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The quantum nuclear kinematic interactions with electrons (or nonadiabatic interactions) are the inherent driving force that possibly causes a mixture of the adiabatic electronic states in molecules. Particularly in systems whose electron wavepackets lie in a densely quasi-degenerate electronic-state manifold where many-dimensional and many-state nonadiabatic interactions last continually, we have found before that those extensive mixings can lead to a quantum electronic-state chaos [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 159, 074110 (2023)]. This chaos of electron dynamics is a new kind yet generic. This Communication identifies the mathematical/physical mechanism of this class of chaos by means of the collective coordinate analysis of the nonadiabatic interactions, along with the numerical applications to excited states of boron clusters. Some physical consequences of the present chaos are also discussed. [ABSTRACT FROM AUTHOR]

In general, for many-dimensional and many-state nonadiabatic dynamics composed of slow and fast modes, we geometrically decompose the nonadiabatic interactions by means of the method of singular value decomposition. Each pair of the left and right singular vectors connecting the slow (nuclear) and fast (electronic) modes gives rise to a one-dimensional collective coordinate, and the sum of them amounts to the total nonadiabatic interaction. The analysis identifies how efficiently the slow modes, thus decomposed, can induce a transition in their fast counterparts. We discuss the notions of nonadiabatic resonance and nonadiabatic chaos in terms of the decomposition. [ABSTRACT FROM AUTHOR]

We study the electronic spin flux (atomic-scale flow of the spin density in molecules) by a perturbation analysis and ab initio nonadiabatic calculations. We derive a general perturbative expression of the charge and spin fluxes and identify the driving perturbation of the fluxes to be the time derivative of the electron-nucleus interaction term in the Hamiltonian. We then expand the expression in molecular orbitals so as to identify relevant components of the fluxes. Our perturbation theory describes the electronic fluxes in the early stage of reactions in an intuitively clear manner. The perturbation theory is then applied to an analysis of the spin flux obtained in ab initio calculations of the radical reaction of O2 and CH3· starting from three distinct spin configurations; (a) CH3· and triplet O2 with total spin of the system set S t o t = 1 / 2 (b) CH3· and singlet O2, S t o t = 1 / 2 , and (c) CH3· and triplet O2, S t o t = 3 / 2. Further analysis of the time-dependent behaviors of the spin flux in these numerical simulations reveals (i) the spin flux induces rearrangement of the local spin structure, such as reduction of the spin polarization arising from the triplet O2 and (ii) the spin flux flows from O2 to CH3· in the reaction starting from spin configuration (a) and from CH3· to O2 in that starting from configuration (b), whereas no major intermolecular spin flux was observed in that starting from configuration (c). Our study thus establishes the mechanism of the spin flux that rearranges the local spin structures associated with chemical bonds. [ABSTRACT FROM AUTHOR]

