Conical Intersections: The New Conventional Wisdom

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

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

Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings

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

Development of Parallel On-the-Fly Algorithm for Global Exploration of Conical Intersection Seam Space

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100 fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

Revisiting fulgide photochromism: Mechanistic decoding and electron transport from computational exploration

The photochromic behavior of the fulgide molecule relies on ring-closure and ring-opening processes involving conical intersections during excited state transformation between isomers. The precise location and topography of these conical intersections significantly shape the decay process and fluorescence phenomena inherent to the molecule. This work combines electronic structure theory calculations using the density functional theory and wavefunction methods, as well as surface hopping simulation to analyze the photochemical behavior of an experimentally synthesized fulgide molecule, (E)-p-methylacetophenylisopropylidenesuccinic anhydride (1E). Our study reveals the conical intersection between the first excited state (S1) and the ground electronic state (S0), which emerges beyond the S1 minimum of 1E to the ring-closing side. The distinctive topography of this conical intersection appears to be sloped. These findings suggest a reduced quantum yield for the formation of the closed isomer, indicating a higher likelihood of reformation of the open isomer(s). The surface hopping simulation further supports this observation, revealing a mere ∼8% quantum yield for the formation of the closed isomer. In addition, the photoisomerization of the fulgide molecule initiates a cascade of conduction switching and holds great potential for applications in molecular electronics. Delving into the realm of molecular electronics, we have further examined the electron transport properties, disclosing the higher conductivity of the closed isomer.

Floquet Engineering of a Diatomic Molecule through a Bichromatic Radiation Field

We report on a theoretical study of a Cs2 molecule illuminated by two lasers and show how this can result in novel quantum dynamics. We reveal that these interactions facilitate the bypass of the non-crossing rule, forming light-induced conical intersections and modifiable avoided crossings. Our findings show how laser field orientation and strength, along with initial phase differences, can control molecular-state transitions, especially on the micromotion scale. We also extensively discuss how the interaction of radiation with matter gives rise to the emergence of potential energy surfaces of hybrids of radiation and molecular states. This research advances a technique for manipulating photoassociation processes in Cs2 molecules, offering potential new avenues in quantum control.

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

Topology of Conical Intersection Seams and the Geometric Phase

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

Highly efficient implementation of analytic nonadiabatic derivative couplings within the pseudospectral method

A pseudospectral implementation of nonadiabatic derivative couplings in the Tamm-Dancoff approximation is reported, and the accuracy and efficiency of the pseudospectral nonadiabatic derivative couplings are studied. Our results demonstrate that the pseudospectral method provides mean absolute errors of 0.2%-1.9%, while providing a significant speedup. Benchmark calculations on fullerenes (Cn, n up to 100) using B3LYP achieved 10- to 15-fold, 8- to 17-fold, and 43- to 75-fold speedups for 6-31G**, 6-31++G**, and cc-pVTZ basis sets, respectively, when compared to the conventional spectral method.

Fast and accurate excited states predictions: machine learning and diabatization

The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

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.

Which Electronic Structure Method to Choose in Trajectory Surface Hopping Dynamics Simulations? Azomethane as a Case Study

Nonadiabatic dynamics simulations have become a standard approach to explore photochemical reactions. Such simulations require underlying potential energy surfaces and couplings between them, calculated at a chosen level of theory, yet this aspect is rarely assessed. Here, in combination with the popular trajectory surface hopping dynamics method, we use a high-accuracy XMS-CASPT2 electronic structure level as a benchmark for assessing the performances of various post-Hartree-Fock methods (namely, CIS, ADC(2), CC2, and CASSCF) and exchange-correlation functionals (PBE, PBE0, and CAM-B3LYP) in a TD-DFT/TDA context, using the isomerization around a double bond as test case. Different relaxation pathways are identified, and the ability of the different methods to reproduce their relative importance and time scale is discussed. The results show that multireference electronic structure methods should be preferred, when studying nonadiabatic decay between excited and ground states. If not affordable, TD-DFT with TDA and hybrid functionals and ADC(2) are efficient alternatives but overestimate the nonradiative decay yield and thus may miss deexcitation pathways.

