相关论文: {H$_2^+$, HeH and H$_2$}: approximating potential …
Basics of the Born-Oppenheimer (B-O) approximation are reviewed. Assuming the domain of applicability of B-O approximation is limited to 4 significant digits (s.d.) in energy spectrum, where mass, relativistic and QED corrections do NOT…
Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in {\it J. Phys. B44, 101002 (2011)}. The ten low-lying eigenstates of…
An analytical representation for the potential energy curve for the ground state $X^1\Sigma^+$ of the hydrogen fluoride molecule (HF) is presented in the frame of the Born-Oppenheimer approximation. The analytical expression for the…
Following the first principles the elements of the analytic theory of potential curves for diatomic molecules (diatomics) are presented. It is based on matching the perturbation theory at small internuclear distances $R$ and multipole…
This work presents the bound-state spectra of Morse oscillator, which remains one of the oldest important model potentials for molecules. Accurate ro-vibrational energies are obtained by means of a generalized pseudospectral method that…
The experimentally-observed non-trivial electronic structure of the Cr$_2$ dimer has made the calculation of its potential energy curve a theoretical challenge in the last decades. By matching the perturbation theory at small internuclear…
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 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…
A potential energy curve (PEC) accurate to a fraction of 1 ppm ($1:10^6$) is computed for the $^3\Sigma_\mathrm{u}^+$ state of He$_2$ endowed with relativistic and QED corrections. The nuclear Schr\"odinger equation is solved on this PEC…
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 $\Pi_u$…
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…
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…
The main motivation for this work is the exploration of rotational-vibrational states corresponding to electronic excitations in a pre-Born-Oppenheimer quantum theory of molecules. These states are often embedded in the continuum of the…
Bound-state spectra of shifted Deng-Fan oscillator potential are studied by means of a generalized pseudospectral method. Very accurate results are obtained for \emph{both low as well as high} states by a non-uniform optimal discretization…
We present an ab initio study of the HeH$^+$ molecule. Using the quantum chemistry package MOLPRO and a large adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 $^1 \Sigma^+$, 19 $^3\Sigma^+$, 12…
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…
Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schr\"odinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization.…
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 non-relativistic three-body Schr\"odinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or…
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…