hexaphosphabenzene

File:((CpMo)2(P6)).png₅C₅)Mo}₂(μ,η⁶-P₆)|203x203px]]

Isolation of hexaphosphabenzene was first achieved within a triple-decker sandwich complex in 1985 by Scherer et al. Amber coloured, air-stable crystals of [{(η⁵-Me₅C₅)Mo}₂(μ,η⁶-P₆)] are formed by reaction of {{chem2|[CpMo(CO)2_{/}3]2}} with excess {{chem2|P4}} in dimethylbenzene, albeit with a yield of approximately 1%.{{Clarification needed|What is "Cp"? What is "[CpMo(CO)2/3]2"?|date=August 2022}}{{Cite journal|last1=Scherer|first1=Otto J.|last2=Sitzmann|first2=Helmut|last3=Wolmershäuser|first3=Gotthelf|date=1985|title=Hexaphosphabenzene as Complex Ligand|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.198503511|journal=Angewandte Chemie International Edition in English|volume=24|issue=4|pages=351–353|doi=10.1002/anie.198503511|issn=1521-3773}}{{Cite journal|last1=Meier|first1=Herbert|last2=Zeller|first2=Klaus-Peter|date=1975|title=The Wolff Rearrangement of α-Diazo Carbonyl Compounds|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.197500321|journal=Angewandte Chemie International Edition in English|language=en|volume=14|issue=1|pages=32–43|doi=10.1002/anie.197500321|issn=1521-3773}} The crystal structure of this complex is a centrosymmetric molecule, and both five-membered rings as well as the central bridge-ligand {{chem2|P6}} ring are planar and parallel. The average P–P distance for the hexaphosphabenzene within this complex is 2.170 Å.{{Cite journal|last=Scherer|first=Otto J.|date=2000|title=Small Neutral Pn Molecules|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291521-3773%2820000317%2939%3A6%3C1029%3A%3AAID-ANIE1029%3E3.0.CO%3B2-6|journal=Angewandte Chemie International Edition|volume=39|issue=6|pages=1029–1030|doi=10.1002/(SICI)1521-3773(20000317)39:6<1029::AID-ANIE1029>3.0.CO;2-6|pmid=10760912|issn=1521-3773}}

Thirty years later, Fleischmann et al. improved the synthetic yield of [{(η⁵-Me₅C₅)Mo}₂(μ,η⁶-P₆)] up to 64%. This was achieved by increasing the reaction temperature of the thermolysis of {{chem2|[CpMo(CO)2_{/}3]2}} with {{chem2|P4}} to approximately 205 °C in boiling diisopropylbenzene, thus favouring the formation of [{(η⁵-Me₅C₅)Mo}₂(μ,η⁶-P₆)] as the thermodynamic product.{{Cite journal|last1=Fleischmann|first1=Martin|last2=Dielmann|first2=Fabian|last3=Gregoriades|first3=Laurence J.|last4=Peresypkina|first4=Eugenia V.|last5=Virovets|first5=Alexander V.|last6=Huber|first6=Sebastian|last7=Timoshkin|first7=Alexey Y.|last8=Balázs|first8=Gábor|last9=Scheer|first9=Manfred|date=2015|title=Redox and Coordination Behavior of the Hexaphosphabenzene Ligand in [(Cp*Mo)2(μ,η6:η6-P6)] Towards the "Naked" Cations Cu+, Ag+, and Tl+|journal=Angewandte Chemie International Edition|language=en|volume=54|issue=44|pages=13110–13115|doi=10.1002/anie.201506362|issn=1521-3773|pmc=4675074|pmid=26337857}}

