{"title":"用氦等电子序列中基态和激发态的相关能和纠缠熵探测柯林斯猜想","authors":"Yen-Chang Lin, Yew Kam Ho","doi":"10.1002/qua.27420","DOIUrl":null,"url":null,"abstract":"<p>In the present work, we present an investigation of Collins Conjecture, a hypothesis made by D. M. Collins in 1993 relating correlation energy and entanglement entropy, by calculating the ground state and singly-excited triplet-spin 1s2s <sup>3</sup><i>S</i> and 1s3s <sup>3</sup><i>S</i> state energies of the helium iso-electronic sequence, with <i>Z</i> = 2–15. By using extensive orthonormal configuration interaction (CI) type wave functions with <i>B</i>-Spline basis up to about 6000 terms, linear entropy and von Neumann entropy for the abovementioned atomic systems are determined. Together with the Hartree-Fock energies obtained following a self-consistent field theory, we have found that there exist linearly proportionalities between the renormalized correlation energies and entanglement entropies of both linear and von Neumann, showing a support for Collins Conjecture applicable to the ground and singly-excited triplet-spin states in the helium sequence, for a range of finite <i>Z</i>-values.</p>","PeriodicalId":182,"journal":{"name":"International Journal of Quantum Chemistry","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Probing Collins Conjecture with correlation energies and entanglement entropies for the ground and excited states in the helium iso-electronic sequence\",\"authors\":\"Yen-Chang Lin, Yew Kam Ho\",\"doi\":\"10.1002/qua.27420\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In the present work, we present an investigation of Collins Conjecture, a hypothesis made by D. M. Collins in 1993 relating correlation energy and entanglement entropy, by calculating the ground state and singly-excited triplet-spin 1s2s <sup>3</sup><i>S</i> and 1s3s <sup>3</sup><i>S</i> state energies of the helium iso-electronic sequence, with <i>Z</i> = 2–15. By using extensive orthonormal configuration interaction (CI) type wave functions with <i>B</i>-Spline basis up to about 6000 terms, linear entropy and von Neumann entropy for the abovementioned atomic systems are determined. Together with the Hartree-Fock energies obtained following a self-consistent field theory, we have found that there exist linearly proportionalities between the renormalized correlation energies and entanglement entropies of both linear and von Neumann, showing a support for Collins Conjecture applicable to the ground and singly-excited triplet-spin states in the helium sequence, for a range of finite <i>Z</i>-values.</p>\",\"PeriodicalId\":182,\"journal\":{\"name\":\"International Journal of Quantum Chemistry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Quantum Chemistry\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/qua.27420\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Quantum Chemistry","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/qua.27420","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
摘要
在本研究中,我们通过计算氦等电子序列(Z = 2-15)的基态和单激发三重自旋 1s2s 3S 和 1s3s 3S 态能量,对柯林斯猜想(D. M. Collins 于 1993 年提出的关于相关能和纠缠熵的假设)进行了研究。通过使用广泛的正交构型相互作用(CI)型波函数和多达约 6000 项的 B-Spline,确定了上述原子系统的线性熵和冯-诺依曼熵。结合根据自洽场理论得到的哈特里-福克能量,我们发现重归一化相关能与线性熵和冯-诺伊曼熵之间存在线性比例关系,这表明柯林斯猜想得到了支持,该猜想适用于氦序列中有限 Z 值范围内的基态和单激发三重自旋态。
Probing Collins Conjecture with correlation energies and entanglement entropies for the ground and excited states in the helium iso-electronic sequence
In the present work, we present an investigation of Collins Conjecture, a hypothesis made by D. M. Collins in 1993 relating correlation energy and entanglement entropy, by calculating the ground state and singly-excited triplet-spin 1s2s 3S and 1s3s 3S state energies of the helium iso-electronic sequence, with Z = 2–15. By using extensive orthonormal configuration interaction (CI) type wave functions with B-Spline basis up to about 6000 terms, linear entropy and von Neumann entropy for the abovementioned atomic systems are determined. Together with the Hartree-Fock energies obtained following a self-consistent field theory, we have found that there exist linearly proportionalities between the renormalized correlation energies and entanglement entropies of both linear and von Neumann, showing a support for Collins Conjecture applicable to the ground and singly-excited triplet-spin states in the helium sequence, for a range of finite Z-values.
期刊介绍:
Since its first formulation quantum chemistry has provided the conceptual and terminological framework necessary to understand atoms, molecules and the condensed matter. Over the past decades synergistic advances in the methodological developments, software and hardware have transformed quantum chemistry in a truly interdisciplinary science that has expanded beyond its traditional core of molecular sciences to fields as diverse as chemistry and catalysis, biophysics, nanotechnology and material science.