Exploring the Conical Intersection Seam: The Seam Space Nudged Elastic Band Method

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.

Excited State Dynamics in Unidirectional Photochemical Molecular Motors

Unidirectional photochemically driven molecular motors (PMMs) convert the energy of absorbed light into continuous rotational motion. As such they are key components in the design of molecular machines. The prototypical and most widely employed class of PMMs is the overcrowded alkenes, where rotational motion is driven by successive photoisomerization and thermal helix inversion steps. The efficiency of such PMMs depends upon the speed of rotation, determined by the rate of ground state thermal helix inversion, and the quantum yield of photoisomerization, which is dependent on the excited state energy landscape. The former has been optimized by synthetic modification across three generations of overcrowded alkene PMMs. These improvements have often been at the expense of photoisomerization yield, where there remains room for improvement. In this perspective we review the application of ultrafast spectroscopy to characterize the excited state dynamics in PMMs. These measurements lead to a general mechanism for all generations of PMMs, involving subpicosecond decay of a Franck-Condon excited state to populate a dark excited state which decays within picoseconds via conical intersections with the electronic ground state. The model is discussed in the context of excited state dynamics calculations. Studies of PMM photochemical dynamics as a function of solvent suggest exploitation of intramolecular charge transfer and solvent polarity as a route to controlling photoisomerization yield. A test of these ideas for a first generation motor reveals a high degree of solvent control over isomerization yield. These results suggest a pathway to fine control over the performance of future PMMs.

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3 s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200 fs, with dissociation events finished after 300 fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

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.

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.

Galván I, Rivalta I, Aquilante F, Garavelli M, Lindh R, Segarra-Martí J. Characterizing Conical Intersections in DNA/RNA Nucleobases with Multiconfigurational Wave Functions of Varying Active Space Size

We characterize the photochemically relevant conical intersections between the lowest-lying accessible electronic excited states of the different DNA/RNA nucleobases using Cholesky decomposition-based complete active space self-consistent field (CASSCF) algorithms. We benchmark two different basis set contractions and several active spaces for each nucleobase and conical intersection type, measuring for the first time how active space size affects conical intersection topographies in these systems and the potential implications these may have toward their description of photoinduced phenomena. Our results show that conical intersection topographies are highly sensitive to the electron correlation included in the model: by changing the amount (and type) of correlated orbitals, conical intersection topographies vastly change, and the changes observed do not follow any converging pattern toward the topographies obtained with the largest and most correlated active spaces. Comparison across systems shows analogous topographies for almost all intersections mediating population transfer to the dark 1nO/Nπ* states, while no similarities are observed for the "ethylene-like" conical intersection ascribed to mediate the ultrafast decay component to the ground state in all DNA/RNA nucleobases. Basis set size seems to have a minor effect, appearing to be relevant only for purine-based derivatives. We rule out structural changes as a key factor in classifying the different conical intersections, which display almost identical geometries across active space and basis set change, and we highlight instead the importance of correctly describing the electronic states involved at these crossing points. Our work shows that careful active space selection is essential to accurately describe conical intersection topographies and therefore to adequately account for their active role in molecular photochemistry.

Investigation on pore structure regulation of activated carbon derived from sargassum and its application in supercapacitor

In order to realize the effective regulation of the pore structure of activated carbon and optimize its pore structure properties as electrode material, the effects of activation temperature, activation time and impregnation ratio on the specific surface area, total pore volume and average pore diameter of activated carbon prepared by sargassum are studied by orthogonal experiment. In addition, the electrochemical properties of sargassum-based activated carbon (SAC) and the relationship between the gravimetric capacitance and specific surface area of SAC are also studied. The SACs prepared under all conditions have high specific surface area (≥ 2227 m2 g-1) and developed pore structure, in which the pore diameter of micropores mainly concentrated in 0.4 ~ 0.8 nm, the pore diameter of mesopores mainly concentrated in 3 ~ 4 nm, and the number of micropores is far more than that of mesopores. In the activation process, the impregnation ratio has the greatest effect on the specific surface area of SAC, the activation temperature and impregnation ratio have significant effect on the total pore volume of SAC, and the regulation of the average pore diameter of SAC is mainly realized by adjusting the activation temperature. The SACs exhibit typical electric double layer capacitance performances on supercapacitors, delivering superior gravimetric capacitance of 237.3 F g-1 in 6 mol L-1 KOH electrolyte system at current density of 0.5 A g-1 and excellent cycling stability of capacitance retention of 92% after 10,000 cycles. A good linear relationship between gravimetric capacitance and specific surface area of SAC is observed.

