Variational principle for the ground-state energy as a functional of the one-particle density matrix: Beyond Hartree-Fock theory

1998 ◽  
Vol 57 (4) ◽  
pp. 2485-2495 ◽  
Author(s):  
Abraham Klein ◽  
Reiner M. Dreizler
Keyword(s):  
Variational Principle ◽  
Density Matrix ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Particle Density ◽  
Hartree Fock ◽  
The One

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

2018 ◽  
Vol 71 (4) ◽  
pp. 295 ◽  
Author(s):  
Dylan Jayatilaka ◽  
Kunal K. Jha ◽  
Parthapratim Munshi
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Ground State ◽  
Density Functional ◽  
Particle Density ◽  
Density Matrices ◽  
Hartree Fock ◽  
Electron Density Matrix ◽  
Ground State Electron ◽  
Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

An Interpolating Ansatz for the Ground State of the Spinless Fermion Hamiltonian in D=1 and 2

1997 ◽  
Vol 11 (13) ◽  
pp. 1545-1563
Author(s):  
Miguel A. Martín-Delgado ◽  
Germán Sierra
Keyword(s):  
Critical Point ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Phase Transitions ◽  
Hartree Fock ◽  
Spinless Fermion ◽  
A Value ◽  
Bifurcation Phenomena ◽  
Half Filling

We propose an interpolating ansatz between the strong coupling and weak coupling regimes of a system of spinless interacting fermions in 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. In 1D our method is capable of unveiling the existence of a critical point in the coupling constant at (t/U) c =0.7483 as in fact occurs in the exact solution at a value of 0.5. In our approach this phase transition is described as an example of Bifurcation Phenomena in the variational computation of the ground state energy. In 2D the van Hove singularity plays an essential role in changing the asymptotic behaviour of the system for large values of t/U. In particular, the staggered magnetization for large t/U does not display the Hartree–Fock law [Formula: see text] but instead we find the law [Formula: see text]. Moreover, the system does not exhibit bifurcation phenomena and thus we do not find a critical point separating a CDW state from a fermion "liquid" state.

On the Ground State of H-

1981 ◽  
Vol 36 (7) ◽  
pp. 782
Author(s):  
Uday Vanu Das Gupta ◽  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Oscillator Strength ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Expectation Values ◽  
Hartree Fock ◽  
Present Procedure

Abstract A simple and effective method is described to calculate the ground state energy of H~ starting with the Hartree Fock wavefunction. The expectation values of the opera­ tors 〈r1 • r2〉, 〈r1n + r2n〉 and 〈p1 • p2〉 can be estimated easily with the present procedure. Oscillator strength sums S(k) for k= -1,0, 1 are also evaluated.

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