Correlation energy matrix

Hence the operators Vext and exc[ p(r)] are required to calculate the matrix elements of the external energy matrix and the exchange-correlation energy matrix. 

To study the structure of the exchange-correlation energy functional, it is useful to relate this quantity to the pair-correlation function. The pair-correlation function of a system of interacting particles is defined in terms of the diagonal two-particle density matrix (for an extensive discussion of the properties of two-particle density matrices see [30]) as... 

G. Gidofalvi and D. A. Mazziotti, Boson correlation energies via variational minimization with the two-particle reduced density matrix exact iV-representabihty conditions for harmonic interactions. Phys. Rev. A 69, 042511 (2004). 

Levy identified the unknown part of the exact universal D functional as the correlation energy Ed D] and investigated a number of properties of c[ D], including scaling, bounds, convexity, and asymptotic behavior [11]. He suggested approximate explicit forms for Ec[ D] for computational purposes as well. Redondo presented a density-matrix formulation of several ab initio methods [26]. His generalization of the HK theorem followed closely Levy s... 

In quantum chemistry, the correlation energy Ecorr is defined as Econ = exact HF- In Order to Calculate the correlation energy of our system, we show how to calculate the ground state using the Hartree-Fock approximation. The main idea is to expand the exact wavefunction in the form of a configuration interaction picture. The first term of this expansion corresponds to the Hartree-Fock wavefunction. As a first step we calculate the spin-traced one-particle density matrix [5] (IPDM) y ... 

The effects of adding secondary off axis basis functions are smnmarized in Table 4. The results obtained with the largest basis set considered in Table 3, 30s ac 30s be 28s oa(ac) p. = 4] 26s oa bc) [n j = 4], are used as a reference with respect to which the results presented in Table 4 are analyzed. The addition of secondary off axis basis functions reduces the error in the matrix Hartree-Fock energy to 4 Hartree. For the second order correlation energy the addition of secondary off axis basis subsets reduces the error to 723 / Hartree, thereby achieving the target accuracy of the present study. 

The accurate description of correlation effects requires the inclusion of functions of higher symmetry than those required for the matrix Hartree-Fock model. The most important of these functions for the F anion are functions of d-type. In this section, the convergence of the total energy through second order and the second order correlation energy component for a systematic sequence of even-tempered basis sets of Gaussian functions of s-, p-and d-type is investigated. 

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