Optimizing conical intersections by spin-flip density functional theory: application to ethylene

GPU-accelerated on-the-fly nonadiabatic semiclassical dynamics

GPU-accelerated on-the-fly nonadiabatic dynamics is enabled by interfacing the linearized semiclassical dynamics approach with the TeraChem electronic structure program. We describe the computational workflow of the "PySCES" code interface, a Python code for semiclassical dynamics with on-the-fly electronic structure, including parallelization over multiple GPU nodes. We showcase the abilities of this code and present timings for two benchmark systems: fulvene solvated in acetonitrile and a charge transfer system in which a photoexcited zinc-phthalocyanine donor transfers charge to a fullerene acceptor through multiple electronic states on an ultrafast timescale. Our implementation paves the way for an efficient semiclassical approach to model the nonadiabatic excited state dynamics of complex molecules, materials, and condensed phase systems.

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

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.

Twisted Intramolecular Charge-Transfer State Addition to Electron-Poor Olefins

When electron-rich arylpyrrolinium salts are irradiated with ultraviolet light in the presence of Michael acceptors, the pyrrolinyl and aryl fragments add to the activated and polarized double bond in a regioselective manner, forming two C-C bonds and fragmenting the substrate. In this paper, we present a model for this intriguing reaction, supported by spectroscopy and computational analyses, and provide evidence for rectifying previously misassigned structures. We postulate that the photochemical reaction is inefficient because the reaction between the twisted intramolecular charge-transfer state and the olefin competes with fluorescence from this state upon photon absorption. We also discuss the practical advantages of performing this photochemical reaction in a continuous flow setup. Additionally, we explore several subsequent reactions that allow us to further modify the products of the photochemical step, ultimately leading to the creation of new chemical structures.

Electronic relaxation mechanism of 9-methyl-2,6-diaminopurine and 2,6-diaminopurine-2'-deoxyribose in solution

Prolonged ultraviolet exposure results in the formation of cyclobutane pyrimidine dimers (CPDs) in RNA. Consequently, prebiotic photolesion repair mechanisms should have played an important role in the maintenance of the structural integrity of primitive nucleic acids. 2,6-Diaminopurine is a prebiotic nucleobase that repairs CPDs with high efficiency when incorporated into polymers. We investigate the electronic deactivation pathways of 2,6-diaminopurine-2'-deoxyribose and 9-methyl-2,6-diaminopurine in acetonitrile and aqueous solution to shed light on the photophysical and excited state properties of the 2,6-diaminopurine chromophore. Evidence is presented that both are photostable compounds exhibiting similar deactivation mechanisms upon the population of the S1 (ππ* La ) state at 290 nm. The mechanism involves deactivation through the C2- and C6-reaction coordinates and >99% of the excited state population decays through nonradiative pathways involving two conical intersections with the ground state. The radiative and nonradiative lifetimes are longer in aqueous solution compared to acetonitrile. While τ1 is similar in both derivatives, τ2 is ca. 1.5-fold longer in 2,6-diaminopurine-2'-deoxyribose due to a more efficient trapping in the S1 (ππ* La ) minimum. Therefore, 2,6-diaminopurine could have accumulated in significant quantities during prebiotic times to be incorporated into non-canonical RNA and play a significant role in its photoprotection.

Isolation of Fluorescent 2π-Aromatic 1,3-Disiladiboretenes

Herein, we reported the isolation of 2π-aromatic disiladiboretenes (L2Si2B2Ph2) [L = ArC(NtBu)2, Ar = Ph (1), Mes (2)], which have been synthesized from the straightforward reduction of silylene-borane adducts (LSiX → BX2Ph) [X = Cl, Br] with potassium graphite (KC8). X-ray diffraction analysis of 1 and 2 revealed that the Si2B2 units are completely planar, and DFT calculations suggested delocalization of 2π-electrons over the Si2B2 rings. Moreover, their photophysical properties and reactivity toward sulfur were also investigated in detail.

