Optimizing conical intersections without derivative coupling vectors: application to multistate multireference second-order perturbation theory (MS-CASPT2)

Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.

Using Adiabatic Energy Splitting To Compute Dexter Energy Transfer Couplings

Dexter energy transfer and transport (DET) are of broad interest in energy science, and DET rates depend on electronic couplings between donor and acceptor species. DET couplings are challenging to compute since they originate from both one- and two-particle interactions, and the strength of this interaction drops approximately exponentially with donor-acceptor distances. Using adiabatic energy splitting to compute DET couplings has advantages because adiabatic states can be calculated directly using conventional quantum chemical methods. We describe a minimum energy splitting method to compute the DET coupling by altering molecular geometries to drive the systems into a T1/T2 energy quasi-degenerate-activated DA complex. We explore the accuracy of various quantum chemical approaches to calculate the Dexter couplings.

XMECP: Reaching State-of-the-Art MECP Optimization in Multiscale Complex Systems

The Python-based program, XMECP, is developed for realizing robust, efficient, and state-of-the-art minimum energy crossing point (MECP) optimization in multiscale complex systems. This article introduces the basic capabilities of the XMECP program by theoretically investigating the MECP mechanism of several example systems including (1) the photosensitization mechanism of benzophenone, (2) photoinduced proton-coupled electron transfer in the cytosine-guanine base pair in DNA, (3) the spin-flip process in oxygen activation catalyzed by an iron-containing 2-oxoglutarate-dependent oxygenase (Fe/2OGX), and (4) the photochemical pathway of flavoprotein adjusted by the intensity of an external electric field. MECPs related to multistate reaction and multistate reactivity in large-scale complex biochemical systems can be well-treated by workflows suggested by the XMECP program. The branching plane updating the MECP optimization algorithm is strongly recommended as it provides derivative coupling vector (DCV) with explicit calculation and can equivalently evaluate contributions from non-QM residues to DCV, which can be nonadiabatic coupling or spin-orbit coupling in different cases. In the discussed QM/MM examples, we also found that the influence on the QM region by DCV can occur through noncovalent interactions and decay with distance. In the example of DNA base pairs, the nonadiabatic coupling occurs across the π-π stacking structure formed in the double-helix system. In contrast to general intuition, in the example of Fe/2OGX, the central ferrous and oxygen part contribute little to the spin-orbit coupling; however, a nearby arginine residue, which is treated by molecular mechanics in the QM/MM method, contributes significantly via two hydrogen bonds formed with α-ketoglutarate (α-KG). This indicates that the arginine residue plays a significant role in oxygen activation, driving the initial triplet state toward the productive quintet state, which is more than the previous knowledge that the arginine residue can bind α-KG at the reaction site by hydrogen bonds.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Unexpected longer T1 lifetime of 6-sulfur guanine than 6-selenium guanine: the solvent effect of hydrogen bonds to brake the triplet decay

The decay of the T1 state to the ground state is an essential property of photosensitizers because it decides the lifetime of excited states and, thus, the time window for sensitization. The sulfur/selenium substitution of carbonyl groups can red-shift absorption spectra and enhance the triplet yield because of the large spin-orbit coupling, modifying nucleobases to potential photosensitizers for various applications. However, replacing sulfur with selenium will also cause a much shorter T1 lifetime. Experimental studies found that the triplet decay rate of 6-seleno guanine (6SeGua) is 835 times faster than that of 6-thio guanine (6tGua) in aqueous solution. In this work, we reveal the mechanism of the T1 decay difference between 6SeGua and 6tGua by computing the activation energy and spin-orbit coupling for rate calculation. The solvent effect of water is treated with explicit microsolvation and implicit solvent models. We find that the hydrogen bond between the sulfur atom of 6tGua and the water molecule can brake the triplet decay, which is weaker in 6SeGua. This difference is crucial to explain the relatively long T1 lifetime of 6tGua in an aqueous solution. This insight emphasizes the role of solvents in modulating the excited state dynamics and the efficiency of photosensitizers, particularly in aqueous environments.

The Role of Aqueous Solvation on the Intersystem Crossing of Nitrophenols

The photochemistry of nitrophenols is a source of smog as nitrous acid is formed from their photolysis. Nevertheless, computational studies of the photochemistry of these widespread toxic molecules are scarce. In this work, the initial photodeactivation of ortho-nitrophenol and para-nitrophenol is modeled, both in gas phase and in aqueous solution to simulate atmospheric and aerosol environments. A large number of excited states, six for ortho-nitrophenol and 11 for para-nitrophenol, have been included and were all populated during the decay. Moreover, periodic time-dependent density functional theory (TDDFT) is used for both the explicitly included solvent and the solute. A comparison to periodic QM/MM (TDDFT/MM), with electrostatic embedding, is made, showing notable differences between the decays of solvated nitrophenols simulated with QM/MM and full (TD)DFT. A reduced intersystem crossing in aqueous solution could be observed thanks to the surface hopping approach using explicit, periodic TDDFT solvation including spin-orbit couplings.

Photochemical formation of the elusive Dewar isomers of aromatic systems: why are substituted azaborines different?

Photochemical reactions enabling efficient transformation of aromatic systems into energetic but stable non-aromatic isomers have a long history in organic chemistry. One recently discovered reaction in this realm is that where derivatives of 1,2-azaborine, a compound isoelectronic with benzene in which two adjacent C atoms are replaced by B and N atoms, form the non-hexagon Dewar isomer. Here, we report quantum-chemical calculations that explain both why 1,2-azaborine is intrinsically more reactive toward Dewar formation than benzene, and how suitable substitutions at the B and N atoms are able to increase the corresponding quantum yield. We find that Dewar formation from 1,2-azaborine is favored by a pronounced driving force that benzene lacks, and that a large improvement in quantum yield arises when the reaction of substituted 1,2-azaborines proceeds without involvement of an intermediary ground-state species. Overall, we report new insights into making photochemical use of the Dewar isomers of aromatic compounds.

Excited-state antiaromaticity relief drives facile photoprotonation of carbons in aminobiphenyls

A combined computational and experimental study reveals that ortho-, meta- and para-aminobiphenyl isomers undergo distinctly different photochemical reactions involving proton transfer. Deuterium exchange experiments show that the ortho-isomer undergoes a facile photoprotonation at a carbon atom via excited-state intramolecular proton transfer (ESIPT). The meta-isomer undergoes water-assisted excited-state proton transfer (ESPT) and a photoredox reaction via proton-coupled electron transfer (PCET). The para-isomer undergoes a water-assisted ESPT reaction. All three reactions take place in the singlet excited-state, except for the photoredox process of the meta-isomer, which involves a triplet excited-state. Computations illustrate the important role of excited-state antiaromaticity relief in these photoreactions.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Topology of Conical Intersection Seams and the Geometric Phase

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

The tautomer-specific excited state dynamics of 2,6-diaminopurine using resonance-enhanced multiphoton ionization and quantum chemical calculations

2,6-Diaminopurine (2,6-dAP) is an alternative nucleobase that potentially played a role in prebiotic chemistry. We studied its excited state dynamics in the gas phase by REMPI, IR-UV hole burning, and ps pump-probe spectroscopy and performed quantum chemical calculations at the SCS-ADC(2) level of theory to interpret the experimental results. We found the 9H tautomer to have a small barrier to ultrafast relaxation via puckering of its 6-membered ring. The 7H tautomer has a larger barrier to reach a conical intersection and also has a sizable triplet yield. These results are discussed relative to other purines, for which 9H tautomerization appears to be more photostable than 7H and homosubstituted purines appear to be less photostable than heterosubstituted or singly substituted purines.

Photo-oxidation of methanol in complexes with pyrido[2,3-b]pyrazine: a nonadiabatic molecular dynamics study

Excited-state Proton-Coupled Electron Transfer (PCET) constitutes a key step in the photo-oxidation of small, electron-rich systems possessing acidic hydrogen atoms, such as water or alcohols, which can play a vital role in green hydrogen production. In this contribution, we employ ab initio quantum-chemical methods and on-the-fly nonadiabatic molecular dynamics simulations to study the mechanism and the photodynamics of PCET in 1 : 1 pyrido[2,3-b]pyrazine complexes with methanol. We find the process to be ultrafast and efficient when the intramolecular hydrogen bond is formed with one of the β-positioned nitrogen atoms. The complex exhibiting a hydrogen bond with an isolated nitrogen site, on the contrary, shows much lower reactivity. We explain this effect with the stabilization of the reactive ππ* charge-transfer electronic state in the former case.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

The Lack of Triplet Fusion for an Intramolecular Singlet Fission Chromophore: The Expected, the Unexpected, and a Reconciliation

Singlet fission (SF) has the potential to play a key role in photovoltaics since it generates a larger number of longer-lived triplet excitons after photoabsorption. Intramolecular SF (iSF) is of special interest since it enables tuning of SF efficiency by adjusting interchromophore configuration through covalent interaction. However, as elaborated in the present work, iSF chromophores are doomed to dissatisfy one general thermodynamic criterion for all SF chromophores, intramolecular or not: E(T2) ≥ 2E(T1), and therefore, the fusion of two triplet excitons to one triplet exciton is thermodynamically favorable. In our nonadiabatic quantum dynamics simulation for a model iSF chromophore, this expected fusion does not occur, because of the inefficient intersystem crossing hidden under the cover of internal conversion of the triplet fusion. A reconciliation is achieved between the dissatisfaction of E(T2) ≥ 2E(T1) and the large tetraradical character for general iSF chromophores.

