We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.
We investigate geometric phase (GP) effects in nonadiabatic transitions through a conical intersection (CI) in an N-dimensional linear vibronic coupling (ND-LVC) model. This model allows for the coordinate transformation encompassing all nonadiabatic effects within a two-dimensional (2D) subsystem while the other N-2 dimensions form a system of uncoupled harmonic oscillators identical for both electronic states and coupled bi-linearly with the subsystem coordinates. The 2D subsystem governs ultra-fast nonadiabatic dynamics through the CI and provides a convenient model for studying GP effects.…
The rates and outcomes of virtually all photophysical and photochemical processes are determined by Conical Intersections. These are regions of degeneracy between electronic states on the nuclear landscape of molecules where electrons and nuclei evolve on comparable timescales and become strongly coupled, enabling radiationless relaxation channels upon optical excitation. Due to their ultrafast nature and vast complexity, monitoring Conical Intersections experimentally is an open challenge. We present a simulation study on the ultrafast photorelaxation of uracil, which demonstrates a new windo…
Conical intersections (CIs) have been widely studied using spectroscopic techniques. However, CIs have mainly been identified by rapid internal conversion transitions that take place after the photoexcitation. Such identifications cannot distinguish various types of intersections as well as to separate the actual intersection from an avoided crossing. In this paper, we investigate how ultrafast IR laser pulses can be utilized to stimulate nuclear dynamics revealing geometric phase features associated with CIs. We consider two low-dimensional nonadiabatic models to obtain optimal two- and three…
Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 90, 013001 (2003)]. It was also found that these states are destroyed within the Born-Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original two-dimensional two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove …
Nonadiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natu…
We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally the nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization…
We have studied the photo-induced isomerization from 1,3-cyclohexadiene to 1,3,5-hexatriene in the presence of an intense ultrafast laser pulse. We find that the laser field maximally suppresses isomerization if it is both polarized parallel to the excitation dipole and present 50 fs after the initial photoabsorption, at the time when the system is expected to be in the vicinity of a conical intersection that mediates this structural transition. A modified ab initio multiple spawning (AIMS) method shows that the laser induces a resonant coupling between the excited state and the ground state, …
The effect of conical intersections (CIs) on electronic relaxation, transitions from excited states to ground states, is well studied, but their influence on hyperfine quenching in a reactant molecule is not known. Here, we report on ultracold collision dynamics of the hydroxyl free-radical OH with Sr atoms leading to quenching of OH hyperfine states. Our quantum-mechanical calculations of this process reveal that quenching is efficient due to anomalous molecular dynamics in the vicinity of the conical intersection at collinear geometry. We observe wide scattering resonance features in both el…
We present derivation and implementation of the Multi-Configurational Strong-Field Approximation with Gaussian nuclear Wave Packets (MC-SFA-GWP) -- a version of the molecular strong-field approximation which treats all electronic and nuclear degrees of freedom, including their correlations, quantum-mechanically. The technique allows, for the first time, realistic simulation of high-harmonic emission in polyatomic molecules without invoking reduced-dimensionality models for the nuclear motion or the electronic structure. We use MC-SFA-GWP to model isotope effects in high-harmonics generation (H…
We observe a series of conical intersections in the potential energy curves governing both the collision between a Rydberg atom and a ground-state atom and the structure of Rydberg molecules. By employing the electronic energy of the Rydberg atom as a synthetic dimension we circumvent the von Neumann-Wigner theorem. These conical intersections can occur when the Rydberg atom's quantum defect is similar in size to the electron--ground-state atom scattering phase shift divided by $π$, a condition satisfied in several commonly studied atomic species. The conical intersections have an observable c…
Nonradiative energy dissipation in electronically excited polyatomic molecules proceeds through conical intersections, loci of degeneracy between electronic states. We observe a marked enhancement of laser-induced double ionization in the vicinity of a conical intersection during a non-radiative transition. We measured double ionization by detecting the kinetic energy of ions released by laser-induced strong-field fragmentation during the ring-opening transition between 1,3-cyclohexadiene and 1,3,5-hexatriene. The enhancement of the double ionization correlates with the conical intersection be…
Conical intersections are degeneracies between electronic states and are very common in nature. It has been found that they can also be created both by standing or by running laser waves. The latter are called light-induced conical intersections. It is well known that conical intersections are the sources for numerous topological effects which are manifested e.g. in the appearance of the geometric or Berry phase. In one of our former works by incorporating the diabatic-to-adiabatic transformation angle with the line-integral technique we have calculated the Berry-phase of the light-induced con…
Many recent experimental ultrafast spectroscopy studies have hinted at non-adiabatic dynamics indicating the existence of conical intersections, but their direct observation remains a challenge. The rapid change of the energy gap between the electronic states complicated their observation by requiring bandwidths of several electron volts. In this manuscript, we propose to use the combined information of different X-ray pump-probe techniques to identify the conical intersection. We theoretically study the conical intersection in pyrrole using transient X-ray absorption, time-resolved X-ray spon…
