Electronic structure,optical properties and Compton profiles of Bi2S3 and Bi2Se3

In this paper, we present the Compton profiles of Bi₂S₃ and Bi₂Se₃ using our 20 Ci ¹³⁷Cs Compton spectrometer. To compare our experimental data, we have computed the Compton profiles, energy bands and density of states using linear combination of atomic orbitals with density functional theory (DFT) and Hartree-Fock (HF) scheme. It is seen that hybrid functional involving HF and DFT approximations gives a relatively better agreement with experimental momentum densities than other approximations of DFT. We have also reported the band structure, density of states, valence charge densities, dielectric functions and electron energy loss spectra using full potential linearized augmented plane wave scheme. On the basis of charge densities, Mulliken’s population data and equal-valence-electron-density profiles, Bi₂S₃ is found to be more ionic than Bi₂Se₃. The calculated dielectric functions for the parallel and perpendicular polarizations show a small anisotropic effect. The electron energy loss spectrum for Bi₂Se₃ is found to be in good agreement with the available experimental data.     

Molecular momentum distributions and compton profiles. Effects of bonding on some small molecules

Electronic momentum distributions and Compton profiles have been calculated from minimum basis set SCF wavefunctions for H₂O, H₂O₂, CO, CO₂ and H₂CO. Radial distributions and profiles have also been estimated for these molecules from localized molecular orbitals. The results suggest that (a) the height of the Compton peak, <p^?1>, may be as sensitive to the effects of chemical bonding as the kinetic energy, <p²>/2, and that (b) the virial theorem may provide a more useful criterion than energy minimization in assessing the accuracy of calculated bonding effects and Compton profiles.     

Electronic structure,Compton profiles and cohesive properties of Cs-halides

We have reported energy bands, density of states, valence electron charge densities and Compton profiles of CsCl, CsBr and CsI using linear combination of atomic orbitals with Hartree–Fock and density functional theories. We have also computed these properties, except the momentum densities, using full potential linearized augmented plane wave method. The general features of the energy bands and the density of states in these halides are found to be almost similar. To interpret the theoretical data on Compton line shapes, we have also measured the Compton profiles using our 20 Ci ¹³⁷Cs spectrometer. It is seen that the Hartree–Fock calculations give relatively a better agreement with the experimental momentum densities. On the basis of equal-valence-electron-density profiles, a comparison of relative nature of bonding is made which is in agreement with the valence charge densities and atomic charges by means of Mulliken analysis. Using our experimental and theoretical Compton profiles, we have also computed the cohesive energy of the halides.     

Electron momentum density and band structure calculations of α- and β-GeTe

We have measured isotropic experimental Compton profile of α-GeTe by employing high energy (662 keV) γ-radiation from a ¹³⁷Cs isotope. To compare our experiment, we have also computed energy bands, density of states, electron momentum densities and Compton profiles of α- and β-phases of GeTe using the linear combination of atomic orbitals method. The electron momentum density is found to play a major role in understanding the topology of bands in the vicinity of the Fermi level. It is seen that the density functional theory (DFT) with generalised gradient approximation is relatively in better agreement with the experiment than the local density approximation and hybrid Hartree–Fock/DFT.     

Observation of Interference Effects in (e, 2e) Electron Momentum Spectroscopy of SF6 (cited: 1)

Two-dimensional electron density map (2D map) of binding energy and relative azimuthal angle (i.e., momentum) for the outer-valence molecular orbitals of SF₆ has been measured by a highly sensitive electron momentum spectrometer with noncoplanar symmetric geometry at the impact energy of 1.2 keV plus binding energy. The experimental electron momentum profiles for the relevant molecular orbitals have been extracted from the 2D map and interpreted on the basis of the quantitative calculations using the density functional theory with B3LYP hybrid functional. For the outermost F2p nonbonding orbitals of SF₆, the interference patterns are clearly observed in the ratios of the electron momentum profiles of molecular orbitals to that of atomic F2p orbital.     

