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This account places a particular emphasis on recent progress in the theory and its applications of nonadiabatic electron dynamics in chemical science. After a brief description of the fundamental r...

Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B12), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.

Much insight into the basic mechanisms of photoexcited and collision-induced ground-state water splitting has been accumulated in our nonadiabatic electron wavepacket dynamics studies based on a building-block approach reaching up to systems of binuclear Mn oxo complexes. We here extend the study to a ground-state water-splitting catalytic cycle with tetranuclear Mn oxo complex Mn4CaO5, or Mn3Ca(H2O)2(OH)4-OH-Mn(4)(H2O)2, where Mn3Ca(H2O)2(OH)4 is fixed to a skewed cubic structure by μ-hydroxo bridges and is tied to the terminal group Mn(4)(H2O)2. We show using the method of real-time nonadiabatic electron wavepacket dynamics that four charge separation steps always take place only through the terminal group Mn(4)(H2O)2 alone, thereby producing 4 electrons and 4 protons which are transported to the acceptors. Each of the three charge separation steps is followed by a reloading process from the skewed cubic structure, by which electrons and protons are refilled to the vacant terminal group so that the next charge separation dynamics can resume. After the fourth charge separation an oxygen molecule is generated. It is emphasized that the mechanisms of O2 generation should depend on the multiple channels of reloading.

Intra- and inter-molecular electronic energy current is formulated by defining the probability current of electronic energy, called the energy flux. Among vast possible applications to electronic energy transfer phenomena, including chemical reaction dynamics, here we present a first numerical example from highly excited nonadiabatic electron wavepacket dynamics of a boron cluster B12.

We propose a methodology to unify electronic and nuclear quantum wavepacket dynamics in molecular processes including nonadiabatic chemical reactions. The canonical and traditional approach in the full quantum treatment both for electrons and nuclei rests on the Born–Oppenheimer fixed nuclei strategy, the total wavefunction of which is described in terms of the Born–Huang expansion. This approach is already realized numerically but only for small molecules with several number of coupled electronic states for extremely hard technical reasons. Besides, the stationary-state view of the relevant electronic states based on the Born–Oppenheimer approximation is not always realistic in tracking real-time electron dynamics in attosecond scale. We therefore incorporate nuclear wavepacket dynamics into the scheme of nonadiabatic electron wavepacket theory, which we have been studying for a long time. In this scheme thus far, electron wavepackets are quantum mechanically propagated in time along nuclear paths that can naturally bifurcate due to nonadiabatic interactions. The nuclear paths are in turn generated simultaneously by the so-called matrix force given by the electronic states involved, the off-diagonal elements of which represent the force arising from nonadiabatic interactions. Here we advance so that the nuclear wavepackets are directly taken into account in place of path (trajectory) approximation. The nuclear wavefunctions are represented in terms of the Cartesian Gaussians multiplied by plane waves, which allows for feasible calculations of atomic and molecular integrals together with the electronic counterparts in a unified manner. The Schrödinger dynamics of the simultaneous electronic and nuclear wavepackets are to be integrated by means of the dual least action principle of quantum mechanics [K. Takatsuka, J. Phys. Commun. 4, 035007 (2020)], which is a time-dependent variational principle. Great contributions of Vincent McKoy in the electron dynamics in the fixed nuclei approximation and development in time-resolved photoelectron spectroscopy are briefly outlined as a guide to the present work.

