Tunnel-exchange states of square-planar bielectron transfer clusters

The tunnel states of square-planar bielectron transfer dⁿ-dⁿ-dⁿ⁺¹-dⁿ⁺¹ (n=0–4) clusters are considered. The nature of the ground spin state is revealed in the limiting case of a strong double exchange. It is shown that the magnetic properties of these systems radically differ from those of clusters with one migrating electron (hole) and tetrameric tetrahedral bielectron transfer clusters. Moldova State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 826–833, September–October, 1996. Translated by I. Izvekova     

Magnetic properties and tunnel exchange states of dimeric mixed-valence clusters with two-electron transfer

Tunnel states of dimeric mixed-valence clusters with dⁿ-dⁿ⁺² type two-electron transfer are considered. General expressions for the matrix elements of the double exchange operator are obtained taking into account the contributions of the excited states. The energy spectrum of the clusters is calculated and the magnetic properties are studied. Allowance for the dⁿ⁺¹-dⁿ⁺¹ excited states considerably affects the energy spectrum and the magnetic properties of the systems. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1038–1045, November–December, 1997.     

Double exchange in polynuclear mixed-valence clusters. 1. General solution of the electronic problem

The problem of calculating the electronic energy spectra of mixed-valence clusters with one “extra” electron (dⁿ-dⁿ...dⁿ⁺¹) or hole (dⁿ⁺¹-dⁿ⁺¹...dⁿ) delocalized in the paramagnetic cores of transition metals is solved. Unlike the available particular solutions, which are restricted to small numbers of ions and electrons, the solution proposed in this work is general and is suitable for many-electron systems of arbitrary numbers of nuclei and arbitrary symmetries. The new microscopic approach to the double exchange problem is based on the combination of the sequential (“chain”) scheme of spin coupling and angular momentum method. In terms of this approach, an analytical dependence of the matrix elements of the double exchange, Heisenberg exchange, and vibronic interaction on all spin quantum numbers is obtained. The final equations contain only the 6j symbols and are free of the higher-order nj symbols, which obstructed the solution of the double exchange problem in previous works. Valencia University, Spain. Bordeaux University, France. Moldova State University. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 805–815, September–October, 1996. Translated by I. Izvekova     

Double exchange in polynuclear mixed-valence clusters. 2. Iron-sulfur proteins [Fe4S4]+ and [Fe4S4]3+

The energy states of tetrameric iron clusters with d⁶-d⁶-d⁶-d⁵ and d⁵-d⁵-d⁵-d⁶ electronic configurations, which form the metal frameworks of the [Fe₄S₄]⁺ and [Fe₄S₄]³⁺ iron-sulfur proteins, are calculated using a general approach. It is revealed that the structural distortions of these systems significantly affect the composition of the magnetic states. The effect of the isotropic Heisenberg exchange is considered. Valencia University, Spain. Bordeaux University, France. Moldova State University. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 816–825, September–October, 1996. Translated by I. Izvekova     

Electronic and vibronic states of an asymmetric trimeric mixed-valence cluster

Electronic and adiabatic vibronic states of d¹-d¹-d² trimeric clusters are considered in terms of the many-electron theory of mixed-valence states. The initial model includes two d-orbitals on each center and allows for Heisenberg and double exchange, asymmetry of the system, and vibronic coupling with local shifts of ligands. Influence of distortions in the trimers on the structure of tunnel-exchange states, on ferro-or antiferromagnetism of the clusters, and on the form of the adiabatic potential is examined. State University, Moldova Republic. Valencia University, Spain. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 4, pp. 35–45, July–August, 1994. Translated by L. Smolina     

Density functional theory study on (F2AlN3) n (n = 1–4) clusters

Possible geometrical structures and relative stabilities of (F₂AlN₃) _n (n = 1–4) clusters were studied using density functional theory at the B3LYP/6-311+G* level. The optimized clusters (F₂AlN₃) _n (n = 2–4) possess cyclic structure containing Al–N_α–Al linkages, and azido in azides has linear structure. The IR spectra of the optimized (F₂AlN₃) _n (n = 1–4) clusters have three vibrational sections, the whole strongest vibrational peaks lie in 2218–2246 cm⁻¹, and the vibrational modes are N₃ asymmetric stretching vibrations. Trends in thermodynamic properties with temperature and oligomerization degree n are discussed, respectively. A study of their thermodynamic properties suggests that monomer 1A forms the most stable clusters (2A, 3A, and 4B) can occur spontaneously in the gas phase at temperatures up to 800 K.     

