Effects of electron correlation and relativistic effects in X-ray diffraction

Atomic scattering factors for the first row transition metal atoms cobalt and nickel have been evaluated using non-relativistic and ‘relativistic-corrected’ configuration interaction wavefunctions in the |αLSM _LM_S〉 representation. Relaxing the constraints imposed by the Hartree-Fock model results in a very small reduction of the atomic scattering factor at small momentum transfer with a negligible change at higher momentum transfer. Better agreement with the relativistic Hartree-Fock atomic scattering factors at small momentum transfer is obtained when theLS-dependent relativistic effects are included in the Breit-Pauli approximation.     

Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

Calculations of electronic structure of the UF<Subscript>6</Subscript> molecule and the UO<Subscript>2</Subscript> crystal with a relativistic pseudopotential

The influence of relativistic effects on the properties of uranium hexafluoride was considered. Detailed comparison of the spectrum of one-electron energies obtained in the nonrelativistic (by the Hartree-Fock method), relativistic (by the Dirac-Fock method), and scalar-relativistic (using a relativistic potential of the uranium atom core) calculations was carried out. The methods of optimization of atomic basis in the LCAO calculations of molecules and crystals are discussed which make it possible to consider distortion of atomic orbitals upon the formation chemical bonds. The influence of the atomic basis optimization on the results of scalar-relativistic calculations of the molecule UF₆ properties is analyzed. Calculations of the electronic structure and properties of UO₂ crystals with relativistic and nonrelativistic pseudopotentials are fulfilled.     

SCA calculations of the inner shell ionization with Dirac-Fock electronic wave functions

The theory of inner shell ionization for arbitrary atomic shells is reviewed. Emphasis is onL- andM-shells in order to show how the proper screening formalism entering the electronic form factor affects the ionization probabilities. The radial wavefunctions in the form factor are computed as relativistic Hartree-Fock orbitals for both bound and continuum states. The continuum orbitals were evaluated in theV(N–1) potential with correct exchange. These results are then compared with the previous ones using screened hydrogen-like wavefunctions and also with the experimental data in some cases.     

A periodic ab initio Hartree-Fock calculation on corundum

The electronic structure of corundum (α-Al₂O₃) is calculated at the ab initio Hartree-Fock level. Cohesive energy, total and projected densities of states, atomic multipoles, bond populations and electron charge density distribution maps are given. The oxygen-aluminium bond is found to be partially covalent in nature; the atomic charges are −0.73 e and +1.09 e for O and Al respectively.     

Compton profiles and momentum space inequalities

Rigorous upper and lower bounds to the atomic Compton profileJ(q) are obtained for any value of the momentum transferredq in terms of radial expectation values 〈p ⁿ 〉 of the atomic momentum density γ(p). In doing so, a procedure based on moment-theoretic techniques and Chebyshev inequalities has been used. This type of results can be employed to study the compatibility of diverse information obtained by using different models, techniques, numerical calculations or experimental data. The same method allows also to obtain approximations to the Compton profile and to bound other relevant characteristics ofJ(q). A comparison of the approximations with some previously known Maximum Entropy Approximations is done. In order to test the accuracy of the bounds, a numerical study of the results is carried out in a Hartree-Fock framework for atomic systems.     

Hydrogen-like relativistic corrections for electric and magnetic hyperfine integrals

Expressions are derived for the n-dependent, hydrogen-like relativistic corrections to the magnetic dipole and electric quadrupole radial hyperfine integrals of an arbitrary atomic state. Good agreement has been obtained earlier between these corrections and the relativistic Hartree-Fock results for s_1/2 states. The agreement remains good for the p_1/2 states. For the p_3/2 states in heavier atoms the hydrogenic corrections still reproduce the Hartree-Fock trend. For the higher l values the agreement is poor. Numerical tables are given for 1 ≤ Z ≤ 100 for the s_1/2, p_1/2, and p_3/2 magnetic dipole cases and the p_3/2 quadrupole case.     

Minima and maxima in the generalized oscillator strengths for the lithium isoelectronic sequence

We have calculated the ionization generalized oscillator strengths (GOS) f(K,k) as a function of the momentum transfer K for the allowed dipole transitions ns → kp (with n = 2) in the lithium isoelectronic sequence through Z = 10, in the Hartree-Fock (HF) approximation. Our results clearly show (i) the regular and systematic trends of the occurrence of the extrema, (ii) the shift of their positions towards the higher values of K with increase of K, and finally, the gradual decrease of the magnitude of f(K,k) with increase of atomic number Z. The results are discussed qualitatively.     

