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

Role of conical intersection seam topography in the chemiexcitation of 1,2-dioxetanes

Chemiexcitation, the generation of electronic excited states by a thermal reaction initiated on the ground state, is an essential step in chemiluminescence, and it is mediated by the presence of a conical intersection that allows a nonadiabatic transition from ground state to excited state. Conical intersections classified as sloped favor chemiexcitation over ground state relaxation. The chemiexcitation yield of 1,2-dioxetanes is known to increase upon methylation. In this work we explore to which extent this trend can be attributed to changes in the conical intersection topography or accessibility. Since conical intersections are not isolated points, but continuous seams, we locate regions of the conical intersection seams that are close to the configuration space traversed by the molecules as they react on the ground state. We find that conical intersections are energetically and geometrically accessible from the reaction trajectory, and that topographies favorable to chemiexcitation are found in all three molecules studied. Nevertheless, the results suggest that dynamic effects are more important for explaining the different yields than the static features of the potential energy surfaces.

Photoisomerization of a 4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran analog dye: a combined photophysical and theoretical investigation

A combination of experimental and theoretical investigations of a photoisomerizable analog of 4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran (DCM) dye molecule is presented. We provide evidences that the 4 main isomers and conformers of DCM...

Towards developing novel and sustainable molecular light-to-heat converters

Light-to-heat conversion materials generate great interest due to their widespread applications, notable exemplars being solar energy harvesting and photoprotection. Another more recently identified potential application for such materials is in molecular heaters for agriculture, whose function is to protect crops from extreme cold weather and extend both the growing season and the geographic areas capable of supporting growth, all of which could help reduce food security challenges. To address this demand, a new series of phenolic-based barbituric absorbers of ultraviolet (UV) radiation has been designed and synthesised in a sustainable manner. The photophysics of these molecules has been studied in solution using femtosecond transient electronic and vibrational absorption spectroscopies, allied with computational simulations and their potential toxicity assessed by in silico studies. Following photoexcitation to the lowest singlet excited state, these barbituric absorbers repopulate the electronic ground state with high fidelity on an ultrafast time scale (within a few picoseconds). The energy relaxation pathway includes a twisted intramolecular charge-transfer state as the system evolves out of the Franck–Condon region, internal conversion to the ground electronic state, and subsequent vibrational cooling. These barbituric absorbers display promising light-to-heat conversion capabilities, are predicted to be non-toxic, and demand further study within neighbouring application-based fields.

The synthesis and photophysical properties of phenolic barbiturics are reported. These molecules convert absorbed ultraviolet light to heat with high fidelity and may be suitable for inclusion in foliar sprays to boost crop protection and production.

Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme

The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.

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

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

Analytical Gradient Theory for Resolvent-Fitted Second-Order Extended Multiconfiguration Perturbation Theory (XMCQDPT2)

We present the formulation and implementation of an analytical gradient algorithm for extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT2) with the resolvent-fitting approximation by Granovsky. This algorithm is powerful when optimizing molecular configurations with a moderate-sized active space and many electronic states. First, we present the powerfulness and accuracy of resolvent-fitting approximations compared to canonical XMCQDPT2 theory. Then, we demonstrate the utility of the current algorithm in frequency analyses, optimizing the minimum energy conical intersection geometries of the retinal chromophore model RPSB6 and evaluating nuclear gradients when there are many electronic states. Furthermore, we parallelize the algorithm using the OpenMP/MPI hybrid approach. Additionally, we report the computational cost and parallel efficiency of the program.

Vibronic Excitons and Conical Intersections in Semiconductor Quantum Dots

Surface defects and organic surface-capping ligands affect the photoluminescence properties of semiconductor quantum dots (QDs) by altering the rates of competing nonradiative relaxation processes. In this study, broadband two-dimensional electronic spectroscopy reveals that absorption of light by QDs prepares vibronic excitons, excited states derived from quantum coherent mixing of the core electronic and ligand vibrational states. Rapidly damped coherent wavepacket motions of the ligands are observed during hot-carrier cooling, with vibronic coherence transferred to the photoluminescent state. These findings suggest a many-electron, molecular theory for the electronic structure of QDs, which is supported by calculations of the structures of conical intersections between the exciton potential surfaces of a small ammonia-passivated model CdSe nanoparticle.

