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Multielectron effects in high harmonic generation in N2 and benzene: Simulation using a non-adiabatic quantum molecular dynamics approach for laser-molecule interactions
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10.1063/1.4718590
/content/aip/journal/jcp/136/19/10.1063/1.4718590
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4718590

Figures

Image of FIG. 1.
FIG. 1.

Illustration of local adaptation around the 12 atoms in the benzene molecule (denoted by the grey circles) using the transformation between Cartesian and curvilinear coordinates described by Eq. (26). The molecule lies in the xy plane and for clarity only two dimensions are shown. (a) Shows the Cartesian grid under no adaptation, while (b) shows the deformation of the grid when adaptation is present.

Image of FIG. 2.
FIG. 2.

Schematic diagram of communication pattern required for application of the Laplacian given in Eqs. (30) and (31) for a 3D domain decomposition of the finite difference grid. Processor boundaries are represented by the solid lines and for clarity only two dimensions are shown. The grid points local to a given processor are represented by (●) while the halo points required from other processors are denoted by (■) and (▲). Halo points denoted by (▲) are required for application of those terms in the Laplacian in Eq. (30) that involve derivatives in different variables when using non-orthogonal curvilinear coordinates. Therefore, the use of non-orthogonal coordinates introduces an increased communications overhead in a given calculation.

Image of FIG. 3.
FIG. 3.

Isosurface plots of the valence Kohn-Sham orbital densities in N2 considered in our calculations. The occupation of each Kohn-Sham orbital is 2. The ground state energy configuration of N2 is and so each orbital is labeled as follows: (a) = 2σ g , (b) = 2σ u , (c) = 1π u , (d) = 1π u , and (e) = 3σ g . In these plots, the molecular axis is aligned along the z-axis and for the HHG results the laser polarization will either be along the x- or the z-axis.

Image of FIG. 4.
FIG. 4.

HHG spectra for N2. The molecule interacts with a 10-cycle linearly polarized Ti-sapphire (λ = 780 nm) laser pulse having a peak intensity of 4.0 × 1014W/cm2. The molecular axis is aligned along the z-axis. The black line shows the spectrum when the laser polarization lies perpendicular to the molecular axis while the red line denotes the spectrum when the laser polarization lies parallel to the molecular axis.

Image of FIG. 5.
FIG. 5.

Occupation of the valence Kohn-Sham orbitals of N2 during interaction with a 10-cycle linearly polarized Ti-sapphire (λ = 780 nm) laser pulse having a peak intensity of 4.0 × 1014W/cm2. The laser polarization direction is perpendicular to the molecular axis. We see that the more tightly bound 1π u (d) orbital responds more than the 3σ g HOMO. The change in the occupation of the 2σ g orbital during the interaction with the pulse is too small to show up on this scale.

Image of FIG. 6.
FIG. 6.

HHG spectra for benzene. The molecule interacts with a 10-cycle linearly polarized Ti-sapphire (λ = 780 nm) laser pulse having a peak intensity of 4.0 × 1014W/cm2. The molecule lies in the xy plane as shown if Fig. 1. The red line shows the spectrum when the laser-polarization lies perpendicular to the molecular plane while the black line denotes the spectrum when the laser-polarization lies parallel to the plane of the molecule.

Image of FIG. 7.
FIG. 7.

Isosurface plots of the two degenerate HOMO Kohn-Sham orbital densities for benzene in our calculations. The molecule lies in the xy plane as denoted in Fig. 1. The occupation of each Kohn-Sham orbital is 2. We label these orbitals as HOMO (a) and HOMO (b). In these plots, the molecule lies in the xy plane and for the HHG results the laser polarization will either be along the x- or the z-axis.

Image of FIG. 8.
FIG. 8.

Occupation of the valence Kohn-Sham orbitals of benzene during interaction with a 10-cycle linearly polarized Ti-sapphire (λ = 780 nm) laser pulse having a peak intensity of 4.0 × 1014W/cm2. The molecule lies in the xy plane and the laser-polarization lies along the x-axis (parallel to the molecular plane). For clarity only the HOMO (a) and HOMO (b) orbital populations are labeled, with the response of all other orbitals shown in red. We see that the response of the HOMO (b) orbital is suppressed with respect to the HOMO (a) orbital.

Tables

Generic image for table
Table I.

Comparison of the efficiency of the TRLan and CheFSI eigensolvers in calculating the ground state of N2. The time taken to obtain a converged, accurate ground state is given for various Lanczos and Chebyshev filter orders. Other calculation parameters are detailed in the text.

Generic image for table
Table II.

xLDA all-electron atomic ground state energies and ionization potentials calculated using a locally adapted finite difference grid in 3D. The results of the present work are compared with experiment and with the theoretical calculations of Grabo et al. 104 The current results agree well with the xLDA results of Grabo et al. Both ground state energies and ionization potentials are generally underestimated using xLDA. The ionization potentials, calculated as vertical ionization potentials, show much better agreement with experiment than the ground state energies. The grid adaptation and Coulomb potential parameters used were chosen to reproduce the correct hydrogenic energy levels of nitrogen: these parameters are used for all other species considered. Other calculation parameters are detailed in the text.

Generic image for table
Table III.

xLDA all-electron equilibrium molecular bond lengths, dissociation energies, and ionization potentials using a locally adapted finite difference grid in 3D. The results of the present work are compared with experimental results. As in the atomic case, we see that ionization potentials are underestimated using xLDA. The grid adaptation and Coulomb potential parameters used were chosen to reproduce the correct hydrogenic energy levels in the nitrogen atom: these parameters are used for all other species considered. Other calculation parameters are detailed in the text.

Generic image for table
Table IV.

xLDA all-electron static properties of benzene. The equilibrium C–C and C–H bond lengths, atomization energy and ionization potential are compared with experiment. We see that the atomization energy is greatly overestimated, in common with other LDA calculations.108,109 The grid adaptation and Coulomb potential parameters used were chosen to reproduce the correct hydrogenic energy levels in the nitrogen atom. Other calculation parameters are detailed in the text.

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/content/aip/journal/jcp/136/19/10.1063/1.4718590
2012-05-17
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multielectron effects in high harmonic generation in N2 and benzene: Simulation using a non-adiabatic quantum molecular dynamics approach for laser-molecule interactions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4718590
10.1063/1.4718590
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