Investigation of photoionization and photodissociation of an oxygen molecule by the method of coupled differential equations

The photoionization and photodissociation of an oxygen molecule are investigated theoretically by the method of coupled differential equations. The molecular orbitals of the core are calculated in the MO LCAO approximation. The molecular orbitals of a photoelectron in the discrete and continuous spectra are determined by the single-center method. The wave functions of vibrational motion of the oxygen molecule are obtained within the diabatic approach. The described method is used for calculating the predissociation and autoionization widths of the 2σ _u ^?1 (c ⁴Σ _u ^? )n/σ_g, v Rydberg states of the oxygen molecule. The total cross sections of the resonant photoionization and neutral predissociation calculated for the oxygen molecule in the excitation energy range 20.6–24.8 eV are in good agreement with the available experimental data.     

Vortex core shapes measured by STM

We have studied vortex core shapes in superconducting NbSe₂ by STM, as function of temperature and bias voltage. The experimentally measured tunnel current profiles are compared with the results of calculations using microscopic theory. We find that, at low temperatures (T/T _c ? 0.25), the apparent vortex core radius strongly depends on the bias voltage, which demonstrates the energy dependence of the scale for spatial variation of the quasiparticle density of states. Good quantitative agreement between measured and calculated profiles is found by using the accepted value for the superconducting coherence length Ξ_S, without further adjustable parameters. This shows that the bias dependence is a useful extra tool in the interpretation of local density of states measurements.     

AB initio energy band structure of polysulfur nitride, (SN)x

All electron energy band structure is reported for an infinite one-dimensional model of polysulfur nitride, (SN)_x, using the ab initio LCAO Hartree-Fock method. The calculated values of the effective mass and density of states at the Fermi level are ?0.72 m_e and 0.06 states/(eV spin molecule), respectively. An appreciable amount of charge transfer (0.30 e) from sulfur to nitrogen was obtained. Finally, comparison is made with the results of a semi-empirical version of the same method.     

Ab initio potential energy curves and vibrational levels for the C and D 1Πu states of the hydrogen molecule

Two lowest eigenvalues of the Hamiltonian for the hydrogen molecule corresponding to the ¹Π_u symmetry have been calculated in the Born-Oppenheimer approximation. They represent the C and D states, respectively. Different highly flexible wavefunctions were used for both states and the calculations were performed for a wide range of internuclear distances: 1 ≤ R ≤ 12 a.u. for the C state, and 1 ≤ R ≤ 25 a.u. for the D state. The calculated potential energy curves are more accurate than any previous ab initio results for the above states. The vibrational Schrödinger equation for both states has been solved for H₂, HD, and D₂ using the Numerov method. The resulting energies and rotational constants are compared with the experimental values.     

Theoretical and experimental study of the electronic structure of tin dioxide

The electronic structure of tin dioxide has been theoretically studied within the linearized augmented plane wave method using the Wien2k program package. The total and local partial electron densities of states have been calculated. The X-ray emission K-spectrum of oxygen has been calculated. The X-ray absorption spectra of the tin M _4,5-edge and oxygen K-edge have been calculated by simulating the supercell and core hole. The calculated results have been compared with the experimental data obtained using synchrotron radiation.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.     

Influence of solvent and intramolecular relaxation on dynamics of luminescence spectra in donor–acceptor complexes

The oscillator strengths for Rydberg states of a NaHe molecule are calculated using a semianalytic procedure with the l-coupling effect taken into account (due to the dipole potential of a core). This effect gives rise to nonzero oscillator strengths for transitions forbidden in the atomic model of molecular Rydberg states. The difference between calculations in terms of the atomic model and calculations with consideration of the dipole moment of a core is shown for allowed transitions.     