Theoretical study on cooperative and extra-additive behavior of hydrogen-bonded clusters

The stabilization energy △ E(n) and four typical properties of hydrogen bond F-H…F in chain-like and cyclic (HF)n clusters (n = 1-5) have been calculated using MP2 and three DF levels of theory with the Gaussian 98 program, and 6-31++G** bases set. The results demonstrate that the extra-additive or cooperative behavior in (HF)n clusters is very obvious. In addition, we studied much larger chain-like (HF)n (n = 6, 9, 12,18, 24) clusters using one of these DF methods.     

Calculated properties of neutral and charged Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> clusters by density functional theory

Density functional calculations are performed to study the structures and electronic properties of Al _n Co _m clusters with n = 1–7 and m = 1–2. Frequency analysis is also performed after structural optimization to make sure that the calculated ground states are real minima. The corresponding total and binding energies, adiabatic electron affinities and ionization potentials are presented and discussed to aid the identification of our calculations. The BSSE correction is also considered in our calculation. Among Al _n Co _m , Al _n Co _m ⁻, and Al _n Co _m ⁼ clusters (n = 1–7 and m = 1–2), Al₄Co⁻, Al₆Co⁻, Al₂Co₂, and Al₆Co₂ are predicted to be more stable. Our results are consistent with the available experimental data.     

Cobalt(II) chloro complexation in N-methylformamide–N, N-dimethylformamide mixtures

Cobalt(II) chloro complexation has been studied by titration calorimetry and spectrophotometry in solvent mixtures of N-methylformamide (NMF) and N,N-dimethylformamide (DMF). It revealed that a series of mononuclear CoCln_n ^(2–n)+ (n=1–4) complexes are formed in the mixtures of NMF mole fraction x _NMF=0.05 and 0.25, and the CoCl⁺, CoCl₃ ^– and CoCl₄ ^2– complexes in the mixture of x _NMF=0.5, and their formation constants, enthalpies and entropies were obtained. As compared with DMF, the complexation is markedly suppressed in the mixtures, as well as in NMF. The decreasing formation constant of CoCl⁺ with the NMF content is mainly ascribed to the decreasing formation entropy. DMF is aprotic and thus less-structured, whereas NMF is protic to form hydrogen- bonded clusters. In DMF-NMF mixtures, solvent clusters in neat NMF are ruptured to yield new clusters involving DMF, the structure of which depends on the solvent composition. The entropy of formation of CoCl⁺ will be discussed in relation to the liquid structure of DMF, NMF and their mixtures.     

Theoretical studies on anionic clusters of sulfate anions and carbon dioxide, SO 4?1/?2 (CO2)n, n?=?1?4

Geometry optimizations were performed on monoanionic and dianionic clusters of sulfate anions with carbon dioxide, SO₄^−1/−2(CO₂) _n , for n = 1–4, using the B3PW91 density functional method with the 6-311 + G(3df) basis set. Limited calculations were carried out with the CCSD(T) and MP2 methods. Binding energies, as well as adiabatic and vertical electron detachment energies, were calculated. No covalent bonding is seen for monoanionic clusters, with O₃SO–CO₂ bond distances between 2.8 and 3.0 ?. Dianionic clusters show covalent bonding of type [O₃S–O–CO₂]⁻², [O₃S–O–C(O)O–CO₂]⁻², and [O₂C–O–S(O₂)–O–CO₂]⁻², where one or two oxygens of SO₄⁻² are shared with CO₂. Starting with n = 2, the dianionic clusters become adiabatically more stable than the corresponding monoanionic ones. Comparison with SO₄^−1/−2(SO₂) _n and CO₃^−1/−2(SO₂) _n clusters, the binding energies are smaller for the present SO₄^−1/−2(CO₂) _n systems, while stabilization of the dianion occurs at n = 2 for both SO₄⁻²(CO₂) _n and SO₄⁻²(SO₂) _n , but only at n = 3 for CO₃⁻²(SO₂) _n .     

A density functional theory study on the Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H (<Emphasis Type="Italic">n</Emphasis> = 1–10) clusters

Density functional GGA-PW91 method with DNP basis set is applied to optimize the geometries of Ag _n H (n = 1–10) clusters. For the lowest energy geometries of Ag _n H (n = 1–10) clusters, the hydrogen atom prefers to occupy the two-fold coordination bridge site except the occupation of single-fold coordination site in AgH cluster. After adsorption of hydrogen atom, most Ag _n structures are slightly perturbed and only the Ag₆ structure in Ag₆H cluster is distorted obviously. The Ag–Ag bond is strengthened and the strength of Ag–H bond exhibits a clear odd–even oscillation like the strength of Au–H bond in Au _n H clusters, indicating that the hydrogen atom is more favorable to be adsorbed by odd-numbered pure silver clusters. The adsorption strength of small silver cluster toward H atom is obviously weaker than that of small gold cluster toward H atom due to the strong scalar relativistic effect in small gold cluster. The pronounced odd–even alternation of the magnetic moments is observed in Ag _n H systems, indicating that the Ag _n H clusters possess tunable magnetic properties by adsorbing hydrogen atom onto odd-numbered or even-numbered small silver cluster.     

