arXiv subjects

Michał Przybytek

Publications and source records attributed to Michał Przybytek.

17 recordsLinked to original sources

arXiv2026

Determination of fundamental properties of nitrogen from first principles. I. Atomic polarizabilities and long-range dispersion coefficients

This work is the first in a series of papers in which we perform theoretical calculations of various fundamental properties of nitrogen relevant for gas thermometry experiments. In this part we focus on the properties of nitrogen atom, namely dynamic polarizabilities and dispersion coefficients that describe interaction between two nitrogen atoms at large internuclear separations. These quantities are calculated using a composite scheme based on coupled cluster and full configuration interaction methods and large Gaussian basis sets optimized specifically for the purposes of this work. The dispersion coefficients, $C_n$ with $n=6,8,10$, are obtained using Casimir--Polder formulas by numerical integration over dipole, quadrupole, and octuple polarizabilities for imaginary frequencies represented analytically by Padé approximants. Special attention is paid to careful error control and uncertainty estimation of the calculated quantities.

physics.chem-ph↗

arXiv2026

Determination of fundamental properties of nitrogen from first principles. II. Potential energy curve and spectroscopic properties of N$_2$

This work is the second part of the series devoted to first-principles determination of the fundamental properties of nitrogen. In this part, we calculate the potential energy curve for the electronic ground state of N$_2$. The potential is divided into three components: short-, medium-, and long-range, and a different computational protocol is applied to each component, based on a composite coupled cluster approach, genuine multireference methods, and asymptotic expansion of the interaction energy. A particular focus is on the short-range part, as the accuracy of this component is critical from the point of view of metrological applications, including the temperature dependence of many properties of nitrogen gas. Uncertainties of the theoretical data, originating both from basis set incompleteness and applied theoretical method, are rigorously analyzed and provided at $2σ$ level, i.e. expanded ($k=2$) uncertainties. The developed potential energy curve is used to calculate the spectroscopic parameters of the N$_2$ ground state and the results are compared with the available theoretical and experimental data.

physics.chem-ph↗

arXiv2026

Determination of fundamental properties of nitrogen from first principles. III. Temperature and frequency dependence of the molecular polarizability and magnetic susceptibility

This work is the third part of the series of papers that focus on the theoretical determination of the properties of nitrogen that are relevant in metrology. Here we present first-principles calculations of the temperature and frequency dependence of the molecular polarizability and magnetic susceptibility of the nitrogen molecule (N$_2$). The purely electronic contributions to the static polarizability, Cauchy coefficients (up to sixth order), and isotropic magnetic susceptibility are computed over a range of internuclear distances using a robust composite scheme combining several electronic structure methods. The temperature dependence, evaluated from $50$~K to $2000$~K, is determined using two independent methods: rovibrational averaging and path integral Monte Carlo (PIMC). The polarizabilities obtained from theory agree with the recent high-precision thermometry measurements, wherever the latter are available, but are significantly less accurate. However, the main usefulness of the theoretical data revolves around combining it with the available experimental results to generate semi-empirical estimates of various quantities that have never been measured thus far. As an example, we determine highly accurate semi-empirical estimates of the static polarizability at key reference temperatures, $α_0(T)=11.735\,962$~a.u.\ at $T=303$~K and $α_0(T)=11.735\,585$~a.u.\ at $T=273.16$~K. Furthermore, we report theoretical values for the magnetic susceptibility, highlighting the importance of the paramagnetic contribution, and address a significant discrepancy with the experimental data for this quantity.

physics.chem-ph↗

arXiv2026

Density effects in precision laser spectroscopy of exotic helium atoms

Exotic helium atoms act as unique atomic traps for heavy, negatively charged particles, protecting them from nuclear annihilation and nuclear capture on timescales long enough to enable high-precision laser spectroscopy. Such measurements serve as stringent tests of three-body quantum electrodynamics and offer a direct route to determining fundamental particle masses. Motivated by upcoming spectroscopic efforts targeting pionic ($π^{-\,4}\mathrm{He}^+$) and kaonic ($K^{-\,4}\mathrm{He}^+$) helium, we present a rigorous theoretical evaluation of the collisional and density effects governing these systems. Using an ab initio potential energy surface and coupled-channel quantum scattering calculations, we study the collisional stability of the candidate metastable states against inelastic quenching in a cryogenic helium buffer gas. Furthermore, we provide theoretical reference values for the pressure broadening and pressure shift coefficients of the targeted transitions. These results establish an essential benchmark for future experiments, paving the way for refined determinations of the pion and kaon masses.

