Franck-Condon Geometry Research Articles

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory.

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Evidence of Short-Lived High-Energy Emissive State and Triplet Character of the Self-Trapped Exciton in Cs3Cu2I5 Perovskite.

Cs3Cu2I5 perovskite displays a Stokes-shifted photoluminescence (PL) at 445 nm, attributed to the self-trapped excitons (STEs). Unlike that observed in other perovskite materials, the free-exciton emission is not evidenced in this case. Herein, we reveal the existence of a short-lived high-energy emission centered around 375 nm through the reconstruction of time-resolved emission spectra (TRES), which is independent of the shape/size of Cs3Cu2I5 perovskite. This high-energy emission is proposed to originate from the free-exciton-derived distorted S1 state of the 0D Cs3Cu2I5 moiety. Moreover, STE PL (∼445 nm) was found to have phosphorescence characteristics. Theoretical calculation confirms a facile intersystem crossing at the Franck-Condon geometry, indicating the high lifetime of the STE and its triplet nature. The existence of a high-energy emissive state and the phosphorescent nature of the STE PL band provide valuable insights that could advance our understanding of the photophysics in these materials.

Ab initio investigation of excited state charge transfer pathways in differently capped bithiophene cages.

The electronic excitations of conformationally constrained bithiophene cage systems as previously investigated by Lewis et al. (J. Am. Chem. Soc. 143, 18548 (2021)) are revisited, employing the correlated ab initio Scaled Opposite-Spin Algebraic Diagrammatic Construction Second Order electronic structure method. Quantitative descriptors are determined to assess the extent of charge transfer between the bithiophene moieties and the capping domains, represented by either phenyl or triazine groups. The investigation substantiates intrinsic differences in the photophysical behavior of these two structural variants and reveals the presence of lower-energy excited states characterized by noteworthy charge transfer contributions in the triazine cage system. The manifestation of this charge transfer character is discernible even at the Franck-Condon geometry, persisting throughout the relaxation of the excited state. By examining isolated monomer building blocks, we confirm the existence of analogous charge transfer contributions in their excitations. Employing this methodological approach facilitates the prospective identification of potential wall/cap chromophore pairs, wherein charge transfer pathways can be accessed within the energetically favorable regime.

Ultrafast ESIPT dynamics of 4-methyl-2,6-diformylphenol

We investigate the gas-phase photodynamics associated with the S1 (nπ*), S2 (ππ*) and S3 (nπ*) states of 4-methyl-2,6-diformylphenol using trajectory-based surface hopping dynamics simulations. A rapid internal conversion would populate S1 and S3 upon initiating the trajectories on “bright” S2. This nonadiabatic population behavior would lead to intramolecular proton-transfer tautomerization via three states, where the predominant tautomerization happens via S2. An average timescale of ∼ 44 fs is estimated for the tautomerization. The triplet formation can occur via energetically feasible S1-T3 (at the Franck-Condon geometry of normal tautomer) and S1-T2 (at the S1 equilibrium minimum of proton-transferred tautomer) pathways. Intersystem crossing and the forbidden nature of S1 (nπ*) makes the molecule exhibit weak fluorescence.

Photophysics of Anionic Bis(4H-imidazolato)CuI Complexes.

In this paper, the photophysical behavior of four panchromatically absorbing, homoleptic bis(4H-imidazolato)CuI complexes, with a systematic variation in the electron-withdrawing properties of the imidazolate ligand, were studied by wavelength-dependent time-resolved femtosecond transient absorption spectroscopy. Excitation at 400, 480, and 630 nm populates metal-to-ligand charge transfer, intraligand charge transfer, and mixed-character singlet states. The pump wavelength-dependent transient absorption data were analyzed by a recently established 2D correlation approach. Data analysis revealed that all excitation conditions yield similar excited-state dynamics. Key to the excited-state relaxation is fast, sub-picosecond pseudo-Jahn-Teller distortion, which is accompanied by the relocalization of electron density onto a single ligand from the initially delocalized state at Franck-Condon geometry. Subsequent intersystem crossing to the triplet manifold is followed by a sub-100 ps decay to the ground state. The fast, nonradiative decay is rationalized by the low triplet-state energy as found by DFT calculations, which suggest perspective treatment at the strong coupling limit of the energy gap law.

