Threshold photoionization behaviour of (Li2O)Lin clusters produced by a laser vaporization source

We report on the production of small and medium size lithium and lithium oxide clusters by a laser vaporization cluster source. The isotopomeric distribution of natural lithium allowed to identify Li_kO clusters as the most abundant components in the mass spectrum. Photoionization efficiency curves of Li_kO clusters with photon energies from 3.4 to 4.7 eV were measured for 8 ≤ k ≤ 27. Using linear extrapolation of the increase in photoionization efficiency with photon energy, ionization potentials were extracted. With the chemical bond of the O^2- anion to two Li atoms, leaving n = k-2 valence electrons in the (Li₂O)Li_n clusters, clear shell closure effects are present at n = 8 and n = 20.     

Structure and energetics of Li/Na, Li/K, and K/Na bimetallic hexamers

A systematic study of neutral mixed clusters, Li_6?x Na _x , Li_6?x K _x and K_6?x Na _x (x = 0–6), was performed within the framework of density functional theory. The aim of this work is to explore the geometry variation and the energy change of homonuclear hexamers (Li₆ and K₆) induced by impurities. It is found that the geometry of bimetallic hexamers varies with their compositions. The geometries of resulting clusters show evolution from D_4h symmetry for Li₆ to D_3h symmetry for Na₆ and K₆. The stability of bimetallic hexamers has been also explained in terms of binding energy, excess energy, the second difference in energy, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps. It is found that replacing each Li–Li bond with Li–Na or Li–K bonds decreases the cluster stability, while replacing each K–K bond by K–Na leads to stability enhancement. Examining the cluster stability, excess energy and second difference in energy reveal that among studied bimetallic hexamers, Li₂Na₄ is the most stable mixed hexamer.     

Linear Group 13 E≡E Triple Bonds in E2Li62+

The triply bonded heavier main-group compounds have a textbook trans-bent geometry, in contrast to a familiar linear form found for the lightest analogues. Strikingly, the unexpected linear group 13 E≡E triple bonds were herein found in the D_4h-symmetry E₂Li₆²⁺ clusters, and they possess a large barrier (>18.0 kcal/mol) towards the dissociation of Li⁺. The perfectly surrounded Li₄ motifs and two linear coordinated Li atoms strongly suppress the increasing nonbonded electron density of heavier E atoms, making two degenerate π bonds and one multi-center σ bond in linear heavier main-group triple bonds. The surrounding Li₆ motifs not only creates an effective electronic structure to form a linear E≡E triple bond, but the resulting electrostatic interactions account for the highly stable global E₂Li₆²⁺ clusters.     

Model study of the relaxation accompanying adsorption of atomic hydrogen on the Li(100) cluster surface

Relaxation effects in the (4, 1, 4) and (5, 4) Li₉ clusters induced by interaction with H are studied using the diatomics-in-molecules method. Total electronic energies for the clusters are determined as functions of the Li-Li bond lengths, both in the absence and in the presence of hydrogen adsorbed in a position of C_4v symmetry. Two models of cluster relaxation are considered, differing in which part of the cluster is allowed to relax. The calculations reveal that hydrogen adsorbed on the (100) cluster surface causes quite a significant contraction of the metal atoms. The effect of the cluster relaxation on the nonadiabatic coupling between the lowest two Born-Oppenheimer states of the hydrogen-cluster system is discussed.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Theoretical prediction for the structures of gas phase lithium oxide clusters: (Li2O)n (n = 1–8)

We apply genetic algorithm combining directly with density functional method to search the potential energy surface of lithium‐oxide clusters (Li₂O)_n up to n = 8. In (Li₂O)_n (n = 1–8) clusters, the planar structures are found to be global minimum up to n = 2, and the global minimum structures are all three‐dimensional at n ≥ 3. At n ≥ 4, the tetrahedral unit (TU) is found in most of the stable structures. In the TU, the central Li is bonded with four O atoms in sp³ interactions, which leads to unusual charge transformation, and the probability of the central Li participating in the bonding is higher by adaptive natural density partitioning analysis, so the central Li is in particularly low positive charge. At large cluster size, distortion of structures is viewed, which breaks the symmetry and may make energy higher. The global minimum structures of (Li₂O)₂, (Li₂O)₆, and (Li₂O)₇ clusters are the most stable magic numbers, where the first one is planar and the later both have stable structural units of tetrahedral and C_4v. © 2012 Wiley Periodicals, Inc.     

