Dynamic dipole polarizabilities of the ground and excited states of confined hydrogen atom computed by means of a mapped Fourier grid method

Abstract

Accurate theoretical estimates of static and dynamic dipole polarizabilities are reported for the ground and excited states of hydrogen atom confined at the center of a spherical "box" with impenetrable walls using a novel theoretical algorithm that combines the variational-perturbation approach with an appropriately adapted mapped Fourier grid method and uniformly maintains the numerical accuracy. A variation of computed polarizabilities is observed as a function of the number of grid points. However, rapid convergence to their correct values, even far into the anomalous dispersion region, is achieved by an extrapolation procedure to the limit of an infinitely large number of grid points using a small number of the lowest-order Padé approximants. It is shown that dipole polarizabilities strongly depend upon the electronic state and the radius of confinement. In particular, the static polarizability of 2s state changes sign under strong confinement.

Static and dynamic dipole polarizabilities and electron density at origin: Ground and excited states of hydrogen atom confined in multiwalled fullerenes

“…The values found for the static and dynamic polarizabilities with our B-spline-based computing code reproduce very well those obtained in the previous computations following the mapped Fourier grid method [7]. The addition of new walls does not change significantly the polarizability of the ground state.…”

“…The effect of spatial confinement has been described in some of these works. The most extended contribution on the dynamic polarizabilities of spatially confined H-atom was proposed recently by Cohen et al [7]. In a recent study, the calculations of the electric dipole polarizability of hydrogen confined to a single-walled fullerene (H@C 60 ) have been reported (see Ref.…”

The Lagrange-mesh method

“…In Refs. [128,129], a mapped Fourier grid method has been applied. However, the convergence can be much faster with the LMM [51].…”

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

“…A few notable ones are: hyperfine splitting constant, dipole shielding factor, nuclear magnetic screening constant, pressure, excited‐state life time, nuclear volume isotope effect, density derivatives at the nucleus and so forth. A significant amount of work exists on static and dynamic polarizability within the Kirkwood, Buckingham, Unsold approximations and many other methods as well. It offers some interesting properties in higher dimensions as well.…”