Excited state intramolecular proton transfer and topography of conical intersection of aromatic hydrazone Schiff bases

We investigated the energy landscapes of several aromatic hydrazone Schiff base molecules using the SA-CASSCF and MS-CASPT2 theories. We located the energy-minimized conical intersection (MECI) of the S1/S0 surfaces. Furthermore, we evaluated the dot products of the S1 energy gradient in the Franck-Condon geometry with the gradient difference and the interstate coupling vectors. Additionally, we obtained the topographical parameters of the MECIs. We examined the excited state intramolecular proton transfer (ESIPT) using TD-DFT, which reveal that ESIPT on the S1 surfaces involve very small barriers. Some of the investigated Schiff base compounds are potential photoswitches.

Excited State Intramolecular Proton Transfer (ESIPT) from -NH2 to the Carbon Atom of a Naphthyl Ring.

Excited state intramolecular proton transfer (ESIPT) has been documented from an amino NH2 group to a carbon atom of an adjacent aromatic ring. This finding changes the paradigm, as hitherto such processes have not been considered as plausible due to slow protonation of carbon and low (photo)acidity of the NH2 group. The ESIPT was studied by irradiation of 2-(2-aminophenyl)naphthalene in CH3CN-D2O, whereupon regiospecific incorporation of deuterium takes place at the naphthalene position 1, with a quantum yield of Φ = 0.11. A synergy of experimental and computational investigations completely unraveled the mechanism of this important photochemical reaction. Upon excitation to the photoreactive S2(La) state, a favorable redistribution of charge sets the stage for ESIPT to the carbon atom in naphthalene position 1. H2O molecules are needed, as they increase the excitation energy and oscillator strength for the population of the S2(La) state. The gain in energy is used to surmount a small energy barrier on the pathway from the Franck-Condon geometry to the conical intersection with the S0, delivering aza-quinone methide.

Toward Simulation of Fe(II) Low-Spin → High-Spin Photoswitching by Synergistic Spin-Vibronic Dynamics.

A new theoretical approach is presented and applied for the simulation of Fe(II) low-spin (LS, singlet, t2g6eg0) → high-spin (HS, quintet, t2g4eg2) photoswitching dynamics of the octahedral model complex [Fe(NCH)6]2+. The utilized synergistic methodology heavily exploits the strengths of complementary electronic structure and spin-vibronic dynamics methods. Specifically, we perform 3D quantum dynamics (QD) and full-dimensional trajectory surface hopping (TSH, in conjunction with a linear vibronic coupling model), with the modes for QD selected by TSH. We follow a hybrid approach which is based on the application of time-dependent density functional theory (TD-DFT) excited-state potential energy surfaces (PESs) and multiconfigurational second-order perturbation theory (CASPT2) spin–orbit couplings (SOCs). Our method delivers accurate singlet–triplet–quintet intersystem crossing (ISC) dynamics, as assessed by comparison to our recent high-level ab initio simulations and related time-resolved experimental data. Furthermore, we investigate the capability of our simulations to identify the location of ISCs. Finally, we assess the approximation of constant SOCs (calculated at the Franck–Condon geometry), whose validity has central importance for the combination of TD-DFT PESs and CASPT2 SOCs. This efficient methodology will have a key role in simulating LS → HS dynamics for more complicated cases, involving higher density of states and varying electronic character, as well as the analysis of ultrafast experiments.

Formation of electronic coherences in conical intersection-mediated dynamics

We consider the formation of vibrationally-induced transient electronic coherences driven by conical intersection (CI)-mediated population transfer between two electronic states. By invoking fundamental symmetry arguments, we identify several important factors which modulate the magnitude of these electronic coherences. We consider the sub-cases where the two electronic states have either the same or different Abelian point group symmetry at the Franck–Condon geometry. For the different symmetry case, due to the inherent symmetry of the molecular Hamiltonian, significant electronic coherences are unlikely to form. In contrast, for electronic states of the same symmetry, large magnitude electronic coherences can form. However, the magnitude of these coherences is highly dependent on the topography of the CI. These results offer a guide to experimental studies of electronic coherences which may (or may not) be induced by nuclear motion in the vicinity of a CI, as well as to ab initio simulations which are employed to simulate them.

Insights into the Ultrafast Dynamics of CH2 OO and CH3 CHOO Following Excitation to the Bright 1 ππ* State: The Role of Singlet and Triplet States.

