Dynamics of the Molecular Geometric Phase.

The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wave function and a recently proposed quantum hydrodynamical description of its dynamics. An instantaneous, gauge-invariant phase is introduced for arbitrary paths in nuclear configuration space in terms of hydrodynamical variables, and shown to reduce to the adiabatic geometric phase when the state is adiabatic and the path is closed. The evolution of the closed-path phase over time is shown to adhere to a Maxwell-Faraday induction law, with nonconservative forces arising from the electron dynamics that play the role of electromotive forces. We identify the pivotal forces that are able to change the value of the phase, thereby challenging any topological argument. Nonetheless, negligible changes in the phase occur when the local dynamics along the probe loop is approximately adiabatic. That is, the geometric phase effects that arise in an adiabatic limiting situation remain suitable to effectively describe certain dynamic observables.

Controlled destabilization of caged circularized DNA oligonucleotides predicted by replica exchange molecular dynamics simulations.

Spatiotemporal control is a critical issue in the design of strategies for the photoregulation of oligonucleotide activity. Efficient uncaging, i.e., activation by removal of photolabile protecting groups (PPGs), often necessitates multiple PPGs. An alternative approach is based on circularization strategies, exemplified by intrasequential circularization, also denoted photo-tethering, as introduced in [Seyfried et al., Angew. Chem., Int. Ed., 2017, 56, 359]. Here, we develop a computational protocol, relying on replica exchange molecular dynamics (REMD), in order to characterize the destabilization of a series of circularized, caged DNA oligonucleotides addressed in the aforementioned study. For these medium-sized (32 nt) oligonucleotides, melting temperatures are computed, whose trend is in good agreement with experiment, exhibiting a large destabilization and, hence, reduction of the melting temperature of the order of ΔTm ∼ 30 K as compared with the native species. The analysis of free energy landscapes confirms the destabilization pattern experienced by the circularized oligonucleotides. The present study underscores that computational protocols that capture controlled destabilization and uncaging of oligonucleotides are promising as predictive tools in the tailored photocontrol of nucleic acids.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation.

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S1) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

On the Cooperative Origin of Solvent-Enhanced Symmetry-Breaking Charge Transfer in a Covalently Bound Tetracene Dimer Leading to Singlet Fission.

Singlet fission in covalently bound acene dimers in solution is driven by the interplay of excitonic and singlet correlated triplet 1(TT) states with intermediate charge-transfer states, a process which depends sensitively on the solvent environment. We use high-level electronic structure methods to explore this singlet fission process in a linked tetracene dimer, with emphasis on the symmetry-breaking mechanism for the charge-transfer (CT) states induced by low-frequency antisymmetric vibrations and polar/polarizable solvents. A combination of the second-order algebraic diagrammatic construction (ADC(2)) and density functional theory/multireference configuration interaction (DFT/MRCI) methods are employed, along with a state-specific conductor-like screening model (COSMO) solvation model in the former case. This work quantifies, for the first time, an earlier mechanistic proposal [Alvertis et al., J. Am. Chem. Soc. 2019, 141, 17558] according to which solvent-induced symmetry breaking leads to a high-energy CT state which interacts with the correlated triplet state, resulting in singlet fission. An approximate assessment of the nonadiabatic interactions between the different electronic states underscores that the CT states are essential in facilitating the transition from the bright excitonic state to the 1(TT) state leading to singlet fission. We show that several types of symmetry-breaking inter- and intra-fragment vibrations play a crucial role in a concerted mechanism with the solvent environment and with the symmetric inter-fragment torsion, which tunes the admixture of excitonic and CT states. This offers a new perspective on how solvent-induced symmetry-breaking CT can be understood and how it cooperates with intramolecular mechanisms in singlet fission.

Quantum Dynamics with Electronic Friction.