Ultrafast nonadiabatic excited-state intramolecular proton transfer in 3-hydroxychromone: A surface hopping approach

We employ the ab initio molecular dynamics within the surface hopping method to explore the excited-state intramolecular proton transfer taking place on the coupled "bright" S₁ (ππ*) and "dark" S₂ (nπ*) states of 3-hydroxychromone. The nonadiabatic population transfer between these states via an accessible conical intersection would open up multiple proton transfer pathways. Our findings reveal the keto tautomer formation via S₁ on a timescale similar to the O-H in-plane vibrational period (<100 fs). Structural analysis indicates that a few parameters of the five-membered proton transfer geometry that constitute the donor (hydroxyl) and acceptor (carbonyl) groups would be adequate to drive the enol to keto transformation. We also investigate the role of O-H in-plane and out-of-plane vibrational motions in the excited-state dynamics of 3-hydroxychromone.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Nonadiabatic Dynamics Mechanism of Chalcone Analogue Sunscreen FPPO-HBr: Excited State Intramolecular Proton Transfer Followed by Conformation Twisting

Nowadays, traditional sunscreen molecules face many adverse problems: single energy relaxation pathway, lack of adequate UVA light protection, and therefore no longer meeting the growing demand for UVA protection. In this work, we reported a novel sunscreen molecule (E)-3-(5-bromofuran-2-yl)-1-(2-hydroxyphenyl)prop-2-en-1-one (hereinafter referred to as FPPO-HBr) which tackled adverse problems of traditional sunscreen molecules as single energy relaxation pathway, lacking effective UVA light protection. Various nonradiative pathways were proposed and verified by combining the steady-state and femtosecond transient absorption (FTA) spectroscopy and theoretical calculation. Upon UV excitation, the FPPO-HBr mainly decays via excited-state intramolecular proton transfer (ESIPT) followed by conformation twist in ultrafast manner. Importantly, ¹H NMR spectra proved that the FPPO-HBr could not undergo trans-cis photoisomerization. Additionally, excellent photostability was also observed for newly synthesized FPPO-HBr. The current work could provide new perspectives for sunscreen molecules synthesis and mechanism.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Mechanistic Aspects of the Photophysics of UVA Filters Based on Meldrum Derivatives

Skin photoprotection against UVA radiation is crucial, but it is hindered by the sparsity of approved commercial UVA filters. Sinapoyl malate (SM) derivatives are promising candidates for a new class of UVA filters. They have been previously identified as an efficient photoprotective sunscreen in plants due to their fast nonradiative energy dissipation. Combining experimental and computational results, in our previous letter (J. Phys. Chem. Lett. 2021, 12, 337-344) we showed that coumaryl Meldrum (CMe) and sinapoyl Meldrum (SMe) are outstanding candidates for UVA filters in sunscreen formulations. Here, we deliver a comprehensive computational characterization of the excited-state dynamics of these molecules. Using reaction pathways and excited-state dynamics simulations, we could elucidate the photodeactivation mechanism of these molecules. Upon photoexcitation, they follow a two-step logistic decay. First, an ultrafast and efficient relaxation stabilizes the excited state alongside a 90° twisting around the allylic double bond, giving rise to a minimum with a twisted intramolecular excited-state (TICT) character. From this minimum, internal conversion to the ground state occurs after overcoming a 0.2 eV barrier. Minor differences in the nonradiative decay and fluorescence of CMe and SMe are associated with an additional minimum present only in the latter.

2,6-diaminopurine promotes repair of DNA lesions under prebiotic conditions

High-yielding and selective prebiotic syntheses of RNA and DNA nucleotides involve UV irradiation to promote the key reaction steps and eradicate biologically irrelevant isomers. While these syntheses were likely enabled by UV-rich prebiotic environment, UV-induced formation of photodamages in polymeric nucleic acids, such as cyclobutane pyrimidine dimers (CPDs), remains the key unresolved issue for the origins of RNA and DNA on Earth. Here, we demonstrate that substitution of adenine with 2,6-diaminopurine enables repair of CPDs with yields reaching 92%. This substantial self-repairing activity originates from excellent electron donating properties of 2,6-diaminopurine in nucleic acid strands. We also show that the deoxyribonucleosides of 2,6-diaminopurine and adenine can be formed under the same prebiotic conditions. Considering that 2,6-diaminopurine was previously shown to increase the rate of nonenzymatic RNA replication, this nucleobase could have played critical roles in the formation of functional and photostable RNA/DNA oligomers in UV-rich prebiotic environments.

UV-induced photodamage that likely occurred during the prebiotic synthesis of DNA and RNA is still an untackled issue for their origin on early Earth. Here, the authors show that substitution of 2,6-diaminopurine for adenine enables repair of cyclobutane pyrimidine dimers with high yields, and demonstrate that both 2,6-diaminopurine and adenine nucleosides can be formed under the same prebiotic conditions.

