Structure and spectroscopy of phosphorus cluster anions: Theory (simulated annealing) and experiment (photoelectron detachment)

Triple-chain boron clusters: lengthening via phosphorus doping and enhancing stability through {P} by {CH} substitution

This theoretical study presents novel insights into the doping of boron clusters with an increasing number of dopant atoms, ranging from 1 to 4, that preserve the integrity of the original boron framework. The triple-chain forms of clusters B10 and B16 remain unchanged upon sequential addition of P atoms, showcasing a perfect isolobal substitution of {P} with {CH}. Similarities in the number of delocalized electrons are observed between pure and doped boron clusters, alongside the subsequent substitution of {P} with {CH}. All triple-chain structures exhibit high thermodynamic stability, having low vertical attachment energies and high vertical ionization energies. The lowest-lying isomer of B16P4 has thus a triple-chain shape instead of a tetrahedral Td form as previously reported. While AdNDP analysis confirms the number of globally delocalized electrons, it differs much from a previous interpretation. The magnetic ring current maps support the double aromaticity of triple-chain structures. Electron counting rules established for triple-chain structures are verified. The particle-in-a-rectangular-box model elucidates the relationship between the structure size and electron configuration and aids in understanding the transition from antiaromatic to aromatic configurations. The self-locking phenomenon is crucial for adhering to the triple-chain model and satisfying electron configuration requirements.

The Quest for Stable Borozene Core in Main-Group Capped Inverse Sandwich Complexes, [(HE)2B6H6]2- (E=B, Al, Ga, In, and Tl)

The ubiquitous chemistry of benzene led us to explore ways to stabilise analogous borozene, by capping them with appropriate groups. The mismatch in overlap of ring-cap fragment molecular orbitals in [(HB)2B6H6]2- is overcome by replacing the two BH caps with higher congeners of boron. We calculated the relative energies of all the polyhedral structural candidates for [(HE)2B6H6]2- (E=Al-Tl) and found hexagonal bipyramid (HBP) to be more stable with Al-H caps. A global minimum search also gives HBP as the most stable structure for [Al2B6H8]2-. The capped B6H6 ring in [(HAl)2B6H6]2- has aromaticity comparable to that of benzene.

Phosphorus nanoclusters and insight into the formation of phosphorus allotropes

Elemental phosphorus has a striking variety of allotropes, which we analyze by looking at stable phosphorus clusters. We determine the ground-state structures of P_n clusters in a wide range of compositions (n = 2-50) using density functional calculations and global optimization techniques. We explain why the high-energy white phosphorus is so easily formed, compared to the much more stable allotropes - the tetrahedral P₄ cluster is so much more stable than nearby compositions that only by increasing the size to P₁₀ one can get a more stable non-P₄-based structure. Starting from 17 atoms, phosphorus clusters have a single-stranded structure, consisting of a set of well-resolved structural units connected by P₂ linking fragments. The investigation of relative stability has revealed even-odd alternations and structural magic numbers. The former are caused by the higher stability of clusters with even numbers of atoms due to closed electronic shells. The structural magic numbers are associated with the presence of particular stable structural units and lead to enhanced stability of P_18+12k (k = 0, 1, 2) clusters. We also compare the energies of the obtained ground-state structures with clusters of different phosphorus allotropes. Clusters of fibrous phosphorus are energetically the closest to the ground states, white phosphorus clusters are found to be less stable, and the least stable allotrope at the nanocluster scale is black phosphorene.

A super stable assembled P nanowire with variant structural and magnetic/electronic properties via transition metal adsorption

By means of first-principles calculations, we systematically investigated the structure, stability and magnetic and electronic properties of one-dimensional P nanowire (1D-P10 NW) assembled by Pn subunits (n = 2, 8) and transition metal doped 1D-P10 NW. Our calculations showed that the assembled 1D-P10 NW is super stable in thermodynamic, dynamic, thermal and chemical perspectives. Moreover, when the assembled 1D-P10 NW is decorated with transition metals (TM = Ti ∼ Zn, Zr ∼ Mo), structural transformation occurs (to sandwich or quasi-sandwich chains), and various magnetic and electronic characteristics are introduced to the nanowire. Particularly, the sandwich chains 1D-Mn2@P10 and 1D-V1@P5 are a ferromagnetic semiconductor and a ferromagnetic half-metal, respectively, and the magnetic anisotropy energies are both ∼0.3 meV per Mn/V atom. Our theoretical studies proposed a super stable 1D P nanowire and also offer a feasible approach to reach P5-TM-P5-TM chains with diverse magnetic and electronic properties, as well as ferromagnetic vdW-type 2D systems, which are promising in nanoelectronic devices and spintronics.

