Density of levels in vibrational spectra of molecules

Density distribution of the discrete spectrum of a Hamiltonian which represents a system of N-coupled oscillators and, hence may describe molecular vibrations in the local mode approximation, is analyzed. The spectral density moments are expressed as linear combinations of products of coefficients which depend on the molecular topology (analogs of the propagation coefficients in the statistical theory of nuclear and atomic spectra) and of one-particle moments describing individual bonds and interactions between them. The dependence of the first three moments of the energy-level density on the structural parameters of the molecule is discussed. Detailed expressions for several special cases are derived. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63 : 835–842, 1997     

Extrapolation of real-space quantum chemical calculations from finite-size supercells to the ideal infinite system. III. Application to two-dimensional systems

A previously presented extrapolation method of the density matrix of a standard finite supercell calculation to an infinite supercell is extended to two-dimensional systems. The density matrix of the finite supercell is transformed into q space where it is interpolated and extrapolated in such a way that all its fundamental properties are guaranteed by construction. The resulting modified density matrix contains information from a continuum of q points in the first Brillouin zone which allows for a more realistic calculation of properties like the total energy E_tot per atom and the band structure ϵ₁(q). It is shown that this more realistic calculation takes better care of the crystal symmetries and is essential in reproducing both important degeneracies in the band structure and rotationally symmetric results. In the special case of π electrons only, an exact analytical solution for the density matrix of the infinite supercell is presented. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 895–911, 1997     

True detection limit of rare earth elements in atomic emission analysis with an arc two-jet plasmatron

The “true detection limit” C_L,true was measured by a method proposed by Boumans et al. for 10 prominent lines of La, Ce, Pr, Nd and Sm, the most abundant rare earth elements (REEs) in geological samples. It is demonstrated how spectral interferences can increase of C_L,true. The spectra were excited in an argon arc plasma jet with evaporation powders of five complex natural samples. The data show that there is a significant increase of C_L,true in real samples containing large concentrations of such elements as Ti, Zr, Cr, Nb, Ta and REEs emitting complex spectra. Received: 17 June 1997 / Revised: 20 October 1997 / Accepted: 26 October 1997     

Reaction of copper(II) fluoro- and chloroacetates with triphenylphosphine oxide

Triphenylphosphine oxide adducts of copper(II) dichloro-, trichloro- and trifluoroacetate were prepared. Electronic, IR and EPR spectra as well as magnetic data over the temperature range 81–301 K have been mainly used for the determination of the stereochemistry and electronic structure of the adducts. The spectral and magnetic behaviours of the adducts are similar to that of copper(II) acetate hydrate. Some correlations between the magnetic and spectral data as well as the acidity of the respective acids are discussed. Cu(F₃CCOO)₂Ph₃PO, represent the first example of a stable binuclear copper(II) trifluoroacetate adduct.     

Ilimaquinone,a sesquiterpenoid quinone from a marine sponge

Ilimaquinone (1) is a new sponge metabolite of composition C₂₂H₃₀O₄. Its structure, which was determined by spectral correlations and X-ray crystallography, comprises a rearranged drimane sesquiterpene moiety linked to a 2-hydroxy-5-methoxybenzoquinone at C-3.     

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

A new method based on linear response theory is proposed for the determination of the Kohn-Sham potential corresponding to a given electron density. The method is very precise and affords a comparison between Kohn-Sham potentials calculated from correlated reference densities expressed in Slater-(STO) and Gaussian-type orbitals (GTO). In the latter case the KS potential exhibits large oscillations that are not present in the exact potential. These oscillations are related to similar oscillations in the local error function δ _i (r)=(−ɛ _i )ϕ _i (r) when SCF orbitals (either Kohn-Sham or Hartree-Fock) are expressed in terms of Gaussian basis functions. Even when using very large Gaussian basis sets, the oscillations are such that extreme care has to be exercised in order to distinguish genuine characteristics of the KS potential, such as intershell peaks in atoms, from the spurious oscillations. For a density expressed in GTOs, the Laplacian of the density will exhibit similar spurious oscillations. A previously proposed iterative local updating method for generating the Kohn-Sham potential is evaluated by comparison with the present accurate scheme. For a density expressed in GTOs, it is found to yield a smooth “average” potential after a limited number of cycles. The oscillations that are peculiar to the GTO density are constructed in a slow process requiring very many cycles. Received: 24 February 1997 / Accepted: 18 June 1997     