Criegee intermediates make up a class of molecules that are of significant atmospheric importance. Understanding their electronically excited states guides experimental detection and provides insight into whether solar photolysis plays a role in their removal from the troposphere. The latter is particularly important for large and functionalized Criegee intermediates. In this study, the excited state chemistry of two small Criegee intermediates, formaldehyde oxide (CH2 OO) and acetaldehyde oxide (CH3 CHOO), was modeled to compare their specific dynamics and mechanisms following excitation to the bright ππ* state and to assess the involvement of triplet states to the excited state decay process. Following excitation to the bright ππ* state, the photoexcited population exclusively evolves to form oxygen plus aldehyde products without the involvement of triplet states. This occurs despite the presence of a more thermodynamically stable triplet path and several singlet/triplet energy crossings at the Franck-Condon geometry and contrasts with the photodynamics of related systems such as acetaldehyde and acetone. This work sets the foundations to study Criegee intermediates with greater molecular complexity, wherein a bathochromic shift in the electron absorption profiles may ensure greater removal via solar photolysis.

Signatures of Conical Intersection Dynamics in the Time-Resolved Photoelectron Spectrum of Furan: Theoretical Modeling with an Ensemble Density Functional Theory Method.

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck–Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics.

Dynamics and spectroscopy of molecular ensembles in a lossy microcavity.

The radiative and nonradiative relaxation dynamics of an ensemble of molecules in a microcavity are investigated with emphasis on the impact of the cavity lifetime on reactive and spectroscopic properties. Extending a previous study [I. S. Ulusoy et al., J. Phys. Chem. A 123, 8832-8844 (2019)], it is shown that the dynamics of the ensemble and of single molecules are influenced by the presence of a cavity resonance as long as the polariton splitting can be resolved spectroscopically, which critically depends on the lifetime of the system. Our simulations illustrate how the branching between nonradiative intersystem crossing and radiative decay through the cavity can be tuned by selecting specific cavity photon energies resonant at specific molecular geometries. In the case of cavity-photon energies that are not resonant at the Franck-Condon geometry of the molecules, it is demonstrated numerically and analytically that collective effects are limited to a handful of molecules in the ensemble.

A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran.

We present a model for the lowest two potential energy surfaces (PESs) that describe the photoinduced ring-opening reaction of benzopyran taken as a model compound to study the photochromic ring-opening reaction of indolinobenzospiropyran and its evolution toward its open-chain analog. The PESs are expressed in terms of three effective rectilinear coordinates. One corresponds to the direction between the equilibrium geometry in the electronic ground state, referred to as the Franck-Condon geometry, and the minimum of conical intersection (CI), while the other two span the two-dimensional branching space at the CI. The model correctly reproduces the topography of the PESs. The ab initio calculations are performed with the extended multiconfiguration quasidegenerate perturbation theory at second order method. We demonstrate that accounting for electron dynamic correlation drastically changes the global energy landscape since some zwitterionic states become strongly stabilized. Quantum dynamics calculations using this PES model produce an absorption spectrum that matches the experimental one to a good accuracy.

Femtosecond dynamics of metal-centered and ligand-to-metal charge-transfer (t2g-based) electronic excited states in various solvents: A comprehensive study of IrBr6 2.

The photophysical properties of intraconfigurational metal-centered (MC) and ligand-to-metal charge transfer (LMCT) states were studied in a prototype low spin heavy d5 transition metal complex, IrBr6 2-. The femtosecond-to-picosecond dynamics of this complex was investigated in solutions of drastically different polarity (acetonitrile, chloroform, and water) by means of ultrafast broadband transient absorption spectroscopy. We observed that the system, when excited into the third excited [second LMCT, 2Uu'(T1u)] state, undergoes distortion from the Franck-Condon geometry along the t2g vibrational mode as a result of the Jahn-Teller effect, followed by rapid internal conversion to populate (90 fs) the second excited [first LMCT, 2Ug'(T1g)] state. Vibrational decoherence and vibrational relaxation (∼400 fs) in 2Ug'(T1g) precede the decay of this state via internal conversion (time constants, 2.8 and 3 ps in CH3CN and CHCl3 and 0.76 ps in water), which can also be viewed as back electron transfer and which leads into the intraconfigurational MC 2Ug'(T2g) state. This is the lowest-excited state, from which the system returns to the ground state. This MC state is metastable in both CH3CN and CHCl3 (lifetime, ∼360 ps), but is quenched via OH-mediated energy transfer in aqueous environments, with the lifetime shortening up to 21 ps in aqueous solutions. The cascade relaxation mechanism is the same upon excitation into the second excited state. Excitation of IrBr6 2- in chloroform into higher 2Uu'(T2u), 2Eu″(T2u), and 2Eg'(T1g) states is observed to populate the third excited 2Uu'(T1u) state within 100 fs. These experiments allow us to resolve the ultrafast relaxation coordinate and emphasize that the excited-state Jahn-Teller effect is a driving force in the ultrafast dynamics, even for heavy transition metal complexes with very significant spin-orbit interactions.

