Quantum Wave Packet Dynamics Research Articles

Identification of a receiver triplet state in the ultrafast intersystem crossing of carbonylpyrenes.

The near-unity triplet quantum yield of photoexcited carbonyl functionalized pyrenes is theoretically investigated. The estimated energetics of singlet-triplet manifolds and relevant spin-orbit coupling parameters strongly suggest triplet state formation via the S1→ T4/T5 pathway. Quantum wavepacket dynamics of triplet manifolds within the linear vibronic coupling approach reveal that the receiver triplet state would undergo rapid internal conversion decay to the lower triplet state(s), facilitating efficient triplet generation by minimizing the reverse intersystem crossing possibilities. On the basis of these results, a unified mechanism is proposed to describe the ultrafast intersystem crossing process in these molecules.

Dynamics studies of the H + HBr reaction: Based on a new potential energy surface.

The initial state specific quantum wave packet dynamics studies of the H + HBr (v0 = 0, j0 = 0-2) reaction were performed using a new global potential energy surface (PES) of the ground state of the BrH2 system for the collision energy ranging from 0.01 to 2.0 eV. The PES was constructed using the permutation invariant polynomial neural network method based on approximately 63 000 ab initio points, which were calculated by the multireference configuration interaction method with AVTZ and AVQZ basis sets. To improve the accuracy of the PES, Davidson's correction and spin-orbit coupling effects were considered in the ab initio calculation and the basis set was extrapolated to complete basis set limit. The new PES was compared with the previous ones and also the available experimental data, which suggests that the new PES is more accurate. The state-to-state quantum wave packet dynamics was carried out using the reactant-coordinate based approach. The reaction probabilities, integral and differential cross sections, rovibrational state distributions of product and rate constants, etc., were compared with the available theoretical and experimental studies. In general, the present work is in better agreement with the available experimental data. The quantum dynamics studies suggest that the rotational excitation of HBr has little effect on the reaction.

Simulation of ultrafast excited-state dynamics and elastic x-ray scattering by quantum wavepacket dynamics.

Simulation of the ultrafast excited-state dynamics and elastic X-ray scattering of the [Fe(bmip)2]2+ [bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-4-pyridine] complex is presented and analyzed. We employ quantum wavepacket dynamics simulations on a 5-dimensional potential energy surface (PES) calculated by time-dependent density functional theory with 26 coupled diabatic states. The simulations are initiated by explicit inclusion of a time-dependent electromagnetic field. In the case of resonant excitation into singlet metal-to-ligand charge transfer (1MLCT) states, kinetic (exponential) population dynamics are observed with small nuclear motion. In agreement with transient optical absorption spectroscopy experiments, we observe a subpicosecond 1MLCT → 3MLCT intersystem crossing and a subsequent decay into triplet metal-centered (3MC) states on a picosecond time scale. The simulated time-resolved difference scattering signal is dominated by the 3MC component, for which the structural distortions are significant. On the other hand, excitation into 1MC states leads to ballistic (nonexponential) population dynamics with strong nuclear motion. The reason for these ballistic dynamics is that in this case, the excitation occurs into a nonequilibrium region, i.e., far from the minimum of the 1MC PES. This results in wavepacket dynamics along the principal breathing mode, which is clearly visible in both the population dynamics and difference scattering. Finally, the importance of decomposing the difference scattering into components by electronic states is highlighted, information which is not accessible from elastic X-ray scattering experiments.

Three-dimensional spin-dependent dynamics in linearly polarized standing-wave fields

There is a revival of the problem of how a relativistic particle with spin moves through an electromagnetic field. Our paper focuses on the spin-dependent dynamics of electrons in linearly polarized laser fields based on the Dirac equation and a classical spin model. It is proved that an electron at rest undergoes a three-dimensional motion moving out of the polarization-propagation plane when the initial spin is perpendicular to the magnetic field. We make a comprehensive investigation of the dynamics of quantum wave packets and classical electrons in both plane-wave and standing-wave fields. The wave packet travels in accordance with its center of mass in a plane-wave field but spreads heavily in a standing-wave field. The ensembles of classical electrons turn out to well simulate the quantum wave-packet dynamics in the standing-wave fields. We give the extended calculations of the electron dynamics with spin in the standing-wave field in the chaotic regime and find the quantum correspondence to the classical chaotic dynamics.