Solvent-polarity dependence of ultrafast excited-state dynamics of trans-4-nitrostilbene

Ultrafast excited-state dynamics of the simplest nitrostilbenes, namely trans-4-nitrostilbene (t-NSB), was studied in solvents of various polarities with ultrafast broadband time-resolved fluorescence and transient absorption spectroscopies, and by quantum-chemical computations. The results revealed that the initially excited S1(ππ*) state deactivation dynamics is strongly influenced by the solvent polarity. Specifically, the t-NSB S1-state lifetime decreases by three orders of magnitude from ∼60 ps in high-polarity solvents to ∼60 fs in nonpolar solvents. The strong solvent-polarity dependence arises from the differences in dipole moments among the S1 and relevant states, including the major intersystem crossing (ISC) receiver triplet states, and therefore, the solvent polarity can modulate their relative energies and ISC rates. In nonpolar solvents, the sub-100 fs lifetime is due to a combination of efficient ISC and internal conversion. In medium-polarity solvents, the S1-state population decays via a competing ISC relaxation mechanism in a biphasic manner, and the ISC rates are found to obey the inverse energy gap law of the strong coupling case. In high-polarity solvents, the S1 state is stabilized to a much lower energy such that ISC becomes energetically infeasible, and the S1 state decays via barrier crossing along the torsion angle of the central ethylenic bond to the nonfluorescent perpendicular configuration. Regardless of the initial S1-state deactivation pathways in various solvents, the excited-state population is ultimately trapped in the metastable T1-state perpendicular configuration, at which a slower ISC occurs to bring the system to the ground state and bifurcate into either trans or cis form of NSB.

Unexplored Isomerization Pathways of Azobis(benzo-15-crown-5): Computational Studies on a Butterfly Crown Ether

Computational studies on trans → cis and cis → trans isomerizations of photoresponsive azobis(benzo-15-crown-5) have been reported in this work. The photoexcited ππ* state (S2) of the trans isomer relaxes through the planar S2 minimum and the planar S2/S1 conical intersection (both situated around 9 kcal/mol below the vertically excited S2 state) arising along the N═N stretching coordinate. The nπ* state (S1) of this isomer has both planar and rotated (clockwise and anticlockwise) minima, which may lead to a torsional conical intersection (S0/S1) geometry having a Collapse

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Affiliation(s)

Dilawar Singh Sisodiya Department of Chemistry, Birla Institute of Technology and Science (BITS), Pilani, K.K. Birla Goa Campus, Zuarinagar 403726, India
Sk Musharaf Ali Chemical Engineering Division, Bhabha Atomic Research Centre (BARC), Mumbai 400085, India
Anjan Chattopadhyay Department of Chemistry, Birla Institute of Technology and Science (BITS), Pilani, K.K. Birla Goa Campus, Zuarinagar 403726, India

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Intermolecular-Type Conical Intersections in Benzene Dimer

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm^-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm^-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm^-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

All Visible Light Photoswitch Based on the Dimethyldihydropyrene Unit Operating in Aqueous Solutions with High Quantum Yields

Molecular systems and devices whose properties can be modulated using light as an external stimulus are the subject of numerous research studies in the fields of materials and life sciences. In this context, the use of photochromic compounds that reversibly switch upon light irradiation is particularly attractive. However, for many envisioned applications, and in particular for biological purposes, illumination with harmful UV light must be avoided and these photoactivable systems must operate in aqueous media. In this context, we have designed a benzo[e]-fused dimethyldihydropyrene compound bearing a methyl-pyridinium electroacceptor group that meets these requirements. This compound (closed state) is able to reversibly isomerize under aerobic conditions into its corresponding cyclophanediene form (open isomer) through the opening of its central carbon-carbon bond. Both the photo-opening and the reverse photoclosing processes are triggered by visible light illumination and proceed with high quantum yields (respectively 14.5% yield at λ = 680 nm and quantitative quantum yield at λ = 470 nm, in water). This system has been investigated by nuclear magnetic resonance and absorption spectroscopy, and the efficient photoswitching behavior was rationalized by spin-flip time-dependent density functional theory calculations. In addition, it is demonstrated that the isomerization from the open to the closed form can be electrocatalytically triggered.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

Providing theoretical insight into the role of symmetry in the photoisomerization mechanism of a non-symmetric dithienylethene photoswitch

