Theoretical study of excitations in furan: Spectra and molecular dynamics

Calculation of quasi-diabatic states within the DFT/MRCI(2) framework: The QD-DFT/MRCI(2) method

We describe a procedure for the calculation of quasi-diabatic states within the recently introduced DFT/MRCI(2) framework [S. P. Neville and M. S. Schuurman, J. Chem. Phys. 157, 164103 (2022)]. Based on an effective Hamiltonian formalism, the proposed procedure, which we term QD-DFT/MRCI(2), has the advantageous characteristics of being simultaneously highly efficient and effectively black box in nature while directly yielding both quasi-diabatic potentials and wave functions of high quality. The accuracy and efficiency of the QD-DFT/MRCI(2) formalism are demonstrated via the simulation of the vibronic absorption spectra of furan and chlorophyll a.

Few-fs resolution of a photoactive protein traversing a conical intersection

The structural dynamics of a molecule are determined by the underlying potential energy landscape. Conical intersections are funnels connecting otherwise separate potential energy surfaces. Posited almost a century ago¹, conical intersections remain the subject of intense scientific interest^2-5. In biology, they have a pivotal role in vision, photosynthesis and DNA stability⁶. Accurate theoretical methods for examining conical intersections are at present limited to small molecules. Experimental investigations are challenged by the required time resolution and sensitivity. Current structure-dynamical understanding of conical intersections is thus limited to simple molecules with around ten atoms, on timescales of about 100 fs or longer⁷. Spectroscopy can achieve better time resolutions⁸, but provides indirect structural information. Here we present few-femtosecond, atomic-resolution videos of photoactive yellow protein, a 2,000-atom protein, passing through a conical intersection. These videos, extracted from experimental data by machine learning, reveal the dynamical trajectories of de-excitation via a conical intersection, yield the key parameters of the conical intersection controlling the de-excitation process and elucidate the topography of the electronic potential energy surfaces involved.

High-resolution vacuum ultraviolet absorption spectra of 2,3- and 2,5-dihydrofuran

Using a synchrotron-based Fourier-transform spectrometer, the high-resolution absorption spectra of the C₁-symmetric 2,3-dihydrofuran (23DHF) and C_2v-symmetric 2,5-dihydrofuran (25DHF) have been measured from 5.5 eV to 9.4 eV with an absolute absorption cross section scale. Oscillator strengths and vertical excitation energies of the lowest 18 states have been computed using the average of the second- and third-order algebraic diagrammatic construction polarization propagator method and the equation-of-motion coupled-cluster method at the level of singles and doubles model. These show that the bright valence transitions of ππ^*-character are embedded into Rydberg transitions, whose oscillator strengths are at least one order of magnitude lower. To account for intensity borrowing, the first broad valence transition between 5.5 eV and 6.8 eV was simulated using a nuclear ensemble, and the agreement between experiment and theory is excellent. Whereas 23DHF only exhibits one broad valence transition followed by d/f Rydberg series converging to the ionization energy, the absorption spectrum of 25DHF has four bands, attributed to a valence nπσ → π^*-transition, nπσ → 3p_x,z/3d_xz transitions, a second valence nπ → π^*-transition followed by d/f Rydberg series converging to the ionization energy, respectively. All Rydberg series converging to the ionization energy have been characterized in terms of their quantum defects.

The ring-opening channel and the influence of Rydberg states on the excited state dynamics of furan and its derivatives

One important relaxation pathway for photo-excited five-membered heterocyclic organic molecules is ring-opening via a dissociative πσ^* state. In this study, we investigate the influence of this pathway in furan and several hydrogenated and methylated derivatives by combining time-resolved photoelectron spectroscopy with time-dependent density functional theory and coupled cluster calculations. We find strong experimental evidence that the ring-opening channel is the major relaxation channel in furan, 2,3-dihydrofuran, and 2-methylfuran (2-MF). In 2,5-dimethylfuran (25-DMF), however, we observe that the molecules relax either via a π3s Rydberg state or through a direct return to the ground state by undergoing ring-puckering motions. From the supporting calculations, for 2-MF and 25-DMF, we predict that there is strong mixing between the πσ^* state and the π3s Rydberg state along the ring opening pathway. However, in 25-DMF, no crossing between the πσ^*/π3s state and the initially excited ππ^* state can be found along the ring opening coordinate, effectively blocking this channel.