Electronic structure of octavinyl- and octaphenylsilsesquioxane from XPS and DFT data

X-ray photoelectron spectroscopy (XPS) and density functional theory are employed to study the electronic structure of octasilsesquioxanes (RSiO_1.5)₈ with vinyl and phenyl terminal groups. Quantitative compositions determined from the XPS data are close to those estimated by empirical formulas. Narrow spectral lines corresponding to ionization from C1 _s core levels indicate similar chemical states of carbon atoms for both compounds. Experimental data are confirmed by close calculated values of effective charges on carbon atoms when polarization functions are included in the basis set and also by small energy ranges of core level electrons. The valence spectral region is interpreted based on the calculated energy values of electronic levels with regard to the density of states and ionization cross-sections.     

Density functional study of the relationship between energy,hardness, and polarizability of molecules in nonequilibrium situations

We have studied the variation of hardness, polarizability, and electronic and nuclear repulsion energy components of molecules in different nonequilibrium situations obtained by bond distortion and also by placing external point charges on the symmetry axis of the molecules. The above quantities are calculated through Kohn-Sham version of spin-polarized density functional theory with nonlocal exchange correlation functional. Interesting correlations have been found to exist between different energy components, hardness, and polarizability. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 917–926, 1997     

First principles calculation of the thermodynamic properties of silicon clusters

The thermodynamic properties of Si clusters are calculated using first principles quantum methods combined with molecular dynamics for simulating the trajectories of clusters. A plane wave basis is used with ab initio pseudo potentials and the local density approximation for determining the electronic energies and forces. Langevin molecular dynamics simulates thermal contact with a constant temperature reservoir. Vibrational spectra, moments of inertia, anharmonic corrections, and free energies are predicted for Si₂ through Si₅. The translational contribution is based on the ideal gas limit. The rotation contribution is approximated using a classical rigid rotator. Vibrational modes are determined from the dynamical matrix in the harmonic approximation. Corrections due to anharmonicity and coupling between rotational and vibrational modes are fit from the molecular dynamics simulations. Received: 17 September 1997 / Accepted: 14 October 1997     

Achieving reliability of calculations for flat potential surfaces in density functional theory: The case of Al4 and Al4+1

Harmonic frequencies obtained by finite-differences from nonlocal density functional calculations are presented for the ground states of Al₄ (neutral and cationic). The effect of varying the step size used in the finite-difference evaluation and the influence of the density convergence threshold are discussed. Potential energy curves along the most important normal coordinates are shown. With these results, we found that for Al₄ the square and the rhombus minima are almost degenerate with each other, while for Al₄⁺¹, the rhombus is more stable and the square is a transition state. © 1997 John Wiley & Sons, Inc.     

The vibrational frequencies of CaO2, ScO2, and TiO2: a comparison of theoretical methods

The vibrational frequencies of several states of␣CaO₂, ScO₂, and TiO₂ are computed using density functional theory (DFT), the Hartree-Fock approach, second-order M?ller-Plesset perturbation theory (MP2), and the complete-active-space self-consistent-field theory. Three different functionals are used in the DFT calculations, including two hybrid functionals. The coupled cluster singles and doubles approach including the effect of connected triples, determined using perturbation theory, is applied to selected states. The Becke-Perdew 86 functional appears to be the most cost-effective method of choice, although even this functional does not perform well for one state of CaO₂. The MP2 approach is significantly inferior to the DFT approaches. Received: 3 September 1997 / Accepted: 8 December 1997     

Numerical study of the exchange effects in the valence and core energy bands of the metallic lithium chain

Minimal basis-set STO-3G calculations on the infinite metallic chain of lithium atoms, (SINGLE BOND Li SINGLE BOND)_x, performed within the Fourier space-restricted Hartree-Fock approach (FS-RHF), are reported to illustrate that the Fourier representation method, in which all lattice summations are accurately carried out to infinity, is able to reproduce the genuine features of the RHF approach for the metallic cases, i.e., the vanishing of the density of states at the Fermi energy. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 709–718, 1997     

Density functional theory for triplet superconductors

The density functional theory of superconductivity is extended to triplet superconductors and superfluid helium 3. We prove a Hohenberg-Kohn-type theorem for these systems and derive effective single-particle equations. The latter include exchange and correlations in a formally exact way and allow the treatment of both electronic and phonon-induced superconductivity. The relation of this approach to the Bogolubov-de Gennes mean-field theory and to phenomenological theories based on Ginzburg-Landau functionals is discussed. © 1997 John Wiley & Sons, Inc.     

