Bond Length Contraction Research Articles

Ab initio investigation of the electronic structure and bondingproperties of the layered ternary compound Ti3SiC2at high pressure

The pressure dependences of the lattice parameters, electronic structure,and bonding properties of the layered ternary compound Ti3SiC2were investigated by performing ab initio plane-wave pseudopotential total energycalculations. The material exhibited elastic anisotropy. The lattice constants andaxial ratio were studied for different pressures, and the same trend was obtainedas is measured in experiment. It was found that although the structure was stableat high pressure, the electronic structure and atomic bonding were definitelyaffected. The electrical conductivity was predicted to reduce with pressure, whichwas interpreted by analysing the band dispersion curve and density ofstates at the Fermi level. The strengths of the atomic bonds in Ti3SiC2were considered by analysing the Mulliken population and by examiningthe bond length contraction for various pressures. A redistribution ofcharge density that accompanied high pressures was also revealed.

Facile access to enantiomerically pure bis(sulfoxide) chelates of late transition metals

Herein contains a report detailing the synthesis and characterization of six, chiral, late-transition metal complexes all chelated using R S,R S-bis( p-tolylsulfinyl)ethane, R S,R S-BTSE. All complexes revealed S-ligation to the metal with an expected contraction of the sulfinyl-oxygen bond length when compared to free sulfoxide. The presented data serve to illustrate three attractive, yet unexplored, aspects of the bis(sulfoxide) bidentate ligand: (i) bidentate sulfoxide ligands, when chelated to a metal, give rise to complexes that are pseudo-C 2 symmetric in terms of both sterics and electronics, (ii) the sulfoxides, unlike typical N-, P-, and O-based ligands, present the coordination sphere with a significant amount of steric and electronic mismatch, and (iii) the data support the fact that sulfoxides are moderate σ-donors and good-to-excellent π-acceptors – an aspect that should afford such metal chelates with a wide degree of reactivity. Finally, X-ray crystallographic experiments, coupled with an extensive CCDC search, provide an opportunity to establish the following ligand-ranking scheme for bidentate ligands spanned by an ethylene bridge, R 2N–<RS(O)–<RS–<R 2P–, based on the trans influence of chloride salts of Pt(II).

Carbon 1s photoelectron spectroscopy of CF4 and CO: Search for chemical effects on the carbon 1s hole-state lifetime

Carbon 1s photoelectron spectra for CF4 and CO have been measured at several photon energies near the carbon 1s threshold. The spectra have been analyzed in terms of the vibrational structure and the natural linewidth. For CO the vibrational structure shows evidence for anharmonicity in both the energy spacing and the intensity. Analysis of the results using an anharmonic model gives an equilibrium bond length for core-ionized CO that is 4.85 pm shorter than that of neutral CO. For CF4, the vibrational structure is very weak, and the analysis shows that the change in equilibrium CF bond length upon ionization is no more than 0.54 pm. Ab initio theoretical calculations give results in accord with these bond-length changes. The unusually small bond-length contraction in CF4 can be understood in terms of nonbonded fluorine–fluorine repulsion. The natural linewidth for core-ionized CO, 95±5 meV, is essentially the same as that of CH4. This result is in contrast with expectations based on the one-center model of Auger decay and earlier predictions based on semiempirical molecular orbital theory. More recent calculations indicate, however, that there is only a small difference between CO and CH4, in agreement with the observed result. For CF4, the natural linewidth is 77±6 meV. This value differs from that for CH4 in the direction expected from the electronegativities of hydrogen and fluorine, but is greater than the prediction based on semiempirical theory. The natural linewidth for CO with a carbon 1s electron excited to the 2π resonance is 83 meV, which is significantly less than is found for core-ionized CO. Although this difference is supported by theoretical calculations, the direction of the difference is counterintuitive. An overview is presented of the current state of experimental and theoretical knowledge on carbon 1s linewidths.