A theory of electronic friction is developed using the exact factorization of the electronic-nuclear wave function. No assumption is made regarding the electronic bath, which can be made of independent or interacting electrons, and the nuclei are treated quantally. The ensuing equation of motion for the nuclear wave function is a nonlinear Schrödinger equation including a friction term. The resulting friction kernel agrees with a previously derived mixed quantum-classical result by Dou et al., [Phys. Rev. Lett. 119, 046001 (2017)]PRLTAO0031-900710.1103/PhysRevLett.119.046001, except for a pseudomagnetic contribution in the latter that is here removed. More specifically, it is shown that the electron dynamics generally washes out the gauge fields appearing in the adiabatic dynamics. However, these are fully re-established in the typical situation where the electrons respond rapidly on the slow time scale of the nuclear dynamics (Markov limit). Hence, we predict Berry's phase effects to be observable also in the presence of electronic friction. Application to a model vibrational relaxation problem proves that the proposed approach represents a viable way to account for electronic friction in a fully quantum setting for the nuclear dynamics.

Quantum Dynamics of Exciton Transport and Dissociation in Multichromophoric Systems.

Due to the subtle interplay of site-to-site electronic couplings, exciton delocalization, nonadiabatic effects, and vibronic couplings, quantum dynamical studies are needed to elucidate the details of ultrafast photoinduced energy and charge transfer events in organic multichromophoric systems. In this vein, we review an approach that combines first-principles parameterized lattice Hamiltonians with accurate quantum dynamical simulations using advanced multiconfigurational methods. Focusing on the elementary transfer steps in organic functional materials, we address coherent exciton migration and creation of charge transfer excitons in homopolymers, notably representative of the poly(3-hexylthiophene) material, as well as exciton dissociation at polymer:fullerene heterojunctions. We emphasize the role of coherent transfer, trapping effects due to high-frequency phonon modes, and thermal activation due to low-frequency soft modes that drive a diffusive dynamics.

Signatures of coherent vibronic exciton dynamics and conformational control in the two-dimensional electronic spectroscopy of conjugated polymers.

Two-dimensional electronic spectroscopy (2DES) signals for homo-oligomer J-aggregates are computed, with a focus on the role of structural change induced by low-frequency torsional modes, along with quasi-stationary trapping effects induced by high-frequency polaronic modes. To this end, a model system is derived from an ab initio parametrized site-based Hamiltonian for oligothiophenes [Binder et al., Phys. Rev. Lett., 2018, 120, 227401]. To obtain a compact representation, we introduce a collective lattice mode whose vibronic coupling depends nonlinearly on the exciton density. As a result, an N-site model with a single polaronic mode and a single torsional mode is obtained. Furthermore, a quantum-classical treatment is employed where the torsional mode is treated within a mean-field Ehrenfest/Langevin approximation. 2D electronic spectra are computed using the equation-of-motion phase-matching approach (EOM-PMA) within a wavefunction description. It is seen that the spectra combine the vibronic fine structure, due to the polaronic mode, and a dynamic Stokes shift, due to torsional relaxation. The signatures of the coherent effects and adiabatic evolution in the 2DES signals are discussed.

Ultrafast and efficient energy transfer in a one- and two-photon sensitized rhodamine-BODIPY dyad: a perspective for broadly absorbing photocages.

In view of the demand for photoactivatable probes that operate in the visible (VIS) to near infrared (NIR) region of the spectrum, we designed a bichromophoric system based on a rhodamine fluorophore and a BODIPY photocage. Two-photon excited fluorescence (TPEF) measurements and quantum chemical calculations reveal excellent two-photon properties of the employed rhodamine derivative. Excitation of the rhodamine unit via a one- or two-photon process leads to excitation energy transfer (EET) onto the BODIPY part, which is followed by the liberation of the leaving group. Ultrafast transient absorption spectroscopy provides evidence for a highly efficient EET dynamics on a sub-500 femtosecond scale. Complementary quantum dynamical calculations using the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach highlight the quantum coherent character of the EET transfer. Photorelease of p-nitroaniline (PNA) was investigated by UV/vis absorption spectroscopy by either excitation of the rhodamine or the BODIPY moiety. Even though a quantitative assessment of the PNA yield could not be achieved for this particular BODIPY cage, the present study provides a design principle for a class of photocages that can be broadly activated between 500 and 900 nm.

Quantum dynamical study of inter-chain exciton transport in a regioregular P3HT model system at finite temperature: HJ vs H-aggregate models.