Isothermal pressure dependence of the solubility of some triazines in supercritical CO2

 The solubility of two related series of each three triazine compounds has been determined in supercritical CO₂, at 40 °C and pressures between 80 and 220⋅10⁵ Pa. A high pressure small volume cell with adjustable optical path and built-in circulation pump has been constructed to be used with quartz windows in a Perkin Elmer UV-VIS spectral photometer. At 220 bar solubilities are between 0.3 and 25 g/L, dependent on the specific triazine structure. The isothermal pressure dependence of the solubility could be modelled using the pressure dependent dielectric constant of CO₂ as the only variable. Received: 30 October 1996/Revised: 3 April 1997/Accepted: 13 April 1997     

Second-order quantum similarity measures from intracule and extracule densities

The calculation of quantum similarity measures from second-order density functions contracted to intracule and extracule densities obtained at the Hartree-Fock level is presented and applied to a series of atoms, (He, Li, Be, and Ne), isoelectronic molecules (C₂H₂, HCN, CNH, CO, and N₂), and model hydrogen-transfer processes (H₂/H⁺, H₂/Hot, H₂/H⁻). Second-order quantum similarity measures and indices are found to be suitable measures for quantitatively analyzing electron-pair density reorganizations in atoms, molecules, and chemical processes. For the molecular series, a comparative analysis between the topology of pairwise similarity functions as computed from one-electron, intracule, and extracule densities is carried out and the assignment of each particular local similarity maximum to a molecular alignment discussed. In the comparative study of the three hydrogen-transfer reactions considered, second-order quantum similarity indices are found to be more sensitive than first-order indices for analyzing the electron-density reorganization between the reactant complex and the transition state, thus providing additional insights for a better understanding of the mechanistic aspects of each process. Received: 7 July 1997 / Accepted: 29 October 1997     

An extended saturated liquid density equation

The recently developed saturated liquid density correlation of Iglesias-Silva and Hall for halogenated paraffins is extended to other classes of compounds involving paraffins, cycloparaffins, olefins, diolefins, cyclic-olefins, aromatics, alcohols, ethers, liquefied inorganic gases, and others. The two adjustable parameters of the correlation are optimized and reported for 126 compounds. The average error for 5377 experimental data points was 0.27%. The correlation is extended to multicomponent mixtures. A set of mixing rules is proposed. The correlation with this set of mixing rules is used to predict the saturated liquid density of 86 multicomponent systems consisting of LNG, heavy hydrocarbons, CO₂, H₂S, alcohols and halogenated paraffins. The average of error for 1378 experimental data points was 1.03% with 0 bias with respect to experimental data. These values compare well with the values from well-known correlations. For polar compounds or multicomponent systems containing polar compounds, the computation of saturated liquid density by this correlation shows superiority with respect to the other correlations.     

Assignment of the Internal Vibrational Modes of C70 by Inelastic Neutron Scattering Spectroscopy and Periodic-DFT

The fullerene C₇₀ may be considered as the shortest possible nanotube capped by a hemisphere of C₆₀ at each end. Vibrational spectroscopy is a key tool in characterising fullerenes, and C₇₀ has been studied several times and spectral assignments proposed. Unfortunately, many of the modes are either forbidden or have very low infrared or Raman intensity, even if allowed. Inelastic neutron scattering (INS) spectroscopy is not subject to selection rules, and all the modes are allowed. We have obtained a new INS spectrum from a large sample recorded at the highest resolution available. An advantage of INS spectroscopy is that it is straightforward to calculate the spectral intensity from a model. We demonstrate that all previous assignments are incorrect in at least some respects and propose a new assignment based on periodic density functional theory (DFT) that successfully reproduces the INS, infrared, and Raman spectra.     

CIDNP magnetic field dependence in biradicals

The biradical S-T_?1 CIDNP magnetic field dependence can be treated as a spectral line shape problem in which the S-T_?1 levels are tuned by the magnetic field; the shape is related to fluctuations in the through-space electron exchange interaction, J, modulated by conformational changes in the biradical. A density matrix treatment is applied to a two-conformer model of a polymethylene biradical.