Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

A relativistic CI study on OIII: wavefunctions,excitation energies and transition probabilities

The relativistic CI method is used to determine N-electron wavefunctions for the 1s ² 2s ² 2p ² (³ P ₀,³ P ₂,¹ D ₂), 1s ² 2p ^{4 3} P ₂ even levels, and the 1s ²2s2p ³ (³ D ₁,³ P ₁,³ S ₁,¹ P ₁), 1s ²2s ²2p3s (³ P ₁ and¹ P ₁), 1s ²2s ²2p3d (³ D ₁,³ P ₁,¹ P ₁)J=1 OIII levels. Excitation energies and emission probabilities between these levels are reported in the electric dipole approximation, both for the Coulomb and the Babushkin gauges.ns, p,np,nd- andnd (n17) numerical basis functions have been used for the construction of CSF's entering the CI expansion for the ASF's of these levels. Radiative matrix elements of the type calculated here within the framework of the relativistic CI method, may be used in laser assisted spectroscopic studies of atoms and ions.     

Large atomic natural orbital basis sets for the first transition row atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu atoms. The primitive sets are taken from the large sets optimized by Partridge, namely (21s13p8d) for Sc and Ti and (20s12p9d) for V to Cu. These primitive sets are supplemented with threep, oned, sixf, and fourg functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d ⁿ 4s ² and 3d ⁿ⁺¹4s ¹ occupations. For Ni, the¹ S(3d ¹⁰) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.     

Hyperfine structure and isotope shift of some even parity levels in the YbI spectrum

Using laser induced fluorescence spectroscopy the hyperfine structure of the even parity levels 4f ¹⁴6s6d ³ D ₁, 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 as well as of the odd parity level 4f ¹⁴ 6s6p ³ P ₂ in neutral ytterbium has been investigated. The isotope shift of the transitions 4f ¹⁴6s6p ³ P ₀ → 4f ¹⁴ 6s6p ³ D ₁ and 4f ¹⁴ 6s6p ³ P ₂ → 4f ¹⁴ 6s8s ³ S ₁, 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 could be measured with high accuracy. The results for the 4f ¹⁴ 6s6p ³ D ₁ level show a considerable influence of second order effects of the hyperfine interaction. The isotope shifts of the 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1 levels indicate a possible configuration mixing for these levels.     

Triazènes. Etude XPS. et 1H-RMN. des complexes mercuriques des diaryl-1,3-triazènes

XPS. and ¹H-NMR. spectra of 1,3-diaryltriazenes complexes of Hg(II) The core binding energies C 1s, N 1s, Hg 4f_7/2, Hg 4f_5/2 in 7 symmetrical p-substituted 1,3-diphenyltriazenes complexes of Hg(II) have been measured by XPS. Within the limits of experimental error (± 0.2 eV) only one N 1s signal could be detected. This indicates the equivalence of the 3 N-atoms. Invariance of C 1s, N 1s, Hg 4f_7/2, Hg 4d_5/2 signals with the para substituents on the phenyl ring is explained on the basis of ionic character in the Hg, N bond. These results are corroborated by the ¹H-NMR. spectra.     

Lifetimes of the 4s4p 3 P 1 and 4s3d 1 D 2 states of Ca I

The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ metastable states of Ca have been studied using the time-of-flight technique. Two kinds of observations were performed. First, the exponential decay of the fluorescence, using a (continuous) dc discharge for excitation and then the velocity distribution of the radiating atoms, using a pulsed discharge, were measured. From the combined results of these measurements the lifetimes were derived. The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ states of Ca are determined to be 0.57±0.03 ms and 1.5±0.4 ms, respectively.     

Hyperfine structure in 5s 4d 3 D —5snf transitions of87Sr

The hyperfine spectra of the 5s4d ³ D ₁-5s20f, 5s4d ³ D ₂-5s23f, and 5s 4d ³ D ₃-5s32f transitions of⁸⁷Sr (I=9/2) have been measured by collinear fast beam laser spectroscopy. The structure in the upper configurations is highly perturbed by fine structure splitting that is of comparable size to the hyperfine interaction energy. These perturbations can be adequately treated with conventional matrix diagonalization methods, using the 5s-electron magnetic dipole interaction terma _5s and the unperturbed fine structure splittings as input parameters. Additionally, hyperfine constants for the lower 5s4d ³ D configurations, including theA- andB-factors and a separation of the individuals- andd-electron contributions to these factors, are derived.     

