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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 propose a method using reduced size of Hilbert space to describe an electron dynamics in molecule and aggregate based on our previous theoretical scheme [ T. Yonehara and T. Nakajima, J. Chem. Phys. \textbf{147}, 074110 (2017) ]. The real-time time-dependent density functional theory is combined with newly introduced projected group diabatic Fock matrix. First, this projection method is applied to a test donor--acceptor dimer, namely, a naphthalene--tetracyanoethylene with and without initial local excitations and light fields. Secondly, we calculate an absorption spectrum of five-unit-polythiophene monomer. The importance of feedback of instantaneous density to Fock matrix is also clarified. In all cases, half of the orbitals were safely reduced without loss of accuracy in descriptions of properties. The present scheme provides one possible way to investigate and analyze a complex excited electron dynamics in molecular aggregates within a moderate computational cost., 18 pages ( Main 14 pages + Supplementary materials 4 pages ), 8 figures ( Main 5 figures + SI 3 figures ), 5 tables ( Main 3 tables + SI 2 tables ) , geometry data of molecular aggregates treated in the article

Proton dynamics in a tropolone crystal was studied by 2D quantization of nuclear motions using Born-Oppenheimer molecular dynamics. This study presents the characteristics of the conjugated system of O H stretching vibrations in the tropolone crystal. The MD simulations elucidate the presence of a pseudo-cyclic dimer structure in the crystal phase. The results obtained herein were compared with the IR spectroscopic data for the tropolone crystal. The skeleton and butterfly motions of the seven carbon rings strongly influence the strength of the hydrogen bonds in the cyclic dimers and are extensively discussed in this paper.

We introduce a practical calculation scheme for the description of excited electron dynamics in molecular aggregated systems within a locally group diabatic Fock representation. This scheme makes it easy to analyze the interacting time-dependent excitations of local sites in complex systems. In addition, light-electron couplings are considered. The present scheme is intended for investigations on the migration dynamics of excited electrons in light-energy conversion systems. The scheme was applied to two systems: a naphthalene(NPTL)-tetracyanoethylene(TCNE) dimer and a 20-mer circle of ethylene molecules. Through local group analyses of the dynamical electrons, we obtained an intuitive understanding of the electron transfers between the monomers.

We report a theoretical study of non-adiabatic electrons–nuclei coupled dynamics of diborane H 2 BH 2 BH 2 under several types of short pulse lasers. This molecule is known to have particularly interesting geometrical and electronic structures, which originate from the electron-deficient chemical bondings. We revisit the chemical bonding of diborane from the view point of electron wavepacket dynamics coupled with nuclear motions, and attempt to probe the characteristics of it by examining its response to intense laser fields. We study in the following three aspects, (i) bond formation of diborane by collision between two monoboranes, (ii) attosecond electron wavepacket dynamics in the ground state and first excited state by circularly polarized laser pulse, and (iii) induced fragmentation back to monoborane molecules by linearly polarized laser. The wave lengths of two types of laser field employed are 200 nm (in UV range) and 800 nm (in IR range), and we track the dynamics from hundreds of attoseconds up to few tens of femtoseconds. To this end, we apply the ab initio semiclassical Ehrenfest theory, into which the classical vector potential of a laser field is introduced. Basic features of the non-adiabatic response of electrons to the laser fields is elucidated in this scheme. To analyze the electronic wavepackets thus obtained, we figure out bond order density that is a spatial distribution of the bond order and bond order flux density arising only from the bonding regions, and so on. Main findings in this work are: (i) dimerization of monoboranes to diborane is so efficient that even intense laser is hard to prevent it; (ii) collective motions of electron flux emerge in the central BHHB bonding area in response to the circularly polarized laser fields; (iii) laser polarization with the direction of central two BH bonding vector is efficient for the cleavage of BH 3 –BH 3 ; and (iv) nuclear derivative coupling plays a critical role in the field induced fragmentation dynamics.

