Periodic Electron Circulation Induced by Circularly Polarized Laser Pulses: Quantum Model Simulations for Mg Porphyrin

Self-Heterodyne Diffractive Imaging of Ultrafast Electron Dynamics Monitored by Single-Electron Pulses

The direct imaging of time-evolving molecular charge densities on atomistic scale and at femtosecond resolution has long been an elusive task. In this theoretical study, we propose a self-heterodyne electron diffraction technique based on single electron pulses. The electron is split into two beams, one passes through the sample and its interference with the second beam produces a heterodyne diffraction signal that images the charge density. Application to probing the ultrafast electronic dynamics in Mg-phthalocyanine demonstrates its potential for imaging chemical dynamics.

Time-Dependent Extension of Grimme's Continuous Chirality Measure for Electronic Chirality Flips in Femto- and Attosecond Time Domains

Grimme's Continuous Chirality Measure (C C M ${CCM}$ ) was developed for comparisons of the chirality of the electronic wave functions of molecules, typically in their ground states. For example,C C M = 14 . 5 ${CCM=14.5}$ ,1 . 2 ${1.2}$ and0 . 0 ${0.0}$ for alanine, hydrogen-peroxide, and for achiral molecules, respectively. Well-designed laser pulses can excite achiral molecules from the electronic ground state to time-dependent chiral superposition states, with chirality flips in the femto- or even attosecond (fs or as) time domains. Here we provide a time-dependent extensionC C M t ${CCM\left(t\right)}$ of Grimme'sC C M ${CCM}$ for trailing the electronic chirality flips. As examples, we consider two laser driven electronic wavefunctions which represent flips between opposite electronic enantiomers of oriented NaK within4 . 76 f s ${4.76\ {\rm f}{\rm s}}$ and433 a s ${433\ {\rm a}{\rm s}}$ . The correspondingC C M t ${CCM\left(t\right)}$ vary respectively from14 . 5 ${14.5}$ or from13 . 3 ${13.3}$ to0 . 0 ${0.0}$ , and back.

Inverse Optically-Induced Ring Currents in Ring-Shaped Molecules

Permanent electronic ring currents are supported within manifolds of ΓE degenerate excited electronic states as E± = Ex ± iEy excitations. In [ Phys. Rev. Res. 2021, 3, L042003] we showed the existence of inverse-current manifolds, where the direction of the electronic ring current in each degenerate state E± is opposite to the circular polarization of the generating light fields. This vibronic effect is caused by the exchange of orbital angular momentum between the electrons and the vibrational modes with the required symmetry. Here we consider the case of fixed nuclei and find that ring-shaped molecular systems possess inverse-current manifolds on a purely electronic-structure basis, i.e., without intervention of vibronic coupling. The effect is explained first on a tight-binding model with cyclic symmetry and then considering the ab initio electronic structure of benzene and sym-triazine. A framework for discriminating regular- and inverse-current ΓE manifolds in molecules using quantum chemistry calculations is provided.

Ultrafast chirality: the road to efficient chiral measurements

Today we are witnessing the electric-dipole revolution in chiral measurements. Here we reflect on its lessons and outcomes, such as the perspective on chiral measurements using the complementary principles of "chiral reagent" and "chiral observer", the hierarchy of scalar, vectorial and tensorial enantio-sensitive observables, the new properties of the chiro-optical response in the ultrafast and non-linear domains, and the geometrical magnetism associated with the chiral response in photoionization. The electric-dipole revolution is a landmark event. It has opened routes to extremely efficient enantio-discrimination with a family of new methods. These methods are governed by the same principles but work in vastly different regimes - from microwaves to optical light; they address all molecular degrees of freedom - electronic, vibrational and rotational, and use flexible detection schemes, i.e. detecting photons or electrons, making them applicable to different chiral phases, from gases to liquids to amorphous solids. The electric-dipole revolution has also enabled enantio-sensitive manipulation of chiral molecules with light. This manipulation includes exciting and controlling ultrafast helical currents in vibronic states of chiral molecules, enantio-sensitive control of populations in electronic, vibronic and rotational molecular states, and opens the way to efficient enantio-separation and enantio-sensitive trapping of chiral molecules. The word "perspective" has two meanings: an "outlook" and a "point of view". In this perspective article, we have tried to cover both meanings.