On the line intensity ratios of prominent Si II,Si III,and Si IV multiplets

Line intensities of singly, doubly and triply ionized silicon (Si II, Si III, and Si IV, respectively) belonging to the prominent higher multiplets, are of interest in laboratory and astrophysical plasma diagnostics. We measured these line intensities in the emission spectra of pulsed helium discharge. The Si II line intensity ratios in the 3s3p²²D–3s²4p²P^o, 3s²3d²D–3s²4f²F^o, and 3s²4p²P^o–3s²4d²D transitions, the Si III line intensity ratios in the 3s3d³D–3s4p³P^o, 3s4p³P^o–3s4d³D, 3s4p³P^o–3s5s³S, 3s4s³S–3s4p³P^o, and 3s4f³F^o–3s5g³G transitions, and the Si IV line intensity ratios in the 4p²P^o–4d²D and 4p²P^o–5s²S transitions were obtained in a helium plasma at an electron temperature of about 17,000 ± 2000 K. Line shapes were recorded using a spectrograph and an ICCD camera as a highly-sensitive detection system. The silicon atoms were evaporated from a Pyrex discharge tube designed for the purpose. They represent impurities in the optically thin helium plasma at the silicon ionic wavelengths investigated. The line intensity ratios obtained were compared with those available in the literature, and with values calculated on the basis of available transition probabilities. The experimental data corresponded well with line intensity ratios calculated using the transition probabilities obtained from a Multi Configuration Hartree–Fock approximation for Si III and Si IV spectra. We recommend corrections of some Si II transition probabilities.     

Coupling between the convergence behavior of basis set and electron correlation: a quantitative study

The coupling between improvement of the basis set and the valence electron correlation method has been studied quantitatively for the total atomization energies (TAEs) of a number of small molecules, using basis sets of up to [7s6p5d4f3g2h/5s4p3d2f1g] quality. Very significant coupling is found to exist. Using a scaled basis set extrapolation beyond [6s5p4d3f2g/ 4s3p2d1f] at the MP2 or CCSD level, mean absolute errors of 0.18 and 0.15 kcal/mol, respectively, can be obtained for the TAEs of a number of small polyatomic molecules, compared to 0.12 kcal/mol using CCSD(T) throughout. Received: 7 February 1997 / Accepted: 6 May 1997     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted basis sets for first row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations. The starting primitive sets are 8s4p3d for hydrogen, 9s4p3d for helium, and 14s9p4d3f for the heavier first row atoms.     

Isotope Shifts of Nitrogen around 800 nm

The Doppler-limited absorption spectra of ¹⁴N and ¹⁵N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets (3s⁴P_J→3p⁴D_J^o, 3s⁴P_J→3p⁴P_J^o, 3s²D_J→5s²P_J^o, and 3p²P_J^o→5s²D_J^o) were measured and their J-dependent specific mass shifts were observed and discussed.     

Ionic bonding of lanthanides,as influenced by d‐ and f‐atomic orbitals,by core–shells and by relativity

Lanthanide trihalide molecules LnX₃ (X = F, Cl, Br, I) were quantum chemically investigated, in particular detail for Ln = Lu (lutetium). We applied density functional theory (DFT) at the nonrelativistic and scalar and SO‐coupled relativistic levels, and also the ab initio coupled cluster approach. The chemically active electron shells of the lanthanide atoms comprise the 5d and 6s (and 6p) valence atomic orbitals (AO) and also the filled inner 4f semivalence and outer 5p semicore shells. Four different frozen‐core approximations for Lu were compared: the (1s²–4d¹⁰) [Pd] medium core, the [Pd+5s²5p⁶ = Xe] and [Pd+4f¹⁴] large cores, and the [Pd+4f¹⁴+5s²5p⁶] very large core. The errors of Lu? X bonding are more serious on freezing the 5p⁶ shell than the 4f¹⁴ shell, more serious upon core‐freezing than on the effective‐core‐potential approximation. The Ln? X distances correlate linearly with the AO radii of the ionic outer shells, Ln³⁺‐5p⁶ and X^?‐np⁶, characteristic for dominantly ionic Ln³⁺‐X^? binding. The heavier halogen atoms also bind covalently with the Ln‐5d shell. Scalar relativistic effects contract and destabilize the Lu? X bonds, spin orbit coupling hardly affects the geometries but the bond energies, owing to SO effects in the free atoms. The relativistic changes of bond energy BE, bond length R_e, bond force k, and bond stretching frequency v_s do not follow the simple rules of Badger and Gordy (R_e～BE～k～v_s). The so‐called degeneracy‐driven covalence, meaning strong mixing of accidentally near‐degenerate, nearly nonoverlapping AOs without BE contribution is critically discussed. © 2015 Wiley Periodicals, Inc.     

