Haruhide Miyagi

Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics

We present the time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory as a new framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high-order harmonic generation spectra of a one-dimensional model of atomic beryllium interacting with a strong laser pulse, the TD-RASSCF method is reasonably accurate while largely reducing the computational complexity. The TD-RASSCF method has the potential to treat large atoms and molecules beyond the capability of the MCTDHF method.

Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics. II. Extended formulation and numerical analysis

The time-dependent restricted-active-space self-consistent-field (TD-RASSCF) method is formulated based on the TD variational principle. In analogy with the configuration-interaction singles (CIS), singles-and-doubles (CISD), singles-doubles-and-triples (CISDT) methods in quantum chemistry, the TD-RASSCF-S, -SD, and -SDT methods are introduced as extensions of the TD-RASSCF dou- bles (-D) method [Phys. Rev. A 87, 062511 (2013)]. Based on an analysis of the numerical cost and test calculations for one-dimensional (1D) models of atomic helium, beryllium, and carbon, it is shown that the TD-RASSCF-S and -D methods are computationally feasible for systems with many electrons and more accurate than the TD Hartree-Fock (TDHF) and TDCIS methods. In addition to the discussion of methodology, an analysis of electron dynamics in the high-order harmonic generation (HHG) process is presented. For the 1D beryllium atom, a state-resolved analysis of the HHG spectrum based on the time-independent HF orbitals shows that while only single-orbital excitations are needed in the region below the cutoff, single- and double-orbital excitations are es- sential beyond, where accordingly the single-active-electron (SAE) approximation and the TDCIS method break down. On the other hand, the TD-RASSCF-S and -D methods accurately describe the multi-orbital excitation processes throughout the entire region of the HHG spectrum. For the 1D carbon atom, our calculations show that multi-orbital excitations are essential in the HHG process even below the cutoff. Hence, in this test system a very accurate treatment of electron correlation is required. The TD-RASSCF-S and -D approaches meet this demand, while the SAE approximation and the TDCIS method are inadequate.

Time-dependent restricted-active-space self-consistent-field singles method for many-electron dynamics

The time-dependent restricted-active-space self-consistent-field singles (TD-RASSCF-S) method is presented for investigating TD many-electron dynamics in atoms and molecules. Adopting the SCF notion from the muticonfigurational TD Hartree-Fock (MCTDHF) method and the RAS scheme (single-orbital excitation concept) from the TD configuration-interaction singles (TDCIS) method, the TD-RASSCF-S method can be regarded as a hybrid of them. We prove that, for closed-shell Ne-electron systems, the TD-RASSCF-S wave function can be fully converged using only Ne/2 + 1 ⩽ M ⩽ Ne spatial orbitals. Importantly, based on the TD variational principle, the converged TD-RASSCF-S wave function with M = Ne is more accurate than the TDCIS wave function. The accuracy of the TD-RASSCF-S approach over the TDCIS is illustrated by the calculation of high-order harmonic generation spectra for one-dimensional models of atomic helium, beryllium, and carbon in an intense laser pulse. The electronic dynamics during the process is investigated by analyzing the behavior of electron density and orbitals. The TD-RASSCF-S method is accurate, numerically tractable, and applicable for large systems beyond the capability of the MCTDHF method.

Doubly excited states of methane produced by photon and electron interactions

The formation and decay of doubly excited methane in photon and electron interactions have been investigated through measuring (i) the cross sections for the emission of the Lyman-α fluorescence in the photoexcitation of CH4 as a function of incident photon energy in the range 18–51 eV and (ii) the electron-energy-loss spectrum of CH4 tagged with the Lyman-α photons at 80 eV incident electron energy and 10° electron scattering angle in the range of the energy loss 20–45 eV. Five superexcited states have been found, three of which are doubly excited states with the others being singly excited states. It has been found that the electron interaction with CH4 at 80 eV incident electron energy and 10° electron scattering angle accelerates the double excitation against the single excitation as compared with the photon interaction.

Inner-valence excited and multiply excited states of molecular oxygen around the double-ionization potential as probed by a pair of fluorescence photons

The cross sections for the generation of a pair of fluorescence photons in the photoexcitation of O2 differential with respect to solid angles for the emission of the photon pair have been measured as a function of incident photon energy in the range 23?47 eV using the photon?photon coincidence method, the (?, 2?) method, to investigate the inner-valence excited states and multiply excited states of O2 as superexcited states. Four superexcited states of O2 with the 3??u or 3?u symmetry have been newly found around 29, 36, 38 and 44 eV in the measured cross section curve free from ionization. It turns out that they are inner-valence excited states and multiply excited states. Two remarkable points are shown: (1) there exist superexcited states of O2 dissociating into neutral fragments even in the energy range above the double-ionization potential of O2 at 36.13 eV and (2) the values of the doubly differential cross sections decrease to a large extent around the double-ionization potential with increasing incident photon energy, both of which have been compared with the results of N2 by our previous (?, 2?) experiment. The origin of (2) is discussed in detail.

Exterior time scaling with the stiffness-free Lanczos time propagator: Formulation and application to atoms interacting with strong midinfrared lasers

Aiming at efficient numerical treatment of tunneling ionization of atoms and molecules by mid-infrared (IR) lasers, exterior time scaling (ETS) theory is formulated as a generalization of the time-scaled coordinate approach. The key idea of ETS is the division of the spatial volume into a small region around the nucleus and its outside; the radial coordinates are time scaled only in the outer region. The continuum components of photoelectron wave packets are prevented from reaching the edge of the spatial simulation volume, enabling the long-time evolution of wave packets with a relatively small number of basis functions without concerns of electron reflections. On the other hand, the bound-state components are free from shrinking toward the origin because of non-time scaling in the inner region. Hence, the equations of motion in ETS are less stiff than the ones in the original time-scaled coordinate approach in which the shrinking bound states make the equations of motion seriously stiff. For numerical implementation of ETS, the working equations are derived in terms of finite-element discrete-variable-representation functions. Furthermore, the stiffness-free Lanczos time propagator is introduced to remove any persistent stiffness in the treatment of mid-IR lasers due to the involvement of hundreds of angular-momentum states. The test calculations for atomic hydrogen interacting with linearly polarized mid-IR pulses demonstrate the accuracy and numerical efficiency of the new scheme, and exhibit its special capability if there is no recollision with the parent ion. Hence, ETS will show its true potential for the detailed analysis of photoelectron wave packet dynamics in circularly or near-circularly polarized mid-IR fields.

The electron-energy-loss spectra of methane tagged with Lyman-α photons in the range of doubly excited states

The doubly excited states of methane produced in electron interaction have been investigated by measuring the electron-energy-loss spectra tagged with Lyman-α photons at 80 eV incident electron energy and electron scattering angles of 12° and 24°. The triply differential cross sections at both angles have been put on the same relative scale for the first time as a function of energy loss. It turned out that electron interaction with methane at 80 eV incident electron energy increases double excitation against single excitation as compared with photon interaction up to 24° electron scattering angle.

Theoretical study on the angular correlation of two Lyman-α photons generated by single-photon absorption of a hydrogen molecule

The angular correlation of two Lyman-α photons generated by the linearly polarized single-photon absorption of H2(X 1Σg+) followed by the neutral dissociation of the doubly excited Q21Πu(1) state has been theoretically investigated with the second-order correlation function in quantum optics. A strong angular correlation has been obtained even for the molecules randomly oriented in space, due to the complicated entanglement of two H(2p) atoms in the intermediate state. It has been revealed how the symmetry properties in the electronic state are transferred to the two-photon state and how they manifest themselves in the angular correlation function.