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Synopsis We discuss the implementation (https://commons.lbl.gov/display/csd/LBNL-AMO-MCTDHF) of Multiconfiguration Time-Dependent Hartree-Fock for polyatomic molecules using a Cartesian product grid of sinc basis functions, and present absorption cross sections and other results calculated with it.

Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are maximal. We identify the CF's quantum numbers as the angular momentum L in (L_e L_v)L, its magnetic projection m_L, the electron number N, with L_v={N-1)/2, and magnetic \\nu-spin, m_\\nu=L_e-L_v. Translationally invariant FQHE states are formed by filling p subshells with their respective CFs, in order of ascending L for fixed L_e and L_v, beginning with the lowest allowed value, L=|m_\\nu|. We show that this wave function has an exactly equivalent hierarchical form. FQHE states can be grouped into \\nu-spin multiplets mirror symmetric around m_\\nu=0, with N held constant. Electron particle-hole conjugation with respect to this vacuum is identified as the mirror symmetry relating FQHE states of the same N but distinct fillings \\nu = p/(2p+1} and p/( 2p-1). Alternatively, mirror symmetric \\nu-spin multiplets can be constructed in which the magnetic field strength is held fixed: the valence states are electron particle-vortex hole excitations. Particle-hole symmetry -- relating the N-particle FQHE state of filling \\nu=p/(2p+1} to the \\(\\bar{N}\\)-particle state of filling {p+1)/(2p+1} -- is shown to be equivalent to electron-vortex exchange. In this construction \\(\\bar{N}\\)-N CFs of the higher density state occupy an extra zero-mode subshell. We link this structure, familiar from supersymmetric quantum mechanics, to the CF Pauli Hamiltonian, which we show is isospectral, quadratic in the \\nu-spin raising and lowering operators, and four-fold degenerate. On linearization, it takes a Dirac form similar to that found in the integer quantum Hall effect (IQHE).

The global optimum for valence population transfer in the NO\\(_2\\) molecule driven by impulsive x-ray stimulated Raman scattering of one-femtosecond x-ray pulses tuned below the Oxygen K-edge is determined with the Multiconfiguration Time-Dependent Hartree-Fock method, a fully-correlated first-principles treatment that allows for the ionization of every electron in the molecule. Final valence state populations computed in the fixed-nuclei, nonrelativistic approximation are reported as a function of central wavelength and intensity. The convergence of the calculations with respect to their adjustable parameters is fully tested. Fixing the 1fs duration but varying the central frequency and intensity of the pulse, without chirp, orientation-averaged maximum population transfer of 0.7\\% to the valence B\\(_1\\) state is obtained at an intensity of 3.16\\(\\times\\)10\\(^{17}\\) W cm\\(^{-2}\\), with the central frequency substantially 6eV red-detuned from the 2nd order optimum; 2.39\\% is obtained at one specific orientation. The behavior near the global optimum, below the Oxygen K-edge, is consistent with the mechanism of nonresonant Raman transitions driven by the near-edge fine structure oscillator strength.

A set of scalar operators are employed to generate explicit representations of both hierarchy states (e.g., the series of fillings 1/3, 2/5, 3/7, ... ) and their conjugates (fillings 1, 2/3, 3/5, ...) as non-interacting quasi-electrons filling fine-structure sub-shells within the FLL. This yields, for planar and spherical geometries, a quasi-electron representation of the incompressible FLL state of filling p/(2p +1) in a magnetic field of strength B that is algebraically identical to the IQHE state of filling p in a magnetic field of strength B/(2p+1). The construction provides a precise definition of the quasi-electron/composite fermion that differs in some respects from common descriptions: they are eigenstates of L,Lz; they and the FLL subshells they occupy carry a third index I that is associated with breaking of scalar pairs; they absorb in their internal wave functions one, not two, units of magnetic flux; and they share a common, simple structure as vector products of a spinor creating an electron and one creating magnetic flux. We argue that these properties are a consequence of the breaking of the degeneracy of noninteracting electrons within the FLL by the scale-invariant Coulomb potential. We discuss the sense in which the wave function construction supports basic ideas of both composite fermion and hierarchical descriptions of the FQHE. We describe symmetries of the quasi-electrons at half filling, where a deep Fermi sea of quasi-electrons forms, and the quasi-electrons take on Majorana and pseudo-Dirac characters. Finally, we show that the wave functions can be viewed as fermionic excitations of the bosonic half-filled shell, producing at half filling an operator that differs from but plays the same role as the Pfaffian.

