[Paper Review] General static polarizability in spherical neutral metal clusters and fullerenes within Thomas-Fermi theory

D. I. Palade, V. Baran|arXiv (Cornell University)|Jun 15, 2014

Advanced Chemical Physics Studies15 references3 citations

TL;DR

This paper proposes a simplified Thomas-Fermi-based differential equation to compute static linear response, including multipolar polarizabilities, in spherical neutral metal clusters and fullerenes. Using the jellium model and perturbation theory, it achieves <10% deviation from experimental polarizability values—demonstrating high accuracy with minimal computational cost.

ABSTRACT

We study the static linear response in spherical Thomas-Fermi systems deriving a simple diferen- tial equation for general multipolar moments and associated polarizabilities. We test the equation on sodium clusters between 20 and 100 atoms and on fullerenes between C60 and C240 and propose it for general Thomas-Fermi systems. Our simple method provides results which deviates from experimental data with less then 15%.

Motivation & Objective

• To develop a computationally efficient method for calculating static linear response in spherical mesoscopic systems like metal clusters and fullerenes.
• To address the limitations of classical models and the high cost of ab initio methods in predicting polarizability for medium-sized systems.
• To test the validity of the Thomas-Fermi approximation with a simple differential equation for multipolar moments under external fields.
• To evaluate the method’s accuracy against experimental data for sodium clusters (20–100 atoms) and fullerenes (C60 to C240).

Proposed method

• Formulates a general differential equation for multipolar moments in spherical Thomas-Fermi systems under a static external potential.
• Applies the jellium model to represent the ionic background as a spherically symmetric, smooth positive charge distribution.
• Uses perturbation theory to derive the induced electron density change from the external field, enabling calculation of polarizability.
• Employs two jellium parametrizations: a homogeneous spherical shell and a narrow Gaussian profile, to test sensitivity of results.
• Solves the differential equation numerically for dipole response to compute static dipolar polarizability.
• Validates results against experimental data and higher-level methods like RPA for comparison.

Experimental results

Research questions

• RQ1 Can a simple differential equation derived from Thomas-Fermi theory accurately predict static multipolar polarizabilities in spherical clusters?
• RQ2 How does the choice of jellium model parametrization (e.g., Gaussian vs. shell) affect the computed polarizability values?
• RQ3 To what extent does the method reproduce experimental polarizability values for Na clusters and fullerenes with minimal computational effort?
• RQ4 Why does the Gaussian jellium profile yield better agreement with experiment than the sharp-shell model for C60?
• RQ5 How does the method perform as cluster size increases, particularly beyond C60?

Key findings

• The method achieves less than 10% deviation from experimental polarizability values for sodium clusters with 20–100 atoms.
• For C60, the Gaussian jellium parametrization yields a polarizability of 80–85 ų, closely matching the experimental value of 78 ų.
• The homogeneous shell jellium model overestimates C60 polarizability at 92 ų, indicating sensitivity to jellium geometry.
• For C180 and C240 fullerenes, the method predicts 260 ų and 340 ų respectively, showing reasonable agreement with RPA results (300 ų and 432 ų).
• The method remains computationally efficient and provides accurate results even as system size increases, though performance degrades slightly due to symmetry breaking.
• The induced electron density shift under a dipole field shows the expected volumetric redistribution along the field axis, confirming physical consistency.