Narrow Results

We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.

The polycyclic aromatic hydrocarbons (PAHs) are chemical compounds of obvious technical and medical interest. In the present work, we analyze the optical and reactive properties of several small (6–50 Carbon atoms) and large (100–5000 Carbon atoms) irregular PAHs. These properties have been calculated by using the (Frozen) spin molecular orbital (SMO) Hartree-Fock (HF) approach, referred to as FHF, because of its high computational efficiency. There is a reasonable agreement of our results with those previously obtained by other authors. The FHF approach is (about 1000 times) faster than the conventional semi-empirical methods, and only requires the chemical formula of the PAH as input.

First-principles calculations based on Hartree–Fock (HF) and density functional theory (DFT) levels of approximation have been carried out in order to study the stability of graphene clusters as a function of number of carbon atoms (N). The variation of calculated binding energy per carbon atom with corresponding number of carbon atoms (N) in graphene cluster almost saturates after the cluster size consisting of 96 carbon atoms, with binding energy per carbon atom 8.24 eV/atom. Adsorption of halogen atoms, (F, Cl and Br), on hydrogen passivated graphene (H-graphene) was also studied systematically through first-principles DFT calculations by taking five different H-graphene clusters. The calculations showed that the most stable adsorption site for halogen adatoms on H-graphene being T site with binding energy 2.41 eV (F), 1.48 eV (Cl) and 1.19 eV (Br) on the H-graphene cluster consisting 96 carbon atoms. Moreover, on increasing the size of H-graphene cluster, the binding energy of halogen adatoms found to be increasing. The distances of adatom from the nearest carbon atom of H-graphene sheet were 1.47 Å (F), 2.71 Å (Cl) and 3.01 Å (Br), however, the adatom heights from the H-graphene basal plane were 2.22 Å (F), 2.90 Å (Cl), and 3.19 Å (Br). The bonding of halogen adatoms on H-graphene were through the charge transfer; 0.30 |e| (F), 0.37 |e| (Cl) and 0.19 |e| (Br), from H-graphene to adatoms and includes the negligible local distortion in the underlying planner H-graphene. Charge redistribution upon adsorption induces significant dipole moments 2.16 D (F), 4.81 D (Cl) and 3.08 D (Br) on H-graphene. The calculated HOMO–LUMO energy gap of adatom-H-graphene and H-graphene does not differ significantly up to the cluster size N = 30, however, beyond N = 30 adsorption of halogen adatoms significantly opens the HOMO–LUMO energy gap on H-graphene and the opening of HOMO–LUMO energy gap also saturates from N = 96. Correlation of computed HOMO–LUMO energy gap and corresponding binding energy of adatom-H-graphene systems have been also studied.

In [Setting and analysis of the multi-configuration time-dependent Hartree–Fock equations, Arch. Ration. Mech. Anal.198 (2010) 273–330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree–Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N_cr.

Using HF + BCS method we study light nuclei with nuclear charge in the range 2 ≤ Z ≤ 8 and lying near the neutron drip line. The HF method uses effective Skyrme forces and allows for axial deformations. We find that the neutron drip line forms stability peninsulas at ¹⁸He and ⁴⁰C. These isotopes are found to be stable against one neutron emission and possess the highest known neutron to proton ratio in stable nuclei.

Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes.

A simple expression for the distance between two electrons, (δr₁₂)_ab, has been defined from one-electron expectation values. This value is calculated for triplet and singlet systems of two electrons, and closed-shell molecules of up to 58 electrons. When (δr₁₂)_ab is compared to the corresponding coulomb integral, J_ab, an interesting relationship is observed. The relationship is followed extremely closely by all pairs of electrons, except for some deviations involving delocalized core–core electron pairs.

Tryptophan methyl ester (Trp-ME) degrades with singlet oxygen and produce compounds which are photosensitizers and may react to form other derivatives such as N’-Formylkynurénine (NFK) and kynurenine, which are the final products of this oxidation. In order to study and optimize the molecular structure of NFK and determine its different thermodynamic properties, we performed a conformational analysis by DFT/B3LYP method with 3-21G basis set. Six most stable conformations were observed through the analysis of the potential energy surfaces, obtained by a relaxed scan of the dihedral angles.