physics.atom-ph↗

arXiv2025

Quantum calculation of the collision-induced line-shape effects in antiprotonic helium and the new accurate ab initio $\bar{p}$He$^{+}$-He potential energy surface

We present the first fully ab initio calculations of collision-induced broadening and shift of spectral lines in antiprotonic helium ($\bar{p}$He$^{+}$) perturbed by atomic helium. To overcome critical limitations of previous studies, we construct a new highly accurate potential energy surface (PES) that spans a wide range of $\bar{p}$He$^{+}$-He geometries relevant to all metastable states of the exotic helium atom. Rigorous quantum scattering calculations performed using the new PES yield scattering $S$-matrices from which we extract pressure broadening and shift coefficients for 50 transitions in antiprotonic helium-4 ($\bar{p}^{4}$He$^{+}$). This dataset provides the first rigorous benchmark for earlier semiclassical calculations and establishes a robust theoretical reference for high-precision spectroscopy of antiprotonic helium, which is used to test the fundamental charge, parity, and time reversal (CPT) symmetry. The results extend to temperatures relevant to non-gaseous phases of helium, supporting a new class of precision measurements. This study introduces a methodological framework for future investigations of other exotic systems, such as pionic or kaonic helium atoms, enabling the development of reference data for high-precision spectroscopy of these species - an essential component for improving the determination of the pion and kaon masses.

physics.atom-ph↗

arXiv2025

First-Order Symmetry-Adapted Perturbation Theory with Double Exchange for Multireference Systems

We extend first-order multiconfigurational symmetry-adapted perturbation theory, SAPT(MC), [Hapka M. et al. JCTC, 2021, 17], to account for double-exchange effects, where up to two electron pairs are exchanged between interacting monomers. To achieve this, we derive density-matrix-based expressions for the first-order exchange energy to arbitrary orders in the overlap expansion. As a numerical demonstration, we apply the double-exchange approximation to strongly orthogonal geminal wave functions. Additionally, we propose an approximate method for evaluating double-exchange energy with complete active space (CAS) wave functions of the valence type, i.e., with n active electrons distributed over n orbitals. We analyze the performance of these methods on model dimers in both ground and excited states.

physics.chem-ph↗

arXiv2025

Estimating complete basis set extrapolation error through random walk

We propose a method of estimating the uncertainty of a result obtained through extrapolation to the complete basis set limit. The method is based on an ensemble of random walks which simulate all possible extrapolation outcomes that could have been obtained if results from larger basis sets had been available. The results assembled from a large collection of random walks can be then analyzed statistically, providing a route for uncertainty prediction at a confidence level required in a particular application. The method is free of empirical parameters and compatible with any extrapolation scheme. The proposed technique is tested in a series of numerical trials by comparing the determined confidence intervals with reliable reference data. We demonstrate that the predicted error bounds are reliable, tight, yet conservative at the same time.

physics.data-an↗

arXiv2023

Efficient calculation of dispersion energy for multireference systems with Cholesky decomposition. Application to excited-state interactions

We propose an algorithm, that scales with the fifth power of the system size, for computing the second-order dispersion energy for monomers described with multiconfigurational wave functions. This scaling can be achieved when the number of virtual (unoccupied) orbitals largely exceeds the number of active orbitals, which is the case in practical calculations. Our approach employs Cholesky decomposition of Coulomb integrals and a recently developed recursive formula for density response functions of the monomers, enabling dispersion energy computations for systems in nondegenerate ground or excited states with arbitrary spin. As a numerical illustration, we apply the new algorithm in the framework of multiconfigurational symmetry adapted perturbation theory, SAPT(MC), to study interactions in dimers with localized excitons. The SAPT(MC) analysis reveals that the dispersion energy may be the main force stabilizing excited-state dimers.