We study the chaotic, huge fluctuation of electronic state, resultant intramolecular energy redistribution, and strong chemical bonding surviving the fluctuation with exceedingly long lifetimes of highly excited boron clusters. Those excited states constitute densely quasi-degenerate state manifolds. The huge fluctuation is induced by persisting multidimensional nonadiabatic transitions among the states in the manifold. We clarify the mechanism of their coexistence and its physical significance. In doing so, we concentrate on two theoretical aspects. One is quantum chaos and energy randomization, which are to be directly extracted from the properties of the total electronic wavefunctions. The present dynamical chaos takes place through frequent transitions from adiabatic states to others, thereby making it very rare for the system to find dissociation channels. This phenomenon leads to the concept of what we call intramolecular nonadiabatic electronic-energy redistribution, which is an electronic-state generaliztion of the notion of intramolecular vibrational energy redistribution. The other aspect is about the peculiar chemical bonding. We investigate it with the energy natural orbitals (ENOs) to see what kind of theoretical structures lie behind the huge fluctuation. The ENO energy levels representing the highly excited states under study appear to have four robust layers. We show that the energy layers responsible for chaotic dynamics and those for chemical bonding are widely separated from each other, and only when an event of what we call "inter-layer crossing" happens to burst can the destruction of these robust energy layers occur, resulting in molecular dissociation. This crossing event happens only rarely because of the large energy gaps between the ENO layers. It is shown that the layers of high energy composed of complex-valued ENOs induce the turbulent flow of electrons and electronic-energy in the cluster. In addition, the random and fast time-oscillations of those high energy ENOs serve as a random force on the nuclear dynamics, which can work to prevent a concentration of high nuclear kinetic energy in the dissociation channels. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The one-electron picture in molecular electronic state theory, particularly the molecular orbital (MO) theory with the Hartree–Fock approximation, has set a foundation to develop chemical science. Frontier orbital theory, or the theory of HOMO (highest occupied MO)–LUMO (lowest unoccupied MO) interaction, and the conservation rule of orbital symmetry are among the brightest achievements in a molecular orbital picture. After 70 years from the birth of frontier orbital theory, however, electronic wavefunctions treated in current quantum chemistry are often highly correlated and consist of extensive scales of electronic configurations to be more accurate and to cope with far more complicated reactions than concerted reactions. Under such circumstances, the MO approximation itself readily loses its validity, let alone the utter dominance of the HOMO–LUMO interaction. Recently, we have proposed an invariant method to extract general orbitals from such correlated electronic wavefunctions, which we refer to as Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. The energies of ENOs are summed exactly to the total electronic energy. The topological (symmetry) properties of a total wavefunction are represented by the relative phases of ENOs along with the continuity and crossing (avoided and conical intersection) among them. Only a small number of ENOs often dominate and characterize chemical reactions. With these properties of ENO, we explore a couple of simple and typical symmetry forbidden reactions, illustrating the effects of electron correlation and degeneracy in relevant ENOs. We propose the notion of "internal conical intersection" among ENOs, which leads to Jahn–Teller effect, pseudo-Jahn–Teller effect, and so on. We dare to explain the primary origin of elementary conical intersections and multidimensional avoided crossing in chemical reactions with the use of the notion of orbital crossing between those of HOMO–HOMO and LUMO–LUMO interactions and so on. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Löwdin, 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Schrödinger equation with the Coulombic and retarded transversal photon-exchange interactions. We also discuss a wavepacket type nuclear dynamics adapted for such dynamics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A theoretical method for real-time dynamics of nonadiabatic reorganization of electronic configurations in molecules is developed, with dual aim that the intramolecular electron dynamics can be probed by means of direct and/or indirect photoionizations and that the physical origins behind photoionization signals attained in the time domain can be identified in terms of the language of time-dependent quantum chemistry. In doing so, we first formulate and implement a new computational scheme for nonadiabatic electron dynamics associated with molecular ionization, which well fits in the general theory of nonadiabatic electron dynamics. In this method, the total nonadiabatic electron wavepackets are propagated in time directly with complex natural orbitals without referring to Hartree-Fock molecular orbitals, and the amount of electron flux from a molecular region leading to ionization is evaluated in terms of the relevant complex natural orbitals. In the second half of this paper, we apply the method to electron dynamics in the elementary processes consisting of the Auger decay to demonstrate the methodological significance. An illustrative example is taken from an Auger decay starting from the 2a1 orbital hole-state of H2O+. The roles of nuclear momentum (kinetic) couplings in electronic-state mixing during the decay process are analyzed in terms of complex natural orbitals, which are schematically represented in the conventional language of molecular symmetry of the Hartree-Fock orbitals. [ABSTRACT FROM AUTHOR]

A study is conducted to explore the dynamics of evaporation process of a high energy atomic cluster undergoing frequent structural isomerization which behaves like a liquid droplet. The findings from the studies could be used to study multichannel chemical reactions of nonrigid molecules having many local potential basins.

The time-dependent characteristics of quantum mechanical tunneling, fast tunneling in the early stage and slow and long-lasting tunneling in the later stage are studied. The results show that slow tunneling in the long time region is important, because it should dominate the time-dependent feature of tunneling.

We investigate how the nuclear dynamics at an avoided crossing is affected and can be controlled by the introduction of a laser field whose cycle is comparable to the time-scale of the nuclear dynamics. By introducing the concepts of light-induced effective potential energy curves and dynamical avoided crossing, we describe the laser controlled nuclear dynamics and present basic control scenarios, giving a detailed explanation of the underlying dynamical mechanisms. The scenarios presented allow for examples to understand from a different perspective the results of dynamic Stark control experiments. The proposed interpretation is applied to the laser-controlled nonadiabatic dynamics between the two lowest ¹Σ+ states of LiF, where the usefulness of the concepts developed is elucidated. [ABSTRACT FROM AUTHOR]