Pseudopotential approach of the electronic structure in clusters: application to Alkali Halides and Rare Gases

We examine here the use of pseudopotentials in limit cases where only a very small number of electrons (much less than the usual number of valence electrons), eventually excited, can be singled out and considered as active to determine the electronic structure. Two applications are considered. The first one concerns the family of nonstoechiometric ionic clusters for which only the excess electrons are active. The relevance and accuracy of such ab initio determined pseudopotentials is illustrated on Na_nF_n-1 clusters which are treated as one-electron systems. The second application concerns excited states of neutral rare gas clusters Rg _n ^* . In this case, the excited electron may be coupled to different core states and a resonant hole-particle treatment involving e-Rg and e-Rg ⁺ pseudopotentials is presented.     

Non-local pseudopotentials for electron-rare gas atom interaction

Non-local (l-dependent) pseudopotentials for electron-rare gas atom interaction have been determined from scattering data. In the low-energy region the proposed pseudopotentials reproduce very well the experimental scattering phase shifts. Two independent calculations have been carried out in order to test the pseudopotentials for the helium atom. The results point out good quality of the present pseudopotentials.     

Evaporation rates of hot sodium clusters

A scheme based in density functional theory with pseudopotentials is used to obtain the normal modes of vibration of Na _n clusters (4 ≤n ≤ 22). The monomer and dimer evaporation rates from thermally excited clusters are obtained in this harmonic approximation. The time evolution of the abundance spectra from an initial uniform mass distribution of hot clusters is studied and its influence in the experimentally observed spectra is discussed.     

Stability of isomeric Na n clusters

A method which combines density functional theory and the use of pseudopotentials is applied to obtain ground state and low-lying metastable geometries of Na _n clusters (7≤n≤40). The large variation in the magnitude of energy gaps between isomers suggests that the melting temperature is not a simple monotonous function of size. A detailed study of the differences between electronically stabilized (n=8, 20, 40) and structurally stabilized (n=13) clusters suggests some clues to understand the intriguing behaviour of Na₁₃.     

Franck—condon factors of the T1 ↷ S0 radiative and nonradiative transitions of naphthalene-h8 and -d8-a correlation function analysis

Franck—Condon factors for the T₁ ? S₀ transition in naphthalene-h₈ and naphthalene-d₈ are calculated employing the correlation function approach which allows us to investigate the distribution of the released electronic energy among the normal modes of the Final ground state. The relevant coupling parameters relating to geometry, frequency and anharmonicity changes due to excitation are included. Those related to geometry changes are obtained from the vibronic intensities of the phosphorescence spectrum as well as from a calculation implementing a semi-empirical relation between bond order and bond length. The calculated nonradiative rates compare well with the experimental rates in terms of absolute magnitude and deuterium effect. The semi-empirical calculations of the ribtonic intensities provide detailed information about force fields that are otherwise indistinguishable on the basis of their ability to reproduce infrared frequencies.     

Triphenylene based metal-pyridine cages

C₃-symmetric pyridine containing tris-benzyl-O-substituted hexahydroxytriphenylene derivatives were prepared and used in combination with square-planar Pd(II) and Pt(II) complexes for the self-assembly of molecular cages in solution. The formation of a trigonal bipyramid M₃L₂ cage was demonstrated by multinuclear NMR analyses and pseudo 2D DOSY experiments and supported by semi-empirical calculations.     

Mass transfer problems in electrolysis with flowing solution on single and stacked screens

The semi-empirical model of limiting current on flow-through porous electrodes, as described before by Sioda, is compared with the usual presentation of mass transfer processes involving mass transfer coefficients and dimensionless correlations. The earlier experimental results of reduction of K₃Fe(CN)₆ in 1 M KCl solution in water on single and stacked 80-mesh platinum screen electrodes have been presented in form of dimensionless correlations for Sherwood number and j_D-factor.     

