Density functional study of phosphorus and arsenic clusters using local and nonlocal energy functionals

Homoatomic cations: From [P5]+ to [P9]. SCIENCE ADVANCES 2022;8:eabq8613. [PMID: 36070385 PMCID: PMC9451154 DOI: 10.1126/sciadv.abq8613]

Recent synthetic approaches to a series of [P₉]X salts (X = [F{Al(OR^F)₃}₂], [Al(OR^F)₄], and (R^F = C(CF₃)₃); Ga₂Cl₇) overcome limitations in classical synthesis methods that proved unsuitable for phosphorus cations. These salts contain the homopolyatomic cation [P₉]⁺ via (I) oxidation of P₄ with NO[F{Al(OR^F)₃}₂], (II) the arene-stabilized Co(I) sandwich complex [Co(arene)₂][Al(OR^F)₄] [arene = ortho-difluorobenzene (o-DFB) and fluorobenzene (FB)], or (III) the reduction of [P₅Cl₂][Ga₂Cl₇] with Ga[Ga₂Cl₇] as Ga(I) source in the presence of P₄. Quantum chemical CCSD(T) calculations suggest that [P₉]⁺ formation from [Co(arene)₂]⁺ occurs via the nido-type cluster [(o-DFB)CoP₄]⁺, which resembles the isoelectronic, elusive [P₅]⁺. Apparently, the nido-cation [P₅]⁺ forms intermediately in all reactions, particularly during the Ga(I)-induced reduction of [P₅Cl₂]⁺ and the subsequent pick up of P₄ to yield the final salt [P₉][Ga₂Cl₇]. The solid-state structure of [P₉][Ga₂Cl₇] reveals the anticipated D_2d-symmetric Zintl-type cage for the [P₉]⁺ cation. Our approaches show great potential to bring other [P_n]⁺ cations from the gas to the condensed phase.

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.

Density functional study of structure and dynamics in liquid antimony and Sbn clusters

Density functional/molecular dynamics simulations have been performed on liquid antimony (588 atoms and six temperatures between 600 K and 1300 K) and on neutral Sb clusters with up to 14 atoms. We study structural patterns (coordination numbers, bond angles, and ring patterns, structure factors, pair distribution functions) and dynamical properties (vibration frequencies, diffusion constants, power spectra, dynamical structure factors, viscosity) and compare with available experimental results and with the results of our previous simulations on Bi. Three short covalent bonds characteristic of pnictogens are common in the clusters, and higher temperatures lead in the liquid to broader bond angle distributions, larger total cavity volumes, and weaker correlations between neighboring bond lengths. There are clear similarities between the properties of Sb and Bi aggregates.

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.

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.

A reactive force field simulation of liquid–liquid phase transitions in phosphorus

A force field model of phosphorus has been developed based on density functional (DF) computations and experimental results, covering low energy forms of local tetrahedral symmetry and more compact (simple cubic) structures that arise with increasing pressure. Rules tailored to DF data for the addition, deletion, and exchange of covalent bonds allow the system to adapt the bonding configuration to the thermodynamic state. Monte Carlo simulations in the N-P-T ensemble show that the molecular (P(4)) liquid phase, stable at low pressure P and relatively low temperature T, transforms to a polymeric (gel) state on increasing either P or T. These phase changes are observed in recent experiments at similar thermodynamic conditions, as shown by the close agreement of computed and measured structure factors in the molecular and polymer phases. The polymeric phase obtained by increasing pressure has a dominant simple cubic character, while the polymer obtained by raising T at moderate pressure is tetrahedral. Comparison with DF results suggests that the latter is a semiconductor, while the cubic form is metallic. The simulations show that the T-induced polymerization is due to the entropy of the configuration of covalent bonds, as in the polymerization transition in sulfur. The transition observed with increasing P is the continuation at high T of the black P to arsenic (A17) structure observed in the solid state, and also corresponds to a semiconductor to metal transition.

The arsenic clusters Asn (n = 1-5) and their anions: Structures, thermochemistry, and electron affinities

The molecular structures, electron affinities, and dissociation energies of the As(n)/As(-) (n) (n = 1-5) species have been examined using six density functional theory (DFT) methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. These methods have been carefully calibrated (Chem Rev 2002, 102, 231) for the prediction of electron affinities. The geometries are fully optimized with each DFT method independently. Three different types of the neutral-anion energy separations reported in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The first dissociation energies D(e)(As(n-1)-As) for the neutral As(n) species, as well as those D(e)(As(-) (n-1)-As) and D(e) (As(n-1)-As(-)) for the anionic As(-) (n) species, have also been reported. The most reliable adiabatic electron affinities, obtained at the DZP++ BLYP level of theory, are 0.90 (As), 0.74 (As(2)), 1.30 (As(3)), 0.49 (As(4)), and 3.03 eV (As(5)), respectively. These EA(ad) values for As, As(2), and As(4) are in good agreement with experiment (average absolute error 0.09 eV), but that for As(3) is a bit smaller than the experimental value (1.45 +/- 0.03 eV). The first dissociation energies for the neutral arsenic clusters predicted by the B3LYP method are 3.93 eV (As(2)), 2.04 eV (As(3)), 3.88 eV (As(4)), and 1.49 eV (As(5)). Compared with the available experimental dissociation energies for the neutral clusters, the theoretical predictions are excellent. Two dissociation limits are possible for the arsenic cluster anions. The atomic arsenic results are 3.91 eV (As(-) (2) --> As(-) + As), 2.46 eV (As(-) (3) --> As(-) (2) + As), 3.14 eV (As(-) (4) --> As(-) (3) + As), and 4.01 eV (As(-) (5) --> As(-) (4) + As). For dissociation to neutral arsenic clusters, the predicted dissociation energies are 2.43 eV (As(-) (3) --> As(2) + As(-)), 3.53 eV (As(-) (4) --> As(3) + As(-)), and 3.67 eV (As(-) (5) --> As(4) + As(-)). For the vibrational frequencies of the As(n) series, the BP86 and B3LYP methods produce good results compared with the limited experiments, so the other predictions with these methods should be reliable.

Electronic structures and properties of eight-coordinate metal-polyarsenic complexes MAs8n- (M = V, Nb, Ta, Cr, Mo, W, Mn, Tc, Re)

The eight-coordinate early transition metal polyarsenic complexes, MAs(8)3- (M = V, Nb, Ta), MAs(8)2- (M = Cr, Mo, W), and MAs8- (M = Mn, Tc, Re), have been studied using density functional theory (DFT). The geometry optimizations of these complexes indicate that in the most stable structures the transition metal atoms are trapped in a crownlike cavity consisting of a zigzag eight-membered ring of As8 cluster. The scalar-relativistic effects and spin-orbit coupling effects on the electronic structures and energy levels were taken into account. The stabilities of gas-phase MAs8n- ions and bonding between the As8 ring and early transition metals are discussed on the basis of population analysis, atomization energies, and decomposition reaction energies. All these complex ions are found to be diamagnetic with notable HOMO-LUMO energy gaps. The vibrational frequencies and infrared absorption intensities of the MAs8n- series are predicted theoretically. Brief theoretical calculations of the similar MoA(8)2- pnictide ions indicate that the analogous P, Sb, and even Bi complexes are likely to be stable, whereas the crownlike MoN(8)2- is not a stable complex.