5} 2 is exclusively attributable to the change in ΔS Diss and may be qualitatively explained by assuming that the restrictions in the conformational freedom upon dimerization decrease with the number of bulky o-alkyl substituents in the N-aryl moieties.
Aggravating conformational restrictions with increasing steric demand of substituents may also help to rationalize the observation that the values of ΔS Diss in the acyclic diphosphanes {7} 2 -{9} 2 exhibit comparable changes as in the heterocycles 3c-5. Apart from that, the dissociation enthalpies are for {7} 2 , {8} 2 by some 5-10 kJ mol −1 lower than for {4} 2 , {5} 2 , and display a further sharp decrease in case of {9} 2 where ΔH Diss is even smaller than for {3c} 2 . While this last finding is deemed to reflect the exceptional degree of strain that had already become evident in the extreme P-P bond lengthening and enforcement of the energetically unfavourable pseudo-ecliptic conformation, the reason for the low dissociation enthalpies in {7} 2 and {8} 2 is at first glance less obvious. We assume, however, that their increased conformational flexibility enables the acyclic (R 2 N) 2 P moieties to yield to the steric congestion upon dimerization as in the case of {1P} 2 6 and {7} 2 4d by a distortion of dihedral angles that loads the dimers with some extra steric strain energy. Since the release of this energy during dissociation in a "Jack-in-the-box" manner 6 amounts to a relative stabilization of the radicals, this effect is suitable to explain the reduction of ΔH Diss in comparison to the cyclic derivatives where the conformational constraints of the ring render such structural relaxation unfeasible.
Last, but not least, {6} 2 shows the largest value of ΔH Diss of all derivatives in this study which is, however, compensated by an unusually high entropic contribution that must be seen as main driving force of the dissociation. Whereas the large dissociation enthalpy is not unexpected if one considers that the moderately sized N-alkyl groups seem inappropriate for loading the dimer with a large amount of strain energy, we have currently no good explanation for the atypically large entropy term.

Computational studies
In order to validate our hypotheses on the origin of the trends in dissociation enthalpies and improve our understanding of the bond fission process, we performed computational studies of the dissociation reactions of {4} 2 -{9} 2 . Acknowledging that a realistic description of molecular structures and energetics requires inclusion of long-range and dispersion interactions, 4k,8 all calculations were carried out at the ωB97x-D/cc-pVDZ level which had been previously shown to give an appropriate description of the molecular structure of {3c} 2 . 4k Mole-  (Table 5) and experimental (Table 1) P-P distances for the remaining compounds yields a liner relation P-P calc = 0.95 P-P exp + 0.11 Å (R 2 = 0.93). The computations reproduce also the molecular conformation of 7 determined by gas phase electron diffraction. 4d Comparing the geometries of the (R 2 N) 2 P units in radicals and diphosphanes reveals that formation of N-heterocyclic radicals is mainly associated with a deformation of bond angles at the nitrogen atoms, whereas formation of acyclic species involves also appreciable conformational changes (see Fig. S12 †). Energies (including corrections for zero point vibrational energy, ΔE zpe ) and (free) enthalpies (ΔH 298 , ΔG 298 ) for the dissociation reactions were computed with the inclusion of basis set superposition errors as determined from counterpoise calculations and are listed in Table 5. In addition, we computed also a decomposition 13 of the total reaction energy into a fragmentation energy ΔE frag (the negative of the interaction energy 13 E int between two radical fragments having the same geometry as the R 2 P units in the dimer) and a relaxation energy ΔE relax (the energy released upon relaxation of the distorted radicals to their equilibrium geometry, i.e. the negative of the preparation energy 13 ΔE prep ).
Comparison of absolute values and trends in computed (ΔH 298 ) and experimental (ΔH Diss ) dissociation enthalpies (Fig. 4) reveals a reasonable match for N-alkyl-/silyl-substituted diphosphanes ({6} 2 -{9} 2 ) while the dissociation enthalpies of N-aryl derivatives ({3c} 2 -{5} 2 ) are clearly overestimated in the computations (as had already been noted for 3c 4k ).k A similar result emerges for comparison of ΔE zpe with ΔH Diss (Fig. 4). While it is known that most density functionals have problems with a proper description of the difference in intermolecular binding energies between aromatic and aliphatic moieties, 14 a deviation of some 50 kJ mol −1 as found here is far too large to refer to this explanation, and we are currently unable to provide a consistent rationalization for this effect.