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

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

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

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

Representation and conservation of angular momentum in the Born-Oppenheimer theory of polyatomic molecules

This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter κ = (m/M)^1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born-Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born-Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (-F) and donating (-CH₃ ) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the -CH₃ substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to -F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with -F or -CH₃ , the conversion proceeds via the conrotatory pathway.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

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.

Direct geometric probe of singularities in band structure

A quantum system’s energy landscape may have points where multiple energy surfaces are degenerate and that exhibit singular geometry of the wave function manifold, with major consequences for the system’s properties. Ultracold atoms in optical lattices have been used to indirectly characterize such points in the band structure. We measured the non-Abelian transformation produced by transport directly through the singularities. We accelerated atoms along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic band-touching points of a honeycomb lattice. Measurements after transport identified the topological winding numbers of these singularities to be 1 and 2, respectively. Our work introduces a distinct method for probing singularities that enables the study of non-Dirac singularities in ultracold-atom quantum simulators.

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

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

The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics

The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born-Oppenheimer corrections (DBOCs) are non-integrable, and the geometric phase effect on the nuclear wavepackets cannot be accounted for unless a model is available. To circumvent these difficulties, the moving crude adiabatic (MCA) representation was proposed and successfully tested in low energy dynamics where the wavepacket skirts the conical intersection. We assess the MCA representation in the case of non-adiabatic transitions through conical intersections. First, we show that using a Gaussian basis in the adiabatic representation indeed exhibits the aforementioned difficulties with a special emphasis on the possibility to regularize the DBOC terms. Then, we show that MCA is indeed able to properly model non-adiabatic transitions. Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

Conical intersection and coherent vibrational dynamics in alkyl iodides captured by attosecond transient absorption spectroscopy

The photodissociation dynamics of alkyl iodides along the C–I bond are captured by attosecond extreme-ultraviolet (XUV) transient absorption spectroscopy employing resonant ∼20 fs UV pump pulses. The methodology of previous experiments on CH3I [Chang et al., J. Chem. Phys. 154, 234301 (2021)] is extended to the investigation of a C–I bond-breaking reaction in the dissociative A-band of C2H5I, i-C3H7I, and t-C4H9I. Probing iodine 4 d core-to-valence transitions in the XUV enables one to map wave packet bifurcation at a conical intersection in the A-band as well as coherent vibrations in the ground state of the parent molecules. Analysis of spectroscopic bifurcation signatures yields conical intersection crossing times of 15 ± 4 fs for CH3I, 14 ± 5 fs for C2H5I, and 24 ± 4 fs for i-C3H7I and t-C4H9I, respectively. Observations of coherent vibrations, resulting from a projection of A-band structural dynamics onto the ground state by resonant impulsive stimulated Raman scattering, indirectly reveal multimode C–I stretch and CCI bend vibrations in the A-bands of C2H5I, i-C3H7I, and t-C4H9I.

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.

Spectroscopic application of few-femtosecond deep-ultraviolet laser pulses from resonant dispersive wave emission in a hollow capillary fibre

We exploit the phenomenon of resonant dispersive wave (RDW) emission in gas-filled hollow capillary fibres (HCFs) to realize time-resolved photoelectron imaging (TRPEI) measurements with an extremely short temporal resolution. By integrating the output end of an HCF directly into a vacuum chamber assembly we demonstrate two-colour deep ultraviolet (DUV)-infrared instrument response functions of just 10 and 11 fs at central pump wavelengths of 250 and 280 nm, respectively. This result represents an advance in the current state of the art for ultrafast photoelectron spectroscopy. We also present an initial TRPEI measurement investigating the excited-state photochemical dynamics operating in the N-methylpyrrolidine molecule. Given the substantial interest in generating extremely short and highly tuneable DUV pulses for many advanced spectroscopic applications, we anticipate our first demonstration will stimulate wider uptake of the novel RDW-based approach for studying ultrafast photochemistry – particularly given the relatively compact and straightforward nature of the HCF setup.

We exploit the phenomenon of resonant dispersive wave emission in gas-filled hollow capillary fibres to realize time-resolved photoelectron imaging measurements with an extremely short temporal resolution.

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.

