Electronic Population Transfer Research Articles

Generalized nonequilibrium Fermi's golden rule and its semiclassical approximations for electronic transitions between multiple states.

The nonequilibrium Fermi's golden rule (NE-FGR) approach is developed to simulate the electronic transitions between multiple excited states in complex condensed-phase systems described by the recently proposed multi-state harmonic (MSH) model Hamiltonian. The MSH models were constructed to faithfully capture the photoinduced charge transfer dynamics in a prototypical organic photovoltaic carotenoid-porphyrin-C60 molecular triad dissolved in tetrahydrofuran. A general expression of the fully quantum-mechanical NE-FGR rate coefficients for transitions between all pairs of states in the MSH model is obtained. Besides, the linearized semiclassical NE-FGR formula and a series of semiclassical approximations featuring Wigner and classical nuclear sampling choices and different dynamics during the quantum coherence period for the MSH model are derived. The current approach enables all the possible population transfer pathways between the excited states of the triad, in contrast to the previous applications that only addressed the donor-to-acceptor transition. Our simulations for two triad conformations serve as a demonstration for benchmarking different NE-FGR approximations and show that the difference between all levels of approximation is small for the current system, especially at room temperature. By comparing with nonadiabatic semiclassical dynamics, we observe similar timescales for the electronic population transfer predicted by NE-FGR. It is believed that the general formulation of NE-FGR for the MSH Hamiltonian enables a variety of applications in realistic systems.

Coupled Cluster Simulation of Impulsive Stimulated X-ray Raman Scattering.

Time-dependent equation-of-motion coupled cluster (TD-EOM-CC) is used to simulate impulsive stimulated X-ray Raman scattering (ISXRS) of ultrashort laser pulses by neon, carbon monoxide, pyrrole, and p-aminophenol. The TD-EOM-CC equations are expressed in the basis of field-free EOM-CC states, where the calculation of the core-excited states is simplified through the use of the core-valence separation (CVS) approximation. The transfer of electronic population from the ground state to the core- and valence-excited states is calculated for different numbers of included core- and valence-excited states, as well as for electric field pulses with different polarizations and carrier frequencies. The results indicate that Gaussian pulses can transfer significant electronic populations to the valence states through the Raman process. The sensitivity of this population transfer to the model parameters is analyzed. The time-dependent electronic density for p-aminophenol is also showcased, supporting the interpretation that ISXRS involves localized core excitations and can be used to rapidly generate valence wavepackets.

On the UV spectroscopy and photodynamics of octatetraene

The UV absorption spectrum of all-trans-octatetraene is reinvestigated theoretically, focussing on the strongly dipole-allowed – transition. The dynamical calculations rely on ab initio multistate CASPT2 (MS-CASPT2) computations of the underlying potential energy surfaces and coupling elements, and the multiconfiguration time-dependent Hartree (MCTDH) method for solving the time-dependent Schrödinger equation for the nuclear motion. The vibronic structure of the absorption band near 2700 Å is well reproduced, better than ever before by a purely ab initio approach. The C–C single bond and double bond stretching modes dominate the vibrational structure of the transition. While the latter resembles nearly harmonic motion on weakly coupled potential energy surfaces, the time-dependent calculations reveal a subpicosecond electronic population transfer from the state to the lower-lying state proceeding on a time scale of . The details of this internal conversion process and its relation to the conical intersection between the two excited states are discussed, paying particular attention to the impact of the – energy gap on the dynamics.

Excitation Dynamics Among Impurity Doped Quantum Dot Eigenstates in a Polychromatic Field: Role of Gaussian White Noise

AbstractCurrent study focuses on realizing the role of Gaussian white noise (GWN) and external sinusoidal polychromatic radiation field (PRF) on the time‐average excitation rate (TAER) of impurity doped quantum dot (QD). The PRF induces the transfer of electronic population from the ground state to the excited states in course of time‐evolution. The PRF has been envisaged to be composed of four component fields that maintain either a prime or a non‐prime frequency ratio. GWN couples with the system additively and multiplicatively. The study highlights the role of various physical parameters, presence of noise, mode of application of noise and the features of PRF (amplitude, phase and type of frequency ratio of the components) in shaping the TAER profiles. The TAER profiles have been found to be enriched with steady growth, steady decline, maximization (useful for obtaining large nonlinear optical response), minimization and saturation (the dynamic freezing). The study reveals promising scope of obtaining desired TAER of doped QD by judicious adjustment/regulation of several control parameters which may bear serious technological implications.