physics.chem-ph↗

arXiv2023

Ab initio potential energy curves, scattering lengths, and rovibrational levels of the He$_2^+$ molecular ion in excited electronic states

We calculate accurate potential energy curves for a ground-state He$^+$ ion interacting with a He atom in the lowest-energy metastable $^3\!S$ electronic state. We employ the full configuration interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the He$_2^+$ molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the He$_2^+$ molecular ion in the excited electronic state and collisional studies of He$^+$ ions immersed in ultracold gases of metastable He atoms.

physics.atom-ph↗

arXiv2022

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from $5 \times 10^{13}\:\rm W/cm^2$ to $5 \times 10^{14}\:\rm W/cm^2$. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

physics.chem-ph↗

arXiv2022

Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study

In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method), and analyse obtained HHG spectra. The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory.

physics.chem-ph↗

arXiv2021

Theoretical determination of polarizability and magnetic susceptibility of neon

We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value $α_0=2.66080(36)$ for the static polarizability, and $α_2=2.850(7)$ and $α_4=4.932(14)$ for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)], but our estimated uncertainty is significantly larger. For the dispersion coefficients, the results obtained in this work appear to be the most accurate to date overall compared to published theoretical and experimental data. We also calculated the static magnetic susceptibility of the neon atom, needed to obtain the refractive index of gaseous neon. Our result, $χ_0 = -8.484(19) \cdot 10^{-5}$ a.u., is about 9% larger in absolute value than the recommended experimental value [CRC Handbook of Chemistry and Physics, CRC Press, 2019, p. 4-145].

physics.atom-ph↗

arXiv2020

Second virial coefficients for helium-4 and helium-3 from accurate relativistic interaction potential

The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5 - 1000K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

physics.chem-ph↗

arXiv2018

Ab initio potential energy curve for the ground state of beryllium dimer

This work concerns \emph{ab initio} calculations of the complete potential energy curve and spectroscopic constants for the ground state $X^1Σ_g^+$ of the beryllium dimer, Be$_2$. High accuracy and reliability of the results is one of the primary goals of the paper. To this end we apply large basis sets of Slater-type orbitals combined with high-level electronic structure methods including triple and quadruple excitations. The effects of the relativity are also fully accounted for in the theoretical description. For the first time the leading-order quantum electrodynamics effects are fully incorporated for a many-electron molecule. Influence of the finite nuclear mass corrections (post-Born-Oppenheimer effects) turns out to be completely negligible for this system. The predicted well-depth ($D_e=934.5\pm2.5\,\mbox{cm}^{-1}$) and the dissociation energy ($D_0=808.0\,\mbox{cm}^{-1}$) are in a very good agreement with the most recent experimental data. We confirm the existence of the weakly bound twelfth vibrational level [Patkowski et al., Science 326, 1382 (2009)] and predict that it lies just about 0.5 $\mbox{cm}^{-1}$ below the onset of the continuum.

physics.chem-ph↗

arXiv2015

Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment

We employ \textit{ab initio} methods of quantum chemistry to investigate spin-1/2 fermions interacting via a two-body contact potential in a one-dimensional harmonic trap. The convergence of the total energy with the size of the one-particle basis set is analytically investigated for the two-body problem and the same form of the convergence formula is numerically confirmed to be valid for the many-body case. Benchmark calculations for two to six fermions with the full configuration interaction method equivalent to the exact diagonalization approach, and the coupled cluster method including single, double, triple, and quadruple excitations are presented. The convergence of the correlation energy with the level of excitations included in the coupled cluster model is analyzed. The range of the interaction strength for which single-reference coupled cluster methods work is examined. Next, the coupled cluster method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed to study a two-component Fermi gas composed of 6 to 80 atoms in a one-dimensional harmonic trap. The density profiles of trapped atomic clouds are also reported. Finally, a comparison with experimental results for few-fermion systems is presented. Upcoming possible applications and extensions of the presented approach are discussed.

cond-mat.quant-gas↗

arXiv2015

Crossover between few and many fermions in a harmonic trap

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the non-analytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

cond-mat.quant-gas↗

arXiv2015

Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer

In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order $α^2$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0$\,\pm\,$1.9 $cm^{-1}$, in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

physics.chem-ph↗