Several analogues of this {{chem2|P6}} triple‐decker complex where the coordinating metal and η⁵-ligand has been varied have also been reported. These include {{chem2|P6}} triple‐decker complexes for Ti, V, Nb, and W, whereby the synthetic method is still based on the originally reported thermolysis of {{chem2|[CpM(CO)2_{/}3]2}} with {{chem2|P4}}.{{Cite journal|last1=Herberhold|first1=Max|last2=Frohmader|first2=Gudrun|last3=Milius|first3=Wolfgang|date=1996-09-20|title=Neue vanadium-komplexe mit substituentenfreien phosphorliganden|journal=Journal of Organometallic Chemistry|language=de|volume=522|issue=2|pages=185–196|doi=10.1016/0022-328X(96)06305-X|issn=0022-328X}}{{Cite journal|last1=Scherer|first1=Otto J.|last2=Schwalb|first2=Joachim|last3=Swarowsky|first3=Herbert|last4=Wolmershäuser|first4=Gotthelf|last5=Kaim|first5=Wolfgang|last6=Gross|first6=Renate|date=1988-03-01|title=Tripeldecker-Sandwichkomplexe mit cyclo-P6-Mitteldeck|url=https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cber.19881210309|journal=Chemische Berichte|volume=121|issue=3|pages=443–449|doi=10.1002/cber.19881210309|issn=0009-2940}}{{Cite journal|last1=Scherer|first1=Otto J.|last2=Vondung|first2=Jürgen|last3=Wolmershäuser|first3=Gotthelf|date=1989|title=Tetraphosphacyclobutadiene as Complex Ligand|url=https://www.onlinelibrary.wiley.com/doi/abs/10.1002/anie.198913551|journal=Angewandte Chemie International Edition in English|volume=28|issue=10|pages=1355–1357|doi=10.1002/anie.198913551|issn=1521-3773}}{{Cite journal|last1=Reddy|first1=A. Chandrasekhar|last2=Jemmis|first2=Eluvathingal D.|last3=Scherer|first3=Otto J.|last4=Winter|first4=Rainer|last5=Heckmann|first5=Gert|last6=Wolmershaeuser|first6=Gotthelf|date=1992-11-01|title=Electronic structure of triple-decker sandwich complexes with P6 middle rings. Synthesis and x-ray structure determination of bis(.eta.5-1,3-di-tert-butylcyclopentadienyl)(.mu.-.eta.6:.eta.6-hexaphosphorin)diniobium|url=https://doi.org/10.1021/om00059a064|journal=Organometallics|volume=11|issue=11|pages=3894–3900|doi=10.1021/om00059a064|issn=0276-7333}}

File:Qualitative molecular orbital diagram for triple-decker sandwich complexes.png metal interactions in the triple-decker sandwich complexes, imposed on a qualitative energy diagram for [{(η⁵-Cp)Mo}₂(μ,η⁶-P₆)]|407x407px]]

File:P6 Geometry.pnges with 28, 26, and 24 valence electron counts|left|299x299px]]

If one regards the planar {{chem2|P6}} ring as a 6π electron donor ligand, then [{(η⁵-Me₅C₅)Mo}₂(μ,η⁶-P₆)] is a triple-decker sandwich complex with 28 valence electrons. If {{chem2|P6}}, similar to C₆H₆, is taken as a 10π electron donor, a 32 valence electron count may be obtained. In most triple-decker complexes with an electron count ranging from 26 to 34, the structure of the middle ring is planar ([{(η⁵-Cp)M}₂(μ,η⁶-P₆)] with M = Mo, Sc, Y, Zr, Hf, V, Nb, Ta, Cr, and W).{{Cite journal|last1=Jemmis|first1=Eluvathingal D.|last2=Reddy|first2=A. Chandrasekhar.|date=1988-07-01|title=Electronic structure of triple-decker sandwich compounds with P5, P6, As5, and CnHn as middle rings|url=https://doi.org/10.1021/om00097a019|journal=Organometallics|volume=7|issue=7|pages=1561–1564|doi=10.1021/om00097a019|issn=0276-7333}}{{Cite journal|last1=Jemmis|first1=Eluvathingal D.|last2=Reddy|first2=A. Chandrasekhar|date=1990-06-01|title=Structure and bonding in metallocenes and oligomers|url=https://www.ias.ac.in/public/Volumes/jcsc/102/03/0379-0393.pdf|journal=Proceedings of the Indian Academy of Sciences - Chemical Sciences|language=en|volume=102|issue=3|pages=379–393|doi=10.1007/BF02841950|s2cid=92733876|issn=0973-7103}} In the 24 valence electron [{(η⁵-Cp)Ti}₂(μ,η⁶-P₆)] complex, however, a distortion is observed, and the {{chem2|P6}} ring is puckered.{{Cite journal|last1=Scherer|first1=Otto J.|last2=Swarowsky|first2=Herbert|last3=Wolmershäuser|first3=Gotthelf|last4=Kaim|first4=Wolfgang|last5=Kohlmann|first5=Stephan|date=1987|title=[(η5-C5Me5)2 Ti2P6], a Distorted Dimetallaphosphacubane|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.198711531|journal=Angewandte Chemie International Edition in English|volume=26|issue=11|pages=1153–1155|doi=10.1002/anie.198711531|issn=1521-3773}}

