Description of Conical Intersections with Density Functional Methods

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.

The Role of Aqueous Solvation on the Intersystem Crossing of Nitrophenols

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

Signatures of Conical Intersections in Extreme Ultraviolet Photoelectron Spectra of Furan Measured with 15 fs Time Resolution

Ultrafast internal conversion of furan upon deep UV excitation at 200 nm is studied by using extreme ultraviolet time-resolved photoelectron spectroscopy with a time resolution of 15 fs. Ballistic nuclear wavepacket motion from the 1B2(ππ*) state to the ground state is fully observed using 21.7 eV probe pulses. Through the performance of a comparison with the results of electronic structure calculations at the MS(3)-CASPT2(10,10)/cc-pVTZ level of theory, the photoelectron signals from the conical intersection regions are identified.

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.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory

The density functional theory (DFT) and linear response (LR) time-dependent (TD)-DFT are of the utmost importance for routine computations. However, the single reference formulation of DFT suffers in the description of open-shell singlet systems such as diradicals and bond-breaking. LR-TDDFT, on the other hand, finds difficulties in the modeling of conical intersections, doubly excited states, and core-level excitations. In this Perspective, we demonstrate that many of these limitations can be overcome by recently developed mixed-reference (MR) spin-flip (SF)-TDDFT, providing an alternative yet accurate route for such challenging situations. Empowered by the practicality of the LR formalism, it is anticipated that MRSF-TDDFT can become one of the major workhorses for general routine tasks.

Ultrafast Excited State Aromatization in Dihydroazulene

Excited-state aromatization dynamics in the photochemical ring opening of dihydroazulene (DHA) is investigated by nonadiabatic molecular dynamics simulations in connection with the mixed-reference spin-flip (MRSF)-TDDFT method. It is found that, in the main reaction channel, the ring opening occurs in the excited state in a sequence of steps with increasing aromaticity. The first stage lasting ca. 200 fs produces an 8π semiaromatic S₁ minimum (S_1, min) through an ultrafast damped bond length alternation (BLA) movement synchronized with a partial planarization of the cycloheptatriene ring. An additional ca. 200 fs are required to gain the vibrational energy needed to overcome a ring-opening transition state characterized by an enhanced Baird aromaticity. Unlike other BLA motions of ππ* state, it was shown that their damping is a characteristic feature of aromatic bond-equalization process. In addition, some minor channels of the reaction have also been discovered, where noticeably higher barriers of the S₁ non/antiaromatic transition structures must be surmounted. These anti-Baird channels led to reformation of DHA or other closed-ring products. The observed competition between the Baird and anti-Baird channels suggests that the quantum yield of photochemical products can be controllable by tipping their balance. Hence, here we suggest including the concept of anti-Baird, which would expand the applicability of Baird rule to much broader situations.

A Look Inside the Black Box of Machine Learning Photodynamics Simulations

ConspectusPhotochemical reactions are of great importance in chemistry, biology, and materials science because they take advantage of a renewable energy source, mild reaction conditions, and high atom economy. Light absorption can excite molecules to a higher energy electronic state of the same spin multiplicity. The following nonadiabatic processes induce molecular transformations that afford exotic molecular architectures and high-energy-isomers that are inaccessible by thermal means. Computational simulations now complement time-resolved instrumentation to reveal ultrafast excited-state mechanistic information for photochemical reactions that is essential in disentangling elusive spectroscopic features, excited-state lifetimes, and excited-state mechanistic critical points. Nonadiabatic molecular dynamics (NAMD), powered by surface hopping techniques, is among the most widely applied techniques to model the photochemical reactions of medium-sized molecules. However, the computational efficiency is limited because of the requisite thousands of multiconfigurational quantum-chemical calculations multiplied by hundreds of trajectories. Machine learning (ML) has emerged as a revolutionary force in computational chemistry to predict the outcome of the resource-intensive multiconfigurational calculations on the fly. An ML potential trained with a substantial set of quantum-chemical calculations can predict the energies and forces with errors under chemical accuracy at a negligible cost. The integration of ML potentials in NAMD dramatically extends the maximum simulation time scale by ∼10 000-fold to the nanosecond regime.In this Account, we present a comprehensive demonstration of ML photodynamics simulations and summarize our most recent applications in resolving complex photochemical reactions. First, we address three fundamental components of ML techniques for photodynamics simulations: the quantum-chemical data set, the ML potential, and NAMD. Second, we describe best practices in building training data and our procedure toward training the ML photodynamics model with our recent literature contributions. We introduce a convenient training data generation scheme combining Wigner sampling and geometrical interpolation. It trains reliable and effective ML potentials suitable for subsequent active learning to detect undersampled data. We demonstrate how active learning automatically discovers new mechanistic pathways and reproduces experimental results. We point out that atomic permutation is an essential data augmentation approach to improve the learnability of distance-based molecular descriptors for highly symmetric molecules. Third, we demonstrate the utility of ML-photodynamics by showing the results of ML photodynamics simulations of (1) photo-torquoselective 4π disrotatory electrocyclic ring closing of norbornyl cyclohexadiene, which reveals a thermal conversion from experimentally unobserved intermediates to the reactant in 1 ns; (2) [2 + 2] photocycloaddition of substituted [3]-syn-ladderdienes in competition with 4π and 6π electrocyclic ring-opening reactions, uncovering substituent effects to explain the reported increased quantum yield of substituted cubane precursors; and (3) photochemical 4π disrotatory electrocyclic reactions of fluorobenzenes in nanoseconds with XMS-CASPT2-level training data. We expect this Account to broaden understanding of ML photodynamics and inspire future developments and applications to increasingly large molecules within complex environments on long time scales.

