Hylleraas-Configuration Interaction study of the 1S ground state of the negative Li ion.

In a previous work Sims and Hagstrom [J. Chem. Phys. 140, 224312 (2014)] reported Hylleraas-Configuration Interaction (Hy-CI) method variational calculations for the neutral atom and positive ion 1S ground states of the beryllium isoelectronic sequence. The Li- ion, nominally the first member of this series, has a decidedly different electronic structure. This paper reports the results of a large, comparable calculation for the Li- ground state to explore how well the Hy-CI method can represent the more diffuse L shell of Li- which is representative of the Be(2sns) excited states as well. The best non-relativistic energy obtained was -7.500 776 596 hartree, indicating that 10 - 20 nh accuracy is attainable in Hy-CI and that convergence of the r12r34 double cusp is fast and that this correlation type can be accurately represented within the Hy-CI model.

Hylleraas-configuration-interaction nonrelativistic energies for the ¹S ground states of the beryllium isoelectronic sequence.

In a previous work, Sims and Hagstrom ["Hylleraas-configuration-interaction study of the 1 (1)S ground state of neutral beryllium," Phys. Rev. A 83, 032518 (2011)] reported Hylleraas-configuration-interaction (Hy-CI) method variational calculations for the (1)S ground state of neutral beryllium with an estimated accuracy of a tenth of a microhartree. In this work, the calculations have been extended to higher accuracy and, by simple scaling of the orbital exponents, to the entire Be 2 (1)S isoelectronic sequence. The best nonrelativistic energies for Be, B(+), and C(++) obtained are -14.6673 5649 269, -24.3488 8446 36, and -36.5348 5236 25 hartree, respectively. Except for Be, all computed nonrelativistic energies are superior to the known reference energies for these states.

Exponentially correlated Hylleraas-configuration interaction non-relativistic energy of the 1S ground state of the helium atom.

A generalization of the Hylleraas-Configuration Interaction method (Hy-CI) first proposed by Wang, et al., the Exponentially Correlated Hylleraas-Configuration Interaction method (E-Hy-CI) in which the single r ij of an Hy-CI wave function is generalized to a form of the generic type r i j ν i j e - ω i j r i j , is explored. This type of correlation, suggested by Hirshfelder in 1960, has the right behavior both in the vicinity of the rij cusp as rij goes to 0 and as rij goes to infinity; this work explores whether wave functions containing both linear and exponential r ij factors converge more rapidly than either one alone. The method of calculation of the two-electron E-Hy-CI kinetic energy and electron repulsion integrals in a stable and efficient way using recursion relations is discussed, and the relevant formulas are given. The convergence of the E-Hy-CI wave function expansion is compared with that of the Hy-CI wave function without exponential correlation factors, demonstrating both convergence acceleration and an improvement in the accuracy for the same basis. This makes the application of the E-Hy-CI method to systems with N > 4, for which this formalism with at most a single r i j ν i j e - ω i j r i j factor per term leads to solvable integrals, very promising. E-Hy-CI method variational calculations with up to 10080 expansion terms are reported for the ground 1 S state of the neutral helium atom, with a resultant nonrelativistic energy of -2.9037 2437 7034 1195 9831 1084 hartree for the best expansion.

Accelerating Scientific Discovery Through Computation and Visualization III. Tight-Binding Wave Functions for Quantum Dots.

This is the third in a series of articles that describe, through examples, how the Scientific Applications and Visualization Group (SAVG) at NIST has utilized high performance parallel computing, visualization, and machine learning to accelerate scientific discovery. In this article we focus on the use of high performance computing and visualization for simulations of nanotechnology.

Simulation of Sheared Suspensions With a Parallel Implementation of QDPD.

A parallel quaternion-based dissipative particle dynamics (QDPD) program has been developed in Fortran to study the flow properties of complex fluids subject to shear. The parallelization allows for simulations of greater size and complexity and is accomplished with a parallel link-cell spatial (domain) decomposition using MPI. The technique has novel features arising from the DPD formalism, the use of rigid body inclusions spread across processors, and a sheared boundary condition. A detailed discussion of our implementation is presented, along with results on two distributed memory architectures. A parallel speedup of 24.19 was obtained for a benchmark calculation on 27 processors of a distributed memory cluster.

Accelerating Scientific Discovery Through Computation and Visualization II.

This is the second in a series of articles describing a wide variety of projects at NIST that synergistically combine physical science and information science. It describes, through examples, how the Scientific Applications and Visualization Group (SAVG) at NIST has utilized high performance parallel computing, visualization, and machine learning to accelerate research. The examples include scientific collaborations in the following areas: (1) High Precision Energies for few electron atomic systems, (2) Flows of suspensions, (3) X-ray absorption, (4) Molecular dynamics of fluids, (5) Nanostructures, (6) Dendritic growth in alloys, (7) Screen saver science, (8) genetic programming.

High precision variational calculations for the Born-Oppenheimer energies of the ground state of the hydrogen molecule.

Born-Oppenheimer approximation Hylleraas variational calculations with up to 7034 expansion terms are reported for the 1sigma(g)+ ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be -1.174 475 714 220(1) hartree at R = 1.4 bohr, which is four orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz [J. Chem. Phys. 103, 1792 (1995)]. This result agrees well with the best previous variational energy, -1.174 475 714 216 hartree, of Cencek (personal communication), obtained using explicitly correlated Gaussians (ECGs) [Cencek and Rychlewski, J. Chem. Phys. 98, 1252 (1993); Cencek et al., ibid. 95, 2572 (1995); Rychlewski, Adv. Quantum Chem. 31, 173 (1998)]. The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be -1.174 475 931 399(1) hartree at the equilibrium R = 1.4011 bohr distance. This result also agrees well with the best previous variational energy, -1.174 475 931 389 hartree, of Cencek and Rychlewski [Rychlewski, Handbook of Molecular Physics and Quantum Chemistry, edited by S. Wilson (Wiley, New York, 2003), Vol. 2, pp. 199-218; Rychlewski, Explicitly Correlated Wave Functions in Chemistry and Physics Theory and Applications, edited by J. Rychlewski (Kluwer Academic, Dordrecht, 2003), pp. 91-147.], obtained using ECGs.