Terms Of Occupation Numbers Research Articles

Analytic second-order energy derivatives in natural orbital functional theory

The analytic energy gradients in the atomic orbital representation have recently been published (J. Chem. Phys. 146, 014102, 2017) within the framework of the natural orbital functional theory (NOFT). We provide here an alternative expression for them in terms of natural orbitals, and use it to derive the analytic second-order energy derivatives with respect to nuclear displacements in the NOFT. The computational burden is shifted to the calculation of perturbed natural orbitals and occupancies, since a set of linear coupled-perturbed equations obtained from the variational Euler equations must be solved to attain the analytic Hessian at the perturbed geometry. The linear response of both natural orbitals and occupation numbers to nuclear geometry displacements need only specify the reconstruction of the second-order reduced density matrix in terms of occupation numbers.

Nonequilibrium steady states of ideal bosonic and fermionic quantum gases.

We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.

A quasi-classical mapping approach to vibrationally coupled electron transport in molecular junctions

We develop a classical mapping approach suitable to describe vibrationally coupled charge transport in molecular junctions based on the Cartesian mapping for many-electron systems [B. Li and W. H. Miller, J. Chem. Phys. 137, 154107 (2012)]. To properly describe vibrational quantum effects in the transport characteristics, we introduce a simple transformation rewriting the Hamiltonian in terms of occupation numbers and use a binning function to facilitate quantization. The approach provides accurate results for the nonequilibrium Holstein model for a range of bias voltages, vibrational frequencies, and temperatures. It also captures the hallmarks of vibrational quantum effects apparent in step-like structure in the current-voltage characteristics at low temperatures as well as the phenomenon of Franck-Condon blockade.

A nucleon in the nuclear medium: A tale of all energies

Although the conventional shell model approach has been successful in describing low-energy nuclear phenomena based on a realistic interaction between nucleons, several important shortcomings have become apparent as well. These shortcomings provide the motivation to employ the self-consistent Green's function (SCGF) method which can overcome these problems. Additional inspiration for the use of this method is provided by recent exclusive electron scattering results which involve the ejection of a proton from the nucleus. Such experiments have established quantitative information on the distribution of single-particle (sp) removal strength which is theoretically described in terms of the sp Green's function. The distribution of the experimental sp strength displays properties of the nucleus that can be brought into one-to-one correspondence with Fermi Liquid properties of infinite homogeneous systems. Theoretical calculations of the sp Green's function in finite nuclei are discussed which establish these “Fermi Liquid” properties by including the coupling of sp motion to more complicated states in an energy domain of about 100 MeV around the Fermi energy. Although sufficient to explain the shape of the experimental strength distributions, these calculations need to be supplemented by the inclusion of the coupling to even higher energy states for quantitative agreement. Such calculations are reported for nuclear matter. These results clearly establish the importance of the coupling between low-lying sp states and very high-lying two-particle-one-hole states. This coupling is provided within the constraints of nonrelativistic many-particle theory by the use of a strongly repulsive realistic interaction between nucleons. Including both experimental and theoretical results, it is possible to pinpoint the properties of the 3 s 1 2 Pb. In addition, it is possible to compare the strength of nuclear correlations in terms of occupation numbers, with those of other Fermi systems with weaker (atoms) or stronger (liquid 3He) correlations.

The electronic structure of a liquid of interacting hydrogenic atoms: A prototype for expanded liquid metals

The electronic structure of a metal heated above its critical temperature (an ‘‘expanded liquid metal’’) shows dramatic changes as the density is increased. There is some experimental evidence that as one proceeds from insulating to metallic behavior the substance can even go through two separate phase transitions: from an ordinary insulator to a so-called excitonic insulator, and then from an excitonic insulator to a metal. In an effort to study how the metallic phase is approached, we have used discretized-path-integral methods to look at the statistical mechanics and the electronic structure of a model liquid. In the gas phase, the atoms in the model have a single valence electron constrained to occupy one of the s or p orbitals of the valence shell, but at higher densities, the orbitals hybridize, leading to instantaneous dipole–dipole interaction. We show that formulating this electronic structure in terms of occupation numbers allows us to monitor the hybridization evolution via an imaginary-time correlation function—which we calculate from an analytical solution to the mean-spherical approximation for the model. The numerical results strongly suggest that the model has a sudden hybridization transition, suggesting, in turn, that it might be profitable to think of the excitonic insulator transition in this language.

The electronic structure of a series of tin complexes studied by XPS and Mössbauer spectroscopy

The isomer shift and 3d5/2 core electron binding energy shift have been measured for a series of complexes. By using a simple model for the interpretation of these shifts in terms of occupation numbers of valence orbitals an estimate of the electronic structure is obtained.