Systematic Investigation of the Reliability of the Frozen Nuclei Approximation for Short-Pulse Excitation: The Example of HCCI+

In this work we quantitatively study the reliability of the frozen nuclei approximation for ultrafast dynamics. Specifically we study laser excitation of HCCI⁺ from its ground state to the first electronically excited state. The population of the first excited state is obtained by both the frozen nuclei approximation and by multidimensional nuclear dynamics. Detailed comparison of the results by the two methods are performed to provide quantitative criteria for the reliability of the frozen nuclei approximation for this system.

Polariton ring currents and circular dichroism of Mg-porphyrin in a chiral cavity

By placing Mg-porphyrin molecules in a chiral optical cavity, time reversal symmetry is broken, and polariton ring currents can be generated with linearly polarized light, resulting in a circular dichroism signal. Since the electronic state degeneracy in the molecule is lifted by the formation of chiral polaritons, this signal is one order of magnitude stronger than the bare molecule signal induced by circularly polarized light. Enantiomer-selective photochemical processes in chiral optical cavities is an intriguing future possibility.

Placing aromatic molecules in a chiral optical cavity can break time-reversal symmetry and generate polariton ring currents with a linearly polarized pump. Such currents can be probed by circular dichroism, with one order of magnitude enhancement.

Coherent ring-current migration of Mg-phthalocyanine probed by time-resolved X-ray circular dichroism

The coherent ring current of Mg-phthalocyanine created by a broad band UV-visible pump pulse shows variation with time, where the ring currents at the corner benzene rings, around the Mg cation and on the outer ring oscillate with different time periods and the current density migrates among these regions. The 7 pairs of E_u degenerate excited states populated upon photoexcitation, generate 21 distinct coherent ring currents. We further calculate the time-resolved X-ray circular dichroism (TRXCD) spectrum of the coherences contributing to the ring current obtained by an attosecond X-ray probe pulse resonant with the nitrogen K-edge. A frequency domain TRXCD signal obtained by a Fourier transform of the signal with respect to the pump-probe delay time clearly separates the currents induced by different state pairs.

The coherent ring current of Mg-phthalocyanine are created by a broad band UV-visible pump pulse and migrate into different regions within the molecule. This coherent ring current dynamics is probed by time-resolved X-ray circular dichroism.

Rotational dynamics and transitions between Λ-type doubling of NO induced by an intense two-color laser field

We numerically investigate the rotational dynamics of NO in the electronic ground X²Π state induced by an intense two-color laser field (10 TW/cm²) as a function of pulse duration (0.3-25 ps). In the short pulse duration of less than 12 ps, rotational Raman excitation is effectively induced and results in molecular orientation. On the contrary, when the pulse duration is longer than 15 ps, the rotational excitation is suppressed. In addition to the rotational excitation, we find that transitions between Λ-type doubling are induced. Significantly, the maximum coherent wave packet between Λ-type doubling in J = 0.5 is generated using the pulse duration of 19.8 ps. The wave packet changes to the eigenstates of Λ = +1 or -1 alternatively, where Λ is the projection of the electronic orbital angular momentum on the N-O axis, which is regarded as the unidirectional rotation of an unpaired 2π electron around the N-O axis in a space-fixed frame as well as in a molecule-fixed frame. The experimental method to observe the alternation of the rotational direction of the electron around the N-O axis is proposed.