A technique for measuring photoionization time delays with attosecond precision is combined with calculations of photoionization matrix elements to demonstrate how multi-electron dynamics affect photoionization time delays in carbon dioxide. Electron correlation is observed to affect the time delays through two mechanisms: autoionization of molecular Rydberg states and accelerated escape from a continuum shape resonance.

Total and partial cross sections for breakup of ground rovibronic state of H\\(_2^+\\)by photon impact are calculated using the exact nonadiabatic nonrelativistic Hamiltonian without approximation. The converged results span six orders of magnitude. The breakup cross section is divided into dissociative excitation and dissociative ionization. The dissociative excitation channels are divided into contributions from principal quantum numbers 1 through 4. For dissociative ionization the kinetic energy sharing is calculated using a formally exact expression. These results are compared with approximate expressions, and it is shown that the Born-Oppenheimer result is surprisingly accurate, whereas using Born-Oppenheimer final states to extract the cross sections from the full nonadiabatic wave function produces pathologies near threshold.

We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multi-configurational time-dependent Hartree-Fock (MCTDHF) method. For the optimal control, which requires running multiple propagations to determine the optimal pulse sequence, we used the computationally inexpensive time-dependent configuration interaction singles (TDCIS) method. TDCIS captures all of the necessary correlation of the desired processes but assumes that ionization pathways reached via double excitations are not present. MCTDHF includes these pathways and all multiparticle correlations in a set of time-dependent orbitals. The mechanism that was determined to be optimal in the Raman excitation of the Ne \\(1s^22s^22p^53p^1\\) valence state via the metastable \\(1s^22s^12p^63p^1\\) resonance state involves a sequential resonance-valence excitation. First, a long pump pulse excites the core-hole state, and then a shorter Stokes pulse transfers the population to the valence state. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a factor of 4.

The dynamics of autoionizing Rydberg states of oxygen are studied using attosecond transient absorption technique, where extreme ultraviolet (XUV) initiates molecular polarization and near infrared (NIR) pulse perturbs its evolution. Transient absorption spectra show positive optical density (OD) change in the case of \\(ns\\sigma_g\\) and \\(nd\\pi_g\\) autoionizing states of oxygen and negative OD change for \\(nd\\sigma_g\\) states. Multiconfiguration time-dependent Hartree-Fock (MCTDHF) calculation are used to simulate the transient absorption spectra and their results agree with experimental observations. The time evolution of superexcited states is probed in electronically and vibrationally resolved fashion and we observe the dependence of decay lifetimes on effective quantum number of the Rydberg series. We model the effect of near-infrared (NIR) perturbation on molecular polarization and find that the laser induced phase shift model agrees with the experimental and MCTDHF results, while the laser induced attenuation model does not. We relate the electron state symmetry dependent sign of the OD change to the Fano parameters of the static absorption lineshapes.

Impulsive X-ray Raman excitations of Lithium, Neon, and Sodium are calculated using the Multiconfiguration Time-Dependent Hartree-Fock method. Using linearly polarized laser pulses without chirp, we determine the optimum central frequency, intensity, and duration for maximum population transfer to valence excited states. We demonstrate the existence of two local optima or \"sweet spots\" for population transfer, either of which, depending on the system, may be superior. For some systems we find that population transfer can be maximized by nonresonant Raman transitions, red-detuned below K-edge, because such detuning minimizes core-excited populations and ionization loss. For instance, in Neon near the K-edge the global optimum for population transfer occurs at high intensity (8 \\(\\times\\) 10\\(^{19}\\) W cm\\(^{-2}\\)), short duration (82as full-width-at-half-maximum), and 24eV red-detuned from the K-edge.

The HeH\\(^+\\) cation undergoes dissociative recombination with a free electron to produce neutral He and H fragments. We present calculations using ab initio quantum defects and Fano's rovibrational frame transformation technique, along with the methodology of PRL 89, 263003 (2002), to obtain the recombination rate both in the low-energy (1-300 meV) and high-energy (ca. 0.6 hartree) regions. We obtain very good agreement with experimental results, demonstrating that this relatively simple method is able to reproduce observed rates for both indirect dissociative recombination, driven by rovibrationally autoionizing states in the low-energy region, and direct dissociative recombination, driven by electronically autoionizing Rydberg states attached to higher-energy excited cation channels.