Role of electronic correlations in photoionization of NO2 in the vicinity of the 2A1/2B2 conical intersection

We present the first ab initio multi-channel photoionization calculations for NO₂ in the vicinity of the ²A₁/²B₂ conical intersection, for a range of nuclear geometries, using our newly developed set of tools based on the ab initio multichannel R-matrix method.

Optical Shaping of X-Ray Free-Electron Lasers

In this Letter we report the experimental demonstration of a new temporal shaping technique for x-ray free-electron lasers (FELs). This technique is based on the use of a spectrally shaped infrared (IR) laser and allows optical control of the x-ray generation process. By accurately manipulating the spectral amplitude and phase of the IR laser, we can selectively modify the electron bunch longitudinal emittance thus controlling the duration of the resulting x-ray pulse down to the femtosecond time scale. Unlike other methods currently in use, optical shaping is directly applicable to the next generation of high-average power x-ray FELs such as the Linac Coherent Light Source-II or the European X-FEL, and it enables pulse shaping of FELs at the highest repetition rates. Furthermore, this laser-shaping technique paves the way for flexible tailoring of complex multicolor FEL pulse patterns required for nonlinear multidimensional x-ray spectroscopy as well as novel multicolor diffraction imaging schemes.

Excited-state dynamics of furan studied by sub-20-fs time-resolved photoelectron imaging using 159-nm pulses

The excited-state dynamics of furan were studied by time-resolved photoelectron imaging using a sub-20-fs deep UV (198 nm) and vacuum UV (159 nm) light source. The 198- and 159-nm pulses produce photoionization signals in both pump-probe and probe-pump pulse sequences. When the 198-nm pulse precedes the 159-nm pulse, it creates the (1)A2(3s) Rydberg and (1)B2(ππ(∗)) valence states, and the former decays exponentially with a time constant of about 20 fs whereas the latter exhibits more complex wave-packet dynamics. When the 159-nm pulse precedes the 198-nm pulse, a wave packet is created on the (1)A1(ππ(∗)) valence state, which rapidly disappears from the observation window owing to structural deformation. The 159-nm photoexcitation also creates the 3s and 3px,y Rydberg states non-adiabatically.

Classical blended quantum formulation of the parallel TDDVR method to the dynamics on furan

A major portion (∼98%) of the quantum-classical molecular dynamics approach, namely, Time-Dependent Discrete Variable Representation (TDDVR) method, is recently parallelized using shared-memory parallelization scheme with the aim of performing dynamics on relatively large molecular systems. Therefore, we have chosen the furan as a model system for dynamical simulation. Four lowest singlet excited electronic states 1A2(3s), 1B2(V), 1A1(V*), and 1B1(3p) of furan are vibronically coupled through several conical intersections in the vicinity of Frank-Condon region. The major focus of the present paper is to explore the efficiency of our newly implemented parallelized TDDVR algorithm to perform dynamics on large dimensional quantum systems in vibronically coupled electronic manifold. The present version of parallelized TDDVR algorithm show closely linear speed up with increasing number of computing processors. As a significant speed up is achieved by cycling in the correct way over arrays, all dynamical simulations are performed within a reasonable wall clock time. The photoelectron spectra calculated by the TDDVR method show peak by peak correspondence with the experimental spectra. The TDDVR calculated quantum-classical dynamical outcomes, viz., population and photoelectron spectra, etc. show good agreement with the findings of the well-established quantum dynamical method, i.e. Multi Configuration Time-Dependent Hartree (MCTDH) approach.

A theoretical exploration on electronically excited states of protonated furan and thiophene

MPE profiles of the ground and S1 excited states of protonated furan along C–O bond-stretching reaction coordinate, computed at the RI-CC2/aug-cc-pVDZ level of theory.

