Many-particle covalency, ionicity, and atomicity revisited for a few simple example molecules

We analyze two-particle binding factors of $H_{2}$, $LiH$, and $HEH^{+}$ molecules/ions with the help of our original exact diagonalization ab initio approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding

Toward complementary characterization of the chemical bond

A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics of the canonical example of the H2 molecule. This is achieved by starting from an analytic form for the two-particle wave function for electrons forming the bond, in which we single out the atomic contribution (atomicity) in an unequivocal manner. The presence of the atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atom correspondent is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (Mottness) to the intrinsic covalency and ionicity is established. This goal is achieved formally by combining the single-particle wave function readjustment in the entangled state with a simultaneous determination of two-particle states in the particle (second quantization) representation

Degree of atomicity in the chemical bonding: Why to return to the H2 molecule?

We analyze two-particle binding factors for the case of \ch{H2} molecule with the help of our original Exact Diagonalization \textit{Ab Intio} (EDABI) approach. Explicitly, we redefine the many-particle covalency and ionicity factors as a function of interatomic distance. Insufficiency of those basic characteristics is stressed and the concept of \textit{atomicity} is introduced and corresponds to the Mott and Hubbard criteria concerning the localization in many-particle systems. This additional characteristic introduces atomic ingredient into the essentially molecular states and thus eliminates a spurious behavior of the standard covalency factor with the increasing interatomic distance, as well as provides a physical reinterpretation of the chemical bond's nature

Degree of atomicity in the chemical bonding : why return to the H2 molecule?

We analyze two-particle binding factors for the case of the H2 molecule with the help of our original exact diagonalization ab initio approach. Explicitly, we redefine the many-particle covalency and ionicity factors as a function of interatomic distance. Insufficiency of those basic characteristics is stressed, and the concept of atomicity is introduced and corresponds to the Mott and Hubbard criteria concerning the electron localization in many-particle systems. This additional characteristic introduces atomic ingredients into the essentially molecular states and thus eliminates a spurious behavior of the standard covalency factor with the increasing interatomic distance, and also provides a physical reinterpretation of the chemical bond’s nature

Temporal trends of transcatheter aortic valve implantation in a high-volume academic center over 10 years

Background: Indications for transcatheter aortic valve implantation (TAVI) have gradually expanded since its introduction.Aims: The aim was to analyze temporal trends in TAVI characteristics based on the experience of a high-volume academic center over the period of 10 years.Methods: Five hundred and six consecutive (n = 506) patients with 1-year follow-up were divided into early (G1, years 2010–2013, n = 130), intermediate (G2, 2014–2016, n = 164) and recent (G3, 2017–2019, n = 212) experience groups.Results: Patient’s age remained constant over time (mean [SD]; G1 = 79.1 [7.1] years vs G2 = 79.1 [7.1] years vs G3 = 79.7 [6.6] years, P = 0.73) but surgical risk in G3 was lower (log Euroscore, median [IQR]: G1 = 14.0 [8.4–20.2] vs G2 = 12.0 [7.0–22.2] vs G3 = 5.1 [3.5–8.5]; P <0.001). Major/life-threatening bleeding (G1 = 26.9% vs G2 = 12.8% vs G3 = 9.4%; P <0.001), major vascular complications (G1 = 15.4% vs G2 = 8.5% vs G3 = 5.7%; P = 0.02) and moderate/severe paravalvular leak (G1 = 16.2% vs G2 = 11% vs G3 = 7.5%; P = 0.046) were decreasing with time. There was a significant drop in all-cause 1-year mortality in G3 (G1 = 20% vs G2 = 17.7% vs G3 = 9.1%; log rank = 0.01).Conclusions: The age of TAVI recipients remained unchanged over the last decade. Decreasing surgical risk coupled with improvements in procedural technique and care resulted in fewer periprocedural complications and better 1-year survival

Wybrane systemy molekularne w podejściu pierwszej i drugiej kwantyzacji

Ze względu na rozwój technologii, w szczególności tych związanych z technologiami in-formacyjnymi, inżynieria materiałowa sprowadzona została do skali nano. Z tego powodu kluczowa stała się znajomość właściwości elektronowych systemów molekularnych. Mimo iż istnieje wiele metod, którymi można traktować takie systemy, wiele pytań o naturę tychże pozostaje bez odpowiedzi. W związku z tym, w niniejszej pracy, rozważono wybrane systemy molekularne w podejściu pierwszej i drugiej kwantyzacji z użyciem metody Exact Diagonalization Ab Initio. Metoda ta została zaproponowana przez prof. J. Spałka orazjego współpracowników do obliczeń kwantowo-mechanicznych dla układów skorelowanych(silnie skorelowanych). Wszystkie obliczenia w oparciu o metodę EDABI zostały przeprowad-zone z użyciem biblioteki Quantum Metallization Tools, które to narzędzie zostało stwor-zone przez A. Kądzielawę i A. Biborskiego.Na początku pracy, wprowadzony został język drugiej kwantyzacji oraz przywołanezostało formalne wyprowadzenie modelu Hubbarda, wychodząc od operatorów pola. Następ-nie, w sposób podstawowy, opisany został rozszerzony model Hubbarda jako model parametryczny. W kolejnym kroku rozwiązany został w sposób ścisły, w ramach modelu Hubbarda, problem molekularnego jonu wodorowego oraz problem molekuły wodoru.W drugiej części pracy wprowadzone zostały podstawowe założenia metody EDABI. Następnie przedstawione zostały wyniki obliczeń prowadzonych w oparciu o metodę EDABI, dla molekuły wodoru oraz kryształu wodorku litu. Wartości energii stanu podstawowego, energii wiązania , a także energii kohezji zostały porównane z wynikami uzyskanymi innymi metodami obliczeniowymi oraz z wartościami pochodzącymi z eksperymentu.In view of the development of the technology, in particular related to the information technology, materials science came down to the nanoscale. For this reason, the knowledge of electronic properties of molecular systems is crucial. Although there exist many methods to treat them, still we can not answer many questions about the nature of such systems. In this Bachelor thesis we consider selected molecular systems in combined first andsecond quantization scheme within Exact Diagonalization Ab Initio method (EDABI). The method was proposed by prof. J. Spałek and coworkers as a tool to the correlated electrons (strong correlated electrons) related quantum properties. All calculations based on the EDABI method were performed using the library Quantum Metallization Tools developed by A. Kądzielawa and A. Biborski.First, we introduce the second quantization language and repeat the Hubbard model derivation starting from the definition of field operators. Afterwards we describe basically the extended Hubbard model as a parametric model. In the next step, we solve the hydrogen molecular ion and hydrogen molecule problem as examples of exact solution in the Hubbard model framework. In the second part of thesis we introduce basic assumptions of the Exact Diagonalization Ab Initio method. In the following chapters we present the results from EDABI calculations for the hydrogen molecule and lithium hydride cluster (solid state). We compare the numerical values of the ground state energy, bonding and cohesive energies and compare the results with other quantum computations method, as well with the experimental value