Calculations have concluded that completely filled 2a*and 2b* orbitals in 28 valence electron complexes lead to a planar symmetrical {{chem2|P6}} middle ring. In 26 valence electron complexes, the occupancy of either 2a*or 2b* results in in-plane or bisallylic distortions and an asymmetric planar middle ring. The puckering of {{chem2|P6}} in 24 valence electron complexes is due to the stabilization of 5a, as well as that conferred by the tetravalent oxidation state of Ti in [{(η⁵-Cp)Ti}₂(μ,η⁶-P₆)].{{Cite journal|last1=Rani|first1=Dandamudi Usha|last2=Prasad|first2=Dasari L. V. K.|last3=Nixon|first3=John F.|last4=Jemmis|first4=Eluvathingal D.|date=2007|title=Electronic structure and bonding studies on triple-decker sandwich complexes with a P6 middle ring|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.20521|journal=Journal of Computational Chemistry|language=en|volume=28|issue=1|pages=310–319|doi=10.1002/jcc.20521|pmid=17103397|s2cid=25386398|issn=1096-987X}}

File:Oxidized ((η5- Me5C5)Mo)2(μ,η6-P6).png⁺ cation|221x221px|left]]

The reactivity of [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)] toward silver and copper monocationic salts of the weakly coordinating anion [Al{OC(CF₃)₃}₄]⁻ ([TEF]) was studied by Fleischmann et al. in 2015. Addition of a solution of Ag[TEF] or Cu[TEF] to a solution of [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)] in chloroform results in oxidation of the complex, which can be observed by an immediate colour change from amber to dark teal. The magnetic moment of the dark teal crystals determined by the Evans NMR method is equal to 1.67 μB, which is consistent with one unpaired electron. Accordingly, [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)]⁺ is detected by ESI mass spectrometry.

The crystal structure of the teal product shows that the triple‐decker geometry is retained during the one‐electron oxidation of [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)]. The Mo—Mo bond length of the [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)]⁺ cation is 2.6617(4) Å; almost identical to the bond length determined for the unoxidized species at 2.6463(3) Å. However, the P—P bond lengths are strongly affected by the oxidation. While the P1—P1′ and P3—P3′ bonds are elongated, the remaining P—P bonds are shortened compared to the average P—P bond length of about 2.183 Å in the unoxidized species. Therefore, the middle deck of the 27 valence electron [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)]⁺ complex can best be described as a bisallylic distorted P₆ ligand, intermediate between the 28 valence electron complexes with a perfectly planar symmetrical ring, and those with 26 valence electrons displaying a more amplified in-plane distortion. Density functional theorem (DFT) calculations confirm that this distortion is due to depopulation of the P bonding orbitals upon oxidation of the triple-decker sandwich complex.

File:Reactivity of (((η5- Me5C5)Mo)2(μ,η6-P6)).pngs Cu⁺, Ag⁺, and Tl⁺|299x299px]]

To avoid oxidation of [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)], further reactions were performed in toluene to decrease the redox potential of the cations. This resulted in a bright orange coordination product upon reaction with copper, although a mixture also containing the dark teal oxidation product was obtained upon reaction with silver.

Single‐crystal X‐ray analysis reveals that this product displays a distorted square‐planar coordination environment around the central cation through two side‐on coordinating P—P bonds. The Ag—P distances are approximately 2.6 Å, whereas the Cu—P distances are determined to be approximately 2.4 Å. The P—P bonds are therefore elongated to 2.2694(16) Å and 2.2915(14) Å upon coordination to copper and silver, respectively, whilst the remaining P—P bonds are unaffected.