Optical properties of para‐oligophenylenes: A case study of electronic absorption spectrum and relaxation dynamics of terphenyl

AbstractWe present a detailed quantitative description of vibronic‐coupling effects on the singlet photophysics of para‐oligophenylenes. Four energetically close‐lying singlet states (S1, S2, S3, and S4) are taken into consideration to interpret the first UV/Vis absorption band of these molecules. As a representative example, the energetics of those four states are evaluated for para‐terphenyl by performing extensive electronic structure calculations within the linear vibronic coupling framework. We obtain absorption spectral profiles by wavepacket propagation technique using the multi‐configuration time‐dependent Hartree method. Computed spectral profiles are in accord with the experiment. A minor electronic population transfer to upper states on a timescale of 10 fs is observed, suggesting the excited‐state nonadiabatic behavior of the molecule. Our findings necessitate the experimental validation of the role of higher states in the spectroscopy and dynamics of photoexcited para‐oligophenylenes.

Mechanistic Photophysics of Tellurium-Substituted Uracils: Insights from Multistate Complete-Active-Space Second-Order Perturbation Calculations.

The photophysical mechanisms of tellurium-substituted uracils were studied at the multistate complete-active-space second-order perturbation level with a particular focus on how the position and number of tellurium substitutions affect their nonadiabatic relaxation processes. Electronic structure analysis reveals that the lowest several excited states are closely concerned with the n and π orbitals at the Te7-C2 [Te8-C4] moiety of 2-tellurouracil (2TeU) [4TeU and 24TeU]. Both planar and twisted minima were optimized for 2TeU, whereas only planar ones were obtained for 4TeU and 24TeU, except for a twisted T1 minimum of 4TeU. Based on intersection structures and linearly interpolated internal coordinate paths, we proposed several feasible excited-state deactivation paths. It is found that the relaxation channels for 2TeU are more complicated than those of 4TeU and 24TeU. The electronic population transfer to the T1 state for 2TeU is easier than that for 4TeU and 24TeU in consideration of the barrier heights from the S2 Franck-Condon point to the S2/S1 or S2/T2 intersections. In addition, the recovery of the ground state from the T1 state for 2TeU will be more efficient than that for the other two systems as well.

Interatomic Coulombic decay of a Li dimer in a coupled electron and nuclear dynamics approach

Interatomic Coulombic decay (ICD) is a fundamental process between atoms or molecules via a neighbor interaction that produces a relaxation of an electronically excited atom or molecule when embedded in an environment. Due to the physical nature of the process, the electronic and nuclear degrees of freedom are coupled. In this paper, we study the ICD process for a lithium dimer by means of the electron and nuclear dynamics (END) approach. The END approach incorporates a full time-dependent description of the electronic and nuclear degrees of freedom, although its current version does not properly account for continuum states and has limitations in the electronic description by using a single determinantal wave function. Despite this, we confirm that the ICD process takes place via a dipole interaction that induces the nuclear motion of the dimer with a consequent electronic population transfer to higher excited states simulating the ionization process. When the dimer approaches a distance of around 11.5 a.u. (6 \AA{}), this ionization process takes place due to the dipole coupling and occurs at the place of the strongest attractive dipole force. Passing that point, we find that the two lithium atoms repel each other via a Coulomb explosion process followed with a consequent kinetic-energy release (KER). We determine the KER and the timing of the ICD process. We point out the strengths and weaknesses of the END approach and the required enhancements to account for a better description of the ICD process in a coupled electron and nuclear dynamics.

Electronic Population Transfer via Impulsive Stimulated X-Ray Raman Scattering with Attosecond Soft-X-Ray Pulses.