Origin of Vibronic Coherences During Carrier Cooling in Colloidal Quantum Dots

Recent two-dimensional electronic spectroscopy experiments [Tilluck et al. J. Phys. Chem. Lett. 2021, 12 (39), 9677-9683] indicate the creation of coherent vibronic wavepackets in the first femtoseconds of hot carrier cooling in hexadecylamine-passivated CdSe quantum dots. Here we present a quantum chemical study of the origin of these coherences in a CdSe nanocrystal. We find that coherent wavepacket motions along vibrational coordinates with alkylamine character promote nonradiative relaxation through conical intersections between the exciton states of the inorganic core. Electronic excitations in the core are found to pass energy to the vibrations of the ligands via two distinct mechanisms: excitation of core phonon modes that are coupled to the ligand vibrations and direct excitation of ligand vibrations by delocalization of the exciton onto the ligands, both of which naturally arise within a photochemical framework based on many-electron potential energy surfaces. If these findings are demonstrated to be general, vibronic coherences may be leveraged to control photophysical outcomes in colloidal quantum dots.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Galván I, Rivalta I, Aquilante F, Garavelli M, Lindh R, Segarra-Martí J. Characterizing Conical Intersections in DNA/RNA Nucleobases with Multiconfigurational Wave Functions of Varying Active Space Size

We characterize the photochemically relevant conical intersections between the lowest-lying accessible electronic excited states of the different DNA/RNA nucleobases using Cholesky decomposition-based complete active space self-consistent field (CASSCF) algorithms. We benchmark two different basis set contractions and several active spaces for each nucleobase and conical intersection type, measuring for the first time how active space size affects conical intersection topographies in these systems and the potential implications these may have toward their description of photoinduced phenomena. Our results show that conical intersection topographies are highly sensitive to the electron correlation included in the model: by changing the amount (and type) of correlated orbitals, conical intersection topographies vastly change, and the changes observed do not follow any converging pattern toward the topographies obtained with the largest and most correlated active spaces. Comparison across systems shows analogous topographies for almost all intersections mediating population transfer to the dark 1nO/Nπ* states, while no similarities are observed for the "ethylene-like" conical intersection ascribed to mediate the ultrafast decay component to the ground state in all DNA/RNA nucleobases. Basis set size seems to have a minor effect, appearing to be relevant only for purine-based derivatives. We rule out structural changes as a key factor in classifying the different conical intersections, which display almost identical geometries across active space and basis set change, and we highlight instead the importance of correctly describing the electronic states involved at these crossing points. Our work shows that careful active space selection is essential to accurately describe conical intersection topographies and therefore to adequately account for their active role in molecular photochemistry.

Temperature effects on the internal conversion of excited adenine and adenosine

This work aims to elucidate the dependence of the excited-state lifetime of adenine and adenosine on temperature. So far, it has been experimentally shown that while adenine's lifetime is unaffected by temperature, adenosine's lifetime strongly depends on it. However, the non-Arrhenius temperature dependence has posed a challenge in explaining this phenomenon. We used surface hopping to simulate the dynamics of adenine and adenosine in the gas phase at 0 and 400 K. The temperature effects were observed under the initial conditions via Wigner sampling with thermal corrections. Our results confirm that adenine's excited-state lifetime does not depend on temperature, while adenosine's lifetime does. Adenosine's dependency is due to intramolecular vibrational energy transfer from adenine to the ribose group. At 0 K, this transfer reduced the mean kinetic energy of adenine's moiety so much that internal conversion is inhibited, and the lifetime elongated by a factor of 2.3 compared to that at 400 K. The modeling also definitively ruled out the influence of viscosity, which was proposed as an alternative explanation previously.