In another experiment Cu[TEF] is treated with [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)] in pure toluene and the solution shows the bright orange color of the complex cation [Cu([{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)])₂]⁺. However, analysis of crystals from this solution reveals a distorted tetrahedral coordination environment around Cu. The resulting Cu—P distances are somewhat shorter than their counterparts discussed above. The coordinating P—P bonds are a little longer, which is attributed to less steric crowding in the tetrahedral coordination geometry around the Cu center.

The successful isolation of [Cu([{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)])₂]⁺ either as its tetrahedral or square‐planar isomer is therefore achievable. DFT calculations show that the enthalpy for the tetrahedral to square‐planar isomerization is positive for both metals, with the tetrahedral coordination being favored. When entropy is taken into account, small positive values for Cu⁺ and larger, but negative, values for Ag⁺ are observed. This means that the tetrahedral geometry is predominant for Cu⁺, but a significant percentage of the complexes adopt a square‐planar geometry in solution. For Ag⁺, the equilibrium is shifted significantly to the right side, which is presumably why a tetrahedral coordination of [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)] and Ag⁺ has not yet been observed.

Examination of the crystal packing reveals that these products are layered compounds that crystallize in the monoclinic C2/c space group with alternating negatively charged layers of the [TEF] anions and positively charged layers of isolated [M([{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)])₂]⁺ complexes. The layers lie inside the bc plane, alternate along the a axis, and do not form a two‐dimensional network.

The treatment of [{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)] with Tl[TEF] in chloroform gives an immediate color change from amber to a deep red. The crystal structure reveals a trigonal pyramidal coordination of the thallium cation, Tl⁺, by three side‐on coordinating P—P bonds of the P₆ ligands. Two of these P₆ ligands show shorter and uniform Tl—P distances of 3.2–3.3 Å with P—P bonds elongated to about 2.22 Å, whilst the third unit shows an unsymmetrical coordination with long Tl—P distances of approximately 3.42 and 3.69 Å and no P—P bond elongation.

File:Crystal packing of (Ag((((η5- Me5C5)Mo)2(μ,η6-P6)))2)+ and (Tl((((η5- Me5C5)Mo)2(μ,η6-P6)))2)+.png of a) [Ag([{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)])₂]⁺and b) [Tl([{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)])₂]⁺ showing the alternation of anionic and cationic layers along the a axis. Tl⁺ positions are half‐occupied.|350x350px]]

Although the environment of Tl⁺ is distinctly different from that of Cu⁺ and Ag⁺, their structures are related by the two‐dimensional coordination network that propagates inside the bc plane. Crucially, whilst Cu⁺ and Ag⁺ form layered structures with isolated [M([{(η⁵- Me₅C₅)Mo}₂(μ,η⁶-P₆)])₂]⁺ complex cations, there is a statistical distribution of the Tl⁺ cations inside the two‐dimensional coordination, which shows further interconnection of the P₆ ligands to form an extended 2D network that could be regarded as a supramolecular analogue of graphene.