Physical nature of the chemical bond and potential barrier is studied in terms of energy natural orbitals (ENOs), which are extracted from highly correlated electronic wavefunctions. ENO provides an objective one-electron picture about energy distribution in a molecule, just as the natural orbitals (NOs) represent one electron view about electronic charge distribution. ENO is invariant in the same sense as NO is, that is, ENOs converge to the exact ones as a series of approximate wavefunctions approach the exact one, no matter how the methods of approximation are adopted. Energy distribution analysis based on ENO can give novel insights about the nature of chemical bonding and formation of potential barriers, besides information based on the charge distribution alone. With ENOs extracted from full configuration interaction wavefunctions in a finite yet large enough basis set, we analyze the nature of chemical bonding of three low-lying electronic states of a hydrogen molecule, all being in different classes of the so-called covalent bond. The mechanism of energy lowering in bond formation, which gives a binding energy, is important, yet not the only concern for this small molecule. Another key notion in chemical bonding is whether a potential basin is well generated stiff enough to support a vibrational state(s) on it. Based on the virial theorem in the adiabatic approximation and in terms of the energy and force analyses with ENOs, we study the roles of the electronic kinetic energy and its nuclear derivative(s) on how they determine the curvature (or the force constant) of the potential basins. The same idea is applied to the potential barrier and, thereby, the transition states. The rate constant within the transition-state theory is formally shown to be described in terms of the electronic kinetic energy and the nuclear derivatives only. Thus, the chemical bonding and rate process are interconnected behind the scenes. Besides this aspect, we pay attention to (1) the effects of electron correlation that manifests itself not only in the orbital energy but also in the population of ENOs and (2) the role of nonadiabaticity (diabatic state mixing), resulting in double basins and a barrier on a single potential curve in bond formation. These factors differentiate a covalent bond into subclasses.

A detailed flux analysis on nonadiabatically coupled electronic and nuclear dynamics in the intramolecular electron transfer of LiF is presented. Full quantum dynamics both of electrons and nuclei within two-state model has uncovered interesting features of the individual fluxes (current of probability density) and correlation between them. In particular, a spatiotemporal oscillatory pattern of electronic flux has been revealed, which reflects the coherence coming from spatiotemporal differential overlap between nuclear wavepackets running on covalent and ionic potential curves. In this regard, a theoretical analogy between the nonadiabatic transitions and the Rabi oscillation is surveyed. We also present a flux-flux correlation between the nuclear and electronic motions, which quantifies the extent of deviation of the actual electronic and nuclear coupled dynamics from the Born-Oppenheimer adiabatic limit, which is composed only of a single product of the adiabatic electronic and nuclear wavefunctions. © 2018 Wiley Periodicals, Inc.

The path-branching theory as a nonadiabatic electron wavepacket theory (Yonehara et al., 2012), in which nonadiabatic electron wavepackets are propagated in time along branching nuclear paths, is extended so that Gaussian nuclear wavepackets are to be evolved in time along the variational quantum paths, which are determined consistently with the electron dynamics.

We propose and numerically demonstrate that highly correlated electronic wavefunctions such as those of configuration interaction, the cluster expansion, and so on, and electron wavepackets superposed thereof can be analyzed in terms of one-electron functions, which we call energy natural orbitals (ENOs). As the name suggests, ENOs are members of the broad family of natural orbitals defined by Lowdin, in that they are eigenfunctions of the energy density operator. One of the major characteristics is that the (orbital) energies of all the ENOs are summed up exactly equal to the total electronic energy of a wavefunction under study. Another outstanding feature is that the population of each ENO varies as the chemical reaction proceeds, keeping the total population constant though. The study of ENOs has been driven by the need for new methods to analyze extremely complicated nonadiabatic electron wavepackets such as those embedded in highly quasi-degenerate excited-state manifolds. Yet, ENOs can be applied to scrutinize many other chemical reactions, ranging from the ordinary concerted reactions, nonadiabatic reactions, and Woodward–Hoffman forbidden reactions, to excited-state reactions. We here present the properties of ENOs and a couple of case studies of numerical realization, one of which is about the mechanism of nonadiabatic electron transfer.

Much insight into the basic mechanisms of photoexcited and collision-induced ground-state water splitting has been accumulated in our nonadiabatic electron wavepacket dynamics studies based on a building-block approach reaching up to systems of binuclear Mn oxo complexes. We here extend the study to a ground-state water-splitting catalytic cycle with tetranuclear Mn oxo complex Mn4CaO5, or Mn3Ca(H2O)2(OH)4-OH-Mn(4)(H2O)2, where Mn3Ca(H2O)2(OH)4 is fixed to a skewed cubic structure by μ-hydroxo bridges and is tied to the terminal group Mn(4)(H2O)2. We show using the method of real-time nonadiabatic electron wavepacket dynamics that four charge separation steps always take place only through the terminal group Mn(4)(H2O)2 alone, thereby producing 4 electrons and 4 protons which are transported to the acceptors. Each of the three charge separation steps is followed by a reloading process from the skewed cubic structure, by which electrons and protons are refilled to the vacant terminal group so that the next charge separation dynamics can resume. After the fourth charge separation an oxygen molecule is generated. It is emphasized that the mechanisms of O2 generation should depend on the multiple channels of reloading.