Multiple Core and Vibronic Coupling Effects in Attosecond Stimulated X-Ray Raman Spectroscopy (SXRS)

Attosecond Stimulated X-ray Raman Spectroscopy (SXRS) is a promising technique for investigating molecular electronic structure and photochemical processes with high spatial and temporal resolution. We present a theoretical study of SXRS from multiple core excitation sites of the same element. Two issues are addressed: interference between pathways contributing the signals from different sites; and how nuclear vibrations influence the signals. Taking furan as a model system, which contains two types of carbons Cα and Cβ, we performed time-dependent density functional theory calculations and computed the SXRS signals with two pulses tuned at the carbon K-edge. Our simulations demonstrate that the SXRS signal from the Cα and Cβ sites are non-additive, owing to the significant mixed contributions (Cα 1s excitations by the pump pulse followed by Cβ 1s excitations by the probe, or vice verse). Harmonic vibrations linearly coupled to the electronic transitions are incorporated using the cumulant expansion. The nuclei act as a bath for electronic transitions which accelerate the decay of time-domain signal. The frequency-domain spectrum is modified by a small red shift and high-resolution fine-structure features are introduced.

Ultrafast photodynamics of furan

Ultrafast photodynamics of furan has been studied by time-resolved photoelectron imaging (TRPEI) spectroscopy with an unprecedented time resolution of 22 fs. The simulation of the time-dependent photoelectron kinetic energy distribution (PKED) has been performed with ab initio nonadiabatic dynamics "on the fly" in the frame of time-dependent density functional theory. Based on the agreement between experimental and theoretical time-dependent photoelectron signal intensity as well as on PKED, precise time scales of ultrafast internal conversion from S(2) over S(1) to the ground state S(0) of furan have been revealed for the first time. Upon initial excitation of the S(2) state which has π-π* character, a nonadiabatic transition to the S(1) state occurs within 10 fs. Subsequent dynamics invokes the excitation of the C-O stretching and C-O-C out of plane vibrations which lead to the internal conversion to the ground state after 60 fs. Thus, we demonstrate that the TRPEI combined with high level nonadiabatic dynamics calculations provide fundamental insight into ultrafast photodynamics of chemically and biologically relevant chromophores.

Theoretical study of photoinduced ring-opening in furan

The potential energy surfaces (PESs) of the two lowest excited singlet states of furan [correlating with the Rydberg (1)A(2)(3s) and valence (1)B(2)(V) states at the C(2v) ground-state molecular configuration] have been studied in some detail with regard to the photoinduced ring-opening reaction. The surfaces have been characterized in terms of their stationary points and points of minimum energy conical intersections along the ring-opening pathway. The optimization of the geometrical parameters has been performed with the equation of motion coupled cluster singles and doubles method. The ab initio PESs have been modeled by energy grids and Taylor series. The resulting 11-dimensional PESs reproduce the ab initio results to a good accuracy and can be used in dynamical calculations.

Generalized CC-TDSCF and LCSA: The system-energy representation

Typical (sub)system-bath quantum dynamical problems are often investigated by means of (approximate) reduced equations of motion. Wavepacket approaches to the dynamics of the whole system have gained momentum in recent years and there is hope that properly designed approximations to the wavefunction will allow one to correctly describe the subsystem evolution. The continuous-configuration time-dependent self-consistent field (CC-TDSCF) and local coherent-state approximation (LCSA) methods, for instance, use a simple Hartree product of bath single-particle-functions for each discrete variable representation (DVR) state introduced in the Hilbert space of the subsystem. Here we focus on the above two methods and replace the DVR states with the eigenstates of the subsystem Hamiltonian, i.e., we adopt an energy-local representation for the subsystem. We find that stable and semiquantitative results are obtained for a number of dissipative problems, at the same (small) computational cost of the original methods. Furthermore, we find that both methods give very similar results, thus suggesting that coherent-states are well suited to describe (local) bath states. As a whole, present results highlight the importance of the system basis-set in the selected-multiconfiguration expansion of the wavefunction. They suggest that accurate and yet computationally cheap methods may be simply obtained from CC-TDSCF/LCSA by letting the subsystem states be variationally optimized.