Ultrafast attosecond-magnetic-field generation of the charge migration process based on HeH2+ and H2 + electronically excited by circularly polarized laser pulses

The ultrafast process by the electron in molecular ions from one site or region to another that has come to be known as charge migration (CM), which is of fundamental importance to photon induced chemical or physical reactions. In this work, we study the electron current and ultrafast magnetic-field generation based on CM process of oriented asymmetric (HeH²⁺) and symmetric (H₂ ⁺) molecular ions. Calculated results show that they are ascribed to quantum interference of electronic states for these molecular ions under intense circularly polarized (CP) laser pulses. The two scenarios of (i) resonance excitation and (ii) direct ionization are considered through appropriately utilizing designed laser pulses. By comparison, the magnetic field induced by the scenario (i) is stronger than that of scenario (ii) for molecular ions. However, the scheme (ii) is very sensitive to the helicity of CP field, which is opposite to the scenario (i). Moreover, the magnetic field generated by H₂ ⁺ is stronger than that by HeH²⁺ through scenario (i). Our findings provide a guiding principle for producing ultrafast magnetic fields in molecular systems for future research in ultrafast magneto-optics.

Time-resolved imaging of correlation-driven charge migration in light-induced molecular magnets by X-ray scattering

In this contribution, we investigate the effect of correlation-induced charge migration on the stability of light-induced ring currents, with potential application as molecular magnets. Laser-driven electron dynamics is simulated using density-matrix based time-dependent configuration interaction. The time-dependent many-electron wave packet is used to reconstruct the transient electronic current flux density after excitation of different target states. These reveal ultrafast correlation-driven fluctuations of the charge migration over the molecular scaffold, sometimes leading to large variations of the induced magnetic field. The effect of electron correlation and non-local pure dephasing on the charge migration pattern is further investigated by means of time-resolved X-ray scattering, providing a connection between theoretical predictions of the charge migration mechanism and experimental observables.

Laser-Induced Electron Symmetry Restoration in Oriented Molecules Made Simple

Electron symmetry determines many important properties of molecules, from selection rules for photoelectron spectroscopy to symmetry selection rules for chemical reactions. The original electron symmetry is broken if a laser pulse changes the initial state, typically the ground state g, to a superposition of g and an excited state e with different irreducible representations (IRREPs). Quantum dynamics simulations for two examples, the oriented benzene and LiCN molecules, show that the original electron symmetry can be restored by means of a reoptimized π-laser pulse which transfers the component in the excited state e to another state e', or to several others with the same IRREP as the ground state. This method lends itself to much easier experimental applications than all previous ones because it allows the healing of electron symmetry immediately, without any attosecond constraint on the timing of the second pulse.

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h and D4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses.

On the generation of electronic ring currents under vibronic coupling effects

We study the generation of electronic ring currents in the presence of nonadiabatic coupling using circularly polarized light. For this, we introduce a solvable model consisting of an electron and a nucleus rotating around a common center and subject to their mutual Coulomb interaction. The simplicity of the model brings to the forefront the non-trivial properties of electronic ring currents in the presence of coupling to the nuclear coordinates and enables the characterization of various limiting situations transparently. Employing this model, we show that vibronic coupling effects play a crucial role even when a single E degenerate eigenstate of the system supports the current. The maximum current of a degenerate eigenstate depends on the strength of the nonadiabatic interactions. In the limit of large nuclear to electronic masses, in which the Born-Oppenheimer approximation becomes exact, constant ring currents and time-averaged oscillatory currents necessarily vanish.

Monitoring aromatic ring-currents in Mg-porphyrin by time-resolved circular dichroism

Time-resolved circular dichroism signals (TRCD) in the X-ray regime can directly probe the magnitude and the direction of ring currents in molecules. The electronic ring currents in Mg-porphyrin, generated by a coherent superposition of electronic states induced by a circularly polarized UV pulse, are tracked by a time-delayed circularly polarized attosecond X-ray pulse. The signals are calculated using the minimal coupling Hamiltonian, which directly makes use of transition current densities. The TRCD signals obtained from the left and right circularly polarized light pump have opposite signs, revealing the direction of the ring current. Molecular aromaticity and its role in photochemical reactions such as ring opening or closure can be studied using this technique.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses

Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, $ {\rm H}_2^ + $H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrödinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.