Many-electron relativistic quantum theories of stationary molecular electronic states have been developed in so-called quantum chemistry, in which nuclear configuration is frozen in space-time under the Born-Oppenheimer approximation. These time-independent methods are concerned with energetics, which are supposed to determine molecular structures and dominate low-energy chemical reactions. Yet, rapid progress in laser technology demands that theoretical chemistry should get prepared for relativistic electron-nucleus coupled dynamics driven by unconventional ultrastrong laser pulses. We therefore generalize our previously developed path-integral formalism of nonadiabatic electron dynamics [Hanasaki and Takatsuka, Phys. Rev. A 81, 052514 (2010)] to cover the relativistic regime in radiation fields. Starting from a formal relativistic path-integral formulation of electron-nucleus coupled systems interacting with quantum radiation fields, we reduce it to a tractable level of approximations to set a theoretical foundation for future applications.

Analysis of electron flux within and in between molecules is crucial in the study of real-time dynamics of molecular electron wavepacket evolution such as those in attosecond laser chemistry and ultrafast chemical reaction dynamics. We here address two mutually correlated issues on the conservation law of molecular electronic flux, which serves as a key consistency condition for electron dynamics. The first one is about a close relation between "weak" nonadiabaticity and the electron dynamics in low-energy chemical reactions. We show that the electronic flux in adiabatic reactions can be consistently reproduced by taking account of nonadiabaticity. Such nonadiabaticity is usually weak in the sense that it does not have a major effect on nuclear dynamics, whereas it plays an important role in electronic dynamics. Our discussion is based on a nonadiabatic extension of the electronic wavefunction similar in idea to the complete adiabatic formalism developed by Nafie [J. Chem. Phys. 79, 4950 (1983)], which has also recently been reformulated by Patchkovskii [J. Chem. Phys. 137, 084109 (2012)]. We give straightforward proof of the theoretical assertion presented by Nafie using a time-dependent mixed quantum-classical framework and a standard perturbation expansion. Explicitly taking account of the flux conservation, we show that the nonadiabatically induced flux realizes the adiabatic time evolution of the electronic density. In other words, the divergence of the nonadiabatic flux equals the time derivative of the electronic density along an adiabatic time evolution of the target molecule. The second issue is about the accurate computationability of the flux. The calculation of flux needs an accurate representation of the (relative) quantum phase, in addition to the amplitude factor, of a total wavefunction and demands special attention for practical calculations. This paper is the first one to approach this issue directly and show how the difficulties arise explicitly. In doing so, we reveal that a number of widely accepted truncation techniques for static property calculations are potential sources of numerical flux non-conservation. We also theoretically propose alternative strategies to realize better flux conservation.

A computational scheme of energy- and geometry-dependent photoelectron signals from the dynamics near a conical intersection based on a simplified path-branching representation of nonadiabatic electron wavepacket dynamics is proposed. Taking the NO2 X / A conical intersection as an example, the results of the present scheme compared to those from previous study based on the method of full quantum vibrational wavepacket shows qualitative agreement suggesting promising application to computation in larger systems intractable to full quantum exact methods.

We perform a full-dimensional nonadiabatic electron wavepacket study of Mn-oxide catalytic charge separation to be created on an accepting molecular system, which is of Y-shaped branching structure and has a track-branching function of proton and electron. This branching is necessary in cases where the transferred electrons and protons are to be eventually carried to mutually different destinations without quick annihilation of thus created pair (charge separation). However, as a result of the larger size of such a branching shaped acceptor, the distance between the Mn-oxide and the acceptor is so long that it can be far from obvious whether an electron is successfully delivered through conical intersections. We here show that this can really take place.

