Search Results (29)

Co(II) complexes have shown promising applications as single-molecule magnets (SMMs) in quantum computing and structural biology. Deciphering the Co(II) complexes may facilitate the development of SMM materials. Structural optimizations and calculations of chemical and magnetic properties were performed for Co(II) complexes with a tripodal tetradentate phenolate-amine ligand using MP2/aug-cc-pvdz, MP2/Def2svp, and CASSCF/Def2svp methods. The Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis unravels that Co(II) ions form unusual coordinate quasi-double bonds with ligand oxygen donor atoms, and the bond strengths range from 142.01 kcal/mol to 167.36 kcal/mol but lack further spectrometric evidence. The average 151.70 kcal/mol of the Co(II-O coordinates quasi-double bonds are formed mainly by two lone pairs of electrons from the ligand phenolate donor oxygen atoms. Dispersion forces contribute 24%, 28%, 27%, and 31% to the Co(II)-ligand interaction. Theoretical results of ZFS D, transversal ZFS E, and g-factor agree well with the experimental values. Magnetic susceptibility parameters calculated based on 5 doublet roots account for 85% of results computed 40 doublet roots are specified. These insights may aid in the rational design of SMM materials and Co(II) porphyrin fullerene conjugate for CO₂ electroreduction with superior magnetic properties. Full article

We investigate the energetics of the quasi-one-dimensional layered compound ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ in the excitonic phase within the six-band model using Hartree–Fock calculations. We calculate energies of states with different kinds of excitonic order and show that they differ by less than meV and depend sensitively on precise values of interchain hopping matrix elements. Full article

In quantum chemistry, constructing the Fock matrix is essential to compute Coulomb interactions among atoms and electrons and, thus, to determine electron orbitals and densities. In the fundamental framework of quantum chemistry such as the Hartree–Fock method, the iterative computation of the Fock matrix is a dominant process, constituting a critical computational bottleneck. Although the Fock matrix computation has been accelerated by parallel processing using GPUs, the issue of performance degradation due to memory contention remains unresolved. This is due to frequent conflicts of atomic operations accessing the same memory addresses when multiple threads update the Fock matrix elements concurrently. To address this issue, we propose a parallel algorithm that efficiently and suitably distributes the atomic operations; and significantly reduces the memory contention by decomposing the Fock matrix into multiple replicas, allowing each GPU thread to contribute to different replicas. Experimental results using a relevant set/configuration of molecules on an NVIDIA A100 GPU show that our approach achieves up to a $3.75\times$ speedup in Fock matrix computation compared to conventional high-contention approaches. Furthermore, our proposed method can also be readily combined with existing implementations that reduce the number of atomic operations, leading to a $1.98\times$ improvement. Full article

A simple method of non-relativistic variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation, all matrix elements of which are reduced to a numerical calculation of one-dimensional integrals. The distinctive features of the method are as follows: The use of the hyperspherical coordinate system. The inclusion of logarithms of the hyperspherical radius R in the basis functions, similar to the Fock expansion. Using a special basis function including the leading angular Fock coefficients to provide the correct behavior of the wave function near the nucleus. The main numerical parameters characterizing the properties of the helium atom and a number of helium-like ions near the nucleus are calculated and presented in tables. Among others, the specific coefficients, $a_{21}$, of the Fock expansion, which can only be calculated using a wave function with the correct behavior near the nucleus, are presented in table and graphs. Full article

The deformed shell model (DSM), based on Hartree–Fock intrinsic states with angular momentum projection and band mixing, has been found to be quite successful in describing many spectroscopic properties of nuclei in the A = 60–100 region. More importantly, DSM has been used recently with good success in calculating nuclear structure factors, which are needed for a variety of weak interaction processes. In this article, in addition to giving an overview of this, we discuss the applications of DSM to obtain cross-sections for coherent and incoherent neutrino nucleus scattering on ^96,98,100Mo targets and also for obtaining two neutrino double beta decay nuclear transition matrix elements for ¹⁰⁰Mo. Full article