Theoretical Study on the Spectroscopic Observation of Intersystem Crossing between 3B1 and 1A1 States of GeH2 Using the GeH2- (2B1) Anion.

We performed nonadiabatic quantum wave packet dynamics calculations to simulate the photodetachment spectrum of the GeH2- (2B1) anion. We developed the (4 × 4) diabatic potential energy surfaces to describe the intersystem crossing transitions between the neutral 1A1 and 3B1 states induced by spin-orbit interactions based on ab initio calculations. The spin-orbit coupling matrix elements were calculated using the Breit-Pauli Hamiltonian with the spin-free states obtained from the multireference configuration interaction method. The calculated photodetachment spectrum showed many intense peaks that could be assigned to the vibrational states mostly associated with the pure singlet or triplet spin states. However, we also found weak satellite peaks that could be assigned to vibrational states consisting of the highly excited vibrational state on the singlet surface and the low-lying vibrational state on the triplet surface.

Ultrafast carbon monoxide photolysis and heme spin-crossover in myoglobin via nonadiabatic quantum dynamics

Light absorption of myoglobin triggers diatomic ligand photolysis and a spin crossover transition of iron(II) that initiate protein conformational change. The photolysis and spin crossover reactions happen concurrently on a femtosecond timescale. The microscopic origin of these reactions remains controversial. Here, we apply quantum wavepacket dynamics to elucidate the ultrafast photochemical mechanism for a heme–carbon monoxide (heme–CO) complex. We observe coherent oscillations of the Fe–CO bond distance with a period of 42 fs and an amplitude of ∼1 Å. These nuclear motions induce pronounced geometric reorganization, which makes the CO dissociation irreversible. The reaction is initially dominated by symmetry breaking vibrations inducing an electron transfer from porphyrin to iron. Subsequently, the wavepacket relaxes to the triplet manifold in ∼75 fs and to the quintet manifold in ∼430 fs. Our results highlight the central role of nuclear vibrations at the origin of the ultrafast photodynamics of organometallic complexes.

Quantum dynamics of Rb atoms desorbing off the surface of He nanodroplets

The desorption of excited rubidium (Rb) atoms off the surface of helium (He) nanodroplets is studied in detail using femtosecond time-resolved photoion and photoelectron imaging spectroscopy in combination with quantum wave packet simulations. The good agreement of the measured time-dependent velocity distributions with the simulation when exciting the Rb dopant atoms into the 6p-state supports the pseudo-diatomic model (PDM) for the Rb-He droplet interaction, even on the level of quantum wave packet dynamics. Time-resolved photoelectron spectra reveal the partitioning of excitation energy into the dopant and the droplet degrees of freedom.

Quantum wave packet dynamics of the H + Li2 reaction at state-to-state level of theory

The time-dependent wave packet method with a second order split operator is employed to study the state-to-state resolved reaction dynamics of the H+Li2 system. The dynamics properties, such as reaction probability, integral cross-section, differential cross-section and the rovibrational state distribution of the product are fully calculated in the present work. Both forward and backward scattering signals peaked at two extreme angles, indicating that the insert reaction mechanism plays an important role and that the statistic model is highly suitable to assess the reaction dynamics H+Li2.