Probing Electronic Fluxes via Time-Resolved X-Ray Scattering

The current flux density is a vector field that can be used to describe theoretically how electrons flow in a system out of equilibrium. In this work, we unequivocally demonstrate that the signal obtained from time-resolved x-ray scattering does not only map the time evolution of the electronic charge distribution, but also encodes information about the associated electronic current flux density. We show how the electronic current flux density qualitatively maps the distribution of electronic momenta and reveals the underlying mechanism of ultrafast charge migration processes, while also providing quantitative information about the timescales of electronic coherences.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses.

Timing the recoherences of attosecond electronic charge migration by quantum control of femtosecond nuclear dynamics: A case study for HCCI. J Chem Phys 2019;151:244306. [PMID: 31893866 DOI: 10.1063/1.5134665]

This work suggests an approach to a new target of laser control of charge migration in molecules or molecular ions. The target is motivated by the fact that nuclear motions can not only cause decoherence of charge migration, typically within few femtoseconds, but they may also enable the reappearance of charge migration after much longer times, typically several tens or even hundreds of femtoseconds. This phenomenon is called recoherence of charge migration, opposite to its decoherence. The details depend on the initiation of the original charge migration by an ultrashort strong intense pump laser pulse. It may reappear quasiperiodically, with reference period T_r. We show that a well-designed pump-dump laser pulse can enforce recoherences of charge migration at different target times T_c, for example, at T_c ≈ T_r/2. The approach is demonstrated by quantum dynamics simulations of the laser driven electronic and nuclear motions in the oriented linear cation HCCI⁺. First, the concept is explained in terms of a didactic one-dimensional (1D) model that accounts for the decisive CI stretch. The 1D results are then confirmed by a three-dimensional model for the complete set of the CH, CC, and CI stretches.

De- and Recoherence of Charge Migration in Ionized Iodoacetylene

During charge migration, electrons flow rapidly from one site of a molecule to another, perhaps inducing subsequent processes (e.g., selective breaking of chemical bonds). The first joint experimental and theoretical preparation and measurement of the initial state and subsequent quantum dynamics simulation of charge migration for fixed nuclei was demonstrated recently for oriented, ionized iodoacetylene. Here, we present new quantum dynamics simulations for the same system with moving nuclei. They reveal the decisive role of the nuclei, i.e. they switch charge migration off (decoherence) and on (recoherence). This is a new finding in attosecond-to-femtosecond chemistry and physics which opens new prospects for laser control over electronic dynamics via nuclear motions.

Probing Attosecond Electron Coherence in Molecular Charge Migration by Ultrafast X-Ray Photoelectron Imaging

Electron coherence is a fundamental quantum phenomenon in today’s ultrafast physics and chemistry research. Based on attosecond pump–probe schemes, ultrafast X-ray photoelectron imaging of molecules was used to monitor the coherent electron dynamics which is created by an XUV pulse. We performed simulations on the molecular ion H 2 + by numerically solving time-dependent Schrödinger equations. It was found that the X-ray photoelectron angular and momentum distributions depend on the time delay between the XUV pump and soft X-ray probe pulses. Varying the polarization and helicity of the soft X-ray probe pulse gave rise to a modulation of the time-resolved photoelectron distributions. The present results provide a new approach for exploring ultrafast coherent electron dynamics and charge migration in reactions of molecules on the attosecond time scale.

From Symmetry Breaking via Charge Migration to Symmetry Restoration in Electronic Ground and Excited States: Quantum Control on the Attosecond Time Scale

This article starts with an introductory survey of previous work on breaking and restoringthe electronic structure symmetry of atoms and molecules by means of two laser pulses. Accordingly,the first pulse breaks the symmetry of the system in its ground state with irreducible representationIRREPg by exciting it to a superposition of the ground state and an excited state with differentIRREPe. The superposition state is non-stationary, representing charge migration with period T inthe sub- to few femtosecond time domains. The second pulse stops charge migration and restoressymmetry by de-exciting the superposition state back to the ground state. Here, we present a newstrategy for symmetry restoration: The second laser pulse excites the superposition state to the excitedstate, which has the same symmetry as the ground state, but different IRREPe. The success dependson perfect time delay between the laser pulses, with precision of few attoseconds. The new strategyis demonstrated by quantum dynamics simulation for an oriented model system, benzene.