Free-electron lasers provide a source of x-ray pulses short enough and intense enough to drive nonlinearities in molecular systems. Impulsive interactions driven by these x-ray pulses provide a way to create and probe valence electron motions with high temporal and spatial resolution. Observing these electronic motions is crucial to understand the role of electronic coherence in chemical processes. A simple nonlinear technique for probing electronic motion, impulsive stimulated x-ray Raman scattering (ISXRS), involves a single impulsive interaction to produce a coherent superposition of electronic states. We demonstrate electronic population transfer via ISXRS using broad bandwidth (5.5eV full width at half maximum) attosecond x-ray pulses produced by the Linac Coherent Light Source. The impulsive excitation is resonantly enhanced by the oxygen 1s→2π^{*} resonance of nitric oxide (NO), and excited state neutral molecules are probed with a time-delayed UV laser pulse.

Time-resolved electron(e,2e)momentum spectroscopy: Application to laser-driven electron population transfer in atoms

Owing to its ability to provide unique information on electron dynamics, time-resolved electron momentum spectroscopy (EMS) is used to study theoretically a laser-driven electronic motion in atoms. Specifically, a chirped laser pulse is used to adiabatically transfer the populations of lithium atoms from the ground state to the first excited state. During this process, impact ionization near the Bethe ridge by time-delayed ultrashort, high-energy electron pulses is used to image the instantaneous momentum density of this electronic population transfer. Simulations with 100 fs and 1 fs pulse durations demonstrate the capability of EMS to image the time-varying momentum density, including its change of symmetry as the population transfer progresses. Moreover, the spectra corresponding to different pulse durations reveal different kinds of electronic motion. We discuss how to properly interpret these time-resolved EMS spectra, which represent a generalization of time-independent EMS.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer.

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Ab Initio Benchmark Study of Nonadiabatic S1-S2 Photodynamics of cis- and trans-Hexatriene.

The dynamics of the nonadiabatically coupled lowest singlet excited states of cis- and trans-hexatriene are studied theoretically, in a comprehensive electronic structure and quantum dynamical investigation. At the ground state equilibrium geometry the relevant S2 and S1 states carry the A1 (Ag) and B2 (Bu) symmetry labels, for the cis (trans) isomer. Various high-level electronic structure methods are used, including the recently reparametrized DFT/MRCI method, and the results are critically compared. Key parameters of interest are the vertical energy gap and the strength of vibronic coupling between the interacting electronic states. To estimate their influence, suitable comparison calculations are performed. The results are used as the basis for quantum dynamical calculations on the UV absorption spectrum and electronic population transfer involving the S1 and S2 states. Up to nine nonseparable degrees of freedom are included in the calculations. The experimental UV absorption spectrum in the 5-5.2 eV energy range can be very well reproduced. The time-dependent wavepacket propagations reveal a population transfer on the order of 30-50 fs, which becomes increasingly complete with more degrees of freedom included in the calculation. The results are briefly compared with analogous data for the s-trans-butadiene system treated by some of us recently.

Quantum dynamics study of singlet–triplet transitions in s-trans-1,3-butadiene

The intersystem crossing dynamics of s-trans-1,3-butadiene in its lowest singlet and triplet states is studied theoretically, employing a fully quantal approach for the first time. The electronic states 21Ag, 11Bu, 13Bu and 13Ag, which interact vibronically and via the spin-orbit coupling are treated in the calculation, thus covering the lowest spin-forbidden electronic transitions. Up to five nuclear degrees of freedom, including out-of-plane dihedral angles are included in our investigation. The calculation of potential energy surfaces relies on the CASPT2 method, and the evaluation of spin-orbit coupling matrix elements using the full two-electron Breit–Pauli Hamiltonian is performed by utilizing the MRCI wavefunction. The latter dependence on the nuclear coordinates is included for the first time. An electronic population transfer on the sub-picosecond time scale due to intersystem crossing is obtained, a mechanism that can contribute to the singlet–triplet transitions in the electron energy loss spectrum of s-trans-1, 3-butadiene. It is found that the dependence of the spin-orbit coupling on the out-of-plane coordinates plays a dominant role in these singlet–triplet transitions. The amount of population transfer to the 13Ag and 13Bu states is roughly of the same order of magnitude.

Quantum dynamics on a three-sheeted six-dimensional ab initio potential-energy surface of the phosphine cation: Simulation of the photoelectron spectrum and the ultrafast radiationless decay dynamics.

