Abstract
Conditions for the N-representability of the pair density (PD) are needed for the development of the PD functional theory. We derive sufficient conditions for the N-representability of the PD that is calculated from the Jastrow wave function within the lowest order. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.
Highlights
The pair density (PD), which is defined as the diagonal element of the second-order reduced density matrix, has more information about the electron correlation than the electron density[1,2,3,4]
Using the properties of the LO-Jastrow PD, we derive the sufficient conditions that are imposed on the correlation function of the Jastrow wave function
The number of steps rapidly increases with that of electrons, the concrete steps that are presented in the previous section are feasible for a small-electron system
Summary
The pair density (PD), which is defined as the diagonal element of the second-order reduced density matrix, has more information about the electron correlation than the electron density[1,2,3,4]. Concerning the N-representability of the PD or the second-order reduced density matrix, there are a lot of works[29,30,31,32,33,34,35,36,37,38,39]. The possibility of it being N-representable has not been discussed[17] This is an arguable problem that is concerned with whether the reproduced PD is physically reasonable or not. The aim of this paper is to discuss the N-representability of Eq (2) and to show the way to search the suitable correlation function f (|ri − rj|). The sufficient conditions for the N-representability of Eq (2), which are imposed on the correlation function, will be derived recursively. Concrete steps for searching the correlation function that meets these conditions are discussed
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