A Comparison of Partial Atomic Charges for Electronically Excited States

Partial atomic charges are a useful and intuitive concept for understanding molecular properties and chemical reaction mechanisms, showing how changes in molecular geometry can affect the flow of electronic charge within a molecule. However, the use of partial atomic charges remains relatively uncommon in the characterization of excited-state electronic structure. Here, we show how well-established partial atomic charge methods perform for interatomic, intermolecular, and interbond electron transfer in electronically excited states. Our results demonstrate the utility of real-space partial atomic charges for interpreting the electronic structures that arise in excited-state processes. Furthermore, we show how this analysis can be used to demonstrate that analogous electronic structures arise near photochemically relevant conical intersection regions for several conjugated polyenes. On the basis of our analysis, we find that charges computed using the iterative Hirshfeld approach provide results which are consistent with chemical intuition and are transferable between homologous molecular systems.

Internal conversion of the anionic GFP chromophore: in and out of the I-twisted S1/S0 conical intersection seam

The functional diversity of the green fluorescent protein (GFP) family is intimately connected to the interplay between competing photo-induced transformations of the chromophore motif, anionic p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI^-). Its ability to undergo Z/E-isomerization is of particular importance for super-resolution microscopy and emerging opportunities in optogenetics. Yet, key dynamical features of the underlying internal conversion process in the native HBDI^- chromophore remain largely elusive. We investigate the intrinsic excited-state behavior of isolated HBDI^- to resolve competing decay pathways and map out the factors governing efficiency and the stereochemical outcome of photoisomerization. Based on non-adiabatic dynamics simulations, we demonstrate that non-selective progress along the two bridge-torsional (i.e., phenolate, P, or imidazolinone, I) pathways accounts for the three decay constants reported experimentally, leading to competing ultrafast relaxation primarily along the I-twisted pathway and S₁ trapping along the P-torsion. The majority of the population (∼70%) is transferred to S₀ in the vicinity of two approximately enantiomeric minima on the I-twisted intersection seam (MECI-Is). Despite their sloped, reactant-biased topographies (suggesting low photoproduct yields), we find that decay through these intersections leads to products with a surprisingly high quantum yield of ∼30%. This demonstrates that E-isomer generation results at least in part from direct isomerization on the excited state. A photoisomerization committor analysis reveals a difference in intrinsic photoreactivity of the two MECI-Is and that the observed photoisomerization is the combined result of two effects: early, non-statistical dynamics around the less reactive intersection followed by later, near-statistical behavior around the more reactive MECI-I. Our work offers new insight into internal conversion of HBDI^- that both establishes the intrinsic properties of the chromophore and enlightens principles for the design of chromophore derivatives and protein variants with improved photoswitching properties.

On Electron Pair Rearrangements in Photochemical Reactions: 1,3-Cyclohexadiene Ring Opening

1,3-Cyclohexadiene ring opening has been studied within the bonding evolution theory (BET) framework. We have focused on describing for the first time the electron pair rearrangements leading to the cis-1,3,5-hexatriene (HT) product from CHD. The nature of bonding in this process begins with the weakening of the double bonds in the Franck-Condon region. Along the 1¹B surface, the C-C sigma bond weakens. Meanwhile, its density redistributes toward the whole CHD ring, mainly over double bonds. Breaking of this bond occurs on the 2¹A surface due to the symmetrical splitting of pair density from this region. This density redistributes toward the reaction center once the pericyclic minimum is reached. The formation of the double bonds that characterize HT occurs gradually in the ground state. However, near the 2¹A/1¹A intersection, these bonds are partially established.

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.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

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

metaFALCON: A Program Package for Automatic Sampling of Conical Intersection Seams Using Multistate Metadynamics

The multistate metadynamics for automatic exploration of conical intersection seams and systematic location of minimum energy crossing points in molecular systems and its implementation into the software package metaFALCON is presented. Based on a locally modified energy gap between two Born-Oppenheimer electronic states as a collective variable, multistate metadynamics trajectories are driven toward an intersection point starting from an arbitrary ground state geometry and are subsequently forced to explore the conical intersection seam landscape. For this purpose, an additional collective variable capable of distinguishing structures within the seam needs to be defined and an additional bias is introduced into the off-diagonal elements of an extended (multistate) electronic Hamiltonian. We demonstrate the performance of the algorithm on the examples of the 1,3-butadiene, benzene, and 9H-adenine molecules, where multiple minimum energy crossing points could be systematically located using the Wiener number or Cremer-Pople parameters as collective variables. Finally, with the example of 9H-adenine, we show that the multistate metadynamics potential can be used to obtain a global picture of a conical intersection seam. Our method can be straightforwardly connected with any ab initio or semiempirical electronic structure theory that provides energies and gradients of the respective electronic states and can serve for systematic elucidation of the role of conical intersections in the photophysics and photochemistry of complex molecular systems, thus complementing nonadiabatic dynamics simulations.

