Application of MP2 Results in Comparative Studies of Semiempirical Ground-State Energies of Large Atoms

2003 ◽  
Vol 68 (2) ◽  
pp. 240-252 ◽  
Author(s):  
Jesus R. Flores ◽  
Karol Jankowski ◽  
Romuald Słupski

To study the usefulness of second-order Møller-Plesset (MP2) correlation energies for ground states of closed-shell atoms (referred to as MP2/CA energies) in estimations of the total correlation energies of larger closed-shell atoms, we have considered atoms and ions containing from 10 to 86 electrons. First, it is demonstrated that for N-electron systems, 10 ≤ N ≤ 18, the MP2/CA energies provide very good approximations to the very accurate estimates of atomic correlation energies by Chakravorty and Davidson. Next, for systems with 10 ≤ N ≤ 54, comparisons are made with the semiempirical energies obtained when using the models by Chakravorty and Clementi as well as by Clementi and Corongiu. Finally, for atoms with 10 ≤ N ≤ 86, the MP2/CA energies are employed for comparison with DFT energies recently obtained by Andrae et al. (Int. J. Quantum Chem. 2001, 82, 227). The MP2/CA results proved to provide reasonable estimates to the total correlation energies in all the cases considered.

1985 ◽  
Vol 28 (1) ◽  
pp. 27-37 ◽  
Author(s):  
J. Karwowski ◽  
J. Styszy?ski

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.


1998 ◽  
Vol 12 (23) ◽  
pp. 2325-2348 ◽  
Author(s):  
A. K. Kolezhuk ◽  
H.-J. Mikeska

We study two-leg S=1/2 ladders with general isotropic exchange interactions between spins on neighboring rungs, whose ground state can be found exactly in a form of finitely correlated (matrix product) wave function. Two families of models admitting an exact solution are found: one yields translationally invariant ground states and the other describes spontaneously dimerized models with twofold degenerate ground state. Several known models with exact ground states (Majumdar–Ghosh and Shastry–Sutherland spin-1/2 chains, Affleck–Kennedy–Lieb–Tasaki spin-1 chain, Δ-chain, Bose–Gayen ladder model) can be obtained as particular cases from the general solution of the first family, which includes also a set of models with only bilinear interactions. Those two families of models have nonzero intersection, which enables us to determine exactly the phase boundary of the second-order transition into the dimerized phase and to study the properties of this transition. The structure of elementary excitations in the dimerized phase is discussed on the basis of a variational ansatz. For a particular class of models, we present exact wave functions of the elementary excitations becoming gapless at second-order transition lines. We also propose a generalization of the Bose–Gayen model which has a rich phase diagram with all phase boundaries being exact.


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