Computed free enthalpies ΔG 298 (Table 5) are generally much smaller than the experimental values (Table 4), which is mainly due to the fact that the computations heavily overestimate the entropy terms. This deviation may in part reflect the difference between gas phase and solution (it has been claimed that the entropy contribution to ΔG in solution at room temperature is roughly half of that in the gas phase 15 ) and had been noted previously. 4k With the exception of {6} 2 , which we consider an outlier, a comparison between computed and experimental free enthalpies gives a similar result as had already been observed for the enthalpies (Fig. 4).  Table 5 Bond distances (P-P in Å) and energy data (all quantities in kJ mol −1 ) for the dissociation reaction R 2 P-PR 2 ⇄ 2R 2 P • (R 2 P = 3c, 4-9) computed at the ωB97x-D/cc-pVDZ level of theory k A similar deviation between calculated bond enthalpies/energies of N-alkyl/ silyl-and N-aryl-substituted diphosphanes was also found at the M06-2X/cc-pVDZ level.
The results of the energy decomposition analysis listed in Table 5 indicate that the variations in ΔE frag are not only much smaller than those of the total energy term (ΔE zpe or ΔH 298 ), but show also a different response to structural changes. With the exception of {3c} 2 (where a contribution from electronic stabilization by π-delocalization must be taken into account), ΔE frag in both N-heterocyclic and acylic compounds dwindles with increasing steric demand of the substituents, which suggests that its variation reflects mainly the bond weakening or strengthening associated with the modulation of repulsive interactions between bulky peripheral groups. Given that the P-P bond lengthening in sterically congested diphosphanes is commonly ascribed to the same origin, 8 it is not surprising that the changes in ΔE fragunlike those in the total energy terms (ΔE zpe or ΔH 298 ) or experimentally determined enthalpies ΔH Disscorrelate with the variation in P-P distances (Fig. 5). Even if a clear-cut partitioning between 'intrinsic' bond energy and strain energy in congested molecules is not a trivial task, 7 we conclude that ΔE frag can serve as anat least approximatemeasure of P-P bond strength. Since the values of ΔE frag come close to the average P-P bond enthalpy 9 of 201 kJ mol −1 and approach the dissociation energies of sterically uncongested diphosphanes (239-368 kJ mol −1 for R 2 P-PR 2 with R = H, Et, F, Cl, I 16 ), the P-P bonds in {3c} 2 -{9} 2 cannot be considered as intrinsically particularly weak. It must be conceded, however, that as in case of 1 8 attractive dispersion forces (epitomized by the empirical dispersion term E D ) make a considerable contribution to the total adhesion energy. This contribution is clearly dominant for {3c} 2 and {4} 2 where it represents 70-80% of the fragmentation energy.
The relaxation energies ΔE relax which stabilize the radicals 3c-9 through structural adaptation and conformation changes are, like in 1P, 8 smaller than the fragmentation energies, but with 20-60% of the magnitude of ΔE frag still substantial. Furthermore, the variation between different radicals (ΔΔE relax = 80.5 kJ mol −1 ) is twice as large as that of the fragmentation energies (ΔΔE frag = 41.0 kJ mol −1 ) and must thus be seen as the dominant energetic contribution in explaining the trend in dissociation energies between different diphosphanes. Structural relaxation of the acyclic radicals 6-9 provides generally a larger energy release (ΔE relax 80-122 kJ mol −1 ) than relaxation of the N-heterocyclic species 3c-5 (ΔE relax 41-60 kJ mol −1 ) and is associated with additional conformational changes (Fig. S12 in the ESI †). These findings support at first glance the perception of the dimers {6} 2 -{9} 2 as sterically strained "Jack-in-thebox" molecules which can release their strain energy by undergoing geometrical and conformational adaptation during dissociation. However, we must also consider that the variation in skew angles or the pyramidalization of NR 2 groups associated with a conformational change may affect the spin density delocalization, and thus the electronic stability, of the radicals. In order to assess the importance of these effects, we analysed the conformational preferences of the parent diaminophosphanyl radical (H 2 N) 2 P • (10 • ) and the appropriate cation [(H 2 N) 2 P + ] (10 + ), assuming that the impact of steric constraints is in these species negligible and any changes will be dominated by electronic effects. Geometry optimizations were carried out using DFT (B3LYP with (aug)-cc-pVDZ and aug-cc-pVTZ basis sets) and coupled cluster (CCSD/aug-cc-pvdz) methods. The results did not differ significantly, and we will only discuss those of the CCSD calculations (Fig. 6).