Guided by a notion of symmetry-breaking modulation or control of the so-called symmetry-allowed conical intersection by shining laser pulses [Arasaki, Y.; et al. Phys. Chem. Chem. Phys. 2010, 12, 1239], we here explore a possibility of the modulation of the symmetry-allowed conical intersection by chemical substitution with functional groups. As a first case study, we choose photoisomerization dynamics of s-trans-1,3-butadiene H2C═CH—CH═CH2 with one of the terminal hydrogen atoms being replaced by −CF3. The target here is not the control of the rate of nonadiabatic transition but to know which one of the double bonds is more frequently isomerized in the radiationless quenching process on the way back to the ground state. We analyze when and how the symmetry is broken by tracking ab initio molecular dynamics paths, the mean-field paths with use of the nonadiabatic electron wavepacket dynamics, and the associated branching paths.

We propose a general theoretical scheme of relativistic electron-nucleus coupled dynamics of molecules in radiation fields, which is derived from quantum electrodynamical formalism. Aiming at applications to field-induced dynamics in ultrastrong laser pulses to the magnitude of 1016 W/cm2 or even larger, we derive a nonperturbative formulation of relativistic dynamics using the Tamm-Dancoff expansion scheme, which results in, within the lowest order expansion, a time-dependent Schrodinger equation with the Coulombic and retarded transversal photon-exchange interactions. We also discuss a wavepacket type nuclear dynamics adapted for such dynamics.

We propose a set of chemical reaction mechanisms of unidirectional proton transfers, which may possibly work as an elementary process in chemical and biological systems. Being theoretically derived based on our series of studies on charge separation dynamics in water splitting by Mn oxides, the present mechanisms have been constructed after careful exploration over the accumulated biological studies on cytochrome c oxidase (CcO) and bacteriorhodopsin. In particular, we have focused on the biochemical findings in the literature that unidirectional transfers of approximately two protons are driven by one electron passage through the reaction center (binuclear center) in CcO, whereas no such dissipative electron transfer is believed to be demanded in the proton transport in bacteriorhodopsin. The proposed basic mechanisms of unidirectional proton transfers are further reduced to two elementary dynamical processes, namely, what we call the coupled proton and electron-wavepacket transfer (CPEWT) and the inverse CPEWT. To show that the proposed mechanisms can indeed be materialized in a molecular level, we construct model systems with possible molecules that are rather familiar in biological chemistry, for which we perform the ab initio calculations of full-dimensional nonadiabatic electron-wavepacket dynamics coupled with all nuclear motions including proton transfers.

Formation of chemical bonds is theoretically discerned by the presence of static nuclear configuration on a potential energy surface given within the Born-Oppenheimer framework. We here study dynamical chemical bonding for molecules residing in the electronic excited states that are in a densely quasi-degenerate electronic state manifold and thereby keep undergoing extremely frequent nonadiabatic transitions. For this type of the states, the notion of global potential energy surfaces based on the adiabatic representation loses the usual sense. Nonetheless, chemical bonding exists and associated chemical reactions certainly proceed, for which we call chemistry without potential surfaces. As such, we investigate the highly excited states of boron clusters, which have extraordinarily long lifetimes with neither ionization nor dissociation. The dynamical chemical bonds keep rearranging themselves without converging to a static structure, the vivid electron dynamics of which is tracked by means of the nonadiabatic electron wavepacket dynamics theory. To characterize the dynamical bonding theoretically, we propose the notion of hyper-resonance.

