Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.

OPTIMIZED QUASIPARTICLE DENSITY FUNCTIONAL AND GREEN’S FUNCTIONS METHOD TO COMPUTING BOND ENERGIES OF DIATOMIC MOLECULES

It is presented an advanced approach to computing the energy and spectral parameters of the diatomic molecules, which is based on the hybrid combined density functional theory (DFT) and the Green’s-functions (GF) approach. The Fermi-liquid quasiparticle version of the density functional theory is modified and used. The density of states, which describe the vibrational structure in photoelectron spectra, is defined with the use of combined DFT-GF approach and is well approximated by using only the first order coupling constants in the optimized one-quasiparticle approximation. Using the combined DFT-GF approach to computing the spectroscopic factors of diatomic molecules leads to significant simplification of the calculation procedure and increasing an accuracy of theoretical prediction. As illustration, the results of computing the bond energies in a number of known diatomic molecules are presented and compared with alternative theoretical results, obtained within discrete-variational , muffin-tin orbitals and other methods.

Electron Impact Ionization of Metastable States of Diatomic Molecules

The Binary-Encounter Bethe approach was applied to the estimation of total ionization induced by electron impact in metastable states of diatomic molecules. The cross sections recently obtained for N2 and CO are reviewed and the new results for H2 are presented, discussing their reliability through the comparison with other theoretical methods.

Theory of polarization-averaged core-level molecular-frame photoelectron angular distributions: III. new formula for p- and s-wave interference analogous to Young's double-slit experiment for core-level photoemission from hetero-diatomic molecules

We present a new variation of Young's double-slit formula for polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) of hetero-diatomic molecules, which may be used to extract the bond length. So far, empirical analysis of the PA-MFPADs has often been carried out employing Young's formula in which each of the two atomic centers emits a s-photoelectron wave. The PA-MFPADs, on the other hand, can consist of an interference between the p-wave from the X-ray absorbing atom emitted along the molecular axis and the s-wave scattered by neighboring atom, within the framework of Multiple Scattering theory. The difference of this p-s wave interference from the commonly used s-s wave interference causes a dramatic change in the interference pattern, especially near the angles perpendicular to the molecular axis. This change involves an additional fringe, urging us to caution when using the conventional Young's formula for retrieving the bond length. We have derived a new formula analogous to Young's formula but for the p-s wave interference. The bond lengths retrieved from the PA-MFPADs via the new formula reproduce the original C-O bond lengths used in the reference ab-initio PA-MFPADs within the relative error of 5 %. In the high energy regime, this new formula for p-s wave interference converges to the ordinary Young’s formula for the s-s wave interference. We expect it to be used to retrieve the bond length for time-resolved PA-MFPADs instead of the conventional Young's formula.

Complexes formed in collisions between ultracold alkali-metal diatomic molecules and atoms

We explore the properties of 3-atom complexes of alkali-metal diatomic molecules with alkali-metal atoms, which may be formed in ultracold collisions. We estimate the densities of vibrational states at the energy of atom-diatom collisions, and find values ranging from 3.9 to 350 K$^{-1}$. However, this density does not account for electronic near-degeneracy or electron and nuclear spins. We consider the fine and hyperfine structure expected for such complexes. The Fermi contact interaction between electron and nuclear spins can cause spin exchange between atomic and molecular spins. It can drive inelastic collisions, with resonances of three distinct types, each with a characteristic width and peak height in the inelastic rate coefficient. Some of these resonances are broad enough to overlap and produce a background loss rate that is approximately proportional to the number of outgoing inelastic channels. Spin exchange can increase the density of states from which laser-induced loss may occur.

Quantum alchemy beyond singlets: Bonding in diatomic molecules with hydrogen

Bonding energies are key for the relative stability of molecules in chemical space. Therefore methods employed to search for relevant molecules in chemical space need to capture the bonding behavior for a wide range of molecules, including radicals. In this work, we investigate the ability of quantum alchemy to do so for exploring hypothetical chemical compounds, here diatomic molecules involving hydrogen with various electronic structures. We evaluate equilibrium bond lengths, ionization ener- gies, and electron affinities of these fundamental systems. We compare and contrast how well manual quantum alchemy calculations, i.e. quantum mechanical calculations in which the nuclear charge is altered, and quantum alchemy approximations using a Taylor series expansion can predict these molecular properties. We also investigate the extent of error cancellation of these approaches in terms of ionization energies and electron affinities when using thermodynamic cycles. Our results suggest that the accuracy of Taylor series expansions are greatly improved by error cancellation in thermodynamic cycles, and errors also appear to be generally system-dependent. Taken together, this work provides insights into how quantum alchemy predictions us- ing a Taylor series expansion may be applied to future studies of non-singlet systems as well as which challenges remain open for these cases.

Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules

In this paper, we derive the `-states energy spectrum of the q-deformed hyperbolic Barrier Potential. Within the Feynman path integral formalism, we propose an appropriate approximation of the centrifugal term. Then, using Euler angles and the isomorphism between S3and SU(1, 1), we convert the radial path integral into a maniable one. The obtained eigenvalues are in very good agreement with the numerical results. In addition, we applied our results to some diatomic molecules and obtained accurate results compared to the experimental (RKR) values.