Fukutome symmetry classification of the Kohn-Sham auxiliary one-matrix and its associated state or ensemble

Weiner, Brian; Trickey, S. B.

doi:10.1002/(sici)1097-461x(1998)69:4<451::aid-qua2>3.0.co;2-u

Cited by 33 publications

(7 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It has induced many improvements and modifications of DFT formalism allowed to introduce the symmetry, to study the excited states, etc. 23, 27, 34–42. However, as was demonstrated by Bersuker 43 and follows from our results (Section 4), in reality the constraint search cannot solve the problems arising in DFT in the case of the degenerate states.…”

Section: Introductionsupporting

confidence: 55%

Problems in DFT with the total spin and degenerate states

Kaplan

2007

Int J of Quantum Chemistry

View full text Add to dashboard Cite

ABSTRACT:The problems arising in the density functional theory when it is applied to the spin-and space-degenerate states are discussed. It is rigorously proved that in the case of orthonormal orbital set, the electron density of an arbitrary Nelectron system does not depend upon the total spin S and for all values of S has the same form as it has for a single-determinantal wave function. From this follows that the conventional Kohn-Sham equations cannot distinguish the states with different total spin values. A critical survey of the existing DFT methods of taking into account the total spin is performed. It is shown that all these methods, including state-and orbitaldependent functional method, modify only the expression for the exchange energy and use the correlation functionals not corresponding to the total spin of the state. It is also proved that the diagonal element of the density matrix is invariant with respect to the symmetry of the state, hence in this respect there is no difference between degenerate and nondegenerate states. On the other hand, for the degenerate states, the Born-Oppenheimer approximation fails, so that makes it impossible to apply the density functional formalism.

show abstract

Section: Introductionsupporting

confidence: 55%

Problems in DFT with the total spin and degenerate states

Kaplan

2007

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…For our purposes it is enough to define K̂ and Θ̂ by their action on a single determinant. Suppose a determinant Φ is specified by a matrix of occupied molecular orbital coefficients Then the determinants K̂ Φ and Θ̂Φ are specified by matrices of occupied molecular orbital coefficients which are respectively Thus, we have The classifications in Table were presented originally in terms of occupied molecular orbital coefficients; here, we list the corresponding constraints on the density matrix components, which were also discussed earlier by Weiner and Trickey . Note that we prefer to define any collinear solution as UHF, reserving GHF for genuinely noncollinear states which are not eigenfunctions of Ŝ n̂ for any direction n̂ .…”

Section: Classification Of Hartree–fock Solutionsmentioning

confidence: 99%

Magnetic Structure of Density Matrices

Henderson

Jiménez-Hoyos

Scuseria

2017

J. Chem. Theory Comput.

View full text Add to dashboard Cite

The spin structure of wave functions is reflected in the magnetic structure of the one-particle density matrix. Indeed, for single determinants we can use either one to determine the other. In this work we discuss how one can simply examine the one-particle density matrix to faithfully determine whether the spin magnetization density vector field is collinear, coplanar, or noncoplanar. For single determinants, this test suffices to distinguish collinear determinants which are eigenfunctions of Ŝ from noncollinear determinants which are not. We also point out the close relationship between noncoplanar magnetism on the one hand and complex conjugation symmetry breaking on the other. Finally, we use these ideas to classify the various ways single determinant wave functions break and respect symmetries of the Hamiltonian in terms of their one-particle density matrix.

show abstract

“…r) не обладает симметрией внешнего потенциала из-за асимметрии электронной плотности. Подробное обсуждение проблемы асимметрии в ТФП и ее последствий можно найти в работах [8][9][10][11][12]. B недавней работе A.K.…”

Section: Introductionunclassified

Параметризованный Эффективный Потенциал Для Возбужденных Состояний И Его Применение К Расчету Дипольных Моментов Перехода

Глушков¹,

Фесенко²

2020

Журнал Технической Физики

View full text Add to dashboard Cite

Метод параметризованного эффективного потенциала, предложенный ранее для основного состояния, развит для возбужденных состояний с симметрией основного. Обсуждены различные приближения для определения обменно-корреляционных потенциалов, Vxc. В частности, на основе требования симметрии Vxc представлен один из рецептов построения нового класса Vxc, который является функционалом внешнего потенциала (взаимодействия электрон-ядро) в отличие от традиционных подходов, где Vxc явно или неявно зависят от электронной плотности. Возможности метода исследованы на примере расчета электронных дипольных моментов перехода молекулы НеН с однодетерминантной волновой функцией. Показано, что предложенный метод расчета дипольных моментов перехода можно рассматривать как компромисс между точностью и вычислительными усилиями. Ключевые слова: параметризованный эффективный потенциал, дипольные моменты перехода, возбужденные состояния.

show abstract

Fukutome symmetry classification of the Kohn-Sham auxiliary one-matrix and its associated state or ensemble

Cited by 33 publications

References 44 publications

Problems in DFT with the total spin and degenerate states

Problems in DFT with the total spin and degenerate states

Magnetic Structure of Density Matrices

Параметризованный Эффективный Потенциал Для Возбужденных Состояний И Его Применение К Расчету Дипольных Моментов Перехода

Contact Info

Product

Resources

About