•Equations of motion for the variables of floating Gaussian are derived analytically.•Electron-nuclear wave functions are described well by a floating Gaussian basis set.•Non-adiabatic electron-nuclear couplings appear in the Fourier transformed spectra.•High frequency electron oscillations are interpreted by the electronic configurations.•Low frequency proton oscillation is non-adiabatically modulated by electron motion.Time-dependent electron-nuclear wave functions of H2 were described by the floating Gaussian method. The equations of motion for the parameters that specify the wave functions are explicitly derived. By the imaginary time propagation, the ground-state wave functions were obtained. Five high frequency components appearing in the Fourier transformed spectra of the squared inter-particle distances were ascribed to the motion of electrons, and the two lowest frequency components among the five were identified as those representing coupling of the motions of electrons and nuclei.

•Hydrogen migration in CH3OH+ was probed with intense few-cycle laser pulses.•In the non-migration pathway, CO bond breaking proceeds from the A˜ state of CH3OH+.•In the migration pathway, bifurcation of a vibrational wave packet occurs at ∼150 fs.Ultrafast nuclear dynamics in CH3OH+ has been studied based on the released kinetic energy distributions of the fragment ions in the non-migration (CH3OH2+ → CH3+ + OH+) and migration (CH3OH2+ → CH2+ + OH2+) pathways obtained by pump-probe coincidence momentum imaging with few-cycle laser pulses (6.0(5) fs, 2.1(2) × 1014 W/cm2). A characteristic oscillatory structure with a bifurcation at ∼150 fs in the kinetic energy distribution of the migration pathway is interpreted as the motion of a vibrational wave packet on a bound well around the migrated geometry, oscillating first along the CO bond and bifurcating into bound and dissociating components.

•Non-Born–Oppenheimer wave functions of H2 are obtained by the extended MCTDHF method.•The electronic orbitals do not depend on the internuclear distance explicitly.•The ground-state energy of H2 converges to the exact value by this method.•The required memory size is much smaller than in the Born–Huang expansion method.A ground state wave function of a one-dimensional H2 molecule is derived numerically by the extended multi-configuration time-dependent Hartree–Fock (MCTDHF) method. The electronic orbitals and the amplitudes for the nuclear motion constituting the ground-state wave function are derived by solving the coupled equations of motion by the imaginary time propagation. Comparisons with the results obtained by the Born–Huang (BH) expansion method as well as with the exact wave function reveal that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method.

•Asymmetric CD bond breaking of C2D22+ in a few-cycle laser pulse was investigated.•The absolute carrier envelope phase was estimated from the recoil momentum of C2D2+.•The CEP dependent asymmetry was observed in the ejection direction of D+ from C2D22+.•The asymmetry in the D+ ejection was interpreted by recollision double ionization.The carrier envelope phase (CEP) dependence in the CD bond breaking of C2D2 induced by an intense few-cycle laser pulse is investigated. The ejection direction of D+ ions generated from the Coulomb explosion, C2D22+→C2D+ and D+, exhibits the CEP dependent asymmetry, while its CEP dependence is out of phase by π with respect to the CEP dependence of the recoil momentum of C2D2+. From a recollisional double ionization model, the asymmetry in the ejection direction of D+ was ascribed to the laser-assisted CD bond weakening in the few-cycle laser field.

•The length of the femtosecond laser induced filament is defined experimentally.•The fluorescence intensity from the filament is interpreted by a numerical model.•The filament acts as a gain medium for the amplification of spontaneous emission.•The vibrational and rotational temperatures are derived from the emission spectra.•The laser intensity clamping in the filament is confirmed by the spectral analysis.A femtosecond laser-induced filament in air was investigated by detecting the C3Πu–B3Πg (0, 0) fluorescence of N2. The intensity of the backward fluorescence increased exponentially as a function of the filament length, showing the amplification of the spontaneous emission. The vibrational and rotational temperatures of N2 in the C state determined by spectroscopic analyses were found to take respectively almost the same values of 2800(200) and 450(100) K in the wide laser intensity range between 0.5 and 6 mJ/pulse, which can be regarded as evidence of the clamping of the laser field intensity in the filament.

