Calculated properties of P2, P4, and of closed‐shell clusters up to P18

Two P, Ten P, White P, Red P: Mechanistic Exploration of the Oligomerization of Red Phosphorus from Diphosphorus with the Ab Initio Nanoreactor

Phosphorus is critical to humans on many fronts, yet we do not have a mechanistic understanding of some of its most basic transformations and reactions─namely the oligomerization of white phosphorus to red. With heat or under ultraviolet (UV) exposure, it has been experimentally demonstrated that white phosphorus dissociates into diphosphorus units which readily form red phosphorus. However, the mechanism of this process is unknown. The ab initio nanoreactor approach was used to explore the potential energy surface of phosphorus clusters. Density functional theory and metadynamics simulations were used to characterize potential reaction pathways. A mechanism for oligomerization is proposed to take place via diphosphorus additions at π-bonds and weak σ-bonds through three membered ring intermediates. Downhill paths through P6 and P8 clusters eventually result in P10 clusters that can oligomerize into red phosphorus chains. The initial, rate limiting step for this process has an energy barrier of 24.2 kcal/mol.

Renaissance of elemental phosphorus materials: properties, synthesis, and applications in sustainable energy and environment

The polymorphism of phosphorus-based materials has garnered much research interest, and the variable chemical bonding structures give rise to a variety of micro and nanostructures. Among the different types of materials containing phosphorus, elemental phosphorus materials (EPMs) constitute the foundation for the synthesis of related compounds. EPMs are experiencing a renaissance in the post-graphene era, thanks to recent advancements in the scaling-down of black phosphorus, amorphous red phosphorus, violet phosphorus, and fibrous phosphorus and consequently, diverse classes of low-dimensional sheets, ribbons, and dots of EPMs with intriguing properties have been produced. The nanostructured EPMs featuring tunable bandgaps, moderate carrier mobility, and excellent optical absorption have shown great potential in energy conversion, energy storage, and environmental remediation. It is thus important to have a good understanding of the differences and interrelationships among diverse EPMs, their intrinsic physical and chemical properties, the synthesis of specific structures, and the selection of suitable nanostructures of EPMs for particular applications. In this comprehensive review, we aim to provide an in-depth analysis and discussion of the fundamental physicochemical properties, synthesis, and applications of EPMs in the areas of energy conversion, energy storage, and environmental remediation. Our evaluations are based on recent literature on well-established phosphorus allotropes and theoretical predictions of new EPMs. The objective of this review is to enhance our comprehension of the characteristics of EPMs, keep abreast of recent advances, and provide guidance for future research of EPMs in the fields of chemistry and materials science.

Lone Pair Electrons with Weak Nuclear Binding Inducing Sensitive Nonlinear Optical Responses in Phosphorus Clusters

Phosphorus clusters have broadband optical responses, adjustable geometries, and electronic structures, potentially balancing transparency and nonlinearity. In this study, the optical properties of phosphorus clusters are analyzed by using first-principles calculations. Phosphorus clusters exhibit strong light absorption in the ultraviolet region while remaining transparent in the visible to far-infrared bands. Importantly, the third-order nonlinear optical performance of phosphorus clusters surpasses that of p-nitroaniline with a D-π-A structure. The analysis reveals that lone pair electrons with weak nuclear binding induce sensitive nonlinear optical responses of phosphorus clusters. Furthermore, a practical approach for enhancing nonlinear optical effects in a medium via atom replacement and its application to hydride systems are discussed. Lone pair electron materials provide an alternative to conventional organic π-conjugated molecules for nonlinear optical devices, while potentially achieving a better trade-off of nonlinearity versus transparency. This study provides a novel concept for the development of high-performance nonlinear optical materials.

Computational Assessment of an Elusive Aromatic N3P3 Molecule

We computationally proved that the planar aromatic hexagonal isomer N₃P₃ with the alteration of N and P is the second most stable structure for the N₃P₃ stoichiometry. We found that the aromatic isomer has high barriers for transition into the global minimum structure or into the three isolated NP molecules, making this structure kinetically stable. We showed that the sandwich N₃P₃CrN₃P₃ molecule corresponds to a minimum on the potential energy surface; thus, the aromatic N₃P₃ molecule has a potential to be a new ligand in chemistry.

