Compact basis sets for LCAO-LSD calculations. Part I: Method and bases for Sc to Zn

A method for preparing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed. The method has been applied to construct basis sets for first row transition metal atoms from Sc to Zn for the 3d^n?14s¹ and 3d^n?24s² configurations. The properties of different expansion patterns have been tested in atomic calculations for the chromium atom.     

Lifetime measurements and stark mixing of autoionizing Cu I-states

Using a combination of collisional and laser excitation the lifetimes of 17 autoionizing Cu I states in the configurations 3d ⁹ 4s 6s and 3d ⁹ 4s4d were measured. The lifetimes are in the range of 1–50 ps and depend strongly on the coupling properties, the mixing with different configurations, and the radial integrals of the discrete with the continuum states. For the level 3d ⁹ 4s 4d ⁴ S _3/2 the influence of an electric field via Stark mixing of 3d ⁹ 4s 5p ⁴ P _1/2 on the autoionizing rate was investigated. The experimental values are compared with theoretical results which follow from ab initio calculations for the transition probabilities and least square fit values deduced from the experimental positions. Good agreement is found only for theJ=3/2 levels of both configurations 3d ⁹ 4s 4d and 3d ⁹ 4s 6s.     

Optical isotope shifts in titanium I: new measurements

The optical isotope shifts between ⁴⁶Ti, ⁴⁸Ti and ⁵⁰Ti have been measured for eight 3d ³ 4s a ⁵F-3d ² 4s 4p y ³ F lines of titanium by use of a Doppler-free experiment. By contrast with the positive shifts previously measured for 3d ² 4s ² a ³ F-3d ² 4s 4p z ⁵ D lines, these shifts are negative and reveal the presence of large negative specific mass shifts attributed to a d-p electron jump. The interpretation of the present measurements and of former ones is made by means of Hartree-Fock calculations.     

Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

Perturbation calculation of atomic correlation energies for the first transition period

Results are presented for calculations of Hartree—Fock and correlation energies for the 3dⁿ 4s² and 3dⁿ⁺¹ 4s ground and excited states of the first transition series atoms using second-order Møller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.     

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.     

Theoretical study of Na(4p2P) + Na(3s2S) and Cd(5p3P0) + Na(3s2S) collisions and their role in the energy transfer between Cd.* and Na

We have computed the cross sections for the energy transfer process Cd(5p³P₀) + Na(3s²S) → Cd(5s¹S) + Na(4p²P) and for the state changing collision Na(4p²P) + Na(3s²S) → Na(3d²D) + Na(3s²S), based on theoretical interaction potentials for the NaCd and Na2 systems, respectively. Our calculations shed light on the interpretation of experiments with laser excited Na+Cd vapour mixtures [1]. It turns out that Cd(5p³P₀), in rapid equilibrium with the doorway state Cd(5p³P₁), efficiently transfers energy to Na, populating the 4p²P state. The collisions with ground state Na cause a very fast conversion of the 4p³P₁ to the 3d²D state, from which the strongest emission is observed.     

A matrix-induced change in the electronic ground state of nickel atoms isolated in rare gases

Comparison of the absorption spectra for matrix-isolated Ni atoms with gas-phase data reveals that the electronic ground-state configuration of the isolated atom can be changed by the matrix. While Ni in Ne has the same configuration as in the gas phase, namely 3d⁸4s² we find in Ar, Kr, and Xe the 3d⁹4s¹ configuration to be the ground state. The matrix-induced changes is explained by the repulsive matrix-dopant interaction, which is sufficiently lowered in the 3d⁹4s¹ configuration to overcompensate for the energy difference of 205 cm^?1 by which the 3d⁹4s¹ level lies above the 3d⁸4s² in the free atom.     

A theoretical investigation of the ground and core hole states of linear and bent NiCO; a prototype for CO adsorbed on nickel

Non-empirical LCAO MO SCF calculations within the Hartree-Fock formalism have been performed on linear and bent conformations of NiCO, for both the states arising from the 3d⁹4s¹ and 3d¹⁰ electronic configurations of Ni, for ground and core ionized species. Binding and relaxation energies are computed for the nickel atom, the free ligand (CO) and the absorbed species (NiCO). Comparison with available experimental data reveals good agreement for the shifts in core binding energies for the bent, 3d⁹4s¹ NiCO system. The main contribution to these binding energy shifts is found to be due to relaxation effects, which may be rationalized in terms of atomic population and bond overlap changes accompanying core ionization.     