The most stable form of NFK has been registered for D$1=-148.96^{\circ }$, D$2=-116.89^{\circ }$, D$3=-39.99^{\circ }$, D$4=-65.50^{\circ }$, D$5=163.75^{\circ }$, and D$6=30.22^{\circ }$. The study was conducted by HF and DFT/B3LYP with 6-31G(d,p), 6-3$1+\mathrm{\text{G}}$(d,p) and 6-31$1+\mathrm{\text{G}}$(d,p) basis sets, on the optimized geometry of the most stable conformation and its thermodynamic and orbital properties. Two absorption bands were recorded at $\lambda =250$nm and at $\lambda =340$nm and were also determined by TD-DFT method. They showed good agreement with the UV experimental spectrum which confirms that it is a powerful tool to determine the dynamic and static properties of molecules. The surface of the electrostatic potential (ESP) of the NFK was also analyzed.

Endofullerenes M@C₆₀ with M = Li, Na, Ag are considered theoretically at the ab initio level. The electronic structure is calculated to reveal effects of the nature of metal atoms inside C₆₀ upon features of the minimum energy endostructures. The Hartree–Fock and DFT methods with all-electronic (Li and Na) and effective core potential (Ag) basis sets were used admitting an arbitrary symmetry distortion (down to the C₁ point group). All structures display the off-center position of the endoatoms. The charge transfer between metal atoms and the carbon cage is also strongly dependent on the nature of the metals. Ionization potentials and atomic radii are proposed as the basic factors providing properties of the endofullerenes.

We first present a new and more realistic Skyrme type interaction, named KDE0, obtained by fitting Hartree-Fock results to an extensive experimental data under some constraints and using the simulating annealing method. We then discuss the issue of deducing the nuclear matter incompressibility coefficient from data on the energies of the breathing mode within relativistic and non-relativistic models.

New sd-shell Hamiltonians, USDA and USDB, are discussed. The application to sd-shell energies is reviewed and results are shown for M1 transition matrix elements and magnetic moment data. The predictions for the properties of the oxygen isotopes near the drip-line nucleus ²⁴O are shown and compared with recent data. The empirical values for the proton and neutron single-particle energies in ²⁴O are compared with Skyrme EDF calculations. The systematic properties of the single-particle energies from Skyrme EDF for ²⁴O, ³⁴Si and ⁴²Si are shown and discussed.

For more than three decades, the inner crust of neutron stars, formed of a solid lattice of nuclear clusters coexisting with a gas of electrons and neutrons, has been traditionally studied in the Wigner-Seitz approximation. The validity of this approximation is discussed in the general framework of the band theory of solids, which has been recently applied to the nuclear context. Using this novel approach, it is shown that the unbound neutrons move in the crust as if their mass was increased.

In the present volume, several contributions are devoted to the study of the properties of exotic nuclear matter (nuclei at the drip lines or neutron stars) by using implementations of the Density Functional Theory (DFT) in atomic nuclei, either in the nonrelativistic or covariant formalism. In our contribution, we argue that tensor correlations are important to be included in the functionals; the necessity to include other kind of correlations, namely those associated with the particle-vibration coupling, is discussed by using the specific example of ¹³²Sn.

In the attempt to reach a global view of the effects on single-particle states caused by the tensor interaction, we analyze the evolution of the spin-orbit splittings in the Ca isotopes and in the N = 28 isotones.

The first excited state of the nucleus ²²⁹Th has an exceptionally small excitation energy of 7.8 eV, which is expected to be very sensitive to changes in the fine structure constant α. A small difference in the Coulomb energies of the two states, which both are of the order 10⁹ eV, would amplify variations in α into large variations of the transition frequency. Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute the Coulomb energies of the two states. The kinetic energies are also calculated which reflect a possible variation in the nucleon or quark masses or local Lorentz invariance violation.

Nuclear matter is studied by using beyond relativistic Hartree-Fock (RHF) model with the realistic nucleon-nucleon (NN) interaction. We use the unitary correlation operator method (UCOM) to treat the strong repulsive interaction in the short-range region between two nucleons. We find that the equation of state (EOS) of pure neutron matter is completely comparable with the results of Dirac-Brueckner-Hartree-Fock (DBHF) theory. However, for the symmetric nuclear matter, the EOS is largely different from the DBHF result particularly in the low density region.

Using HF+BCS method with Skyrme forces we analyze the neutron drip line. It is shown that the drip line may form stability peninsulas. These peninsulas locate along fixed neutron numbers on the nuclear chart, which correspond to magic and new magic numbers and are the same for all Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.