A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde.

We developed an approximate method for quantum reaction dynamics simulations, namely, a structure-based Gaussian (SBG) expansion approach, where SBG bases for the expansion of the wave function Ψ, expressed by a product of single-atom Cartesian Gaussians centered at the positions of respective nuclei, are mainly placed around critical structures on reaction pathways such as on the intrinsic reaction coordinate (IRC) through a transition state. In the present approach, the "pseudo-lattice points" at which SBGs are deployed are selected in a perturbative manner so as to make moderate the expansion length. We first applied the SBG idea to a two-dimensional quadruple-well model and obtained accurate tunneling splitting values between the lowest four states. We then applied it to hydrogen tunneling in malonaldehyde and achieved a tunneling splitting of 27.1 cm-1 with only 875 SBGs at the MP2/6-31G(d,p) level of theory, in good agreement with 25 cm-1 by the more elaborate multiconfiguration time-dependent Hartree method. Reasonable results were also obtained for singly and doubly deuterated malonaldehyde. We analyzed the tunneling states by utilizing expansion coefficients of individual SBGs and found that 40-45% of the SBGs in Ψ are nonplanar structures and SBGs away from the IRC contribute a little to hydrogen transfer.

Electron-atom Compton profiles due to the intramolecular motions of the H and D atoms in HD.

We report an atomic momentum spectroscopy (AMS) experiment on HD, performed at a scattering angle of 135° and at an incident electron energy of 2.0 keV. The electron-atom Compton profiles due to the intramolecular motions of the H and D atoms in HD were obtained. The two Compton profiles are shown to be identical with each other in both shape and intensity, proving that the experimental responses of the intramolecular atomic motions are disentangled from the effect of molecular translational motion. It is also shown that the Compton profiles are in agreement with associated quantum chemistry-based calculations, indicating that the large momentum transfer limit is achieved under the experimental conditions. These observations demonstrate the ability of AMS not only to map the intramolecular motion of each atom with different masses but also to perform elemental composition analysis of a molecular system.

Identification of an ultrafast internal conversion pathway of pyrazine by time-resolved vacuum ultraviolet photoelectron spectrum simulations.

The internal conversion from the optically bright S2 (1B2u, ππ*) state to the dark S1 (1B3u, nπ*) state in pyrazine is a standard benchmark for experimental and theoretical studies on ultrafast radiationless decay. Since 2008, a few theoretical groups have suggested significant contributions of other dark states S3 (1Au, nπ*) and S4 (1B2g, nπ*) to the decay of S2. We have previously reported the results of nuclear wave packet simulations [Kanno et al., Phys. Chem. Chem. Phys. 17, 2012 (2015)] and photoelectron spectrum calculations [Mignolet et al., Chem. Phys. 515, 704 (2018)] that support the conventional two-state picture. In this article, the two different approaches, i.e., wave packet simulation and photoelectron spectrum calculation, are combined: We computed the time-resolved vacuum ultraviolet photoelectron spectrum and photoelectron angular distribution for the ionization of the wave packet transferred from S2 to S1. The present results reproduce almost all the characteristic features of the corresponding experimental time-resolved spectrum [Horio et al., J. Chem. Phys. 145, 044306 (2016)], such as a rapid change from a three-band to two-band structure. This further supports the existence and character of the widely accepted pathway (S2 → S1) of ultrafast internal conversion in pyrazine.

A fast and robust trajectory surface hopping method: Application to the intermolecular photodissociation of a carbon dioxide dimer cation (CO2)2.

Our recently developed trajectory surface hopping method uses numerical time derivatives of adiabatic potential gradients to estimate the nonadiabatic transition probability and the hopping direction. To demonstrate the practicality of the novel method, we applied it to the intermolecular photodissociation of a carbon dioxide dimer cation (CO2)2 +. Our simulations reproduced the measured velocity distribution of CO2 + fragments consisting of two (fast and slow) components and revealed that nonadiabatic transitions occur promptly toward the electronic ground state regardless of the fragment velocity. The structure of (CO2)2 + at optical excitation governs the fate of subsequent nonadiabatic dynamics leading to a fast or slow dissociation. Our method gave similar results to the fewest switches algorithm at lower computational expense. Our fast and robust surface hopping method is promising for the investigation of nonadiabatic dynamics in large and complex systems.

