arXiv subjects

Dávid Ferenc

Publications and source records attributed to Dávid Ferenc.

17 recordsLinked to original sources

arXiv2025

Gaussian basis set approach to one-loop self-energy

We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian basis set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a one-electron atom, our results show excellent agreement with those obtained using the exact Dirac--Coulomb wave functions. The developed method can be of interest for high-precision studies of heavy few-electron molecular systems, where the rigorous computation of QED corrections is currently a formidable task.

quant-ph↗

arXiv2024

Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians

Drachmann's regularization approach is implemented for floating explicitly correlated Gaussians (fECGs) and molecular systems. Earlier applications of drachmannized relativistic corrections for molecular systems were hindered due to the unknown analytic matrix elements of $1/r_{ix}1/r_{jy}$-type operators with fECGs. In the present work, one of the $1/r$ factors is approximated by a linear combination of Gaussians, which results in calculable integrals. The numerical approach is found to be precise and robust over a range of molecular systems and nuclear configurations, and thus, it opens the route towards an automated evaluation of high-precision relativistic corrections over potential energy surfaces of polyatomic systems. Furthermore, the newly developed integration approach makes it possible to construct the matrix representation of the square of the electronic Hamiltonian relevant for energy lower-bound as well as time-dependent computations of molecular systems with a flexible and high-precision fECG basis representation.

physics.chem-ph↗

arXiv2023

Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems

The sixteen-component, no-pair Dirac--Coulomb--Breit equation, derived from the Bethe--Salpeter equation, is solved in a variational procedure using Gaussian-type basis functions for the example of positronium, muonium, hydrogen atom, and muonic hydrogen. The $α$ fine-structure-constant dependence of the variational energies, through fitting a function of $α^n$ and $α^n\text{ln}α$ terms, shows excellent agreement with the relevant energy expressions of the (perturbative) non-relativistic QED framework, and thereby, establishes a solid reference for the development of a computational relativistic QED approach.

quant-ph↗

arXiv2023

The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules

Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum electrodynamics has been established by the mid-twentieth century, primarily as a scattering theory. To describe atoms and molecules, it is important to consider bound states. In the non-relativistic quantum mechanics framework, bound states can be efficiently computed using robust and general methodologies with systematic approximations developed for solving wave equations. With the sight of the development of a computational quantum electrodynamics framework for atomic and molecular matter, the field theoretic Bethe-Salpeter wave equation expressed in space-time coordinates, its exact equal-time variant and emergence of a relativistic wave equation is reviewed. A computational framework, with initial applications and future challenges in relation with precision spectroscopy, is also highlighted.

physics.chem-ph↗

arXiv2023

Evaluation of the Bethe logarithm: from atom to chemical reaction

A general computational scheme for the (non-relativistic) Bethe logarithm is developed opening the route to `routine' evaluation of the leading-order quantum electrodynamics correction (QED) relevant for spectroscopic applications for small polyatomic and polyelectronic molecular systems. The implementation relies on Schwartz' method and minimization of a Hylleraas functional. In relation with electronically excited states, a projection technique is considered, which ensures positive definiteness of the functional over the entire parameter (photon momentum) range. Using this implementation, the Bethe logarithm is converged to a relative precision better than 1:10$^3$ for selected electronic states of the two-electron H$_2$ and H$_3^+$, and the three-electron He$_2^+$ and H+H$_2$ molecular systems. The present work focuses at nuclear configurations near the local minimum of the potential energy surface, but the computations can be repeated also for other structures.

physics.chem-ph↗

arXiv2023

Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen

For rovibronic states corresponding to the $B$ and $B'\ ^1Σ_\text{u}^+$ electronic states of the hydrogen molecule, the pre-Born--Oppenheimer (four-particle) non-relativistic energy is converged to a 1-3 parts-per-billion relative precision. The four-particle non-relativistic energy is appended with leading-order relativistic, leading- and estimated higher-order quantum-electrodynamics corrections. The resulting term values referenced to the rovibronic ground state are obtained in an excellent agreement with the experimental results. Further results are reported and discussed for other rovibronic states assignable to the $C\ ^1Π_\text{u}$ and the $EF,GK,$ and $HH\ ^1Σ_\text{g}^+$ electronic states.

physics.chem-ph↗

arXiv2022

Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac$-$Coulomb$-$Breit (DCB) equation to all orders of the $α$ fine-structure constant. The analysis of the polynomial $α$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit$-$Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $α$ dependence of the no-pair DCB energy shows that the higher-order ($α^4 E_\mathrm{h}$) non-radiative QED correction is 5 % of the leading-order ($α^3 E_\mathrm{h}$) non-radiative QED correction for $Z=2$ (He), but it is 40 % already for $Z=4$ (Be$^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

physics.chem-ph↗

arXiv2022

Benchmark potential energy curve for collinear H$_3$

A benchmark-quality potential energy curve is reported for the H$_3$ system in collinear nuclear configurations. The electronic Schrödinger equation is solved using explicitly correlated Gaussian (ECG) basis functions using an optimized fragment initialization technique that significantly reduces the computational cost. As a result, the computed energies improve upon recent orbital-based and ECG computations. Starting from a well-converged basis set, a potential energy curve with an estimated sub-parts-per-billion precision is generated for a series of nuclear configurations using an efficient ECG rescaling approach.

physics.chem-ph↗

arXiv2022

Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ $^1Σ_\text{g}^+$ manifold of molecular hydrogen