We report on quantum dynamical simulations of inter-chain exciton transport in a model of regioregular poly(3-hexylthiophene), rr-P3HT, at finite temperature using the Multi-Layer Multi-Configuration Time-Dependent Hartree method for a system of up to 63 electronic states and 180 vibrational modes. A Frenkel Hamiltonian of HJ aggregate type is used along with a reduced H-aggregate representation; electron-phonon coupling includes local high-frequency modes as well as anharmonic intermolecular modes. The latter are operative in mediating inter-chain transport by a mechanism of transient localization type. Strikingly, this mechanism is found to be of quantum coherent character and involves non-adiabatic effects. Using periodic boundary conditions, a normal diffusion regime is identified from the exciton mean-squared displacement, apart from early-time transients. Diffusion coefficients are found to be of the order of 3 × 10-3 cm2/s, showing a non-linear increase with temperature.

Multi-layer Gaussian-based multi-configuration time-dependent Hartree (ML-GMCTDH) simulations of ultrafast charge separation in a donor-acceptor complex.

We report on first applications of the Multi-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (ML-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] beyond its basic two-layer variant. The ML-GMCTDH scheme provides an embedding of a variationally evolving Gaussian wavepacket basis into a hierarchical tensor representation of the wavefunction. A first-principles parameterized model Hamiltonian for ultrafast non-adiabatic dynamics in an oligothiophene-fullerene charge transfer complex is employed, relying on a two-state linear vibronic coupling model that combines a distribution of tuning type modes with an intermolecular coordinate that also modulates the electronic coupling. Efficient ML-GMCTDH simulations are carried out for up to 300 vibrational modes using an implementation within the QUANTICS program. Excellent agreement with reference ML-MCTDH calculations is obtained.

Local-in-Time Error in Variational Quantum Dynamics.

The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrödinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact expressions are provided for this error, which are then evaluated in illustrative cases, notably the widely used mean-field approach and the adiabatic quantum molecular dynamics. Based on these findings, we demonstrate the rigorous formulation of an adaptive scheme that resizes on the fly the underlying variational manifold and, hence, optimizes the overall computational cost of a quantum dynamical simulation. Such adaptive schemes are a crucial requirement for devising and applying direct quantum dynamical methods to molecular and condensed-phase problems.

First-principles description of intra-chain exciton migration in an oligo(para-phenylene vinylene) chain. II. ML-MCTDH simulations of exciton dynamics at a torsional defect.

The first-principles parameterized Frenkel-Holstein Hamiltonian developed in Paper I [R. Binder et al., J. Chem. Phys. 152, 204119 (2020)] is employed to carry out full quantum-dynamical simulations of an elementary exciton migration event in an oligo-(para-phenylene vinylene) chain with 20 repeat units (OPV-20). We consider a dynamic scenario where an initial torsional defect, creating a conjugation break, relaxes on a time scale of about 500 fs toward a planarized structure and triggers the spatial displacement of the photogenerated exciton. Accurate quantum dynamical simulations are performed using the multi-layer multi-configuration time-dependent Hartree method as applied to an OPV-20 system comprising 20 electronic states of Frenkel type and 60 vibrational modes. These include site-local quinoid-distortion modes, site-correlated bond-length alternation (BLA) modes, and an active ring torsional mode at the central junction. The simulations fully account for correlations between the ring torsional mode and the anharmonically coupled BLA coordinate located at the same junction. In accordance with our earlier studies of a related oligothiophene (OT) system [R. Binder, D. Lauvergnat, and I. Burghardt, Phys. Rev. Lett. 120, 227401 (2018)], these simulation results highlight that exciton migration is a coherent process driven by the fluctuations of "soft" modes, exemplified by the ring torsions. Conversely, these results also show that trapping due to high-frequency modes, leading to energetic stabilization of the exciton-polaron species, is weaker in OPV than in the OT system. This underscores not only the generic features of exciton dynamics in conjugated polymer systems, but also the role of molecular specificities.