Capturing the photo-induced dynamics of nano-molecules by X-ray free electron laser induced Coulomb explosion.

We performed reaction dynamics simulations to demonstrate that the vibrational dynamics of C60 induced by infrared (IR) pulses can be traced by triggering Coulomb explosion with intense femtosecond X-ray free electron laser (XFEL) probe pulses. The time series of the angular anisotropy ß(t) of fast C+ and C2+ fragments of C60 60+ produced by such an XFEL pulse reflects the instantaneous structure of C60 vibrationally excited by IR pulses. The phases and amplitudes of excited vibrational modes and the coupling between excited modes can be successfully extracted from the expansion of ß(t) in terms of vibrational modes. This proof-of-principle simulation clearly demonstrates that various information of the structures and reaction dynamics of large clusters or biomolecules can be retrieved by decomposing the experimentally determined ß(t) into vibrational modes.

Real-time observation of X-ray-induced intramolecular and interatomic electronic decay in CH2I2.

The increasing availability of X-ray free-electron lasers (XFELs) has catalyzed the development of single-object structural determination and of structural dynamics tracking in real-time. Disentangling the molecular-level reactions triggered by the interaction with an XFEL pulse is a fundamental step towards developing such applications. Here we report real-time observations of XFEL-induced electronic decay via short-lived transient electronic states in the diiodomethane molecule, using a femtosecond near-infrared probe laser. We determine the lifetimes of the transient states populated during the XFEL-induced Auger cascades and find that multiply charged iodine ions are issued from short-lived (∼20 fs) transient states, whereas the singly charged ones originate from significantly longer-lived states (∼100 fs). We identify the mechanisms behind these different time scales: contrary to the short-lived transient states which relax by molecular Auger decay, the long-lived ones decay by an interatomic Coulombic decay between two iodine atoms, during the molecular fragmentation.

Diffractive Imaging of C_{60} Structural Deformations Induced by Intense Femtosecond Midinfrared Laser Fields.

Theoretical studies indicated that C_{60} exposed to linearly polarized intense infrared pulses undergoes periodic cage structural distortions with typical periods around 100 fs (1 fs=10^{-15} s). Here, we use the laser-driven self-imaging electron diffraction technique, previously developed for atoms and small molecules, to measure laser-induced deformation of C_{60} in an intense 3.6 µm laser field. A prolate molecular elongation along the laser polarization axis is determined to be (6.1±1.4)% via both angular- and energy-resolved measurements of electrons that are released, driven back, and diffracted from the molecule within the same laser field. The observed deformation is confirmed by density functional theory simulations of nuclear dynamics on time-dependent adiabatic states and indicates a nonadiabatic excitation of the h_{g}(1) prolate-oblate mode. The results demonstrate the applicability of laser-driven electron diffraction methods for studying macromolecular structural dynamics in four dimensions with atomic time and spatial resolutions.

Visible photodissociation of the CO2 dimer cation: fast and slow dissociation dynamics in the excited state.

Velocity and angular distributions of photofragment CO2+ ions produced from mass-selected (CO2)2+ at 532 nm excitation were observed in an ion imaging experiment. The velocity distribution was assigned to two components, fast and slow velocity components, which was consistent with the previous study by Bowers et al. The anisotropy parameters of the angular distributions for the fast and slow velocity components were experimentally determined to be ßfast = 1.52 ± 0.14 and ßslow = 0.46 ± 0.10, respectively. In the theoretical approach, potential energy surfaces (PESs) of (CO2)2+ were calculated along two coordinates, the intermolecular distance and mutual orientations of the CO2 monomers. In addition, molecular dynamics simulations were performed. The visible transition of the most stable staggered structure of (CO2)2+ was attributed to C[combining tilde]2Ag ← X[combining tilde]2Bu by an excited state calculation. On the PES of the C[combining tilde] state, a potential well was found in which the two CO2 monomers lay side by side to each other, in addition to a repulsive slope along the intermolecular distance. The results of the simulations confirmed that the fragment CO2+ ions with fast velocity and large anisotropy originated from the rapid dissociation of (CO2)2+ on the repulsive slope. Meanwhile, the fragment CO2+ ions with slow velocity and small anisotropy were expected to emerge from statistical dissociation after large amplitude libration of CO2 molecules which was caused by the potential well in the excited state PES.

