Local-Energy Method in Electronic Energy Calculations

Frost, Arthur A.; Kellogg, R. E.; Curtis, E. C.

doi:10.1103/revmodphys.32.313

Cited by 106 publications

(31 citation statements)

References 9 publications

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“…Some years ago [ 1,2] the local energy was defined as Eloc = HI)/$, and its variance was used to gauge the goodness of an approximate wave function $. More recently [3] the local orbital energy has been defined as E , = F$,/+i, where F is the effective one-electron operator from a self-consistent field method [for example the Fock operator of Hartree-Fock (HF) theory], and $t is an approximate molecular orbital.…”

Section: Introduction and Theorymentioning

confidence: 99%

The local orbital energy and density functional theory

Pearson¹,

Palke²

1990

Int J of Quantum Chemistry

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From the viewpoint of density functional theory, an expression is derived which improves the average energy of a trial density. Applications to atoms and molecules are made using wave function methods and are based on properties of the variance, which is defined as (2 -(E)')"*, where E is the local orbital energy. Calculated results for both Hartree-Fock and correlated wave functions are quite encouraging.

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Section: Introduction and Theorymentioning

confidence: 99%

The local orbital energy and density functional theory

Pearson¹,

Palke²

1990

Int J of Quantum Chemistry

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“…If we adopt the language of Frost [9] and describe ~( x ) as the local energy, then P ( E ) is the local energy distribution. The properties of P ( E ) are of interest to us.…”

Section: Eq (3) By Using a Statistical Approach Suggested By Metropomentioning

confidence: 99%

Assessing the quality of a wavefunction using quantum monte carlo

McDowell

2009

Int. J. Quantum Chem.

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A procedure is proposed in the framework of the quantum Monte Carlo method whereby the root mean square deviation u of a local energy distribution P ( E ) serves as a measure for assessing quantitatively the quality of a trial ground state wavefunction. In particular it is shown that u goes to zero for the exact wavefunction. A sample computation on the helium atom is presented to provide a working example and to show that P ( E ) can be obtained analytically in some cases.

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“…Namely, an unconditional maximum is required for G(cZ , ck), where (6) w:, Ck) = w c ; , Ck) -w;, Ck)…”

Section: Lower-bound Wave Functionsmentioning

confidence: 99%

Error analysis of variationally optimized upper‐ and lower‐bound wave functions for H

Ley

Thorpe

Rothstein

1974

Int J of Quantum Chemistry

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AbstractsWave functions which are a linear combination of HZ-type elliptical orbitals are optimized to provide either an upper bound or a lower bound to the H$ ground state. For the latter, Temple's formula is used. Three criteria are considered to determine the relative accuracy of these wave functions: ( i ) energy (calculated versus exact eigenvalue) ; (ii) average error; and (iii) local energy. Although the lower-bound optimized wave functions obtained are the most accurate available for H$ from approximate wave functions, they are still inferior to the corresponding upper-bound wave functions by criteria (i) and (ii). I n particular, using criterion (ii), it is shown numerically that the upper-bound functions are "correct to second order," while the lower-bound functions are almost, but not quite, "correct to second order." Despite this, the local energy analysis, criterion (iii), reveals that the lower-bound wave functions can be more accurate than the upper-bound functions in some regions of space, and hence give more accurate values for physical properties sensitive to these regions. Examples considered are the dipole-dipole and Fermi contact interactions. Des fonctions d'ondes

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Local-Energy Method in Electronic Energy Calculations

Cited by 106 publications

References 9 publications

The local orbital energy and density functional theory

The local orbital energy and density functional theory

Assessing the quality of a wavefunction using quantum monte carlo

Error analysis of variationally optimized upper‐ and lower‐bound wave functions for H

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