H.T. Clarke,A handbook of organic analysis,qualitative and quantitative, (Fifth Edition), Edward Arnold,London (1975), Revised by B. Haynes,with E.C. Brick and G.G. Shone,pp. x + 291, price £12.00 (clothbound), 4.95 (paperback)

Ab initio calculations at minimal (STO-3G) and extended (4-31G) basis levels have been carried out for the cyclopropylcarbinyl radical using the unrestricted Hartree-Fock procedure. It is found that the ordering of the long-range proton isotropic hyperfine coupling constants are opposite to the results obtained from semi-empirical INDO calculations. The coupling constants for the extended basis set are a_exo = ?1.71 G, a_endo = ?4.25 G, a_β= 11.41 G, a_α1 = ?66.01 G and a_α2 = ?64.73 G.     

Characteristic and non-characteristic X-ray emission from SF6 and SO2 molecules by electron impact

Cross sections for K-shell ionization of sulphur in collisions of electrons with kinetic energies of 3.5–14.0 keV with SF₆ and SO₂ gases have been measured. In addition, the impact energy dependence of the bremsstrahlung radiation emitted at different photon energies was investigated. The experimental results are compared with theoretical calculations in plane wave Born approximation and with the available semi-empirical models.     

A semi-empirical method for prediction of critical concentrations for polymer overlap in solution

The hydrodynamic volumes of solvated polymers shrink with increasing concentrations in solution until a concentration (c_x) is reached at which the effective dimensions are the same as those in a Flory theta solvent. Further increases beyond c_x result in progressively greater overlapping of separate macromolecules. Several theories are available for the prediction of c_x but none is entirely satisfactory. A semi-empirical method is described here for the estimation of c_x, using intrinsic viscosities as input parameters. The magnitude of c_x is shown to be solvent dependent; its lower limit is zero, in a theta solvent.     

Semi-empirical LCAO-xα theory for transition metal complexes. II. Application to ionization potentials

Ionization potentials for 17 nd-transition metal complexes are calculated by a semi-empirical LCAO-Xα theory excluding (n + 1)s and (n + 1)p atomic orbitals. The results agree well with both photoelectron data and discrete-variational Xα results, which include the (n + 1) atomic orbitals. Implications of the (n + 1)-atomic orbital exclusion are noted. Also, new assignments for photoelectron spectra of VCl₃0, MnCl₃O, CrCl₂O₂, and MoCl₂O₂ are proposed.     

The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path

A new composition path, X_i-X_j=constant, is suggested for the semi-empirical calculation of the thermodynamic properties of ternary ‘substitutional’ solutions from binary data, when the binary systems show deviations from the regular solution model. A comparison is made between the results obtained for integral and partial properties using this composition path and those calculated employing other composition paths suggested in literature. It appears that the best estimate of the ternary properties is obtained when binary data at compositions closest to the ternary composition are used.     

Analysis of exact valence shell hamiltonian: Nonclassical terms and molecular based parameters

The exact valence shell effective hamiltonian is analyzed for one- and two-valence orbital systems using a second quantized formulation. The exact solutions of the exact effective hamiltonian are used, to display the meaning of each of its terms. The well-known α_υ = ?I_p and γ_υυ = I_p ? A_f relations are provided a molecular basis for certain special cases, thereby enabling molecular definitions for molecular “integrals” and allowing the determination of the molecule and bond length dependence of traditional semi-empirical “integrals”. It is shown how the presence of nonclassical terms in the effective hamiltonian destroys the pairing symmetry of alternate hydrocarbons.     

LiPN<Subscript>2</Subscript> and NaPN<Subscript>2</Subscript> crystals: Structural features and chemical bonding

The band structure spectra, densities of states, and valence and difference densities of LiPN₂ and NaPN₂ crystals were obtained by DFT self-consistent calculations using the nonlocal pseudopotentials and the localized pseudoorbital basis. Crystal-chemical analysis of these compounds shows that they occupy an intermediate position between the ideal structures of β-cristobalite and chalcopyrite, which manifests itself in the peculiarities of the electronic structure and chemical bonding. The valence band consists of three allowed subbands and differs radically from the typical valence band of chalcopyrite crystals in both subband structure and contributions of the s, p, and d atomic orbitals to the crystal orbitals.     