Role of Ultrafast Internal Conversion and Intersystem Crossing in the Nonadiabatic Relaxation Dynamics of ortho-Nitrobenzaldehyde

ortho-Nitrobenzaldehyde (oNBA) is a well-known photoactivated acid and a prototypical photolabile nitro-aromatic compound. Despite extensive investigations, the ultrafast relaxation dynamics of oNBA is still not properly understood, especially concerning the role of the triplet states. In this work, we provide an in-depth picture of this dynamics by combining single- and multireference electronic structure methods with potential energy surface exploration and nonadiabatic dynamics simulations using the Surface Hopping including ARbitary Couplings (SHARC) approach. Our results reveal that the initial decay from the bright ππ* state to the S₁ minimum is barrierless. It involves three changes in electronic structure from ππ* (ring) to nπ* (nitro group), to nπ* (aldehyde group), and then to another nπ* (nitro group). The decay of the ππ* takes 60-80 fs and can be tracked with time-resolved luminescence spectroscopy, where we predict for the first time a short-lived coherence of the luminescence energy with a 25 fs period. Intersystem crossing can occur already during the S₄ → S₁ deactivation cascade but also from S₁, with a time constant of about 2.4 ps and such that first a triplet ππ* state localized on the nitro group is populated. The triplet population first evolves into an nπ* and then quickly undergoes hydrogen transfer to form a biradical intermediate, from where the ketene is eventually produced. The majority of the excited population decays from S₁ through two conical intersections of equal utilization, a previously unreported one involving a scissoring motion of the nitro group that leads back to the oNBA ground state and the one involving hydrogen transfer that leads to the ketene intermediate.

Smooth Things Come in Threes: A Diabatic Surrogate Model for Conical Intersection Optimization

The optimization of conical intersection structures is complicated by the nondifferentiability of the adiabatic potential energy surfaces. In this work, we build a pseudodiabatic surrogate model, based on Gaussian process regression, formed by three smooth and differentiable surfaces that can adequately reproduce the adiabatic surfaces. Using this model with the restricted variance optimization method results in a notable decrease of the overall computational effort required to obtain minimum energy crossing points.

Finding Excited-State Minimum Energy Crossing Points on a Budget: Non-Self-Consistent Tight-Binding Methods

The automated exploration and identification of minimum energy conical intersections (MECIs) is a valuable computational strategy for the study of photochemical processes. Due to the immense computational effort involved in calculating non-adiabatic derivative coupling vectors, simplifications have been introduced focusing instead on minimum energy crossing points (MECPs), where promising attempts were made with semiempirical quantum mechanical methods. A simplified treatment for describing crossing points between almost arbitrary diabatic states based on a non-self-consistent extended tight-binding method, GFN0-xTB, is presented. Involving only a single diagonalization of the Hamiltonian, the method can provide energies and gradients for multiple electronic states, which can be used in a derivative coupling-vector-free scheme to calculate MECPs. By comparison with high-lying MECIs of benchmark systems, it is demonstrated that the identified geometries are good starting points for further MECI refinement with ab initio methods.

Triplet Separation after the Fastest Intramolecular Singlet Fission in the Smallest Chromophore

Singlet fission is of key importance in harvesting solar energy in solar cells, as it generates a pair of triplet excitons on the incidence of a photon. This phenomenon is not yet widely employed in the organic photovoltaics industry mostly because of the rarity of singlet fission chromophores. Pyrazino[2,3-g]quinoxaline-1,4,6,9-tetraoxide was recently designed as the smallest intramolecular singlet fission chromophore, and it undergoes the fastest singlet fission with a 16 fs time scale. The subsequent separation of the generated triplet-pair is of likewise importance as their efficient generation. Through quantum chemistry calculations and quantum dynamics simulations, we show that the triplet-pair separates to residing on two chromophores with an ∼80% probability on each collision between a chromophore with the triplet-pair and a ground state chromophore. Avoided crossing, instead of conical intersection, is involved in the efficient exciton separation.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

Analytical derivative couplings within the framework of time-dependent density functional theory coupled with conductor-like polarizable continuum model: Formalism, implementation, and applications

The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost.

Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems

Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.

Photoisomerization of phytochrome chromophore models: an XMS-CASPT2 study

Phytochromes are a superfamily of photoreceptors that harbor linear tetrapyrroles as chromophores. Upon light illumination, the linear tetrapyrrole chromophore undergoes a double bond isomerization which starts a photocycle. In this work, we studied the photoisomerization of chromophore models designed based on the C- and D-rings of the phycocyanobilin (PCB) chromophore. In total, five different models with varying substitutions were investigated. Firstly, the vertical excitation energies were benchmarked using different computational methods to establish the relative order of the excited states. Based on these calculations, we computed the photoisomerization profiles using the extended multi-state (XMS) version of the CASPT2 method. The profiles were obtained for both the clockwise and counterclockwise rotations of the C₁₅C₁₆ bond in the Z and E isomers using a linear interpolation of internal coordinates between the Franck-Condon and MECI geometries. In the minimal chromophore model that lacks the substitutions at the pyrrole rings, the isomerization involves both C₁₄-C₁₅ and C₁₅C₁₆ bonds of the methine bridge between the C- and D-rings, resembling the hula-twist motion. The MECIs are characterized by a partial charge transfer between the two pyrrole rings pointing towards a twisted intramolecular charge transfer. Systematic introduction of substituents leads to an increase in the steric repulsion between the two pyrrole rings causing a pretwist of the dihedral around the C₁₅C₁₆ bond, which creates a preference for the counterclockwise isomerization. An introduction of the carbonyl group at the D-ring increases the extent of charge transfer which changes the isomerization mechanism from hula-twist to one-bond flip.