Cage Structure Formation of Singly Doped Aluminum Cluster Cations Al<Subscript><Emphasis Type="BoldItalic">n</Emphasis></Subscript><Emphasis Type="BoldItalic">TM</Emphasis><Superscript>+</Superscript> (<Emphasis Type="BoldItalic">TM</Emphasis> = Ti,V, Cr)

Structural information on free transition metal doped aluminum clusters, Al _n TM ⁺ (TM = Ti, V, Cr), was obtained by studying their ability for argon physisorption. Systematic size (n = 5 – 35) and temperature (T = 145 – 300 K) dependent investigations reveal that bare Al _n ⁺ clusters are inert toward argon, while Al _n TM ⁺ clusters attach one argon atom up to a critical cluster size. This size is interpreted as the geometrical transition from surface-located dopant atoms to endohedrally doped aluminum clusters with the transition metal atom residing in an aluminum cage. The critical size, n _crit , is found to be surprisingly large, namely n _crit = 16 and n _crit = 19 – 21 for TM = V, Cr, and TM = Ti, respectively. Experimental cluster–argon bond dissociation energies have been derived as function of cluster size from equilibrium mass spectra and are in the 0.1–0.3 eV range.     

Fragmentation of sputtered vanadium and niobium cluster ions,kinetic release and dissociation energy

The generation and unimolecular fragmentation of V _n ⁺ and Nb _n ⁺ clusters formed in sputtering vanadium and niobium surfaces by Xe⁺ ions has been studied. The method of measuring the kinetic energy of fragment ions (kinetic energy release distribution) has been used to determine the dissociation energy. Kinetic energy spectra have been measured in the field-free zone (corresponding to a time window of 10⁻⁵–10⁻⁴ sec after emission) of an ion microanalyzer with double focusing in reverse geometry. The results of spectra measurement were treated using the Rice-Ramsperge-Kassel theory of unimolecular reactions and the “evaporative ensemble”, which allowed us to calculate the dissociation energies of homonuclear V _n ¹ (n= 5–11) and Nb _n ¹ (n = 3–8) clusters.     

All-electron relativistic calculations on hydrogen atom adsorption onto small copper clusters

An all-electron scalar relativistic calculation on Cu _n H (n = 1–13) clusters has been performed by using density functional theory with the generalized gradient approximation at the PW91 level. Our results reveal that the hydrogen atom prefers to occupy the two fold coordination site for Cu _n H (n = 2, 4–6, 8, 10–13) clusters, the single fold coordination site for Cu _n H (n = 1, 3, 7) and the three fold coordination site for Cu₉H cluster. For all Cu _n H clusters, only the Cu₁₁ structure in Cu₁₁H is distorted obviously. After adsorption, the Cu–Cu bond is strengthened and the Cu–H bond of odd-numbered Cu _n H clusters is relatively stronger than that of adjacent even-numbered Cu _n H clusters. The Cu–Cu bond-length and Cu–H bond-length for all Cu _n H clusters of our work are significantly shorter than those of previous work. This discrepancy can be explained in terms of the scalar relativistic effect. The most favorable adsorption between small copper clusters and hydrogen atom takes place in the case that hydrogen atom is adsorbed onto an odd-numbered pure Cu _n cluster and becomes Cu _n H cluster with even number of valence electrons. The odd–even alteration of magnetic moments is observed in Cu _n H clusters and may provide the material with tunable code capacity of “0” and “1” by adsorbing a hydrogen atom onto odd- or even-numbered copper clusters.     

Structure and stability of the mixed polymolecular complexes of nitrogen and carbon nonooxide: A quantum chemical study

The structure and stability of heteromolecular van der Waals clusters (N₂) _n CO _m ( _n = 1–7; m = 1–3) was studied using ab initio MP2(full)/6-311+G* and CCSD(full)/6-311+G* methods. For clusters with (n + m) > 3 the polyhedron structures are the most preferable, whose stability increases with the number of interacting molecules. Incorporation of CO molecules results in weakening of binding in the cluster and lowering the stereochemical rigidity relative to homomolecular systems. Increase of percentage of CO is followed by a decrease of stability of the clusters.     