In this paper, we update the phase-space factors for all two-neutrino double electron capture processes. The Dirac–Hartree–Fock–Slater self-consistent method is employed to describe the bound states of captured electrons, enabling a more realistic treatment of atomic screening and more precise binding energies of the captured electrons compared to previous investigations. Additionally, we consider all s-wave electrons available for capture, expanding beyond the K and $L_1$ orbitals considered in prior studies. For light atoms, the increase associated with additional captures compensates for the decrease in decay rate caused by the more precise atomic screening. However, for medium and heavy atoms, an increase in the decay rate, up to 10% for the heaviest atoms, is observed due to the combination of these two effects. In the systematic analysis, we also include capture fractions for the first few dominant partial captures. Our precise model enables a close examination of low Q-value double electron capture in ¹⁵²Gd, ¹⁶⁴Er, and ²⁴²Cm, where partial $KK$ captures are energetically forbidden. Finally, with the updated phase-space values, we recalculate the effective nuclear matrix elements and compare their spread with those associated with $2\nu {\beta }^{-}{\beta }^{-}$ decay. Full article

Within the de Sitter ambient space framework, the two different bases of the one-particle Hilbert space of the de Sitter group algebra are presented for the scalar case. Using field operator algebra and its Fock space construction in this formalism, we discuss the existence of asymptotic states in de Sitter QFT under an extension of the adiabatic hypothesis and prove the Fock space completeness theorem for the massive scalar field. We define the quantum state in the limit of future and past infinity on the de Sitter hyperboloid in an observer-independent way. These results allow us to examine the existence of the S-matrix operator for de Sitter QFT in ambient space formalism, a question which is usually obscure in spacetime with a cosmological event horizon for a specific observer. Some similarities and differences between QFT in Minkowski and de Sitter spaces are discussed. Full article

This study reports on the absolute photoionization cross sections for the magnesium-like Cl⁵⁺ ion over the 190–370 eV photon energy range, corresponding to the L-shell (2s and 2p subshells) excitation regime. The experiments were performed using the Multi-Analysis Ion Apparatus (MAIA) on the PLéIADES beamline at the SOLEIL synchrotron radiation storage ring facility. Single and double ionization ion yields, produced by photoionization of the 2p subshell of the Cl⁵⁺ ion from the 2p⁶3s^2 1S₀ ground state and the 2p⁶3s3p ³P_0,1,2 metastable levels, were observed, as well as 2s excitations. Theoretical calculations of the photoionization cross sections using the Multi-Configuration Dirac-Fock and R-matrix approaches were carried out, and the results were compared with the experimental data. The Cl⁵⁺ results were examined within the overall evolution of L-shell excitation for the early members of the Mg-like isoelectronic sequence (Mg, Al⁺, Si²⁺, S⁴⁺, Cl⁵⁺). Characteristic photon energies for P³⁺ were estimated by interpolation. Full article

In flat spacetime, the Dirac equation is the “square root” of the Klein–Gordon equation in the sense that, by applying the square of the Dirac operator to the Dirac spinor, one recovers the equation duplicated for each component of the spinor. In the presence of gravity, applying the square of the curved-spacetime Dirac operator to the Dirac spinor does not yield the curved-spacetime Klein–Gordon equation, but instead yields the Schrödinger–Dirac covariant equation. First, we show that the latter equation gives rise to a generalization to spinors of the covariant Gross–Pitaevskii equation. Then, we show that, while the Schrödinger–Dirac equation is not conformally invariant, there exists a generalization of the equation that is conformally invariant but which requires a different conformal transformation of the spinor than that required by the Dirac equation. The new conformal factor acquired by the spinor is found to be a matrix-valued factor obeying a differential equation that involves the Fock–Ivanenko line element. The Schrödinger–Dirac equation coupled to the Maxwell field is then revisited and generalized to particles with higher electric and magnetic moments while respecting gauge symmetry. Finally, Lichnerowicz’s vanishing theorem in the conformal frame is also discussed. Full article

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar–scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo-field dynamics and the Schwinger–Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at finite times and other non-equilibrium processes, including those found in the theory of open quantum systems. Full article