Nonadiabatic Dynamics of 1,3-Cyclohexadiene by Curvature-Driven Coherent Switching with Decay of Mixing

The photoinduced ring-opening reaction of 1,3-cyclohexadiene to produce 1,3,5-hexatriene is a classic electrocyclic reaction and is also a prototype for many reactions of biological and synthetic importance. Here, we simulate the ultrafast nonadiabatic dynamics of the reaction in the manifold of the three lowest valence electronic states by using extended multistate complete-active-space second-order perturbation theory (XMS-CASPT2) combined with the curvature-driven coherent switching with decay of mixing (κCSDM) dynamical method. We obtain an excited-state lifetime of 79 fs, and a product quantum yield of 40% from the 500 trajectories initiated in the S₁ excited state. The obtained lifetime and quantum yield values are very close to previously reported experimental and computed values, showing the capability of performing a reasonable nonadiabatic ring-opening dynamics with the κCSDM method that does not require nonadiabatic coupling vectors, time derivatives, or diabatization. In addition, we study the ring-opening reaction by initiating the trajectories in the dark state S₂. We also optimize the S₀/S₁ and S₁/S₂ minimum-energy conical intersections (MECIs) by XMS-CASPT2; for S₁/S₂, we optimized both an inner and an outer local-minimum-energy conical intersections (LMECIs). We provide the potential energy profile along the ring-opening coordinate by joining selected critical points via linear synchronous transit paths. We find the inner S₁/S₂ LMECI to be more crucial than the outer one.

The involvement of triplet states in the isomerization of retinaloids

Rhodopsins form a family of photoreceptor proteins which utilize the retinal chromophore for light energy conversion. Upon light absorption the retinal chromophore undergoes a photoisomerization. This reaction involves a non-radiative relaxation through a conical intersection between the singlet excited state and the ground state. In this work we studied the possible involvement of triplet states in the photoisomerization of retinaloids using the extended multistate (XMS) version of CASPT2. To this end, truncated models of three retinaloids were considered: protonated Schiff base, deprotonated Schiff base and the aldehyde form. The optimized geometries of the reactant, the product and the conical intersection were connected by a linear interpolation of internal coordinates to describe the isomerization. The energetic position of the low-lying singlet and triplet states as well as their spin-orbit coupling matrix elements (SOCME) were calculated along the isomerization profile. The SOCME values peaked in vicinity of the conical intersection for all the retinaloids. Furthermore, the magnitude of SOCME is invariant to the number of double bonds in the model. The SOCME for the protonated Schiff base is negligible (1.5 cm^-1) which renders the involvement of the triplet state as improbable. However, the largest SOCME value of 30 cm^-1 was found for the aldehyde form, followed by 15 cm^-1 for the deprotonated Schiff base.

Towards the engineering of a photon-only two-stroke rotary molecular motor

The rational engineering of photoresponsive materials, e.g., light-driven molecular motors, is a challenging task. Here, we use structure-related design rules to prepare a prototype molecular rotary motor capable of completing an entire revolution using, exclusively, the sequential absorption of two photons; i.e., a photon-only two-stroke motor. The mechanism of rotation is then characterised using a combination of non-adiabatic dynamics simulations and transient absorption spectroscopy measurements. The results show that the rotor moiety rotates axially relative to the stator and produces, within a few picoseconds at ambient T, an intermediate with the same helicity as the starting structure. We discuss how such properties, that include a 0.25 quantum efficiency, can help overcome the operational limitations of the classical overcrowded alkene designs.

Synergistic interplay between photoisomerization and photoluminescence in a light-driven rotary molecular motor

Photoactuators and photoluminescent dyes utilize light to perform mechanical motion and undergo spontaneous radiation emission, respectively. Combining these two functionalities in a single molecule would benefit the construction of advanced molecular machines. Due to the possible detrimental interaction between the two light-dependent functional parts, the design of hybrid systems featuring both functions in parallel remains highly challenging. Here, we develop a light-driven rotary molecular motor with an efficient photoluminescent dye chemically attached to the motor, not compromising its motor function. This molecular system shows efficient rotary motion and bright photoluminescence, and these functions can be addressed by a proper choice of excitation wavelengths and solvents. The moderate interaction between the two parts generates synergistic effects, which are beneficial for lower-energy excitation and chirality transfer from the motor to the photoluminescent dye. Our results provide prospects towards photoactive multifunctional systems capable of carrying out molecular rotary motion and tracking its location in a complex environment.