Pressure-induced magnetic and electronic transitions in the layered Mott insulatorFeI2

Powder x-ray diffraction, electrical resistance, and ${}^{57}\mathrm{Fe}$ M\"ossbauer spectroscopy at pressures to at least 40 GPa in diamond anvil cells have been employed to investigate the pressure evolution of the structural, electrical-transport, and magnetic properties of the antiferromagnetic insulator ${\mathrm{FeI}}_{2}.$ Up to 18 GPa, the volume decreases by 25%, the resistivity decreases by eight orders of magnitude, ${T}_{N}$ increases 16-fold to 150 K, and the ${\mathrm{Fe}}^{2+}$ moments remain parallel to the c axis. The change in the isomer shift (IS), which is negatively proportional to the change in the s-electron density at the Fe nucleus, follows the volume reduction by continuously decreasing from 1.0 to 0.8 mm/s, the quadrupole splitting (QS) increases monotonically from 0.6 mm, peaking at 0.85 mm/s by 12 GPa, and decreases to 0.75 at 18 GPa, and the magnetic hyperfine field ${H}_{\mathrm{hf}}$ composed of spin and orbital terms with opposite signs increases from 8 to 12 T. At \ensuremath{\sim}18 GPa the orbital term quenches, as is evident from a M\"ossbauer component characterized by ${H}_{\mathrm{hf}}=32\mathrm{T}$ and ${e}^{2}{q}_{\mathrm{zz}}Q(3{\mathrm{cos}}^{2}\ensuremath{\theta}\ensuremath{-}1)=0,$ where the moments tilt to 55\ifmmode^\circ\else\textdegree\fi{}, and ${T}_{N}$ increases to 260 K. At 20 GPa an isostructural first-order phase transition occurs, accompanied by a discontinuous \ensuremath{\sim}5% decrease in volume and a considerably lower QS and IS. The c axis decreases by 5% with no decrease in the a axis, suggesting a considerable contraction of the Fe-I bond lengths. The high-pressure phase (HP) is diamagnetic, as characterized by a pure quadrupole-split spectrum to the lowest temperature of 5 K. The abundance of this diamagnetic phase increases with rising pressure reaching 100% by \ensuremath{\sim}38 GPa. The HP phase is also metallic, as shown by $R(P,T)$ data. The observation of diamagnetism, metallic behavior, and the considerable reduction in volume distances establishes that-a Mott or charge-transfer transition has occurred, resulting in the total collapse of any electron correlation. The coexistence of several phases and their respective abundances were determined from the M\"ossbauer data.

Spectroscopic and structural characterisation of a VO x ( x≈1) ultrathin epitaxial film on Pt (111)

VO x ultrathin epitaxial films (0.8≤ x≤1.3), grown on Pt(111) by evaporating vanadium in a controlled water background (1×10 −7 Pa), have been chemically characterised by X-ray photoelectron spectroscopy (XPS) and X-ray-excited Auger electron spectroscopy (AES), which confirm the presence of V(II). The VO film shows a NaCl-type structure exposing the (111) plane, as proven by XPD. Multiple scattering calculations are compatible with an O-terminated surface and a surface relaxation of the outermost atomic layers, which leads to a VO bond length contraction amounting to 7%.

Neptunium redox speciation

Insights about the redox speciation of neptunium in an aqueous mineral acid electrolyte were obtained through a combination of in situ EXAFS (extended X-ray absorption fine structure) spectroelectrochemistry, density functional theory (DFT), and simple geometric modeling. A single solution of neptunium in 1 M perchloric acid was used to extract metrical information about the Np coordination environment, in terms of hydration numbers (n) and Np-O interatomic distances. Four aquo ions - Np3+·nH2O, Np4+· n´H2O, [Np5+O2]+· n´´H2O, and [Np6+O2]2+· n´´´H2O - were electrolytically prepared and precisely maintained by use of constant potential bulk electrolysis (with coulometry) throughout the simultaneous EXAFS data acquisition. For the Np(III) and Np(IV) aquo ions, the experiments revealed a contraction of the average Np-O bond lengths from 2.48(2) to 2.37(2) Å, respectively. The data analyses suggest that there are 9 water molecules in the first or inner hydration sphere about Np3+in [Np(OH2)9]3+and Np4+in [Np(OH2)9]4+. The DFT calculations reveal 8-9 water molecules coordinated to Np(III), supporting the EXAFS results. Simple geometric modeling supports a coordination number of 8 for both trivalent and tetravalent Np. For the Np(V) and Np(VI) aquo ions, the EXAFS revealed bond length contractions. The average interatomic distances for the trans-dioxygen atoms in [NpO2]+and [NpO2]2+decreased from 1.80(2) Å for Np(V) to 1.73(2) Å for Np(VI). The average interatomic distances to the oxygen atoms of the coordinated H2O molecules decreased from 2.44(3) Å to 2.36(3) Å, respectively. The oxygen coordination numbers were identical, suggesting that 5 water molecules are bound to Np5+in [NpO2(OH2)5]+and to Np6+in [NpO2(OH2)5]2+.