Vibrational Sampling and Solvent Effects on the Electronic Structure of the Absorption Spectrum of 2-Nitronaphthalene.

The influence of vibrational motion on electronic excited state properties is investigated for the organic chromophore 2-nitronaphtalene in methanol. Specifically, the performance of two vibrational sampling techniques - Wigner sampling and sampling from an ab initio molecular dynamics trajectory- is assessed, in combination with implicit and explicit solvent models. The effects of the different sampling/solvent combinations on the energy and electronic character of the absorption bands are analyzed in terms of charge transfer and exciton size, computed from the electronic transition density. The absorption spectra obtained using sampling techniques and its underlying properties are compared to those of the electronic excited states calculated at the Franck-Condon equilibrium geometry. It is found that the absorption bands of the vibrational ensembles are red-shifted compared to the Franck-Condon bright states, and this red-shift scales with the displacement from the equilibrium geometry. Such displacements are found larger and better described when using ensembles from the harmonic Wigner distribution than snapshots from the molecular dynamics trajectory. Particularly relevant is the torsional motion of the nitro group that quenches the charge transfer character of some of the absorption bands. This motion, however, is better described in the molecular dynamics trajectory. Thus, none of the vibrational sampling approaches can satisfactorily capture all important aspects of the nuclear motion. The inclusion of solvent also red-shifts the absorption bands with respect to the gas phase. This red-shift scales with the charge-transfer character of the bands and is found larger for the implicit than for the explicit solvent model. The advantages and drawbacks of the different sampling and solvent models are discussed to guide future research on the calculation of UV-vis spectra of nitroaromatic compounds.

How Methylation Modifies the Photophysics of the Native All- trans-Retinal Protonated Schiff Base: A CASPT2/MD Study in Gas Phase and in Methanol.

A comparison between the free-energy surfaces of the all- trans-retinal protonated Schiff base (RPSB) and its 10-methylated derivative in gas phase and methanol solution is performed at CASSCF//CASSCF and CASPT2//CASSCF levels. Solvent effects were included using the average solvent electrostatic potential from molecular dynamics method. This is a QM/MM (quantum mechanics/molecular mechanics) method that makes use of the mean field approximation. It is found that the methyl group bonded to C10 produces noticeable changes in the solution free-energy profile of the S1 excited state, mainly in the relative stability of the minimum energy conical intersections (MECIs) with respect to the Franck-Condon (FC) point. The conical intersections yielding the 9- cis and 11- cis isomers are stabilized while that yielding the 13- cis isomer is destabilized; in fact, it becomes inaccessible by excitation to S1. Furthermore, the planar S1 minimum is not present in the methylated compound. The solvent notably stabilizes the S2 excited state at the FC geometry. Therefore, if the S2 state has an effect on the photoisomerization dynamics, it must be because it permits the RPSB population to branch around the FC point. All these changes combine to speed up the photoisomerization in the 10-methylated compound with respect to the native compound.

Ultrafast Wiggling and Jiggling: Ir2(1,8-diisocyanomenthane)42.