We perform an electronic and nuclear flux analysis for nonadiabatic dynamics and its corresponding adiabatic counterpart, both of the wavefunctions of which are represented in the Born-Huang expansion. It is well known that the electronic-nuclear configurations (terms) in the expansion of the total wavefunction interfere each other through the nonadiabatic interactions and give birth to electronic and nuclear fluxes. Interestingly, even in the adiabatic dynamics without such nonadiabatic interactions, a wavefunction composed of more than one adiabatic state can undergo interference among the components and give the electronic and nuclear fluxes. That is, the individual pieces of the wavepacket components associated with the electronic wavefunctions in the adiabatic representation can propagate in time independently with no nonadiabatic interaction, and yet they can interfere among themselves to generate the specific types of electronic and nuclear fluxes. We refer to the dynamics of this class of total wavefunction as multiple-configuration adiabatic Born-Huang dynamics. A systematic way to distinguish the electronic and nuclear fluxes arising from nonadiabatic and the corresponding adiabatic dynamics is discussed, which leads to the deeper insight about the nonadiabatic dynamics and quantum interference in molecular processes. The so-called adiabatic flux will also be discussed.

In this perspective article, we review, along with presenting new results, a series of our theoretical analyses on the excited-state mechanism of charge separation (proton–electron pair creation) relevant to the photoinduced water-splitting reaction (2H 2 O → 4H + + 4e − + O 2 ) in organic and biological systems, which quite often includes Mn clusters in various molecular configurations. The present mechanism is conceived to be universal in the triggering process of the photoexcited water splitting dynamics. In other words, any Mn-based catalytic charge separation is quite likely to be initiated according to this mechanism. As computationally tractable yet realistic models, we examine a series of systems generally expressed as X–Mn–OH 2 ⋯A, where X = (OH, Ca(OH) 3 ) and A = ( N -methylformamidine, guanidine, imidazole or ammonia cluster) in terms of the theory of nonadiabatic electron wavepacket dynamics. We first find both an electron and a proton are simultaneously transferred to the acceptors through conical intersections upon photoexcitation. In this mechanism, the electron takes different pathways from that of the proton and reaches the densely lying Rydberg-like states of the acceptors in the end, thereby inducing charge separation. Therefore the presence of the Rydberg-like diffused unoccupied states as an electron acceptor is critical for this reaction to proceed. We also have found another crucial nonadiabatic process that deteriorates the efficiency of charge separation by rendering the created pair of proton and electron back to the originally donor site through the states of d–d band originated from Mn atom. Repetition of this process gradually annihilates the created pair of proton and electron in a way different from the usual charge recombination process. We address this dynamics by means of our proposed path-branching representation. The dynamical roles of a doped Ca atom are also uncovered, which are relevant to controlling the pathways of electron flow and moreover to reduction of the annihilation dynamics of proton–electron pair.

Symmetry allowed conical intersection plays a central role in excited state symmetry-forbidden reactions. As an illustrative example as such, we track the dynamical sequence of spatial-symmetry breaking of B 4 cluster, which has a rich electronic structure in the low-lying excited states, to see how the relevant reaction proceeds. We use the semiclassical Ehrenfest method to detect the nonadiabatic electronic state mixing along the reactions. The essential feature of the nonadiabatic electron dynamics is clarified in terms of electron flux and unpaired-electron distribution induced by the nonadiabatic transitions. To facilitate understanding electron dynamics of symmetry breaking, we begin with symmetry consideration in terms of the Huckel orbitals, which are shown to be qualitatively useful enough to foresee the possible existence of symmetry allowed conical intersections.

We present a basic theory to study real-time dynamics embedded in a large environment that is treated using a statistical method. In light of great progress in the molecular-level studies on time-resolved spectroscopies, chemical reaction dynamics, and so on, not only in the gas phase but also in condensed phases like liquid solvents and even in crowded environments in living cells, we need to bridge over a gap between statistical mechanics and microscopic real-time dynamics. For instance, an analogy to gas-phase dynamics in which molecules are driven by the gradient of the potential energy hyper-surfaces (PESs) suggests that particles in condensed phases should run on the free energy surface instead. The question is whether this anticipation is correct. To answer it, we here propose a mixed dynamics and statistical representation to treat chemical dynamics embedded in a statistical ensemble. We first define the entropy functional, which is a function of the phase-space position of the dynamical subsystem, being dressed with statistical weights from the statistical counterpart. We then consider the functionals of temperature, free energy, and chemical potential as their extensions in statistical mechanics, through which one can clarify the relationship between real-time microscopic dynamics and statistical quantities. As an illustrative example we show that molecules in the dynamical subsystem should run on the free-energy functional surface, if and only if the spatial gradients of the temperature functional are all zero. Otherwise, additional forces emerge from the gradient of the temperature functional. Numerical demonstrations are presented at the very basic level of this theory of molecular dissociation in atomic cluster solvents.