Impact of the Dynamic Electron Correlation on the Unusually Long Excited-State Lifetime of Thymine

Non-radiative relaxation of the photoexcited thymine in the gas phase shows an unusually long excited-state lifetime, and, over the years, a number of models, i.e., S₁-trapping, S₂-trapping, and S₁&S₂-trapping, have been put forward to explain its mechanism. Here, we investigate this mechanism using non-adiabatic molecular dynamics (NAMD) simulations in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) method. We show that the previously predicted S₂-trapping model was due to an artifact caused by an insufficient account of the dynamic electron correlation. The current work supports the S₁-trapping mechanism with two lifetimes, τ₁ = 30 ± 1 fs and τ₂ = 6.1 ± 0.035 ps, quantitatively consistent with the recent time-resolved experiments. Upon excitation to the S₂ (ππ*) state, thymine undergoes an ultrafast (ca. 30 fs) S₂→S₁ internal conversion and resides around the minimum on the S₁ (n_Oπ*) surface, slowly decaying to the ground state (ca. 6.1 ps). While the S₂→S₁ internal conversion is mediated by fast bond length alternation distortion, the subsequent S₁→S₀ occurs through several conical intersections, involving a slow puckering motion.

Computational and photophysical characterization of a Laurdan malononitrile derivative

The malononitrile group is considered one of the strongest natural electron-withdrawing groups in a chemist's arsenal. However, surprisingly little is known about how this group functions in push-pull fluorophores. In a recent computational study, we reported that replacing the ketone group of the traditional push-pull dye Laurdan with a malononitrile group significantly improves the optical properties while retaining the membrane behavior of the parent molecule Laurdan. Motivated by these results, we report here the synthesis and photophysical characterization of the said compound, 6-(1-undecyl-2,2-dicyanovinyl)-N,N-dimethyl-2-naphthylamine (CN-Laurdan). To our surprise, this new CN-Laurdan probe is found to be much less bright than the parent Laurdan due to a large drop in the fluorescence quantum yield. Using computational methods, we determine that the origin of this low quantum yield is related to the existence of a non-radiative decay pathway related to a rotation of the malononitrile moiety, suggesting that the molecule could nonetheless function very well as a molecular rotor. We confirm experimentally that CN-Laurdan functions as a molecular rotor by measuring the quantum yield in methanol/glycerol mixtures of increasing viscosity. Specifically, we found a consistent increase in the quantum yield across the entire range of tested viscosities.

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.

Exploring the effects of quantum decoherence on the excited-state dynamics of molecular systems

Fewest-switches surface hopping (FSSH) is employed in order to investigate the nonadiabatic excited-state dynamics of thiophene and related compounds and hence to establish a connection between the electronic system, the critical points in configuration space and the deactivation dynamics. The potential-energy surfaces of the studied molecules were calculated with complete active space self-consistent field and time-dependent density-functional theory. They are analyzed thoroughly to locate and optimize minimum-energy conical intersections, which are essential to the dynamics of the system. The influence of decoherence on the dynamics is examined by employing different decoherence schemes. We find that irrespective of the employed decoherence algorithm, the population dynamics of thiophene give results which are sound with the expectations grounded on the analysis of the potential-energy surface. A more detailed look at single trajectories as well as on the excited-state lifetimes, however, reveals a substantial dependence on how decoherence is accounted for. In order to connect these findings, we describe how ensemble averaging cures some of the overcoherence problems of uncorrected FSSH. Eventually, we identify carbon–sulfur bond cleavage as a common feature accompanying electronic transitions between different states in the simulations of all thiophene-related compounds studied in this work, which is of interest due to their relevance in organic photovoltaics.

Optimization of Three State Conical Intersections by Adaptive Penalty Function Algorithm in Connection with the Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory Method (MRSF-TDDFT)

A new adaptive algorithm for penalty function optimization for minimum-energy three-states conical intersections (ME3CI) is suggested. The new algorithm differs from the original penalty function algorithm by (a) removing the redundancy in the target function, (b) using an adaptive increment for the penalty function weighting factor, and (c) using tighter convergence criteria for the energy gap. The latter was introduced to guarantee convergence to a true conical intersection rather than to a narrowly avoided crossing geometry. The new algorithm was tested in the optimization of the ME3CI geometries in butadiene and malonaldehyde, where all of the previously found true ME3CI geometries were recovered. The previously found butadiene's CI_3/2/1 turned out to be a narrowly avoided crossing. For butadiene, seven new ME3CI geometries have been located. Because of the removal of the redundancy and the use of the adaptive weighting factor, the convergence rate of the new algorithm is noticeably improved as compared to that of the previously proposed penalty function algorithm. The application to malonaldehyde and butadiene demonstrates that the three-state conical intersections may be more abundant and hence more involved in the photochemistry than previously thought. The recently developed mixed-reference spin flip (MRSF)-TDDFT method yields ME3CI geometries and relative energies quantitatively consistent with the previously reported calculations at a much reduced computational cost.