Binuclear complexes of d8 metals (PtII, IrI, RhI,) exhibit diverse photonic behavior, including dual emission from relatively long-lived singlet and triplet excited states, as well as photochemical energy, electron, and atom transfer. Time-resolved optical spectroscopic and X-ray studies have revealed the behavior of the dimetallic core, confirming that M-M bonding is strengthened upon dσ* → pσ excitation. We report the bridging ligand dynamics of Ir2(1,8-diisocyanomenthane)42+ (Ir(dimen)), investigated by fs-ns time-resolved IR spectroscopy (TRIR) in the region of C≡N stretching vibrations, ν(C≡N), 2000-2300 cm-1. The ν(C≡N) IR band of the singlet and triplet dσ*pσ excited states is shifted by -22 and -16 cm-1 relative to the ground state due to delocalization of the pσ LUMO over the bridging ligands. Ultrafast relaxation dynamics of the 1dσ*pσ state depend on the initially excited Franck-Condon molecular geometry, whereby the same relaxed singlet excited state is populated by two different pathways depending on the starting point at the excited-state potential energy surface. Exciting the long/eclipsed isomer triggers two-stage structural relaxation: 0.5 ps large-scale Ir-Ir contraction and 5 ps Ir-Ir contraction/intramolecular rotation. Exciting the short/twisted isomer induces a ∼5 ps bond shortening combined with vibrational cooling. Intersystem crossing (70 ps) follows, populating a 3dσ*pσ state that lives for hundreds of nanoseconds. During the first 2 ps, the ν(C≡N) IR bandwidth oscillates with the frequency of the ν(Ir-Ir) wave packet, ca. 80 cm-1, indicating that the dephasing time of the high-frequency (16 fs)-1 C≡N stretch responds to much slower (∼400 fs)-1 Ir-Ir coherent oscillations. We conclude that the bonding and dynamics of bridging di-isocyanide ligands are coupled to the dynamics of the metal-metal unit and that the coherent Ir-Ir motion induced by ultrafast excitation drives vibrational dephasing processes over the entire binuclear cation.

Distortion dependent intersystem crossing: A femtosecond time-resolved photoelectron spectroscopy study of benzene, toluene, and p-xylene.

The competition between ultrafast intersystem crossing and internal conversion in benzene, toluene, and p-xylene is investigated with time-resolved photoelectron spectroscopy and quantum chemical calculations. By exciting to S2 out-of-plane symmetry breaking, distortions are activated at early times whereupon spin-forbidden intersystem crossing becomes (partly) allowed. Natural bond orbital analysis suggests that the pinnacle carbon atoms distorting from the aromatic plane change hybridization between the planar Franck-Condon geometry and the deformed (boat-shaped) S2 equilibrium geometry. The effect is observed to increase in the presence of methyl-groups on the pinnacle carbon-atoms, where largest extents of σ and π orbital-mixing are observed. This is fully consistent with the time-resolved spectroscopy data: Toluene and p-xylene show evidence for ultrafast triplet formation competing with internal conversion, while benzene appears to only decay via internal conversion within the singlet manifold. For toluene and p-xylene, internal conversion to S1 and intersystem crossing to T3 occur within the time-resolution of our instrument. The receiver triplet state (T3) is found to undergo internal conversion in the triplet manifold within ≈100–150 fs (toluene) or ≈180–200 fs (p-xylene) as demonstrated by matching rise and decay components of upper and lower triplet states. Overall, the effect of methylation is found to both increase the intersystem crossing probability and direct the molecular axis of the excited state dynamics.

Potential‐Energy Surfaces, the Born–Oppenheimer Approximations, and the Franck–Condon Principle: Back to the Roots

The concept of a potential-energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as "adiabatic", "Born-Oppenheimer", or "Born-Oppenheimer adiabatic" approximation. Concerning the closely relevant and important Franck-Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as "Franck-Condon (excited) state", or a vertical transition to the "Franck-Condon point" with the "Franck-Condon geometry" that relaxes to the excited-state equilibrium geometry. The Born-Oppenheimer approximation and the "classical" model of the Franck-Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts.

Mechanism of Fluorescence Switching in One ESIPT-Based Al(3+) Probe.

A recently synthesized Schiff base used as a probe for aluminum cations was studied with ab initio models. The primary reason for the lack of fluorescence in aprotic solvents was found to be the presence of an efficient conical intersection (CI) between the ground-states and the first singlet excited-states close to the Franck-Condon geometry. The excited-state pathway leading to this CI is barrierless but implies large amplitude motions, explaining why the fluorescence was observed in frozen acetonitrile matrix. Our calculations suggest that constraining the molecule by impending the rotation around the imino bond enables excited-state intramolecular proton transfer. A similar stiffening mechanism is responsible for the strong fluorescence turn-on after formation of complexes between Al(3+) cations and dehydrogenated Schiff base. Finally, the analysis of the possible fluorescence mechanisms in water indicates that the anion of 1 is the likely fluorescence source. Overall, this work allows one to disentangle the various origins of fluorescence switching in a probe.