The cumulative reaction probabilities are calculated for the dissociation and isomerization reactions of formaldehyde in the ground state by the use of the Watson Hamiltonian. We devise an efficient computational procedure for treating the vibrational angular momentum operator. We employ an improved global potential function at the CCSD(T) level derived from the MP2 level one. The resultant cumulative reaction probability for the dissociation channel is ∼1.5 times larger than that for the isomerization one at the energy region of interest. It is also found that the transition state theory reproduces the result with the full Watson Hamiltonian within 10% error.

We constructed a full dimensional potential energy function of H2CO that can describe both the dissociation and isomerization channels by the modified Shepard interpolation method. Ab initio calculations at the MP2/cc-pVTZ level were carried out to obtain the local potential functions at about 4700 points. The interpolant points were sampled by classical trajectory calculations and by the grid searches in the internal coordinate space. Classical trajectory calculations were performed to examine the intramolecular dynamics associated with the dissociation as well as the product state distributions. The time scale of intramolecular vibrational energy randomization was much faster than that of the dissociation reaction. The dissociation rate was obtained from the classical trajectory results and the effect of the isomerization channel on the dissociation was estimated. The calculated rate constants were compared with those by Rice–Ramsperger–Kassel–Marcus theory.

Path-branching representation (or phase-space averaging and natural branching method (PSANB) as its approximation) of nonadiabatic electron wavepacket dynamics is now known to work well for avoided crossings in many dimensional nonadiabatic transitions [Yonehara, T.; Hanasaki, K.; Takatsuka, K. Chem. Rev. 2012, 112, 499]. In this paper we examine feasibility of the path-branching representation in the theoretical studies of conical intersection (CI). The most characteristic feature of CI is the Herzberg-Longuet-Higgins phase (or the Berry phase) arising from the electronic part of the total wave function, and accordingly quantum phases of both electronic and nuclear dynamics should be taken into account in a balanced manner. We first show the PSANB can well capture the essential feature of the phase dynamics of CI. However, the nuclear phases, the wavelength of which is far shorter than that of the electronic phases, make the computation of nonadiabatic transition extremely oscillatory, resulting in very slow convergence with respect to the number of sampling paths. A similar difficulty quite often takes place in theoretical chemical dynamics. To cope with this situation, we devise a simple and tractable approximation in the application of PSANB resting on the fact that a small number of PSANB paths already reproduce accurate nonadiabatic transition probability.

We develop a theory and the method of its application for chemical dynamics in systems, in which the adiabatic potential energy hyper-surfaces (PES) are densely quasi-degenerate to each other in a wide range of molecular geometry. Such adiabatic electronic states tend to couple each other through strong nonadiabatic interactions. Technically, therefore, it is often extremely hard to accurately single out the individual PES in those systems. Moreover, due to the mutual nonadiabatic couplings that may spread wide in space and due to the energy-time uncertainty relation, the notion of the isolated and well-defined potential energy surface should lose the sense. On the other hand, such dense electronic states should offer a very interesting molecular field in which chemical reactions to proceed in characteristic manners. However, to treat these systems, the standard theoretical framework of chemical reaction dynamics, which starts from the Born-Oppenheimer approximation and ends up with quantum nuclear wavepacket dynamics, is not very useful. We here explore this problem with our developed nonadiabatic electron wavepacket theory, which we call the phase-space averaging and natural branching (PSANB) method [T. Yonehara and K. Takatsuka, J. Chem. Phys. 129, 134109 (2008)], or branching-path representation, in which the packets are propagated in time along the non-Born-Oppenheimer branching paths. In this paper, after outlining the basic theory, we examine using a one-dimensional model how well the PSANB method works with such densely quasi-degenerate nonadiabatic systems. To do so, we compare the performance of PSANB with the full quantum mechanical results and those given by the fewest switches surface hopping (FSSH) method, which is known to be one of the most reliable and flexible methods to date. It turns out that the PSANB electron wavepacket approach actually yields very good results with far fewer initial sampling paths. Then we apply the electron wavepacket dynamics in path-branching representation and the so-called semiclassical Ehrenfest theory to a hydrogen molecule embedded in twelve membered boron cluster (B(12)) in excited states, which are densely quasi-degenerate due to the vacancy in 2p orbitals of boron atom [1s(2)2s(2)2p(1)]. Bond dissociation of the hydrogen molecule quickly takes place in the cluster and the resultant hydrogen atoms are squeezed out to the surface of the cluster. We further study collision dynamics between H(2) and B(12), which also gives interesting phenomena. The present study suggests an interesting functionality of the boron clusters.