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

A generalized Frenkel-Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al. [J. Chem. Phys. 141, 014101 (2014)] to translate one-dimensional (1D) and two-dimensional (2D) potential energy surface (PES) scans to a fully anharmonic, generalized Frenkel-Holstein (FH) Hamiltonian. A 1D PES scan is carried out for intra-ring quinoid distortion modes, while 2D PES scans are performed for the anharmonically coupled inter-monomer torsional and vinylene bridge bond length alternation modes. The kinetic energy is constructed in curvilinear coordinates by an exact numerical procedure, using the TNUM Fortran code. As a result, a fully molecular-based, generalized FH Hamiltonian is obtained, which is subsequently employed for quantum exciton dynamics simulations, as shown in Paper II [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)].

Quantum dynamical simulations of intra-chain exciton diffusion in an oligo (para-phenylene vinylene) chain at finite temperature.

We report on quantum dynamical simulations of exciton diffusion in an oligo(para-phenylene vinylene) chain segment with 20 repeat units (OPV-20) at finite temperature, complementary to our recent study of the same system at T = 0 K [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)]. Accurate quantum dynamical simulations are performed using the multi-layer multi-configuration time-dependent Hartree method as applied to a site-based Hamiltonian comprising 20 electronic states of Frenkel type and 460 vibrational modes, including site-local quinoid-distortion modes along with site-correlated bond-length alternation (BLA) modes, ring torsional modes, and an explicit harmonic-oscillator bath. A first-principles parameterized Frenkel-Holstein type Hamiltonian is employed, which accounts for correlations between the ring torsional modes and the anharmonically coupled BLA coordinates located at the same junction. Thermally induced fluctuations of the torsional modes are described by a stochastic mean-field approach, and their impact on the excitonic motion is characterized in terms of the exciton mean-squared displacement. A normal diffusion regime is observed under periodic boundary conditions, apart from transient localization features. Even though the polaronic exciton species are comparatively weakly bound, exciton diffusion is found to be a coherent-rather than hopping type-process, driven by the fluctuations of the soft torsional modes. Similar to the previous observations for oligothiophenes, the evolution for the most part exhibits a near-adiabatic dynamics of local exciton ground states (LEGSs) that adjust to the local conformational dynamics. However, a second mechanism, involving resonant transitions between neighboring LEGSs, gains importance at higher temperatures.

First-principles quantum simulations of exciton diffusion on a minimal oligothiophene chain at finite temperature.

High-dimensional multiconfigurational quantum dynamics simulations are carried out at finite temperature to simulate exciton diffusion on an oligothiophene chain, representative of a segment of the poly(3-hexylthiophene) (P3HT) polymer. The ab initio parametrized site-based Hamiltonian of Binder et al. [Phys. Rev. Lett., 2018, 120, 227401] is employed to model a 20-site system, including intra-ring and inter-ring high-frequency modes as well as torsional modes which undergo thermal fluctuations induced by an explicit harmonic oscillator bath. The system-bath dynamics is treated within the setting of a stochastic mean-field Schrödinger equation. For the 20-site excitonic system, a total of 20 Frenkel states and 248 modes are propagated using the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. The resulting dynamics can be interpreted in terms of the coherent motion of an exciton-polaron quasi-particle stochastically driven by torsional fluctuations. This dynamics yields a near-linear mean squared displacement (MSD) as a function of time, from which a diffusion coefficient can be deduced which increases with temperature, up to 5.7 × 10-3 cm2 s-1 at T = 300 K.

Time-resolved spectra of I2 in a krypton crystal by G-MCTDH simulations: nonadiabatic dynamics, dissipation and environment driven decoherence.

The multi-state photodynamics following the B 3Πu(0+) ← X 1Σ+g excitation of molecular iodine in a krypton crystal are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). Calculations are performed using a 9-state 18-dimensional Hamiltonian parametrized via diatomics-in-molecules calculations. The simulations reproduce the low predissociation yield deduced by time resolved spectroscopic experiments, and allow the elucidation of the diabatic population dynamics in the dense manifold of covalent electronic states of the embedded I2. The wave packet dynamics are used to calculate pump-probe spectra involving excited state absorption which terminates in the ion pair manifold. The simulated signals are in excellent agreement with the experimental ones, and are interpreted by reducing the full-dimensional wavefunction to the density matrix of the I2 subsystem. It is proved formally that the pump-probe traces can be obtained as convolution between the Wigner function of the chromophore and a time- and frequency-gate function also represented in the phase space. The analysis of the spectra with probe frequency in resonance with the ß â† A 3Πu transition reveals that the mechanism of predissociation out of the B state is pump photon energy-dependent. The quantum nature of the nonradiative transitions is imprinted in the strongly non-classical features of the Wigner function on the A state surface, which is detected in the pump-probe process.