Unbiased Rotational Motions of an Ellipsoidal Guest in a Tight Yet Pliable Host.

In the design of machinery such as steel bearings, a fundamental understanding of material characteristics provides an indispensable basis for the design. Although hydrocarbon cycloarylenes have started to be used for providing unique supramolecular bearings with anomalous dynamic behaviors, their fundamental understanding is immature. A unique property of the cycloarylene host is now reported: the cyclic host is so pliable that it tracks the orientational changes of the ellipsoidal guest, that is, C70 fullerene. Unique structures of the complex were revealed by spectroscopic and crystallographic analyses, and additional theoretical investigations deepened our understanding by revealing the structural changes associated with unbiased rotational motions.

Magnetism-tuning strategies for graphene oxide based on magnetic oligoacene oxide patches model.

Graphene oxide (GO) has wide application potential owing to its 2D structure and diverse modification sites for various targeted uses. The introduction of magnetism into GO structures has further advanced the controllability of the application of GO materials. Herein, the concept of modular design and modeling was applied to tune the magnetism of GO. To obtain desirable magnetic properties, diradical-structured GO patches were formed by the introduction of two functional groups to break the Kekule structure of the benzene ring. In these diradical GO patches, the energy of the triplet state was lower than those of the open-shell broken-symmetry singlet state and closed-shell singlet state. To create such multi-radical patches, a practical approach is to determine a substantial spatial separation of the α and ß spin densities in the molecule. Thus, systematic design strategies and tests were evaluated. The first strategy was extending the distance between the distribution center of the α and ß spin densities; the second was controlling the delocalization directions of the α and ß electrons; the third was controlling the delocalization extension of the α and ß electrons by oxidative modification, and finally introducing multi-radical structures into the molecular system and controlling the position of each radical. Herein, successful molecular models with a large magnetic coupling constant (∼3600 cm-1) were obtained. This study paves the way to explore ferromagnetic MGO guided by theoretical study, which may become reality soon.

An efficient approximate algorithm for nonadiabatic molecular dynamics.

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields.

Single-active-electron analysis of laser-polarization effects on atomic/molecular multiphoton excitation.

We theoretically explore the effects of optical ellipticity on single-active-electron multiphoton excitation in atoms and (nearly) spherical molecules irradiated by intense polarized laser fields. This work was motivated by the experimental and theoretical studies of Hertel et al. [Phys. Rev. Lett. 102, 023003 (2009) and Phys. Rev. A 79, 053414 (2009)], who reported pronounced changes in the near-infrared-induced ion yields of xenon and C60 as a function of ellipticity (in particular, yield reduction for circular polarization) at low light intensities and derived a perturbative cross section formula to describe such polarization effects by assuming that the excited-state energies and radial transition electric dipole moments of the system are independent of the azimuthal quantum number l. First, by reformulating the N-photon absorption cross section of a single active electron, we prove that their assumptions reduce the network of optically allowed transition pathways into what we call the "Pascal triangle" consisting of (N + 1) (N + 2)/2 states only. Next, nonperturbative analytical and numerical solutions of the time-dependent Schrödinger equation for a simple model of two-photon excitation are presented not only in the low-intensity regime but also in the high-intensity regime. The results show that the determining factor of ellipticity-dependent multiphoton excitation probability is transition moment magnitudes and that the detailed energetic structure of the system also becomes important at high intensities. The experimentally observed flattening of the ion yields of xenon and C60 with increasing intensity can be explained without a saturation effect, which was previously deemed to be responsible for it. We also argue the applicability range of the cross section formula by Hertel et al. and the identity of the "doorway state" for ionization of C60.

Ultrafast Coulomb explosion of a diiodomethane molecule induced by an X-ray free-electron laser pulse.

