Photoionization of few electron systems with a hybrid Coupled Channels approach

We present the hybrid anti-symmetrized coupled channels method for the calculation of fully differential photo-electron spectra of multi-electron atoms and small molecules interacting with strong laser fields. The method unites quantum chemical few-body electronic structure with strong-field dynamics by solving the time dependent Schr\"odinger equation in a fully anti-symmetrized basis composed of multi-electron states from quantum chemistry and a one-electron numerical basis. Photoelectron spectra are obtained via the time dependent surface flux (tSURFF) method. Performance and accuracy of the approach are demonstrated for spectra from the helium and berryllium atoms and the hydrogen molecule in linearly polarized laser fields at wavelength from 21 nm to 400 nm. At long wavelengths, helium and the hydrogen molecule at equilibrium inter-nuclear distance can be approximated as single channel systems whereas beryllium needs a multi-channel description

Configuration Interaction calculations of positron binding to Be(3Po)

The Configuration Interaction method is applied to investigate the possibility of positron binding to the metastable beryllium (1s^22s2p 3Po) state. The largest calculation obtained an estimated energy that was unstable by 0.00014 Hartree with respect to the Ps + Be^+(2s) lowest dissociation channel. It is likely that positron binding to parent states with non-zero angular momentum is inhibited by centrifugal barriers.Comment: 12 pages, 2 figures, Elsevier tex format, In press Nucl.Instrum.Meth.Phys.Res.B positron issu

1D states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions

Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five 1D states (1s2 2p2, 1s2 2s1 3d1, 1s2 2s1 4d1, 1s2 2s1 5d1, and 1s2 2s1 6d1) of the beryllium atom (9Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular state

Prediction of 1P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the seven lowest 1s22s np (1P), n = 2. . . 8, states of the beryllium atom. The calculations explicitly include the effect of finite mass of 9Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12 500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s22s np(1P)→1s22s2 (1S) transition is about 12 cm−1. The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm−

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

The New Resonating Valence Bond Method for Ab-Initio Electronic Simulations

The Resonating Valence Bond theory of the chemical bond was introduced soon after the discovery of quantum mechanics and has contributed to explain the role of electron correlation within a particularly simple and intuitive approach where the chemical bond between two nearby atoms is described by one or more singlet electron pairs. In this chapter Pauling's resonating valence bond theory of the chemical bond is revisited within a new formulation, introduced by P.W. Anderson after the discovery of High-Tc superconductivity. It is shown that this intuitive picture of electron correlation becomes now practical and efficient, since it allows us to faithfully exploit the locality of the electron correlation, and to describe several new phases of matter, such as Mott insulators, High-Tc superconductors, and spin liquid phases

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

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, {\it without} the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of $D_e$=931.2 cm$^{-1}$ which agrees very well with recent experimentally derived estimates $D_e$=929.7$\pm 2$~cm$^{-1}$ [Science, 324, 1548 (2009)] and $D_e$=934.6~cm$^{-1}$ [Science, 326, 1382 (2009)]], as well the best composite theoretical estimates, $D_e$=938$\pm 15$~cm$^{-1}$ [J. Phys. Chem. A, 111, 12822 (2007)] and $D_e$=935.1$\pm 10$~cm$^{-1}$ [Phys. Chem. Chem. Phys., 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [Science, 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1$^1\Sigma^-_g$ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schr\"odinger equation in small molecules