Dithienylethene (DTE) molecular photoswitches have shown to be excellent candidates in the design of efficient optoelectronic devices, due to their high photoisomerization quantum yield (QY), for which symmetry is suggested to play a crucial role. Here, we present a theoretical study on the photochemistry of a non-symmetric dithienylethene photoswitch, with a special emphasis on the effect of asymmetric substitution on the photocyclization and photoreversion mechanisms. We used the Spin-Flip Time Dependent Density Functional Theory (SF-TDDFT) method to locate and characterize the main structures (conical intersections and minima) of the ground state and the first two excited states, S₁ and S₂, along the ring-opening/closure reaction coordinate of the photocyclization and photoreversion processes, and to identify the important coordinates governing the radiationless decay pathways. Our results suggest that while the main features that characterize the photoisomerization of symmetric DTEs are also present for the photoisomerization of the non-symmetric DTE, the lower energy barrier on S₁ along the cycloreversion reaction speaks in favor of a more efficient and therefore a higher cycloreversion QY for the non-symmetric DTEs, making them a better candidate for molecular optoelectronic devices than their symmetric counterparts.

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.

On the Photostability of Cyanuric Acid and Its Candidature as a Prebiotic Nucleobase

Cyanuric acid is a triazine derivative that has been identified from reactions performed under prebiotic conditions and has been proposed as a prospective precursor of ancestral RNA. For cyanuric acid to have played a key role during the prebiotic era, it would have needed to survive the harsh electromagnetic radiation conditions reaching the Earth’s surface during prebiotic times (≥200 nm). Therefore, the photostability of cyanuric acid would have been crucial for its accumulation during the prebiotic era. To evaluate the putative photostability of cyanuric acid in water, in this contribution, we employed density functional theory (DFT) and its time-dependent variant (TD-DFT) including implicit and explicit solvent effects. The calculations predict that cyanuric acid has an absorption maximum at ca. 160 nm (7.73 eV), with the lowest-energy absorption band extending to ca. 200 nm in an aqueous solution and exhibiting negligible absorption at longer wavelengths. Excitation of cyanuric acid at 160 nm or longer wavelengths leads to the population of S_5,6 singlet states, which have ππ* character and large oscillator strengths (0.8). The population reaching the S_5,6 states is expected to internally convert to the S_1,2 states in an ultrafast time scale. The S_1,2 states, which have nπ* character, are predicted to access a conical intersection with the ground state in a nearly barrierless fashion (ca. ≤ 0.13 eV), thus efficiently returning the population to the ground state. Furthermore, based on calculated spin–orbit coupling elements of ca. 6 to 8 cm⁻¹, the calculations predict that intersystem crossing to the triplet manifold should play a minor role in the electronic relaxation of cyanuric acid. We have also calculated the vertical ionization energy of cyanuric acid at 8.2 eV, which predicts that direct one-photon ionization of cyanuric acid should occur at ca. 150 nm. Collectively, the quantum-chemical calculations predict that cyanuric acid would have been highly photostable under the solar radiation conditions reaching the Earth’s surface during the prebiotic era in an aqueous solution. Of relevance to the chemical origin of life and RNA-first theories, these observations lend support to the idea that cyanuric acid could have accumulated in large quantities during the prebiotic era and thus strengthens its candidature as a relevant prebiotic nucleobase.

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...

Synthesis of a Negative Photochrome with High Switching Quantum Yields and Capable of Singlet-Oxygen Production and Storage

A dimethyldihydropyrene (DHP) photochromic unit has been functionalized by donor (triphenylamine group) and acceptor (methylpyridinium) substituents. This compound was characterized by NMR, absorption and emission spectroscopies as well as cyclic voltammetry, and its properties were rationalized by theoretical calculations. The incorporation of both electron-donor and -withdrawing groups at the photochromic center allows i) an efficient photo-isomerization of the system when illuminated at low energy (quantum yield: Φ_c-o =13.3 % at λ_ex =660 nm), ii) the reversible and quantitative formation of two endoperoxyde isomers when illuminated under aerobic conditions at room temperature, and iii) the storage and production of singlet oxygen. The photo-isomerization mechanism was also investigated by spin-flip TD-DFT (SF-TD-DFT) calculations.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

Origins of the photoinitiation capacity of aromatic thiols as photoinitiatiors: a computational study

