### 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 c and were found to be 1.0578 and 1.0711 respectively using Mller-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 = 1.2891 and c = 1.1259. With time-dependent density functional theory (TDDFT) using the hybrid functional B3LYP resulted in c = 1.0160. The ab initio results compare well with the exact results = 1 and c = 1.0971. The method is general and can be extended to calculate critical parameters for larger systems.

Original language | English |
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Pages (from-to) | 203-212 |

Number of pages | 10 |

Journal | Molecular Physics |

Volume | 106 |

Issue number | 2-4 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

Externally published | Yes |

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### Keywords

- Critical parameters
- Finite size scaling
- Gaussian basis sets

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Molecular Physics*,

*106*(2-4), 203-212. https://doi.org/10.1080/00268970701528714