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.

Furan−Formic Acid Dimers: An ab Initio and Matrix Isolation Study

The dimers formed by formic acid (FA) and furan are investigated by ab initio methods and matrix isolation spectroscopy. Nine complexes with binding energies between -3.91 and -0.82 kcal/mol (MP2/6-311++G(d,p) + ZPE + BSSE) are identified. Another five weaker bound complexes are localized at lower level of theory only. The binding in the furan-FA dimers can be described in terms of OH...O, C=O...H, HO...H, CH...O, OH...pi, and CH...pi interactions. Therefore, the furan-FA complexes are classified in two types: (1) the dimers where the OH hydrogen of formic acid interacts with the furan molecule and (2) the dimers where the main interactions of FA with the furan molecule are via the less acidic CH hydrogen. Duning's and Pople's triple and double basis sets were used to study the dependence of the geometries and energies of the complexes from the basis set. BSSE (basis set superposition error) counterpoise corrections (CP) were included during the geometry optimizations of all dimers at the MP2/6-31G(d,p) level of theory. Matrix isolation spectroscopy allowed us to record the IR spectrum of aggregates between FA and furan. By comparison of the experimental IR spectrum with calculated IR spectra of a variety of complexes, it was possible to identify the most stable furan-FA dimer as the major product of the aggregation.

Combined experimental-theoretical study of the lower excited singlet states of paravinyl phenol, an analog of the paracoumaric acid chromophore

The low-lying excited singlet states of paravinyl phenol (pVP) are investigated experimentally and theoretically paying attention to their similarity to excited states of paracoumaric acid, the chromophore of the photoactive yellow protein (PYP). Resonance enhanced multiphoton ionization and laser induced fluorescence spectroscopic techniques are employed to obtain supersonically cooled, vibrationally resolved excitation and emission spectra related to the lowest (1)A'(V') excited state of pVP. Comprehensive analyses of the spectral structures are carried out by means of the equation-of-motion coupled cluster singles and doubles and time dependent density functional theory methods in combination with the linear vibronic coupling model and Franck-Condon calculations. The assignments of the spectral patterns are given, mostly in terms of excitations of totally symmetric modes. Weak activity of the non-totally-symmetric modes indicates low probability of photochemical processes in the Franck-Condon region of the (1)A'(V') state. The second (1)A'(V) and third (1)A" (Ryd) excited states of pVP are characterized with regard to their electronic structure, properties, and effects of geometry relaxations. The lengthening of the double bond relevant to the trans-cis isomerization of the PYP chromophore is found for the (1)A'(V) state. A possibility of photochemical processes and strong vibronic interactions in this state can be expected. The theoretical results for the (1)A"(Ryd) state predict that dissociation with respect to the O-H bond is possible.

Multistate multimode vibronic dynamics: Entanglement of electronic and vibrational degrees of freedom in the benzene radical cation

An earlier theoretical treatment of multimode and multistate vibronic coupling in the benzene radical cation [Koppel et al., J. Chem. Phys. 117, 2657 (2002)] is extended to investigate also the behavior of the nuclear degrees of freedom and to include additional electronic states. The five lowest doublet electronic states are considered which have been shown earlier to be all interconnected through a series of conical intersections of their potential-energy surfaces. In the most extensive calculations, they are all included simultaneously in the quantum dynamical calculations performed, which represent a system of unprecedented complexity treated in this way. The results are compared with various reduced-dimensionality treatments (i.e., employing reduced vibrational and electronic function spaces). The different temporal behavior of the various electronic populations is emphasized and traced to the different locations of the various seams of conical intersections: due to the coherent oscillations of the time-dependent wave packet this leads to an oscillatory behavior in some cases and to monotonous behavior in others. A seemingly irreversible behavior of the system dynamics in this strictly microscopic treatment is confirmed. The importance of this benchmark system to highlight complex, entangled multimode, and multistate vibronic dynamics is pointed out.

Simulation of a complex spectrum: Interplay of five electronic states and 21 vibrational degrees of freedom in C5H4+

Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B (2)E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum.