Natural orbitals and their occupation numbers in a non-interacting two-anyon system in the magnetic gauge

We investigate the properties of natural orbitals and their occupation numbers of the ground state of two non-interacting anyons characterised by the fractional exchange parameter $\alpha$ and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modelled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law $n^{-(4+2\alpha)}$, where $n$ is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wavefunction. We explain that the same results apply to the fermion magnetic gauge.Comment: 10 pages, 3 figure

Ab Initio Electronic Structure Calculations of Molecular Similarity: A Case Study of 4-Aminobutyric Acid and Its Agonists

A new quantum mechanical measure of molecular similarity, based on the overlap between the first-order density matrices is applied in studies of the structure-activity relationships in the GABAA agonists: /rans-4-amino- crotonic acid, 5-aminomethylisoxazul-3-ol, and 3-aminomethylisoxazol-5-ol. The geometries of these molecules are optimized at the HF/6-31G** level and their electronic structures compared to that of 4-aminobutyric acid. Factors affecting the GABAergic activity of these substances are discussed. The present study demonstrates that ab initio electronic structure calculations of molecular similarity are feasible for medium-sized molecules of biological interest

Contactium: A strongly correlated model system

At the limit of an infinite confinement strength $\omega$, the ground state of a system that comprises two fermions or bosons in a harmonic confinement interacting through the Fermi--Huang pseudopotential remains strongly correlated. A detailed analysis of the one-particle description of this ``contactium'' reveals several peculiarities that are not encountered in conventional model systems (such as the two-electron harmonium atom, ballium, and spherium) involving Coulombic interparticle interactions. First of all, none of the natural orbitals (NOs) $\{ \psi_\mathfrak{n}(\omega;\vec r) \}$ of the contactium is unoccupied, which implies nonzero collective occupancies for all the angular momenta. Second, the NOs and their nonascendingly ordered occupation numbers $\{ \nu_\mathfrak{n} \}$ turn out to be related to the eigenfunctions and eigenvalues of a zero-energy Schr\"odinger equation with an attractive Gaussian potential. This observation enables the derivation of their properties such as the $\mathfrak{n}^{-4/3}$ asymptotic decay of $\nu_\mathfrak{n}$ at the $\mathfrak{n} \to \infty$ limit (which differs from that of $\mathfrak{n}^{-8/3}$ in the Coulombic systems), the independence of the confinement energy {v_\mathfrak{n} = \langle \psi_\mathfrak{n}(\omega;\vec r) | \frac{1}{2} % \omega^2r^2 | \psi_\mathfrak{n}(\omega;\vec r) \rangle} of $\mathfrak{n}$, and the $\mathfrak{n}^{-2/3}$ asymptotic decay of the respective contribution $\nu_\mathfrak{n}t_\mathfrak{n}$ to the kinetic energy. Upon suitable scaling, the weakly occupied NOs of the contactium turn out to be virtually identical with those of the two-electron harmonium atom at the ${\omega \to \infty}$ limit, despite the entirely different interparticle interactions in these systems.Comment: 9 pages, 5 figures, 1 tabl

Electronic Structure Calculations on Endohedral Complexes of Fullerenes: Reminiscences and Prospects

The history of electronic structure calculations on the endohedral complexes of fullerenes is reviewed. First, the long road to the isolation of new allotropes of carbon that commenced with the seminal organic syntheses involving simple inorganic substrates is discussed. Next, the focus is switched to author’s involvement with fullerene research that has led to the in silico discovery of endohedral complexes. The predictions of these pioneering theoretical studies are juxtaposed against the data afforded by subsequent experimental developments. The successes and failures of the old and modern quantum-chemical calculations on endohedral complexes are summarized and their remaining deficiencies requiring further attention are identified

Benchmark full configuration interaction calculations on harmonium atoms

Harmonium atoms, i.e. assemblies of electrons trapped in a harmonic potential, are encountered in diverse branches of chemistry and physics. In physics, they emerge in description of quantum dots, particles in dusty plasmas, and ions in cold traps, whereas in quantum chemistry they are often employed in calibration of density and density matrix functionals. Despite the importance of harmonium atoms, their properties have been systematically studied only in the two-electron case. When used in conjunction with appropriate extrapolation schemes, full configuration interaction (FCI) calculations employing systematic sequences of spherical Gaussian primitives with even-tempered exponents shared by functions of different angular momenta are capable of affording the ground-state energies of the two-electron harmonium atoms with a few-micro-Hartree accuracy that is sufficient for calibration and benchmarking of approximate electron correlation theories of quantum chemistry. The present approach, which is subsequently employed in computations of electronic properties of harmonium atoms with three electrons, calls for a series of between 15 and 17 FCI runs involving basis sets with between four and eight Gaussian primitives of the sp, spd, spdf, and spdfg type. Details of these calculations, which are limited by linear dependencies among basis functions that become significant for small values of the force constant, are presente

Electronic Structure Studies of 1,2-Didehydrogenation of Arenes and Rearrangement of Arynes to Annelated Cyclopentadienylidenecarbenes

CCSD(T)/6-311G electronic structure calculations confirm the experimentally postulated existence of cyclopentadienylidenecarbene (CPDC) and verify the reliability of the BLYP/6-311G predictions for thermochemistry and kinetics of the 1,2-didehydrogenation of arenes and the ring contraction of the resulting arynes. The former process is found to possess low site specificity, its energetics being influenced mostly by steric overcrowding of hydrogens. On the other hand, the energetics and barriers of rearrangements of higher arynes to annelated CPDCs are determined by the nature of bonding in the reaction products. Three distinct types of isomerizations are readily recognizable. The type I rearrangements produce relatively stable, planar CPDCs with aromatic conjugation unaffected by cyclopentadienylidene moiety. The type II rearrangements yield planar CPDCs with partially fixed C-C bonds that are barely protected from the respective reverse reactions by vanishingly low energy barrie..