InteraChem: Exploring Excited States in Virtual Reality with Ab Initio Interactive Molecular Dynamics

InteraChem is an ab initio interactive molecular dynamics (AI-IMD) visualizer that leverages recent advances in virtual reality hardware and software, as well as the graphical processing unit (GPU)-accelerated TeraChem electronic structure package, in order to render quantum chemistry in real time. We introduce the exploration of electronically excited states via AI-IMD using the floating occupation molecular orbital-complete active space configuration interaction method. The optimization tools in InteraChem enable identification of excited state minima as well as minimum energy conical intersections for further characterization of excited state chemistry in small- to medium-sized systems. We demonstrate that finite-temperature Hartree-Fock theory is an efficient method to perform ground state AI-IMD. InteraChem allows users to track electronic properties such as molecular orbitals and bond order in real time, resulting in an interactive visualization tool that aids in the interpretation of excited state chemistry data and makes quantum chemistry more accessible for both research and educational purposes.

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.

Theoretical Study of Light-Induced Crosslinking Reaction Between Pyrimidine DNA Bases and Aromatic Amino Acids

Low-lying electronic excited states and their relaxation pathways as well as energetics of the crosslinking reaction between uracil as a model system for pyrimidine-type building blocks of DNA and RNA and benzene as a model system for aromatic groups of tyrosine (Tyr) and phenylalanine (Phe) amino acids have been studied in the framework of density functional theory. The equilibrium geometries of the ground and electronic excited states as well as the crossing points between the potential energy surfaces of the uracil–benzene complex were computed. Based on these results, different relaxation pathways of the electronic excited states that lead to either back to the initial geometry configuration or the dimerization between the six-membered rings of the uracil–benzene complex have been identified, and the energetic conditions for their occurrence are discussed. It can be concluded that the DNA–protein crosslinking reaction can be induced by the external electromagnetic field via the dimerization reaction between the six-membered rings of the uracil–benzene pair at the electronic excited-state level of the complex. In the case of the uracil–phenol complex, the configuration of the cyclic adduct (dimerized) conformation is less likely to be formed.

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.

Signatures of Conical Intersection Dynamics in the Time-Resolved Photoelectron Spectrum of Furan: Theoretical Modeling with an Ensemble Density Functional Theory Method

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck-Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics.

Nonadiabatic Dynamics Simulation Predict Intersystem Crossing in Nitroaromatic Molecules on a Picosecond Time Scale

Previous time-resolved spectroscopic experiments and static quantum-chemical calculations attributed nitronaphthalene derivatives one of the fastest time scales for intersystem crossing within organic molecules, reaching the 100 fs mark. Nonadiabatic dynamics simulations on three nitronaphthalene derivatives challenge this view, showing that the experimentally observed ∼100 fs process corresponds to internal conversion in the singlet manifolds. Intersystem crossing, instead, takes place on a longer time scale of ∼1 ps. The dynamics simulations further reveal that the spin transitions occur via two distinct pathways with different contribution for the three systems, which are determined by electronic factors and the torsion of the nitro group. This study, therefore, indicates that the existence of sub-picosecond intersystem crossing in other nitroaromatic molecules should be questioned.

Conical Intersections in Organic Molecules: Benchmarking Mixed-Reference Spin-Flip Time-Dependent DFT (MRSF-TD-DFT) vs Spin-Flip TD-DFT

The mixed-reference spin-flip time-dependent density functional theory (MRSF-TD-DFT) method eliminates the erroneous spin contamination of the SF-TD-DFT methodology, while retaining the conceptual and practical simplicity of the latter. The availability of the analytic gradient of the energy of the MRSF-TD-DFT response states enables automatic geometry optimization of the targeted states. Here, we apply the new method to optimize the geometry of several S₁/S₀ conical intersections occurring in typical organic molecules. We demonstrate that MRSF-TD-DFT is capable of producing the correct double-cone topology of the intersections and describing the geometry of the lowest-energy conical intersections and their relative energies with accuracy matching that of the best multireference wavefunction ab initio methods. In this regard, MRSF-TD-DFT differs from many popular single-reference methods, such as, e.g., the linear response TD-DFT method, which fail to produce the correct topology of the intersections. As the new methodology completely eliminates the ambiguity with the identification of the response states as proper singlets or triplets, which is plaguing the SF-TD-DFT calculations, it can be used for automatic geometry optimization and molecular dynamic simulations not requiring constant human intervention.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series.

