Exact factorization of the photon-electron-nuclear wavefunction: Formulation and coupled-trajectory dynamics.

We employ the exact-factorization formalism to study the coupled dynamics of photons, electrons, and nuclei at the quantum mechanical level, proposing illustrative examples of model situations of nonadiabatic dynamics and spontaneous emission of electron-nuclear systems in the regime of strong light-matter coupling. We make a particular choice of factorization for such a multi-component system, where the full wavefunction is factored as a conditional electronic amplitude and a marginal photon-nuclear amplitude. Then, we apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm to perform trajectory-based simulations, by treating photonic and nuclear degrees of freedom on equal footing in terms of classical-like trajectories.

Efficient vibrationally correlated calculations using -mode expansion-based kinetic energy operators.

Due to its efficiency and flexibility, the -mode expansion is a frequently used tool for representing molecular potential energy surfaces in quantum chemical simulations. In this work, we investigate the performance of -mode expansion-based models of kinetic energy operators in general polyspherical coordinate systems. In particular, we assess the operators with respect to accuracy in vibrationally correlated calculations and their effect on potential energy surface construction with the adaptive density guided approach.

Vibrationally correlated calculations in polyspherical coordinates: Taylor expansion-based kinetic energy operators.

The efficiency of quantum chemical simulations of nuclear motion can in many cases greatly benefit from the application of curvilinear coordinate systems. This is rooted in the fact that a set of smartly selected curvilinear coordinates may represent the motion naturally well, thus decreasing the couplings between motions in these coordinates. In this study, we assess the validity of different Taylor expansion-based approximations of kinetic energy operators in a (curvilinear) polyspherical parametrization.

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics.

Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy.

Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality.

In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)].

The coupling of the hydrated proton to its first solvation shell.

The Zundel ([Formula: see text]) and Eigen ([Formula: see text]) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit.

Adiabatic and Nonadiabatic Dynamics with Interacting Quantum Trajectories.

We present a quantum dynamics method based on the propagation of interacting quantum trajectories to describe both adiabatic and nonadiabatic processes within the same formalism. The idea originates from the work of Poirier [ 4-14] and Schiff and Poirier [ 031102] on quantum dynamics without wavefunctions. It consists of determining the quantum force arising in the Bohmian hydrodynamic formulation of quantum dynamics using only information about quantum trajectories.

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics.

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry.

Smolyak Algorithm Adapted to a System-Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions.

A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom.

Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories.

The exact factorization of the electron-nuclear wavefunction is applied to the study of photo-isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects.

Quantum dynamics with curvilinear coordinates: models and kinetic energy operator.

In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived for small systems or special kinds of coordinates, a and approach allows one to compute them in terms of sophisticated curvilinear coordinates.

Electronic Structure and Excited States of the Collision Reaction O(P) + CH: A Multiconfigurational Perspective.

We present a study of the O(P) + CH scattering reaction, a process that takes place in the interstellar medium and is of relevance in atmospheric chemistry as well. A comprehensive investigation of the electronic properties of the system has been carried out based on multiconfigurational ab initio CASSCF/CASPT2 calculations, using a robust and consistent active space that can deliver accurate potential energy surfaces in the key regions visited by the system. The paper discloses detailed description of the primary reaction pathways and the relevant singlet and triplet excited states at the CASSCF and CASPT2 level, including an accurate description of the critical configurations, such as minima and transition states.

Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies.

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys.

Quantum and Quantum-Classical Studies of the Photoisomerization of a Retinal Chromophore Model.

We report an in-depth analysis of the photo-induced isomerization of the 2--penta-2,4-dieniminium cation: a minimal model of the 11- retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently developed three-dimensional potentials parametrized on multi-state multi-configurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic wavepacket propagation and, therefore, a purely quantum treatment.

Internal Conversion and Intersystem Crossing with the Exact Factorization.

We present a detailed derivation of the generalized coupled-trajectory mixed quantum-classical (G-CT-MQC) algorithm based on the exact-factorization equations. The ultimate goal is to propose an algorithm that can be employed for molecular dynamics simulations of nonradiative phenomena, as the spin-allowed internal conversions and the spin-forbidden intersystem crossings. Internal conversions are nonadiabatic processes driven by the kinetic coupling between electronic states, whereas intersystem crossings are mediated by the spin-orbit coupling.