Spectroscopic properties of the low-lying electronic states and laser cooling feasibility for the SrI molecule

Laser cooling of a molecule with heavy nuclei is often complicated because of the density distribution of the electronic states. Here, we evaluate the feasibility of the laser cooling of the SrI molecule by calculating the potential energy curves and transition dipole moments of the ground and low-lying excited states using the multi-reference configuration interaction plus Davidson corrections (MRCI + Q) and the all-electron basis sets of ANO-RCC. The relativistic effect and the spin-orbit coupling splits are included, because both Sr and I are heavy atoms. Based on the obtained potential energy curves, we solve the Schrödinger equation of nuclear motion to determine the rovibrational energy levels and the Franck-Condon factors. The spectroscopic parameters are obtained by fitting the rovibrational energy levels with the Dunham expression. The radiation lifetimes, the Doppler and recoil temperatures between the X²Σ⁺ and the ²Π_1/2/²Π_3/2/B²Σ⁺ states are calculated. 5-color laser cooling schemes for the molecule are proposed, which can lead to the total effective Franck-Condon factors being 0.99983, 0.99979, and 0.99941 for the three transitions, respectively. All the obtained results suggest that the SrI molecule is a feasible candidate for laser cooling.     

Theoretical study of structural and energy parameters of the van der Waals complex of the Li<Superscript>+</Superscript> cation with the N<Subscript>2</Subscript> molecule

The three-dimensional vibrational problem for the isolated van der Waals complex formed by the Li⁺ cation with the N₂ molecule is solved by the variational method. The potential energy and dipole moment surfaces are calculated using different basis sets of atomic functions and different approaches for taking electron correlation into account. The anharmonic effects caused by the interaction of vibrational degrees of freedom of the complex are consistently considered for the first time. The energy levels of three-dimensional vibrational states are determined. The frequency shift of the N₂ molecule vibration upon complexation and the fundamental transition intensity for this vibration in the complex are calculated. The frequencies and intensities for a number of spectral transitions between the states associated with excitation of low-frequency modes are determined. The average values of geometrical parameters and their variances are calculated for the ground state and excited vibrational states of the complex.     

A Study of New Resonances in a Molecule Scenario

The new resonances X(3872) and Λ _c (2940) are considered as weakly bound states of other hadrons in a molecule scenario using phenomenological Lagrangians.     

Electronic structure and superconductivity of europium

We have calculated the electronic structure of Eu for the bcc, hcp, and fcc crystal structures for volumes near equilibrium up to a calculated 90 GPa pressure using the augmented-plane-wave method in the local-density approximation. The frozen-core approximation was used with a semi-empirical shift of the f-states energies in the radial Schrödinger equation to move the occupied 4f valence states below the Γ₁ energy and into the core. This shift of the highly localized f-states yields the correct europium phase ordering with lattice parameters and bulk moduli in good agreement with experimental data. The calculated superconductivity properties under pressure for the bcc and hcp structures are also found to agree with and follow a T_c trend similar to recent measurement by Debessai et al. [1].     

Electronic structures of the LaBO3 (B = Co, Fe, Al) perovskite oxides related to their catalysis

The discrete-variational (DV) X α molecular orbital method has been applied to investigate the bulk and surface electronic structures of perovskite oxides such as LaCoO₃, LaFeO₃ and LaAlO₃. The calculated XPS spectra for these oxides are in good agreement with the experimental ones and only the LaCoO₂ exhibited a rather high electron density of states near the Fermi level (E_F). The catalytic behavior of these oxides is discussed on the basis of their electronic structures; the marked catalysis by LaCoO₃ is associated with electron occupation of crystal field d states near E_F and with the buildup of surface charge so as to enhance the electron transfer between a surface cation and an interacting molecule.     

Approximate SCF calculations on the [Mn(H2O)6]2+ complex with a minimal basis set

In the restricted Hartree-Fock scheme approximate SCF-LCAO calculations have been performed for the [Mn(H₂O)]₆ ²⁺ complex using a minimal basis set consisting of nine Slater-type orbitals of the manganese ion and four Slater-type orbitals of the water molecule. The 1s, 2s and 2p orbitals of the manganese ion and the 1s orbital of the oxygen atom are treated as frozen core orbitals. In evaluating the different parts of the Hartree-Fock operators we used a two-centre approximation for the multicentre integrals. A new aspect of the calculations is the use of the Hartree-Fock orbital energies of the free water molecule as a first approximation for the corresponding orbital energies of the complex. The calculations have been done for the ground states and six excited states of the complex with symmetry T _h and also for the ground states of two distorted complexes. From the resulting eigenvectors we calculated the hyperfine interaction of the valence electrons of the central ion with the protons of the water molecules for three different geometries. The excited states give two different ways of finding values of 10 Dq and the Racah parameters B and C. The results are encouraging.     

Theoretical study of the <Emphasis Type="Italic">K</Emphasis>-photoabsorption cross section of carbon in the acetylene molecule

The magnitudes and the shape of the K-absorption spectrum of carbon in the C₂H₂ molecule are found by the one-center method. Within this method, one-electron wave functions of occupied and unoccupied states are calculated in the approximation of nonorthogonal orbitals. The processes of single and double excitation/ionization with additional excitation of an electron from the external 1π_u shell to the 1π_g state are taken into account. The mechanism of formation of a fine structure in the photoionization spectrum is refined. The calculated cross sections are compared with experimental and theoretical results obtained by other researchers. The results of calculation of the oscillator strengths of single photoexcitation are predictive.     

Photoionization cross sections of Fe XXI

Total and partial photoionization cross sections for (Fe XXI+hν→Fe XXII+e) are presented for the ground and excited bound states with n?10 and l?9. Fe XXI is prevalent in high-temperature astrophysical plasmas as well as in photoionized plasmas excited by hard X-rays. Results are reported for the first time for the high-energy photoionization with core excitations to n=2,3 states. Details of photoionization, especially the high-energy features that often dominate considerably over the low energy ones, are illustrated. These prominent features will affect the photoionization and the recombination rates in high-temperature plasmas. Calculations are carried out in the close coupling (CC) approximation using the R-matrix method. A large CC wavefunction expansion for Fe XXII which includes the ground and 28 excited core states from n=2 and 3 complexes and spans over a wide energy range is used. A total of 835 discrete bound states of Fe XXI in the singlet, triplet, and quintet symmetries are obtained. Total photoionization cross sections, σ_PI(nLS), for ionization into all 29 states are presented for all 835 final bound states and partial photoionization cross sections, σ_PI(g,nLS), for ionization into the ground ²P⁰ state of the core are presented for 685 states. While the n=2 core excitations are at relatively lower energy range (within 15 Ry from the ionization threshold), the n=3 excitations lie at considerably higher energy, 73 Ry and above, yet introduce resonant features and enhancements more prominent than those of n=2 states. Larger numbers of resonances are formed due to Rydberg series of autoionizing states converging on to the 29 core states. However, most noticeable structures are formed in the excited state cross sections by the photoexcitation-of-core (PEC) resonances in the photon energy range of 73-82 Ry. All these high-energy features are absent in the currently available results. The present results should enable more accurate modeling of the emission spectrum of highly excited plasma from the optical to far-ultraviolet region.     

Spin-orbit coupling and dissociation of CO2 molecules

Potential surfaces of the CO₂ molecule for the ground and excited ³ B ₂, ¹ B ₂ electronic states are calculated by quantum chemistry methods. The calculation of the spin-orbit coupling in the molecule shows a large the matrix element, which removes the prohibition for the dissociation-recombination process CO₂(X ¹Σ) + M ? CO(X ¹Σ) + O(³ P) + M. The barrier on the potential curve for ³ B ₂, the energy of which exceeds the limit of dissociation into components in the ground states, explains the data on the dissociation and recombination energies measured in experiments with shock tubes. The absorption cross section of CO₂ molecules in the UV spectral region measured at high temperatures allowed us to plot branches of potential curves near their minima for two upper singlet states assigned to the ¹ B ₂ and ¹ A ₂ symmetry.     

Effective quadrupole operators for the second half of the 2p-1f shell

The one body matrix elements of the effective quadrupole operator in the 2p _3/2, 1f _5/2 2p _1/2 configurations have been calculated taking into account the renormalization effects due to excitations from the closed 1f _7/2 shell. First and second order perturbations of the residual interaction as well as an infinite series involving one particle-one hole core excitations are considered. The results are used to calculate quadrupole moments of odd mass nuclei together withBE 2 values between low-lying states. Agreements with experimental results, whereever known, are seen to be generally greatly improved.     

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyB _n are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. Thek _E1- andk _M1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofk _E1 are 1.5–2 times larger and the values ofk _M1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.