Density Functional Derived Structures and Molecular Properties of Nickel Dithiolenes and Related Complexes

The molecular and electronic structure of the planar nickel dithiolene (1c, R = H) and of related complexes derived from nickel dithiolene by replacement of Ni by Pd (palladium dithiolene, 2c, R = H) or by Pt (platinum dithiolene, 3c, R = H), or by replacement of S by NH (nickel diiminolene, 1a, R = H), O (nickel dioxylene, 1b, R = H) or Se (nickel diselenolene, 1d, R = H), were studied by density functional theory using the B3LYP functional and the valence triple-zeta basis set 6-311+G* for all atoms except Pd and Pt. For the latter atoms the quasirelativistic effective core potentials of the Stuttgart group were employed. The molecular structure of nickel dithiolene (1c, R = H) is satisfactorily reproduced by DFT calculations. The geometry of the corresponding platinum complexes 3a–3d is more sensitive to relativistic effects, resulting in the contraction of the X–Pt bonds. As shown with the metal dithiolenes, the two ligands are structurally related to mononegative ions of open shell structure. The C–C bond lengths of the complexes are close to those of aromatic and chain-type polymethine structures (about 1.4 A). The nickel dithiolene (1c, R = H) and related complexes have D2h symmetry and are 14 π-electron systems with 10 π-electrons at the ligands and 4 π-electrons at the metal center. The natural population analysis has confirmed that metal M++ does accept electrons from the ligands but to a lesser extent than expected. The empty d-orbitals of M++ are only partly occupied in the molecular ground state. The positive charge of the metal decreases in the order Ni > Pd > Pt. The 1H chemical shifts and the nucleus-independent chemical shifts (NICSs) of the ring moieties calculated by GIAO-DFT display a pronounced electron delocalization. In agreement with the calculated C–C bond lengths the 1H chemical shifts and the NICS values show a marked bond delocalization. The NICS values show a change of the aromatic delocalization in the order Ni > Pd O < S < Se. The wave numbers of the IR spectra of the complexes calculated by DFT are grouped in separate frequency regions. The very intense absorption of 1c (R = H) in the visible region of the spectrum is surprisingly well reproduced by ab initio single-only configuration interaction calculations. While the color band of the palladium complex is predicted to be red-shifted relative to the nickel complex, a blue shift is calculated on passing from the palladium to the platinum complex. The blue shift is, in part, due to the relativistic contraction of bond lengths in the Pt complexes.

Relativistic effects on geometry and electronic structure of small Pdn species (n=1, 2, 4)

Relativistic effects on the properties of small neutral Pdn species (n=1, 2, 4) and Pd2− have been examined for the first time at the all-electron level by performing scalar-relativistic and nonrelativistic density functional calculations using a gradient-corrected density functional. Relativistic effects are found to be important: They lead to a contraction of bond lengths, increase of vibrational frequencies, and a significant enhancement of binding energies. While relativistic effects are quite uniform for several states of Pd4, they vary for the states examined for Pd2, leading to a change of ground state due to relativity. The calculated relativistic properties of Pd2 and Pd2− are in good agreement with available experimental data from mass spectrometry and photoelectron spectroscopy. For Pd4 three-dimensional structures are found to be preferred to planar ones and many nearly isoenergetic isomers exist. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 405–416, 1999

Deformation of boron networks at the LaB 6(111) surface

The dispersion of the phonons of the LaB 6(111) surface has been measured and reproduced on the basis of lattice dynamical calculations. The surface force constants were found to be different from the bulk force constants. In particular, the force constant of an interoctahedral boron–boron bond at the surface increases by 50% from the corresponding bulk force constant. From the relationship between the force constant and bond length in various hexaborides, we have estimated the contraction of the interoctahedral bond length to be 0.007 nm. The deformation of the boron network on the (111) surface, the behavior of which is similar to that on the (100) surface, is explained by the inherent nature of the boron network.

