Electron affinity of the sodium atom within the coupled-channel hyperspherical approach

Abstract

We present a nonadiabatic calculation, within the hyperspherical adiabatic approach, for the ground state energy of the alkali-metal negative ions. An application to the sodium negative ion (Na-) is considered. This system is treated as a two-electron problem in which a model potential is used for the interaction between the Na+ core and the valence electrons. Potential curves and nonadiabatic couplings are obtained by a direct numerical calculation, as well as the channel functions. An analysis of convergence is made and comparisons of the electron affinity with results of prior work of other authors are given.

Discontinuities of the Chemical Potential in Reduced Density Matrix Functional Theory

“…[27]; b from Ref. [28]; c Ionization potential from [27], electron affinity from [29]; d Closed-shell treatment; e Open-shell treatment; f CISD using the same basis set as in RDMFT; g Ionization potential from [30], electron affinity from [31]. carbons, and 15 inorganic hydrides.…”

Bound states of the barium atom by the hyperspherical approach

“…With its inclusion, a short-range repulsive effect is added to the potential terms, 3,4,28 dropping the error significantly for the lower states, while keeping the good precision of the excited ones. There is a sensitive improvement of the accuracy of the energies, as seen in Fig.…”

“…For the sodium atom, three coupled channels are enough for electron affinity calculation error below 0.1%. 28 The HAA is an ab initio procedure with approximations due to the truncation on the number of coupled second order ordinary differential equations and the usual numerical floating point error propagation. It is based on the hyperspherical coordinates R and ␣, which correlates the electronic radial variables r 1 and r 2 in a transformation similar to the bidimensional Cartesian to the polar one, R sin ␣ϭr 1 , R cos ␣ ϭr 2 .…”

Local Tilt Optimization of Photovoltaic Solar Panels for Maximum Radiation Absorption

“…The method used is called Regula-Falsi [25], also known as the False Position method. This method has been used successfully in atomic [26][27][28][29][30][31][32][33][34][35][36] and solid-state physics [37,38], in which the quantum mechanical equations call for very efficient numerical methods for minimizations. Thus, using this technique adds a novelty to the PV field.…”