It is postulated that the overexpression of Carbonic Anhydrase isozyme IX in some cancers contributes to the acidification of the extracellular matrix. It was proved that this promotes the growth and metastasis of the tumor. These observations have made Carbonic Anhydrase IX an attractive drug target. In the light of the findings and importance of the glycoprotein in the cancer treatment, we have employed quantum–chemical approaches to study non-covalent interactions in the binding pocket. As a ligand, the acetazolamide (AZM) molecule was chosen, being known as a potential inhibitor exhibiting anticancer properties. First-Principles Molecular Dynamics was performed to study the chalcogen and other non-covalent interactions in the AZM ligand and its complexes with amino acids forming the binding site. Based on Density Functional Theory (DFT) and post-Hartree–Fock methods, the metric and electronic structure parameters were described. The Non-Covalent Interaction (NCI) index and Atoms in Molecules (AIM) methods were applied for qualitative/quantitative analyses of the non-covalent interactions. Finally, the AZM–binding pocket interaction energy decomposition was carried out. Chalcogen bonding in the AZM molecule is an important factor stabilizing the preferred conformation. Free energy mapping via metadynamics and Path Integral molecular dynamics confirmed the significance of the chalcogen bond in structuring the conformational flexibility of the systems. The developed models are useful in the design of new inhibitors with desired pharmacological properties. Full article

We extend a previously developed model for the Stark resonances of the water molecule. The method employs a partial-wave expansion of the single-particle orbitals using spherical harmonics. To find the resonance positions and decay rates, we use the exterior complex scaling approach which involves the analytic continuation of the radial variable into the complex plane and yields a non-hermitian Hamiltonian matrix. The real part of the eigenvalues provides the resonance positions (and thus the Stark shifts), while the imaginary parts $\mathrm{-}\mathrm{\Gamma }\mathrm{/}\mathrm{2}$ are related to the decay rates $\mathrm{\Gamma }$, i.e., the full-widths at half-maximum of the Breit–Wigner resonances. We focus on the three outermost (valence) orbitals, as they dominate the ionization process. We find that for forces directed along the three Cartesian co-ordinates, the fastest ionizing orbital always displays a non-monotonic Stark shift. For the case of fields along the molecular axis we show results as a function of the number of spherical harmonics included (${\ell }_{max}=3,4$). Comparison is made with total molecule resonance parameters from the literature obtained with Hartree–Fock and coupled cluster methods. Full article

Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify the Hilbert space of the low energy sector of $\mathrm{U}\left(N\right)$ quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites with the carrier space of irreducible representations of $\mathrm{U}\left(N\right)$ described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces $\mathrm{U}\left(N\right)/\mathrm{U}\left(M\right)\times \mathrm{U}(N-M)$. We embed this N-component fermion mixture in Fock space through a Schwinger–Jordan (boson and fermion) representation of $\mathrm{U}\left(N\right)$-spin operators. We provide different realizations of basis vectors using Young diagrams, Gelfand–Tsetlin patterns and Fock states (for an electron/flux occupation number in the fermionic/bosonic representation). $\mathrm{U}\left(N\right)$-spin operator matrix elements in the Gelfand–Tsetlin basis are explicitly given. Coherent state excitations above the ground state are computed and labeled by complex $(N-M)\times M$ matrix points Z on the Grassmannian phase space. They adopt the form of a $\mathrm{U}\left(N\right)$ displaced/rotated highest-weight vector, or a multinomial Bose–Einstein condensate in the flux occupation number representation. Replacing $\mathrm{U}\left(N\right)$-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy (long wavelength) $\mathrm{U}\left(N\right)$-spin-wave coherent excitations (skyrmions) of $\mathrm{U}\left(N\right)$ quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models. Full article

Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with the position operator, the momentum matrix elements do not fully capture the oscillator strength, while the length-gauge velocity matrix elements do. So far, length-gauge velocity matrix elements were not accessible in the all-electron full-potential WIEN2k package. We demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k for a hybrid exchange-correlation functional based on a finite difference approach. To illustrate the implementation we determined matrix elements for optical transitions between the conduction and valence bands in GaAs, GaN, (CH${}_3$NH${}_3$)PbI${}_3$ and a monolayer MoS${}_2$. The non-locality of the Hartree–Fock exact exchange potential leads to a strong enhancement of the oscillator strength as noticed recently in calculations employing pseudopotentials (Laurien and Rubel: arXiv:2111.14772 (2021)). We obtained an analytical expression for the enhancement factor for the difference in eigenvalues not captured by the kinetic energy. It is expected that these results can also be extended to other non-local potentials, e.g., a many-body $GW$ approximation. Full article

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds. Full article