Theoretical study of the activation barriers of elementary reactions of hydrogenation of aluminide clusters X@Al<Subscript>12</Subscript> and X@Al<Stack><Subscript>12</Subscript><Superscript>−</Superscript></Stack> with dopants X = Al,Si, and Ge

The transition states and activation barriers h of elementary reactions of addition of the H₂ molecule to aluminide clusters Al₁₃, Al ₁₃ ^? , Al₁₃H ₂ ^? , Al₁₃H ₄ ^? , Si@Al₁₂, Ge@Al₁₂, and LiAl₁₃ were calculated within the B3LYP approximation of the density functional theory using 6–31G* and 6–311+G* basis sets. The barriers h for all diamagnetic clusters were found to be high (～30–40 kcal/mol). The outer-sphere cation Li⁺ decreases while the endohedral electronegative dopants Si and Ge increase the barrier by a few kcal/mol. The hydrogenation barrier of the neural paramagnetic cluster Al₁₃, which has free valence, decreases to ～20 kcal/mol. The addition of a hydrogen atom or a Cl₂ molecule to both paramagnetic and diamagnetic aluminum clusters occurs without a barrier. The first stage of the reaction (addition of H₂ to an Al-Al edge) is in all cases the critical stage of aluminide hydrogenation. The barrier h of this reaction is several times higher than the barriers to migration of hydrogen atoms over the metal cage. The migration of H atoms occurs simultaneously with considerable distortions of the Al₁₃ cage even to the extent that it changes its structural motif. The addition of the H₂ molecule to the Al@TiAl₁₁ cluster containing the peripheral titanium atom occurs with a small barrier, whereas the barrier to elimination of H₂ from the dihydride Al@TiAl₁₁H₂ is reduced to ～15 kcal/mol. Based on the calculations, the conclusion was drawn that the elementary reactions of hydrogenation and dehydrogenation for Ti-doped aluminide clusters should occur considerably faster and under milder conditions than for homonuclear aluminides.     

A Topological Study of the Ferromagnetic “No-Pair Bonding” in Maximum-Spin Lithium clusters: n+1Li n (n=2–6)

The nature of the bonding between lithium atoms, in low-spin and maximum-spin clusters, was investigated using the topological electron localization function (ELF) approach. The maximum-spin clusters are especially intriguing since their bonding is sustained without having even a single electron pair! Hence this type of bonding had been called “no-pair ferromagnetic-bonding” [Danovich, Wu, Shaik J Am Chem Soc 121:3165 (1999); Glokhovtsev, Schleyer Isr J Chem 33: 455 (1993); de Visser, Danovich, Wu, Shaik J Phys Chem A 106:4961 (2002)]. The following conclusions were reached in the study: (a) In the ground state of Li _n , covalent bonding between Li atoms is accounted by the presence of the disynaptic valence basins, which exhibit a significant degree of inter-basin delocalization. (b) Except for the ³Li₂ case, the valence basins of all maximum-spin clusters are populated by unpaired electrons. The valence basins are located off Li–Li axis (or Li–Li–Li plane), so that their spatial distribution minimizes the mutual Pauli repulsion and screens the electrostatic repulsion between the Li cores. The inter-basin delocalization is rather high, thereby indicating that the unpaired electrons are virtually delocalized over all the valence basins. (c) The ELF analysis shows that Li atoms in the low-spin clusters are bonded by “two-center two-electron” and “three-center two-electron” bonds. (d) In the maximum-spin species, bonding is sustained by “two-center one-electron” and “three-center one-electron” bonds. The latter picture is complementary to the valence bond picture [Danovich, Wu, Shaik J Am Chem Soc 121 3165 (1999); de Visser, Danovich, Wu, Shaik J Phys Chem A 106: 4961 (2002)], in which the bicentric ferromagnetic-bonding is delocalized over all the short Li–Li contacts, by the mixing of the ionic structures and other nonredundant structures into the repulsive high-spin covalent structure in which all the electrons populate the 2s atomic orbitals, i.e., the configuration. In such a manner bonding can be sustained from “purely ferromagnetic interactions” without electron pairing.Dedicated to Jean-Paul Malrieu, a friend and a poet-scientist     

Molecular orbital analysis of the bonding in high nuclearity gold cluster compounds

Extended Hückel molecular orbital calculations on high nuclearity gold clusters of the general type [Au(AuPH₃)_n]^x+ have demonstrated that they can be classified into two broad topological classes according to the three-dimensional disposition of the peripheral gold atoms. If they lie approximately on a sphere they are characterised by a total of 12n + 18 valence electrons, but if they adopt a toroidal or eliptical arrangement the total electron count is 12n + 16. The computed energy differences between alternative polyhedral geometries is generally small and accounts for the stereochemical non-rigidity of the gold cluster compounds in solution. Detailed aspects of the structures of the high nuclearity gold cluster compounds have been interpreted in terms of molecular orbital calculations on clusters derived from the centred chair [Au₇(PH₃)₆]⁺ by edge- and face-capping with Au(PH₃)⁺ fragments.     