In this work, we report the photophysical properties of three thiol derivatives, commonly used as photoinitiators in thiol-ene free radical polymerization, the ultimate goal being to rationalize the main reason behind the photoinitiation efficiency. For this aim, time dependent density functional theory is used to simulate the absorption spectra of alkyl thiol (R-SH), thiophenol (PhSH) and p-(trifluoromethyl) thiophenol (p-CF₃PhSH), describe their excited state topologies, and explore their potential energy surfaces along the S-H dissociation. Excited state calculations have shown that the S-H photolysis is achieved through the triplet excited states following intersystem crossing from the originally populated singlet manifolds. More specifically, while in aromatic thiol derivatives dissociation is mainly triplet-state mediated, the first excited singlet state and first triplet state of alkyl thiol are both dissociative and hence potentially capable of generating the photoinduced radical species. We have also justified the experimental findings concerning the photoinitiator efficiency considering both their potential energy surface topologies and the absorption intensity, in the lowest energy region.

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiff base C5H6NH2. J Chem Phys 2021;155:124111. [PMID: 34598550 DOI: 10.1063/5.0062757]

Nonadiabatic trajectory surface hopping simulations are reported for trans-C₅H₆NH₂ ⁺, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C₅H₆NH₂ ⁺, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S₁/S₀ conical intersections is immaterial to the photodynamics.

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.

Photoinduced phenomena in water solution of melamine explaining the photostability of the compound

Two tautomers of melamine (triamino and imino-diamino) were studied at the BLYP/aug-cc-pVDZ theoretical level. It was found that the two tautomers are bridged with the ¹πσ^* excited-state reaction path. The high photostability of melamine in water solution was explained with the mechanism of ring deformation which occurs along the ¹ππ^* excited-state reaction path. The two mechanisms are investigated at the TD BLYP level of theory using the linear interpolation in internal coordinates approach.

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

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.

Investigating the Nonradiative Decay Pathway in the Excited State of Silepin Derivatives: A Study with Second-Order Multireference Perturbation Wavefunction Theory

The fluorescence quantum yield for fluorescent organic molecules is an important molecular property, and tuning it up is desired for various applications. For the computational estimation of the fluorescence quantum yield, the theoretical prediction of the nonradiative decay rate constant has become an attractive subject of study. The rate constant of thermally activated nonradiative decay is related to the activation energy in the photoreaction; thus, the accuracy and reliability of the excited-state potential energies in the quantum chemical computation are critical. In this study, we employed a second-order multireference perturbation wavefunction theory for studying the thermally activated decay via conical intersection (CI) of 1,1-dimethyldibenzo[b,f]silepin derivatives. The correlation between the computed activation energy to reach the CI geometry in the S₁ state and the experimentally determined fluorescence quantum yield implied that silepins nonradiatively decay via the CI triggered by the twisting of the central C-C bond. Geometry optimization of the transition state using multireference perturbation theory drastically reduced the estimated activation energy. Our computation gave reasonable predictions of the activation free energies of photoexcited 1,1-dimethyldibenzo[b,f]silepin. The energy profiles and geometry optimizations using proper quantum chemical methods played a critical role in reliable estimation of the rate constant and fluorescence quantum yield.

The Trip to the Density Functional Theory Zoo Continues: Making a Case for Time-Dependent Double Hybrids for Excited-State Problems

This account is written for general users of time-dependent density functional theory (TD-DFT) methods as well as chemists who are unfamiliar with the field. It includes a brief overview of conventional TD-DFT approaches and recommendations for applications to organic molecules based on our own experience. The main emphasis of this work, however, lies in providing the first in-depth review of time-dependent double-hybrid density functionals. They were first established in 2007 with very promising follow-up studies in the subsequent four years before developments or applications became scarce. The topic has regained more interest since 2017, and this account reviews those latest developments led by our group. These developments have shown unprecedented robustness for a variety of different types of electronic excitations when compared to more conventional TD-DFT methods. In particular, time-dependent double hybrids do not suffer from artificial ghost states and are able to reproduce exciton-coupled absorption spectra. Our latest methods include range separation and belong to the currently best TD-DFT methods for singlet-singlet excitations in organic molecules. While there is still room for improvement and further development in this space, we hope that this account encourages users to adjust their computational protocols to such new methods to provide more real-life testing and scenarios.