Theoretical investigation of a novel xylene-based light-driven unidirectional molecular motor

In this study, the working mechanism of the first light-driven rotary molecular motors used to control an eight-base-pair DNA hairpin has been investigated. In particular, this linker was reported to have promising photophysical properties under physiological conditions, which motivated our work at the quantum mechanical level. Cis-trans isomerization is triggered by photon absorption at wavelengths ranging 300 nm-400 nm, promoting the rotor to the first excited state, and it is mediated by an energy-accessible conical intersection from which the ground state is reached back. The interconversion between the resulting unstable isomer and its stable form occurs at physiological conditions in the ground state and is thermally activated. Here, we compare three theoretical frameworks, generally used in the quantum description of medium-size chemical systems: Linear-Response Time-Dependent Density Functional Theory (LR-TDDFT), Spin-Flip TDDFT (SF-TDDFT), and multistate complete active space second-order perturbation theory on state-averaged complete active space self consistent field wavefunctions (MS-CASPT2//SA-CASSCF). In particular, we show the importance of resorting to a multireference approach to study the rotational cycle of light-driven molecular motors due to the occurrence of geometries described by several configurations. We also assess the accuracy and computational cost of the SF-TDDFT method when compared to MS-CASPT2 and LR-TDDFT.

Ultrafast nonradiative deactivation of photoexcited 8-oxo-hypoxanthine: a nonadiabatic molecular dynamics study

In the scientific endeavor to understand the chemical origins of life, the photochemistry of the smallest life building blocks, nucleobases, has been a constant object of focus and intense research. Here, we report the results of the first theoretical study on the photo-properties of an 8-oxo-hypoxanthine molecule, the chromophore of 8-oxo-inosine, which is relevant to the recently proposed, prebiotically plausible synthetic routes to the formation of purine- and pyrimidine-nucleotides. With ab initio and semi-empirical OM2/MRCI quantum-chemistry calculations, we predict a strong photostability of the 8-oxo-hypoxanthine system and see the origin of this effect in ultrafast nonradiative relaxation through puckering of the 6-membered heterocyclic ring.

Role of Conical Intersections on the Efficiency of Fluorescent Organic Molecular Crystals

Organic molecular crystals are attractive materials for luminescent applications because of their promised tunability. However, the link between the chemical structure and emissive behavior is poorly understood because of the numerous interconnected factors which are at play in determining radiative and nonradiative behaviors at the solid-state level. In particular, the decay through conical intersection dominates the nonadiabatic regions of the potential energy surface, and thus, their accessibility is a telling indicator of the luminosity of the material. In this study, we investigate the radiative mechanism for five organic molecular crystals which display a solid-state emission, with a focus on the role of conical intersections in their photomechanisms. The objective is to situate the importance of the accessibility of conical intersections with regards to emissive behavior, taking into account other nonradiative decay channels, namely, vibrational decay, and exciton hopping. We begin by giving a brief overview of the structural patterns of the five systems within a larger pool of 13 crystals for a richer comparison. We observe that because of the prevalence of sheet like and herringbone packing in organic molecular crystals, the conformational diversity of crystal dimers is limited. Additionally, similarly spaced dimers have exciton coupling values of a similar order within a 50 meV interval. Next, we focus on three exemplary cases, where we disentangle the role of nonradiative decay mechanisms and show how rotational minimum energy conical intersections in vacuum lead to puckered ones in the crystal, increasing their instability upon crystallization in typical packing motifs. In contrast, molecules with puckered conical intersections in vacuum tend to conserve this trait upon crystallization, and therefore, their quantum yield of fluorescence is determined predominantly by other nonradiative decay mechanisms.

Free energy profile analysis to identify factors activating the aggregation-induced emission of a cyanostilbene derivative

An approach to quantitatively analyze the factors contributing to the activation of aggregation-induced emission (AIE) of a molecule is proposed using molecular simulations. A cyanostilbene derivative, 1-cyano-1,2-bis-(4'-methylbiphenyl)ethylene (CN-MBE), has two isomers, E and Z forms. The E-form of CN-MBE exhibits AIE, and is non-emissive in dilute solutions but becomes highly emissive in aggregated states. The Z-form is non-emissive, even in the solid state, that is, the E-form of CN-MBE is AIE-active, while its Z-form is AIE-inactive. In this study, the free energy profiles of the AIE processes of the E and Z forms of CN-MBE are investigated using the free energy perturbation method at the quantum mechanics/molecular mechanics level. The free energy profiles reveal significant differences in the extent to which steric hindrance from surrounding molecules restricts the intramolecular motions of the E and Z forms in the aggregated states. The structural features of the E and Z forms are characterized based on the conformational changes in the excited state relaxation process to reach the conical intersections and the free volume space around the molecules in the aggregated states. This study determines the contributing factors that cause the AIE activity of the molecule by identifying characteristic differences in the free energy profiles of the AIE processes of the AIE-active E-form of CN-MBE and the inactive Z-form. The approach used in this study can be applied to the rational design of highly efficient AIE luminogens utilizing computer modeling.

Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach

We present a machine learning-assisted excited state molecular dynamics (ML-ESMD) based on the ensemble density functional theory framework. Since we represent a diabatic Hamiltonian in terms of generalized valence bond ansatz within the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS) method, we can avoid singularities near conical intersections, which are crucial in excited state molecular dynamics simulations. We train the diabatic Hamiltonian elements and their analytical gradients with the SchNet architecture to construct machine learning models, while the phase freedom of off-diagonal elements of the Hamiltonian is cured by introducing the phase-less loss function. Our machine learning models show reasonable accuracy with mean absolute errors of ∼0.1 kcal/mol and ∼0.5 kcal/mol/Å for the diabatic Hamiltonian elements and their gradients, respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting the diabatic representation, our models can predict correct conical intersection structures and their topologies. In addition, our ML-ESMD simulations give almost identical result with a direct dynamics at the same level of theory.

Nonadiabatic dynamics simulation of photoinduced ring-opening reaction of 2(5H)-thiophenone with internal conversion and intersystem crossing

In the present work, the quantum trajectory mean-field approach, which is able to overcome the overcoherence problem, was generalized to simulate internal conversion and intersystem crossing processes simultaneously. The photoinduced ring-opening and subsequent rearrangement reactions of isolated 2(5H)-thiophenone were studied based on geometry optimizations on critical structures and nonadiabatic dynamics simulations using this method. Upon 267 nm irradiation, the molecule is initially populated in the 1ππ* state. After a sudden rupture of one C-S bond within 100 fs in this state, the lowest two singlet excited states and the lowest two triplet excited states become quasi-degenerated, and then the intersystem crossing processes between singlet and triplet states accompanied by rearrangement reactions can be observed several times. Compared with our previous nonadiabatic simulations in the absence of intersystem crossing (ChemPhotoChem, 2019, 3, 897-906), some new nonadiabatic relaxation pathways involving triplet states and different ring-opening products were identified. The present work provides new mechanistic insights into the photoinduced ring-opening of thio-substituted heterocyclic molecules and reveals the importance of nonadiabatic dynamics simulation that is able to deal with multiple electronic states with different spin multiplicities.

Extended conjugation of ESIPT-type dopants in nematic liquid crystalline phase for enhancing fluorescence efficiency and anisotropy

Organic compounds capable of excited-state intramolecular proton transfer (ESIPT) show fluorescence with a large Stokes shift and serve as solid-state emitters, luminescent dopants, and fluorescence-based sensing materials. Fluorescence of ESIPT molecules is usually increased in the solid state, but is weak in solvents due to the accelerated non-radiative decays by rotational motions of a part of the molecular core in these environments. Here we report, using a representative ESIPT motif 2-(2-hydroxyphenyl)benzothiazole (HBT), the extended-conjugation strategy of keeping sufficient fluorescence efficiency both in the solid state and in organic media. The introduction of an alkyl-terminated phenylene-ethynylene group into the HBT molecule dramatically enhances the fluorescence quantum yield from 0.01 to 0.20 in toluene and from 0.07 to 0.32 in a representative room-temperature nematic liquid crystal, 4-pentyl-4'-cyano biphenyl (5CB). The newly-synthesized CnP-C[triple bond, length as m-dash]C-HBT (n = 5 or 8) serves as a fluorescent dopant in 5CB and exhibits anisotropic fluorescence with the order parameter of 0.48, where the luminescence is controlled by the applied electric-field. The enhanced emission efficiency is rationalized by the larger height of energy barrier for the ESIPT process due to the introduction of phenylene-ethynylene groups.

The Photoisomerization Pathway(s) of Push-Pull Phenylazoheteroarenes*

Azoheteroarenes are the most recent derivatives targeted to further improve the properties of azo-based photoswitches. Their light-induced mechanism for trans-cis isomerization is assumed to be very similar to that of the parent azobenzene. As such, they inherited the controversy about the dominant isomerization pathway (rotation vs. inversion) depending on the excited state (nπ* vs. ππ*). Although the controversy seems settled in azobenzene, the extent to which the same conclusions apply to the more structurally diverse family of azoheteroarenes is unclear. Here, by means of non-adiabatic molecular dynamics, the photoisomerization mechanism of three prototypical phenyl-azoheteroarenes with increasing push-pull character is unraveled. The evolution of the rotational and inversion conical intersection energies, the preferred pathway, and the associated kinetics upon both nπ* and ππ* excitations can be linked directly with the push-pull substitution effects. Overall, the working conditions of this family of azo-dyes is clarified and a possibility to exploit push-pull substituents to tune their photoisomerization mechanism is identified, with potential impact on their quantum yield.