Comparative analysis of the state of lithium and sodium atoms in water clusters

Structures and energetic characteristics of Li(H₂O) _n and Li⁺(H₂O) _n clusters with n = 1–6, 19, and 27 determined in the second order of the Møller-Plesset perturbation theory with 6–31++G(d,p) basis set are analyzed. The electron density redistribution, which takes place upon the electron addition to a Li⁺(H₂O) _n cluster, is found to be provided by hydrogen-bonded water molecules: initially almost neutral molecules, which are most distant from lithium, become negatively charged. The calculated energies of the electron capture by Li⁺(H₂O) _n clusters are approximated with the appropriate electrostatic model, and estimates of the lithium ionization energy in water clusters of various sizes are found. Similar estimates obtained earlier for sodium are made more accurate.     

VIBRATIONAL SPECTRA OF (t-C4H9 6Li)4 AND (t-C4H9 7Li)4: Raman Intensities and the Question of Li-Li Bonding

Abstract

Raman frequencies and intensities in methylcyclohexane solution and infrared frequencies in Nujol mull, have been obtained and assigned for the skeletal modes of (t-C₄H₉ ⁶Li)₄ and (t-C₄H₉ ⁷Li)₄. A normal coordinate analysis, neglecting hydrogen atoms, gave an overall frequency fit of 2% with a reasonable set of valence force constants. The calculated eigenvectors were used to transform the Raman intensities into bond polarizability derivatives. Because of coordinate mixing and the inherent sign ambiguity of molecular polarizability derivatives, there are eight sets of bond polarizability derivatives which are consistent with the measured intensities. Only one set, however, gives reasonable polarizability derivatives for CC stretching and CCC bending, and also shows the requisite invariance to isotope substitution. This set gives a low value for the Li-Li polarizability derivative, and application of the delta function potential equation suggests that the extent of Li-Li bonding is small, amounting to perhaps 5% of the total bonding electron density in the Li₄C₄ cage. This conclusion is consistent with the failure to observe Li[sbnd]Li spin-spin coupling in (t-C₄H₉Li)₄.     

One-Electron Pseudo-Potential Determination of Stable Isomers of the Li*Ar n Excited Clusters: Absorption Spectra

We present pseudo-potential calculations of geometrical structures of stable isomers of LiAr _n clusters with both an electronic ground state and excited states of the lithium atom. The Li atom is perturbed by argon atoms in LiAr _n clusters. Its electronic structure obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Li⁺Ar _n core, the Li⁺ and Ar atoms are replaced by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for the polarization and correlation of the inert core with the valence Lithium electron [J Chem Phys 116, 1839 1]. The geometry optimization of the ground and excited states of LiAr _n (n = 1–12) clusters is carried out via the Basin-Hopping method of Wales et al. [J Phys Chem 101, 5111 2; J Chem Phys 285, 1368 3]. The geometries of the ground and ionic states of LiAr _n clusters were used to determine the energy of the high excited states of the neutral LiAr _n clusters. The variation of the excited state energies of LiAr _n clusters as a function of the number of argon atoms shows an approximate Rydberg character, corresponding to the picture of an excited electron surrounding an ionic cluster core, is already reached for the 3s state. The result of optical transitions calculations shows that the absorption spectral features are sensitive to isomer structure. It is clearly the case for transitions close to the 2p levels of Li which are distorted by the cluster environment.     

