arXiv subjects

Ali Bagci

Publications and source records attributed to Ali Bagci.

8 recordsLinked to original sources

arXiv2026

Foldy--Wouthuysen Transformation of the Generalized Dirac Equation in Symmetric Teleparallel Gravity

We investigate the non-relativistic limit of the generalized Dirac equation in a weak, static, and spherically symmetric background of symmetric teleparallel gravity. The underlying generalized spinor connection incorporates the complete Clifford-algebra basis and introduces additional couplings to the non-metricity sector beyond those of the conventional Dirac theory. Working in the coincident gauge and adopting the weak-field Schwarzschild geometry in isotropic coordinates, we derive the corresponding generalized Dirac Hamiltonian and perform successive Foldy--Wouthuysen transformations up to order $1/m^2$, retaining terms to first order in the gravitational potential and its spatial derivatives. The resulting block-diagonal Hamiltonian contains not only the expected gravitational counterparts of the kinetic, spin--orbit, and Darwin interactions, but also additional operator structures generated by the generalized spinor connection. In particular, direct spin--gravity, anisotropic spin--momentum--gravity, and tidal spin--momentum couplings arise naturally from the generalized metric-affine interaction. We further perform an order-of-magnitude analysis for an electron in the Earth's weak gravitational field to justify the adopted truncation of the inverse-mass expansion. These results demonstrate that the generalized Dirac equation in a symmetric teleparallel background gives rise to new low-energy interaction channels involving the fermion spin, momentum, and spatial derivatives of the gravitational field. The resulting effective Hamiltonian provides a framework for exploring phenomenological constraints on the additional couplings entering the generalized spinor connection.

gr-qc↗

arXiv2026

N-dimensional Coulomb-Sturmians with noninteger quantum numbers

Coulomb-Sturmian functions are complete, orthonormal, and include the full spectrum of continuum states. They are restricted to integer values of quantum numbers, as imposed by boundary and orthonormality conditions. Bagci-Hoggan exponential-type orbitals remove this restriction through a generalization to quantum number with fractional order. The differential equations for N-dimensional Bagci-Hoggan orbitals are derived. It is demonstrated that Coulomb-Sturmian functions satisfy a particular case of these equations. Additionally, Guseinov's Psi-alpha-ETOs are identified as N-dimensional Coulomb-Sturmians with a shifted dimensional parameter alpha, rather than representing an independent complete orthonormal sets of basis in a weighted Hilbert space.

quant-ph↗

arXiv2025

Complete and Orthonormal Sets of Exponential-type Orbitals with non-integer quantum numbers. On the results for many-electron atoms using Roothaan's LCAO method

Complete orthonormal sets of exponential-type orbitals with non-integer principal quantum numbers are discussed as basis functions in non-relativistic Hartree-Fock-Roothaan electronic structure calculations of atoms. A method is proposed to construct accurate and computationally efficient basis sets using these orbitals. It is demonstrated that principal quantum numbers of fractional order cannot be treated solely as variational parameters, since such a procedure may lead to unphysical basis sets (in particular, linearly dependent Slater-type functions). Ground-state total energies for the Be- and Ne- isoelectronic series are calculated. The results obtained are lower than those reported using other published basis sets. However, the energies obtained using Slater-type functions with non-integer principal quantum numbers are omitted from the comparison. These "orbitals" have no physical interpretation (except the "1s", which coincides with a hydrogenlike eigenfunction). In general linear independence of such Slater-type orbitals is not guaranteed. The results confirm that the parameter alpha, used to represent the complete orthonormal exponential-type orbitals in the weighted Hilbert space, is neither observable nor suitable to be considered as a variational parameter, despite its treatment as such in some prior work.

quant-ph↗

arXiv2025

The Generalized Dirac Equation in the Metric Affine Spacetime

We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two approaches. First, the generalized Dirac equation is directly formulated by applying the minimal coupling prescription to the original Dirac equation. It is referred to as the {\it direct Dirac equation} for seek of clarity and to preserve the tractability. Second, through the application of variational calculation to the original Dirac Lagrangian, the resulting Dirac equation is referred to as the {\it variational Dirac equation}. A consistency crosscheck is performed between these two approaches, leading to novel constraints on the arbitrary coupling constants appearing in the covariant derivative of spinor. Following short analysis on the generalized Dirac Lagrangian, it is observed that two of the novel terms give rise to a shift in the spinor mass by sensing its handedness.

math-ph↗

arXiv2025

Short time-to-solution Quantum Monte Carlo for catalysed hydrogen synthesis. Tools give CO hydrolysis activation barriers to 1kJ/mol on Pt(111)