On the inclusion of one double within CIS and TDDFT

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

Multiphoton Control of 6π Photocyclization via State-Dependent Reactant-Product Correlations

Multiphoton excitation promises opportunities for opening new photochemical reaction pathways and controlling photoproduct distributions. We demonstrate photonic control of the 6π photocyclization of ortho-terphenyl to make 4a,4b-dihydrotriphenylene (DHT). Using pump-repump-probe spectroscopy we show that 1 + 1' excitation to a high-lying reactant electronic state generates a metastable species characterized by a red absorption feature that accompanies a repump-induced depletion in the one-photon trans-dihydro product (trans-DHT); signatures of the new photoproduct are clearer for a structural analogue of the reactant that is sterically inhibited against one-photon cyclization. Quantum-chemical computations support assignment of this species to cis-DHT, which is accessible photochemically along a disrotatory coordinate from high-lying electronic states reached by 1 + 1' excitation. We use time-resolved spectroscopy to track photochemical dynamics producing cis-DHT. In total, we demonstrate that selective multiphoton excitation opens a new photoreaction channel in these photocyclizing reactants by taking advantage of state-dependent correlations between reactant and product electronic states.

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.

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.

The non-adiabatic nanoreactor: towards the automated discovery of photochemistry

The ab initio nanoreactor has previously been introduced to automate reaction discovery for ground state chemistry. In this work, we present the nonadiabatic nanoreactor, an analogous framework for excited state reaction discovery. We automate the study of nonadiabatic decay mechanisms of molecules by probing the intersection seam between adiabatic electronic states with hyper-real metadynamics, sampling the branching plane for relevant conical intersections, and performing seam-constrained path searches. We illustrate the effectiveness of the nonadiabatic nanoreactor by applying it to benzene, a molecule with rich photochemistry and a wide array of photochemical products. Our study confirms the existence of several types of S₀/S₁ and S₁/S₂ conical intersections which mediate access to a variety of ground state stationary points. We elucidate the connections between conical intersection energy/topography and the resulting photoproduct distribution, which changes smoothly along seam space segments. The exploration is performed with minimal user input, and the protocol requires no previous knowledge of the photochemical behavior of a target molecule. We demonstrate that the nonadiabatic nanoreactor is a valuable tool for the automated exploration of photochemical reactions and their mechanisms.

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.

Photoisomerization of a phosphorus-based biradicaloid: ultrafast dynamics through a conical intersection

As previously reported, photoisomerization of the open-shell singlet biradicaloid [TerNP]₂CNDmp (2) yields its closed-shell housane-type isomer (3). In the present study, pump-probe spectroscopy was applied to investigate the excited-state dynamics of the photoisomerization, indicating ultrafast de-excitation of the S₁ state through a conical intersection, in agreement with computational predictions. The structural and electronic changes during the isomerization process are discussed to gain an understanding of the reaction pathway and the transformation of the biradicaloid to a closed-shell species.

Modeling photophysical properties of the bacteriophytochrome-based fluorescent protein IFP1.4

An enhanced interest in the phytochrome-based fluorescent proteins is explained by their ability to absorb and emit light in the far-red and infra-red regions particularly suitable for bioimaging. The fluorescent protein IFP1.4 was engineered from the chromophore-binding domain of a bacteriophytochrome in attempts to increase the fluorescence quantum yield. We report the results of simulations of structures in the ground S₀ and excited S₁ electronic states of IFP1.4 using the methods of quantum chemistry and quantum mechanics/molecular mechanics. We construct different protonation states of the biliverdin (BV) chromophore in the red-absorbing form of the protein by moving protons from the BV pyrrole rings to a suitable acceptor within the system and show that these structures are close in energy but differ by absorption bands. For the first time, we report structures of the minimum energy conical intersection points S₁/S₀ on the energy surfaces of BV in the protein environment and describe their connection to the local minima in the excited S₁ state. These simulations allow us to characterize the deactivation routes in IFP1.4.

Improved insights in time-resolved photoelectron imaging

We review new light source developments and data analysis considerations relevant to the time-resolved photoelectron imaging technique. Case studies illustrate how these themes may enhance understanding in studies of excited state molecular dynamics.

Nonadiabatic Molecular Quantum Dynamics with Quantum Computers

The theoretical investigation of nonadiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavorable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of nonadiabatic phenomena is still unexplored. In this Letter, we propose a quantum algorithm for the simulation of fast nonadiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wave packet on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.

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.

