Stable and efficient algorithms for Xα multiple scattering calculations

Solutions to some practical problems that arise in multiple scattering calculations on large molecules are discussed. (1) Numerical instabilities near the zero of energy can be removed by rescaling the secular matrix. (2) The calculation of structure factors can be made much more efficient by the application of symmetry projection operators. (3) An energy search procedure is described that ensures that no states are inadvertently neglected. Test calculations incorporating these changes illustrate the improved numerical stability, and show decreases in computation time of 30–60%, when compared to previous codes. The procedures suggested here are applicable to both relativistic and nonrelatitistic calculations.     

“Non-muffin tin” corrections of the SCF Xα-SW Method. I

The recently developed crystalline cluster method within the framework of the Johnson multiple scattering technique was successfully used in calculations of ionic cubic crystals and the defects with a cubic symmetry. In this paper a simple way of extension of the method to noncubic systems by a partial elimination of “muffin-tin” approximation (MTA ) is proposed. The procedure suggested does reduce the intermediate integrals to the one-dimensional ones, and they are calculated analytically. It is supposed that an approach of taking into account the nonspherical shape of the potential inside the “muffin-tin” (MT ) spheres will be effective in crystals with an ionic type of chemical bond.     

The preparation,structure and reactions of some “malonyl-α-aminopyridines”

The reaction of several substituted 2-aminopyridines with diethyl malonate was studied. The “methylmalonyl-α-aminopyridines” were shown to exist in the same tautomeric form as “malonyl-α-aminopyridine”. Formylation of these compounds takes place in the 3-position and has led to the formation of a new tricyclic compound.     

Electronic structure of helium-trapped vacancy in aluminum using multiple scattering Xα method

The self-consistent multiple scattering X_α (MSX _α) method is used to arrive at the electronic structure of a helium-trapped vacancy in aluminum using a cluster model. The calculated orbital energies, electron density, and charge distributions are compared with the available theoretical results. It is shown that helium trapping causes the reshuffling and upward movement of the cluster levels (with vacancy).     

Can triorganoboroxins exist in a “monomeric” R---B=O form? MNDO calculations and ebulliometric molecular weight determination

MNDO calculations were made for triethylboroxin (EtBO)₃ and triphenylboroxin (PhBO)₃ using both X-ray determined and optimized geometry of these molecules. The results were compared with hypothetical “monomeric” molecules R---B=O. Calculated energies of trimerization are about −200 kJ mol⁻¹ for both compounds and confirm the much higher stability of the “trimer”. Ebulliometric determination of molecular weight of triphenylboroxin in 2-pentanone confirms its trimeric character.     

Studies of unoccupied orbitals of BF3 and BCL3 by electron transmission spectroscopy and multiple scattering Xα calculations

Electron transmission spectroscopy (ETS ) and bound-state and continuum multiple-scattering Xα (MS -Xα) calculations are employed to characterize the unoccupied a′₂, a′₁ and e′ orbitals of BF₃ and BCl₃. The a′₂ orbital of BF₃, which produces a peak about 7 eV below threshold in the x-ray absorption spectrum (XAS ), generates a scattering resonance at 3.5 eV in ETS. Similarly, the e′ orbital that lies about 2 eV above threshold in XAS occurs about 13?16 eV above threshold in ETS . Dissociation of F^? from BF₃ due to electron attachment is attributed to a core-excited shape resonance involving an e″ → a″₂ excitation and electron capture into the a′₂ orbital. In BCl₃ all the unoccupied orbitals lie at lower energy than in BF₃ and are closely spaced, making definitive spectral assignments difficult. Both Hartree-Fock (HF ) and MS -Xα methods apparently underestimate the stability of the unoccupied e′ orbital of BCl₃. Vibronic coupling due to out-of-plane bending may significantly affect the spectral intensities. Feshbach resonances are observed for BCl₃ at energies close to those observed in the vacum-UV absorption spectrum. The lower energies of the unoccupied orbitals of BCl₃ are consistent with their stronger bonding to nucleophiles.     

Atomic Xα calculations based on EHFS(α) = Eexp

The total energies and one-electron energies for first- and second-row atoms were calculated by using the Hartree–Fock and the Hartree–Fock-Slater Hamiltonian with X_α orbitals, u_i(α_exp); α was parametrized from E^HFS (α_exp) = E^exp. The E^HF (α_exp) total energies are always higher than the Hartree–Fock energies for the atoms. The relation of the calculated ionization potential to the experimental ionization potential depends on the α used to define u_i(α), α_exp, or α_HF.