Third-nearest-neighbor carbon pairs in epitaxialSi1−yCyalloys: Local order for carbon in silicon characterized by x-ray photoelectron diffraction and Raman spectroscopy

The local order around carbon atoms in epitaxial ${\mathrm{Si}}_{1\ensuremath{-}y}{\mathrm{C}}_{y}$ alloys (with $y$ around 1%) grown by Si molecular-beam epitaxy and thermal decomposition of ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ on Si(001) or Si(111) has been studied as a function of growth temperature. To this end, information from local probes such as x-ray photoelectron spectroscopy C $1s$ binding energies, experimental and simulated C $1s$ core-level x-ray photoelectron diffraction (XPD) distributions, and Raman spectroscopy are compared. Between the growth conditions leading to a solid solution of substitutional C at lower temperature and those leading to SiC precipitation at higher temperature, original metastable and ordered C-rich alloy phases appear, which may be coherently embedded in Si without degrading crystal quality. The results for such phases probed by the two latter techniques are indicative of a crystalline order implying concentrated third-nearest-neighbor (NN) carbon pairs. The comparison of experimental XPD distributions recorded in different azimuthal planes with simulated ones with C either in substitutional or in interstitial sites is in favor of substitution with a local contraction of the first-neighbor Si-C bond length between 10% and 20%. If we admit that the surface ordering of the C atoms in the Si(001) surface layers is the extension of such particular bulk arrangements in third NN C pairs we are able to explain an experimentally observed $c\ensuremath{-}(4\ifmmode\times\else\texttimes\fi{}4)$ low-energy electron diffraction pattern.

Relativistic Effects on Covalent Bonding: Role of Individual Valence Atomic Orbitals

Relativistic effects on covalent bonding, in particular the role of individual valence atomic orbitals, have been investigated for diatomic (AuH and Pb 2 ) and hexafluoride (XF 6 : X=S, Se, Mo, Ru, Rh, Te, W, Re, Os, Ir, Pt, Po, Np, U and Pu) molecules, by analysis of bond overlap population using both nonrelativistic and relativistic DV-Xα molecular orbital methods. The contributions of valence atomic orbitals to the relativistic effects on covalent bonding for the molecules are clarified. The present approach is applied to interpret the physical picture of the relativistic effects on bond length of the AuH molecule. The origin of the relativistic bond-length contraction is discussed in comparison with previously reported results obtained by bonding energy calculations.

Theoretical study of nonpolar surfaces of aluminum nitride: Zinc blende (110) and wurtzite (101-|Am0)

All-electron density-functional calculations are performed to study atomic structure and electronic properties of the nonpolar surfaces, namely zinc blende (110) and wurtzite (101-|Am0) of AlN. Both surfaces are modeled using a two-dimensional periodic slab allowing the relaxation of the first two surface layers in the calculations. The results predict a small layer rotation angle accompanied by a contraction of Al-N bond length for both surfaces. These results do not follow the well-accepted rotation-relaxation model that predicts large layer rotation angles (\ensuremath{\sim}28\ifmmode^\circ\else\textdegree\fi{}) with no change in the bond length for most of the III-V semiconductor surfaces. Analysis of the relaxed configurations of the AlN surfaces in terms of atomic geometry, density of states, and charge density plots shows a presence of partial double-bond character in the surface Al-N bond. A similarity of these results with an earlier study on GaN nonpolar surfaces [J. E. Jaffe, R. Pandey, and P. Zapol, Phys. Rev. B 53, R4209 (1996)] led us to suggest the contraction-relaxation model where the relaxation proceeds via strengthening of the surface bond. The primary driving force of such a type of relaxation appears to be the ability of nitrogen to form a double bond that facilitates redistribution of the charge density associated with anion dangling bond to the surface bond.

A Density Functional Study of Metal-Ligand Bonding in [(PR(3))(2)M](+) and [PR(3)MCl] (M = Ag, Au; R = H, Me) Complexes.