The Mechanics of the Bicycle Pedal Photoisomerization in Crystalline cis,cis-1,4-Diphenyl-1,3-butadiene

Direct irradiation of crystalline cis,cis-1,4-diphenyl-1,3-butadiene (cc-DPB) forms trans,trans-1,4-diphenyl-1,3,-butadiene via a concerted two-bond isomerization called the bicycle pedal (BP) mechanism. However, little is known about photoisomerization pathways in the solid state and there has been much debate surrounding the interpretation of volume-conserving isomerization mechanisms. The bicycle pedal photoisomerization is investigated using the quantum mechanics/molecular mechanics complete active space self-consistent field/Amber force-field method. Important details about how the steric environment influences isomerization mechanisms are revealed including how the one-bond flip and hula-twist mechanisms are suppressed by the crystal cavity, the nature of the seam space in steric environments, and the features of the bicycle pedal mechanism. Specifically, in the bicycle pedal, the phenyl rings of cc-DPB are locked in place and the intermolecular packing allows a passageway for rotation of the central diene in a volume-conserving manner. In contrast, the bicycle pedal rotation in the gas phase is not a stable pathway, so single-bond rotation mechanisms become operative instead. Furthermore, the crystal BP mechanism is an activated process that occurs completely on the excited state; the photoproduct can decay to the ground state through radiative and non-radiative pathways. The present models, however, do not capture the quantitative activation barriers, and more work is needed to better model reactions in crystals. Last, the reaction barriers of the different crystalline conformations within the unit cell of cc-DPB are compared to investigate the possibility for conformation-dependent isomerization. Although some difference in reaction barriers is observed, the difference is most likely not responsible for the experimentally observed periods of fast and slow conversion.

Role of Multistate Intersections in Photochemistry

It has been generally accepted that the intersection of potential energy surfaces can facilitate nonadiabatic transitions and plays a crucial role in photochemistry. Although most previous studies have focused on the conical intersection of two electronic states, multistate intersections are common in polyatomic molecules, and their key roles in photochemistry have been uncovered by electronic structure calculations and nonadiabatic dynamics simulations. In this Perspective, the algorithms for searching two- or three-state intersections are first examined with an emphasis on the latest development in a general algorithm for location of multistate intersections. Then, we focus on intersystem crossing (ISC) that occurs in the region of multistate intersection, paying more attention to how the state-specific spin-orbit coupling interaction influences nonadiabatic ISC processes. Finally, the interweaving of nonadiabatic dynamics simulation and electronic structure calculation has been recognized as a correct way to ascertain the vital roles of multistate intersections in photochemical reactions.

Extending nudged elastic band method to reaction pathways involving multiple spin states

There are diverse reactions including spin-state crossing, especially the reactions catalyzed by transition metal compounds. To figure out the mechanisms of such reactions, the discussion of minimum energy intersystem crossing (MEISC) points cannot be avoided. These points may be the bottleneck of the reaction or inversely accelerate the reactions by providing a better pathway. It is of great importance to reveal their role in the reactions by computationally locating the position of the MEISC points together with the reaction pathway. However, providing a proper initial guess for the structure of the MEISC point is not as easy as that of the transition state. In this work, we extended the nudged elastic band (NEB) method for multiple spin systems, which is named the multiple spin-state NEB method, and it is successfully applied to find the MEISC points while optimizing the reaction pathway. For more precisely locating the MEISC point, a revised approach was adopted. Meanwhile, our examples also suggest that special attention should be paid to the criterion to define an image optimized as the MEISC point.

Toward Quantitative Prediction of Fluorescence Quantum Efficiency by Combining Direct Vibrational Conversion and Surface Crossing: BODIPYs as an Example

Accurate theoretical description of the electronic structure of boron dipyrromethene (BODIPY) molecules has been a challenge, let alone the prediction of fluorescence quantum efficiency. In this Letter, we show that the electronic structures of BODIPYs can be accurately evaluated via the spin-flip time-dependent density functional theory with the B3LYP functional. With the resulting electronic structures, the experimental spectral line shapes of representative BODIPYs are successfully reproduced by our previously developed thermal vibration correlation function method. Most importantly, a two-channel scheme is proposed to describe the internal conversion of S₁ to S₀ in BODIPYs: channel I via direct vibrational relaxation within the harmonic region and channel II via a distorted S₀/S₁ minimum energy crossing point well away from the harmonic region. The fluorescence quantum yields are accurately predicted within this two-channel scheme, which can therefore serve as a generalized method for predicting the photophysical parameters of organic fluorescent compounds.