Geometric Phase Effects in Nonadiabatic Dynamics near Conical Intersections

Dynamical consideration that goes beyond the common Born-Oppenheimer approximation (BOA) becomes necessary when energy differences between electronic potential energy surfaces become small or vanish. One of the typical scenarios of the BOA breakdown in molecules beyond diatomics is a conical intersection (CI) of electronic potential energy surfaces. CIs provide an efficient mechanism for radiationless electronic transitions: acting as "funnels" for the nuclear wave function, they enable rapid conversion of the excessive electronic energy into the nuclear motion. In addition, CIs introduce nontrivial geometric phases (GPs) for both electronic and nuclear wave functions. These phases manifest themselves in change of the wave function signs if one considers an evolution of the system around the CI. This sign change is independent of the shape of the encircling contour and thus has a topological character. How these extra phases affect nonadiabatic dynamics is the main question that is addressed in this Account. We start by considering the simplest model providing the CI topology: two-dimensional two-state linear vibronic coupling model. Selecting this model instead of a real molecule has the advantage that various dynamical regimes can be easily modeled in the model by varying parameters, whereas any fixed molecule provides the system specific behavior that may not be very illustrative. After demonstrating when GP effects are important and how they modify the dynamics for two sets of initial conditions (starting from the ground and excited electronic states), we give examples of molecular systems where the described GP effects are crucial for adequate description of nonadiabatic dynamics. Interestingly, although the GP has a topological character, the extent to which accounting for GPs affect nuclear dynamics profoundly depends on topography of potential energy surfaces. Understanding an extent of changes introduced by the GP in chemical dynamics poses a problem of capturing GP effects by approximate methods of simulating nonadiabatic dynamics that can go beyond simple models. We assess the performance of both fully quantum (wave packet dynamics) and quantum-classical (surface-hopping, Ehrenfest, and quantum-classical Liouville equation) approaches in various cases where GP effects are important. It has been identified that the key to success in approximate methods is a method organization that prevents the quantum nuclear kinetic energy operator to act directly on adiabatic electronic wave functions.

Photodissociation dynamics of the pyridinyl radical: Time-dependent quantum wave-packet calculations.

The H-atom photodissociationreaction from the pyridinyl radical (C5H5NH) via the low-lying πσ* excited electronic state is investigated by nonadiabatic time-dependent quantum wave-packet dynamics calculations. A model comprising three electronic states and three nuclear coordinates has been constructed using ab initio multi-configurational self-consistent-field and multi-reference perturbation theory methods. Two conical intersections among the three lowest electronic states have been characterized in the framework of the linear vibronic-coupling model. Time-dependent wave-packet simulations have been performed using the multi-configuration time-dependent Hartree method. The population dynamics of the diabatic and adiabatic electronic states and the time-dependent dissociation behavior are analyzed for various vibrational initial conditions. The results provide detailed mechanistic insight into the photoinduced H-atom dissociation process from a hypervalent aromatic radical and show that an efficient dissociationreaction through two conical intersections is possible.

Photophysics of a copper phenanthroline elucidated by trajectory and wavepacket-based quantum dynamics: a synergetic approach.

On-the-fly excited state molecular dynamics is a valuable method for studying non-equilibrium processes in excited states and is beginning to emerge as a mature approach much like its ground state counterparts. In contrast to quantum wavepacket dynamics methods, it negates the need for modelling potential energy surfaces, which usually confine nuclear motion within a reduced number of vibrational modes. In addition, on-the-fly molecular dynamics techniques are easily combined with the atomistic description of the solvents (through the QM/MM approach) making it possible to explicitly address the effect of the environment. Herein, we study the nonadiabatic relaxation of photoexcited [Cu(dmp)2]+ (dmp = 2,9-dimethyl-1,10-phenanthroline) using QM/MM Trajectory Surface Hopping (TSH). We show that the decay of the initially excited singlet state into the lowest singlet (S1) state occurs within 100 fs, in agreement with previous experiments, and is slightly influenced by the solvent. Using a principal component analysis (PCA), we also identify the dominant normal modes activated during the excited state decay, which are then used to design the vibronic Hamiltonian for quantum wavepacket dynamics simulations.

Time-dependent quantum wave packet dynamics to study charge transfer in heavy particle collisions.