Coulomb explosion of diiodomethane CH2I2 molecules irradiated by ultrashort and intense X-ray pulses from SACLA, the Japanese X-ray free electron laser facility, was investigated by multi-ion coincidence measurements and self-consistent charge density-functional-based tight-binding (SCC-DFTB) simulations. The diiodomethane molecule, containing two heavy-atom X-ray absorbing sites, exhibits a rather different charge generation and nuclear motion dynamics compared to iodomethane CH3I with only a single heavy atom, as studied earlier. We focus on charge creation and distribution in CH2I2 in comparison to CH3I. The release of kinetic energy into atomic ion fragments is also studied by comparing SCC-DFTB simulations with the experiment. Compared to earlier simulations, several key enhancements are made, such as the introduction of a bond axis recoil model, where vibrational energy generated during charge creation processes induces only bond stretching or shrinking. We also propose an analytical Coulomb energy partition model to extract the essential mechanism of Coulomb explosion of molecules from the computed and the experimentally measured kinetic energies of fragment atomic ions by partitioning each pair Coulomb interaction energy into two ions of the pair under the constraint of momentum conservation. Effective internuclear distances assigned to individual fragment ions at the critical moment of the Coulomb explosion are then estimated from the average kinetic energies of the ions. We demonstrate, with good agreement between the experiment and the SCC-DFTB simulation, how the more heavily charged iodine fragments and their interplay define the characteristic features of the Coulomb explosion of CH2I2. The present study also confirms earlier findings concerning the magnitude of bond elongation in the ultrashort X-ray pulse duration, showing that structural damage to all but C-H bonds does not develop to a noticeable degree in the pulse length of ∼10 fs.

Selective bond breaking of CO2 in phase-locked two-color intense laser fields: laser field intensity dependence.

Selective bond breaking of CO2 in phase-locked ω-2ω two-color intense laser fields (λ = 800 nm and 400 nm, total field intensity I ∼ 1014 W cm-2) has been investigated by coincidence momentum imaging. The CO+ and O+ fragment ions produced by two-body Coulomb explosion, CO22+ → CO+ + O+, exhibit asymmetric distributions along the laser polarization direction, showing that one of the two equivalent C-O bonds is selectively broken by the laser fields. At a field intensity higher than 2 × 1014 W cm-2, the largest fragment asymmetry is observed when the relative phase ϕ between the ω and 2ω laser fields is ∼0 and π. On the other hand, an increase of the asymmetry and a shift of the phase providing the largest asymmetry are observed at lower field intensities. The selective bond breaking and its dependence on the laser field intensity are discussed in terms of a mechanism involving deformation of the potential energy surfaces and electron recollision in intense laser fields.

Reply to the 'Comment on "Theoretical studies on a carbonaceous molecular bearing: association thermodynamics and dual-mode rolling dynamics"' by E. M. Cabaleiro-Lago, J. Rodriguez-Otero and A. Gil, Chem. Sci., 2016, 7, DOI: 10.1039/C5SC04676A.

We reply to the comments raised by Cabaleiro-Lago et al. on our article (H. Isobe et al., Chem. Sci., 2015, 6, 2746-2753). Here we appreciate the common views we share and welcome the clarity this gives, and we discuss and question some of their criticisms of the original piece and clarify our opinion in this area. The most important answer can be found in the equation, ΔG = ΔH - TΔS, derived from one of the best established fields in physics.

Mechanism and Experimental Observability of Global Switching Between Reactive and Nonreactive Coordinates at High Total Energies.

We present a mechanism of global reaction coordinate switching, namely, a phenomenon in which the reaction coordinate dynamically switches to another coordinate as the total energy of the system increases. The mechanism is based on global changes in the underlying phase space geometry caused by a switching of dominant unstable modes from the original reactive mode to another nonreactive mode in systems with more than 2 degrees of freedom. We demonstrate an experimental observability to detect a reaction coordinate switching in an ionization reaction of a hydrogen atom in crossed electric and magnetic fields. For this reaction, the reaction coordinate is a coordinate along which electrons escape and its switching changes the escaping direction from the direction of the electric field to that of the magnetic field and, thus, the switching can be detected experimentally by measuring the angle-resolved momentum distribution of escaping electrons.

Modulation of Energy Conversion Processes in Carbonaceous Molecular Bearings.