Synthesis and Electronic Structures and Linear Optics of Solid State Compound SrB2O4

The cluster (SrB₂O₄)₂ existing in crystalline states is employed to model the electronic structure and linear optical properties of solid state compound SrB₂O₄. This compound is synthesized by high temperature solution reaction, and it crystallizes in the orthorhombic space group Pbcn with cell dimensions a = 1.1995(3), b = 0.4337(1), c = 0.6575(1) nm, V = 0.34202 nm³, and Z = 4, μ = 15.14 cm^?1, D_caled = 3.36 g/cm³. The dynamic refractive indices are obtained in terms of INDO/SCI following combination with the Sum‐Over‐States method. A width of the calculated gap is 4.424 eV between the valence band and conduction band, and the calculated average refractive index is 1.980 at a wavelength of 1.065 μm. The charge transfers from O^2‐ anion orbitals to Sr²⁺cation orbitals make the significant contributions to linear polarizability in terms of analyses of atomic state density contributing to the valence and conduction bands.     

Multiple basis sets in calculations of triples corrections in coupled-cluster theory

Multiple basis sets are used in calculations of perturbational corrections for triples replacements in the framework of single-reference coupled-cluster theory. We investigate a computational procedure, where the triples correction is calculated from a reduced space of virtual orbitals, while the full space is employed for the coupled-cluster singles-and-doubles model. The reduced space is either constructed from a prescribed unitary transformation of the virtual orbitals (for example into natural orbitals) with subsequent truncation, or from a reduced set of atomic basis functions. After the selection of a reduced space of virtual orbitals, the singles and doubles amplitudes obtained from a calculation in the full space are projected onto the reduced space, the remaining set of virtual orbitals is brought into canonical form by diagonalizing the representation of the Fock operator in the reduced space, and the triples corrections are evaluated as usual. The case studies include the determination of the spectroscopic constants of N₂, F₂, and CO, the geometry of O₃, the electric dipole moment of CO, the static dipole polarizability of F⁻, and the Ne⋯Ne interatomic potential. Received: 28 December 1996 / Accepted: 8 April 1997     

Determination of potential-energy surface of molecules in an applied field on the basis of virial relations

The quantum-mechanical virial theorem (in diagonal and nondiagonal forms) for molecules in an external, weak, uniform electric field is used for obtaining the analytical expression of the potentialenergy surface in the Hartree–Fock–Roothaan one-determinantal approximation. The polarizability tensor components of the H₂O molecule are computed on this basis. The dependence of basing the atomic orbitals upon the intensity of the applied field lead to good coincidence of results with the data of near Hartree–Fock calculations.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

Weinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N₂ molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N₂ molecule. For example, the magnitude of F_ab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.     

Electron momentum distributions from valence-bond wave functions

Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H₂. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.     

The Large Second‐Harmonic Generation of LiCs2PO4 is caused by the Metal‐Cation‐Centered Groups

We evaluated the individual atom contributions to the second harmonic generation (SHG) coefficients of LiCs₂PO₄ (LCPO) by introducing the partial response functionals on the basis of first principles calculations. The SHG response of LCPO is dominated by the metal‐cation‐centered groups CsO₆ and LiO₄, not by the nonmetal‐cation‐centered groups PO₄ expected from the existing models and theories. The SHG coefficients of LCPO are determined mainly by the occupied orbitals O 2p and Cs 5p as well as by the unoccupied orbitals Cs 5d and Li 2p. For the SHG response of a material, the polarizable atomic orbitals of the occupied and the unoccupied states are both important.     

Characterization of the excited states of ethylene by MRCI

The excited states of ethylene are systematically analyzed and characterized according to the natural orbitals (NOs) resulting from multireference configuration interaction singles and doubles (MRCISD) calculations. By comparing the shapes and nodal structures of the NOs with those of hydrogen atomic orbitals, the Rydberg series can be classified. Two or three different types of Rydberg series appear within five excited states for each symmetry of D_2h. For example, in the ¹A_g symmetry there are three series having np and two nf hydrogen‐like atomic orbitals. Electronic correlation effects for the (π→π*) V state are also discussed on the basis of a complete active space self‐consistent field (CASSCF) calculation, showing that electron correlation effects merely within the valence space cannot explain contraction of the V state. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

How the Chalcogen Atom Size Dictates the Hydrogen-Bond Donor Capability of Carboxamides,Thioamides, and Selenoamides

The amino groups of thio- and selenoamides can act as stronger hydrogen-bond donors than of carboxamides, despite the lower electronegativity of S and Se. This phenomenon has been experimentally explored, particularly in organocatalysis, but a sound electronic explanation is lacking. Our quantum chemical investigations show that the NH₂ groups in thio- and selenoamides are more positively charged than in carboxamides. This originates from the larger electronic density flow from the nitrogen lone pair of the NH₂ group towards the lower-lying π*_C=S and π*_C=Se orbitals than to the high-lying π*_C=O orbital. The relative energies of the π* orbitals result from the overlap between the chalcogen np and carbon 2p atomic orbitals, which is set by the carbon-chalcogen equilibrium distance, a consequence of the Pauli repulsion between the two bonded atoms. Thus, neither the electronegativity nor the often-suggested polarizability but the steric size of the chalcogen atom determines the amide's hydrogen-bond donor capability.     