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

Configuration Interaction (CI) calculations on the ground ²P state of boron atom are presented using a wave function expansion constructed with L‐S eigenfunction configurations of s‐, p‐, and d‐Slater orbitals. Two procedures of optimization of the orbital exponents have been investigated. First, CI(SD) calculations including few types of configurations and full optimization of the orbital exponents led to the energy ?24.63704575 a.u. Second, full‐CI (FCI) calculations including a large number of configuration types using a fixed set of orbital exponents for all configurations gave ?24.63405222 a.u. using the basis [4s3p2d] and 2157 configurations, and to an improved result of ?24.64013999 a.u. for 3957 configurations and a [5s4p3d] basis. This last result is better than earlier calculations of Schaefer and Harris (Phys Rev 1968, 167, 67), and compares well with the recent ones from Froese Fischer and Bunge (personal communication). In addition, using the same wave functions, CI calculations of the boron isoelectronic ion C⁺ have been performed obtaining an energy of ?37.41027598 a.u. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.     

Potential energy curves for NiH and NiH2

The potential energy curves for the NiH and linear HNiH molecules resulting from the 3d⁸4s² and 3d⁹4s configuration of nickel are calculated using the unrestricted Hartree–Fock and perfect pairing generalized valence bond methods. NiH bonding in the 3d⁸4s² configuration is by means of an sp hybrid orbital which comes from the 4s² shell leaving a singly occupied nonbonding orbital free to bond to another hydrogen atom. The bond to the 3d⁹4s configuration contains primarily the 4s orbital leaving an empty orbital in the nickel 3d shell which in turn bonds very weakly with another hydrogen. These results are compared to similar studies of the hydrogen atom on Sc, Mn and Cu and some implications for hydrocarbon catalysis are considered.     

Investigation of autoionizing CuI-states in the region of the second ionization limit CuII 3d 94s

The combination of collisional and laser excitation was used for the investigation of autoionizing CuI states in the region of the second ionization limit CuII 3d ⁹ 4s at 85000–95000 cm^?1. The analysis of the complicated signal structure was concentrated on the first measurement of CuI 3d ⁹ 4p ² levels. The experimental results are compared with Hartree-Fock calculations of the energy values and level widths of the autoionization resonances.     

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 CNDO-MO calculation of VCl4

The electronic structure of the tetrahedral molecule VCL₄ is investigated within the CNDO-MO approximations. The metal and ligand valence orbitals, 3d, 4s, 4p; and 3s, 3p; respectively, have been systematically varied in an attempt to minimize the total energy; “optimum” V 4s(χ₄ = 1.10) and 4p(d ³ p ²) orbitals have been established, but V 3d(d ⁿ ) and Cl(-δ) valence orbitals are only seen to favor lower energy for expanded orbitals. Since determining the one-electron molecular orbital level which is occupied by the vanadium lone electron is a major aspect of this investigation, all calculations have been performed in triplicate: calculations assuming the unpaired electron occupies the 3a ₁, 2 _e and 4t ₂ molecular orbital (ground state electronic configurations² A ₁,² E, and² T ₂, respectively). The Hartree-Fock equations have been solved by Roothaan's SCF method for open shells, but off-diagonal multipliers between filled and partly filled molecular orbitals of the same symmetry have been neglected. As a qualitative estimate of the error introduced by this simplification, the pertinent overlap integrals between the eigenfunctions from calculations for the three possible configurations,² A ₁,² E, and² T ₂, are investigated as functions of the component 3d(d ⁿ ) and Cl(-δ) valence orbitals. The overlap integrals from the relevant² A ₁ and² T ₂ calculations are reasonably small, but the neglect of off-diagonal multipliers in calculations on the² E state is found to be a poor approximation. An ordering of the non-filled molecular orbitals in VCl₄ of 4t ₂ < 3a ₁ < 2e < 5t ₂ seems most consistent with the numerous calculations. This suggested ground state electronic configuration of² T ₂ introduces new aspects to the consideration of a (dynamic) Jahn-Teller effect in VCl₄. Experimental data pertinent to the electronic structure of VCl₄ has been briefly summarized, but unfortunately it is inadequate to confirm or deny the present calculations.     