The energetics and photodynamics of carbonaceous molecular bearings with discrete molecular structures were investigated. A series of supramolecular bearings comprising belt-persistent tubular cycloarylene and fullerene molecules accepted photonic stimuli to afford charge-separated species via a photoinduced electron transfer process. The energy conversion processes associated with the photoexcitation, however, differed depending on the molecular structure. A π-lengthened tubular molecule allowed for the emergence of an intermediary triplet excited state at the bearing, which should lead to an energy conversion to thermal energy. On the other hand, low-lying charge-separated species induced by an endohedral lithium ion in fullerene enabled back electron transfer processes to occur without involving triplet excited species. The structure-photodynamics relationship was analyzed in terms of the Marcus theory to reveal a large electronic coupling in this dynamic supramolecular system.

Theoretical studies on a carbonaceous molecular bearing: association thermodynamics and dual-mode rolling dynamics.

The thermodynamics and dynamics of a carbonaceous molecular bearing comprising a belt-persistent tubular molecule and a fullerene molecule have been investigated using density functional theory (DFT). Among ten representative methods, two DFT methods afforded an association energy that reasonably reproduced the experimental enthalpy of -12.5 kcal mol-1 at the unique curved π-interface. The dynamics of the molecular bearing, which was assembled solely with van der Waals interactions, exhibited small energy barriers with maximum values of 2-3 kcal mol-1 for the rolling motions. The dynamic motions responded sensitively to the steric environment and resulted in two distinct motions, precession and spin, which explained the unique NMR observations that were not clarified in previous experimental studies.

Ab initio quantum dynamical analysis of ultrafast nonradiative transitions via conical intersections in pyrazine.

We theoretically investigated the mechanism of ultrafast nonradiative transition through conical intersections in photoexcited pyrazine by ab initio quantum dynamical calculations. This work was motivated by the recent theoretical and experimental studies that presented conflicting results: the former is the on-the-fly semiclassical surface hopping calculation combined with the time-dependent density functional theory, which showed that nonadiabatic transitions from the optically bright S2 ((1)B(2u), ππ*) state to the optically dark S3 ((1)A(u), nπ*) and S4 ((1)B(2g), nπ*) states take place predominantly at the initial stage of electronic relaxation [U. Werner et al., Chem. Phys., 2008, 349, 319]; the latter is the pump-probe photoelectron spectroscopic measurement, which reported the S2 lifetime (22 ± 3 fs) of nonradiative decay to the almost dark S1 ((1)B(3u), nπ*) state [Y.-I. Suzuki et al., J. Chem. Phys., 2010, 132, 174302]. We constructed adiabatic and diabatic potential energy surfaces of these ππ* and nπ* states using the multireference configuration interaction method and calculated their diabatic couplings within two-dimensional subspaces spanned by selected ground-state normal coordinates. Contrary to the surface hopping study, our nuclear wave packet simulations demonstrated that nonadiabatic transitions to the S3 and S4 states are so small that the conventional two-state (S1 and S2) picture is valid. Ultrafast internal conversion of pyrazine, which is deemed to proceed with a 22 fs lifetime, in fact consists of three consecutive steps: (i) the wave packet excited to the S2 state travels toward the S2-S1 conical intersection in 10 fs, (ii) the nonadiabatic transition to the S1 state progresses at a rapid rate corresponding to a transient lifetime of 7 fs, and (iii) intramolecular vibrational energy redistribution occurs in the S1 state in about 80 fs after optical excitation. To verify this prediction, time-resolved experiments with a resolution of several fs or shorter are desirable.

Communication: Two-step explosion processes of highly charged fullerene cations C60(q+) (q = 20-60).

To establish the fundamental understanding of the fragmentation dynamics of highly positive charged nano- and bio-materials, we carried out on-the-fly classical trajectory calculations on the fragmentation dynamics of C60(q+) (q = 20-60). We used the UB3LYP/3-21G level of density functional theory and the self-consistent charge density-functional based tight-binding theory. For q ≥ 20, we found that a two-step explosion mechanism governs the fragmentation dynamics: C60(q+) first ejects singly and multiply charged fast atomic cations C(z+) (z ≥ 1) via Coulomb explosions on a timescale of 10 fs to stabilize the remaining core cluster. Thermal evaporations of slow atomic and molecular fragments from the core cluster subsequently occur on a timescale of 100 fs to 1 ps. Increasing the charge q makes the fragments smaller. This two-step mechanism governs the fragmentation dynamics in the most likely case that the initial kinetic energy accumulated upon ionization to C60(q+) by ion impact or X-ray free electron laser is larger than 100 eV.