A diabatic three-sheeted six-dimensional potential-energy surface has been constructed for the ground state and the lowest excited state of the PH3 (+) cation. Coupling terms of Jahn-Teller and pseudo-Jahn-Teller origin up to eighth order had to be included to describe the pronounced anharmonicity of the surface due to multiple conical intersections. The parameters of the diabatic Hamiltonian have been optimized by fitting the eigenvalues of the potential-energy matrix to ab initio data calculated at the CASSCF/MRCI level employing the correlation-consistent triple-ζ basis. The theoretical photoelectron spectrum of phosphine and the non-adiabatic nuclear dynamics of the phosphine cation have been computed by propagating nuclear wave packets with the multiconfiguration time-dependent Hartree method. The theoretical photoelectron bands obtained by Fourier transformation of the autocorrelation function agree well with the experimental results. It is shown that the ultrafast non-radiative decay dynamics of the first excited state of PH3 (+) is dominated by the exceptionally strong Jahn-Teller coupling of the asymmetric bending vibrational mode together with a hyperline of conical intersections with the electronic ground state induced by the umbrella mode. Time-dependent population probabilities have been computed for the three adiabatic electronic states. The non-adiabatic Jahn-Teller dynamics within the excited state takes place within ≈5 fs. Almost 80% of the excited-state population decay to the ground state within about 10 fs. The wave packets become highly complex and delocalized after 20 fs and no further significant transfer of electronic population seems to occur up to 100 fs propagation time.

Two-dimensional Fourier transform electronic spectroscopy at a conical intersection

We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental two-dimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an "asymmetric solvation mode" with a small stabilization energy of ∼2 cm(-1) is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment.

Efficient population transfer in modulation doped single quantum wells by intense few-cycle terahertz pulses

We demonstrate the direct observation of non-equilibrium intersubband dynamics in a modulation-doped multiple quantum well sample subject to intense few-cycle terahertz (THz) pulses. The transmission spectra show a distinct dependence on the incident THz field strength and contain signatures of a multitude of nonlinear effects that can be observed owing to the large THz-pulse bandwidth. We focus our attention on a case of transient nonlinear refractive index caused by the efficient transfer of electronic population from the ground state to higher-excited states of the quantum well sample. By comparing the experimental results with a one-dimensional finite-difference model going beyond the slowly varying envelope approximation, we prove that, depending on the pulse shape, the leading part of the intense pulse efficiently transfers electrons from the ground state to higher lying excited states. For weak electric fields and small-population transfer, the linear Lorentz model holds. For strong electric fields, up to 55 and 20% of the ground-state electrons are transferred to the first and second excited subbands, respectively, which could lead to the observation of the optical gain.

Conformation and Electronic Population Transfer in Membrane-Supported Self-Assembled Porphyrin Dimers by 2D Fluorescence Spectroscopy

Two-dimensional fluorescence spectroscopy (2D FS) is applied to determine the conformation and femtosecond electronic population transfer in a dimer of magnesium meso tetraphenylporphyrin. The dimers are prepared by self-assembly of the monomer within the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. A theoretical framework to describe 2D FS experiments is presented, and a direct comparison is made between the observables of this measurement and those of 2D electronic spectroscopy (2D ES). The sensitivity of the method to varying dimer conformation is explored. A global multivariable fitting analysis of linear and 2D FS data indicates that the dimer adopts a "bent T-shaped" conformation. Moreover, the manifold of singly excited excitons undergoes rapid electronic dephasing and downhill population transfer on the time scale of ∼95 fs. The open conformation of the dimer suggests that its self-assembly is favored by an increase in entropy of the local membrane environment.

