A New Electron-nucleus Correlation Functional forMulticomponent Density Functional Theory

Abstract

最も軽い水素の原子核の運動においては，量子効果が顕著に現れる. 原子核運動の量子効果を直接的に取り込んだ理論として多成分分子理論を開発してきた．また近年では，計算時間のかからない密度汎関数理論が分子理論の中心理論となりつつある．我々は，多成分密度汎関数理論のための簡便な電子-核相関汎関数を開発した. この汎関数は，相関波動関数から簡単かつ正当な物理条件のみにもとづいて導出した汎用性の高い汎関数であり，パラメータを1つしか含まない．にもかかわらず，水素原子を含む小分子の電子-プロトン相関エネルギーを化学的精度(1∼2 kcal/mol程度の誤差)で再現する．

Figure

Figure 1.

 (a) The electron-nucleus correlation factor given by MC_QMC calculations and the original CS correlation factor for H atom, and (b) that given by MC_QMC calculations and new CS correlation factor (eq. (3)) for H atom [12].

Table

Table 1. The sum of the Kohn-Sham BOP energies and the corresponding zero-point vibrational energies (E^BOP + E^ZPE) [Hartree], sum of MC_BOP and electron-proton correlation energies (E^MC_BOP + $E_{\text{c}}^{\text{en}}$) [Hartree], and deviations (E^Dev)[mHartree] for 18 small hydrogen-containing molecules [12].

	H2							HeH+
EBOP + EZPE	–1.16148							–2.96621
EMC_BOP + $E_{\text{c}}^{\text{en}}$	–1.16130							–2.97605
EDev	0.1							–9.8
	LiH	BeH2	BH3	CH4	NH3	H2O	FH	NeH+
EBOP + EZPE	–8.07197	–15.88387	–26.55590	–40.43552	–56.47276	–76.34735	–100.37958	–128.95422
EMC_BOP + $E_{\text{c}}^{\text{en}}$	–8.06673	–15.87819	–26.55287	–40.44337	–56.47904	–76.35237	–100.38158	–128.95672
EDev	5.2	2.8	1.0	–2.0	–2.1	–2.5	–2.0	–2.5
	NaH	MgH2	AlH3	SiH4	PH3	SH2	HCl	ArH+
EBOP + EZPE	–162.82428	–201.19665	–244.12415	–291.76988	–343.03396	–399.29519	–460.72476	–527.58919
EMC_BOP + $E_{\text{c}}^{\text{en}}$	–162.81851	–201.18783	–244.11501	–291.76319	–343.03200	–399.29530	–460.72569	–527.59295
EDev	5.8	4.4	3.0	1.7	0.7	–0.1	–0.9	–3.8

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