Fast Nonadiabatic Molecular Dynamics via Spin-Flip Time-Dependent Density-Functional Tight-Binding Approach: Application to Nonradiative Relaxation of Tetraphenylethylene with Locked Aromatic Rings

Nonadiabatic dynamics around conical intersections between ground and excited states are crucial to understand excited-state phenomena in complex chemical systems. With this background in mind, we present an approach combining fewest-switches trajectory surface hopping and spin-flip (SF) time-dependent (TD) density-functional tight binding (DFTB), which is a simplified version of SF-TD density functional theory (DFT) with semiempirical parametrizations, for computationally efficient nonadiabatic molecular dynamics simulations. The estimated computational time of the SF-TD-DFTB approach is several orders of magnitude lower than that of SF-TD-DFT. In addition, the proposed method reproduces the time scales and quantum yields in photoisomerization reactions of azobenzene at a level comparable with conventional ab initio approaches, demonstrating reasonable accuracy. Finally, we report a practical application of the developed technique to explore the nonradiative relaxation processes of tetraphenylethylene and its derivative with torsionally locked aromatic rings and discuss the effect of locking the rings on the excited-state lifetime.

Analytic gradients and derivative couplings for configuration interaction with all single excitations and one double excitation-En route to nonadiabatic dynamics

We present analytic gradients and derivative couplings for the simplest possible multireference configuration interaction method, CIS-1D, an electronic structure Ansatz that includes all single excitations and one lone double excitation on top of a Hartree-Fock reference state. We show that the resulting equations are numerically stable and require the evaluation of a similar number of integrals as compared to standard CIS theory; one can easily differentiate the required frontier orbitals (h and l) with minimal cost. The resulting algorithm has been implemented within the Q-Chem electronic structure package and should be immediately useful for understanding photochemistry with S₀-S₁ crossings.

Fluorescence Anisotropy Detection of Barrier Crossing and Ultrafast Conformational Dynamics in the S2 State of β-Carotene

Carotenoids are usually only weakly fluorescent despite being very strong absorbers in the mid-visible region because their first two excited singlet states, S₁ and S₂, have very short lifetimes. To probe the structural mechanisms that promote the nonradiative decay of the S₂ state to the S₁ state, we have carried out a series of fluorescence lineshape and anisotropy measurements with a prototype carotenoid, β-carotene, in four aprotic solvents. The anisotropy values observed in the fluorescence emission bands originating from the S₂ and S₁ states reveal that the large internal rotations of the emission transition dipole moment, as much as 50° relative to that of the absorption transition dipole moment, are initiated during ultrafast evolution on the S₂ state potential energy surface and persist upon nonradiative decay to the S₁ state. Electronic structure calculations of the orientation of the transition dipole moment account for the anisotropy results in terms of torsional and pyramidal distortions near the center of the isoprenoid backbone. The excitation wavelength dependence of the fluorescence anisotropy indicates that these out-of-plane conformational motions are initiated by passage over a low-activation energy barrier from the Franck-Condon S₂ structure. This conclusion is consistent with detection over the 80-200 K range of a broad, red-shifted fluorescence band from a dynamic intermediate evolving on a steep gradient of the S₂ state potential energy surface after crossing the activation barrier. The temperature dependence of the oscillator strength and anisotropy indicate that nonadiabatic passage from S₂ through a conical intersection seam to S₁ is promoted by the out-of-plane motions of the isoprenoid backbone with strong hindrance by solvent friction.

Finite-temperature-based time-dependent density-functional theory method for static electron correlation systems

In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems.

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.