Nonlinear dimensionality reduction for nonadiabatic dynamics: The influence of conical intersection topography on population transfer rates

Conical intersections play a critical role in the nonadiabatic relaxation of excited electronic states. However, there are an infinite number of these intersections and it is difficult to predict which are actually relevant. Furthermore, traditional descriptors such as intrinsic reaction coordinates and steepest descent paths often fail to adequately characterize excited state reactions due to their highly nonequilibrium nature. To address these deficiencies in the characterization of excited state mechanisms, we apply a nonlinear dimensionality reduction scheme (diffusion mapping) to generate reaction coordinates directly from ab initio multiple spawning dynamics calculations. As illustrated with various examples of photoisomerization dynamics, excited state reaction pathways can be derived directly from simulation data without any a priori specification of relevant coordinates. Furthermore, diffusion maps also reveal the influence of intersection topography on the efficiency of electronic population transfer, providing further evidence that peaked intersections promote nonadiabatic transitions more effectively than sloped intersections. Our results demonstrate the usefulness of nonlinear dimensionality reduction techniques as powerful tools for elucidating reaction mechanisms beyond the statistical description of processes on ground state potential energy surfaces.

Ab initioquantum dynamical study of photoinduced ring opening in furan

The nonadiabatic photoinduced ring opening occurring in the two lowest excited singlet states of furan is investigated theoretically, using wave-packet propagation techniques. The underlying multidimensional potential energy surfaces (PESs) are obtained from ab initio computations, using the equation-of-motion coupled cluster method restricted to single and double excitations (EOM-CCSD), reported in earlier recent work [E. V. Gromov, A. B. Trofimov, F. Gatti, and H. Köppel, J. Chem. Phys. 133, 164309 (2010)]. Up to five nuclear degrees of freedom are considered in the quantum dynamical treatment. Four of them represent in-plane motion for which the electronic states in question (correlating with the valence (1)B(2)(V) and Rydberg (1)A(2)(3s) states at the C(2v) ground-state molecular configuration) have different symmetries, A(') and A(''), respectively. The fifth mode, representing out-of-plane bending of the oxygen atom against the carbon-atom plane, leads to an interaction of these states, as is crucial for the photoreaction. The nonadiabatic coupling and conical intersection cause an electronic population transfer on the order of ∼10 fs. Its main features, and that of the wave-packet motion, are interpreted in terms of properties of the PES. The lifetime due to the ring-opening process has been estimated to be around 2 ps. The dependence of this estimate on the nuclear degrees of freedom retained in the computations is discussed.

Efficient and robust strong-field control of population transfer in sensitizer dyes with designed femtosecond laser pulses

We demonstrate control of electronic population transfer in molecules with the help of appropriately shaped femtosecond laser pulses. To this end we investigate two photosensitizer dyes in solution being prepared in the triplet ground state. Excitation within the triplet system is followed by intersystem crossing and the corresponding singlet fluorescence is monitored as a measure of population transfer in the triplet system. We record control landscapes with respect to the fluorescence intensity on both dyes by a systematic variation of laser pulse shapes combining second order and third order dispersion. In the strong-field regime we find highly structured topologies with large areas of maximum or minimum population transfer being insensitive over a certain range of applied laser intensities thus demonstrating robustness. We then compare our experimental results with simulations on generic molecular potentials by solving the time-dependent Schrödinger equation for excitation with shaped pulses. Control landscapes with respect to population transfer confirm the general trends from experiments. An analysis of regions with maximum or minimum population transfer indicates that coherent processes are responsible for the outcome of our excitation process. The physical mechanisms of joint motion of ground and excited state wave packets or population of a vibrational eigenstate in the excited state permit us to discuss the molecular dynamics in an atom-like picture.

Quantum-classical description of environmental effects on electronic dynamics at conical intersections

Quantum-classical Liouville theory is used to simulate the dynamics of systems containing conical intersections. In particular quantum dynamical effects on the electronic population transfer and coherence in a quantum subsystem that arise from the presence of an environment are studied. The environment, in turn, is partitioned into an immediate environment representing, say, local molecular vibrations, and a bath representing other degrees of freedom. Population transfer may be enhanced or suppressed, depending on the relative values of the characteristic frequencies of the immediate environment and bath. Electronic decoherence and the destruction of geometric phase effects were observed for bath frequencies that are large relative to the molecular vibrations. The dynamics at higher dimensional conical intersections was found to be very sensitive to the environmental coupling. When a single collective solvent coordinate couples directly to the electronic subsystem, the characteristic frequency of the new coordinate, relative to that of the nuclear vibrational modes, has a strong effect on the population dynamics. The results also serve as a test of the QCL dynamical scheme for future applications to more detailed molecular descriptions of condensed phase environments for conical intersection dynamics.