Composite Wave Variational Method for Solution of the Energy-Band Problem in Solids

Schlosser, Herbert; Marcus, Paul

doi:10.1103/physrev.131.2529

Cited by 155 publications

(46 citation statements)

References 26 publications

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“…This was proposed by a number of authors 10,11,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39 Among practitioners of APW methods, the prevailing opinion is that discontinuous boundary conditions are legitimate. For example Shaughnessy and coll.…”

Section: Discontinuous Functionsmentioning

confidence: 99%

Boundary conditions for augmented plane-wave methods

Brouder

2005

Phys. Rev. B

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The augmented plane wave method uses the Rayleigh-Ritz principle for basis functions that are continuous but with discontinuous derivatives and the kinetic energy is written as a pair of gradients rather than as a Laplacian. It is shown here that this procedure is fully justified from the mathematical point of view. The domain of the self-adjoint Hamiltonian, which does not contain functions with discontinuous derivatives, is extended to its form domain, which contains them, and this modifies the form of the kinetic energy. Moreover, it is argued that discontinuous basis functions should be avoided.

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Section: Discontinuous Functionsmentioning

confidence: 99%

Boundary conditions for augmented plane-wave methods

Brouder

2005

Phys. Rev. B

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“…Recently Weare and Parr [3] have discussed a functional following Schlosser and Marcus [4] which in effect permits the use of discontinuous functions. The essential feature of this functional is that the kinetic energy term is evaluated excluding the surface of discontinuity and that an additional surface integral over the surface is introduced to compensate.…”

Section: Introductionmentioning

confidence: 99%

A minimum principle for atomic systems allowing the use of discontinuous wave functions

Hall

Hyslop

Rees

1969

Int J of Quantum Chemistry

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AbstractsIn this paper a variational principle proposed by Hall [I] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. I t is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh-Ritz method.The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various "cut off" wave functions. It is usually possible to define an optimum "cut off" distance which minimizes the upper bound.On dtmontre qu'un principe variationnel propost par Hall [l] est un principe de minimum pour les systtmes coulombiens. Pour ce principe-ci on peut admettre une classe plus grande de fonctions d'onde d'essai que celle employte dans la mtthode variationelle conventionelle, y inclues des fonctions d'onde avec des discontinuitks. On dtmontre aussi que les bornes suptrieures donntes par cette mtthode sont toujours au moins aussi bonnes que celles donntes par la mtthode de Rayleigh-Ritz.La thtorie a t t t appliquke i l'atome d'hydrogtne et des bornes supkrieures de l'tnergie ont Ctt calcultes pour quelques fonctions d'onde avec "cut off". I1 est possible, en gtnkral, de dtfinir une distance de "cut off" optimale, qui minimise la borne supkrieure.Es wird gezeigt, dass ein von Hall [I] vorgeschlagenes Variationsprinzip ein Minimumprinzip fur coulombische Systeme ist. Mit diesem Prinzip ist es moglich, eine grossere Klasse von Vergleichsfunktionen als in dem konventionellen Variationsverfahren zuzulassen. Diese grossere Klasse enthalt Funktionen die nicht uberall stetig sind. Es wurde auch gezeigt, dass die obere Grenzen die mit dieser Methode erhalten sind, immer mindestens so gut sind wie die, die mit der Rayleigh-Ritzschen Methode berechnet sind.Die hlethode wurde auf das Wasserstoffatom benutzt und obere Grenzen fur die Energie wurden fur verschiedene Funktionen mit "cut off" berechnet. Es ist im allgemeinen moglich einen optimalen "cut off" Apstand zu definieren, der die obere Grenze minimisiert.

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“…(25) and (27), t h e 1 i n e a r response theory i n which t h e induced m a g n e t i z a t i o n i s r e l a t e d w i t h B) by where t h e i n t e g r a t i o n s a r e t o be performed over t h e whole c r y s t a l .…”

Section: A S T R a I G H T F O R W A R D A P P L I C A T I O N O F T mentioning

confidence: 99%

“…(27) , we c o n s i d e r e d t h a t , a s was i n Eq. ( 6 ) , $($ i a p a r a l l e l t o t h e d i r e c t i o n o f g(3 w h i c h i s + p e r p e n d i c u l a r t o Q.…”

Section: A S T R a I G H T F O R W A R D A P P L I C A T I O N O F T mentioning

confidence: 99%

Calculation of induced magnetic form factor of chromium

Oh¹

1975

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Composite Wave Variational Method for Solution of the Energy-Band Problem in Solids

Cited by 155 publications

References 26 publications

Boundary conditions for augmented plane-wave methods

Boundary conditions for augmented plane-wave methods

A minimum principle for atomic systems allowing the use of discontinuous wave functions

Calculation of induced magnetic form factor of chromium

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