Charge Migration in Propiolic Acid: A Full Quantum Dynamical Study

Ionization of molecules very often populates several cationic states launching pure electron dynamics that appear as ultrafast migration of the hole charge throughout the system. A crucial question in the emerging field of attochemistry is whether these pure electronic coherences last long enough to allow for their efficient observation and eventual manipulation with ultrashort laser pulses. We report a full-dimensional quantum calculation of concerted electron-nuclear dynamics initiated by outer-valence ionization of propiolic acid molecule, showing that the charge will oscillate between the carbon triple bond and the carbonyl oxygen for more than 10 fs before getting trapped by the nuclear motion. This time is enough for the charge migration to be observed and controlled. We argue that the molecule is very suitable for experimental studies.

Attosecond Control of Restoration of Electronic Structure Symmetry

Laser pulses can break the electronic structure symmetry of atoms and molecules by preparing a superposition of states with different irreducible representations. Here, we discover the reverse process, symmetry restoration, by means of two circularly polarized laser pulses. The laser pulse for symmetry restoration is designed as a copy of the pulse for symmetry breaking. Symmetry restoration is achieved if the time delay is chosen such that the superposed states have the same phases at the temporal center. This condition must be satisfied with a precision of a few attoseconds. Numerical simulations are presented for the C_{6}H_{6} molecule and ^{87}Rb atom. The experimental feasibility of symmetry restoration is demonstrated by means of high-contrast time-dependent Ramsey interferometry of the ^{87}Rb atom.

Attosecond Dynamics of Molecular Electronic Ring Currents

Ultrafast charge migration is of fundamental importance to photoinduced chemical reactions. However, exploring such a quantum dynamical process requires demanding spatial and temporal resolutions. We show how electronic coherence dynamics induced in molecules by a circularly polarized UV pulse can be tracked by using a time-delayed circularly polarized attosecond X-ray pulse. The X-ray probe spectra retrieve an image at different time delays, encoding instantaneous pump-induced circular charge migration information on an attosecond time scale. A time-dependent ultrafast electronic coherence associated with the periodical circular ring currents shows a strong dependence on the helicity of the UV pulse, which may provide a direct approach to access and control the electronic quantum coherence dynamics in photophysical and photochemical reactions in real time.

Quantum Design of π-Electron Ring Currents in Polycyclic Aromatic Hydrocarbons: Parallel and Antiparallel Ring Currents in Naphthalene

Control of π-electrons in polycyclic aromatic hydrocarbons (PAHs) is one of the fundamental issues in optoelectronics for ultrafast optical switching devices. We have proposed an effective scenario for design of the generation of coherent ring currents in naphthalene (D_2h), which is the smallest unit of planar PAHs. It has been demonstrated by using quantum chemical calculations and quantum optimal control (QOC) simulations that two types of ring currents, parallel and antiparallel, can be generated by resonance excitations by two linearly polarized lasers. A parallel (antiparallel) ring current means that the currents of two benzene rings run in the same (opposite) directions. The two types of ring currents may be experimentally identified by magnetic force microscopy. The QOC simulations indicate that a parallel ring current can be generated by using continuous wave and Gaussian pulse lasers with their time delay without relying on a sophisticated experimental apparatus. The present results provide a guiding principle of coherent π-electronics in PAHs for next-generation organic optical switching devices.

Exploring coherent electron excitation and migration dynamics by electron diffraction with ultrashort X-ray pulses

Exploring ultrafast charge migration is of great importance in biological and chemical reactions.

