Ground-state energy and relativistic corrections for positronium hydride

Variational calculations of the ground state of positronium hydride (HPs) are reported, including various expectation values, electron-positron annihilation rates, and leading relativistic corrections to the total and dissociation energies. The calculations have been performed using a basis set of 4000 thoroughly optimized explicitly correlated Gaussian basis functions. The relative accuracy of the variational energy upper bound is estimated to be of the order of 2×10−10, which is a significant improvement over previous nonrelativistic result

Assessment of the accuracy the experimental energies of the 1Po 1s22s6p and 1s22s7p states of 9Be based on variational calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the six lowest states of the 1Po 1s22snp state series of the 9Be atom. The wave functions of the states are expanded in terms of all-particle, explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations. The exponential parameters of the Gaussians are variationally optimized using the analytical energy gradient determined with respect to those parameters. Besides providing reference non-relativistic energies for the considered states, the calculations also allow to assess the accuracy of the experimental energies of the 1Po 1s22s6p and 1s22s7p states and suggest their refinemen

Non-Born-Oppenheimer variational calculation of the ground-state vibrational spectrum of LiH+

Very accurate, rigorous, variational, non-Born-Oppenheimer non-BO calculations have been performed for the fully symmetric, bound states of the LiH+ ion. These states correspond to the ground and excited vibrational states of LiH+ in the ground 2 + electronic state. The non-BO wave functions of the states have been expanded in terms of spherical N-particle explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance and 5600 Gaussians were used for each state. The calculations that, to our knowledge, are the most accurate ever performed for a diatomic system with three electrons have yielded six bound states. Average interparticle distances and nucleus-nucleus correlation function plots are presente

Nonrelativistic molecular quantum mechanics without approximations: Electron affinities of LiH and LiD

We took the complete nonrelativistic Hamiltonians for the LiH and LiH2 systems, as well as their deuterated isotopomers, we separated the kinetic energy of the center of mass motion from the Hamiltonians, and with the use of the variational method we optimized the ground-state nonadiabatic wave functions for the systems expanding them in terms of n-particle explicitly correlated Gaussian functions. With 3600 functions in the expansions we obtained the lowest ever ground-state energies of LiH, LiD, LiH2, and LiD2 and these values were used to determine LiH and LiD electrons affinities ~EAs! yielding 0.330 30 and 0.327 13 eV, respectively. The present are the first high-accuracy ab initio quantum mechanical calculations of the LiH and LiD EAs that do not assume the Born-Oppenheimer approximation. The obtained EAs fall within the uncertainty brackets of the experimental result

Non-Born–Oppenheimer study of positronic molecular systems: e¿LiH

Very accurate non-Born–Oppenheimer variational calculations of the ground state of e1LiH have been performed using explicitly correlated Gaussian functions with preexponential factors dependent on powers of the internuclear distance. In order to determine the positron detachment energy of e1LiH and the dissociation energy corresponding to the e1LiH fragmentation into HPs and Li1 we also calculated non-BO energies of HPs, LiH, and Li1. For all the systems the calculations provided the lowest ever-reported variational upper-bounds to the ground state energies. Annihilation rates of HPs and e1LiH were also computed. The dissociation energy of e1LiH into HPs and Li1 was determined to be 0.036 548 hartre

Accurate variational calculations of the ground 2Po(1s22s22p) and excited 2S(1s22s2p2) and 2Po(1s22s23p) states of singly ionized carbon atom

In this article we report accurate nonrelativistic variational calculations of the ground and two excited states of C+ ion. We employ extended and well optimized basis sets of all-electron explicitly correlated Gaussians to represent the wave functions of the states. The optimization of the basis functions is performed with a procedure employing the analytic gradient of the energy with respect to the nonlinear parameters of the Gaussians. The calculations explicitly include the effects due to the finite nuclear mass. The calculated transition energies between the three states are compared to the experimentally derived values. Finally, we present expectation values of some small positive and negative powers of the interparticle distances and contact densitie

Nonrelativistic molecular quantum mechanics without approximations: Electron affinities of LiH and LiD

We took the complete nonrelativistic Hamiltonians for the LiH and LiH2 systems, as well as their deuterated isotopomers, we separated the kinetic energy of the center of mass motion from the Hamiltonians, and with the use of the variational method we optimized the ground-state nonadiabatic wave functions for the systems expanding them in terms of n-particle explicitly correlated Gaussian functions. With 3600 functions in the expansions we obtained the lowest ever ground-state energies of LiH, LiD, LiH2, and LiD2 and these values were used to determine LiH and LiD electrons affinities ~EAs! yielding 0.330 30 and 0.327 13 eV, respectively. The present are the first high-accuracy ab initio quantum mechanical calculations of the LiH and LiD EAs that do not assume the Born-Oppenheimer approximation. The obtained EAs fall within the uncertainty brackets of the experimental result

Calculations of the ground states of BeH and BeH+ without the Born-Oppenheimer approximation

Non-Born-Oppenheimer variational calculations employing explicitly correlated Gaussian basis functions have been performed for the ground states of the beryllium monohydride molecule BeH and its ion BeH+ , as well as for the beryllium atom Be and its ion Be+ . An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed. The calculated energies were used to determine the ionization potential of BeH and the dissociation energies of BeH and BeH+. Also, the generated wave functions were used to compute various expectation values, such as the average interparticle distances and the nucleus-nucleus correlation function

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy Coulomb interaction matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule with the negative parity . Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energ

Assessment of the accuracy the experimental energies of the 1Po 1s22s6p and 1s22s7p states of 9Be based on variational calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the six lowest states of the 1Po 1s22snp state series of the 9Be atom. The wave functions of the states are expanded in terms of all-particle, explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations. The exponential parameters of the Gaussians are variationally optimized using the analytical energy gradient determined with respect to those parameters. Besides providing reference non-relativistic energies for the considered states, the calculations also allow to assess the accuracy of the experimental energies of the 1Po 1s22s6p and 1s22s7p states and suggest their refinemen