A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all‐electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy‐optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all‐electron and valence‐electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent.

Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi

The total Xα energy accurate to 0.3 eV is computed for H2, B2, C2, N2, O2, CO, and F2. Relative to experiment, the Xα model (α=0.7) is accurate to within ΔRe=0.1 bohr, ΔDe=2 eV, and Δωe=300 cm−1 for these molecules. Except for the lightest first‐row diatomic molecules, the Xα and experimental dissociation energies are bracketed by those of the Hartree–Fock model (from below) and the Local Spin Density model (from above).

On first‐row diatomic molecules and local density models

We present the theory of laser-induced radiative association in terms of a scattering resonance formalism and apply this theory to the specific case of Na atom collisions at a temperature of 10 mK. Use of ultracold atoms permits a new kind of high-resolution free-bound spectroscopy for the study of near-threshold collisions and excited-state energy levels which are difficult to study by conventional bound state spectroscopy.

Laser-induced photoassociation of ultracold sodium atoms.

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.

/pdf/time-dependent-density-functional-theory-in-the-projector-2fstm72z4a.pdf

Time-dependent density-functional theory in the projector augmented-wave method.

Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two‐center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm−1, and ΔDe=57 cm−1.

Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations

The multiconfiguration self‐consistent field wave functions and potential energy curves for the lowest lying 1Σ+g, 1Σ+u, 3Σ+g, 3Σ+u, 1Πg, 1Πu, 3Πg, and 3Πu states of Na2 are reported. We find good agreement with recent experimental estimates of the dissociation energies for the 1Σ+g and 1Σ+u states. We find the long range hump in the B 1Πu curve to have its maximum height of 520 cm−1 above the separated atom asymptote at R=6.45±0.1 A; recent experimental estimates of the height are 474 and 554±120 cm−1.

The molecular electronic structure of the lowest 1Σ+g, 3Σ+u, 1Σ+u, 3Σ+g, 1Πu, 1Πg, 3Πu, and 3Πg states of Na2

Electronic transition dipole moment functions and difference potentials for transitions among low-lying states of Li2 and Na2

Long-range interactions of sodium(3s2S) with sodium(3s2S) or sodium(3p2P)

A most likely potential curve for the 1 3Σ+u state of Li2 with constants De=340.6±15 cm−1, ωe=65.6±0.9 cm−1, ωexe=3.16±0.04 cm−1, Re=7.77±0.22a0 is obtained by a judicious combination of three disparate ab initio computations.

The ‘‘most likely’’ potential energy curve for the lowest 3Σ+u state of Li2

The MTXαR method: Applications to the ground state Na2 and NaLi molecules

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