Analytical First-Order Derivatives of Second-Order Extended Multiconfiguration Quasi-Degenerate Perturbation Theory (XMCQDPT2): Implementation and Application

Analytical gradient theory for the second-order extended multiconfiguration quasi-degenerate perturbation theory (XMCQDPT2), which can be regarded as the multistate version of the multireference second-order Møller-Plesset perturbation theory (MRMP2), is formulated and implemented. The theory is similar to the previous analytical gradient theory for MCQDPT2, but we take into account the intruder state avoidance (ISA) technique and the "extension" of the MCQDPT2 theory by Granovsky. Although the (X)MCQDPT2 theory is not invariant with respect to rotations among the active orbitals, the resulting analytical gradients are accurate. We demonstrate the utility of the current algorithm in optimizing the minimum energy conical intersections (MECIs) of ethylene, butadiene, benzene, the retinal model chromophore PSB3, and the green fluorescent protein model chromophore pHBI. The XMCQDPT2 MECIs are very similar to the XMS-CASPT2 MECIs in terms of molecular conformation and the computed energies. We also discuss possible improvements of the current algorithm.

Theoretical studies on the photochemistry of 2-nitrofluorene in the gas phase and acetonitrile solution

The photophysical and photochemical mechanisms of 2-nitrofluorene (2-NF) in the gas phase and acetonitrile solution have been studied theoretically. Upon ∼330 nm irradiation to the first bright state (¹ππ*), the 2-NF system can decay to triplet excited states via rapid intersystem crossing (ISC) processes through different surface crossing points or to the ground state via an ultrafast internal conversion (IC) process through the S₁/S₀ conical intersection. The ¹nπ* dark state will serve as a bridge when the system leaves the Franck-Condon (FC) region and approaches to the S₁ minimum. The molecule maintains a planar geometry during the excited-state relaxation processes. The differences on excitation properties such as electronic configurations and spin-orbit coupling (SOC) interactions between those in the gas phase and acetonitrile solution cannot be neglected, indicating possible changes on the efficiency of the related ISC processes for the 2-NF system in solution. Once arrived at the T₁ state, it would further decay to the S₀ state or photodegrade into the Ar-O˙ and NO˙ free radicals. During the intramolecular rearrangement process, the twisting of the nitro group out of the aromatic-ring plane is regarded as a critical structural variation for the photodegradation of the 2-NF system. The free radicals finally form through oxaziridine-type intermediate and transition state structures. The present work provides important mechanistic insights to the photochemistry of nitro-substituted polyaromatic compounds.

TeraChem: Accelerating electronic structure and ab initio molecular dynamics with graphical processing units

Developed over the past decade, TeraChem is an electronic structure and ab initio molecular dynamics software package designed from the ground up to leverage graphics processing units (GPUs) to perform large-scale ground and excited state quantum chemistry calculations in the gas and the condensed phase. TeraChem's speed stems from the reformulation of conventional electronic structure theories in terms of a set of individually optimized high-performance electronic structure operations (e.g., Coulomb and exchange matrix builds, one- and two-particle density matrix builds) and rank-reduction techniques (e.g., tensor hypercontraction). Recent efforts have encapsulated these core operations and provided language-agnostic interfaces. This greatly increases the accessibility and flexibility of TeraChem as a platform to develop new electronic structure methods on GPUs and provides clear optimization targets for emerging parallel computing architectures.

Photoelimination of Nitrogen from Diazoalkanes: Involvement of Higher Excited Singlet States in the Carbene Formation

Although diazoalkanes are important carbene precursors in organic synthesis, a comprehensive mechanism of photochemical formation of carbenes from diazoalkanes has not been proposed. Synergies of experiments and computations demonstrate the involvement of higher excited singlet states in the photochemistry of diazoalkanes. In all investigated diazoalkanes, excitation to S₁ results in nonreactive internal conversion to S₀. On the contrary, excitation to higher-lying singlet states (S_n, n > 1) drives the reaction toward a different segment of the S₁/S₀ conical intersection seam and results in nitrogen elimination and formation of carbenes.

Comparison of Spin-Flip TDDFT-Based Conical Intersection Approaches with XMS-CASPT2

Determining conical intersection geometries is of key importance to understanding the photochemical reactivity of molecules. While many small- to medium-sized molecules can be treated accurately using multireference approaches, larger molecules require a less computationally demanding approach. In this work, minimum energy crossing point conical intersection geometries for a series of molecules have been studied using spin-flip TDDFT (SF-TDDFT), within the Tamm-Dancoff Approximation, both with and without explicit calculation of nonadiabatic coupling terms, and compared with both XMS-CASPT2 and CASSCF calculated geometries. The less computationally demanding algorithms, which do not require explicit calculation of the nonadiabatic coupling terms, generally fare well with the XMS-CASPT2 reference structures, while the relative energetics are only reasonably replicated with the MECP structure as calculated with the BHHLYP functional and full nonadiabatic coupling terms. We also demonstrate that, occasionally, CASSCF structures deviate quantitatively from the XMS-CASPT2 structures, showing the importance of including dynamical correlation.