Air- and Light-Stable P4 and As4 within an Anion-Coordination-Based Tetrahedral Cage

In contrast to the stable dinitrogen molecule, white phosphorus (P₄) and yellow arsenic (As₄) are very reactive allotropic modifications of these two heavier pnictogen elements, which has greatly hampered the study of their properties and applications. Thus, the safe storage and transport of them is imperative. Supramolecular caged structures are one of the most efficient approaches for the encapsulation and stabilization of reactive species; however, their use in the P₄ and As₄ chemistry is very rare. In the current work, we demonstrate a new design strategy for constructing finite cages and including guests based on anion coordination chemistry. The phosphate-coordination-based tetrahedral cages can readily accommodate the tetrahedral guests P₄ and As₄, which is facilitated by the shape and size complementarity as well as favorable σ-π and lone-pair-π interactions. Moreover, the latter case represents the first example of As₄ inclusion in a well-defined tetrahedral cage.

Recent highlights in mixed-coordinate oligophosphorus chemistry

This review aims to highlight and comprehensively summarize recent developments in the field of mixed-coordinate phosphorus chemistry. Particular attention is focused on the synthetic approaches to compounds containing at least two directly bonded phosphorus atoms in different coordination environments and their unexpected properties that are derived from spectroscopic and crystallographic data. Novel substance classes are discussed in order to supplement previous reviews about mixed-coordinate phosphorus compounds.

The approach to 4d/4f-polyphosphides

The first 4d/4f polyphosphides were obtained from reactions of the divalent metallocenes [Cp*₂Ln(thf)₂] (Ln = Sm, Yb) with [{CpMo(CO)₂}₂(μ,η^2:2-P₂)] or [Cp*Mo(CO)₂(η³-P₃)]. New aggregation of the central phosphorus scaffold in combination with P–P bond formation within the coordination sphere of the transition metal was observed.

The first 4d/4f polyphosphides were obtained by reaction of the divalent metallocenes [Cp*₂Ln(thf)₂] (Ln = Sm, Yb) with [{CpMo(CO)₂}₂(μ,η^2:2-P₂)] or [Cp*Mo(CO)₂(η³-P₃)]. Treatment of [Cp*₂Ln(thf)₂] (Ln = Sm, Yb) with [{CpMo(CO)₂}₂(μ,η^2:2-P₂)] gave the 16-membered bicyclic compounds [(Cp₂*Ln)₂P₂(CpMo(CO)₂)₄] (Ln = Sm, Yb) as the major products. From the reaction involving samarocene, the cyclic P₄ complex [(Cp*₂Sm)₂P₄(CpMo(CO)₂)₂] and the cyclic P₅ complex [(Cp*₂Sm)₃P₅(CpMo(CO)₂)₃] were also obtained as minor products. In each reaction, the P₂ unit is reduced and a rearrangement occurred. In dedicated cases, a P–P bond formation takes place, which results in a new aggregation of the central phosphorus scaffold. In the reactions of [Cp*₂Ln(thf)₂] (Ln = Sm, Yb) with [Cp*Mo(CO)₂P₃] a new P–P bond is formed by reductive dimerization and the 4d/4f hexaphosphides [(Cp*₂Ln)₂P₆(Cp*Mo(CO)₂)₂] (Ln = Sm, Yb) were obtained.

On the molecular and electronic structures of AsP3 and P4

The molecular and electronic structures of AsP(3) and P(4) have been investigated. Gas-phase electron diffraction studies of AsP(3) have provided r(g) bond lengths of 2.3041(12) and 2.1949(28) A for the As-P interatomic distances and the P-P interatomic distances, respectively. The gas-phase electron diffraction structure of P(4) has been redetermined and provides an updated value of 2.1994(3) A for the P-P interatomic distances, reconciling conflicting literature values. Gas-phase photoelectron spectroscopy provides experimental values for the energies of ionizations from the valence molecular orbitals of AsP(3) and P(4) and shows that electronically AsP(3) and P(4) are quite similar. Solid-state (75)As and (31)P NMR spectroscopy demonstrate the plastic nature of AsP(3) and P(4) as solids, and an extreme upfield (75)As chemical shift has been confirmed for the As atom in AsP(3). Finally, quantum chemical gauge-including magnetically induced current calculations show that AsP(3) and P(4) can accurately be described as strongly aromatic. Together these data provide a cohesive description of the molecular and electronic properties of these two tetraatomic molecules.

