Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians

We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state conical intersections. The general situation of an arbitrary number of states and arbitrary number of nuclear degrees of freedom (modes) is considered. The macrosystem is decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the vast number of remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment is constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. By considering the system's Hamiltonian along with a few members of the hierarchy, it is shown mathematically by a moment analysis that the quantum dynamics of the entire macrosystem can be numerically exactly computed on a given time-scale. The time scale wanted defines the number of effective Hamiltonians to be included. The contribution of the environment to the quantum dynamics of the macrosystem translates into a sequential coupling of effective modes. The wavefunction of the macrosystem is known in the full space of modes, allowing for the evaluation of observables such as the time-dependent individual excitation along modes of interest, as well a spectra and electronic-population dynamics

Ab initio calculations with a nonspherical Gaussian basis set: Excited states of the hydrogen molecule

A basis set of generalized nonspherical Gaussian functions (GGTOs) is presented and discussed. As a first example we report on Born-Oppenheimer energies of the hydrogen molecule. Although accurate results have been obtained, we conclude that H_2 is too 'simple' to allow for a substantial gain by using nonspherical functions. We rather expect that these functions may be particularly useful in calculations on large systems. A single basis set of GGTOs was used to simultaneously calculate the potential energy curves of several states within each subspace of {1,3}\Sigma_{g,u} symmetry. We hereby considerd the entire region of internuclear distances 0.8 < R < 1000 a.u. In particular the results for the fourth up to sixth electronic states show a high accuracy compared to calculations which invoke explicitely correlated functions, e.g. the relative accuracy is at least of the order of magnitude of 10^{-5}a.u. Energies for the 4 ^1\Sigma_u^+ and 4-6 ^3\Sigma_u^+ were improved and accurate data for the 6 ^3\Sigma_g^+, 5 ^1\Sigma_u^+, and 6 ^1\Sigma_u^+ state are, to the best of the authors knowledge, presented for the first time. Energy data for the seventh up to the nineth electronic state within each subspace were obtained with an estimated error of the order of magnitude of 10^{-4}a.u. The 7 ^1\Sigma_g^+ and the 6 ^1\Sigma_u^+ state were found to exhibit a very broad deep outer well at large internuclear distances.Comment: 4 figures, subm.to J.Chem.Phy

Electron-correlation driven capture and release in double quantum dots

We recently predicted that the interatomic Coulombic electron capture (ICEC) process, a long-range electron correlation driven capture process, is achievable in gated double quantum dots (DQDs). In ICEC an incoming electron is captured by one QD and the excess energy is used to remove an electron from the neighboring QD. In this work we present systematic full three-dimensional electron dynamics calculations in quasi-one dimensional model potentials that allow for a detailed understanding of the connection between the DQD geometry and the reaction probability for the ICEC process. We derive an effective one-dimensional approach and show that its results compare very well with those obtained using the full three-dimensional calculations. This approach substantially reduces the computation times. The investigation of the electronic structure for various DQD geometries for which the ICEC process can take place clarify the origin of its remarkably high probability in the presence of two-electron resonances

Controlled energy-selected electron capture and release in double quantum dots

Highly accurate quantum electron dynamics calculations demonstrate that energy can be efficiently transferred between quantum dots. Specifically, in a double quantum dot an incoming electron is captured by one dot and the excess energy is transferred to the neighboring dot and used to remove an electron from this dot. This process is due to long-range electron correlation and shown to be operative at rather large distances between the dots. The efficiency of the process is greatly enhanced by preparing the double quantum dot such that the incoming electron is initially captured by a two-electron resonance state of the system. In contrast to atoms and molecules in nature, double quantum dots can be manipulated to achieve this enhancement. This mechanism leads to a surprisingly narrow distribution of the energy of the electron removed in the process which is explained by resonance theory. We argue that the process could be exploited in practice.Comment: Lette

Bound states of negatively charged ions induced by a magnetic field

We analyse the bound states of negatively charged ions which were predicted to exist because of the presence of a magnetic field by Avron et al. We confirm that the number of such states is infinite in the approximation of an infinitely heavy nucleus and provide insight into the underlying physical picture by means of a combined adiabatic and perturbation theoretical approach. We also calculate the corresponding binding energies which are qualitatively different for the states with vanishing and non-vanishing angular momentum. An outlook on the case of including center of mass effects is presented.Comment: 14 pages, 2 figure