Photoinduced Double Proton Transfer in the Glyoxal-Methanol Complex Revisited: The Role of the Excited States

Under irradiation in the visible range, the glyoxal-methanol complex in a cryogenic argon matrix undergoes a double proton transfer (DPT) reaction through which the glyoxal molecule isomerizes into hydroxyketene. In this work, we employ electronic structure simulations in order to shed more light on the underlying mechanism. Rewardingly, we find that the lowest singlet excited state (S₁) of the complex acts as a gateway to two previously unknown isomerization pathways, of which one takes place entirely in the singlet manifold and the other also involves the lowest triplet state (T₁). Both of these pathways are fully compatible with the available experimental data, implying that either or both are operative under experimental conditions. In either pathway, the methanol molecule acts as a proton shuttle between the proton-donating and proton-accepting sites of glyoxal, resulting in a dramatic lowering of the potential energy barrier to isomerization with respect to the case of isolated glyoxal. The occurrence of DPT in the singlet manifold is demonstrated directly with the use of nonadiabatic molecular dynamics simulations at the spin-flip time-dependent density functional theory level.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Trans-to-cis photoisomerization of cyclocurcumin in different environments rationalized by computational photochemistry

Cyclocurcumin is a turmeric component that has attracted much less attention compared to the well-known curcumin. In spite of the less deep characterization of its properties, cyclocurcumin has shown promising anticancer effects when used in combination with curcumin. Especially, due to its peculiar molecular structure, cyclocurcumin can be regarded as an almost ideal photoswitch, whose capabilities can also be exploited for relevant biological applications. Here, by means of state-of-the-art computational methods for electronic excited-state calculations (TD-DFT, MS-CASPT2, and XMS-CASPT2), we analyze in detail the absorption and photoisomerization pathways leading from the more stable trans isomer to the cis one. The different molecular surroundings, taken into account by means of the electrostatic solvent effect and compared with available experimental data, have been found to be critical in describing the fate of irradiated cyclocurcumin: when in non-polar environments, an excited state barrier prevents photoisomerization and favours fluorescence, whereas in polar solvents, an almost barrierless path results in a striking decrease of fluorescence, opening the way toward a crossing region with the ground state and thus funneling the photoproduction of the cis isomer.

Spin-flip methods in quantum chemistry

This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.

Analytic non-adiabatic couplings for the spin-flip ORMAS method

Analytic non-adiabatic coupling matrix elements (NACME) are derived and implemented for the spin-flip occupation restricted multiple active space configuration interaction (SF-ORMAS-CI) method.

Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems

We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H₂ specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.

Inverted Singlet-Triplet Gaps and Their Relevance to Thermally Activated Delayed Fluorescence

The basic design principle for emitters exhibiting thermally activated delayed fluorescence (TADF) is the minimization of the singlet-triplet gap. While typically this gap is positive, a possible inversion of states has been proposed as a pathway to improve the efficiency of organic light-emitting diodes. Despite the efforts to design such emitters, there are very few reports indicating that it is at all possible. We analyze the problem of the gap inversion from the perspective of the electronic structure theory. The key result is that inversion is possible but requires a substantial contribution of double excitations and that commonly used cheap electronic structure methods would fail to predict it.

Photophysics of BODIPY-Based Photosensitizer for Photodynamic Therapy: Surface Hopping and Classical Molecular Dynamics

Halogenated BODIPY derivatives are emerging as important candidates for photodynamic therapy of cancer cells due to their high triplet quantum yield. We probed fundamental photophysical properties and interactions with biological environments of such photosensitizers. To this end, we employed static TD-DFT quantum chemical calculations as well as TD-DFT surface hopping molecular dynamics on potential energy surfaces resulting from the eigenstates of the total electronic Hamiltonian including the spin-orbit (SO) coupling. Matrix elements of an effective one-electron spin-orbit Hamiltonian between singlet and triplet configuration interaction singles (CIS) auxiliary wave functions are calculated using a new code capable of dealing with singlets and both restricted and unrestricted triplets built up from up to three different and independent sets of (singlet, alpha, and beta) molecular orbitals. The interaction with a biological environment was addressed by using classical molecular dynamics (MD) in a scheme that implicitly accounts for electronically excited states. For the surface hopping trajectories, an accelerated MD approach was used, in which the SO couplings are scaled up, to make the calculations computationally feasible, and the lifetimes are extrapolated back to unscaled SO couplings. The lifetime of the first excited singlet state estimated by semiclassical surface hopping simulations is 139 ± 75 ps. Classical MD demonstrates that halogenated BODIPY in the ground state, in contrast to the unsubstituted one, is stable in the headgroup region of minimalistic cell membrane models, and while in the triplet state, the molecule relocates to the membrane interior ready for further steps of photodynamic therapy.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.