Theoretical investigation of clusters of phosphorus and arsenic: fascination and temptation of high symmetries

We present a theoretical study of the energetic and thermodynamic stability of selected phosphorus and arsenic clusters containing 18 to 168 atoms. For this purpose we employ MP2 as well as DFT functionals BP86 and B3LYP with extended basis sets. All procedures predict the family of one-dimensional polymers X18+12n, each with 2n-1 isomers of virtually identical energy, to be more stable than other structures investigated so far. Furthermore, islands of stability result for ring-shaped clusters X24n with Dnd symmetry for n=4 (only for arsenic), 5, 6, and 7. Phosphorus and arsenic show otherwise a very similar behavior. An investigation of basis set effects shows that a doubly polarized triple zeta valence basis (TZVPP) is both necessary and sufficient. In comparison to the reliable spin component scaled MP2 (SCS-MP2) procedure, DFT methods underestimate and MP2 overestimates the stability of larger clusters; the discrepancy increases with the number of atoms. The addition of a long-range dispersion correction to B3LYP energies does not rectify the shortcomings of DFT in comparison with SCS-MP2.

Icosahedral and Ring-Shaped Allotropes of Phosphorus

The existence of two new allotropic forms of phosphorus, icosahedral cages and ring-shaped chains, is predicted. The cages and rings are nanostructural modifications of the black and the red phosphorus, respectively. The icosahedral and ring-shaped allotropes are compared with the experimentally known allotropic forms of phosphorus by quantum chemical methods. Both the cages and the rings are thermodynamically favored over the white phosphorus, the rings being comparable to the Hittorf's violet phosphorus and to the recently discovered fibrous red phosphorus. The stabilities of the icosahedral cages increase as a function of their size, having structural resemblance with the rhombohedral black phosphorus. The high thermodynamic stability of the phosphorus nanostructures suggests their experimental synthesis to be viable.

Parity Alternation of Ground-State Pn- and Pn+ (n = 3−15) Phosphorus Clusters

The ground-state structures of neutral, cationic, and anionic phosphorus clusters P(n), P(n)(+), and P(n)(-) (n = 3-15) have been calculated using the B3LYP/6-311+G* density functional method. The P(n)(+) and P(n)(-) (n = 3-15) clusters with odd n were found to be more stable than those with even n, and we provide a satisfactory explanation for such trends based on concepts of energy difference, ionization potential, electron affinity, and incremental binding energy. The result of odd/even alternations is in good accord with the relative intensities of cationic and anionic phosphorus clusters observed in mass spectrometric studies.

Mechanism of White Phosphorus Activation by Three-Coordinate Molybdenum(III) Complexes: A Thermochemical, Kinetic, and Quantum Chemical Investigation

White phosphorus (P(4)) reacts with three-coordinate molybdenum(III) trisamides or molybdaziridine hydride complexes to produce either bridging or terminal phosphide (P(3)(-)) species, depending upon the ancillary ligand steric demands. Thermochemical measurements have been made that place the MoP triple bond dissociation enthalpy at 92.2 kcal.mol(-)(1). Thermochemical measurements together with computational analysis rule out simple P-atom abstraction from P(4) as a step in the phosphorus activation mechanism. Kinetic measurements made by the stopped-flow method show that the reaction between the monomeric molybdenum complexes and P(4) is first-order both in metal complex and in P(4). Cyclo-P(3) complexes can be obtained when ancillary ligand steric demands are small, but kinetic measurements rule them out as monometallic intermediates in the P(4) activation mechanism. Also studied by calorimetric, kinetic, and in one case variable-temperature NMR methods is the process of mu-phosphide bridge formation. Post-rate-determining steps of the P(4) activation process were examined in a search for minima on the reaction's potential energy surface, leading to the proposal of two plausible, parallel, bimetallic reaction channels.

