Theoretical Shaping of Femtosecond Laser Pulses for Molecular Photodissociation with Control Techniques Based on Ehrenfest′s Dynamics and Time‐Dependent Density Functional Theory

The combination of nonadiabatic Ehrenfest‐path molecular dynamics (EMD) based on time‐dependent density functional theory (TDDFT) and quantum optimal control formalism (QOCT) was used to optimize the shape of ultra‐short laser pulses to achieve photodissociation of a hydrogen molecule and the trihydrogen cation H₃⁺. This work completes a previous one [A. Castro, ChemPhysChem, 2013 , 14, 1488–1495], in which the same objective was achieved by demonstrating the combination of QOCT and TDDFT for many‐electron systems on static nuclear potentials. The optimization model, therefore, did not include the nuclear movement and the obtained dissociation mechanism could only be sequential: fast laser‐assisted electronic excitation to nonbonding states (during which the nuclei are considered to be static), followed by field‐free dissociation. Here, in contrast, the optimization was performed with the QOCT constructed on top of the full dynamic model comprised of both electrons and nuclei, as described within EMD based on TDDFT. This is the first numerical demonstration of an optimal control formalism for a hybrid quantum–classical model, that is, a molecular dynamics method.     

Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well‐understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field‐induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time‐dependent processes like ion‐atom/molecule collisions, atom‐field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.     

Electron-nuclear correlations for photo-induced dynamics in molecular dimers

Ultrafast photoinduced dynamics of electronic excitation in molecular dimers is drastically affected by the dynamic reorganization of inter- and intra- molecular nuclear configuration modeled by a quantized nuclear degree of freedom. The dynamics of the electronic population and nuclear coherence is analyzed by solving the chain of coupled differential equations for population inversion, electron-vibrational correlation, etc. Intriguing results are obtained in the approximation of a small change of the nuclear equilibrium upon photoexcitation. In the limiting case of resonance between the electronic energy gap and the frequency of the nuclear mode these results are justified by comparison to the exactly solvable Jaynes-Cummings model. It is found that the photoinduced processes in the model dimer are arranged according to their time scales: (i) Fast scale of nuclear motion, (ii) intermediate scale of dynamical redistribution of electronic population between excited states as well as growth and dynamics of electron-nuclear correlation, (iii) slow scale of electronic population approach to the quasi-equilibrium distribution, decay of electron-nuclear correlation, and decrease of the amplitude of mean coordinate oscillation. The latter processes are accompanied by a noticeable growth of the nuclear coordinate dispersion associated with the overall nuclear wave packet width. The demonstrated quantum relaxation features of the photoinduced vibronic dynamics in molecular dimers are obtained by a simple method, applicable to systems with many degrees of freedom.     

Multistate multimode vibronic dynamics: entanglement of electronic and vibrational degrees of freedom in the benzene radical cation

An earlier theoretical treatment of multimode and multistate vibronic coupling in the benzene radical cation [Koppel et al., J. Chem. Phys. 117, 2657 (2002)] is extended to investigate also the behavior of the nuclear degrees of freedom and to include additional electronic states. The five lowest doublet electronic states are considered which have been shown earlier to be all interconnected through a series of conical intersections of their potential-energy surfaces. In the most extensive calculations, they are all included simultaneously in the quantum dynamical calculations performed, which represent a system of unprecedented complexity treated in this way. The results are compared with various reduced-dimensionality treatments (i.e., employing reduced vibrational and electronic function spaces). The different temporal behavior of the various electronic populations is emphasized and traced to the different locations of the various seams of conical intersections: due to the coherent oscillations of the time-dependent wave packet this leads to an oscillatory behavior in some cases and to monotonous behavior in others. A seemingly irreversible behavior of the system dynamics in this strictly microscopic treatment is confirmed. The importance of this benchmark system to highlight complex, entangled multimode, and multistate vibronic dynamics is pointed out.     

Electronic and nuclear flux analysis on nonadiabatic electron transfer reaction: A view from single-configuration adiabatic born–huang representation

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.     

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.     

The femtosecond dynamics of electron transfer in a modified photosynthesis reaction center: Quantum, classical, and kinetic analyses

The dynamics of electron transfer in a modified photosynthesis reaction center in which electron transfer from the bridge to the acceptor is blocked is considered. A microscopic model of the process is suggested. Within this model, the diabatic electronic states of the donor and bridge are described by one-dimensional displaced harmonic oscillators. The dynamics of the population of electronic states is calculated by the quantum method of wave packets and classical and kinetic modeling. The suggested model is used to study the qualitative dependence of the dynamics of electron transfer on the nonadiabatic interaction potential. The parameters of the model are determined by comparing the experimental and calculated absorption spectra of the product of electron transfer. It is shown that kinetic models can be used to approximately describe the dynamics of electron transfer in reaction centers. The boundaries of the applicability of the kinetic method are considered.     

Symmetry Breaking and Non-Born-Oppenheimer Effects in Radical Cations

The various electronic states in which molecules can exist are often considered to be independent. In this article we turn our attention to the limitations of this assumption, namely the interaction between different electronic states through the nuclear motion. This interaction can have several important consequences, two of which are discussed in some detail. One is a distortion of the molecular framework, leading to a lowering of the symmetry of a molecule in excited or ionic states compared to the neutral ground state. General aspects of this symmetry lowering are outlined and interpreted with the aid of typical examples. The other consequence considered is the ability of the nuclei to “jump” between different molecular potential energy surfaces (non-Born-Oppenheimer effects). The nature of this behavior is analyzed and it is argued that the “jumping” can be very fast and efficient, dominating completely the nuclear motion. To exemplify our general ideas we refer to the photoelectron spectra of ethylene and related compounds and demonstrate that they are governed by strong non-Born-Oppenheimer effects. It emerges that the Franck-Condon principle fails in the analysis of their vibronic structure.     