Hydrogen synthesis is a clean, sustainable alternative to fossil fuel \cite{gals}. It has come of age: prototyping various aspects of hydrogen power are hot topics. In 9 out of 10 reactions, a solid catalyst is used. Here hydrogen production (via water-gas shift) is studied. Adsorbed reactants are optimidsed on model Pt(111). Focus is on partial O-H bond dissociation, when CO is co-adsorbed with water on this plane. hydrogen is the product. Many chemical reactions involve bond-dissociation. This process is often the key to rate-limiting reaction steps at solid surfaces. Bond-breaking is poorly described by Hartree-Fock and DFT methods, our embedded active site approach is used. We showcase Quantum Monte Carlo (QMC) methodology using the ground-state Slater Determinant of a simple four primitive-cell layer model, oriented to expose Pt (111), to initialise the QMC. This stochastic approach solves the Schr{\"o}dinger equation. It recently came of age for heterogeneous systems involving solids. During hydrolysis of carbon monoxide, initial O-H bond stretch is rate-limiting. Its dissociation energy is offset by surface Pt-H bond formation. The reactive formate (H-O-C=O) species formed by initial hydrolysis of CO, also interacting with a vicinal Pt. The products are hydrogen (CO$_2$ by-product is mineralised. A H-atom dissociates from the formate, another is desorbed from Pt(111). This yields pure hydrogen. Single-determinant work with a novel averaging procedure is compared to a high-level configuration interaction (CI) wave-function. Activation barriers are given to 0.86kJ/mol (c.f. 0.7 of the CI benchmark). Active sites embedded in metal lattice (111) faces. These trial wave-functions guide QMC.

cond-mat.mtrl-sci↗

arXiv2024

Relativistic exponential-type spinor orbitals and their use in many-electron Dirac equation solution

Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular components in calculation of many-electron systems. The relativistic Coulomb energy is determined by employing a spectral solution to Poisson's equation for the one-electron potential, which is expressed in terms of radial functions involving incomplete gamma functions. The computation for incomplete gamma functions posses challenges due to slow convergence rate associated with their series representation. Such difficulties are eliminated through use of the bi-directional method along with hyper-radial functions. A new formulation for relativistic auxiliary functions that improve the efficiency in Coulomb energy calculations is presented. These formulations also contribute to inquiring into orthogonal expansions for solutions to Poisson's equation using complete orthonormal sets of exponential orbitals with non-integer principal quantum numbers. They may provide a meaningful alternative series representations.

quant-ph↗

arXiv2022

Quantum Monte Carlo method for metal-film catalysis: water addition to carbon monoxide adsorbed on Pt/Al(111), a route to hydrogen

Hydrogen production as a clean, sustainable replacement for fossil fuels is gathering pace. Doubling the capacity of Paris-CDG airport has been halted, even with the upcoming Olympic Games, until hydrogen powered planes can be used. It is thus timely to work on catalytic selective hydrogen production and optimise catalyst structure. Over 90 % of all chemical manufacture uses a solid catalyst. This work describes adsorption of carbon-monoxide (CO) on platinum thin films, supported by cheap Al(111). CO reacts with water to produce hydrogen (water-gas shift). Quantum Monte Carlo methods are the only ones accurate enough to investigate the early steps of this catalysed reaction at close-packed Pt/Al(111). Many chemical reactions involve bond-dissociation. This process is often the key to rate-limiting reaction steps at solid surfaces. Since bond-breaking is poorly described by Hartree-Fock and DFT methods, our embedded active site approach is used This work demonstrates a novel Quantum Monte Carlo (QMC) methodology. The water-gas shift reaction step studied is water addition to CO pre-adsorbed on a Pt-monolayer supported by Al(111). The water molecule is only partially dissociated. Its oxygen atom binds to CO giving adsorbed COOH and Pt-H. This concerted addition is rate-limiting. In subsequent steps, the adsorbed formate species (with acidic hydrogen) decomposes to carbon dioxide and, after proton migration to Pt-H, the clean product H$_2$ is obtained. The QMC activation barrier found is 64.8 $\pm$ 1.5 kJ/mol. Thus, QMC is shown to be encouraging for investigating similar catalytic systems.

physics.chem-ph↗

arXiv2021

JRAF: A Julia Package for Computation of the Relativistic Molecular Auxiliary Functions

Evaluation of relativistic molecular integrals over exponential-type spinor orbitals require using the relativistic auxiliary functions in prolate spheroidal coordinates. They have derived recently by the author [Physical Review E 91, 023303 (2015)]. They are used in solution of the molecular Dirac equation for electrons moving around Coulomb potential. A series of papers on a method for fully analytical evaluation of relativistic auxiliary functions in following, published [2, 3, 4]. From the computational physics point of view, these works also demonstrate how to deal with the integrals involve product of power functions with non-integer exponents and incomplete gamma functions. The computer program package to calculate these auxiliary functions in high accuracy is presented. It is designed in Julia programming language. It is capable of yielding highly accurate results for molecular integrals over a wide range of orbital parameters and quantum numbers. Additionally, the program package provides numerous tools such as efficient calculation for the angular momentum coefficients arising in the product of two normalized associated Legendre functions centered on different atomic positions, the rotation angular functions used for both complex and real spherical harmonics. Sample calculations are performed for two-center one-electron integrals over non-integer Slater-type orbitals. The results prove that the package is robust.

physics.comp-ph↗