The cation 10 + exhibits, as expected, a C 2v -symmetrical planar geometry with rather short PN distances of 1.643 Å. Geometry optimization of a conformer obtained by rotation of one NH 2 group by 90°led to the localization of a transition state 17.8 kJ mol −1 higher in energy than the ground state. The 'orthogonal' amino substituent is characterized by a lengthened PN bond (1.715 vs. 1.632 Å for the 'in plane' NH 2 group) and a slightly pyramidal geometry at the N-atom. The computational results are in accord with the established view of aminophosphenium ions 17,18 as delocalized, allyl-anion analogue π-systems in which rotation of NR 2 groups (which partially disrupts the π-delocalization) is impeded by a significant energy barrier. In contrast, radical 10 • features a non-planar, C 2 -symmetrical ground state geometry with twisted orientation of the NH 2 groups (skew angle 30°), pyramidal coordination at the N-atoms (sum of bond angles 343°) and lengthened PN bonds (1.752 Å). The search for a rotational transition state yielded a C 1 -symmetrical geometry in which the average PN distance remains essentially unchanged (PN 1.773, 1.737 Å,  average 1.755 Å) and the pyramidalization in the 'orthogonal' NH 2 group increases further (sum of bond angles at N 331°). The transition state energy lies by merely 2.0 kJ mol −1 above that of the ground state, indicating that the energetic barrier to NH 2 -group rotation is negligible and the geometrical changes associated with this process do not affect radical stability. This pronounced difference to the cation is easily rationalized if one considers that placement of an extra electron in the (PN-antibonding) LUMO of the cation reduces the π-bond order, and thus the available stabilization from π-delocalization. Consequently, the remaining interaction between an unpaired electron on the P-atom and the nitrogen lonepairs in aminophosphanyl radicals should be better described as hyperconjugative, and its tuning by rotational reorientation of NH 2 (or NR 2 ) groups offersunlike as in aminophosphenium ions 17only minor opportunities for electronic (de) stabilization.
The computational studies on 10 + and 10 • imply that the orientational preorganisation of phosphorus p-orbitals and nitrogen lone-pairs which arises from embedding of an NPN into a five-membered heterocycle 18,19 offers an energetic advantage for aminophosphenium cations, but not for radicals, and that the NPN unit of the latter provides, apart from possible constraints imposed by a cyclic molecular structure, no further restoring force to maintain local planarity. We are thus prompted to conclude that the structural reorganization of the radicals formed during dissociation of tetraaminodiphosphanes is not associated with any extra electronic stabilization of the unpaired electron, but is essentially driven by steric factors. In turn, the inhibition of structural relaxation by a geometrical constraining cyclic structure must be considered to have an adverse effect on dissociation enthalpies, which helps to explain why P-P bond fission is slightly more endothermic for the heterocyclic dimers {3c} 2 -{5} 2 than for {7} 2 -{9} 2 .

Conclusions
Thermochemical data for the homolytic P-P bond fission of a series of sterically congested diphosphanes (two of which were newly synthesized and fully characterized) were determined. The values of free reaction energies ΔG 295 Diss and pK 295 Diss indicate that the dissociation affects in most cases only a small fraction of the diphosphanes, and the concentration of persistent radicalseven if they may be spectroscopically observable at ambient temperatureremains small. A notable exemption is {9} 2 where the degree of dissociation (for a 1 mM solution at 295 K) is by an order of magnitude larger than for the N-heterocyclic diphosphane {3c} 2 . The acyclic radical 9 must thus be considered as even more stable than 3c which benefits from electronic stabilization by π-delocalization. 4g Analysis of trends in experimental data in connection with computational studies allowed us to relate the variations in ΔG 295 Diss /pK 295 Diss to both enthalpy and entropy effects. Stabilization of radicals relative to dimers with a concomitant decrease in dissociation enthalpies ΔH Diss is mainly due to structural relaxation (adaptation of bond angles andfor the acyclic species 6-9conformational changes) and driven by the need to minimize steric congestion. Electronic stabilization by P,N-π-conjugation, which is crucial for aminophosphenium cations, 17,18 is hardly of importance for aminophosphanyl radicals, and the energetic effect of cyclic π-delocalization in 3c is visible but stands back. The radical stabilizing influences are offset by strong attractive dispersion forces, which are once more 8 confirmed as crucial for the prevalence of diphosphanes. Entropic factors driving the dissociation can be qualitatively related to the gain of conformational flexibility in the radicals, although their origin is not yet understood in detail and cannot be adequately modelled computationally. Still, the supplement of the enthalpic stabilization of the radicals by a particularly large entropic contribution must be seen as decisive for the extensive dissociation of {9} 2 (and {3c} 2 ).