Excitation transport in molecular aggregates with thermal motion

Molecular aggregates can under certain conditions transport electronic excitation energy over large distances due to dipole-dipole interactions. Here, we explore to what extent thermal motion of entire monomers can guide or enhance this excitation transport. The motion induces changes of aggregate geometry and hence modifies exciton states. Under certain conditions, excitation energy can thus be transported by the aggregate adiabatically, following a certain exciton eigenstate. While such transport is always slower than direct migration through dipole-dipole interactions, we show that transport through motion can yield higher transport efficiencies in the presence of on-site energy disorder than the static counterpart. For this we consider two simple models of molecular motion: (i) longitudinal vibrations of the monomers along the aggregation direction within their inter-molecular binding potential and (ii) torsional motion of planar monomers in a plane orthogonal to the aggregation direction. The parameters and potential shapes used are relevant to dye-molecule aggregates. We employ a quantum-classical method, in which molecules move through simplified classical molecular dynamics, while the excitation transport is treated quantum mechanically using Schrödinger's equation. For both models we find parameter regimes in which the motion enhances excitation transport, however these are more realistic for the torsional scenario, due to the limited motional range in a typical Morse type inter-molecular potential. We finally show that the transport enhancement can be linked to adiabatic quantum dynamics. This transport enhancement through adiabatic motion appears a useful resource to combat exciton trapping by disorder.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Spectral Signatures of Ground- and Excited-State Wavepacket Interference after Impulsive Excitation

Impulsive transient absorption spectroscopy is used to track the formation and evolution of vibrational coherences in cresyl violet perchlorate under different excitation conditions. Resonant and off-resonant pump pulses result in the selective formation of excited (S₁)- and ground (S₀)-state wavepackets. Partially resonant and broadband excitation conditions lead to the simultaneous formation of wavepackets in the ground and excited states. The wavepackets are characterized by the phase-flips in the coherent signal associated with wavepacket motion across the absorption and emission maxima and by a red shift of 2-10 cm^-1 in the Raman features of the excited state compared to the ground-state wavepacket. We observe that, when wavepackets are simultaneously excited on the ground- and excited-state surfaces, interference on a picosecond timescale between coherent oscillations in the two wavepackets gives rise to features that cannot be attributed to the passage of a wavepacket through a conical intersection, such as shifting phase-flips and zero-amplitude nodes. Wavepacket filtering using windowed Fourier transforms highlights these interference effects and demonstrates that special care must be taken in order to properly interpret data that have been processed in this manner.

Revealing electronic state-switching at conical intersections in alkyl iodides by ultrafast XUV transient absorption spectroscopy

Conical intersections between electronic states often dictate the chemistry of photoexcited molecules. Recently developed sources of ultrashort extreme ultraviolet (XUV) pulses tuned to element-specific transitions in molecules allow for the unambiguous detection of electronic state-switching at a conical intersection. Here, the fragmentation of photoexcited iso-propyl iodide and tert-butyl iodide molecules (i-C₃H₇I and t-C₄H₉I) through a conical intersection between ³Q₀/¹Q₁ spin–orbit states is revealed by ultrafast XUV transient absorption measuring iodine 4d core-to-valence transitions. The electronic state-sensitivity of the technique allows for a complete mapping of molecular dissociation from photoexcitation to photoproducts. In both molecules, the sub-100 fs transfer of a photoexcited wave packet from the ³Q₀ state into the ¹Q₁ state at the conical intersection is captured. The results show how differences in the electronic state-switching of the wave packet in i-C₃H₇I and t-C₄H₉I directly lead to differences in the photoproduct branching ratio of the two systems.

The reaction trajectories of photoexcited molecules may involve transitions through conical intersections, which are ubiquitous in nature but challenging to characterize. Here the authors provide a complete mapping of molecular dissociation of two model alkyl halides by ultrafast XUV transient absorption.

Roaming Reactions and Dynamics in the van der Waals Region

Roaming reactions were first clearly identified in photodissociation of formaldehyde 15 years ago, and roaming dynamics are now recognized as a universal aspect of chemical reactivity. These reactions typically involve frustrated near-dissociation of a quasibound system to radical fragments, followed by reorientation at long range and intramolecular abstraction. The consequences can be unexpected formation of molecular products, depletion of the radical pool in chemical systems, and formation of products with unusual internal state distributions. In this review, I examine some current aspects of roaming reactions with an emphasis on experimental results, focusing on possible quantum effects in roaming and roaming dynamics in bimolecular systems. These considerations lead to a more inclusive definition of roaming reactions as those for which key dynamics take place at long range.

