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Extended screened exchange functional derived from transcorrelated density functional theory
The Journal of Chemical Physics ( IF 3.1 ) Pub Date : 2017-09-12 , DOI: 10.1063/1.5001260
Naoto Umezawa 1
Affiliation  

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: HTC=1FHF. It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy: E[n]=Ψn|H|Ψn/Ψn|Ψn=Dn|HTC|Dn under the two assumptions: (1) The electron density nr associated with a trial wave function Ψn = DnF is v-representable and (2) Ψn and Dn give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

中文翻译:

从互相关密度泛函理论推导的扩展筛选交换泛函

我们提出了一种从密度泛函理论(TC-DFT)中使用的互相关方法派生出的相关能量函数的新公式。一个有效的哈密顿量,HŤC是由多体哈密顿量的相似性变换引入的, H关于复数函数FHŤC=1个FHF。证明期望值为HŤC对于归一化的单一Slater行列式D n,其对应于总能量:E[ñ]=Ψñ|H|Ψñ/Ψñ|Ψñ=dñ|HŤC|dñ 在两个假设下:(1)电子密度 ñ[R 与试波功能相关 Ψñ= D n Fv-代表和(2) ΨñD n产生相同的电子密度ñ[R。因此,该公式提供了总能量的替代表达式,可用于开发新型相关能量函数。通过将特定功能替换为F,我们成功地推导出了模型相关能量函数,该函数类似于筛选交换方法的函数形式。拟议的功能,称为扩展的屏蔽交换(ESX)功能,在两体积分中进行了描述,并针对均质电子气的精确数值相关能量进行了参数化。ESX功能块不包含任何(半)本地功能块的成分,因此完全没有自我交互。求解自洽场方程的计算成本与Hartree-Fock方法的计算成本相当。我们采用ESX的功能,以电子结构计算的固体硅,H -离子和小原子。结果表明,TC-DFT配方有望系统地改善相关能量功能。
更新日期:2017-09-14
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