First-principles description of intra-chain exciton migration in an oligo(para-phenylene vinylene) chain. I. Generalized Frenkel-Holstein Hamiltonian.

A generalized Frenkel-Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al.

Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator.

We present the first use of curvilinear vibrational coordinates, specifically polyspherical coordinates, in combination with vibrational coupled cluster theory. The polyspherical coordinates are used in the context of both the adaptive density-guided approach to potential energy surface construction and in the subsequent vibrational coupled cluster calculations of anharmonic vibrational states. Results obtained based on the polyspherical coordinate parametrization are compared to results obtained with the use of rectilinear vibrational coordinates, namely, normal coordinates and hybrid optimized and localized coordinates for the formaldehyde molecule.

Spin-Orbit Interactions in Ultrafast Molecular Processes.

We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factorization of the electron-nuclear wave function. We revisit the original derivation by including spin-orbit coupling, and show how the dynamics driven by the time-dependent potential energy surface alleviates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance in the treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets.

Intramolecular stretching vibrational states and frequency shifts of (H) confined inside the large cage of clathrate hydrate from an eight-dimensional quantum treatment using small basis sets.

We report the results of calculations pertaining to the HH intramolecular stretching fundamentals of (p-H) encapsulated in the large cage of structure II clathrate hydrate. The eight-dimensional (8D) quantum treatment assumes rotationless (j = 0) H moieties and a rigid clathrate structure but is otherwise fully coupled. The (H)-clathrate interaction is constructed in a pairwise-additive fashion, by combining the ab initio H-HO pair potential for flexible H and rigid HO [D.

H, HD, and D in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates.

We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H, HD, and D molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 HO molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H in the hydrate domain, based on an ab initio 6D H-HO pair potential for flexible H and rigid HO. They extend to the first excited (v = 1) vibrational state of H, along with two isotopologues, providing a direct computation of vibrational frequency shifts.

A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran.

We present a model for the lowest two potential energy surfaces (PESs) that describe the photoinduced ring-opening reaction of benzopyran taken as a model compound to study the photochromic ring-opening reaction of indolinobenzospiropyran and its evolution toward its open-chain analog. The PESs are expressed in terms of three effective rectilinear coordinates. One corresponds to the direction between the equilibrium geometry in the electronic ground state, referred to as the Franck-Condon geometry, and the minimum of conical intersection (CI), while the other two span the two-dimensional branching space at the CI.

Does cage quantum delocalisation influence the translation-rotational bound states of molecular hydrogen in clathrate hydrate?

In this study, we examine the effect of a flexible description of the clathrate hydrate framework on the translation-rotation (TR) eigenstates of guest molecules such as molecular hydrogen. Traditionally, the water cage structure is assumed to be rigid, thus ignoring the quantum nature of hydrogen nuclei in the water framework. However, it has been shown that protons in a water molecule possess a marked delocalised character in many situations, ranging from water clusters to proton transfer in the bulk.

Conformational Dynamics Guides Coherent Exciton Migration in Conjugated Polymer Materials: First-Principles Quantum Dynamical Study.

We report on high-dimensional quantum dynamical simulations of photoinduced exciton migration in a single-chain oligothiophene segment, in view of elucidating the controversial nature of the elementary exciton transport steps in semiconducting polymers. A novel first-principles parametrized Frenkel J aggregate Hamiltonian is employed that goes significantly beyond the standard Frenkel-Holstein Hamiltonian. Departing from a nonequilibrium state created by photoexcitation, these simulations provide evidence of an ultrafast two-timescale process at low temperatures, involving exciton-polaron formation within tens of femtoseconds (fs), followed by torsional relaxation on an ∼400  fs timescale.

The effect of the condensed-phase environment on the vibrational frequency shift of a hydrogen molecule inside clathrate hydrates.

We report a theoretical study of the frequency shift (redshift) of the stretching fundamental transition of an H molecule confined inside the small dodecahedral cage of the structure II clathrate hydrate and its dependence on the condensed-phase environment. In order to determine how much the hydrate water molecules beyond the confining small cage contribute to the vibrational frequency shift, quantum five-dimensional (5D) calculations of the coupled translation-rotation eigenstates are performed for H in the v=0 and v=1 vibrational states inside spherical clathrate hydrate domains of increasing radius and a growing number of water molecules, ranging from 20 for the isolated small cage to over 1900. In these calculations, both H and the water domains are treated as rigid.

On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections.

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol.