Спиральное магнитное упорядочение и переход металл--диэлектрик в модели Хаббарда на треугольной решeтке

The magnetic phase diagrams of the two-dimensional Hubbard model for isotropic and anisotropic triangular lattices are constructed within the Hartree-Fock and slave boson approximations. The triangular lattice specific non-collinear and spiral magnetic states, as well as phase separation between them, are shown to be realized in a wide range of model parameters along with collinear magnetic states (stripe antiferromagnetic and ferromagnetic). Phase transitions of the first and second order are found, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree-Fock and slave boson, shows that electronic correlations suppress magnetic states, the region of paramagnetism being expand, for values U/t>5. At the same time, when the Fermi level is near the van Hove singularity, electron correlations do not change the diagrams qualitatively, which is consistent with the previously obtained result for square and cubic lattices. The results are compared with the data available in the literature for other methods and approaches.

Reparametrization of the Colle–Salvetti formula

We investigate the Colle–Salvetti (CS) formula, the basis of the Lee, Yang and Parr (LYP) correlation functional used in approximate density functional theory. The CS formula is reparametrized using high-accuracy Hartree–Fock (HF) wavefunctions to determine the accuracy of the formula to calculate anions. Fitting to the hydride ion or the two-electron system just prior to electron detachment at the HF level of theory does not, in general, improve the calculated correlation energies using the parameters derived from the CS/LYP method. An analysis of the CS parameters used in the popular LYP functional demonstrates the ingenuity and perhaps fortuitousness of the original formulation by CS.

Quantum chemical simulation of MoO3 dispergation on hydroxylated SiO2 surface

Метою даної роботи є оцінка енергетичної сприятливості утворення різних молібдатних груп (≡Si‑O‑)2Mo(=O)2 та =Si(‑O‑)2Mo(=O)2 під час термічно ініційованого диспергування MoO3 на гідроксильованій поверхні SiO2. Для цього було здійснено квантовохімічне моделювання реакції O12Si10(OH)16 + MoO3 = O12Si10(OH)14O2MoO2 + H2O в температурному інтервалі 300–1100 K із використанням обмеженого методу Хартрі-Фока (наближення ЛКАО) з валентним базисом SBKJC (Stevens-Basch-Krauss-Jasien-Cundari). Кластер O12Si10(OH)16, який являє собою структурний фрагмент кристала β‑кристобаліту, був використаний як модель високогідроксильованої поверхні кремнезему. Ми розглянули дві структури молібдатних груп (≡Si‑O‑)2Mo(=O)2, прикріплених до кремнеземного кластера O12Si10(OH)16 через силанольні групи. Молібдатні групи (Etot ‑584.60147 Hartree), прикріплені до кремнеземного кластера через віддалені силанольні групи, виявляються більш енергетично вигідними, ніж молібдатні групи (Etot ‑584.56565 Hartree), прикріплені до кремнеземного кластера через сусідні силанольні групи. Енергія молібдатних груп =Si(‑O‑)2Mo(=O)2 (Etot ‑584.48399 Hartree), прикріплених до кремнеземного кластера O12Si10(OH)16 через силандіольні групи, менш енергетично вигідні в порівнянні з подібними групами, прикріпленими через силанольні групи, через більше напруження кута між зв’язками. Знайдено, що реакція O12Si10(OH)16 + MoO3 = O12Si10(OH)14O2MoO2 + H2O в температурному інтервалі 300–1100 K, змодельована шляхом квантовохімічних розрахунків, свідчить, що процес диспергування MoO3 на гідроксильованій поверхні SiO2 є енергетично вигідним. Експ The aim of the present work is to evaluate the energetic favourability of the formation of different molybdate species (≡Si‑O‑)2Mo(=O)2 and =Si(‑O‑)2Mo(=O)2 during the thermally induced MoO3 dispergation on hydroxylated SiO2 surface. In order to do this a quantum chemical modelling of the reaction O12Si10(OH)16 + MoO3 = O12Si10(OH)14O2MoO2 + H2O within the temperature interval of 300–1100 K was undertaken using the Restricted Hartree-Fock method (the LCAO approximation) with the SBKJC (Stevens-Basch-Krauss-Jasien-Cundari) valence basis set. The cluster O12Si10(OH)16 which represents a structural fragment of a β‑cristobalite crystal was used in this work as a model of highly hydroxylated silica surface. We considered two structures of molybdate (≡Si‑O‑)2Mo(=O)2 species attached to O12Si10(OH)16 silica cluster via silanol groups. Molybdate species (Etot ‑584.60147 Hartree) attached to silica cluster via distant silanols appeared more energetically favourable than molybdate species (Etot ‑584.56565 Hartree) attached to silica cluster via nearby silanols. The energy of molybdate =Si(‑O‑)2Mo(=O)2 species (Etot ‑584.48399 Hartree) attached to O12Si10(OH)16 silica cluster via silanediol group is less favourable energetically in comparison with those attached via silanol groups because of higher bond angle straining. The reaction O12Si10(OH)16 + MoO3 = O12Si10(OH)14O2MoO2 + H2O in the temperature interval of 300–1100 K which simulates by quantum chemical calculations the dispergation of MoO3 on hydroxylated SiO2 surface was found to be energetically favourable. The experimentally optimised temperature of ca. 800 K required for dispergation of MoO3 on hydroxylated SiO2 surface is determined by MoO3 evaporation and transportation via the gas phase. ериментальна оптимальна температура (близько 800 K), потрібна для диспергування MoO3 на гідроксильованій поверхні SiO2, визначається випаровуванням та перенесенням MoO3 в газовій фазі.