It should be noted that our results are in principle in accord with the results of a computational study on the dimerization of the radicals 1 8 stating that the monomerdimer equilibrium is predominantly governed by the balance of attractive dispersion forces and entropic factors. However, the results presented here emphasize that the different aspects of structural relaxation (in particular the conformational changes enabling "Jack-in-the-box" behaviour 6 ) are also vital for the explanation of the trends in dissociation enthalpies and entropies between different molecules. Furthermore, it appears that computational models tend to overestimate the entropy term associated with the diphosphane dissociation, and yield thus free reaction energies which are systematically too low.

Materials and methods
All manipulations were carried out under dry argon. Solvents were dried by standard procedures. NMR spectra were recorded on Bruker Avance AV 400 or AV 250 instruments ( 1 H: 400.1/ 250.0 MHz, 13 C: 100.5/62.9 MHz, 31 P: 161.9/101.2 MHz); chemical shifts were referenced to ext. TMS ( 1 H, 13 C), 85% H 3 PO 4 (Ξ = 40.480747 MHz, 31 P). Elemental analyses were carried out using an Elementar Micro Cube. Melting Points were determined with a Büchi B-545 melting point apparatus in sealed capillaries. EPR spectra were measured with a Bruker EMX X-band spectrometer. Hyperfine splittings were determined by spectral simulation with the program EasySpin. 12 Quantitative EPR measurements and evaluation of thermochemical data from the spectral data were carried out using the same protocol that had been applied in case of {3c} 2 . A detailed description has been given elsewhere. 4k Chlorophosphane precursors (iPr 2 NPCl 2 , 19 (Me 3 Si) 2 N(iPr 2 N)-PCl, 4a (iPr 2 N) 2 PCl, 20 and (TMP)(iPr 2 N)PCl 21 ) and the diphosphanes {4} 2 , 4j {5} 2 4l and {6} 2 , 10 were prepared as described elsewhere. Diphosphane {7} 2 was prepared by a modification of the reported procdure, 4c using sodium naphthalenide instead of potassium graphite as reducing agent.

Synthetic procedures
Chloro(diethylamino)(2,2,6,6-tetramethylpiperidyl)phosphane 8_Cl. nBuLi (4.5 mL of a 2.3 M solution in hexane, 10.50 mmol) was added dropwise at −78°C to a solution of 2,2,6,6-tetramethylpiperidine (1.80 mL, 10.50 mmol) in THF (10 mL). The mixture was then allowed to warm to room temperature and stirred for 30 min. This solution was then added dropwise to a cooled (−78°C) solution of Et 2 NPCl 2 (1.83 g, 10.50 mmol) in THF (15 mL). The reaction mixture was allowed to warm to room temperature and stirred overnight. Volatiles were then removed under reduced pressure. The residue was extracted with 15 mL hexane and filtered. The filtrate was evaporated to dryness under reduced pressure and the resulting orange oil used without further purification. 1,2-Bis(diisopropylamino)-1,2-bis(2,2,6,6-tetramethylpiperidyl)diphosphane {9} 2 . Blank pieces of sodium (excess) were added to a solution of TMP(iPr 2 N)PCl (1.51 g, 4.9 mmol) in 10 mL of hexane which had previously been degassed using the pumpand-freeze technique. The mixture was then heated for 7 h at 48°C in an ultrasound bath, allowed to cool to ambient temperature, and filtered. The filtrate was evaporated to dryness and the residue sublimated in vacuum (10 −3 mbar, 90°C) to give the product as colourless solid. Yield 33%. -M.p. 86°C.

Crystal structure determinations
Diffraction studies were carried out using a Bruker diffractometer equipped with an Kappa APEX II Duo CCD-detector and a KRYO-FLEX cooling device with Mo-K α radiation (λ = 0.71073 Å) at T = 100 K. The structures were solved by direct methods (SHELXS-97 22a ) and refined with a full-matrix leastsquares scheme on F 2 (SHELXL-2014 22b ). Semi-empirical absorption corrections were applied for all structures. Nonhydrogen atoms were refined anisotropically, and H atoms with a riding model, on F 2 . Details of the crystal structure determinations are listed in Table 6. For {9} 2 , the absolute structure parameter 22c was refined as x = 0.00 (10). Details of the crystal structure determinations are listed in Table 6 (for 9_Cl in the ESI †).