Related papers: Accurate Born-Oppenheimer potentials for excited $…
We report on accurate variational calculations of the Born-Oppenheimer potential for excited states of the hydrogen molecule with $\Pi$, $\Delta$, and $\Phi$ symmetries. The obtained potential energy curves reach the relative precision of…
We demonstrate high accuracy calculations for the HeH$^+$ molecule using newly developed analytic formulas for two-center two-electron integrals with exponential functions. The Born-Oppenheimer potential for the ground electronic…
A general approach to evaluation of two-centre two-electron exponential integrals with arbitrary parameters is presented. The results for the Born-Oppenheimer potential for various excited states of molecular hydrogen with Ko{\l}…
The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small…
Adopting explicitly correlated Kolos-Wolniewicz-type basis functions, the Born-Oppenheimer potential curves of a number of excited $\Sigma$ states of the hydrogen-antihydrogen system ($\bar{\rm H}$) were calculated for both, even and odd, Q…
Excited states of the hydrogen molecule subject to a homogeneous magnetic field are investigated for the parallel configuration in the complete regime of field strengths B=0-100a.u.. Up to seven excitations are studied for gerade as well as…
Three simple $7-, (7+3)-, 10-$parametric trial functions for the ${\rm H}_3^+$ molecular ion are presented. Each of them provides subsequently the most accurate approximation for the Born-Oppenheimer ground state energy among…
Potential energy surfaces of the hydrogen molecular ion H$_2^+$ in the Born-Oppenheimer approximation are computed by means of the Riccati-Pad\'e method (RPM). The convergence properties of the method are analyzed for different states. The…
The difference of the values of observables for the time-independent Schroedinger equation, with matrix valued potentials, and the values of observables for ab initio Born-Oppenheimer molecular dynamics, of the ground state, depends on the…
The static dipole polarizabibility for the $1s\sigma$ electron state of the $\mathrm{H}_{2}^{+}$ hydrogen molecular ion is calculated within Born-Oppenheimer approximation. The variational expansion with randomly chosen exponents has been…
For rovibronic states corresponding to the $B$ and $B'\ ^1\Sigma_\text{u}^+$ 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…
Bound states of the Hellmann potential, which is a superposition of the attractive Coulomb ($-A/r$) and the Yukawa ($Be^{-Cr}/r$) potential, are calculated by using a generalized pseudospectral method. Energy eigenvalues accurate up to…
Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule \hh in inclined configuration, where the molecular axis forms an angle $\theta$ with respect…
We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state X $^1\Sigma_{\mathrm{g}}^+$ of the $^{39}$K$_2$ molecule. The molecules are prepared in a…
We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We…
In this work, we use the Born-Oppenheimer approximation where the potential between atoms can be approximated as a function of distance between the two nuclei to study the four-quark bound states. By the approximation, Heitler and London…
The total energies and various bound state properties of the excited $2^1S(L = 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He, ${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy. The…
Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a…
The analytic Born-Oppenheimer (B-O) potential curve for the ground state $X^1\Sigma^+$ of the molecule (H,D,T)Cl is constructed for the whole range of internuclear distances $R \in [0,\infty)$ with an accuracy of 3-5 figures in comparison…
We present high-precision non-relativistic variational calculations of bound vibrational-rotational state energies for the $H_2^+$ and $D_2^+$ molecular ions in each of the lowest electronic states of $\Sigma_g$, $\Sigma_u$, and $\Pi_u$…