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Register a new userA sparse-sampling approach for the fast computation of matrices: application to molecular vibrations
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This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes the computational bottleneck. We apply this new method to an important problem in computational chemistry: the determination of molecular vibrations from electronic structure calculations, where our results show that the overall scaling of the procedure can be improved in some cases. Moreover, our method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations, resulting in a significant 3x speed-up in actual calculations.
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Strong field transient grating spectroscopy has shown to be a very versatile tool in time-resolved molecular spectroscopy. Here we use this technique to investigate the high-order harmonic generation from SF6 molecules vibrationally excited by impulsive stimulated Raman scattering. Transient grating spectroscopy enables us to reveal clear modulations of the harmonic emission. This heterodyne detection shows that the harmonic emission generated between 14 to 26 eV is mainly sensitive to two among the three active Raman modes in SF6, i.e. the strongest and fully symmetric nu 1-A1g mode (774 cm-1, 43 fs) and the slowest mode nu5-T2g (524 cm-1, 63 fs). A time-frequency analysis of the harmonic emission reveals additional dynamics: the strength and central frequency of the nu 1 mode oscillate with a frequency of 52 cm-1 (640 fs). This could be a signature of the vibration of dimers in the generating medium. Harmonic 11 shows a remarkable behavior, oscillating in opposite phase, both on the fast (774 cm-1) and slow (52 cm-1) timescales, which indicates a strong modulation of the recombination matrix element as a function of the nuclear geometry. These results demonstrate that the high sensitivity of high-order harmonic generation to molecularvibrations, associated to the high sensitivity of transient grating spectroscopy, make their combination a unique tool to probe vibrational dynamics.
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