Crystal Chemistry of Lithium Intermetallic Compounds: A Survey

The structural chemistry of lithium intermetallic compounds that are formed in Li–М binary systems where М = Ca, Sr, Ba, Mg, Zn, Cd, and Hg is surveyed. It is for the first time that the crystal structures of intermetallic compounds are classified in terms of polyhedral precursor metal clusters (in the program package ToposPro). The precursor metal clusters of crystal structures are identified using the algorithms of partitioning structural graphs into cluster structures and via the design of the basal 3D network of the structure in the form of a graph whose nodes correspond to the positions of the centers of precursor clusters. Tetrahedral precursor metal clusters M₄ are identified for the crystal structures LiZn₃-oC4, LiMg₃-hP2, LiCd₃-hP2, LiHg₃-hP8, (LiMg₃)(Li₂Mg₂)-tI16, Li₂Zn₂-cF16, Li₂Cd₂-cF16, Li₂Hg₂-cP2, Li₃Cd-cF4, and Li₃Hg-cF16; tetrahedral metal clusters M₄ are found for the framework structures with spacer atoms Sr(Li₂Sr₂)-tP20, Ca₂(Li₄)-cF24, and Ca₂(Li₄)-cP12; tetrahedral metal clusters M₄ and rings M₆, for framework structures Ba₃Li₂(Li₁₀)-hP30 and Ba₃Li₂(Li₄In₆)-hP30; icosahedral metal clusters M13 for the framework structure Li(Zn₁₃)-cF112; bilayer tetrahedral metal clusters 0@М₄@M₂₂ for the framework structure Li₂₃Sr₆-cF116; and deltahedra М₁₇ and deltahedra М₃₀, for framework structures Sr₄Li₁₄ [Sr(Sr₄Li₁₂)] [(Sr₂ (Sr₈Li₁₈)]-tI252 and Ba₄Li₁₄ [Ba(Ba₄Li₁₂)][(Ba₂ (Ba₈Li₁₈)]-tI252. The scenario of crystal structure self-assembly from precursor metal clusters S₃⁰ in intermetallic compounds is reconstituted as: primary chain S₃¹→ microlayer S₃²→ microframework S₃³.     

Cluster molecular orbitals and an orbital symmetry view of solid phase transitions in perovskites

The molecular orbitals, normalization constants and energies of the M₈(O_h), M₄(T_d) and M₆(O_h) clusters are derived and tabulated through the d-atomic orbitals. A vector method, adapted to computer application, is devised to compute s, p and d overlap between variously oriented orbitals at atoms that do not have co-directional local axes. Mixing of σ, π and δ orbitals to give the same irreducible representation is also included. As illustrations, the orbitals of Sr₈, La₈, TiO₆ and AlO₆ clusters are computed by the Mulliken—Wolfsberg and Helmholz approximations. During solid phase transitions in the perovskite structures of SrTiO₃ and LaAlO₃, the TiO₆ octahedron rotates about the C₄ axis whereas the AlO₆ octahedron rotates about the C₃ axis. This difference is explained qualitatively in terms of the relative symmetries of the cluster HOMOs and LUMOs using the second-order Jahn—Teller effect. Allusions are made to the application of this cluster symmetry approach to other systems.     

A Theoretical Study of Some Possible Fluxional Pathways for Alkyllithium Hexamers

We examined several possible fluxional pathways for hexameric alkyllithiums, performing ab initio SCF calculations on the model compounds octahedral Li₆H₆, Li₆H₄(CH₃)₂, and Li₆(CH₃)₆. The lowest energy structures for these compounds had an approximately octahedral arrangement of the lithiums, with the H or CH₃ ligands occupying six of the eight faces. The two empty faces were trans related. A concerted mechanism in which each of two ligands on opposite sides of the octahedron moves to an empty face was found to have a low energy barrier. The midpoint structures of this pathway for both Li₆H₆ and Li₆H₄(CH₃)₂ were symmetric or undistorted, whereas the midpoint structure for Li₆(CH₃)₆ was quite distorted. These results are discussed in the light of similar findings on Li₆ clusters. The adequacy of using 3-21G as a basis set for investigating alkyllithium geometries is also discussed.B. Davis Schwartz Memorial Library     

General properties of the electronic structure of alkali metal clusters and Ia-IIa mixed clusters

The results of the systematic ab-initio CI investigation of neutral and charged Li _n , Na _n , BeLi _k and MgNa _k clusters are summarized and analyzed. The general characteristic features of the electronic structure are pointed out:a) The participation of the atomic orbitals, which are empty in Ia and IIa metal atoms, allows for a higher valency of these atoms in clusters.b) Jahn-Teller and pseudo-Jahn-Teller effects strongly influence the electronic and geometric structure of clusters.c) Deformations of cluster geometry can lead to biradicaloid structures with higher spin multiplicity in their ground states.d) The peculiarities of the electronic structures of clusters can be deduced from the presence of many “surface” atoms. The theoretical results agree with experimental data presently available and they are useful for interpretation of the experimental findings.     