Following the previous study on nonadiabatic reaction dynamics including boron clusters [T. Yonehara and K. Takatsuka, J. Chem. Phys. 137, 22A520 (2012)], we explore deep into highly excited electronic states of the singlet boron cluster (B12) to find the characteristic features of the densely quasi-degenerate electronic state manifold, which undergo very frequent nonadiabatic transitions and thereby intensive electronic state mixing among very many of the relevant states. So much so, isolating the individual adiabatic states and tracking the expected potential energy surfaces both lose the physical sense. This domain of molecular situation is far beyond the realm of the Born-Oppenheimer approximation. To survey such a violent electronic state-mixing, we apply a method of nonadiabatic electron wavepacket dynamics, the semiclassical Ehrenfest method. We have tracked those electron wavepackets and found the electronic state mixing looks like an ultrafast diffusion in the Hilbert space, which results in huge fluctuation. Furthermore, due to such a violent mixing, the quantum phases associated with the electronic states are swiftly randomized, and consequently the coherence among the electronic states are lost quickly. Besides, these highly excited states are mostly of highly poly-radical nature, even in the spin singlet manifold and the number of radicals amounts up to 10 electrons in the sense of unpaired electrons. Thus the electronic states are summarized to be poly-radical and decoherent with huge fluctuation in shorter time scales of vibrational motions. The present numerical study sets a theoretical foundation for unknown molecular properties and chemical reactivity of such densely quasi-degenerate chemical species.

We extend our formerly proposed theory for non-Born-Oppenheimer electronic and nuclear wavepacket dynamics within on-the-fly scheme [T. Yonehara, S. Takahashi, and K. Takatsuka, J. Chem. Phys. 130, 214113 (2009)] to a case of nonadiabatic dynamics under an intense laser field: electron wavepacket in a molecule is propagated in attosecond time-scale along non-Born-Oppenheimer nuclear paths that smoothly branch due to nonadiabatic coupling and/or optical interactions. Such branching paths are determined consistently with the motion of the electron wavepackets. Furthermore, these nuclear paths are quantized in terms of Gaussian wavepackets (action decomposed function), which can be applied to nonclassical paths. Both electronic wavepacket dynamics and quantization of non-Born-Oppenheimer paths are generalized so as to include the direct effects of the classical vector potential of electromagnetic fields. In the second half of this paper, we perform numerical studies to explore nonadiabatic dynamics in a laser field by examining two cases: one is a two-state model system having an avoided crossing, and the other is two-state dynamics in HF molecule on the two low lying ab initio potential curves. Both are placed in laser fields. With the former system, we survey some basic properties of the coupling of nonadiabatic dynamics and laser interaction varying the relevant coupling parameters such as the laser timing with respect to the incident of nonadiabatic transition. This investigation will set a foundation for the future studies of control of electronic states in realistic multidimensional molecular systems. Application to the latter system shows that non-Born-Oppenheimer quantum chemistry in laser fields is indeed useful in the study of dynamics in ab initio level. Through the comparison with full quantum data, we verify that the formalism and methodology developed here work accurately. Furthermore, we attain some basic insight about the characteristics of molecules in laser fields.

A practical quantum theory for unifying electronic and nuclear dynamics, which were separated by the Born–Oppenheimer approximation, is proposed. The theory consists of two processes. Nonadiabatic (quantum) electron wavepacket dynamics on branching (non-Born–Oppenheimer) nuclear paths are first constructed. Since these paths are not the classical trajectories, most of the existing semiclassical theories to generate quantum wavepacket do not work. Therefore, we apply our own developed semiclassical wavepacket theory to these generated non-Born–Oppenheimer paths. This wavepacket is generated based on what we call the action decomposed function, which does not require the information of the so-called stability matrix. Thus, the motion of nuclei is also quantized, and consequently the total wave function is represented as a series of entanglement between the electronic and nuclear wavepackets. In the last half of the article, we show the practice to demonstrate how these independent theories can be unified to give electron-nuclear wavepackets in a two-state model. The wavepackets up to the phases and resultant transition probabilities are compared to the full quantum-mechanical counterparts. It turns out that the lowest level approximation to the wavepacket approach already shows a good agreement with the full quantum quantities. Thus, the present theoretical framework gives a basic method with which to study non-Born–Oppenheimer electronic and nuclear wavepacket states relevant to ultrafast chemical events.