The Chemical Bond in Polyphosphides: Crystal Structures, the Electron Localization Function, and a New View of Aromaticity in P42− and P5−

The incongruent solvation of M(I)4P6 species (M(I) = K, Rb, Cs) in liquid ammonia leads to a broad variety of polyphosphides such as P7(3-), P11(3-), and the putatively aromatic P4(2-) and P5(-), which we investigated by using NMR spectroscopy and single-crystal X-ray structure analysis. The structures of Cs2P4 x 2 NH3, (K@[18]crown-6)3K3(P7)2 x 10 NH3, Rb3P7 x 7 NH3, and (Rb@[18]crown-6)3P7 x 6 NH3 are discussed and compared. The electron localization function ELF is used in a comparison of the chemical bonding of various phosphorus species. The variances of the basin populations provide a well-established measure for electron delocalization and therefore aromaticity. While comparable variance is calculated for P4(2-) and P5(-) it is observed in the lone pairs rather than in the basin populations of the bonds as in the prototypical aromatic hydrocarbons such as benzene or the cyclopentadienide anion. For this behavior, the term "lone pair aromaticity" is proposed.

Binding energies, vibrations and structural characteristics of small polyphosphorus molecules from quantum chemical computations

A systematic search for a quick and cost-effective theoretical method suitable for simultaneous studies of the structures, spectra and atomization energies of polyphosphorus compounds has been performed. It is demonstrated that density functional theory in BPW91/cc-pVTZ formulation provides a reasonable description of small Pn (n= 2, 3, 4, 6) clusters and PnRm molecules (R = H, C(SiH3) (3), n= 1, 2; m= 1, 2, 4), close to that achieved by far more expensive coupled cluster calculations. In order to assign intrinsic PP bond strengths compliance matrices have been calculated. It is shown that compliance constants of PP bonds provide a unique tool for assigning individual mechanical bond strengths in small cluster systems.

Calibration of the n-electron valence state perturbation theory approach

Extensive tests have been performed to benchmark and to compare with second-order perturbation theory based on a complete active space self-consistent field reference function (CASPT2), the recently developed n-electron valence state perturbation theory at second order (NEVPT2). Test calculations included the group fifteen diatomic molecules X(2) (X=N, P, As, and Sb) and the (4)S/(2)D and (4)S/(2)P splittings for the corresponding atoms, the (1)A(1)-(3)B(1) splittings for CH(2) and SiH(2), and the absorption spectra of pyrrole and of Cu(Imidazole)(2)(SH)(SH(2))(+), which is a model for plastocyanin. Comparisons with full configuration-interaction calculations and experimental data show that the accuracy of NEVPT2 is in most cases even better than CASPT2. Where intruder states hamper the CASPT2 calculations, NEVPT2 performs significantly better. Care is needed in the choice of active orbitals, for example in the calculation of the (4)S/(2)D and (4)S/(2)P splittings for the group fifteen atoms. This is due to the different treatment of orbitals belonging to the inactive or active spaces, making the NEVPT2 not invariant for the choice of active space, even in cases where the multiconfiguration self-consistent field energy is invariant.

The reactivity of cyclo-(P5tBu4)– towards group 13, 14 and 15 metal chlorides: complexation and formation of cyclooligophosphanes, {cyclo-(P5tBu4)}2 and {cyclo-(P4tBu3)PtBu}2, by reductive elimination

[Na(THF)4][cyclo-(P5tBu4)] (1) reacts with Et2AlCl and GeCl4 to give Et2Al[cyclo-(P5tBu4)](THF) (2) and, in low yield, GeCl3[cyclo-(P5tBu4)], respectively, while the reaction of 1 with SnCl2, PbCl2 or BiCl3 results in the formation of the structural isomers [cyclo-(P5tBu4)]2 (3) and [cyclo-(P4tBu3)PtBu]2 (4)(besides other cyclic phosphanes) and elemental metal.