Discovery of conical intersection mediated photochemistry with growing string methods

Conical intersections (CIs) are important features of photochemistry that determine yields and selectivity. Traditional CI optimizers require significant human effort and chemical intuition, which typically restricts searching to only a small region of the CI space. Herein, a systematic approach utilizing the growing string method is introduced to locate multiple CIs. Unintuitive MECI are found using driving coordinates that can be generated using a combinatorial search, and subsequent optimization allows reaction pathways, transition states, products, and seam-space pathways to be located. These capabilities are demonstrated by application to two prototypical photoisomerization reactions and the dimerization of butadiene. In total, many reaction pathways were uncovered, including the elusive stilbene hula-twist mechanism, and a previously unidentified product in butadiene dimerization. Overall, these results suggest that growing string methods provide a predictive strategy for exploring photochemistry.

A new twist in the photophysics of the GFP chromophore: a volume-conserving molecular torsion couple

Dynamics of a nonplanar GFP chromophore are studied experimentally and theoretically. Coupled torsional motion is responsible for the ultrafast decay.

The simple structure of the chromophore of the green fluorescent protein (GFP), a phenol and an imidazolone ring linked by a methyne bridge, supports an exceptionally diverse range of excited state phenomena. Here we describe experimentally and theoretically the photochemistry of a novel sterically crowded nonplanar derivative of the GFP chromophore. It undergoes an excited state isomerization reaction accompanied by an exceptionally fast (sub 100 fs) excited state decay. The decay dynamics are essentially independent of solvent polarity and viscosity. Excited state structural dynamics are probed by high level quantum chemical calculations revealing that the fast decay is due to a conical intersection characterized by a twist of the rings and pyramidalization of the methyne bridge carbon. The intersection can be accessed without a barrier from the pre-twisted Franck–Condon structure, and the lack of viscosity dependence is due to the fact that the rings twist in the same direction, giving rise to a volume-conserving decay coordinate. Moreover, the rotation of the phenyl, methyl and imidazolone groups is coupled in the sterically crowded structure, with the methyl group translating the rotation of one ring to the next. As a consequence, the excited state dynamics can be viewed as a torsional couple, where the absorbed photon energy leads to conversion of the out-of-plane orientation from one ring to the other in a volume conserving fashion. A similar modification of the range of methyne dyes may provide a new family of devices for molecular machines, specifically torsional couples.

On the importance of initial conditions for excited-state dynamics

The vast majority of ab initio excited-state simulations are performed within semiclassical, trajectory-based approaches. Apart from the underlying electronic-structure theory, the reliability of the simulations is controlled by a selection of initial conditions for the classical trajectories. We discuss appropriate choices of initial conditions for simulations of different experimental arrangements: dynamics initiated by continuum-wave (CW) laser fields or triggered by ultrashort laser pulses.

Geometry optimization made simple with translation and rotation coordinates

The effective description of molecular geometry is important for theoretical studies of intermolecular interactions. Here we introduce a new translation-rotation-internal coordinate (TRIC) system which explicitly includes the collective translations and rotations of molecules, or parts of molecules such as monomers or ligands, as degrees of freedom. The translations are described as the centroid position and the orientations are represented with the exponential map parameterization of quaternions. When TRIC is incorporated into geometry optimization calculations, the performance is consistently superior to existing coordinate systems for a diverse set of systems including water clusters, organic semiconductor donor-acceptor complexes, and small proteins, all of which are characterized by nontrivial intermolecular interactions. The method also introduces a new way to scan the molecular orientations while allowing orthogonal degrees of freedom to relax. Our findings indicate that an explicit description of molecular translation and rotation is a natural way to traverse the many-dimensional potential energy surface.

Early events in the photochemistry of 5-diazo Meldrum's acid: formation of a product manifold in C–N bound and pre-dissociated intersection seam regions

Photolysis of 5-diazo Meldrum's acid yields three different primary products in a sub-ps scale. High-level computations show that this is due to the presence of an extended seam of intersection associated to different reaction paths.

Accurate nonadiabatic dynamics

This Perspective addresses the use of coupled diabatic potential energy surfaces (PESs) together with rigorous quantum dynamics in full or reduced dimensional coordinate spaces to obtain accurate solutions to problems in nonadiabatic dynamics.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

Excited States and Photochemistry of Chromophores in the Photoactive Proteins Explored by the Combined Quantum Mechanical and Molecular Mechanical Calculations

A photoactive protein usually contains a unique chromophore that is responsible for the initial photoresponse and functions of the photoactive protein are determined by the interaction between the chromophore and its protein surroundings. The combined quantum mechanical and molecular mechanical (QM/MM) approach is demonstrated to be a very useful tool for exploring structures and functions of a photoactive protein with the chromophore and its protein surroundings treated by the QM and MM methods, respectively. In this review, we summarize the basic formulas of the QM/MM approach and emphasize its applications to excited states and photoreactions of chromophores in rhodopsin protein, photoactive yellow protein, and green fluorescent protein.