Combining photofunctionalities in a single molecule is challenging due to inherent detrimental interactions. Here, the authors construct a molecular motor that exhibits photoinduced rotary motion together with bright photoluminescence.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Rationalizing the Unexpected Sensitivity in Excited State Lifetimes of Adenine to Tautomerization by Nonadiabatic Molecular Dynamics

The remarkable photostability of canonical nucleobases makes them ideal building blocks for DNA and RNA. Even minor structural changes are expected to lead to drastic alteration of their subpicosecond excited state lifetimes. However, it is interesting to note that while the 9H- and 7H-amino tautomers of adenine possess drastically different lifetimes, 9H- and 7H-keto guanine possess similar excited state lifetimes. With an aim to explain this unexpected difference in sensitivity of lifetimes to tautomerization, we have investigated the excited state relaxation mechanism of UV-excited adenine and guanine tautomers using surface hopping based nonadiabatic molecular dynamics. We find that internal conversion in both guanine tautomers is almost barrierless while both adenine tautomers encounter significant barriers before they can deactivate. Moreover, the major deactivation channel (C2-puckering) in 9H-amino adenine is overall more efficient than the one (C6-puckering) in the 7H-amino form. We trace this difference to the frequent rotation of the amino group which disrupts its conjugation with the heterocyclic ring thereby reducing the strength of nonadiabatic coupling and, hence, delaying internal conversion.

Rapid Intersystem Crossing Induced by Ultrafast Excited-State Intramolecular Proton Transfer in 3-Mercaptopyran-4-one

Investigation into the photoinduced processes of 3-mercaptopyran-4-one is carried out using trajectory-based surface hopping simulations. Excitation into the near-degenerate higher singlet excited states reveals rapid internal conversion (IC) into S₁ on a sub-50 fs timescale. Excited-state intramolecular proton transfer (ESIPT) also takes place simultaneously with IC. We observe that following tautomerization, the molecule has multiple relaxation pathways. A channel exists for it to nonradiatively decay into the tautomer ground-state or undergo rapid intersystem crossing (ISC) into the close-lying higher triplet state, which ultimately decays into T₁. The simulations show that ISC is significantly enhanced after ESIPT, which is studied by tracking the changes in energy gaps and associated spin-orbit coupling elements.

Photochemistry of 2-thiooxazole: a plausible prebiotic precursor to RNA nucleotides

Potentially prebiotic chemical reactions leading to RNA nucleotides involve periods of UV irradiation, which are necessary to promote selectivity and destroy biologially irrelevant side products. Nevertheless, UV light has only been applied to promote specific stages of prebiotic reactions and its effect on complete prebiotic reaction sequences has not been extensively studied. Here, we report on an experimental and computational investigation of the photostability of 2-thiooxazole (2-TO), a potential precursor of pyrimidine and 8-oxopurine nucleotides on early Earth. Our UV-irradiation experiments resulted in rapid decomposition of 2-TO into unidentified small molecule photoproducts. We further clarify the underlying photochemistry by means of accurate ab initio calculations and surface hopping molecular dynamics simulations. Overall, the computational results show efficient rupture of the aromatic ring upon the photoexcitation of 2-TO via breaking of the C-O bond. Consequently, the initial stage of the divergent prebiotic synthesis of pyrimidine and 8-oxopurine nucleotides would require periodic shielding from UV light either with sun screening chromophores or through a planetary scenario that would protect 2-TO until it is transformed into a more stable intermediate compound, e.g. oxazolidinone thione.

Ultrafast Intersystem Crossing Dynamics of 6-Selenoguanine in Water

Rationalizing the photochemistry of nucleobases where an oxygen is replaced by a heavier atom is essential for applications that exploit near-unity triplet quantum yields. Herein, we report on the ultrafast excited-state deactivation mechanism of 6-selenoguanine (6SeGua) in water by combining nonadiabatic trajectory surface-hopping dynamics with an electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) scheme. We find that the predominant relaxation mechanism after irradiation starts on the bright singlet S₂ state that converts internally to the dark S₁ state, from which the population is transferred to the triplet T₂ state via intersystem crossing and finally to the lowest T₁ state. This S₂ → S₁ → T₂ → T₁ deactivation pathway is similar to that observed for the lighter 6-thioguanine (6tGua) analogue, but counterintuitively, the T₁ lifetime of the heavier 6SeGua is shorter than that of 6tGua. This fact is explained by the smaller activation barrier to reach the T₁/S₀ crossing point and the larger spin-orbit couplings of 6SeGua compared to 6tGua. From the dynamical simulations, we also calculate transient absorption spectra (TAS), which provide two time constants (τ₁ = 131 fs and τ₂ = 191 fs) that are in excellent agreement with the experimentally reported value (τ_exp = 130 ± 50 fs) (Farrel et al. J. Am. Chem. Soc. 2018, 140, 11214). Intersystem crossing itself is calculated to occur with a time scale of 452 ± 38 fs, highlighting that the TAS is the result of a complex average of signals coming from different nonradiative processes and not intersystem crossing alone.