Hartree-Fock-Roothaan calculations of dipolar polarizabilities for closed-shell atoms

Methods are suggested for optimization of Slater type atomic orbitals in polarizability calculations of closed-shell atoms using “bound” perturbation theory (algebraic version of the Hartree-Fock method). The size and composition of the basis set of atomic orbitals providing the Hartree-Fock limit for perturbation parameters are considered. Dipolar polarizabilities are calculated for He, Be, Ne, and Mg atoms and their isoelectronic series. Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, pp. 439-448, May–June, 2000.     

Molecular shape,shape of the geometrically active atomic states,and hybridization

In a recent publication [C. A. Nicolaides and Y. Komninos, Int. J. Quant. Chem. 67 , 321 (1998)], we proposed that in certain classes of molecules the fundamental reason for the formation of covalent polyatomic molecules in their normal shape is to be found in the existence of a geometrically active atomic state (GAAS) of the central atom, whose shape, together with its maximum spin‐and‐space coupling to the ligands, predetermines the normal molecular shape (NMS). The shape of any atomic state was defined as that which is deduced from the maxima of the probability distribution ϱ(cos θ₁₂) of the angle formed by the position vectors of two electrons of an N‐electron atom. Because the shape of the GAAS determines the NMS and because the NMS allows the construction of corresponding hybrid orbitals, we examined and discovered the connection between the GAAS shape and Pauling's function for the strength of two equivalent orthogonal orbitals at angle θ₁₂ with one another. It is shown that the computed ϱ(cos θ₁₂) of the GAAS can be cast in a form which allows the deduction of the composition of the hybrid orbitals of maximum spin states with configurations sp³, sp³d⁵, sp³d⁵f⁷, slⁿ, s²lⁿ and the demonstration of the central atom's tendency to form bonds in directions which coincide with the nodal cones of the hybrid bond orbitals. These results not only reinforce the validity of the theory as to the fundamental “mechanism” for the formation in the normal shape of coordination compounds and covalently bonded polyatomic molecules, but also provide the justification for the relevance and importance of the hybridization model. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 25–34, 1999     

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.     

Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Calculations on the Nonlinear Second—Order Optical Polarizabilities for Series of Donor—C60 Molecules

IntroductionThebulkpreparation1ofC6 0 andC70 clusters(fullerenes)hasstimulatedawidevarietyofexperimentalandtheoreticalstudies .2 5Wehavesuccessfullyexaminedthestructures ,UV visiblespectraandthenonlinearthird orderopticalpolarizabilities (γ)ofC6 0 andC70 .6 ,7Byin troductionofsubstituents ,thecentrosymmetriesofC6 0 andC70 arebrokenandthesecond orderopticalnonlinearitiesareinduced .ThechargeseparationinsubstitutedC6 0whichleadstoenhancementofβvaluehasalsobeendis cussed .5Inrecentyears ,a…     

Triple Bonds Between Iron and Heavier Group 15 Elements in AFe(CO)3− (A=As,Sb, Bi) Complexes

Heteronuclear transition‐metal–main‐group‐element carbonyl complexes of AsFe(CO)₃⁻, SbFe(CO)₃⁻, and BiFe(CO)₃⁻ were produced by a laser vaporization supersonic ion source in the gas phase, and were studied by mass‐selected IR photodissociation spectroscopy and advanced quantum chemistry methods. These complexes have C_3v structures with all of the carbonyl ligands bonded on the iron center, and feature covalent triple bonds between bare Group 15 elements and Fe(CO)₃⁻. Chemical bonding analyses on the whole series of AFe(CO)₃⁻ (A=N, P, As, Sb, Bi, Mc) complexes indicate that the valence orbitals involved in the triple bonds are hybridized 3d and 4p atomic orbitals of iron, leading to an unusual (dp–p) type of transition‐metal–main‐group‐element multiple bonding. The σ‐type three‐orbital interaction between Fe 3d/4p and Group 15 np valence orbitals plays an important role in the bonding and stability of the heavier AFe(CO)₃⁻ (A=As, Sb, Bi) complexes.