Why are the Elemental Nonmetals (F2 , Cl2 , Br2 , I2 , S8 , P4 ) of so Many Hues or of Any Hues and Where is the Chromophore? Insight into Intera-X-X Bonds

A unique approach is used to relate the HOMO-LUMO energy difference to the difference between the ionization potential (IP) and electron affinity (EA) to assist in deducing not only the colors, but also chromophores in elemental nonmetals. Our analysis focuses on compounds with lone pair electrons and σ electrons, namely X₂ (X = F, Cl, Br, I), S₈ and P₄ . For the dihalogens, the [IP - EA] energies are found to be: F₂ (12.58 eV), Cl₂ (8.98 eV), Br₂ (7.90 eV), I₂ (6.78 eV). We suggest that the interahalogen X-X bond itself is the chromophore for these dihalogens, in which the light absorbed by the F₂ , Cl₂ , Br₂ , I₂ leads to longer wavelengths in the visible by a π → σ* transition. Trace impurities are a likely case of cyclic S₈ which contains amounts of selenium leading to a yellow color, where the [IP - EA] energy of S₈ is found to be 7.02 eV. Elemental P₄ with an [IP - EA] energy of 9.09 eV contains a tetrahedral and σ aromatic structure. In future work, refinement of the analysis will be required for compounds with π electrons and σ electrons, such as polycyclic aromatic hydrocarbons (PAHs).

Approximate equation-of-motion coupled-cluster methods for electron affinities of closed-shell molecules

We investigate performance of the equation-of-motion coupled-cluster method at the single and doubles level (EOM-CCSD) and a series of approximate methods based on EOM-CCSD on electron affinities (EA) of closed-shell cations and neutral molecules with positive and negative EAs in this work. Our results confirm that P-EOM-MBPT2 can provide reasonable EAs when molecules with significant multireference character are not considered and its mean absolute error on EAs of these molecules is around or less than 0.2 eV. Its accuracy is comparable to that of the more expensive EOM-CCSD(2) method. Results of EOM-CCSD(2), P-EOM-MBPT2, and CIS(D_∞) indicate that the [[H, a_c ⁺], T₂] term in the 1h2p-1h block is more important on EAs than the term neglected in the 1h2p-1h2p block in P-EOM-MBPT2. We proposed an economical method where EAs from CIS(D_∞) are corrected by treating this [[H, a_c ⁺], T₂] term in the 1h2p-1h block perturbatively [corr-CIS(D_∞)]. EAs with corr-CIS(D_∞) agree very well with those of P-EOM-MBPT2 with a difference of less than 0.02 eV. Computational scaling of this method is N⁴ for the iterative part and N⁵ for some non-iterative steps. Its storage requirement is only of OV³. Corr-CIS(D_∞) is an economical and reliable method on EAs, and it can be applied to EAs of large molecules.

GW100: Comparison of Methods and Accuracy of Results Obtained with the WEST Code

The reproducibility of calculations carried out within many-body perturbation theory at the G₀ W₀ level is assessed for 100 closed shell molecules and compared to that of density functional theory. We consider vertical ionization potentials (VIP) and electron affinities (VEA) obtained with five different codes: BerkeleyGW, FHI-aims, TURBOMOLE, VASP, and WEST. We review the approximations and parameters that control the accuracy of G₀ W₀ results in each code, and we discuss in detail the effect of extrapolation techniques for the parameters entering the WEST code. Differences between the VIP and VEA computed with the various codes are within ∼60 and ∼120 meV, respectively, which is up to four times larger than in the case of the best results obtained with DFT codes. Vertical ionization potentials are validated against experiment and CCSD(T) quantum chemistry results showing a mean absolute relative error of ∼4% for data obtained with WEST. Our analysis of the differences between localized orbitals and plane-wave implementations points out molecules containing Cu, I, Ga, and Xe as major sources of discrepancies, which call for a re-evaluation of the pseudopotentials used for these systems in G₀ W₀ calculations.

Long-lived excited states in metal clusters

Long-lived excited states may exist only in metal clusters with a weak coupling between the electronic and geometric structure.

Negative ion photoelectron spectroscopy of P2N3-: electron affinity and electronic structures of P2N3˙

We report here a negative ion photoelectron spectroscopy (NIPES) and ab initio study of the recently synthesized planar aromatic inorganic ion P2N3-, to investigate the electronic structures of P2N3- and its neutral P2N3˙ radical. The adiabatic detachment energy of P2N3- (electron affinity of P2N3˙) was determined to be 3.765 ± 0.010 eV, indicating high stability for the P2N3- anion. Ab initio electronic structure calculations reveal the existence of five, low-lying, electronic states in the neutral P2N3˙ radical. Calculation of the Franck-Condon factors (FCFs) for each anion-to-neutral electronic transition and comparison of the resulting simulated NIPE spectrum with the vibrational structure in the observed spectrum allows the first four excited states of P2N3˙ to be determined to lie 6.2, 6.7, 11.5, and 22.8 kcal mol-1 above the ground state of the radical, which is found to be a 6π-electron, 2A1, σ state.