We propose a simple and tractable method to treat quantum electron wavepacket dynamics that nonadiabatically couples with “classical” nuclear motions in mixed quantum-classical representation. The electron wavepacket is propagated inducing electronic-state mixing along our proposed paths. It has been shown in our previous studies that classical force working on nuclei in a nonadiabatic region is represented in a matrix form (called the force matrix), and the solutions of the Hamilton canonical equations of motion for nuclei based on this force matrix give rise to a cascade of infinitely many branching paths when solved simultaneously with electronic-state mixing. As a tractable approximation to these rigorous solutions, we here devise a method to provide much simpler nonadiabatic paths: (i) extract one or a few number of representative paths by taking an average over the paths in phase space (not averaging over the forces) that should be otherwise undergo the fine branching. (ii) After the nonadiabatic coupling becomes sufficiently small, let these paths naturally branch by running them with their own individual eigenforces (the eigenvalues of the force matrix). Since the eigenforces coincide with the forces of adiabatic potential energy surfaces in the limit of zero nonadiabatic coupling, these branching paths eventually run on one of possible adiabatic potential energy surfaces, converging to a classical path (Born–Oppenheimer path). The paths thus created are theoretically satisfactory in that they realize the coherent mixing of electronic states in the manner of quantum entanglement and yet eventually become consistent with the Born–Oppenheimer classical trajectories. We test the present method numerically with the use of two- and three-state systems that are extracted from ab initio calculations for the excited states of LiH molecule.

We study quantum dynamics of the multichannel reactions of H(2)CO including the molecular and radical dissociation channels as well as the isomerization ones, H(2)CO--trans-HCOH and trans-HCOH--cis-HCOH. For this purpose, the previously developed potential energy function [T. Yonehara and S. Kato, J. Chem. Phys. 117, 11131 (2002)] is refined to give accurate transition state energies and to describe the radical dissociation channel. The cumulative reaction probabilities for the molecular dissociation and two isomerization channels are calculated by using the full Watson Hamiltonian. We also carry out wave packet dynamics calculations starting from the transition state region for the molecular dissociation. A contracted basis set for the angular coordinates is constructed to reduce the size of dynamics calculations. The intramolecular vibrational relaxation dynamics is found to be fast and almost complete within 300 fs. Using the energy filtered wave functions, the time propagation of HCOH population is obtained in the energy range from 81 to 94 kcal/mol. The branching ratio of the radical product is estimated by calculating the time dependent reactive fluxes to the molecular and radical dissociation products.

A theory of quantum electron wavepacket dynamics that nonadiabatically couples with classical nuclear motions in intense optical fields is studied. The formalism is intended to track the laser-driven electron wavepackets in terms of the linear combination of configuration-state functions generated with ab initio molecular orbitals. Beginning with the total quantum Hamiltonian for electrons and nuclei in the vector potential of classical electromagnetic field, we reduce the Hamiltonian into a mixed quantum-classical representation by replacing the quantum nuclear momentum operators with the classical counterparts. This framework gives equations of motion for electron wavepackets in an intense laser field through the time dependent variational principle. On the other hand, a generalization of the Newtonian equations provides a matrix form of forces acting on the nuclei for nonadiabatic dynamics. A mean-field approximation to the force matrix reduces this higher order formalism to the semiclassical Ehrenfest theory in intense optical fields. To bring these theories into a practical quantum chemical package for general molecules, we have implemented the relevant ab initio algorithms in it. Some numerical results in the level of the semiclassical Ehrenfest-type theory with explicit use of the nuclear kinematic (derivative) coupling and the velocity form for the optical interaction are presented.