Debye–Hückel Contributions to the Gibbs Energy Interaction Parameters for Ternary Electrolyte + Non-Electrolyte + Water Systems

The Debye–Hückel and non-Debye–Hückel contributions to the Gibbs energy interaction parameters are investigated for electrolyte (E) + non-electrolyte (N) + water (W) systems. A method is proposed for calculating the interaction parameters, C _n ^DH,C _n ^N, and C _n ^T, which represent the Debye–Hückel, non-Debye–Hückel, and total contributions, respectively. Four ternary E + N + W systems are chosen and the interaction parameters are computed with different forms of the Debye–Hückel equation. Results show that: (1) the Gibbs energy interaction parameters between E and N can be divided into two parts: the Debye–Hückel contribution and the non-Debye–Hückel contribution, C _n ^T=C _n ^DH+C _n ^N; (2) the signs and magnitudes of the Debye–Hückel contribution to the interaction parameters, C _n ^DH, depend mainly on the change in the dielectric constant of the solvent due to the addition of the non-electrolyte into the solvent; and (3) when the addition of the non-electrolyte only affects slightly the dielectric constant of the solvent, C ₁^DH (indicating the Debye–Hückel contribution to the interaction parameter for E + N) has a very small value and consequently can be neglected. In general, C ₁^DH is large, even larger than C ₁^N. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Effect of ligand coordination type on the relative stability of linear mercury clusters

The problem of stabilization of linear mercury clusters with acceptor ligands coordinated along the symmetry axis of the cluster is discussed in terms of the MNDO method. It is shown that stable four-membered rings Hg₂Cl₂ may be formed. It is proposed that the structure of linear mercury clusters with side coordination of ligands be described as the result of “polymerization” of short stable linear molecules XHg_nX (n=1, 2) and HgX ₂ ¹⁻ , HgX ₃ ¹⁻ ions with accepting terminal groups. Mordovia State University. Institute of Organoelement Compounds, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 1, pp. 26–34, January–February, 1998. This work was performed in the framework if the interindustry scientific and technical program “Fullerenes and Atomic Clusters.”     

Structural Growth Sequences and Electronic Properties of Lanthanum-Doped-Gold Clusters

The geometries, stabilities, and electronic properties of Au _n La (n = 2–8) clusters have been systematically investigated by using density-functional theory. The results show that the doped La atom prefers to locate at the center site with the number of Au atom increasing from 2 to 8. Furthermore, the Au _n La clusters are more stable than the Au _n+1 clusters. The charges transfer from La atom to Au atoms at n = 2–4, but charge-transferring is reversed at n = 5.     

Analysis of fragmentation data and molecular orbital calculations of small argon ion clusters

Distributions of argon clusters (Ar _n ⁺ wheren=1–27) obtained in a molecular beam/time-of-flight system were analyzed in order to assess the influence of fragmentation. The results from rudimentary pseudopotential molecular calculations were calculated to predict the most stable structures and stabilities for the smaller argon ion sized clusters (Ar _n ⁺ wheren=3−9).     

Trends in the formation of aggregates and crystals from M@Si<Subscript>16</Subscript> clusters: a study from first principle calculations

We have shown recently that the ground state and low-lying energy isomers of the endohedral M@Si₁₆ clusters (M = Sc⁻, Ti, V⁺) have a nearly spherical cage-like symmetry with a closed shell electronic structure which conforms them as exceptional stable entities. This is manifested, among other properties, by a large Homo–Lumo gap about 2 eV which suggest the possibility of using these clusters as basic units (superatoms) to construct optoelectronic materials. As a first step in that direction, we have studied in this work, by means of first principles calculations, the trends in the formation of [Ti@Si₁₆] _n , [Sc@Si₁₆K] _n , and [V@Si₁₆F] _n aggregates as their size increases, going from linear to planar to three dimensional arrangements. The most favorable configurations for n ≥ 2 are those formed from the fullerene-like D_4d isomer of M@Si₁₆, instead of the ground state Frank–Kasper T _d structure of the isolated M@Si₁₆ unit, joined by Si–Si bonds between the Si atoms of the square faces. In all cases the Homo–Lumo gap for the most favorable structure decrease with the size n. Trends for the binding energy, dipole moment, and other electronic properties are also discussed. Several crystal structures constructed from these superatom, supermolecules, and aggregates have been tested and preliminary results are summarily commented.