Measurement of L subshell fluorescence yields of some elements in the atomic range 75⩽Z⩽92 using photoionization

L subshell fluorescence yields (ω₁, ω₂ and ω₃) for the elements Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Th and U have been measured at the 123.6 keV γ-ray emission excitation energy from a ⁵⁷Co annular radioactive source (925 MBq) using a Si(Li) detector. The measured L subshell fluorescence yields were compared with the theoretical and semi-empirical values.     

Prediction of the chromatographic retention of saturated alcohols on stationary phases of different polarity applying the novel semi-empirical topological index

The novel semi-empirical topological index (I_ET), previously developed by Heinzen and Yunes, was extended to predict the chromatographic retention of saturated alcohols on low polarity stationary phases (OV-1). The predictive ability of I_ET was also verified on stationary phases of different polarity (SE-30, OV-3, OV-7, OV-11, OV-17 and OV-25). Simple linear regressions between the retention indices and the semi-empirical topological index (RI=a+bI_ET) were established for each stationary phase separately, showing good statistical parameters. Statistical analysis showed that the QSRR model used on stationary phases of low polarity (OV-1) has high internal stability and good predictive ability for external groups. The polarity of the SE-30, OV-3, OV-7, OV-11, OV-17 and OV-25 stationary phases, indicated by retention polarity (P_R) given by Tarján et al., is reflected in the ‘a’ (intercept) and ‘b’ (slope) coefficients of the equations obtained for each of these phases. The linear relationship between the ‘a’ coefficient and P_R showed satisfactory statistical quality. Thus, it was possible to generate a single combined model of QSRR, including a parameter that represents the property of the stationary phase P_R. The combined model also has a satisfactory predictive quality, as shown by the plot of calculated versus experimental retention indices for saturated alcohols on six stationary phases of different polarity (r²=0.9956; S.D.=9.54).     

A combination of pseudopotentials and density functionals: Results for Cun, Cun, Agn, and Agn clusters (n ≤ 4)

Structures and binding energies have been calculated for neutral and singly ionized Cu and Ag clusters with up to four atoms. The valence-electron system is treated at the ab initio SCF level; core-valence interaction is accounted for by semi-empirical pseudopotentials, corrected for core polarization; valence correlation is included using a local spin-density-functional approximation, corrected for self-interaction. The results are compared to previous calculations for Li, Na and K clusters, and it is shown that, in spite of the different bulk crystal structure, small group 1a and 1b clusters have many properties in common.     

A quantitative interpretation of the magnetic field effect on hyperfine-coupling-induced triplet fromation from radical ion pairs

Experimentally determined B_1/2 values characterizing the magnetic field dependence of molecular triplet production from radical ion pairs originating from photoinduced electron transfer are compared with semi-empirical values obtained according to B_1/2(hfi) = 2(B₁² + B₂²)/(B₁ + B₂) from the root-mean-square values for the hyperfine coupling of the two radicals, B₁ and B₂. The very good agreement is discussed.     

Infrared and Raman spectra of terephthalonitrile and terephthalonitrile-15N2. Force field for out-of-plane vibrations

A general assignment of the vibrational spectra of terephthalonitrile and terephthalonitrile-¹⁵N₂ is proposed on the basis of their infrared and Raman spectra. The relevant symmetry is found to be D_2h. The force field for the out-of-plane vibrations of these molecules was calculated by refining the general quadratic force field obtained by the semi-empirical MINDO/3 method, starting with a geometry optimized by this method. The refined force field reproduces the observed frequencies of the out-of-plane vibrations to better than ±0.5 cm⁻¹.     

On the transition functional method

The transition operator method of calculating ΔE_SCF ionization and excitation energies using a single calculation, is generalized to embrace any energy change and any variational treatment using approximate wavefunctions. The transition functional obtained is justified using perturbational and variational arguments. The applications of the method are discussed, along with a concrete example, namely a semi-empirical VB treatment of Li₃ and Li₃⁺.