The present work is an attempt to treat hydrogen storage in metals with the aid of field theoretical methods. Starting with the many-body Schrödinger equation, an adiabatic decomposition yields an electronic system, a protonic system and a host lattice system. We define a storage energy consisting of a lattice contribution and an electronic part. The latter one will be evaluated by The New Tamm-Dancoff (NTD) procedure. This formalism is a method to compute differences of eigenvalues in quantum mechanical problems. As an example we derive a one-particle equation describing a single hydrogen atom in a metal crystal.
In the present work, the problem “hydrogen storage in metals” is treated with the aid of the so-called New Tamm-Dancoff (NTD) procedure. We employ this method in lowest approximation for the evaluation of the electronic energy difference eigenvalue between a metal crystal with and without hydrogen centre. As an example we use Magnesium with hexagonal structure. For this system we calculate the difference eigenvalue with dependence on the displacement of the nearest neighbours and next nearest neighbours of the hydrogen centre, respectively. Finally we calculate the radial electron density distribution in the environment of the proton.
The Hohenberg-Kohn theorem proves the existence of a universal energy functional. But still its explicit structure is unknown. Unknown parts of the energy functional, namely the kinetic and the exchange interaction energy are discussed. Based on a functional formulation of the virial theorem "functional equations" for these unknown quantities are deduced establishing a relation between the functional and its derivative. Though there is no general formalism for solving such equations they may be used to determine the structure of the unknown functionals. Starting with simple formal assumptions for the exchange energy, some well-known approximations are derived for this functional thus proving the value of this new technique.Das Hohenberg-Kohn-Theorem weist die Existenz eines universellen Energiefunktionals nach. Allerdings ist seine explizite Struktur nach wie vor unbekannt. Die unbekannten Teile des Energiefunktionals werden diskutiert. Dies sind, das Funktional der kinetischen und der Austausch-Energie. Aufbauend auf einer funktionalen Formulierung des Virial-Theorems werden "Funktionalgleichungen" fur diese unbekannten Energieanteile abgeleitet, welche die Funktionale und ihre Funktionalableitungen in Beziehung zueinander setzen. Obwohl kein allgemeiner Losungsformalismus fur derartige Gleichungen bekannt ist, lassen sie sich zur Bestimmung der unbekannten Funktionale verwenden. Ausgehend von einfachen, formalen Annahmen hinsichtlich der Austausch-Energie werden wohlbekannte Naherungen fur dieses Funktional abgeleitet. Dies zeigt den Nutzen dieser neuen Technik auf.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.