Open system dynamics using Gaussian-based multiconfigurational time-dependent Hartree wavefunctions: Application to environment-modulated tunneling.

A variational approach for the quantum dynamics of statistical mixtures is developed, which is based upon the representation of the natural states of the mixture in terms of hybrid Gaussian-based Multiconfiguration Time-Dependent Hartree (G-MCTDH) wavefunctions. The method, termed ρG-MCTDH, is combined with a treatment of dissipation and decoherence based on the nonstochastic open-system Schrödinger equations. The performance and the convergence properties of the approach are illustrated for a two-dimensional tunneling system, where the primary tunneling coordinate, represented by flexible single-particle functions, is resonantly coupled to a second harmonic mode, represented by Gaussian wave packets. The harmonic coordinate is coupled to the environment and two different processes are studied: (i) vibrational relaxation at zero temperature described by a master equation in the Lindblad form and (ii) thermalization induced by the Caldeira-Leggett master equation. In the second case, the evolution from a quantum tunneling regime to a quasistationary classical-limit distribution, driven by the heat bath, is visualized using a flux analysis.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. II. Theoretical aspects and G-MCTDH simulations of time-resolved coherent Raman spectra of Schrödinger cat states of the embedded I2Kr18 cluster.

This study presents quantum dynamical simulations, using the Gaussian-based multiconfigurational time-dependent Hartree (G-MCTDH) method, of time-resolved coherent Raman four-wave-mixing spectroscopic experiments for the iodine molecule embedded in a cryogenic crystal krypton matrix [D. Picconi et al., J. Chem. Phys. 150, 064111 (2019)]. These experiments monitor the time-evolving vibrational coherence between two wave packets created in a quantum superposition (i.e., a "Schrödinger cat state") by a pair of pump pulses which induce electronic B Πu30+⟵XΣg+1 transitions. A theoretical description of the spectroscopic measurement is developed, which elucidates the connection between the nonlinear signals and the wave packet coherence. The analysis provides an effective means to simulate the spectra for several different optical conditions with a minimum number of quantum dynamical propagations. The G-MCTDH method is used to calculate and interpret the time-resolved coherent Raman spectra of two selected initial superpositions for a I2Kr18 cluster embedded in a frozen Kr cage. The time- and frequency-dependent signals carry information about the molecular mechanisms of dissipation and decoherence, which involve vibrational energy transfer to the stretching mode of the four "belt" Kr atoms. The details of these processes and the number of active solvent modes depend in a non-trivial way on the specific initial superposition.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I2Kr18 cluster using the G-MCTDH method.

The molecular dynamics following the electronic BΠu30+⟵XΣg+1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I2Kr18 cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I2 energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < RI-I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I2-krypton system addressed in Paper II.

Vibronic coupling models for donor-acceptor aggregates using an effective-mode scheme: Application to mixed Frenkel and charge-transfer excitons in oligothiophene aggregates.

A reduced-dimensional effective-mode representation is developed in order to efficiently describe excited-state dynamics of multichromophoric donor-acceptor aggregates within a linear vibronic coupling model. Specifically, we consider systems where vibrational modes pertaining to a given molecular fragment couple both to local excitations of Frenkel type and delocalized states of charge transfer exciton type. A hierarchical chain representation is constructed which is suitable to describe correlated fluctuations, leading to a set of correlated spectral densities. An application is shown for a first-principles parameterized model of an oligothiophene H-type aggregate whose properties are modified due to the presence of charge transfer excitons. Within a pentamer model comprising 13 electronic states and 195 normal modes, good convergence of the effective-mode representation of the spectral densities is achieved at the eighth order of the hierarchy with 104 modes, and a qualitatively correct picture is obtained at the sixth order with 78 modes.