CAS SCF Cl calculations for the 3Σ−g, 1Σ+g, 3Σ+u, and 5Δu states of Sc2

CAS SCF CI (SD) calculations have been carried out for the ³Σ^?_g, ¹Σ⁺_g, ³Σ⁺_u, and ⁵Δ_u states of Sc₂ using large gaussian basis sets. The ³Σ^?_g, ¹Σ⁺_g, and ³Σ⁺_u states arise from the ²D(4s² 3d¹) + ²D(4s² 3d¹) limit of Sc₂ and are found to be only weakly bound (D_c ≈ 0.06 eV and R_c ≈ 8.0a₀). The ⁵Δ_u state arises from the ²D(4s² 3d¹) + ⁴F(4s¹ 3d¹ 4p¹) atomic limit. This state is found to be strongly bound relative to its limits (D_c ≈ 0.8 eV and R_c ≈ 7.0a₀).     

On the hyperfine structure in the yttrium ion

Experimental data on the hyperfine structure in the 4d5s, 4d ² and 4d5p configurations of the yttrium ion have been analysed by means of the effective operator formalism. The effective radial parameters of the magnetic dipole interaction are determined. A comparison with relativistic calculations gives an estimate of the effects due to configuration interaction.     

Why do the second row transition metal atoms prefer 5s14dm+1 to 5s24dm?

Numerical Hartree-Fock (NHF) calculations have been performed for 332 ground and low-lying excited states of the fifth period atoms Rb through Xe, with our special interest in the states arising from the 5s ²4d ^m , 5s ¹4d ^m +1, and 5s ⁰ 4d ^m +2 configurations of the second row transition metal atoms. Among various properties, orbital energies and mean values ofr of the outermost orbitals of each symmetry are presented as well as total energies. It is discussed in some detail why the second row transition metal atoms have a tendency to prefers ¹ d ^m +1 as the ground configuration in contrast to the preferreds ² d ^m configuration in the first row transition metal atoms. Our systematic NHF computations reported in this and the previous papers conclude that the Hartree-Fock method correctly predicts the experimental ground state of the atoms He through Xe with the sole exception for Zr.     

Semiempirical hyperfine structure and ab initio isotope shift predictions in Zr II

The fine structure of the even‐parity low configurations has been reanalyzed by simultaneous parameterization of the one‐ and two‐body interactions for the model space (4d + 5s)³. Using the calculated eigenfunctions, the magnetic‐dipole A hyperfine constants for the whole 37 existing levels of the model space were predicted and compared partially to those obtained using relativistic configuration‐interaction approach. Moreover, volume shifts (VS) and specific mass shifts (SMS) of numerous configurations of singly ionised zirconium are deduced by means of ab initio estimates combined with a few experimental isotope shift data available in literature: VS(4d¹5s²) = 840 MHz, VS(4d³) = ?649 MHz, VS(4d¹5p²) = ?387 MHz, VS(5s²5p¹) = 1250 MHz, and SMS(4d¹5s²) = ?634 MHz, SMS(4d³) = 484 MHz, SMS(5s²5p¹) = ?1459 MHz, referred to 4d²5s for the pair Zr⁹⁰–Zr⁹². © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Beam-foil lifetime data for 3s 3p 3 and 3s 2 3p 3d levels of Si-like Ni14+

In the EUV spectrum of foil-excited 24 MeV Ni ions the decays of the 3s 3p ³ and 3s ² 3p 3d levels to the 3s ² 3p ² levels of the ground configuration have been observed. For most of the levels decay curves have been obtained. The lifetime results compare well with predictions from semi-empirically scaled HXR calculations. Some problems with cascade repopulations will be discussed.