Photostability of the deprotonated forms of the UV filters homosalate and octyl salicylate: molecular dissociation versus electron detachment following UV excitation

While common molecular anions show a strong propensity to undergo electron detachment upon UV excitation, this process often occurs in competition with molecular ion dissociation. The factors that affect the balance between these two major possible decay pathways have not been well understood to date. Laser photodissociation spectroscopy of the deprotonated forms of the UV filter molecules, Homosalate (HS) and Octyl Salicylate (OS), i.e. [HS - H]^- and [OS - H]^-, was used to acquire gas-phase UV absorption spectra for [HS - H]^- and [OS - H]^-via photodepletion from 3.0-5.8 eV. No photofragmentation (i.e. dissociation of the ionic molecular framework) was observed for either [HS - H]^- and [OS - H]^- following photoexcitation, revealing that electron loss entirely dominates the electronic decay pathways for these systems. High-level quantum chemical calculations were used to map out the excited states associated with [HS - H]^- and [OS - H]^-, revealing that the minimum-energy crossing points (MECPs) between the S₁ and S₀ states are located in elevated regions of the potential energy surface, making internal conversion unlikely. These results are consistent with our experimental observation that electron detachment out-competes hot ground state molecular fragmentation. More generally, our results reveal that the competition between molecular dissociation and electron detachment following anion photoexcitation can be determined by the magnitude of the energy gap between the excitation energy and the MECPs, rather than being a simple function of whether the excitation energy lies above the anion's vertical detachment energy.

Role of the Hydrogen Bond on the Internal Conversion of Photoexcited Adenosine

Experiments and theory have revealed that hydrogen bonds modify the excited-state lifetimes of nucleosides compared to nucleobases. Nevertheless, how these bonds impact the internal conversion is still unsettled. This work simulates the non-adiabatic dynamics of adenosine conformers in the gas phase with and without hydrogen bonds between the sugar and adenine moieties. The isomer containing the hydrogen bond (syn) exhibits a significantly shorter excited-state lifetime than the isomer without it (anti). However, internal conversion through electron-driven proton transfer between sugar and adenine plays only a minor (although non-negligible) role in the photophysics of adenosine. Either with or without hydrogen bonds, photodeactivation preferentially occurs following the ring-puckering pathways. The role of the hydrogen bond is to avoid the sugar rotation relative to adenine, shortening the distance to the ring-puckering internal conversion.

Analytic First-Order Derivatives of (X)MS, XDW, and RMS Variants of the CASPT2 and RASPT2 Methods

Crossings between states involve complex electronic structures, making the accurate characterization of the crossing point difficult. In this study, the analytic derivatives of three complete active space second-order perturbation theory (CASPT2) variants as well as an extension of the restricted active space (RASPT2) are developed. These variants are applied to locating minimum energy conical intersections. Our results demonstrate that the three CASPT2 variants predict qualitatively similar results, but a recently developed variant, the rotated multistate CASPT2 (RMS-CASPT2), is least sensitive to the number of states considered in the calculation. We demonstrate that CASPT2 and the reference self-consistent field calculations predict qualitatively different energetics and bond lengths.

Pre-Dewar structure modulates protonated azaindole photodynamics

Recent experimental work revealed that the lifetime of the S₃ state of protonated 7-azaindole is about ten times longer than that of protonated 6-azaindole. We simulated the nonradiative decay pathways of these molecules using trajectory surface hopping dynamics after photoexcitation into S₃ to elucidate the reason for this difference. Both isomers mainly follow a common ππ* relaxation pathway involving multiple state crossings while coming down from S₃ to S₁ in the subpicosecond time scale. However, the simulations reveal that the excited-state topographies are such that while the 6-isomer can easily access the region of nonadiabatic transitions, the internal conversion of the 7-isomer is delayed by a pre-Dewar bond formation with a boat conformation.

