Search Results (8)

The Nikiforov–Uvarov functional analysis (NUFA) formalism is employed to study approximately the eigensolutions of the Schrodinger equation with the Pöschl–Teller-like pseudo-harmonic oscillator (PTPO). The variations in the energy spectra and the wave functions as a function of the screening parameters for different quantum states were investigated. With the energy expression of PTPO, the partition function and other thermodynamic function were obtained as a function of temperature for different values of the screening parameters using the Euler–Maclaurin formula. Using the Hellmann–Feynman theorem (HFT), we evaluate the expectation values of PTPO numerically and graphically for various values of the screening parameters and quantum states. It is observed that the eigensolutions, thermodynamic functions and expectation values of PTPO system are influenced by quantum states, screening parameters and temperature. Full article

We introduce a method for calculating the atomic forces of a molecular or extended system in an excited state described through the GW-BSE approach within the Tamm–Dancoff approximation. The derivative of the so-called excitonic Hamiltonian is obtained by finite differences and its application to the excited state is made possible through the use of suitable projectors. The scheme is implemented with the batch representation of the electron–hole amplitudes, allowing for avoiding sums over empty one-particle orbitals. The geometries of small excited molecules, namely, CO and CH₂O, were in excellent agreement with the results from quantum chemistry methods. Full article

The anomalous dimension ${\gamma }_m=1$ in the infrared region near the conformal edge in the broken phase of the large $N_f$ QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for $N_f=8$ and for $N_c=3$. Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result, ${\gamma }_m=1$, by comparing the pion matrix element of the trace of the energy-momentum tensor $⟨\pi \left(p_2\right)|(1+{\gamma }_m)·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=⟨\pi \left(p_2\right)|{\theta }_{\mu }^{\mu }|\pi \left(p_1\right)⟩=2M_{\pi }^2$ (up to trace anomaly) with the estimate of $⟨\pi \left(p_2\right)|2·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=2M_{\pi }^2$ through the Feynman–Hellmann theorem combined with an assumption $M_{\pi }^2\sim m_f$ characteristic of the broken phase. We show that this is not justified by the explicit evaluation of each matrix element based on the dilaton chiral perturbation theory (dChPT): $⟨\pi \left(p_2\right)|2·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=2M_{\pi }^2+[(1-{\gamma }_m)M_{\pi }^2·2/(1+{\gamma }_m)]=2M_{\pi }^2·2/(1+{\gamma }_m)\ne 2M_{\pi }^2$ in contradiction with his estimate, which is compared with $⟨\pi \left(p_2\right)|(1+{\gamma }_m)·{\sum }_{i=1}^{N_f}{m}_f{\overline{\psi }}_i{\psi }_i|\pi \left(p_1\right)⟩=(1+{\gamma }_m)M_{\pi }^2+\left[(1-{\gamma }_m)M_{\pi }^2\right]=2M_{\pi }^2$ (both up to trace anomaly), where the terms in $\left[\right]$ are from the $\sigma$ (pseudo-dilaton) pole contribution. Thus, there is no constraint on ${\gamma }_m$ when the $\sigma$ pole contribution is treated consistently for both. We further show that the Feynman–Hellmann theorem is applied to the inside of the conformal window where dChPT is invalid and the $\sigma$ pole contribution is absent, and with $M_{\pi }^2\sim m_f^{2/(1+{\gamma }_m)}$ instead of $M_{\pi }^2\sim m_f$, we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of $f_0\left(500\right)$ to $\pi \pi$ for $N_f=2$. It is shown to be consistent with the reality, when $f_0\left(500\right)$ is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance. Full article

Mechanisms responsible for spatiotemporal changes in the atomic-molecular architecture of the human femur in intact and osteoarthritis-affected areas were studied using high-resolution X-ray diffraction and spectroscopic techniques. Comparison of the experimental data demonstrates strong deviations of core electron-binding energies, lattice constants of hydroxyapatite crystal cells, linear sizes of crystallites, and degrees of crystallinity for both intact and osteoarthritic areas. The quantitative values of these characteristics and their standard deviations in each area are measured and presented. A systematic analysis of the site-dependent deviations was carried out within the framework of the 3D superlattice model. It is argued that the main mechanism responsible for the deviations arises primarily as a result of carbonization and catalytic reactions at the mineral-cartilage interface. The impact of the mechanism is enhanced in the vicinities of the area of sclerosed bone, but not inside the area where mechanical loads are maximum. Restoration of the atomic-molecular architecture of mineralized bone in the sclerosis area is revealed. Statistical aspects of the spatiotemporal changes in mineralized bone under pathogenic conditions are discussed. Full article