Time-dependent variational principle (TDVP) provides powerful methods in solving the time-dependent Schröinger equation. As such Kan developed a TDVP (Kan 1981 Phys. Rev. A 24, 2831) and found that there is no Legendre transformation in quantum variational principle, suggesting that there is no place for the Maupertuis reduced action to appear in quantum dynamics. This claim is puzzling for the study of quantum–classical correspondence, since the Maupertuis least action principle practically sets the very basic foundation of classical mechanics. Zambrini showed within the theory of stochastic calculus of variations that the Maupertuis least action principle can lead to the Nelson stochastic quantization theory (Zambrini 1984 J. Math. Phys. 25, 1314). We here revisit the basic aspect of TDVP and reveal the hidden roles of Maupertuis-Hamilton least action in the Schrödinger wavepacket dynamics. On this basis we propose a dual least (stationary) action principle, which is composed of two variational functionals; one responsible for ‘energy related dynamics’ and the other for ‘dynamics of wave-flow’. The former is mainly a manifestation of particle nature in wave-particle duality, while the latter represents that of matter wave. It is also shown that by representing the TDVP in terms of these inseparably linked variational functionals the problem of singularity, which is inherent to the standard TDVPs, is resolved. The structure and properties of this TDVP are also discussed.

We theoretically propose a photoinduced water-splitting cycle catalyzed by a binuclear Mn oxo complex. In our “bottom-up approach” to this problem, we once proposed a working minimal model of water-splitting cycle in terms of a mononuclear Mn oxo complex as a catalyst along with water clusters [K. Yamamoto and K. Takatsuka, Phys. Chem. Chem. Phys. 20, 6708 (2018)]. However, this catalyst is not self-contained in that the cycle additionally needs buffering molecules for electrons and protons in order to reload the Mn complex with electrons and protons, which are lost by photoinduced charge separation processes. We here show that a binuclear Mn oxo complex works as a self-contained photocatalyst without further assistant of additional reagents and propose another catalytic cycle in terms of this photocatalyst. Besides charge separation and proton relay transfer, the proposed cycle consists of other fundamental chemical dynamics including electron–proton reloading, radical relay-transfer, and Mn reduction. The feasibility of the present water-splitting cycle is examined by means of full dimensional nonadiabatic electron–wavepacket dynamics based on multireference electronic wavefunctions and energy profiles estimated with rather accurate quantum chemical methods for all the metastable states appearing in the cycle.We theoretically propose a photoinduced water-splitting cycle catalyzed by a binuclear Mn oxo complex. In our “bottom-up approach” to this problem, we once proposed a working minimal model of water-splitting cycle in terms of a mononuclear Mn oxo complex as a catalyst along with water clusters [K. Yamamoto and K. Takatsuka, Phys. Chem. Chem. Phys. 20, 6708 (2018)]. However, this catalyst is not self-contained in that the cycle additionally needs buffering molecules for electrons and protons in order to reload the Mn complex with electrons and protons, which are lost by photoinduced charge separation processes. We here show that a binuclear Mn oxo complex works as a self-contained photocatalyst without further assistant of additional reagents and propose another catalytic cycle in terms of this photocatalyst. Besides charge separation and proton relay transfer, the proposed cycle consists of other fundamental chemical dynamics including electron–proton reloading, radical relay-transfer, and Mn reduction. T...