Termodynamika procesu fotokatalityczno-katalitycznego: modelowanie reakcji utleniania metanu

Głównym celem pracy magisterskiej był jakościowy opis dyssypacji ciepła w materiale fotokatalitycznym, tj. TiO2, w procesach fotokatalitycznych. W tym celu użyliśmy zarówno metod kwantowo-mechanicznych jak i dynamiki molekularnej. W pierwszej kolejności policzyliśmy podstawowe charakterystyki struktury typu bulk dla anatazu i rutylu. W wyniku tego otrzymaliśmy geomterię układu potrzebną do optymalizacji geometrii powierzchni. W kolejnym kroku wyznaczyliśmy energię oraz geometrię powierzchni dla płaszczyzny (110) rutylu oraz (001) anatazu. Następnie, olbiczyliśmy energię adsoprcji układu składającego się z opdowiedniej powierzchni rutylu bądź anatazu oraz molekuły metanu. Te wyniki pozwoliływykonać symulację przepływu ciepła w materiale metodami dynamiki molekularnej. Na końcu pracy zaprezentowane zostały analityczne rozwiązania równań ciepła z wykorzystaniem wyników uzyskanych w symulacji z użyciem dynamiki molekularnej.The main goal of this master thesis was to describe qualitatively heat dissipation in a photocatalytic material, namely TiO2, through the photocatalytic process. We used both quantum-mechanical and classical dynamics methods to do this. Firstly, we calculated the fundamental characteristics of the bulk for two structuresof titanium dioxide crystal, rutile and anatase. As a result of this, we obtained geometryof the system needed to surface geometry optimization. In the next step, we determined surface energy andgeometry for the (110) rutile surface and the (001) anatase surface. After that, we calculated adsorption energy for the system composed of the proper rutile or anatase surface and methane molecule. These results allowed us to perform classical dynamics simulations of heat transfer in the material. At the end of the work, we presented analytical solutions of heat equations based on thermal characteristics obtained from the molecular dynamics simulation

Towards Complementary Characterization of the Chemical Bond

A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics on the canonical example of H2 molecule. This is achieved by starting from analytic form for the two-particle wave function for electrons forming the bond, in which we single out the atomic contribution (\textit{atomicity}) in an unequivocal manner. The presence the of atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atomic correspondant is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (Mottness) to the intrinsic covalency and ionicity is established. This goal is achieved by combining the single--particle wave function readjustment with a simultaneous determination of two-particle states in the particle (second--quantization) representatio

Role of Kinetic Exchange and Coulomb Interaction in Bonding of Hydrogen Molecular Systems and Excited States

We present a detailed investigation of the electronic structure and bonding characteristics of hydrogen-based molecular systems (\ch{H2+}, \ch{H2}, \ch{H2-}) using the Exact Diagonalization Ab Initio (EDABI) approach within the framework of combined first- and second-quantization. By analyzing the relative contributions of kinetic exchange and effective Coulomb interactions, we provide a comprehensive understanding of covalency, atomicity, and ionicity as a function of interatomic distances. Our approach leverages exact solutions of the extended Heitler-London model to quantify these interactions, extending the analysis to the discussion of properties of excited states and the dissociation limit to these molecules. The findings reveal significant differences in bonding characteristics, particularly highlighting the stability and bonding nature of the neutral \ch{H2} molecule compared to its ionic counterparts. This study not only enhances an understanding of molecular interactions in hydrogen systems but also demonstrates the potential of the EDABI approach in developing more accurate computational models in quantum chemistry

Wpływ wilgotności powietrza i temperatury na współczynnik przewodzenia ciepła tynków perlitowych

Celem artykułu jest przedstawienie zagadnienia związanego z wpływem wilgotności powietrza oraz temperatury na wartość współczynnika przewodzenia ciepła tynków perlitowych. Badania laboratoryjne pozwoliły na wyznaczenie wartości współczynnika λ w zależności od temperatury badania oraz wilgotności powietrza (RH). Na podstawie pomiarów wyznaczono sorpcyjność i gęstość materiałów oraz wytrzymałość próbek na zginanie i ściskanie