arXiv subjects

Michał Siłkowski

Publications and source records attributed to Michał Siłkowski.

5 recordsLinked to original sources

arXiv2026

Nonadiabatic corrections to electric quadrupole transition rates in H$_2$

We derive formulas and perform calculations of nonadiabatic corrections to rates of electric quadrupole transitions in the hydrogen molecule. These corrections can be represented in terms of the quadrupole moment curve $D^{(1)}(R)$, similarly to the Born-Oppenheimer one, $D^{(0)}(R)$, derived originally by Wolniewicz. Numerical results change E2 transition rates for the fundamental band by as much as 0.4 - 12\% depending on rotational quantum numbers.

physics.atom-ph↗

arXiv2023

Leading-order QED effects in the ground electronic state of molecular hydrogen

We perform highly accurate calculations of the leading order QED correction to the ground electronic state of molecular hydrogen. Numerical results are obtained for a grid of the internuclear distances $R=0-10$ au with the relative precision of about $10^{-8}$. The major numerical uncertainty of previous QED results [K. Piszczatowski et al., JCTC $\textbf{5}$, 3039 (2009)] has been eliminated. Nevertheless, the discrepancy with measurements in HD at the level of 1.9 $σ$ persists.

physics.atom-ph↗

arXiv2022

Born-Oppenheimer potentials for $Π$, $Δ$, and $Φ$ states of the hydrogen molecule

We report on accurate variational calculations of the Born-Oppenheimer potential for excited states of the hydrogen molecule with $Π$, $Δ$, and $Φ$ symmetries. The obtained potential energy curves reach the relative precision of $10^{-9}$ or better along internuclear distances of 0.01 -- 20 au. Calculations rely on recursive evaluation of two-center two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first ever reported, and for the previously calculated states constitute an improvement by several orders of magnitude.

physics.atom-ph↗

arXiv2021

Accurate Born-Oppenheimer potentials for excited $Σ^{+}$ states of the hydrogen molecule

We report on highly accurate calculations of Born-Oppenheimer potentials for excited $n\,Σ^{+}$ states of the hydrogen molecule for all possible combinations of singlet/triplet and gerade/ungerade symmetries up to $n=7$. A relative accuracy of $10^{-10}$ (0.00002 cm$^{-1}$) or better is achieved for all the internuclear distances and all the excited states under consideration -- an improvement with respect to the best results available in the literature by at least 6 orders of magnitude. Presented variational calculations rely on efficient evaluation of molecular integrals with the explicitly correlated exponential basis in arbitrary precision arithmetics.

physics.atom-ph↗

arXiv2020

Long-range asymptotics of exchange energy in the hydrogen molecule

The exchange energy, i.e. the splitting $ΔE$ between gerade and ungerade states in the hydrogen molecule has proven very difficult in numerical calculation at large internuclear distances $R$, while known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 au. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form $ΔE \sim R^{5/2}e^{-2R}$, but with the leading coefficient being $2\,σ$ away from the analytically derived value.

physics.atom-ph↗