Search

The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of motional entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.

Atomic charge and its distribution across molecules provide important insight into chemical behavior. Though there are many studies on various routes for the determination of atomic charge, there are few studies that examine the broader impact of basis set and quantum method used over many types of population analysis methods across the periodic table. Largely, such a study of population analysis has focused on main-group species. In this work, atomic charges were calculated using several population analysis methods including orbital-based methods (Mulliken, Löwdin, and Natural Population Analysis), volume-based methods (Atoms-in-Molecules (AIM) and Hirshfeld), and potential derived charges (CHELP, CHELPG, and Merz-Kollman). The impact of basis set and quantum mechanical method choices upon population analysis has been considered. The basis sets utilized include Pople (6-21G**, 6-31G**, 6-311G**) and Dunning (cc-pVnZ, aug-cc-pVnZ; n = D, T, Q, 5) basis sets for main group molecules. For the transition metal and heavy element species examined, relativistic forms of the correlation consistent basis sets were used. This is the first time the cc-pVnZ-DK3 and cc-pwCVnZ-DK3 basis sets have been examined with respect to their behavior across all levels of basis sets for atomic charges for an actinide. The quantum methods chosen include two density functional (PBE0 and B3LYP), Hartree-Fock, and second-order Møller-Plesset perturbation theory (MP2) approaches.

The correlation consistent Composite Approach, ccCA [Deyonker, N. J.; Cundari, T. R.; Wilson, A. K.J. Chem. Phys.2006, 124, 114104] has been demonstrated to predict accurate thermochemical properties of chemical species that can be described by a single configurational reference state, and at reduced computational cost, as compared with ab initio methods such as CCSD(T) used in combination with large basis sets. We have developed three variants of a multireference equivalent of this successful theoretical model. The method, called the multireference correlation consistent composite approach (MR-ccCA), is designed to predict the thermochemical properties of reactive intermediates, excited state species, and transition states to within chemical accuracy (e.g., 1 kcal/mol for enthalpies of formation) of reliable experimental values. In this study, we have demonstrated the utility of MR-ccCA: (1) in the determination of the adiabatic singlet−triplet energy separations and enthalpies of formation for the ground states for a set of diradicals and unsaturated compounds, and (2) in the prediction of energetic barriers to internal rotation, in ethylene and its heavier congener, disilene. Additionally, we have utilized MR-ccCA to predict the enthalpies of formation of the low-lying excited states of all the species considered. MR-ccCA is shown to give quantitative results without reliance upon empirically derived parameters, making it suitable for application to study novel chemical systems with significant nondynamical correlation effects. [ABSTRACT FROM AUTHOR]