Viability of aromatic all-pnictogen anions

Aromaticity in novel cyclic all-pnictogen heterocyclic anions, P2N3(-) and P3N2(-), and in their heavier analogues is studied using quantum mechanical computations. All geometrical parameters from optimized geometry, bonding, electron density analysis from quantum theory of atoms in molecules, nucleus-independent chemical shift, and ring current density plots support their aromaticity. The aromatic nature of these molecules closely resembles that of the prototypical aromatic anion, C5H5(-). These singlet C2v symmetric molecules are comprised of five distinct canonical structures and are stable up to at least 1000 fs without any significant distortion. Mechanistic study revealed a plausible synthetic pathway for P3N2(-) - a click reaction between N2 and P3(-), through a C2v symmetric transition state. Besides this, the possibility of P3N2(-) as a η(5)-ligand in metallocenes is studied and the nature of bonding in metallocenes is discussed through the energy decomposition analysis.

Vibrational Fingerprints of Low-Lying Pt(n)P(2n) (n = 1-5) Cluster Structures from Global Optimization Based on Density Functional Theory Potential Energy Surfaces

Vibrational fingerprints of small Pt(n)P(2n) (n = 1-5) clusters were computed from their low-lying structures located from a global exploration of their DFT potential energy surfaces with the GSAM code. Five DFT methods were assessed from the CCSD(T) wavenumbers of PtP2 species and CCSD relative energies of Pt2P4 structures. The eight first Pt(n)P(2n) isomers found are reported. The vibrational computations reveal (i) the absence of clear signatures made by overtone or combination bands due to very weak mechanical and electrical anharmonicities and (ii) some significant and recurrent vibrational fingerprints in correlation with the different PP bonding situations in the Pt(n)P(2n) structures.

Global minimum structure searches via particle swarm optimization

Novel implementation of the evolutionary approach known as particle swarm optimization (PSO) capable of finding the global minimum of the potential energy surface of atomic assemblies is reported. This is the first time the PSO technique has been used to perform global optimization of minimum structure search for chemical systems. Significant improvements have been introduced to the original PSO algorithm to increase its efficiency and reliability and adapt it to chemical systems. The developed software has successfully found the lowest-energy structures of the LJ(26) Lennard-Jones cluster, anionic silicon hydride Si(2)H(5) (-), and triply hydrated hydroxide ion OH(-) (H(2)O)(3). It requires relatively small population sizes and demonstrates fast convergence. Efficiency of PSO has been compared with simulated annealing, and the gradient embedded genetic algorithm.

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.

Mindless Chemistry

Applications of an automated stochastic search procedure for locating all possible minima with a given composition are illustrated by the pentatomic molecules BCNOS, CAlSiPS, C(4)B(-), C(4)Al(-), and CBe(4)(2-), as well as by C(6)Be, the C(6)Be(2-) dianion, and C(6)H(2). All previously identified minima were reproduced, and many new structures, often with nonintuitive geometries, were found.

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.

Photoelectron spectroscopy of phosphorus hydride anions

Negative-ion photoelectron spectroscopy is applied to the PH-, PH2-, P2H-, P2H2-, and P2H3-molecular anions. Franck-Condon simulations of the photoelectron spectra are used to analyze the spectra and to identify various P2H(n)- species. The simulations employ density-functional theory calculations of molecular geometries and vibrational frequencies and normal modes, and coupled-cluster theory calculations of electron affinities. The following electron affinities are obtained: EA0(PH) = 1.027 +/- 0.006 eV, EA0(PH2) = 1.263 +/- 0.006 eV, and EA0(P2H) = 1.514 +/- 0.010 eV. A band is identified as a mixture of trans-HPPH- and cis-HPPH-. Although the trans and cis bands cannot be definitively assigned from experimental information, using theory as a guide we obtain EA0(trans-HPPH)= 1.00 +/- 0.01 eV and EA0(cis-HPPH) = 1.03 +/- 0.01 eV. A weak feature tentatively assigned to P2H3- has a vertical detachment energy of 1.74 eV. The derived gas-phase acidity of phosphine is delta(acid)G298(PH3) < or = 1509.7 +/- 2.1 kJ mo1(-1).

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.

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.