Interplay of Atomic Interactions in the Intermetallic Semiconductor Be5Pt

Semiconducting substances form one of the most important families of functional materials. However, semiconductors containing only metals are very rare. The chemical mechanisms behind their ground‐state properties are only partially understood. Our investigations have rather unexpectedly revealed the semiconducting behaviour (band gap of 190 meV) for the intermetallic compound Be₅Pt formed at a very low valence‐electron count. Quantum‐chemical analysis shows strong charge transfer from Be to Pt and reveals a three‐dimensional entity of vertex‐condensed empty Be₄ tetrahedrons with multi‐atomic cluster bonds interpenetrated by the framework of Pt‐filled vertex‐condensed Be₄ tetrahedrons with two‐atomic polar Be?Pt bonds. The combination of strong Coulomb interactions with relativistic effects results in a band gap.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Measurement of effective atomic number and Rayleigh-to-Compton cross-section ratio for 145 keV gamma photons

The effective atomic numbers of composites and Rayleigh-to-Compton cross-section ratio of elements, in the range 6 ≤ Z ≤ 82 for 145 keV gamma photons, are determined experimentally. An HPGe (high purity germanium) semiconductor detector is placed, at scattering angle of 90°, to record the spectra originating from interactions of incident gamma photons with the target under investigations. The intensity ratio of Rayleigh-to-Compton scattered peaks, corrected for photo-peak efficiency of gamma detector and absorption of photons in the target and air column, is plotted as a function of atomic number and a best fit-curve is constituted. From this fit-curve, the respective effective atomic numbers of the scientific samples are determined. The measured values of cross-section ratio increases non-linearly with increase in atomic number and are found to agree with theoretical predictions based upon non-relativistic form factor, relativistic form factor, modified form factor and S-matrix theory.     

All-electron scalar relativistic calculation of the adsorption of NCO species onto small copper clusters

An all-electron scalar relativistic calculation of Cu_nNCO (n = 1?C13) clusters has been made using density functional theory with the generalized gradient approximation at BLYP level. In all Cu_nNCO clusters, the NCO species prefered to occupy the single-fold coordination site and the small copper cluster tended to bond with the nitric. The Cu_n structures were only distorted slightly and the NCO species retained linear structure. The N-C bond-length contraction and C-O bond-length elongation were observed clearly. The reactivity enhancement of NCO species toward CO₂ was obvious. But, no reactivity enhancement of NCO to form N₂ related to the N-C bond strength could be observed. It seems that the NCO species is more favorably adsorbed by odd-numbered small copper clusters, relatively. Some discrepancies between our work and earlier works were found which may be explained in terms of the scalar relativistic effect. Further studies to focus on the reactivity enhancement of NCO to form N₂ are clearly in order.     

Maximum-entropy and Padé-like approximations to atomic scattering factors

Three different methods, namely maximum entropy, combination of Dirac deltas and two-point Padé approximants, are used to construct tight model-independent approximations to the atomic form factor F(k) in terms of a few quantities related to its inverse Fourier trnsform, i.e. the one-particle density ρ(r). The accuracy of these approximations is analyzed in a Hartree-Fock framework. These extrapolation techniques, being completely general and modelindependent, can be applied to other kind of physical systems, such as solids, molecules or nuclei.     

Form factors directly determined from momentum space Hartree—Fock solutions: H2 and Li2

The characteristics of the theoretical form factors computed from momentum space wave functions of quantum chemistry (i.e., vectorial quantities including appropriate phase factors) are examined in connection with the so-called atomicity assumption of crystallography. Using molecular orbitals previously computed by direct numerical integration of momentum space Hartree-Fock equations for the H₂ and Li₂ molecules, the patterns of parallel and perpendicular form factors with respect to bond axes are shown to be more significant than are the corresponding spherical averages. The case of the triatomic system H₃ is briefly considered. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 451–457, 1997     

Electrically polarized valence basis sets for the SBKJC effective core potential developed for calculations of dynamic polarizabilities and Raman intensities

