FROM DMFT TO DFT · From density matrix functionals to exchange-correlation functionals in density functional theory
6РП — Действия „Мария Кюри“
- Период
- 2006-08-01 → 2007-07-31
- Финансиране от ЕС
- 76 328 €
- Участници
- 1
- Схема
- EIF
Линиите свързват координатора с партньорите. За проекти отпреди 2014 г. CORDIS не винаги дава точни координати. Тези точки са на ниво град или държава.
Накратко на български
Квантовият химичен анализ изследва нови математически методи за описание на електроните в молекулите, например чрез използване на матрици вместо сложни уравнения. Това помага за по-точното изчисляване на енергията и динамичното поведение на химичните системи при по-ниски разходи.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - FROM DMFT TO DFT (From density matrix functionals to exchange-correlation functionals in density functional theory)
The main goal of all quantum chemistry methods is to replace the full many-electron Schroedinger equation, which is too complex to solve for more than a few electrons, with a simpler, however approximate, problem. It turns out that, in principle, the information contained in an N-electron wave function is also obtainable using a so-called one-electron reduced density matrix, 1-matrix, or even its diagonal part, i.e. electron density. A method based on the functionals of the latter, namely the Density functional theory (DFT), plays currently a crucial role in computational chemistry, since it combines relatively good accuracy with modest computational costs. Density matrix functional theory (DMFT) that exploits 1-matrix as its main variable appears as an attractive alternative to DFT, since the kinetic energy term is explicitly known and the correlation effects are taken into account directly through fractional occupancies of the orbitals. In principle, both DFT and DMFT should be able to provide not only information about the ground state energy, through the energy functional, but also description of the excited states of the system. The work performed during the fellowship concerned fundamental research which aimed at the development of methods exploiting functionals of one-electron density matrix. In particular, a time-dependent formulation of DMFT, the so-called Time-dependent density matrix functional theory (TD-DMFT) was proposed, enabling to obtain dynamic response properties and excitation energies from 1-matrix functionals. More precisely, we derived the equation of motion for 1-matrix in a functional form and showed how to approximate the resulting linear response equations to obtain simple scheme yielding dynamic properties. The new methods were implemented and numerically analysed. Our achievement was an important step forward in rendering the DMFT a fully-fledged quantum chemistry method, thus providing both static and dynamic properties of electronic systems.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The failures of the current Kohn-Sham density functional theory (KS DFT) implementations severely limit their usefulness in modelling of chemical phenomena. Since they are inherent to functionals that express the KS exchange-correlation energy as an integral of a simple function of the electron density and its derivatives, a careful investigation of various alternatives to the conventional KS formalism that retain its low computational cost while improving the description of and unusual and species is highly warranted. In this proposal, a research program aiming at the development of a novel orbital-dependent exchange-correlation electron density functional (ODXC functional) that will not suffer from the deficiencies of the current local and semi local density functionals employed in the KS DFT schemes is outlined. New ODXC functional, which will depend on both occupied and unoccupied KS orbitals, will be specially suited to properly describe dissociation of the molecules, and to reproduce dispers ion interactions. It will be based on the one-electron reduced density matrix (one-matrix) functional approach, namely, the prospective ODXC functional will inherit its form from the one-matrix counterpart. Additionally, new computationally efficient method for approximate solving of the optimised effective potential (OEP) equation that yields the corresponding local exchange-correlation potential will be developed. Special attention will be paid to assuring a correct long-range behaviour of the latter. The novel ODXC functional and the OEP scheme will be efficiently computer-implemented and a number of tests on simple atoms, molecules, and noble gas dimers will be conducted.
Оригинален текст от CORDIS (на английски).
Участници
- VRIJE UNIVERSITEIT · AMSTERDAMКоординаторНиво градНидерландия
Връзки
Данни: CORDIS, © Европейски съюз