Three-state conical intersection optimization methods: development and implementation at QM/MM level

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

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

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

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

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.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

Mechanistic photophysics and photochemistry of unnatural bases and sunscreen molecules: insights from electronic structure calculations

Photophysics and photochemistry are basic subjects in the study of light-matter interactions and are ubiquitous in diverse fields such as biology, energy, materials, and environment. A full understanding of mechanistic photophysics and photochemistry underpins many recent advances and applications. This contribution first provides a short discussion on the theoretical calculation methods we have used in relevant studies, then we introduce our latest progress on the mechanistic photophysics and photochemistry of two classes of molecular systems, namely unnatural bases and sunscreens. For unnatural bases, we disclose the intrinsic driving forces for the ultrafast population to reactive triplet states, impacts of the position and degree of chalcogen substitutions, and the effects of complex environments. For sunscreen molecules, we reveal the photoprotection mechanisms that dissipate excess photon energy to the surroundings by ultrafast internal conversion to the ground state. Finally, relevant theoretical challenges and outlooks are discussed.

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.

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.

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.

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.

QM/MM nonadiabatic dynamics simulations on photoinduced Wolff rearrangements of 1,2,3-thiadiazole

The photoinduced rearrangement reaction mechanism of 1,2,3-thiadiazole remains experimentally elusive. Two possible mechanisms have been proposed to date. The first is a stepwise mechanism via a thiocarbene intermediate; the second is an excited-state concerted rearrangement mechanism. Herein we have adopted both the electronic structure calculations and nonadiabatic dynamics simulations to study the photoinduced rearrangement reactions of 1,2,3-thiadiazole in the S₂, S₁, and S₀ states in solution. On the basis of QM(CASPT2)/MM [quantum mechanics(complete active space self-consistent field second-order perturbation theory)/molecular mechanics] calculations, we have found that (1) the thiocarbene intermediate is not stable; thus, the stepwise mechanism should be unfavorable; (2) the excited-state decay from the S₂ via S₁ to S₀ state is ultrafast and completed within ca. 200 fs; therefore, both the S₂ and S₁ states should not have a long enough time for the excited-state rearrangements. Instead, we have computationally proposed a modified photoinduced rearrangement mechanism. Upon irradiation, the S₂ state is first populated (114.0 kcal/mol), followed by an ultrafast S₂ → S₁ → S₀ excited-state decay along the S-N bond fission, which eventually leads to a very "hot" intermediate with the S-N bond broken (18.3 kcal/mol). Then, thermal rearrangements to thioketene, thiirene, and ethynethiol occur in a concerted asynchronous way. This mechanistic scenario has been verified by full-dimensional trajectory-based nonadiabatic dynamics simulations at the QM(CASPT2)/MM level. Finally, our present computational work provides experimentally interesting mechanistic insights into the photoinduced rearrangement reactions of cyclic and acyclic diazo compounds.

Photoinduced Curtius rearrangements of fluorocarbonyl azide, FC(O)N3: a QM/MM nonadiabatic dynamics simulation

Upon either photolysis or pyrolysis, carbonyl azide can eliminate molecular nitrogen along with the formation of isocyanate.

Theoretical studies of spin state-specific [2 + 2] and [5 + 2] photocycloaddition reactions of n-(1-penten-5-yl)maleimide

N-alkenyl maleimides are found to exhibit spin state-specific chemoselectivities for [2 + 2] and [5 + 2] photocycloadditions; but, reaction mechanism is still unclear. In this work, we have used high-level electronic structure methods (DFT, CASSCF, and CASPT2) to explore [2 + 2] and [5 + 2] photocycloaddition reaction paths of an N-alkenyl maleimide in the S₁ and T₁ states as well as relevant photophysical processes. It is found that in the S₁ state [5 + 2] photocycloaddition reaction is barrierless and thus overwhelmingly dominant; [2 + 2] photocycloaddition reaction is unimportant because of its large barrier. On the contrary, in the T₁ state [2 + 2] photocycloaddition reaction is much more favorable than [5 + 2] photocyclo-addition reaction. Mechanistically, both S₁ [5 + 2] and T₁ [2 + 2] photocycloaddition reactions occur in a stepwise, nonadiabatic means. In the S₁ [5 + 2] reaction, the secondary C atom of the ethenyl moiety first attacks the N atom of the maleimide moiety forming an S₁ intermediate, which then decays to the S₀ state as a result of an S₁ → S₀ internal conversion. In the T₁ [2 + 2] reaction, the terminal C atom of the ethenyl moiety first attacks the C atom of the maleimide moiety, followed by a T₁ → S₀ intersystem crossing process to the S₀ state. In the S₀ state, the second CC bond is formed. Our present computational results not only rationalize available experiments but also provide new mechanistic insights. © 2017 Wiley Periodicals, Inc.

A theoretical study of the light-induced cross-linking reaction of 5-fluoro-4-thiouridine with thymine

In contrast to photophysics of thio-substituted nucleobases, their photoinduced cross-linking reactions with canonical nucleobases remain scarcely investigated computationally. In this work, we have adopted combined CASPT2/PCM//CASSCF and B3LYP-D3/PCM electronic structure methods to study this kind of photochemical reaction of 5-fluoro-4-thiouridine (truncated 5-fluoro-1-methyl-4-thiouracil used in calculations) and 1-methylthymine (referred to as thymine for clarity hereinafter). On the basis of CASPT2/PCM computed results, we have proposed two efficient excited-state relaxation pathways to populate the lowest T₁ state of the complex of 5-fluoro-1-methyl-4-thiouracil and thymine from its initially populated S₂(¹ππ*) state. In the first one, the S₂ system first hops to the S₁ state via an S₂/S₁ conical intersection, followed by a direct S₁ → T₁ intersystem crossing process enhanced by large S₁/T₁ spin-orbit coupling. In the second path, the resultant S₁ system first jumps to the T₂ state, from which an efficient T₂ → T₁ internal conversion occurs. The T₁ cross-linking reaction is overall divided into two phases. The first phase is a stepwise and nonadiabatic photocyclization reaction, which starts from the T₁ complex and ends up with an S₀ thietane intermediate. The second phase is a thermal reaction. The system first rearranges its four- and six-membered rings to form three new rings; then, an S₀ fluorine atom transfer occurs, followed by the formation of photoproducts. Finally, the present work paves the way for studying light-induced cross-linking reactions of thionucleobases with canonical bases in DNA and RNA.

Mechanistic insights into the light-driven hydrogen evolution reaction from formic acid mediated by an iridium photocatalyst

Electronic structure calculations shed important mechanistic light on light-driven hydrogen evolution from formic acid mediated by an iridium photocatalyst.

The excited-state decay mechanism of 2,4-dithiothymine in the gas phase, microsolvated surroundings, and aqueous solution

We have employed computational methods to systematically explore the excited-state decay mechanism of 2,4-dithiothymine.