File:P6 isomers.png and relative energies.|434x434px]]Despite the triple-decker sandwich complex {(η⁵-Me₅C₅)Mo}₂(μ,η⁶-P₆) containing a demonstrably planar P₆ ring with equal P—P bond lengths, theoretical calculations reveal that there are at least 7 non-planar P₆ isomers lower in energy than the planar benzene-like D_6h structure.{{Cite journal|last1=Jones|first1=R.|last2=Hohl|first2=D.|date=1990|title=Structure of phosphorus clusters using simulated annealing—P2 to P8|journal=The Journal of Chemical Physics|volume=92|issue=11|pages=6710–6721|doi=10.1063/1.458306|bibcode=1990JChPh..92.6710J|s2cid=31227289}}{{Cite journal|last1=Jones|first1=R. O.|last2=Ganteför|first2=G.|last3=Hunsicker|first3=S.|last4=Pieperhoff|first4=P.|date=1995-12-08|title=Structure and spectroscopy of phosphorus cluster anions: Theory (simulated annealing) and experiment (photoelectron detachment)|journal=The Journal of Chemical Physics|volume=103|issue=22|pages=9549–9562|doi=10.1063/1.469969|bibcode=1995JChPh.103.9549J|issn=0021-9606|doi-access=free}}{{Cite journal|last1=Warren|first1=D. Scott|last2=Gimarc|first2=Benjamin M.|date=1992-06-01|title=Valence isomers of benzene and their relationship to isomers of isoelectronic P6|url=https://doi.org/10.1021/ja00039a058|journal=Journal of the American Chemical Society|volume=114|issue=13|pages=5378–5385|doi=10.1021/ja00039a058|bibcode=1992JAChS.114.5378W |issn=0002-7863}}{{Cite journal|last1=Olvera de la Cruz|first1=M.|last2=Mayes|first2=A. M.|last3=Swift|first3=B. W.|date=1992-01-01|title=Transition to lamellar-catenoid structure in block-copolymer melts|url=https://doi.org/10.1021/ma00028a067|journal=Macromolecules|volume=25|issue=2|pages=944–948|doi=10.1021/ma00028a067|bibcode=1992MaMol..25..944O|issn=0024-9297}}{{Cite journal|last1=Haeser|first1=Marco|last2=Schneider|first2=Uwe|last3=Ahlrichs|first3=Reinhart|date=1992-11-01|title=Clusters of phosphorus: a theoretical investigation|url=https://doi.org/10.1021/ja00050a039|journal=Journal of the American Chemical Society|volume=114|issue=24|pages=9551–9559|doi=10.1021/ja00050a039|bibcode=1992JAChS.114.9551H |issn=0002-7863}}{{Cite journal|last1=Jones|first1=J. L.|last2=Olvera de la Cruz|first2=M.|date=1994-04-01|title=Transitions to periodic structures: Higher harmonic corrections with concentration fluctuations|url=https://aip.scitation.org/doi/10.1063/1.467191|journal=The Journal of Chemical Physics|volume=100|issue=7|pages=5272–5279|doi=10.1063/1.467191|bibcode=1994JChPh.100.5272J|issn=0021-9606}}{{Cite journal|last1=Häser|first1=Marco|last2=Treutler|first2=Oliver|date=1995-03-01|title=Calculated properties of P2, P4, and of closed-shell clusters up to P18|url=https://aip.scitation.org/doi/abs/10.1063/1.468552|journal=The Journal of Chemical Physics|volume=102|issue=9|pages=3703–3711|doi=10.1063/1.468552|bibcode=1995JChPh.102.3703H|issn=0021-9606}}{{Cite journal|last1=Kobayashi|first1=Kaoru|last2=Miura|first2=Hideki|last3=Nagase|first3=Shigeru|date=1994-07-20|title=The heavier group 15 analogues of benzene, cyclobutadiene and their valence isomers (M6 and M4, M = P, As, Sb and Bi)|url=http://www.sciencedirect.com/science/article/pii/S0166128009800432|journal=Journal of Molecular Structure: THEOCHEM|language=en|volume=311|pages=69–77|doi=10.1016/S0166-1280(09)80043-2|issn=0166-1280}}{{Cite journal|last1=Ballone|first1=P.|last2=Jones|first2=R. O.|date=1994-04-01|title=Density functional study of phosphorus and arsenic clusters using local and nonlocal energy functionals|url=https://aip.scitation.org/doi/10.1063/1.467213|journal=The Journal of Chemical Physics|volume=100|issue=7|pages=4941–4946|doi=10.1063/1.467213|bibcode=1994JChPh.100.4941B|issn=0021-9606}}{{Cite journal|last1=Hiberty|first1=Philippe C.|last2=Volatron|first2=François|date=2007|title=Ab initio conformational study of the P6 potential surface: Evidence for a low-lying one-electron-bonded isomer|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/hc.20324|journal=Heteroatom Chemistry|language=en|volume=18|issue=2|pages=129–134|doi=10.1002/hc.20324|issn=1098-1071}} In increasing order of energy these are: benzvalene, prismane, chair, Dewar benzene, bicyclopropenyl, distorted benzene, and benzene.File:P6 PJT MOs.pngs of P₆ responsible for the distortion of the planar D_6h structure toward the distorted D₂ structure|319x319px]]

