Finite size scaling with gaussian basis sets

Abstract

We combined finite size scaling method with the well-developed electronic structure methods, such as ab initio and density functional methods, to provide a systematic procedure for obtaining quantum critical parameters for atoms and molecules using Gaussian basis sets. The finite size scaling method is based on taking the number of elements in a complete basis set as the size of the system, to calculate the critical parameters for a given quantum system. We present results for the Yukawa potential and helium-like systems by expanding the wave function with a Gaussian basis. The finite size scaling approach was then used with the ab initio methods to find the critical parameters of two-electron atoms. The critical values of λc and α were found to be 1.0578 and 1.0711 respectively using Møller–Plesset (MP2) level of theory. We then applied configuration interaction single and doubles excitation (CISD) to the helium system to improve upon the results. The critical parameters at the CISD level of theory were α = 1.2891 and λc = 1.1259. With time-dependent density functional theory (TDDFT) using the hybrid functional B3LYP resulted in λc = 1.0160. The ab initio results compare well with the exact results α = 1 and λc = 1.0971. The method is general and can be extended to calculate critical parameters for larger systems.