Time-Dependent Density Functional Theory Investigation of Excited State Intramolecular Proton Transfer in Tris(2-hydroxyphenyl)triazasumanene

Previously, our group reported dual-emission spectra for tris(2-hydroxyphenyl)triazasumanene (OHPhTAS), comprising three OH···N-type intramolecular hydrogen bonds from three phenolic rings connected to the nitrogen-doped buckybowl skeleton, corresponding to the excited state intramolecular proton transfer (ESIPT) in the solid state. However, the dual emission is not observed in a nonpolar solution. In this study, the mechanism and multiplicity of potentially photoinduced dynamic ESIPT were investigated both in ground (S₀) and in excited states (S₁) by time-dependent density functional theory calculations. Different pathways, concerted and stepwise (single, double, or triple) PT processes, are considered. The calculated vertical emission energies (S₁ → S₀ states) and adiabatic total energies at S₀ and S₁ states of OHPhTAS and its tautomers revealed that a single PT, trienol (EEE) → monoketo (KEE), is the main contribution in OHPhTAS with an ultrasmall PT energy barrier. The nonradiative decay of OHPhTAS was analyzed by the potential energy curve (PEC) at the S₁ state along EEE* to KEE*. The results indicated that nonradiative decay was prohibited in the solid state but significantly stabilized in nonpolar solutions. The nonradiative routes in the solution state were confirmed by the minimum energy crossing point of the T₁/S₀ pathway, wherein the dihedral angle φ between the phenolic ring and pyridine moiety on the buckybowl structure relaxed to 123°.

Influence of the heavy-atom effect on singlet fission: a study of platinum-bridged pentacene dimers

Two platinum-bridged pentacene dimers undergo efficient singlet fission to form a correlated triplet pair (T₁T₁). The internal heavy-atom effect of the platinum allows for ¹(T₁T₁)–³(T₁T₁) mixing leading to the formation of mainly (T₁S₀).

The process of singlet fission (SF) produces two triplet excited states (T₁ + T₁) from one singlet excited exciton (S₁) and a molecule in its ground state (S₀). It, thus, possesses the potential to boost the solar cell efficiency above the thermodynamic Shockley–Queisser limit of 33%. A key intermediate in the SF mechanism is the singlet correlated triplet pair state ¹(T₁T₁). This state is of great relevance, as its formation is spin-allowed and, therefore, very fast and efficient. Three fundamentally different pathways to formation of ¹(T₁T₁) have been documented so far. The factors that influence which mechanism is associated with which chromophore, however, remain largely unknown. In order to harvest both triplet excitons independently, a decorrelation of the correlated triplet pair state to two individual triplets is required. This second step of the SF process implies a change in the total spin quantum number. In the case of a dimer, this is usually only possible if the coupling between the two pentacenes is sufficiently weak. In this study, we present two platinum-bridged pentacene dimers in which the pentacenes are coupled strongly, so that spin-decorrelation yielding (T₁ + T₁) was initially expected to be outcompeted by triplet–triplet annihilation (TTA) to the ground state. Both platinum-bridged pentacene dimers undergo quantitative formation of the (T₁T₁) state on a picosecond timescale that is unaffected by the internal heavy-atom effect of the platinum. Instead of TTA of (T₁T₁) to the ground state, the internal heavy-atom effect allows for ¹(T₁T₁)–³(T₁T₁) and ¹(T₁T₁)–⁵(T₁T₁) mixing and, thus, triggers subsequent TTA to the (T₁S₀) state and minor formation of (T₁ + T₁). A combination of transient absorption and transient IR spectroscopy is applied to investigate the mechanism of the (T₁T₁) formation in both dimers. Using a combination of experiment and quantum chemical calculations, we are able to observe a transition from the CT-mediated to the direct SF mechanism and identify relevant factors that influence the mechanism that dominates SF in pentacene. Moreover, a combination of time-resolved optical and electron paramagnetic resonance spectroscopic data allows us to develop a kinetic model that describes the effect of enhanced spin–orbit couplings on the correlated triplet pair state.