Related papers: Nonadiabatic relativistic correction in H$_2$, D$_…
Nonadiabatic corrections in molecules composed of a few atoms are considered. It is demonstrated that a systematic perturbative expansion around the adiabatic solution is possible, with the expansion parameter being the electron-nucleus…
The leading nonadiabatic corrections to rovibrational levels of a diatomic molecule are expressed in terms of three functions of internuclear distance: corrections to the adiabatic potential, the effective nuclear mass, and the effective…
Accurate predictions for hydrogen molecular levels require the treatment of electrons and nuclei on an equal footing. While nonrelativistic theory has been effectively formulated this way, calculation of relativistic and quantum…
The mass-correction functions in the second-order non-adiabatic Hamiltonian are computed for the $^4$He$^+_2$ molecular ion using the variational method, floating explicitly correlated Gaussian functions, and a general…
We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation,…
We present a new computational method for the determination of energy levels in four-particle systems like H$_2$, HD, and HeH$^+$ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the…
The nonrelativistic energy together with relativistic and quantum electrodynamic corrections for all the molecular hydrogen isotopologues (D$_2$, T$_2$, HD, HT, DT) were evaluated without expansion in the electron-nucleus mass ratio. The…
General transformation expressions of the second-order non-adiabatic Hamiltonian of the atomic nuclei, including the kinetic-energy correction terms, are derived upon the change from laboratory-fixed Cartesian coordinates to general…
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 $D^{(1)}(R)$,…
The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching…
We present a nonrelativistic calculation of the rotation-vibration levels of the molecular ions H2+, D2+ and HD+, relying on the diagonalization of the exact three-body Hamiltonian. The J=2 levels are obtained with a very high accuracy of…
The nonrelativistic variational calculation of a complete set of ro-vibrational states in the H$_2^+$ molecular ion supported by the ground $1s\sigma$ adiabatic potential is presented. It includes both bound states and resonances located…
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…
The nonrelativistic energy of low lying rovibrational levels of HT, DT, and \T\ is determined to an absolute accuracy of $10^{-7}-10^{-8}$ cm$^{-1}$ using the variational method with the four-body nonadiabatic James-Coolidge functions. The…
The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2S_{1/2}, 2P_{1/2} and 2P_{3/2} were obtained by using…
The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set…
The relativistic corrections for the Dirac-Coulomb system are derived through the method of non-relativistic expansion. By expanding the large and small components of the Dirac wave function and the energy eigenvalues in terms of the square…
We report the potential energy curve, the diagonal Born-Oppenheimer, non-adiabatic mass, relativistic, and leading-order QED corrections for the ground electronic state of the helium dimer cation; the higher-order QED and finite-nuclear…
We analyse a modified Dirac equation based on a noncommutative structure in phase space. The noncommutative structure induces generalised momenta and contributions to the energy levels of the standard Dirac equation. Using techniques of…
The (stationary) Schr\"{o}dinger equation for atomistic systems is solved using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. Despite being very simplistic, this approach is very powerful and used…