Structural, Spectral, Thermodynamic and HOMO, LUMO Analysis of 2, 6 dithenobenzene-3-enyl 3, 5 dimethyl piperdine-4-one: A quantum chemical analysis

In the current work, the vibrational frequencies, infrared intensities, molecular geometry and Raman scattering were determined and investigated using ab initio Hartree–Fock (HF) and density functional methods with a basis set of 6-311++ G (d, p) of the organic molecule under interpretation. The FT-IR and FT-Raman spectra of titled molecule have been recorded in the region 4000-400 cm-1 and 5000-70 cm-1, respectively. The optimized geometry structures (bond lengths and bond angles) achieved using HF shows the best result with the experimental values of the titled molecule. The frontier molecular orbitals help to distinguish chemical responsiveness and molecular kinetic steadiness, thus HOMO-LUMO analysis can be done using the quantum chemistry to improve thermodynamics. The electron density mapping to electrostatic potential surfaces were involved in finding the reactivity sites of the titled compound. With the help of Gauss view 5.0 and Chemcraft packages, the obtained outputs are analyzed. Hyperpolarizability and non-linear optical effect of isolated molecules of NLO materials are observed to be an extensive tool for molecular spectroscopy research. Therefore, for industrial application, Hyperpolarizability of the molecule is also studied.

OPTIMIZED QUASIPARTICLE DENSITY FUNCTIONAL APPROACH FOR MULTIELECTRON ATOMIC SYSTEMS

We present the optimized version of the quasiparticle density functional theory (DFT), constructed on the principles of the Landau-Migdal Fermi-liquids theory and principles of the optimized one-quasiparticle representation in theory of multielectron systems. The master equations can be naturally obtained on the basis of variational principle, starting from a Lagrangian of an atomic system as a functional of three quasiparticle densities. These densities are similar to the Hartree-Fock (HF) electron density and kinetical energy density correspondingly, however the third density has no an analog in the Hartree-Fock or the standard DFT theory and appears as result of account for the energy dependence of the mass operator S. The elaborated approach to construction of the eigen-functions basis can be characterized as an improved one in comparison with similar basises of other one-particle representations, namely, in the HF, the standard Kohn-Sham approximations etc.

THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

NUMERICAL STUDYING ENERGY PARAMETERS OF MULTIELECTRON ATOM IN A MAGNETIC FIELD: HELIUM

There are presented the results of calculating the energies of the helium atom energy in a homogeneous magnetic field on the basis of the new numerical quantum-mechanical approach. The approach is based on the numerical difference solution of the Schrödinger equation, the model potential method and the operator perturbation theory formalism. The obtained results on energy of the helium atom in dependence upon the magnetic field strength are compared with available theoretical results, obtained on the basis of alternative numerical Hartree-Fock and diagonalization methods.

HYPERFINE STRUCTURE PARAMETERS FOR COMPLEX ATOMS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

The calculational results for the hyperfine structure (HFS) parameters for the Mn atom (levels of the configuration 3d64s) and the results of advanced calculating the HFS constants and nuclear quadrupole moment for the radium isotope are obtained on the basis of computing within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. Analysis of the data shows that an account of the interelectron correlation effects is crucial in the calculation of the hyperfine structure parameters. The fundamental reason of physically reasonable agreement between theory and experiment is connected with the correct taking into account the inter-electron correlation effects, nuclear (due to the finite size of a nucleus), relativistic and radiative corrections. The key difference between the results of the relativistic Hartree-Fock Dirac-Fock and many-body perturbation theory methods calculations is explained by using the different schemes of taking into account the inter-electron correlations as well as nuclear and radiative ones.