Three-body Coulomb explosion processes of triply charged positive ions of methylacetylene (CH3–CC–H) and its isotopomer, methyl-d3-acetylene (CD3–CC–H), induced by an ultrashort intense laser field (790 nm, ∼40 fs, 5.0 × 1013 W cm−2) are investigated by the coincidence momentum imaging method. Two types of three-body decomposition processes accompanying the ejection of a proton are identified for methylacetylene, and six types of three-body decomposition processes accompanying the ejection of a proton or a deuteron are identified for methyl-d3-acetylene. From the observed momentum vectors of all the three fragment ions for each decomposition pathway, the proton and deuteron distributions are constructed in the coordinate space, and the hydrogen migration processes are investigated. It was shown that the hydrogen migration proceeds more efficiently from the methyl group than from the methine group. In addition to the decomposition pathways accompanying the migration of one H (or D) atom, the decomposition pathways accompanying the migration of two light atoms (H/D exchange and 2D migration) are identified. Furthermore, the decomposition pathways ascribable to the migration of three light atoms (H/D exchange followed by D migration) are identified, showing the high intramolecular mobilities of H and D atoms within methylacetylene and methyl-d3-acetylene in an intense laser field, resulting in the H/D scrambling.

Two-body decomposition processes of methylacetylene (CH3CCH) and its isotopomer methyl-d3-acetylene (CD3CCH) in intense laser fields (790 nm, 40 fs, 5.0 × 1013 W cm−2) are investigated by the coincidence momentum imaging (CMI). In methyl-d3-acetylene, a total of six decomposition pathways in which one of the C−C bonds is broken and a total of six pathways in which an atomic hydrogen ion (H+ or D+) or a molecular hydrogen ion (H2+, HD+, D3+, or HD2+) is ejected are identified. It is revealed from the analysis of the CMI data that the migration of two deuterons as well as the exchange between a proton and a deuteron occurs prior to the two-body decomposition of a doubly charged parent molecule.

The effect of intensity, duration, and polarization of ultrashort laser pulses (795 nm, 40–100 fs, and 0.15–1.5 × 1015 W/cm2) on the hydrogen migration in methanol is systematically investigated using Coulomb explosion coincidence momentum imaging. The ratio of the ion yield obtained for the migration pathway CH3OH2+ → CH2+ + OH2+ with respect to the sum of the yields obtained for the migration pathway and for the nonmigration pathway CH3OH2+ → CH3+ + OH+ exhibits a small (10–20%) but clear dependence on laser pulse properties, that is, the ratio decreases as the laser peak intensity increases but increases when the pulse duration increases as well as when the laser polarization is changed from linear to circular.

Ultrafast proton migration in 1,3-butadiene in an intense laser field (40 fs, 4.5 × 1014 W cm−2) is investigated by using Coulomb explosion coincidence momentum imaging. The spatial distribution maps of a migrating proton reconstructed for the two three-body Coulomb explosion pathways, C4H63+ → H+ + CH3+ + C3H2+ and C4H63+ → H+ + C2H+ + C2H4+, reveal that two protons migrate within a 1,3-butadiene molecule, prior to the three body decomposition.

Molecular Coulomb explosion has been utilized as a precise temporal clock for probing ultrafast motion of nucleus and electrons during chemical reactions. With an intense attosecond pulse train in the extreme ultraviolet region, we were able to image attosecond molecular Coulomb explosion via two photon double ionization process. The present autocorrelation measurement, from which the duration of the attosecond pulse train was determined to be 300 as, serves as the first step toward a pump-and-probe measurement of molecular dynamics with attosecond temporal resolution.(a) Autocorrelation trace of an attosecond pulse train synthesized by the time-of-flight mass spectra of N2 recorded as a function of the delay Δt of one of the two separated harmonic beams. The delay Δt is expressed in units of one cycle of fundamental laser light T0. (b) Ion signal intensities of the two side-peak areas marked as ‘S’ in the range specified by an arrow is plotted as a function of Δt. (c) Ion signal intensities in the central-peak area ‘C’ in the range specified by an arrow is plotted as a function of Δt. (d) Autocorrelation trace of the fundamental laser light measured by detecting the fragment ions N+ generated by exposing N2 only to the intense fundamental light field at 800 nm.

The ejection of a triatomic or diatomic hydrogen molecular ion from methanol (CH3OH and CD3OH) in intense laser fields (86 fs, 800 nm, ≈1014 W/cm2) is investigated based on the momentum vector distributions of the fragment ions measured by the mass-resolved momentum imaging technique. From the relative yield of D3+,HD2+,D2+ and HD+ ejected from CD3OH2+ and the anisotropic distributions of their momentum vectors, the rates of the formation of triatomic (D3+andHD2+) and diatomic (D2+ and HD+) fragment ions, kt = 0.15 ps−1 and kd = 0.31 ps−1, respectively, and the H/D exchange rate, kex = 0.13 ps−1, are derived.