Lifetime measurements of the 3d 94s(1 D) 4p configuration of Cu I

The radiative lifetimes of the levels in the 3d ⁹4s(¹ D)4p configuration of Cu I are measured. The levels are excited from the metastable 3d ⁹4s ^{2 2} D _3/2,5/2 levels. The metastable Cu atoms are generated in a pulsed hollow cathode discharge. The levels investigated are populated with a 35-ps laser pulse at wavelengths around 220 nm. The laser induced fluorescence signal is detected. The lifetime of the 3d ⁹4s(³ D)4p ⁴ D _1/2 level is also determined by direct excitation from the ground state. A comparison with calculated literature values is given.     

Lifetime measurements of some TmI odd parity levels

Eleven new lifetimes of odd parity excited energy levels in four configurations: 4f ¹² 5d 6s6p, 4f ¹² 6s² 6p, 4f ¹³ 5d6s and 4f ¹³ 6s7s of atomic thulium have been mesured with atomic-beam laser spectrocopy. Two pulsed dye lasers are used for stepwise excitation and the time-resolved fluorescence decay was used to determine lifetime values. The accuracy of the measurements is about 10%.     

Identification of new lines in the beam-foil spectrum of B II–IV

Ten, six, and twenty-one new lines appearing in the beam-foil spectra of boron (30–200 nm) have been identified in B II, B III, and B IV, respectively. Energies have been determined with higher accuracy than obtained before for the 2p3s ¹ P ⁰, 2s6d ³ D, 2p3p ³ D, 2p3p ³ S, 2p3p ³ P, and 2p3p ¹ D terms in B II. First energy values are also reported for the 2s6d ¹ D and 2s7d ³ D terms in B II.     

The atomic states of nickel

The Ni 3d ⁹ 4s ¹(³ D)–3d ¹⁰(¹ S) and 3d ⁹ 4s ¹(³ D)-3d ⁸4s ²(³ F) atomic excitation energies have been computed using large multireference CI wave functions in conjunction with a large ANO basis set. Radial correlation effects in the 3d shell are found to be very important and are included using CASSCF wave functions having the 3d and correlating 3d orbitals in the active space. The previous discrepancy (0.5 eV) with experiment for the ³ D–¹ S excitation is reduced to 0.1 eV when the 3d3d references are included in the CI. For the ³ F state, the 4s-4p near degeneracy gives rise to important 4s ²4p ² excitations in addition to the 3d3d excitations which are important for the ³ D and ¹ S states. Inclusion of only 3d-3d correlation in the ³ F and ³ D CI reference spaces yields a ³ F–³ D separation which is in error by 0.12 eV. Addition of the 4s ²4p ² excitations to the ³ F reference space is estimated to increase the discrepancy with experiment by an additional 0.1 eV.     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

Coupling coefficients for systems with two open electronic shells: Transition metal ions with pM dN configuration

We derived the necessary conditions to which the vector coupling coefficients (VCC) a_mn and b_mn, describing atomic L, S-multiplets of p^Md^N and d^Ns¹ configurations (1 ? N ? 9, 1 ? M ? 5), should satisfy. It is shown that for two-open-shell systems under consideration the unknown VCC should satisfy not only usual restrictions resulting from the spheric symmetry, but also some additional equation introduced in the present paper in the form of a postulate. VCC obtained were used for the ab initio calculations (by the general SCF coupling operator method) of several transitionmetal atoms and ions with electronic configurations 3d¹4p¹, 3p⁴3d³, and 3p⁵3d³. To check the presented theory, we carried out a detailed comparison between these results and analogous data, obtained by the atomic Roothaan-Hartree-Fock method [2]. © 1993 John Wiley & Sons, Inc.