The method of time-dependent quantum wave packet dynamics has been successfully extended to study the charge transfer/exchange process in low energy two-body heavy particle collisions. The collision process is described by coupled-channel equations with diabatic potentials and (radial and rotational) couplings. The time-dependent coupled equations are propagated with the multiconfiguration time-dependent Hartree method and the modulo squares of S-matrix is extracted from the wave packet by the flux operator with complex absorbing potential (FCAP) method. The calculations of the charge transfer process 12Σ+ H-(1s2)+Li(1s22s)→22Σ+/32Σ+/12Π H(1s)+Li-(1s22s2l)(l=s,p) at the incident energy of about [0.3, 1.3] eV are illustrated as an example. It shows that the calculated reaction probabilities by the present FCAP reproduce that of quantum-mechanical molecular-orbital close-coupling very well, including the peak structures contributed by the resonances. Since time-dependent external interactions can be directly included in the present FCAP calculations, the successful implementation of FCAP provides us a powerful potential tool to study the quantum control of heavy particle collisions by lasers in the near future.

High-Efficiency Iron Photosensitizer Explained with Quantum Wavepacket Dynamics.

Fe(II) complexes have long been assumed unsuitable as photosensitizers because of their low-lying nonemissive metal centered (MC) states, which inhibit electron transfer. Herein, we describe the excited-state relaxation of a novel Fe(II) complex that incorporates N-heterocyclic carbene ligands designed to destabilize the MC states. Using first-principles quantum nuclear wavepacket simulations we achieve a detailed understanding of the photoexcited decay mechanism, demonstrating that it is dominated by an ultrafast intersystem crossing from (1)MLCT-(3)MLCT proceeded by slower kinetics associated with the conversion into the (3)MC states. The slowest component of the (3)MLCT decay, important in the context of photosensitizers, is much longer than related Fe(II) complexes because the population transfer to the (3)MC states occurs in a region of the potential where the energy gap between the (3)MLCT and (3)MC states is large, making the population transfer inefficient.

Quantum Nuclear Dynamics Pumped and Probed by Ultrafast Polarization Controlled Steering of a Coherent Electronic State in LiH.

The quantum wave packet dynamics following a coherent electronic excitation of LiH by an ultrashort, polarized, strong one-cycle infrared optical pulse is computed on several electronic states using a grid method. The coupling to the strong field of the pump and the probe pulses is included in the Hamiltonian used to solve the time-dependent Schrodinger equation. The polarization of the pump pulse allows us to control the localization in time and in space of the nonequilibrium coherent electronic motion and the subsequent nuclear dynamics. We show that transient absorption, resulting from the interaction of the total molecular dipole with the electric fields of the pump and the probe, is a very versatile probe of the different time scales of the vibronic dynamics. It allows probing both the ultrashort, femtosecond time scale of the electronic coherences as well as the longer dozens of femtoseconds time scales of the nuclear motion on the excited electronic states. The ultrafast beatings of the electronic coherences in space and in time are shown to be modulated by the different periods of the nuclear motion.

Quantum oscillations and wave packet revival in conical graphene structure

We present analytical expressions for the eigenstates and eigenvalues of electrons confined in a graphene monolayer in the presence of a disclination. The calculations are performed in the continuum limit approximation in the vicinity of the Dirac points, solving Dirac equation by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearence of Aharonov-Bohm oscillation and find out the conditions of gapped and gapless states in the spectrum. We show that the gauge field due to a disclination lifts the orbital degeneracy originating from the existence of two valleys. The broken valley degeneracy has a clear signature on quantum oscillations and wave packet dynamics.

Wavepacket Dynamics of the Axially Chiral Molecule Cl-O-O-Cl under Coherent Radiative Excitation and Including Electroweak Parity Violation.