We present calculations of time-dependent photoelectron spectra of NO

In one type of photocatalytic dynamics of water splitting formally summarized as2H2O + 4hν + MH → 2H2O + M*H → 4H+ + 4e− + O2 + MHthe catalytic center M mainly composed of Mn oxides (clusters) along with supporting molecules like proteins is directly photoexcited and discharges electrons and protons. The mechanism can be comprehended in terms of the coupled proton electron-wavepacket transfer (CPEWT). In another type proposed in the literature, M is not directly photoexcited, and instead, lights are absorbed somewhere other than M, thereby creating complicated sequential steps (a ladder) of oxidation–reduction potential, thus sucking electrons successively from one molecular site to the next, and the final place providing electrons and protons is the catalytic center M. During charge separation dynamics, M is assumed to remain in the electronic ground state, and this type can be schematically summarized asM−H+ + Ω+ → M + H+ + Ω+e−where Ω indicates a cation species (a hole carrier) at the site of photon absorption. It is widely believed that the latter mechanism is responsible for water splitting in plants and cynobacteria, and M in photosystem II (PSII) is known to include Mn4CaO5. However, difficult questions about this mechanism of ground-state charge separation in the latter reaction arise as to whether it is quantum mechanically possible and what is it, if indeed possible? Besides, the time-constant for this reaction reported in the literature is so long, actually far longer than the time-scale for energy dissipation for inter- and intra-molecular vibrational energy redistribution, that the quantum mechanical coherence of the reaction should not be able to be maintained. More seriously, we wonder how protons and electrons can be isolated in the ground state, if any, and how they can be transferred unidirectionally (with no return)? We address these fundamental questions affirmatively by proposing a general chemical principle; collision induced charge separation dynamics in the ground state.

We theoretically studied the chemical principles behind the photodynamics of water splitting: 2H2O + 4hν + M → 4H+ + 4e− + O2 + M. To comprehend this simple looking but very complicated reaction, the mechanisms of at least three crucial phenomena, among others, need to be clarified, each of which is supposed to constitute the foundation of chemistry: (i) charge separation (4H+ + 4e−), (ii) the catalytic cycle for essentially the same reactions to be repeated by each of four photon absorptions with a catalyst M, and (iii) the generation of oxygen molecules of spin triplet. We have previously clarified the photodynamical mechanism of charge separation, which we refer to as coupled proton electron-wavepacket transfer (CPEWT), based on the theory of nonadiabatic electron wavepacket dynamics [K. Yamamoto and K. Takatsuka, ChemPhysChem, 2017, 18, 537]. CPEWT gives an idea of how charge separation can be materialized at each single photon absorption. Yet, this mechanism alone cannot address the above crucial items such as (ii) the catalytic cycle and (iii) O2 formation. In the studies of these fundamental processes, we constructed a possible minimal chemical system and perform semi-quantitative quantum chemical analyses, with which to attain insights about the possible mechanisms of photochemical water splitting. The present study has been inspired by the idea underlying the so-called Kok cycle, although we do not aim to simulate photosystem II in biological systems in nature. For instance, we assume here that a catalyst M (actually simple manganese oxides in this particular study) is pumped up to its excited states leading to charge separation by four-time photon absorption, each excitation of which triggers individual series of chemical reactions including the reorganization of the hydrogen-bonding network (cluster) of water molecules surrounding the photocatalytic center. It is shown that in the successive processes of restructuring of the relevant water cluster, the OO bond is formed and consequently an oxygen molecule of spin triplet can be isolated within a range of a given photon energy of about 3.0 eV.

An electron dynamics mechanism of charge separation in the initial stage of excited-state reactions of the class of XMnOH2 ⋅⋅⋅A${ \to }$XMnOH⋅⋅⋅HA (X=OH or OCaH; A=N-methylformamidine, guanidine, imidazole, or ammonia cluster) is reported. The dynamic effect of calcium doping is also revealed. This study provides a novel factor to be considered in designing efficient systems for photoinduced water splitting.

