Linear expansion of the eigenvalues of a Hermitian matrix and its application to the analysis of the electronic spectra of 3d ions in crystals

It is shown that the eigenvalues E_i of a Hermitian matrix H with matrix elements H_ij = Σ_kA^k_ija_k, where A^k_ij are known numbers and a_k a set of parameters, can be exactly expanded as $\text{E}{}_{\mathrm{i}}\text{= Σ}{}_{\mathrm{k}}\text{(}\text{?E}{}_{\mathrm{i}}\text{?a}{}_{\mathrm{k}}\text{)a}{}_{\mathrm{k}}$. This property is applied to the analysis of the optical spectra of transition metal ions in crystals proposed by L. Pueyo, M. Bermejo, and J. W. Richardson (J. Solid State Chem.31, 217, 1980), and it is shown that this method represents the best fit of the Hamiltonian eigenvalues to the observed (or calculated) spectrum. Further advantages of using this property, in connection with the spectral analysis, are the minimization of the errors associated with the numerical approximations and a reduction in computer time. In the molecular orbital calculation of the optical or uv spectra of these systems, this linear expansion of the eigenvalues give a detailed interpretation of the improvements produced by refined calculations, such as those including configuration interaction. In particular, the changes in one-electron energy and in open-shell repulsion interactions associated with the refinement can be clearly and easily formulated. As examples, the computed spectra of CrF^4?₆ and CrF^3?₆ are discussed.     

Analytical methods for the characterization of proteins and peptides in wines

Although proteins and peptides are minor constituents of wine, they make a significant contribution to its quality. Proteins can cause a number of technological problems during vinification and may be responsible for the appearance of turbidity in bottled wine. Peptides exhibit surfactant and sensory properties that can influence the organoleptic characteristics of wine. These reasons make protein and peptide analysis a necessity. In this paper, some of the applications in sample preparation, electrophoretic and chromatographic analysis, and detection of proteins and peptides in wine are examined. Special attention is paid to the methodologies that the authors have used in previously published studies, in some cases developed by them, and in other cases taken from the literature and used routinely in their laboratory.     

A quality test for the Hartree-Fock-Roothaan SCF wave functions

A quality test for the SCF wave function based on separate examination of the one- and two-electron contributions to the total energy is proposed. The test is applied to 12 different STO basis sets for the ground state of the Ni atom and its predictions compared with those deduced for the minimization of the total energy. The new test allows for a reduction in the cancellation of errors detected in some applications of the standard SCF procedure. Some relations between the quality of the basis set and its size and structure are discussed.     

Comparison of “bottom-up” and “top-down” strategies for the estimation of the uncertainty in organic elemental analysis

The estimation of uncertainty in organic elemental analysis for C, H, N and S is reported. Both “bottom up” and “top down” strategies are used for uncertainty calculations. The bottom up approach used the results of C, H, N, and S obtained from the homogeneity study of two pure chemicals (toluene-4-sulfonamide and 4(6)-methyl-2-thiouracil). Two calibration systems, K factor and calibration curve, were applied in this study and no significant differences were obtained. For the “top down” approach, we used the data obtained from a proficiency test on both pure chemicals from among 45 Spanish laboratories. Both approaches are compared and discussed below.     

Assessment of CaCl2, NaNO3 and NH4NO3 extraction procedures for the study of Cd, Cu, Pb and Zn extractability in contaminated soils

The variety of extraction procedures used in environmental studies makes it very difficult to compare the results obtained; therefore, harmonisation and standardisation is required. The extraction of heavy metals from soil by un-buffered salt solutions is a method used to estimate soil contamination and trace metal availability to plants. The present study assesses three of these methods. All the three methods are standardised or is undergoing standardisation in Europe: 0.01 mol l⁻¹ CaCl₂ (The Netherlands), 0.1 mol l⁻¹ NaNO₃ (Switzerland) and 1 mol l⁻¹ NH₄NO₃ (Germany). The soil-reference material BCR CRM 483, with indicative values for CaCl₂, NaNO₃, NH₄NO₃ extractable metals, was analysed for quality control purposes. The three methods were also applied to 10 contaminated soils and the extracted metals (Cd, Cu, Pb, and Zn) were determined. The procedures were found to be precise (typically <10%) for all metals, taking into account the low metal concentrations extracted. The metal extraction efficiency obtained with each procedure was slightly different, and the three methods provided equivalent information while predicting the relative trace-metal mobility (Cd>Zn>Cu>Pb) in the soils studied. From the experience obtained, the 0.01 mol l⁻¹ CaCl₂ extraction procedure seems to be the most suitable method for performing a harmonisation process, since this procedure combines an appropriate extraction capacity for this type of studies with the lowest salt concentration in the extracts and, consequently, with a more simple matrix for metal determination.     

Basis sets generation: Relation between Adamowicz's and the maximum overlap method

It is shown that the method of Adamowicz for basis sets reduction [Int. J. Quantum Chem. 19 , 545 (1981)] is, in practice, a particular case of the method of maximum overlap. The relationships between these two methods are discussed analytically and by means of a simple numerical example.     

Transferability of empirical crystal-field parameters of Ni(II) complexes of different symmetries

A method of systematic linearization of the crystal-field matrices appropriate for obtaining empirical parameters of transition metal complexes of any symmetry is presented and applied to forty complexes of Ni²⁺ of O_h and D_4h symmetries. The method is a generalization of that proposed by L. Pueyo, M. Bermejo, and J. W. Richardson (J. Solid State Chem.31, 217 (1980)) for complexes of O_h symmetry and incorporates the spin-orbit coupling in a very simple manner. Using this method, classical parameters, such as 10Dq, and punctual quantities, such as the ligand perturbing charges q_i, were obtained for these complexes. The former are transferable within 10% if (a) there are not big changes in the metal-ligand distances and (b) the chemical environments of the ligand atoms are comparable. However, the punctual parameters show variations of 20% or more. Electronic repulsion integrals seem to be nicely transferable by means of addition rules based on the hypothesis of isotropic repulsion in the low-symmetry field. Since one of the fitting parameters is a scaling factor of the R_nl(r) metal function, the process of optimization generates an empirical representation, R_nl(λr), of the locally perturbed metallic state.