Relativistic and nonrelativistic electronic structure calculations were carried out on [(PR(3))(2)M](+)and [PR(3)MCl] (M = Ag, Au; R = H, Me) complexes using the all-electron linear combination of Gaussian-type orbitals density functional (LCGTO-DF) method. The calculated relativistic metal-ligand bond lengths show good agreement with experimental values. The relativistic contraction of the M-P bonds in [(PR(3))(2)M](+) is about 8 and 22 pm for M = Ag and Au, respectively, resulting in Au-P bonds that are about 10 pm shorter than the Ag-P bonds in these species, in good agreement with recent crystallographic results for the cations [(PMes(3))(2)M](+) (M = Ag, Au). The relativistic contraction of the Au-Cl bond in [PR(3)AuCl] is significantly less than that of the Au-P bond, and this explains the experimentally observed differential Au-X and Au-P bond length contractions from [PR(3)AgX] to [PR(3)AuX]. The calculated relativistic bond lengths for corresponding PH(3) and PMe(3) complexes are very similar, confirming a previous conclusion that PH(3) is a good model for structural properties of larger tertiary phosphine ligands. However, the bond lengths for the PMe(3) complexes are all slightly longer than those for the corresponding PH(3) complexes, whereas the M-P dissociation energies are 20-40% higher for the PMe(3) complexes. These findings provide computational support for the concept of "longer but stronger bonds", which was recently proposed on the basis of experimental studies of transition metal complexes involving various substituted phosphine ligands.

Determination of the atomic geometries of the (110) surfaces of CuCl and CuBr by dynamical low-energy electron diffraction intensity analysis.

The atomic geometries of the nonpolar (110) surfaces of CuCl and CuBr are determined by dynamical analysis of the intensities of 13 diffracted beams for CuCl and 16 beams for CuBr associated with normally incident electrons at T=125 and 100 K, respectively. The structural model is specified by six independent variables consisting of the tilt angles (${\mathrm{\ensuremath{\omega}}}_{\mathit{i}}$) of the top two layers, the three independent bond lengths (${\mathit{c}}_{\mathit{i}}$-${\mathit{a}}_{\mathit{j}}$) associated with atoms in the top two layers, and the inner potential. The focus of our analysis is the accuracy and precision with which these six structural parameters can be extracted from the measured intensities. A six-dimensional statistical error analysis was performed for two electron-solid scattering models: one model in which all nonstructural parameters assumed the values used in a family of previous structural analyses for the (110) surface of CuCl and other binary zinc-blende structure materials, and one in which these parameters were treated as adjustable parameters to fit the measured intensities. The structural parameters emanating from these two analyses differ by \ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\le}4\ifmmode^\circ\else\textdegree\fi{} and \ensuremath{\Delta}(${\mathit{c}}_{\mathit{i}}$-${\mathit{a}}_{\mathit{j}}$)\ensuremath{\le}0.3 \AA{}. Statistical analysis of uncertainties in the structural parameters resulting only from uncertainties in the measured intensities yields \ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\le}1.3\ifmmode^\circ\else\textdegree\fi{}, \ensuremath{\Delta}(${\mathit{c}}_{\mathit{i}}$-${\mathit{a}}_{\mathit{j}}$)\ensuremath{\le}0.02 \AA{}. Thus, the uncertainties in the structural parameters associated with the selection of the nonstructural parameters, especially the model of the electron exchange interaction, dominate those associated with the uncertainties in the experimental intensity data. Within these uncertainties we find the top-layer bond lengths are contracted by 0.3 \AA{} for CuCl(110) and 0.1 \AA{} or less for CuBr(110). Changes in the backbonds from the anion and cation cannot be established for CuCl using the existing intensity data in our analysis. For CuBr(110) the backbond from the top-layer cation is contracted by 0.35\ifmmode\pm\else\textpm\fi{}0.2 \AA{}. The tilt angles are ${\mathrm{\ensuremath{\omega}}}_{1}$=(53\ifmmode\pm\else\textpm\fi{}2)\ifmmode^\circ\else\textdegree\fi{} for CuCl and (35\ifmmode\pm\else\textpm\fi{}2)\ifmmode^\circ\else\textdegree\fi{} for CuBr with ${\mathrm{\ensuremath{\omega}}}_{2}$=(-5\ifmmode\pm\else\textpm\fi{}1)\ifmmode^\circ\else\textdegree\fi{} for both. These results are compatible with previously identified structural systematics that the most ionic zinc-blende structures exhibit top-layer bond-length contractions which increase their tilt angles relative to the value of (29\ifmmode\pm\else\textpm\fi{}3)\ifmmode^\circ\else\textdegree\fi{} characteristic of bond-length-conserving rotational relaxations of covalent III-V and II-VI (110) surfaces. \textcopyright{} 1996 The American Physical Society.

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the «cage» results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H2 molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.

