Born–Oppenheimer approximation

About: Born–Oppenheimer approximation is a research topic. Over the lifetime, 1268 publications have been published within this topic receiving 37714 citations. The topic is also known as: Adiabatic approximation & Born–Oppenheimer approximation.

Multimode molecular dynamics beyond the Born-Oppenheimer approximation

Abstract: Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

Breakdown of the adiabatic Born-Oppenheimer approximation in graphene.

Abstract: The adiabatic Born-Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics. ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur. The use of ABO to describe lattice motion in metals is, therefore, questionable. In spite of this, ABO has proved effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state, is a zero-bandgap semiconductor that becomes a metal if the Fermi energy is tuned applying a gate voltage, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO.

Born-Oppenheimer breakdown in graphene

Abstract: The Born-Oppenheimer approximation (BO) has proven effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Graphene, recently discovered in the free state, is a zero band-gap semiconductor, which becomes a metal if the Fermi energy is tuned applying a gate-voltage Vg. Graphene electrons near the Fermi energy have twodimensional massless dispersions, described by Dirac cones. Here we show that a change in Vg induces a stiffening of the Raman G peak (i.e. the zone-center E2g optical phonon), which cannot be described within BO. Indeed, the E2g vibrations cause rigid oscillations of the Dirac-cones in the reciprocal space. If the electrons followed adiabatically the Dirac-cone oscillations, no change in the phonon frequency would be observed. Instead, since the electron-momentum relaxation near the Fermi level is much slower than the phonon motion, the electrons do not follow the Dirac-cone displacements. This invalidates BO and results in the observed phonon stiffening. This spectacular failure of BO is quite significant since BO has been the fundamental paradigm to determine crystal vibrations from the early days of quantum mechanics.

On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei

Abstract: We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear‐motion Schrodinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear‐motion wave functions in the presence of conical intersections and the treatment of nuclear‐interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear‐motion wave functions, and this is discussed in detail.

Diabatic and adiabatic representations for atomic collision problems.

Abstract: The equations of the general Born-Oppenheimer separation into electronic and heavy-particle coordinates are re-examined, and the coupled equations that result for the heavy-particle motion are expressed in a particularly simple form. This is accomplished by introducing a generalized matrix operator for the effective momentum associated with the heavy particles; the matrix portion of this operator represents a coupling of the nuclear momentum with the electronic motion. The commutator between the momentum and potential matrices is a force matrix, which provides an alternative means of evaluating the momentum matrix. The momentum coupling has both radial and angular parts; the angular momentum coupling agrees with Thorson's expression. In the usual adiabatic molecular representation, the potential energy matrix is diagonalized, and all the coupling is thrown into the radial and angular momentum matrices. For collision problems it is often more important to diagonalize the radial momentum matrix, putting the radial off-diagonal coupling into the potential matrix; this generates a family of diabatic representations, the most important of which dissociates to unique separated atom states. This standard diabatic representations has the properties called for by Lichten, is uniquely defined even with the inclusion of configuration interaction, and leads immediately to the Landau-Zener-Stueckelberg limiting case under appropriate conditions.