Related papers: A note about the ground state of the hydrogen mole…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
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…
We consider $N$ interacting dipolar bosonic atoms at zero temperature in a double-well potential. This system is described by the two-space-mode extended Bose-Hubbard (EBH) Hamiltonian which includes (in addition to the familiar BH terms)…
A path integral ground state approach has been used to estimate the ground-state energy and structural properties of hydrogen fluoride molecules pinned to a one-dimensional lattice. In the simulations, the molecules are assumed to be rigid,…
An alternative multipole expansion of the correlation term is derived. Modified spherical Bessel type functions which simplify as a summation of multiple orders of basic trigonometric functions are generated from this new method. We use…
Variational, nonrelativisitic energies have been calculated for the ground state ($^3P_g$) and the lowest quintuplet state ($^5S_u$) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated…
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 treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of…
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…
We consider a finite number $N$ of interacting bosonic atoms at zero temperature confined in a one-dimensional double-well trap and study this system by using the two-site Bose-Hubbard (BH) Hamiltonian. For systems with $N=2$ and $N=3$, and…
An analysis shows that the ground state of the inhomogeneous system of interacting electrons in the static external field, which satisfies the thermodynamic limit, can be consistently described only using the Green function theory based on…
Within the "lowest Landau level approximation", we develop a method to find the ground state of a 2d system of interacting particles confined by a parabolic potential.
The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of…
A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to…
With the eigenfunctional theory, we study a general interacting electron system, and give a rigorous expression of its ground state energy which is composed of two parts, one part is contributed by the non-interacting electrons, and another…
Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the $a\,^3\Sigma_u^+$ state of He$_2$,…
The subject of this study is the exchange-correlation-energy functional of reduced density matrix functional theory. Approximations of this functional are tested by applying them to the homogeneous electron gas. We find that two…
We investigate the ground state energy of an electron coupled to a photon field. First, we regard the self-energy of a free electron, which we describe by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of the…
We recalculate the leading relativistic corrections for the ground electronic state of the hydrogen molecule using variational method with explicitly correlated functions which satisfy the interelectronic cusp condition. The new…
We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$H=((D-A)\cdot\boldsymbol{\sigma})^2-V$$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a…