Assessment of approximate computational methods for conical intersections and branching plane vectors in organic molecules

Quantum-chemical computational methods are benchmarked for their ability to describe conical intersections in a series of organic molecules and models of biological chromophores. Reference results for the geometries, relative energies, and branching planes of conical intersections are obtained using ab initio multireference configuration interaction with single and double excitations (MRCISD). They are compared with the results from more approximate methods, namely, the state-interaction state-averaged restricted ensemble-referenced Kohn-Sham method, spin-flip time-dependent density functional theory, and a semiempirical MRCISD approach using an orthogonalization-corrected model. It is demonstrated that these approximate methods reproduce the ab initio reference data very well, with root-mean-square deviations in the optimized geometries of the order of 0.1 Å or less and with reasonable agreement in the computed relative energies. A detailed analysis of the branching plane vectors shows that all currently applied methods yield similar nuclear displacements for escaping the strong non-adiabatic coupling region near the conical intersections. Our comparisons support the use of the tested quantum-chemical methods for modeling the photochemistry of large organic and biological systems.

A comprehensive spectroscopic investigation of α-(2-naphthyl)-N-methylnitrone: a computational study on photochemical nitrone–oxaziridine conversion and thermal E–Z isomerization processes

CASSCF and 2-layer hybrid ONIOM-based computational studies on α-(2-naphthyl)-N-methylnitrone have proposed its photochemical oxaziridine formation and thermal E–Z isomerization mechanisms.

Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.

Photochemistry and photophysics at extended seams of conical intersection

The role of extended seams of conical intersection in excited-state mechanisms is reviewed. Seams are crossings of the potential energy surface in many dimensions where the decay from the excited to the ground state can occur, and the extended seam is composed of different segments lying along a reaction coordinate. Every segment is associated with a different primary photoproduct, which gives rise to competing pathways. This idea is first illustrated for fulvene and ethylene, and then it is used to explain more complex cases such as the dependence of the isomerisation of retinal chromophore isomers on the protein environment, the dependence of the efficiency of the azobenzene photochemical switch on the wavelength of irradiation and the direction of the isomerisation, and the coexistence of different mechanisms in the photo-induced Wolff rearrangement of diazonaphthoquinone. The role of extended seams in the photophysics of the DNA nucleobases and the relationship between two-state seams and three-state crossings is also discussed. As an outlook, the design of optical control strategies based on the passage of the excited molecule through the seam is considered, and it is shown how the excited-state lifetime of fulvene can be modulated by shaping the energy of the seam.

Conical intersections and low-lying electronic states of tetrafluoroethylene

The low-lying electronic states of tetrafluoroethylene (C2 F4 ) are characterized theoretically for the first time using equation-of-motion coupled cluster theory (EOM-CCSD), and complete active space self-consistent field (CASSCF) and second-order perturbation theory (CASPT2). Computations are performed for vertical excitation energies, equilibrium geometries, minimum-energy conical intersections, and potential energy curves along three geometric coordinates: 1) twisting of the FCCF dihedral angle, 2) pyramidalization of the CF2 group, and 3) migration of a fluorine atom resulting in an ethylidene-like (CF3 CF) structure. The results suggest two relaxation pathways from the Rydberg-3s excited electronic state to the ground state. These relaxation pathways are discussed in conjunction with the femtosecond photoionization spectroscopy results of Trushin et al. [ChemPhysChem- 2004, 5, 1389].

Assessment of Density Functional Methods for Obtaining Geometries at Conical Intersections in Organic Molecules

A number of commonly available density functionals have been tested for their ability to describe the energetics and the geometry at conical intersections in connection with the spin-restricted ensemble referenced Kohn–Sham (REKS) method. The minimum energy conical intersections have been optimized for several molecular systems, which are widely used as paradigmatic models of photochemical rearrangements and models of biological chromophores. The results of the calculations are analyzed using the sign-change theorem of Longuet-Higgins and a method of elementary reaction coordinates of Haas et al. The latter approach helps to elucidate the differences between the geometries at conical intersections as predicted by the multireference wave function ab initio methods and by the density functional methods. Overall, the BH&HLYP density functional yields the best results for the conical intersection geometries and energetics.