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	Relativistic explicit correlation: Coalescence conditions and practical suggestions
	Li, Zhendong ; Shao, Sihong ; Liu, Wenjian
	2012
关键词	COMPLEX-COORDINATE ROTATION BOUND-STATE ENERGIES WAVE-FUNCTIONS ISOELECTRONIC SERIES ELECTRONIC-STRUCTURE SPIN-1/2 PARTICLES QUANTUM-CHEMISTRY HYLLERAAS-CI TERMS HAMILTONIANS
英文摘要	To set up the general framework for relativistic explicitly correlated wave function methods, the electron-electron coalescence conditions are derived for the wave functions of the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), Dirac-Coulomb-Breit (DCB), modified Dirac-Coulomb (MDC), and zeroth-order regularly approximated (ZORA) Hamiltonians. The manipulations make full use of the internal symmetries of the reduced two-electron Hamiltonians such that the asymptotic behaviors of the wave functions emerge naturally. The results show that, at the coalescence point of two electrons, the wave functions of the DCG Hamiltonian are regular, while those of the DC and DCB Hamiltonians have weak singularities of the type r(12)(nu) with nu being negative and of O(alpha(2)). The behaviors of the MDC wave functions are related to the original ones in a simple manner, while the spin-free counterparts are somewhat different due to the complicated electron-electron interaction. The behaviors of the ZORA wave functions depend on the chosen potential in the kinetic energy operator. In the case of the nuclear attraction, the behaviors of the ZORA wave functions are very similar to those of the nonrelativistic ones, just with an additional correction of O(alpha(2)) to the nonrelativistic cusp condition. However, if the Coulomb interaction is also included, the ZORA wave functions become close to the large-large components of the DC wave functions. Note that such asymptotic expansions of the relativistic wave functions are only valid within an extremely small convergence radius R-c of O(alpha(2)). Beyond this radius, the behaviors of the relativistic wave functions are still dominated by the nonrelativistic limit, as can be seen in terms of direct perturbation theory (DPT) of relativity. However, as the two limits a -> 0 and r(12) -> 0 do not commute, DPT is doomed to fail due to incorrect descriptions of the small-small component Psi(SS) of the DC wave function for r(12) < R-c. Another deduction from the possible divergence of Psi(SS) at r(12) = R-c is that the DC Hamiltonian has no bound electronic states, although the last word cannot be said. These findings enrich our understandings of relativistic wave functions. On the practical side, it is shown that, under the no-pair approximation, relativistic explicitly correlated wave function methods can be made completely parallel to the nonrelativistic counterparts, as demonstrated explicitly for MP2-F12. Yet, this can only be achieved by using an extended no-pair projector. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3702631]; Physics, Atomic, Molecular & Chemical; SCI(E); EI; 10; ARTICLE; 14; 136
语种	英语
出处	SCI ; EI
出版者	journal of chemical physics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/150968]
专题	数学科学学院 化学与分子工程学院
推荐引用方式 GB/T 7714	Li, Zhendong,Shao, Sihong,Liu, Wenjian. Relativistic explicit correlation: Coalescence conditions and practical suggestions. 2012-01-01.

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