Generalized Formulation of the Density Functional Tight Binding-Based Restricted Ensemble Kohn-Sham Method with Onsite Correction to Long-Range Correction

We present a generalized formulation for the combination of the density functional tight binding (DFTB) approach and the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method by considering onsite correction (OC) as well as the long-range corrected (LC) functional. The OC contribution provides more accurate energies and analytic gradients for individual microstates, while the multireference character of the SSR provides the correct description for conical intersections. We benchmark the LC-OC-DFTB/SSR method against various DFTB calculation methods for excitation energies and conical intersection structures with π/π* or n/π* characters. Furthermore, we perform excited-state molecular dynamics simulations with a molecular rotary motor with variations of LC-OC-DFTB/SSR approaches. We show that the OC contribution to the LC functional is crucial to obtain the correct geometry of conical intersections.

Photoinduced water-chromophore electron transfer causes formation of guanosine photodamage

UV-induced photolysis of aqueous guanine nucleosides produces 8-oxo-guanine and Fapy-guanine, which can induce various types of cellular malfunction. The mechanistic rationale underlying photodestructive processes of guanine nucleosides is still largely obscure. Here, we employ accurate quantum chemical calculations and demonstrate that an excited-state non-bonding interaction of guanosine and a water molecule facilitates the electron-driven proton transfer process from water to the chromophore fragment. This subsequently allows for the formation of a crucial intermediate, namely guanosine photohydrate. Further (photo)chemical reactions of this intermediate lead to the known products of guanine photodamage.

State-averaged CASSCF with polarizable continuum model for studying photoreactions in solvents: Energies, analytical nuclear gradients, and non-adiabatic couplings

This paper presents state-averaged complete active space self-consistent field in polarizable continuum model (PCM) for studies of photoreactions in solvents. The wavefunctions of the solute and the PCM surface charges of the solvent are optimized simultaneously such that the state-averaged free energy is variationally minimized. The method supports both fixed weights and dynamic weights where the weights are automatically adjusted based on the energy gaps. The corresponding analytical nuclear gradients and non-adiabatic couplings are also derived. Furthermore, we show how the new method can be entirely formulated in terms of seven basic operations, which allows the implementation to benefit from existing high-performance libraries on graphical processing units. Results demonstrating the accuracy and performance of the implementation are presented and discussed. We also apply the new method to the study of minimal conical intersection search and photoreaction energy pathways in solvents. Effects from the polarity of the solvents and different formulas of dynamic weights are compared and discussed.

The photodissociation of solvated cyclopropanone and its hydrate explored via non-adiabatic molecular dynamics using ΔSCF

The decay of cyclopropanone is a typical example of a photodecomposition process. Ethylene and carbon monoxide are formed following the excitation to the first singlet excited state through a symmetrical or asymmetrical pathway. The results obtained with non-adiabatic molecular dynamics (NAMD) using the delta self-consistent field (ΔSCF) method correspond well to previous experimental and multireference theoretical studies carried out in the gas phase. Moreover, this efficient methodology allows NAMD simulations of cyclopropanone in aqueous solution to be performed, which reveal analogue deactivation mechanisms, but a shorter lifetime and reduced photodissociation as compared to the gas-phase. The excited state dynamics of cyclopropanone hydrate, an enzyme inhibitor, in an aqueous environment are reported as well. Cyclopropanone hydrate strongly interacts with the surrounding solvent via the formation of hydrogen bonds. Excitation to the first singlet excited state shows an asymmetric pathway with cyclopropanone hydrate and propionic acid as the main photoproducts.

The lifetime and photodissociation of cyclopropanone are reduced in aqueous solution, while the excitation of solvated cyclopropanone hydrate yields a range of photoproducts.

Understanding the solid state luminescence and piezochromic properties in polymorphs of an anthracene derivative

Luminescent molecular crystals have gained significant research interest for optoelectronic applications. However, fully understanding their structural and electronic relationships in the condensed phase and under external stimuli remains a significant challenge. Here, piezochromism in the molecular crystal 9,10-bis((E)-2-(pyridin-4-yl)vinyl)anthracene (BP4VA) is studied using a combination of density functional theory (DFT) and time-dependent TD-DFT. We investigate the effects that molecular packing and geometry have on the electronic and phonon structure and the excited state properties in this archetypal system. We find that the luminescence properties are red-shifted with the transition from a herringbone to a sheet packing arrangement. An almost continuous red-shift in the band gap is found with the application of an external pressure through the enhancement of π-π and CH-π interactions, and is a mechanism in fine tuning an emissive response. The analysis of the phonon structure of the molecular crystal suggests restriction of motion in the herringbone packing arrangement, with motion restricted at higher pressure. This is supported by the Huang-Rhys factors which show a decrease in the reorganisation energy with the application of pressure. Ultimately, a balance between the decrease in reorganisation energies and the increase in exciton coupling will determine whether nonradiative decay is enhanced or decreased with the increase in pressure in these systems.