The direct observation of non-adiabatic dynamics at conical intersections is a long-standing goal of molecular physics. Novel time-resolved spectroscopies have been proposed which are sensitive to electronic coherences induced by the passage of an excited state wavepacket through a region of conical intersection. Here we demonstrate that inclusion of the geometric phase effect, and its manifestations, is essential for the correct description of the transient electronic coherences that may or may not develop. For electronic states of different symmetry, electronic coherences are suppressed by t…
We develop a systematic study of Jahn-Teller (JT) models with continuous symmetries by explor- ing their algebraic properties. The compact symmetric spaces corresponding to JT models carrying a Lie group symmetry are identified, and their invariants used to reduce their adiabatic potential energy surfaces into orbit spaces. Each orbit consists of a set of JT distorted molecular structures with equal adiabatic electronic spectrum. Molecular motion may be decomposed into pseudorota- tional and radial. The former preserves the orbit, while the latter maps an orbit into another. The dimensionality…
The motion of electrons and nuclei in photochemical events often involve conical intersections, degeneracies between electronic states. They serve as funnels for nuclear relaxation - on the femtosecond scale - in processes where the electrons and nuclei couple nonadiabatically. Accurate ab initio quantum chemical models are essential for interpreting experimental measurements of such phenomena. In this paper we resolve a long-standing problem in coupled cluster theory, presenting the first formulation of the theory that correctly describes conical intersections between excited electronic state…
Conical Intersections Enable Ultrafast Molecular Spin Control in a Chromium Complex
Ningbo University（宁波大学）；Rosalind Franklin Institute（罗莎琳德·富兰克林研究所）；STFC Rutherford Appleton Laboratory（STFC鲁瑟福阿普尔顿实验室）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of Toronto（多伦多大学）；University of Oxford（牛津大学）
The effect of nuclear dynamics and conical intersections on electronic coherences is investigated employing a two-state, two-mode linear vibronic coupling model. Exact quantum dynamical calculations are performed using the multi-configuration time-dependent Hartree method (MCTDH). It is found that the presence of a non-adiabatic coupling close to the Franck-Condon point can preserve electronic coherence to some extent. Additionally, the possibility of steering the nuclear wavepackets by imprinting a relative phase between the electronic states during the photoionization process is discussed. I…
We investigate the nuclear dynamics near a real-valued conical intersection that is perturbed by a complex-valued spin-orbit coupling. For a model Hamiltonian with two outgoing channels, we find that even a small spin-orbit coupling can dramatically affect the pathway selection on account of Berry force, leading to extremely large spin selectivity (sometime as large as 100%). Thus, this Letter opens the door for organic chemists to start designing spintronic devices that use nuclear motion and conical intersections (combined with standard spin-orbit coupling) in order to achieve spin selection…
Conical intersections (CI) between molecular potential energy surfaces with non-vanishing non-adiabatic couplings generally occur in any molecule consisting of at least three atoms. They play a fundamental role in describing the molecular dynamics beyond the Born-Oppenheimer approximation and have been used to understand a large variety of effects, from photofragmentation and isomerization to more exotic applications such as exciton fission in semiconductors. However, few studies have used the features of a CI as a tool for coherent control. Here we demonstrate two modes of control around a co…
Nonadiabatic effects appear due to avoided crossings or conical intersections that are either intrinsic properties in field-free space or induced by a classical laser field in a molecule. It was demonstrated that avoided crossings in diatomics can also be created in an optical cavity. Here, the quantized radiation field mixes the nuclear and electronic degrees of freedom creating hybrid field-matter states called polaritons. In the present theoretical study we go further and create conical intersections in diatomics by means of a radiation field in the framework of cavity quantum electrodynami…
The interaction of a molecule with the quantized electromagnetic field of a nano-cavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables to follow both nuclear wavepacket dynamics on and nonadiabatic population transfer between polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersec…
Nonadiabatic dynamics around an avoid crossing or a conical intersection play a crucial role in the photoinduced processes of most polyatomic molecules. The present work shows that the topological phase in conical intersection makes the behavior of pump-probe high-order harmonic spectroscopy different from the case of avoid crossing. The coherence built up when the system crosses the avoid crossing will lead to the oscillatory behavior of the spectrum, while the geometric phase erodes these oscillations in the case of conical intersection. Additionally, the dynamical blueshift and the splittin…
We introduce multistate metadynamics for automatic exploration of conical intersection seams between adiabatic Born-Oppenheimer potential energy surfaces in molecular systems. By choosing the energy gap between the electronic states as a collective variable the metadynamics drives the system from an arbitrary ground-state configuration toward the intersection seam. Upon reaching the seam, the multistate electronic Hamiltonian is extended by introducing biasing potentials into the off-diagonal elements, and the molecular dynamics is continued on a modified potential energy surface obtained by d…