Induction of unidirectional π-electron rotations in low-symmetry aromatic ring molecules using two linearly polarized stationary lasers

A new laser-control scenario of unidirectional π-electron rotations in a low-symmetry aromatic ring molecule having no degenerate excited states is proposed. This scenario is based on dynamic Stark shifts of two relevant excited states using two linearly polarized stationary lasers. Each laser is set to selectively interact with one of the two electronic states, the lower and higher excited states are shifted up and down with the same rate, respectively, and the two excited states become degenerate at their midpoint. One of the four control parameters of the two lasers, i.e. two frequencies and two intensities, determines the values of all the other parameters. The direction of π-electron rotations, clockwise or counter-clockwise rotation, depends on the sign of the relative phase of the two lasers at the initial time. An analytical expression for the time-dependent expectation value of the rotational angular momentum operator is derived using the rotating wave approximation (RWA). The control scenario depends on the initial condition of the electronic states. The control scenario with the ground state as the initial condition was applied to toluene molecules. The derived time-dependent angular momentum consists of a train of unidirectional angular momentum pulses. The validity of the RWA was checked by numerically solving the time-dependent Schrödinger equation. The simulation results suggest an experimental realization of the induction of unidirectional π-electron rotations in low-symmetry aromatic ring molecules without using any intricate quantum-optimal control procedure. This may open up an effective generation method of ring currents and current-induced magnetic fields in biomolecules such as amino acids having aromatic ring molecules for searching their interactions.

Non-resonant dynamic stark control of vibrational motion with optimized laser pulses

The term dynamic Stark control (DSC) has been used to describe methods of quantum control related to the dynamic Stark effect, i.e., a time-dependent distortion of energy levels. Here, we employ analytical models that present clear and concise interpretations of the principles behind DSC. Within a linearly forced harmonic oscillator model of vibrational excitation, we show how the vibrational amplitude is related to the pulse envelope, and independent of the carrier frequency of the laser pulse, in the DSC regime. Furthermore, we shed light on the DSC regarding the construction of optimal pulse envelopes - from a time-domain as well as a frequency-domain perspective. Finally, in a numerical study beyond the linearly forced harmonic oscillator model, we show that a pulse envelope can be constructed such that a vibrational excitation into a specific excited vibrational eigenstate is accomplished. The pulse envelope is constructed such that high intensities are avoided in order to eliminate the process of ionization.

Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials

The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.

The generation of stationary π-electron rotations in chiral aromatic ring molecules possessing non-degenerate excited states

The electron angular momentum is a fundamental quantity of high-symmetry aromatic ring molecules and finds many applications in chemistry such as molecular spectroscopy. The stationary angular momentum or unidirectional rotation of π electrons is generated by the excitation of a degenerated electronic excited state by a circularly-polarized photon. For low-symmetry aromatic ring molecules having non-degenerate states, such as chiral aromatic ring molecules, on the other hand, whether stationary angular momentum can be generated or not is uncertain and has not been clarified so far. We have found by both theoretical treatments and quantum optimal control (QOC) simulations that a stationary angular momentum can be generated even from a low-symmetry aromatic ring molecule. The generation mechanism can be explained in terms of the creation of a dressed-state, and the maximum angular momentum is generated by the dressed state with an equal contribution from the relevant two excited states in a simple three-electronic state model. The dressed state is formed by inducing selective nonresonant transitions between the ground and each excited state by two lasers with the same frequency but having different polarization directions. The selective excitation can be carried out by arranging each photon-polarization vector orthogonal to the electronic transition moment of the other transition. We have successfully analyzed the results of the QOC simulations of (P)-2,2'-biphenol of axial chirality in terms of the analytically determined optimal laser fields. The present findings may open up new types of chemical dynamics and spectroscopy by utilizing strong stationary ring currents and current-induced magnetic fields, which are created at a local site of large compounds such as biomolecules.

Staircase patterns of nuclear fluxes during coherent tunneling in excited doublets of symmetric double well potentials

Step-by-step flux for one-by-one transfers of the lobes of the density, from the reactant (left) to the product (right) in the excited tunneling doublet.