Relaxations at GaN (1010) and (110) Surfaces

ABSTRACTWe present anab-initiocalculation of GaN wurtzite (1010) and zinc-blende (110) surface structures and formation energies. Our method employs ultrasoft pseudopotentials and plane-wave basis. These features enable us to obtain accurate results using small energy cut-off and large supercells. The (110) surface shows a Ga-N surface dimer rotation of ∼ 14°, i.e. about one half that of the ordinary III–V non-nitride compounds, and a 5% contraction of the surface bond-length (more than the double that occurring in GaAs). For the (1010) surface, a layer rotation angle of about 11° and a bond-length contraction of 6% has been found. Zinc-blende GaAs (110) and wurtzite ZnO (1010) surfaces have been studied as well, for the sake of comparison. GaAs results are in good agreement with the experimental findings. For ZnO a large bond contraction and a rotation angle of around 11% result. Thus, our findings place GaN closer in behaviour to the highly ionic II–VI compounds than to the non-nitride III–V semiconductors.

Effects of relativity on the NiCO, PdCO, and PtCO bonding mechanism: a constrained space orbital variation analysis of density functional results

Using a density functional based constrained space orbital variation technique, we have analyzed the importance of relativistic effects on the various mechanisms which affect the metal-CO bond in Ni, Pd, and Pt monocarbonyls. The bonding is dominated by the π back-donation mechanism which, for Pd and Pt, is considerably reinforced by relativistic effects. The weaker PdCO bonding is rationalized by reduced back-donation. The combined effect of relativistic bond length contraction and of the atomic d orbital energies determines the trend in the metal-CO bond strengths. This trend is different from the one found for the coordinatively saturated M(CO) 4 tetracarbonyls.

Non-adiabatic electron-lattice interactions in the copper-oxide superconductors

Transport measurements distinguish the superconductive phase from the parent antiferromagnetic and the overdoped metallic phases in La2−xSrxCuO4. For small x, holes in the CuO2 sheets form non-adiabatic polarons containing, experimentally, five Cu atoms. Within a polaron, a first-order contraction of the mean Cu-O bond length collapses the Hubbard U and transfers spectral weight from the Hubbard bands to the gap between them. In the superconductive phase above Tc, condensation into a polaron liquid produces an ɛ(k) dispersion curve, and dynamic pseudo Jahn-Teller deformations within the polaron give a Seebeck enhancement with Tmax≈140 K. The polarons order pair-wise into 〈110〉 stripes alternating with parent-phase stripes; below Tc, the stripes are perfectly ordered. In the overdoped phase, the parent phase is squeezed out; the vibronic states become homogeneous.

Effects of the electron and hole doping in the RNiO 3 compounds

We have investigated the effect of electron and hole doping upon the structural and transport properties of RNiO 3 compounds undergoing a metal-insulator transition. Two different mechanisms modifying T MI have been isolated: carrier injection and size effects. Carrier injection leads to a contraction (or expansion) of the Ni-O bondlength, and the supression of the transition with a different rate depending on the sign of extra-carriers. Transport measurements are consistent with a two-band picture in the hole doped compounds.

Structural, electronic, and magnetic properties of small rhodium clusters.

The structural, electronic, and magnetic properties of small Rh-N clusters (N = 2-8,10,12,13, and 19) are studied using the discrete-variational local-spin-density-functional method. The groundstate structures of Rh-2, Rh-3, and Rh-4 are obtained and found to exhibit a tendency toward higherdimensional geometries with longer bond lengths and more nearest-neighbor bonds. The equilibrium bond lengths in the chosen geometry for the Rh-5-Rh-8, Rh-10, Rh-12, and Rh-13 clusters are determined and show 4-6% bond length contractions compared with the bulk interatomic spacing. A. complex size dependence of the magnetic properties of the Rhry clusters is found to be consistent with a recent experiment. The average magnetic moment per atom of the Rh-N clusters varies from 0 mu(B) to 2 mu(B). The clusters with magnetic ground states have ferromagnetic interactions, while-the local moments of the 5s and 5p often align antiferromagnetically with that of the 4d. The calculated magnetic moments of the Rh-10, Rh-12, Rh-13, and Rh-19 clusters are compared and discussed with the experimental ones. Icosahedral growth is suggested for Rh clusters. The reactivity of the Rh-N clusters toward H-2, N-2, and CO molecules is predicted. The densities of states, exchange splittings, valence band widths, and ground-state electronic configurations are presented for all the clusters. Finally an energy difference is identified which may be used as the criterion for the existence of multiple magnetic solutions in local-spin-density-functional calculations.