### 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 |
---|---|

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 |

### Fingerprint

### 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

**Finite size scaling with gaussian basis sets.** / Moy, Winton; Kais, Sabre; Serra, Pablo.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 106, no. 2-4, pp. 203-212. https://doi.org/10.1080/00268970701528714

}

TY - JOUR

T1 - Finite size scaling with gaussian basis sets

AU - Moy, Winton

AU - Kais, Sabre

AU - Serra, Pablo

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

KW - Critical parameters

KW - Finite size scaling

KW - Gaussian basis sets

UR - http://www.scopus.com/inward/record.url?scp=42149125586&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42149125586&partnerID=8YFLogxK

U2 - 10.1080/00268970701528714

DO - 10.1080/00268970701528714

M3 - Article

VL - 106

SP - 203

EP - 212

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 2-4

ER -