The Aggregation Behavior of Butyllithium in Diethyl Ether in the Presence of LiBr,LiClO4, and Phenyllithium: A Deuterium‐Induced Secondary 6Li‐NMR Isotope‐Effect Study

The aggregation of BuLi (LiR) in diethyl ether (Et₂O) in the presence of LiBr was studied by ⁶Li‐ and ¹³C‐NMR spectroscopy. For a 1.0 : 0.8 mixture of both species, the clusters (LiR)₄, Li₄R₃Br, Li₄R₂Br₂, Li₄RBr₃, and/or Li₂RBr in the ratio 7 : 81 : 12 with Li₄RBr₃ and/or Li₂RBr<1 were detected with the isotopic fingerprint method that is based on secondary deuterium (D)‐induced isotope shifts for δ(Li). The raising content of bromide ions causes increased shielding for δ(Li). As in the case of a 1 : 1 MeLi/LiBr mixture in Et₂O, cluster Li₄R₃Br is the most stable one. In the presence of N,N,N′,N′‐tetramethylethylenediamine (TMEDA), only a mixed dimer was found. For LiClO₄, no inclusion of the ClO$\rm{{_{4}^{-}}}$ ion could be detected. A mixture BuLi/PhLi 1 : 1 in Et₂O in the presence of TMEDA showed only dimers with the mixed dimer as the most stable cluster. Chemical exchange of Li between the two homodimers was detected by EXSY spectroscopy. This implies an exchange mechanism with a fluxional tetramer as intermediate.     

Cluster self-organization of TR-containing silicate and germanate systems: Suprapolyhedral precursors and self-assembly of A2HMTO5 (A = Li, Na; M = Sc, Lu, Yb) crystal structures with MTO5 frameworks

The combinatorial topological analysis is carried out using the coordination sequences method (the TOPOS 4.0 program package) and the matrix self-assembly is modeled for silicates Li₂HTRSiO₅ (TR = Lu, Yb; space group $P\bar 1$ ) and germanate Na₂HScGeO₅ (space group P2₁ ab). These compounds, having identical formulas, have different MT frameworks built of M octahedra (TRO₆) and T tetrahedra (SiO₄, GeO₄). New types of crystal-forming binodal nets are discovered: 4 4 6 6 + 4 4 6 for lutetium silicate and 44444(4⁵) + Ge 444(4³) for scandium germanate; the atom-site ratio in the nets is M: T = 1: 1. A ring invariant suprapolyhedral precursor cluster composed of four polyhedra is identified, with two (A = Li, Na) atoms lying one above and one below the center of the cluster. A₂M₂T₂ precursor clusters control the evolution of high-level crystal-forming clusters by means of the matrix assembly mechanism. The evolution routes of the suprapolyhedral precursor clusters bifurcate at the stage where topologically dissimilar layers are formed of equivalent chains. The cluster coordination numbers (CCNs) in a layer for the precursor clusters are four for lutetium silicate and six for scandium germanate.     

Cover Feature: Rare Spin Avoided σ-σ Diradical Planar Tetracoordinate Boron Cluster: A Proto-Star for Planar Pentacoordination (ChemPhysChem 18/2023)

We report a global planar star-like cluster B₃Li₃ featuring three planar tetracoordinate boron centres with a rare spin avoided σ-σ diradical character. The cluster was found to be stable towards dissociation into different fragments. The spin density was found to be localized solely on the three boron atoms in the molecular plane. This spin avoided σ-σ diradical character leads to the extension of the coordination number to yield a neutral B₃Li₃H₃ and a cationic B₃Li₃H₃⁺ cluster with three planar pentacoordinate boron centres in their global minimum structures. The planar geometry of the aninonic B₃Li₃H₃⁻ cluster is slightly higher in energy. The planar global clusters were found to maintain planarity in their ligand protected benzene bound complexes, B₃Li₃(Bz)₃, B₃Li₃H₃(Bz)₃ and B₃Li₃H₃(Bz)₃⁺ with high ligand dissociation energies offering candidature for experimental detection.     

Thermal electronic properties of alkali clusters

We apply the finite-temperature Kohn-Sham method to alkali metal clusters, using the spherical jellium model and treating the valence electrons as a canonical system in the heat bath of the ions. We study the shell effects in the total free energyF(N) and the entropyS(N) for neutral clusters containingN atoms. Their strongest temperature dependence is due to the finite ground-state valueS ₀>0 of the electronic entropy for non-magic clusters. It leads to a decreasing amplitude and an increasing smear-out of the saw-tooth structure in the first difference Δ₁ F(N)=F(N?1)?F(N) with increasing temperatureT and cluster sizeN.     

Kristallstruktur des Lithium‐Trimethylsilanolats [Li7(OSiMe3)7(THF)]

The lithium silanolate LiOSiMe₃ is accessible from the reaction of Me₃SiOSiMe₃ with LiMe in tetrahydrofuran. Single crystals of [Li₇(OSiMe₃)₇(THF)] were obtained from toluene at 25 °C. The structure of [Li₇(OSiMe₃)₇(THF)] (C2/c) features a capped trigonal antiprismatic arrangement of seven Li atoms. The Li atoms in [Li₇(OSiMe₃)₇(THF)] are μ₃‐bridged by seven O atoms of the silanolate ligand.