A pseudo Jahn–Teller effect (PJT) is responsible for distortion of the D_6h benzene-like structure into the D₂ structure,{{Cite journal|last=Bersuker|first=Isaac B.|date=2001-04-01|title=Modern Aspects of the Jahn−Teller Effect Theory and Applications To Molecular Problems|url=https://doi.org/10.1021/cr0004411|journal=Chemical Reviews|volume=101|issue=4|pages=1067–1114|doi=10.1021/cr0004411|pmid=11709858|issn=0009-2665}}{{Cite book|last=Bersuker, I. B.|url=https://www.worldcat.org/oclc/967605700|title=The Jahn–Teller effect|isbn=978-0-511-52476-9|location=Cambridge|oclc=967605700}}{{cite book|author=Isaak Borisovich Bersuker|title=The Jahn–Teller Effect and Beyond: Selected Works of Isaac Bersuker with Commentaries : Dedicated to Isaac B. Bersuker on Occasion of His 80th Birthday|url=https://books.google.com/books?id=kAXwAAAAMAAJ|year=2008|publisher=Academy of Sciences of Moldova|isbn=978-9975-62-212-7}}{{Cite journal|last=Pearson|first=Ralph G.|date=1975-06-01|title=Concerning Jahn–Teller Effects|journal=Proceedings of the National Academy of Sciences|language=en|volume=72|issue=6|pages=2104–2106|doi=10.1073/pnas.72.6.2104|issn=0027-8424|pmid=16592247|pmc=432704|bibcode=1975PNAS...72.2104P|doi-access=free}}{{Cite journal|last=Bersuker|first=I. B.|date=1966-04-01|title=On the origin of ferroelectricity in perovskite-type crystals|journal=Physics Letters|language=en|volume=20|issue=6|pages=589–590|doi=10.1016/0031-9163(66)91127-9|bibcode=1966PhL....20..589B|issn=0031-9163}}{{Cite journal|last1=Öpik|first1=U.|last2=Pryce|first2=Maurice Henry Lecorney|date=1957-01-29|title=Studies of the Jahn–Teller effect. I. A survey of the static problem|journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences|volume=238|issue=1215|pages=425–447|doi=10.1098/rspa.1957.0010|bibcode=1957RSPSA.238..425O|s2cid=119862339}} which occurs along the e_2u doubly degenerate mode as a result of vibronic coupling of the HOMO − 1 (e_2g) and LUMO (e_2u): e_2g ⊗ e_2u = a_1u ⊕ a_2u ⊕ e_2u. The distorted structure is calculated to lie just 2.7 kcal mol⁻¹ lower in energy than the D_6h structure. If the uncomplexed structure were to be successfully synthesized, the aromaticity of the benzene-like P₆ structure would not be sufficient to stabilize the planar geometry, and the PJT effect would result in distortion of the ring.{{Cite journal|last1=Galeev|first1=Timur R.|last2=Boldyrev|first2=Alexander I.|date=2011-11-15|title=Planarity takes over in the CxHxP6−x (x = 0–6) series at x = 4|journal=Physical Chemistry Chemical Physics|language=en|volume=13|issue=46|pages=20549–20556|doi=10.1039/C1CP21959F|pmid=21869975|bibcode=2011PCCP...1320549G|issn=1463-9084}}

File:AdNDP analysis for P6.png

Adaptive Natural Density Partitioning (AdNDP) is a theoretical tool developed by Alexander Boldyrev that is based on the concept of the electron pair as the main element of chemical bonding models. It can therefore recover Lewis bonding elements such as 1c–2e core electrons and lone pairs, 2c–2e objects which are two-center two-electron bonds, as well as delocalized many-center bonding elements with respect to aromaticity.

The AdNDP analysis of the seven representative low-lying P₆ structures reveal that these are well described by the classical Lewis model. A lone pair on each phosphorus atom, a two-center-two-electron (2c–2e) σ-bond in every pair of adjacent P atoms, and an additional 2c–2e π-bond between adjacent 2-coordinated P atoms are found, with occupation numbers (ON) of all these bonding elements above 1.92 |e|.