A variational procedure is described for the computation of the non-adiabatic mass-correction tensor applicable for multi-dimensional electronic manifolds. The 30-year-old computations of Wolniewicz, Dressler, and their co-workers are appended with the computed vibronic mass-correction functions corresponding to the $EF$-$GK$-$H\bar{H}$-$S5$-$S6$ $^1Σ_\text{g}^+$ manifold of the hydrogen molecule. Initial results are reported for the vibronic energies. Necessary further improvements and further developments are discussed.

physics.chem-ph↗

arXiv2022

Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac-Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. The subsequent paper [Paper II: D. Ferenc, P. Jeszenszki, and E. Mátyus (2022)] describes the implementation of the Breit interaction in this framework.

physics.chem-ph↗

arXiv2022

On the Breit interaction in an explicitly correlated variational Dirac-Coulomb framework

The Breit interaction is implemented in the no-pair variational Dirac-Coulomb (DC) framework using an explicitly correlated Gaussian basis reported in the previous paper [Paper I: P. Jeszenszki, D. Ferenc, and E. Mátyus (2022)]. Both a perturbative and a fully variational inclusion of the Breit term is considered. The no-pair DC plus perturbative Breit as well as the no-pair Dirac-Coulomb-Breit energies are compared with perturbation theory results including the Breit-Pauli Hamiltonian and leading-order non-radiative quantum electrodynamics corrections for low $Z$ values. Possible reasons for the observed deviations are discussed.

physics.chem-ph↗

arXiv2021

On the inclusion of cusp effects in expectation values with explicitly correlated Gaussians

This paper elaborates the integral transformation technique of [K. Pachucki, W. Cencek, and J. Komasa, J. Chem. Phys. 122, 184101 (2005)] and uses it for the case of the non-relativistic kinetic and Coulomb potential energy operators, as well as for the relativistic mass-velocity and Darwin terms. The techniques are tested for the ground electronic state of the helium atom and new results are reported for the ground electronic state of the H$_3^+$ molecular ion near its equilibrium structure.

physics.chem-ph↗

arXiv2021

All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis

A variational solution procedure is reported for the many-particle no-pair Dirac-Coulomb-Breit Hamiltonian aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei approximation. The procedure is tested for nuclear charge numbers from $Z=1$ (hydrogen) to $28$ (iron). Already for the lowest $Z$ values, a significant difference is observed from leading-order Foldy-Woythusen perturbation theory, but the observed deviations are smaller than the estimated self-energy and vacuum polarization corrections.

quant-ph↗

arXiv2020

Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of $^4$He$_2^+$ ($X\ ^2Σ_\mathrm{u}^+$)

The rovibrational intervals of the $^4$He$_2^+$ molecular ion in its $X\ ^2Σ_\text{u}^+$ ground electronic state are computed by including the non-adiabatic, relativistic, and leading-order quantum-electrodynamics corrections. Good agreement of theory and experiment is observed for the rotational excitation series of the vibrational ground state and the fundamental vibration. The lowest-energy rotational interval is computed to be $70.937\ 69(10)$ cm$^{-1}$ in agreement with the most recently reported experimental value, $70.937\ 589(23)(60)_\text{sys}$ cm$^{-1}$ [L. Semeria, P. Jansen, G.-M. Camenisch, F. Mellini, H. Schmutz, and F. Merkt, Phys. Rev. Lett. 124, 213001 (2020)].

physics.atom-ph↗

arXiv2019

Non-adiabatic mass correction for excited states of molecular hydrogen: improvement for the outer-well $H\bar{H}\ ^1Σ_\mathrm{g}^+$ term values

The mass-correction function is evaluated for selected excited states of the hydrogen molecule within a single-state non-adiabatic treatment. Its qualitative features are studied under the avoided crossing of the $EF$ with the $GK$ state and also for the outer well of the $H\bar{H}$ state. For the $H\bar{H}$ state, a negative mass correction is obtained for the vibrational motion near the outer minimum, which accounts for most of the deviation between experiment and earlier theoretical work.

physics.chem-ph↗

arXiv2019

Precise computation of rovibronic resonances of molecular hydrogen: $EF\ ^1Σ_\mathrm{g}^+$ inner-well rotational states

Selected states of the $EF\ ^1Σ_\mathrm{g}^+$ electronic manifold of the hydrogen molecule are computed as resonances of the four-body problem. Systematic improvement of the basis representation for the variational treatment is achieved through an energy-tracking optimization procedure. The resulting non-relativistic energy is converged within a few nano Hartree, while the predissociative width is found to be negligible at this level of accuracy. The four-particle non-relativistic energies are appended with relativistic and quantum electrodynamics corrections which close the gap between the experimental observations and earlier theoretical work.

physics.chem-ph↗

arXiv2018

Bound and unbound rovibrational states of the methane-argon dimer

Peculiarities of the intermolecular rovibrational quantum dynamics of the methane-argon complex are studied using a new, ab initio potential energy surface [Y. N. Kalugina, S. E. Lokshtanov, V. N. Cherepanov, and A. A. Vigasin, J. Chem. Phys. 144, 054304 (2016)], variational rovibrational computations, and detailed symmetry considerations within the molecular symmetry group of this floppy complex as well as within the point groups corresponding to the local minimum structures. The computed (ro)vibrational states up to and beyond the dissociation asymptote are characterized using two limiting models: the rigidly rotating molecule's model and the coupled-rotor model of the rigidly rotating methane and an argon atom orbiting around it.

physics.chem-ph↗