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

Correlated-Gaussian calculations of the ground and low-lying excited states of the boron atom

Benchmark variational calculations of the four lowest 2P and 2S states of the boron atom (including the ground state) have been performed. The wave functions of the states have been expanded in terms of all-particle explicitly correlated Gaussian basis functions and the finite mass of the nucleus has been explicitly accounted for.Variational upper bounds for the nonrelativistic finite- and infinite-nuclear-mass energies of all considered states have been obtained with the relative convergence of the order of 10−7–10−8. Expectation values of the powers of the inter-particle distances and Dirac δ functions depending on those distances have also been computed. These calculations provide reference values that can be used to test other high-level quantum chemistry method

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

Variational calculations of excited states with zero total angular momentum vibrational spectrum of H2 without use of the Born–Oppenheimer approximation

Very accurate, rigorous and fully variational, all-particle, non-Born–Oppenheimer calculations of the vibrational spectrum of the H2 molecule have been performed. Very high accuracy has been achieved by expanding the wave functions in terms of explicitly correlated Gaussian functions with preexponential powers of the internuclear distance. An indicator of the high accuracy of the calculations is the new upper bound for the H2 nonrelativistic nonadiabatic ground state energy equal to 21.164 025 030 0 hartre

Nonrelativistic variational calculations of the positronium molecule and the positronium hydride

Highly accurate ground-state nonrelativistic variational calculations of Ps2, 1HPs, and HPs are reported. The calculations have been performed using 5000 explicitly correlated Gaussian basis functions and yielded the lowest variational energy upper bounds for these systems to date. The relative accuracies of the energies obtained are of the order of 4 10−10 a.u. for Ps2 and 2 10−9 a.u. for HP. Several expectation values have also been computed for each system, as well as electron-positron annihilation rate

Explicitly correlated Gaussian calculations of the 2Po Rydberg spectrum of the lithium atom

Accurate quantum-mechanical nonrelativistic variational calculations are performed for the nine lowest members of the 2Po Rydberg series (1s2np1, n = 2, . . . , 10) of the lithium atom. The effect of the finite nuclear mass is included in the calculations allowing for determining the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The calculated state energies are compared with the available experimental dat

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

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximatio

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