We report detailed calculations of the quantum wavepacket dynamics of Cl-O-O-Cl, which serves as a prototype molecule for the stereomutation dynamics of an axially chiral molecule. We include the effects both from electroweak parity violation and from the interaction with a coherent monochromatic laser field. We use the quasiadiabatic channel reaction path Hamiltonian approach to approximately solve the six-dimensional Schrödinger equation describing the vibrational motion, including rotation by an effective Hamiltonian. We calculate time-dependent wave functions based on the time-dependent Schrödinger equation. We study stereomutation dynamics due to tunneling motion and laser-induced population transfer and show results on efficient methods for selectively populating single molecular states in chiral molecules by frequency-modulated laser pulses. We also discuss laser-induced stereomutation (LISM) and a process that may be called resonance Raman induced stereomutation (RRISM). The results are discussed in relation to current experimental attempts to measure the parity violating energy difference ΔpvE between the enantiomers of chiral molecules. Furthermore, we show detailed quantitative simulations of a selection of well-defined parity levels in chiral molecules ("parity isomers") that form the basis of a possible measurement of ΔpvE by the time evolution of parity.

Tunneling time in attosecond experiments and the time-energy uncertainty relation

In this work we present a theoretical model supported with a physical reasoning leading to a relation which performs an excellent estimation for the tunneling time in attosecond and strong field experiments, where we address the important case of the He-atom \cite{Eckle:2008s,Eckle:2008}. Our tunneling time estimation is found by utilizing the time-energy uncertainty relation and represents a quantum clock. The tunneling time is also featured as the time of passage (at the exit of the tunnel) similarly to the Einstein's {\it photon box Gedanken experiment}. Our work tackles an important study case for the theory of time in quantum mechanics and is very promising for the search for a (general) time operator in quantum mechanics. The work can be seen as a new fundamental step in dealing with the tunneling time in strong field and ultra-fast science, and is appealing for more elaborate treatments using quantum wave packet dynamics and especially for complex atoms and molecules.

State-to-State Quantum Dynamics of Reactions O((3)P) + HD (v = 0-1, j = 0) → OH+D and OD+H: Reaction Mechanism and Vibrational Excitation.

Time-dependent quantum wave packet dynamics calculations have been performed in order to characterize the dynamics and mechanism of O((3)P) + HD (v = 0-1, j = 0) → OH+D and OD+H reactive collisions using the adiabatic potential energy surface by Rogers et al. [J. Phys. Chem. A 2000, 104, 2308] Special attention has been paid to the calculations and discussion of the state resolved integral and differential cross sections and the product state distributions. In addition, the intramolecular isotopic branching ratio has been determined. The results revealed that the OD + H is the favored product channel and the product OH has the same quantum number v as the reactant HD. For low collision energy, the product angular distributions concentrate in the backward region being consistent with a rebounding mechanism. In the case of higher collision energy, the stripping collisions with larger impact parameters tend to produce sideways and forward scatterings, especially for the HD vibrationally excited state. The cross section and intramolecular isotopic branching ratio are in agreement with the previous theoretical results. A cartoon depiction collision model is built and works well for our calculation results.

Factors Affecting the Branching Ratio of Photodissociation: Thiophenol Studied through Quantum Wavepacket Dynamics.

The photodissociation dynamics of thiophenol (PhSH) excited to the 1(1) ππ* state was investigated by time-dependent quantum wavepacket propagation within two-dimensional (2D) space consisting of the S-H bond and -SH torsion. We systematically studied the dependence of the branching ratio (Ã/X(~)) between the two electronic states of the phenylthiyl radical (PhS(.) ) on several factors of the 2D potential energy surfaces (PESs). The effect of a reduced initial barrier to the first ππ*/πσ* conical intersection (CI) was found to be marginal, whereas the effects of a reduced torsional barrier of -SH on the excited ππ* state and the mitigated slope of the πσ* PES between the first (ππ*/πσ*) and the second (πσ*/S0 ) CIs were noticeable. The effect of the slope on the branching ratio has never been previously noticed. It was shown that the branching ratio can be sufficiently above unity without pre-excitation of the torsion mode of -SH, which has been assumed so far.

Quantum walks and wavepacket dynamics on a lattice with twisted photons.

The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.