Algorithms for calculating mass-velocity and Darwin relativistic corrections with <i>n</i>-electron explicitly correlated Gaussians with shifted centers

Stanke, Monika; Palikot, Ewa; Adamowicz, Ludwik

doi:10.1063/1.4947553

Cited by 14 publications

(35 citation statements)

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“…[14] and from the present work; b non-adiabatic mass computed in Ref. [15] and in the present work; c relativistic corrections obtained with the integral transformation technique [30] and the 'direct' method [31]; d effect of a hypothetical ±1% change in β el ; e σ is obtained as the sum of the absolute value of the terms; f the effect of the neglected higher-order QED corrections is estimated with the dominant term of E (4) , Eq. 11; g estimate for the coupling of the non-adiabatic and relativistic corrections, see also Ref.…”

Section: Introductionmentioning

confidence: 80%

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Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (
Ferenc
¹
,
Korobov
²
,
Mátyus
³

2020
Phys. Rev. Lett.

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The rovibrational intervals of the 4 He + 2 molecular ion in its X 2 Σ + u ground electronic state are computed by including the non-adiabatic, relativistic, and leading-order quantumelectrodynamics 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) sys cm −1

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Section: Introductionmentioning

confidence: 80%

“…r ix (x = j or a) operators [31] and by using the integral-transformation technique (IT) [30]. Since we have accurate electronic wave functions, we expect that the two routes give very similar rovibrational intervals, still the results obtained with the IT integrals are expected to have a lower uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (
Ferenc
¹
,
Korobov
²
,
Mátyus
³

2020
Phys. Rev. Lett.

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“…The expectation values are calculated using the ECGs optimized for each PEC point. The details of the derivation and implementation of the algorithms are outlined in Stanke et al (2016aStanke et al ( , 2016b.…”

Section: Potential Energy and Dmcsmentioning

confidence: 99%

Benchmark Rovibrational Linelists and Einstein A-coefficients for the Primordial Molecules and Isotopologues

Amaral

Diniz

Jones

et al. 2019

ApJ

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Complete benchmark rovibrational energy linelists calculated for the primordial polar molecules of the universe, namely HD + , HD, and the HeH + isotopologues, with accuracy up to 10 −2 cm −1 for low-lying states, are presented. To allow for these calculations to be performed, new high-accuracy potential energy curves, which include the diagonal Born-Oppenheimer adiabatic corrections and the leading relativistic corrections, are determined. Also, a new approach for calculating non-adiabatic corrections involving an effective vibrational nuclear mass obtained based on the atoms-in-molecules theory is employed. The vibrational and rotational masses are taken as being different and dependent on the nuclear distance. Accurate dipole moment curves are calculated and used to generate lists of Einstein A-coefficients. The energy linelists and the sets of Einstein A-coefficients for HD are upgrades of previous calculations including quasibound states, while for HD + and HeH + and its isotopologues the present results represent significant improvement over the previous calculations. The results obtained here suggest that, with the inclusion of the non-adiabatic corrections, the accuracy limit at least for low-lying states might have been reached. Thus, further progress should involve accounting for even smaller effects such as the quantumelectrodynamics corrections. The present results represent the state-of-the-art of theoretical spectroscopy of the primordial polar molecules.

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“…As similar integrals were calculated in our previous works [25,26], we only show here the final results for term 1, term 2, and term 3.…”

Section: Orbit-orbit Hamiltonian Matrix Elementmentioning

confidence: 88%

Leading relativistic corrections for atomicPstates calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions

et al. 2018

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In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the L = 1 total orbital angular momentum (P states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest The determination of atomic energy levels and transition frequencies with spectroscopic precision (i.e., well below 1 cm −1 ) as well as the corresponding wave functions remains one of the most technically and computationally challenging tasks for the quantum theory of atoms and molecules. The amount of computations required grows very rapidly with each additional electron. As a result, retaining accuracy at manageable computational cost becomes a difficult task even for fewelectron systems. Many accurate methods of various natures have been developed in the electronic structure theory in the past several decades. However, in practical calculations most of them can reach only chemical accuracy (1 kcal/mol) and often cannot be applied to excited states. Yet some emerging physical problems related to precision measurements, atomic clocks, and high-resolution spectroscopy require very accurate quantum-mechanical calculations that exceed chemical accuracy by several orders of magnitude.Precise determination of the atomic energies, transition frequencies, and other basic properties requires precise calculation of the effects resulting not only from the strong Coulombic interactions between the particles but also from more subtle effects due to relativism, quantum electrodynamics (QED), and finite nuclear mass and size. There has been a steady progress Kramida and Martin [6]. Recently, ECGs were used to calculate the lowest S → P transitions of beryllium [7]. The calculations were performed with the infinite-nuclear-mass (INM) approach and the finite-mass effects were obtained using the perturbation theory. In that work, the leading relativistic corrections for the 2 1 S, 3 1 S, and 2 1 P states of beryllium were calculated using the INM wave functions. We should also mentioned our recent high-accuracy calculations of the lowest four 2 S states of the boron atom [8] where similar accuracy as achieved before for four-electron atoms was reached. In those calculations the finite-nuclearmass (FNM) approach was used. Thus, the finite-mass effects were directly incorporated in the nonrelativistic total energy, as well as in the relativistic corrections which were calcul...

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Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

Abstract: Articles you may be interested inIsotope shifts of the three lowest S 1 states of the B + ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections J. Chem. Phys. 132, 114109 (2010)

Cited by 14 publications

References 19 publications

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (
Ferenc
¹
,
Korobov
²
,
Mátyus
³

2020
Phys. Rev. Lett.

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (
Ferenc
¹
,
Korobov
²
,
Mátyus
³

2020
Phys. Rev. Lett.

Benchmark Rovibrational Linelists and Einstein A-coefficients for the Primordial Molecules and Isotopologues

Leading relativistic corrections for atomicPstates calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions

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Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

Abstract: Articles you may be interested inIsotope shifts of the three lowest S 1 states of the B + ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections J. Chem. Phys. 132, 114109 (2010)

Cited by 14 publications

References 19 publications

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ ( Ferenc1, Korobov2, Mátyus3 2020Phys. Rev. Lett.

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ ( Ferenc1, Korobov2, Mátyus3 2020Phys. Rev. Lett.

Benchmark Rovibrational Linelists and Einstein A-coefficients for the Primordial Molecules and Isotopologues

Leading relativistic corrections for atomicPstates calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions

Contact Info

Product

Resources

About

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (
Ferenc
¹
,
Korobov
²
,
Mátyus
³

2020
Phys. Rev. Lett.

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (
Ferenc
¹
,
Korobov
²
,
Mátyus
³

2020
Phys. Rev. Lett.