Electronic coherence dynamics in trans-polyacetylene oligomers

Electronic coherence dynamics in trans-polyacetylene oligomers are considered by explicitly computing the time dependent molecular polarization from the coupled dynamics of electronic and vibrational degrees of freedom in a mean-field mixed quantum-classical approximation. The oligomers are described by the Su-Schrieffer-Heeger Hamiltonian and the effect of decoherence is incorporated by propagating an ensemble of quantum-classical trajectories with initial conditions obtained by sampling the Wigner distribution of the nuclear degrees of freedom. The electronic coherence of superpositions between the ground and excited and between pairs of excited states is examined for chains of different length, and the dynamics is discussed in terms of the nuclear overlap function that appears in the off-diagonal elements of the electronic reduced density matrix. For long oligomers the loss of coherence occurs in tens of femtoseconds. This time scale is determined by the decay of population into other electronic states through vibronic interactions, and is relatively insensitive to the type and class of superposition considered. By contrast, for smaller oligomers the decoherence time scale depends strongly on the initially selected superposition, with superpositions that can decay as fast as 50 fs and as slow as 250 fs. The long-lived superpositions are such that little population is transferred to other electronic states and for which the vibronic dynamics is relatively harmonic.     

Quantum analogue of the Kolmogorov–Arnold–Moser transition in different quantum anharmonic oscillators

The results of numerical computations are presented for the Bohmian trajectories of the family of different one‐ and two‐dimensional anharmonic oscillators, which exhibit regular or chaotic motion in both classical and quantum domains, depending on the values of the parameters appearing in the respective Hamiltonians. Quantum signatures of the Kolmogorov–Arnold–Moser (KAM) transition from the regular to chaotic classical dynamics of these oscillators are studied using a quantum theory of motion (QTM) as developed by de Broglie and Bohm. A phase space distance function between two initially close Bohmian trajectories, the associated Kolmogorov–Sinai–Lyapunov (KSL) entropy, the phase space volume, the autocorrelation function, the associated power spectrum, and the nearest‐neighbor spacing distribution, clearly differentiate the quantum analogues of the corresponding regular and chaotic motions in the classical domain. These quantum anharmonic oscillators are known to be useful in several diverse branches of science. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Influence of nuclear exchange on nonadiabatic electron processes in H(+)+H2 collisions

H(+)+H(2) collisions are studied by means of a semiclassical approach that explicitly accounts for nuclear rearrangement channels in nonadiabatic electron processes. A set of classical trajectories is used to describe the nuclear motion, while the electronic degrees of freedom are treated quantum mechanically in terms of a three-state expansion of the collision wavefunction. We describe electron capture and vibrational excitation, which can also involve nuclear exchange and dissociation, in the E = 2-1000 eV impact energy range. We compare dynamical results obtained with two parametrizations of the potential energy surface of H(3)(+) ground electronic state. Total cross sections for E > 10 eV agree with previous results using a vibronic close-coupling expansion, and with experimental data for E < 10 eV. Additionally, some prototypical features of both nuclear and electron dynamics at low E are discussed.     

Realization of vibronic entanglement in terms of tunneling current in an artificial molecule

Based on the concept of molecular nonadiabatic processes, namely, curve crossing and electronic interstate coupling, here we have introduced a model of an artificial molecule composed of three coupled quantum dots in terms of displaced harmonic oscillators of the confinement potential. We have shown that the static and dynamic features of vibronic entanglement can be realized in terms of the tunneling current in our model. An entanglement sudden-death can be shown to be equivalent to the suppression of tunneling current at the appropriate parameters of the magnetic field. We have also provided the nonclassicality of the vibration of the dot confinement potential which maximizes at the anticrossing zone.     

E ⊗ ϵ Jahn–Teller anharmonic coupling for an octahedral system

The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian derived. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Communication: multistate quantum dynamics of photodissociation of carbon dioxide between 120 nm and 160 nm

UV absorption cross section of CO(2) is studied using high level ab initio quantum chemistry for electrons and iterative quantum dynamics for nuclear motion on interacting global full dimensional potential energy surfaces. Six electronic states-1, 2, 3(1)A(') and 1, 2, 3(1)A(")-are considered. At linearity, they correspond to the ground electronic state X?(1)Σ(g) (+) and the optically forbidden but vibronically allowed valence states 1(1)Δ(u), 1(1)Σ(u) (-), and 1(1)Π(g). In the Franck-Condon region, these states interact via Renner-Teller and conical intersections and are simultaneously involved in an intricate network of non-adiabatic couplings. The absorption spectrum, calculated for many rotational states, reproduces the distinct two-band shape of the experimental spectrum measured at 190 K and the characteristic patterns of the diffuse structures in each band. Quantum dynamics unravel the relative importance of different vibronic mechanisms, while metastable resonance states, underlying the diffuse structures, provide dynamically based vibronic assignments of individual lines.     

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.