Ongoing developments in ultrafast X-ray sources offer powerful new means of probing the com- plex non-adiabatically coupled structural and electronic dynamics of photoexcited molecules. These non-Born-Oppenheimer effects are governed by general electronic degeneracies termed conical in- tersections which play a key role, analogous to that of a transition state, in the electronic-nuclear dynamics of excited molecules. Using high level ab initio quantum dynamics simulations, we studied time-resolved X-ray absorption and photoelectron spectroscopy (TRXAS and TRXPS, respectively) of the prototypic…
We study the behavior of Hartree-Fock (HF) solutions in the vicinity of conical intersections. These are here understood as regions of a molecular potential energy surface characterized by degenerate or nearly-degenerate eigenfunctions with identical quantum numbers (point group, spin, and electron number). Accidental degeneracies between states with different quantum numbers are known to induce symmetry breaking in HF. The most common closed-shell restricted HF instability is related to singlet-triplet spin degeneracies that lead to collinear unrestricted HF (UHF) solutions. Adding geometric …
The absorption spectrum of CO$_2$ in the wavelength range 120\,nm --- 160\,nm is analyzed by means of quantum mechanical calculations performed using vibronically coupled PESs of five singlet valence electronic states and the coordinate dependent transition dipole moment vectors. The thermally averaged spectrum, calculated for T=190\,K via Boltzmann averaging of optical transitions from many initial rotational states, accurtely reproduces the experimental spectral envelope, consisting of a low and a high energy band, the positions of the absorption maxima, their FWHMs, peak intensities, and fr…
Conical intersections (CoIn) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CoIns have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short X-ray (rather than optical) pulses can directly detect the passage through a CoIn with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond/attosecond X-ray puls…
Conical intersections between electronic states often dictate the chemistry of photoexcited molecules. Recently developed sources of ultrashort extreme ultraviolet (XUV) pulses tuned to element-specific transitions in molecules allow for the unambiguous detection of electronic state-switching at a conical intersection. Here, the fragmentation of photoexcited iso-propyl iodide and tert-butyl iodide molecules (i-C$_{3}$H$_{7}$I and t-C$_{4}$H$_{9}$I) through a conical intersection between $^{3}$Q$_{0}$/$^{1}$Q$_{1}$ spin-orbit states is revealed by ultrafast XUV transient absorption measuring io…
We investigate a minimal valence-bond-based model Hamiltonian for photoisomerization of monomethine dyes. These include a broad class of large conjugated organic molecules including diarylmethane and cyanine dyes, and the chromophores of fluorescent proteins. The model fulfills the most basic expectations for a double bond photoisomerization model: 1) it describes favorable twisting in the excited state and 2) it describes conical intersections which can mediate radidationless decay. We examine the topology, topography and extent of the conical intersection seams. Important properties of the m…
The second-order multireference driven similarity renormalization group perturbation theory (DSRG-MRPT2) theory provides an efficient means of correcting the dynamical correlation with the multiconfiguration reference function. The state-averaged DSRG-MRPT2 (SA-DSRG-MRPT2) method is the simplest means of treating the excited states with DSRG-MRPT2. In this method, the Hamiltonian dressed with dynamical correlation is diagonalized in the CASCI state subspace (SA-DSRG-MRPT2c) or the configuration subspace (SA-DSRG-MRPT2). This work develops the analytical gradient theory for spin-free SA-DSRG-MR…
We show that dressing of diatomic molecules by running laser waves gives rise to conical intersections (CIs). Due to presence of such CIs, the rovibronic molecular motions are strongly coupled. A pronounced impact of the CI on the spectrum of $Na_2$ molecule is demonstrated via numerical calculation for weak and moderate laser intensity, and an experiment is suggested on this basis. The position of the light induced CI and the strength of its non-adiabatic couplings can be chosen by changing the frequency and intensity of the used running laser wave. This offers new possibilities to control th…
The ultrafast non-radiative relaxation of a molecular ensemble coupled to a cavity mode is considered theoretically and by real-time quantum dynamics. For equal coupling strength of single molecules to the cavity mode, the non-radiative relaxation rate from the upper to the lower polariton states is found to strongly depend on the number of coupled molecules. For N>2 molecules, the N-1 dark light-matter states between the two optically active polaritons feature true collective conical intersection crossings, whose location depends on the internal atomic coordinates of each molecule in the ense…
We theoretically investigate internal conversion processes of a photoexcited molecule in a condensed phase. The molecular system is described by two-dimensional adiabatic ground and excited potential energy surfaces (PESs) that are coupled to heat baths. We study the role of conical intersection (CI) by computing the time evolution of wavepackets for the PESs both with and without the CI. For this purpose, we employ the multi-state quantum Fokker-Planck equation (MSQFPE) for a two-dimensional Wigner space. Numerically integrating the MSQFPE, we investigated the time evolution of wavepackets fo…
Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray…
Rovibronic spectra of the field-dressed homonuclear diatomic Na2 molecule is in- vestigated to identify direct signatures of the light-induced conical intersection (LICI) on the spectrum. The theoretical framework formulated allows the computation of the (1) field-dressed rovibronic states induced by a medium intensity continuous-wave laser light and the (2) transition amplitudes between these field-dressed states with respect to an additional weak probe pulse. The field-dressed spectrum features ab- sorption peaks resembling the field-free spectrum as well as stimulated emission peaks corresp…