Description of ground and excited electronic states by ensemble density functional method with extended active space

An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the new method correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena.

Challenges in XUV Photochemistry Simulations: A Case Study on Ultrafast Fragmentation Dynamics of the Benzene Radical Cation

The challenges of simulating extreme ultraviolet (XUV)-induced dissociation dynamics of organic molecules on a multitude of coupled potential energy surfaces are discussed for the prototypical photoionization of benzene. The prospects of Koopmans' theorem-based electronic structure calculations in combination with classical trajectories and Tully's fewest switches surface hopping are explored. It is found that a Koopmans' theorem-based approach overestimates the CH dissociation barrier and thus underestimates the fragmentation yield. However, the nonadiabatic population dynamics are in good agreement with previous approaches, indicating that the Koopmans' theorem based potentials are well described around the Franck-Condon point. This is explicitly tested for the ground state potential of the benzene cation employing CASPT2 calculations, for which very good agreement is found. This work highlights the need for efficient electronic structure approaches that can treat medium-sized organic molecules with a multitude of coupled excited states and several dissociation channels.

Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.

QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor

A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S₁ state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S₁ energy minimum and the S₁/S₀ conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S₁ state in the vicinity of the conical intersection.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Benzimidazolylquinoxalines: novel fluorophores with tuneable sensitivity to solvent effects

We report on the photophysical properties, conjugation, conformational behavior, intra- and intermolecular hydrogen bonds (HBs) of a series of novel fluorophores, consisting of 3-arylquinoxaline and benzimidazole moieties linked by a single CC bond. Computations employing density functional theory (DFT) reveal that conjugation between these moieties stabilizes syn-conformers with two HB centers located on the same side of the molecule. Anti-conformers form stronger intermolecular HBs with DMSO and DMF than syn-conformers, and this influences the energy gap between syn- and anti-forms, especially upon excitation of the molecules to the S₁ state. Substituents introduced in various positions of the molecules modify their conformational behavior, and mutual disposition of excited singlet states relative to the ground states. Various substitution patterns produce very different effects on relative quantum yield of luminescence: from a moderate increase in polar DMSO and DMF relative to 1,2-dichloroethane solutions to complete quenching of emission which is observable in polar media. The observed behavior is understood with the aid of DFT and time-dependent DFT calculations. The tuneability of the spectroscopic range of the luminescence and especially of its sensitivity to environmental effects allows rational design of the novel fluorophores of this family for various applications.

Beyond Kohn-Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory

A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn-Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.

A QTAIM and stress tensor investigation of the torsion path of a light-driven fluorene molecular rotary motor

The utility of the QTAIM/stress tensor analysis method for characterizing the photoisomerization of light driven molecular rotary machines is investigated on the example of the torsion path in fluorene molecular motor. The scalar and vector descriptors of QTAIM/stress tensor reveal additional information on the bonding interactions between the rotating units of the motor, which cannot be obtained from the analysis of the ground and excited state potential energy surfaces. The topological features of the fluorene motor molecular graph display that, upon the photoexcitation a certain increase in the torsional stiffness of the rotating bond can be attributed to the increasing topological stability of the rotor carbon atom attached to the rotation axle. The established variations in the torsional stiffness of the rotating bond may cause transfer of certain fraction of the torsional energy to other internal degrees of freedom, such as the pyramidalization distortion. © 2016 Wiley Periodicals, Inc.

Conical Intersections from Particle-Particle Random Phase and Tamm-Dancoff Approximations

The particle-particle random phase approximation (pp-RPA) and the particle-particle Tamm-Dancoff approximation (pp-TDA) are applied to the challenging conical intersection problem. Because they describe the ground and excited states on the same footing and naturally take into account the interstate interaction, these particle-particle methods, especially the pp-TDA, can correctly predict the dimensionality of the conical intersection seam as well as describe the potential energy surface in the vicinity of conical intersections. Though the bond length of conical intersections is slightly underestimated compared with the complete-active-space self-consistent field (CASSCF) theory, the efficient particle-particle methods are promising for conical intersections and nonadiabatic dynamics.

Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases

The photophysics and photochemistry of DNA is of great importance due to the potential damage of the genetic code by UV light. Quantum mechanical studies have played a key role in interpretating the results of modern time-resolved pump-probe spectroscopy, and in elucidating the main photoactivated reactive paths. This review provides a concise, complete picture of the computational studies carried out, approximately, in the past decade. We start with an overview of the photophysics of the nucleobases in the gas phase and in solution. We discuss the proposed mechanisms for ultrafast decay to the ground state, that involve conical intersections, consider the role of triplet states, and analyze how the solvent modulates the photophysics. Then we move to larger systems, from dinucleotides to single- and double-stranded oligonucleotides. We focus on the possible role of charge transfer and delocalized or excitonic states in the photophysics of these systems and discuss the main photochemical paths. We finish with an outlook on the current challenges in the field and future directions of research.