Intermolecular bonding attraction at π-bonded centers is often described as “electrostatically driven” and given quasi-classical rationalization in terms of a “pi hole” depletion region in the electrostatic potential. However, we demonstrate here that such bonding attraction also occurs between closed-shell ions of like charge, thereby yielding locally stable complexes that sharply violate classical electrostatic expectations. Standard DFT and MP2 computational methods are employed to investigate complexation of simple pi-bonded diatomic anions (BO⁻, CN⁻) with simple atomic anions (H⁻, F⁻) or with one another. Such “anti-electrostatic” anion–anion attractions are shown to lead to robust metastable binding wells (ranging up to 20–30 kcal/mol at DFT level, or still deeper at dynamically correlated MP2 level) that are shielded by broad predissociation barriers (ranging up to 1.5 Å width) from long-range ionic dissociation. Like-charge attraction at pi-centers thereby provides additional evidence for the dominance of 3-center/4-electron (3c/4e) n_D-π*_AX interactions that are fully analogous to the n_D-σ*_AH interactions of H-bonding. Using standard keyword options of natural bond orbital (NBO) analysis, we demonstrate that both n-σ* (sigma hole) and n-π* (pi hole) interactions represent simple variants of the essential resonance-type donor-acceptor (Bürgi–Dunitz-type) attraction that apparently underlies all intermolecular association phenomena of chemical interest. We further demonstrate that “deletion” of such π*-based donor-acceptor interaction obliterates the characteristic Bürgi–Dunitz signatures of pi-hole interactions, thereby establishing the unique cause/effect relationship to short-range covalency (“charge transfer”) rather than envisioned Coulombic properties of unperturbed monomers. Full article

Quantum mechanics, through the Hellmann–Feynman theorem and the Schrödinger equation, show that noncovalent interactions are classically Coulombic in nature, which includes polarization as well as electrostatics. In the great majority of these interactions, the positive electrostatic potentials result from regions of low electronic density. These regions are of two types, designated as σ-holes and π-holes. They differ in directionality; in general, σ-holes are along the extensions of covalent bonds to atoms (or occasionally between such extensions), while π-holes are perpendicular to planar portions of molecules. The magnitudes and locations of the most positive electrostatic potentials associated with σ-holes and π-holes are often approximate guides to the strengths and directions of interactions with negative sites but should be used cautiously for this purpose since polarization is not being taken into account. Since these maximum positive potentials may not be in the immediate proximities of atoms, interatomic close contacts are not always reliable indicators of noncovalent interactions. This is demonstrated for some heterocyclic rings and cyclic polyketones. We briefly mention some problems associated with using Periodic Table Groups to label interactions resulting from σ-holes and π-holes; for example, the labels do not distinguish between these two possibilities with differing directionalities. Full article

We analyze the effect of the tensor force and other components of the nucleon-nucleon interaction on the nuclear symmetry energy and its density dependence by using the Hellmann–Feynman theorem. The analysis is performed within the microscopic Brueckner–Hartree–Fock approach using the Argonne V18 potential plus a Urbana IX three-nucleon force. Our results show that the potential part of the nuclear Hamiltonian, and in particular its tensor component, gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy into a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that pure neutron matter is less correlated than symmetric nuclear matter. Full article

We present an overview of procedures that have been developed to compute several energetic quantities associated with noncovalent interactions. These formulations involve numerical integration over appropriate electronic densities. Our focus is upon the electrostatic interaction between two unperturbed molecules, the effect of the polarization of each charge distribution by the other, and the total energy of interaction. The expression for the latter is based upon the Hellmann-Feynman theorem. Applications to a number of systems are discussed; among them are dimers of uracil and interacting pairs of molecules in the crystal lattice of the energetic compound RDX. Full article