A theory for dynamics of molecular photoionization from nonadiabatic electron wavepackets driven by intense pulse lasers is proposed. Time evolution of photoelectron distribution is evaluated in terms of out-going electron flux (current of the probability density of electrons) that has kinetic energy high enough to recede from the molecular system. The relevant electron flux is in turn evaluated with the complex-valued electronic wavefunctions that are time evolved in nonadiabatic electron wavepacket dynamics in laser fields. To uniquely rebuild such wavefunctions with its electronic population being lost by ionization, we adopt the complex-valued natural orbitals emerging from the electron density as building blocks of the total wavefunction. The method has been implemented into a quantum chemistry code, which is based on configuration state mixing for polyatomic molecules. Some of the practical aspects needed for its application will be presented. As a first illustrative example, we show the results of hydrogen molecule and its isotope substitutes (HD and DD), which are photoionized by a two-cycle pulse laser. Photon emission spectrum associated with above threshold ionization is also shown. Another example is taken from photoionization dynamics from an excited state of a water molecule. Qualitatively significant effects of nonadiabatic interaction on the photoelectron spectrum are demonstrated.

The Longuet-Higgins (Berry) phase arising from nonadiabatic dynamics and the Aharonov-Bohm phase associated with the dynamics of a charged particle in the electromagnetic vector potential are well known to be individually a manifestation of a class of the so-called geometrical phase. We herein discuss another similarity between the force working on a charged particle moving in a magnetic field, the Lorentz force, and a force working on nuclei while passing across a region where they have a strong quantum mechanical kinematic (nonadiabatic) coupling with electrons in a molecule. This kinematic force is indeed akin to the Lorentz force in that its magnitude is proportional to the velocity of the relevant nuclei and works in the direction perpendicular to its translational motion. Therefore this Lorentz-like nonadiabatic force is realized only in space of more or equal to three dimensions, thereby highlighting a truly multi-dimensional effect of nonadiabatic interaction. We investigate its physical significance qualitatively in the context of breaking of molecular spatial symmetry, which is not seen otherwise without this force. This particular symmetry breaking is demonstrated in application to a coplanar collision between a planar molecule and an atom sharing the same plane. We show that the atom is guided by this force to the direction out from the plane, resulting in a configuration that distinguishes one side of the mirror plane from the other. This can serve as a trigger for the dynamics towards molecular chirality.

We propose a theoretical principle to directly monitor the bifurcation of quantum wavepackets passing through nonadiabatic regions of a molecule that is placed in intense continuous wave (CW) laser fields. This idea makes use of the phenomenon of laser-driven photon emission from molecules that can undergo nonadiabatic transitions between ionic and covalent potential energy surfaces like Li+ F− and LiF. The resultant photon emission spectra are of anomalous yet characteristic frequency and intensity, if pumped to an energy level in which the nonadiabatic region is accessible and placed in a CW laser field. The proposed method is designed to take the time-frequency spectrogram with an appropriate time-window from this photon emission to detect the time evolution of the frequency and intensity, which depends on the dynamics and location of the relevant nuclear wavepackets. This method is specifically designed for the study of dynamics in intense CW laser fields and is rather limited in scope than other tech...

We present calculations of time-dependent photoelectron spectra of NO2 after excitation to the A-band for comparison with extreme-ultraviolet (XUV) time-resolved photoelectron spectroscopy. We employ newly calculated potential energy surfaces of the two lowest-lying coupled 2A′ states obtained from multi-reference configuration-interaction calculations to propagate the photo-excited wave packet using a split-step-operator method. The propagation includes the nonadiabatic coupling of the potential surfaces as well as the explicit interaction with the pump pulse centered at 3.1 eV (400 nm). A semiclassical approach to calculate the time-dependent photoelectron spectrum arising from the ionization to the eight energetically lowest-lying states of the cation allows us to reproduce the static experimental spectrum up to a binding energy of 16 eV and enables direct comparisons with XUV time-resolved photoelectron spectroscopy.

When vibrational dynamics on an ionic state (large dipole moment) is coupled to that on a neutral state (small dipole moment) such as at an avoided crossing in the alkali halide system, the population transfer between the states cause oscillation of the molecular dipole, leading to dipole emission. Such dynamics may be driven by an external field. We study how the coupled wavepacket dynamics is affected by the parameters (intensity, frequency) of the driving field with the aim of making use of the photoemission as an alternative detection scheme of femtosecond and subfemtosecond vibrational and electronic dynamics or as a characteristic optical source.