Two-body Coulomb explosion processes of acetonitrile (CH3CN) and deuterated acetonitrile (CD3CN), CH3CN2+ → CH3−n+ + HnCN+ and CD3CN2+ → CD3−n+ + DnCN+ (n = 0–2), in an intense laser field (0.15 PW/cm2, 70 fs) are investigated by the coincidence momentum imaging method. The comparable yields derived for the three pathways (n = 0–2) shows that the hydrogen atom migration proceeds in competition with the Coulomb explosion. The angular distributions of the fragment ions for n = 0 exhibits a sharp peak along the laser polarization direction while the angular distribution becomes more isotropic as n increases. Based on a least-squares analysis of the fragment anisotropy, the dissociation lifetimes of the doubly charged acetonitrile were determined, from which the time scale of the hydrogen migration as well as the deformation of the C–C–N skeleton prior to the explosion were discussed.

Using a tandem-type time-of-flight (TOF) mass spectrometer, the mass-selected aniline (AN)–water cluster cations, [AN(H2O)n]+ (n=1, 2), were irradiated with the intense femtosecond (fs) laser fields (λ∼395 nm, I∼5×1015 W/cm2, Δt∼50 fs). By the cluster formation with H2O, decomposition of AN+, AN+→C5H6++HNC, induced by the intense fs laser fields was significantly suppressed. From the observation that the suppression of the decomposition of AN+ occurs from [AN(H2O)n]+ more efficiently than from [AN(NH3)n]+ (n=1, 2), the effect of the cluster formation on the decomposition process was discussed.

The anisotropic two-dimensional (2D) electron diffraction pattern of jet-cooled CS2 in an intense nanosecond Nd:YAG laser field (1064 nm, , 10 ns) was measured by a short-pulsed 25 keV electron beam packet (∼7 ns) generated by irradiating a tantalum photocathode with the fourth harmonics of another nanosecond pulsed YAG laser radiation. The observed anisotropic 2D diffraction pattern is reproduced by simulation, in which the alignment of the S–C–S molecular axis along the laser polarization direction is taken into account. The results indicate that the molecular alignment process in an intense laser field can be probed directly by the pulsed gas electron diffraction method.

The observed anisotropic two-dimensional electron diffraction pattern of jet-cooled CS2 molecules in an intense nanosecond Nd:YAG laser field (1064 nm, , 10 ns) reported in our preceding Letter was analyzed quantitatively. The temporal and spatial distributions of the laser pulses and the electron beam packets were taken into account for a numerical simulation of the observed diffraction pattern. The anisotropy of the spatial distribution of molecular axes of CS2 in the direction of laser polarization is accounted for by the effect of the intense laser field.

Ultrafast proton migration in 1,3-butadiene in an intense laser field (40 fs, 4.5 × 1014 W cm−2) is investigated by using Coulomb explosion coincidence momentum imaging. The spatial distribution maps of a migrating proton reconstructed for the two three-body Coulomb explosion pathways, C4H63+ → H+ + CH3+ + C3H2+ and C4H63+ → H+ + C2H+ + C2H4+, reveal that two protons migrate within a 1,3-butadiene molecule, prior to the three body decomposition.

Three-body Coulomb explosion processes of triply charged positive ions of methylacetylene (CH3–CC–H) and its isotopomer, methyl-d3-acetylene (CD3–CC–H), induced by an ultrashort intense laser field (790 nm, ∼40 fs, 5.0 × 1013 W cm−2) are investigated by the coincidence momentum imaging method. Two types of three-body decomposition processes accompanying the ejection of a proton are identified for methylacetylene, and six types of three-body decomposition processes accompanying the ejection of a proton or a deuteron are identified for methyl-d3-acetylene. From the observed momentum vectors of all the three fragment ions for each decomposition pathway, the proton and deuteron distributions are constructed in the coordinate space, and the hydrogen migration processes are investigated. It was shown that the hydrogen migration proceeds more efficiently from the methyl group than from the methine group. In addition to the decomposition pathways accompanying the migration of one H (or D) atom, the decomposition pathways accompanying the migration of two light atoms (H/D exchange and 2D migration) are identified. Furthermore, the decomposition pathways ascribable to the migration of three light atoms (H/D exchange followed by D migration) are identified, showing the high intramolecular mobilities of H and D atoms within methylacetylene and methyl-d3-acetylene in an intense laser field, resulting in the H/D scrambling.

Two-body decomposition processes of methylacetylene (CH3CCH) and its isotopomer methyl-d3-acetylene (CD3CCH) in intense laser fields (790 nm, 40 fs, 5.0 × 1013 W cm−2) are investigated by the coincidence momentum imaging (CMI). In methyl-d3-acetylene, a total of six decomposition pathways in which one of the C−C bonds is broken and a total of six pathways in which an atomic hydrogen ion (H+ or D+) or a molecular hydrogen ion (H2+, HD+, D3+, or HD2+) is ejected are identified. It is revealed from the analysis of the CMI data that the migration of two deuterons as well as the exchange between a proton and a deuteron occurs prior to the two-body decomposition of a doubly charged parent molecule.