Sadlej’s electric polarization method of Gaussian basis functions was applied to the double-zeta effective core potential basis sets of Stevens, Basch, Krauss, Jasien and Cundari to generate a new augmented polarized valence double-zeta set, named as pSBKJC, which is appropriate for the calculation of dynamic polarizabilities and Raman intensities. The pSBKJC basis set was developed for the atoms of families 14–17 (from C to F, Si to Cl, Ge to Br and Sn to I). In order to assess the performance of this new basis set, these properties were compared to those evaluated using Sadlej’s set, available in the EMSL online library under the name of Sadlej-pVTZ. In these tests, Hartree-Fock/pSBKJC calculations have proved to be less demanding of the computer than the Hartree-Fock/Sadlej-pVTZ ones but give results in excellent agreement with those from the Sadlej-pVTZ basis set. Since the Stevens et al. pseudopotential can represent the scalar relativistic effects, the results obtained at the Hartree-Fock/pSBKJC level show a better agreement with the results of Dirac-Hartree-Fock/Sadlej-pVTZ relativistic calculations using Dyall’s spin-free Hamiltonian. When comparing Hartree-Fock/pSBKJC data of Raman scattering activities, at the excitation wavelength of 488 nm, with those of spin-free Dirac-Hartree-Fock/Sadlej-pVTZ calculations, a very good agreement is observed, where the RMS error is 8.5 Å⁴a.m.u.^?1 and the averaged percentage error is 3.4%. In terms of computer savings in calculations of dynamic Raman intensities, a 20% reduction in the CPU time in the coupled cluster singles and doubles intensities of C₆H₆ and about 40% reduction in the time-dependent Hartree-Fock intensities for C₆F₆ molecules were attained.     

Momentum density and molecular geometry. Bent BH 2 − and linear BH 2 +

Based on a special form of the molecular virial theorem, the recently proposed method of momentum density for interatomic interactions is here applied to the problem of molecular geometry. Two molecules BH ₂ ^– and BH ₂ ⁺ , which have the same nuclear framework but favor respectively bent and linear conformations, are comparatively studied. Using an approximate Hartree-Fock momentum density, the total molecular energy (including the nuclear repulsion) is partitioned into orbital components, and a geometry correlation diagram is derived. An atom-bond partitioning of the total energy is also examined based on the one- and two-center decomposition of the momentum density.     

K X-ray relative transition probabilities for 23≤Z≤33

The K X-ray relative transition probabilities K_b/K_a of some elements for atomic numbers 23Z33 induced by 3 MeV protons were measured. The experimental results are compared with the relativistic Hartree-Fock (RHF) calculations. Good agreements have been obtained considering the experimental error.     

Theoretical approach to the evaluation of spin-only magnetic form factors for many-electron atomic systems

General expressions for evaluating spin-only magnetic form factors for many-electron atomic systems are derived using Racah algebra techniques. The formulas are derived in the |αLSM_LM_S〉 representation. The general formalism allows the evaluation of spin-only magnetic form factors beyond the Hartree-Fock approximation.     

Spontaneous desorption of vibrationally excited molecules physically adsorbed on surfaces

The energy within a vibrationally excited physisorbed molecule often exceeds that needed to break its bond to the surface. Energy transfer from the vibrating chemical bond to the surface bond causes the surface bond to rupture and the vibrationally relaxed adsorbate is released from the surface. We present a theoretical model which allows an estimation of the residence time of a vibrationally excited adsorbate on a surface. Because of uncertainties in the nature of the surface bond, the lifetimes obtained from the analytical expressions presented have only qualitative significance. The results are interpreted in terms of Franck-Condon overlaps between the wavefunctions which describe the adsorbate-substrate complex and the released adsorbate. Lifetimes are calculated for hydrogen isotopes adsorbed on sapphire surfaces. Guide-lines are given for estimating lifetimes of other systems in terms of a few easily calculated parameters.Let us summarize this guide to spontaneous desorption of physically adsorbed vibrationally excited molecules. The most efficient desorption processes will occur for adsorbates with a small number of bound states (d₀ small) and when released the adsorbate has small translational momentum (small q_m). This momentum gap correlation is most succinctly revealed by fig. 3. Smaller translational momentum will be achieved if the adsorbate can take up energy into its internal motions. Absorption of energy into lattice modes of the substrate will also serve to reduce the translational momentum and provide for more efficient desorption. However, if the vibrational frequency of the adsorbate is in near resonance with surface polarons or plasmons of the substrate, energy transfer to the solid will be so efficient that desorption will be quenched.A test of these possible relaxation channels awaits the first experimental measurements of desorption of vibrationally excited molecules.