The chemical bonding in the chair structure is unusual. Based on fragment orbital analysis, it was concluded that two linkages between the two P₃ fragments are of the one-electron hemibond type. The AdNDP analysis reveals a lone pair on each P atom and six 2c–2e P—P σ-bonds. One 3c–2e π-bond in every P₃ triangle was revealed with the user-directed form of the AdNDP analysis, as well as a 4c–2e bond responsible for bonding between the two P₃ triangle, confirming that this isomer cannot be represented by a single Lewis structure, and requires a resonance of two Lewis structures, or can be described by a single formula with delocalized bonding elements.

Both the D_6h benzene-like structure, as well as the D₂ isomer of P₆ is similar to the reported AdNDP bonding pattern of the C₆H₆ benzene molecule:{{Cite journal|last1=Zubarev|first1=Dmitry Yu.|last2=Boldyrev|first2=Alexander I.|date=2008-12-05|title=Revealing Intuitively Assessable Chemical Bonding Patterns in Organic Aromatic Molecules via Adaptive Natural Density Partitioning|journal=The Journal of Organic Chemistry|volume=73|issue=23|pages=9251–9258|doi=10.1021/jo801407e|pmid=18980326|issn=0022-3263}} 2c–2e σ-bond and lone pairs, as well as delocalized 6c-2e π-bonds. The distortion due to the PJT effect therefore does not significantly disturb the bonding picture.

File:PJT effect in P6.png in P₆ upon complexation in a sandwich compound|left|250x250px]]File:P6 PJT Suppression.png.|224x224px]]The planar P₆ hexagonal structure D_6h is a second-order saddle point due to the pseudo-Jahn–Teller effect (PJT), which leads to the D₂ distorted structure. Upon sandwich complex formation the PJT effect is suppressed due to filling of the unoccupied molecular orbitals involved in vibronic coupling in P₆ with electron pairs of Mo atoms.{{Cite journal|last1=Sergeeva|first1=Alina P.|last2=Boldyrev|first2=Alexander I.|date=2010-09-13|title=Flattening a Puckered Pentasilacyclopentadienide Ring by Suppression of the Pseudo Jahn−Teller Effect|journal=Organometallics|volume=29|issue=17|pages=3951–3954|doi=10.1021/om1006038|issn=0276-7333}}{{Cite journal|last1=Pokhodnya|first1=Konstantin|last2=Olson|first2=Christopher|last3=Dai|first3=Xuliang|last4=Schulz|first4=Douglas L.|last5=Boudjouk|first5=Philip|last6=Sergeeva|first6=Alina P.|last7=Boldyrev|first7=Alexander I.|date=2011-01-07|title=Flattening a puckered cyclohexasilane ring by suppression of the pseudo-Jahn–Teller effect|journal=The Journal of Chemical Physics|volume=134|issue=1|pages=014105|doi=10.1063/1.3516179|pmid=21218995|bibcode=2011JChPh.134a4105P|issn=0021-9606}}{{Cite journal|last1=Ivanov|first1=Alexander S.|last2=Bozhenko|first2=Konstantin V.|last3=Boldyrev|first3=Alexander I.|date=2012-08-20|title=On the Suppression Mechanism of the Pseudo-Jahn–Teller Effect in Middle E6 (E = P, As, Sb) Rings of Triple-Decker Sandwich Complexes|journal=Inorganic Chemistry|volume=51|issue=16|pages=8868–8872|doi=10.1021/ic300786w|pmid=22845625|issn=0020-1669}} Specifically, from molecular orbital analysis it was determined that, upon complex formation, the LUMO in the isolated P₆ structure is now occupied in the triple-decker complex as a result of the appreciable δ-type M → L back-donation mechanism from the occupied d_x²_–y² and d_xy atomic orbitals of the Mo atom into the partially antibonding π molecular orbitals of P₆, thus restoring the high symmetry and planarity of P₆.

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Category:Phosphorus

Category:Sandwich compounds

Category:Inorganic chemistry

Category:Solid-state chemistry

Category:Hypothetical chemical compounds

Category:Aromatic compounds

Category:Six-membered rings