Dissociative nature of C(sp2)-N(sp3) bonds of carbazole based materials via conical intersection: simple method to predict the exciton stability of host materials for blue OLEDs: a computational study

In this work, the origin of the singlet and triplet exciton-induced degradation of host materials with C(sp2)-N(sp3) bonds around nitrogen (carbazoles, acridines, etc.), connecting donor and acceptor units, was unravelled using DFT and CASSCF methods. The results reveal that molecules (employed in OLEDs) with basic units containing C(sp2)-N(sp3) bonds (nitrogen connected to carbon in a triangular fashion) have a natural tendency to fragment at the C-N bond through an S1/S0 conical intersection (CI). The calculation of barrier heights, to reach a dissociation point, indicates that degradation via triplet states is kinetically less feasible (ΔGT1-TS* > 25 kcal mol-1) compared to that via the first singlet excited state (ΔGS1-TS* ∼7-30 kcal mol-1). However, the long lifetime of triplets (as compared to singlets) aids in the reverse intersystem crossing from triplet to singlet state for subsequent degradation. From the results and inference, ΔGS1-TS* and ΔES1-T1 are proposed to be the controlling factors for exciton-induced degradation of host materials with C(sp2)-N(sp3) bonds. Furthermore, multiple functionalization of carbazole moieties reveals that polycyclic aromatic systems employed as acceptor units of host materials are best suited for PhOLEDs as they will increase their lifetime due to the larger ΔGS1-TS* and ΔES1-T1. For TADF-based devices, materials with fused ring systems (with N(sp3) at the centre) in the donor unit are the most recommended ones based on the findings of this work, as they avoid the dissociative channel altogether. A negative linear correlation between ΔGS1-TS* and HOMO-LUMO gap is observed, which provides an indirect way to predict the kinetic stability of these materials in excitonic states. These initial results are promising for the future development of the QSAR-type approach for the smart design of host materials for long-life blue OLEDs.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

fromage: A library for the study of molecular crystal excited states at the aggregate scale

The study of photoexcitations in molecular aggregates faces the twofold problem of the increased computational cost associated with excited states and the complexity of the interactions among the constituent monomers. A mechanistic investigation of these processes requires the analysis of the intermolecular interactions, the effect of the environment, and 3D arrangements or crystal packing on the excited states. A considerable number of techniques have been tailored to navigate these obstacles; however, they are usually restricted to in‐house codes and thus require a disproportionate effort to adopt by researchers approaching the field. Herein, we present the FRamewOrk for Molecular AGgregate Excitations (fromage), which implements a collection of such techniques in a Python library complemented with ready‐to‐use scripts. The program structure is presented and the principal features available to the user are described: geometrical analysis, exciton characterization, and a variety of ONIOM schemes. Each is illustrated by examples of diverse organic molecules in condensed phase settings. The program is available at https://github.com/Crespo-Otero-group/fromage.

Four resonance structures elucidate double-bond isomerisation of a biological chromophore

Four resonance structures determining the electronic structure of the chromophore’s ground and first excited states. Changing the relative energies of the structures by hydrogen-bonding interactions tunes all chromophore’s photochemical properties.

Highly Miscible Hybrid Liquid-Crystal Systems Containing Fluorescent Excited-State Intramolecular Proton Transfer Molecules

Doping of luminescent molecules in a nematic liquid-crystal (LC) host is a convenient approach to develop light-emitting LC displays that would be a promising alternative to conventional LC displays. The requirements for the luminescent guest molecules include high miscibility in the host LC, high-order parameters in the host LC media to show anisotropic luminescence, lack of self-absorption, transparency in the visible region, and a large photoluminescence quantum yield independent of its concentration. To address these issues, here, we newly synthesize a highly miscible and fluorescent excited-state intramolecular proton transfer molecule, C₄-C≡C-HBT, based on 2-(2-hydroxyphenyl)benzothiazole (HBT). This compound is highly miscible in a conventional room-temperature nematic LC 4-pentyl-4'-cyano biphenyl (5CB) up to 14 wt % (∼12 mol %) and exhibits a large photoluminescence quantum yield of Φ_FL = 0.32 in the 5CB host, both of which were achieved by the introduction of an alkynyl group into the HBT core. C₄-C≡C-HBT possesses a high-order parameter of S = 0.46 in 5CB, and the C₄-C≡C-HBT/5CB mixtures show anisotropic fluorescence whose intensity is controlled by the applied electric field. A patterned image is demonstrated, which is not visible under an ambient environment but is readable upon UV illumination, relying on the orientational differences of ordered C₄-C≡C-HBT molecules.