Conical Intersections: The New Conventional Wisdom

A finite-element visualization of quantum reactive scattering. II. Nonadiabaticity on coupled potential energy surfaces

This is the second in a series of papers detailing a MATLAB based implementation of the finite element method applied to collinear triatomic reactions. Here, we extend our previous work to reactions on coupled potential energy surfaces. The divergence of the probability current density field associated with the two electronically adiabatic states allows us to visualize in a novel way where and how nonadiabaticity occurs. A two-dimensional investigation gives additional insight into nonadiabaticity beyond standard one-dimensional models. We study the F((2)P) + HCl and F((2)P) + H2 reactions as model applications. Our publicly available code (http://www2.chem.umd.edu/groups/alexander/FEM) is general and easy to use.

Description of Conical Intersections with Density Functional Methods

Conical intersections are perhaps the most significant mechanistic features of chemical reactions occurring through excited states. By providing funnels for efficient non-adiabatic population transfer, conical intersections govern the branching ratio of products of such reactions, similar to what the transition states do for ground-state reactivity. In this regard, intersections between the ground and the lowest excited states play a special role, and the correct description of the potential energy surfaces in their vicinity is crucial for understanding the mechanism and dynamics of excited-state reactions. The methods of density functional theory, such as time-dependent density functional theory, are widely used to describe the excited states of large molecules. However, are these methods suitable for describing the conical intersections or do they lead to artifacts and, consequently, to erroneous description of reaction dynamics? Here we address the first part of this question and analyze the ability of several density functional approaches, including the linear-response time-dependent approach as well as the spin-flip and ensemble formalisms, to provide the correct description of conical intersections and the potential energy surfaces in their vicinity. It is demonstrated that the commonly used linear-response time-dependent theory does not yield a proper description of these features and that one should instead use alternative computational approaches.

A theoretical exploration of the nonradiative deactivation of hydrogen-bond complexes: isoindole–pyridine and quinoline–pyrrole

CC2 potential energy profiles of the ground and excited states of the isoindole–pyridine complex along the proton transfer reaction coordinate are studied.

Identifying and tracing potential energy surfaces of electronic excitations with specific character via their transition origins: application to oxirane

We show that the transition origins of electronic excitations identified by quantified natural transition orbital (QNTO) analysis can be employed to connect potential energy surfaces (PESs) according to their character across a wide range of molecular geometries.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field.

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.

Ab initio study of potential ultrafast internal conversion routes in oxybenzone, caffeic acid, and ferulic acid: implications for sunscreens

Oxybenzone (OB) and ferulic acid (FA) both find use in commercial sunscreens; caffeic acid (CA) differs from FA by virtue of an -OH group in place of a -OCH3 group on the aromatic ring. We report the results of ab initio calculations designed to explore the excited state nonradiative relaxation pathways that provide photostability to these molecules and the photoprotection they offer toward UV-A and UV-B radiation. In the case of OB, internal conversion (IC) is deduced to occur on ultrafast time scales, via a barrierless electron-driven H atom transfer pathway from the S1(1(1)nπ*) state to a conical intersection (CI) with the ground (S0) state potential energy surface (PES). The situation with respect to CA and FA is somewhat less clear-cut, with low energy CIs identified by linking excited states to the S0 state following photoexcitation and subsequent evolution along (i) a ring centered out-of-plane deformation coordinate, (ii) the E/Z isomerism coordinate and, in the case of CA, (iii) an O-H stretch coordinate. Analogy with catechol suggests that the last of these processes (if active) would lead to radical formation (and thus potential phototoxicity), encouraging a suggestion that FA might be superior to CA as a sunscreen ingredient.

Landscapes of four-enantiomer conical intersections for photoisomerization of stilbene: CASSCF calculation

The photoisomerization of cis- and trans-stilbene through conical intersections (CI) is mainly governed by four dihedral angles around central C═C double bonds. The two of them are C-C═C-C and H-C═C-H dihedral angles that are found to form a mirror rotation coordinate, and the mirror plane appears at the two dihedral angles equal to zeros with which the middle state is defined through partial optimization. There exist the first-type of hula-twist-CI enantiomers, the second-type of hula-twist-CI enantiomers, the first-type of one-bond-flip-CI enantiomers, and the second type of one-bond-flip-CI enantiomers as well as cis-enantiomers and trans-enantiomers with respect to this mirror plane. The complete active space self-consistent field method is employed to calculate minimum potential energy profile along the mirror rotation coordinate for each enantiomers, and it is found that the left-hand manifold and the right-hand manifold of potential energy surfaces can be energetically transferred via photoisomerization. Furthermore, two-dimensional potential energy surfaces in terms of the branching plane g-h coordinates are constructed at vicinity of each conical intersection, and the landscapes of conical intersections show distinct feature, and in excited-state four potential wells separated in different section of g-h plane related to different conical intersections which indicate different photoisomerization pathways.

Vibronic structures and dynamics of the predissociating dimethyl sulfide and its isotopomers (CH₃SCH₃, CD₃SCD₃, CH₃SCD₃) at the conical intersection

Conical intersection seam comprised of crossing surfaces of two lowest excited states of dimethyl sulfide (DMS) has been directly accessed by the one-photon excitation from the ground equilibrium state. Since the S-C bond rupture takes place promptly, the molecular structure on the excited state effectively belongs to C(S) symmetry. Namely, excited states of 1(1)B1 and 1(1)A2 in C(2)V become 1(1)A'' and 2(1)A'' states in C(S), respectively, and the optical transition from the ground equilibrium state to the dissociating molecule at the conical intersection seam is symmetry-allowed to facilitate the nonadiabatic transition on the 2(1)A'' state, leading eventually to the CH3S + CH3 products. The dynamic study of DMS, in this sense, gives the great opportunity to unravel the vibronic structure of the conical intersection seam by the conventional one-photon excitation method. In this work, utilizing the photofragment excitation (PHOFEX) spectroscopic method, the vibronic structures of DMS and its isotope analogs (CD3SCD3, CH3SCD3) at the conical intersection seam have been revealed, providing accurate lifetimes and detailed dynamics associated with individual vibronic transitions. The lifetime of the excited DMS is estimated to be ~100 fs, indicating that the dissociation is complete within one single oscillation in the conical intersection region. It is also found that the symmetric CSC stretching mode is strongly coupled to the reaction coordinate, as manifested by our experimental finding that the fragmentation yield of the S-CD3 bond is enhanced compared to that of the S-CH3 bond in the CH3SCD3 dissociation reaction only when the CSC symmetric stretching vibrational mode is excited at the conical intersection region. This work demonstrates that the better understanding of the excited state could make the bond-selective chemistry into reality.

One photon yields two isomerizations: large atomic displacements during electronic excited-state dynamics in ruthenium sulfoxide complexes

Photochromic compounds efficiently transduce photonic energy to potential energy for excited-state bond-breaking and bond-forming reactions. A critical feature of this reaction is the nature of the electronic excited-state potential energy surface and how this surface facilitates large nuclear displacements and rearrangements. We have prepared two photochromic ruthenium sulfoxide complexes that feature two isomerization reactions following absorption of a single photon. We show by femtosecond transient absorption spectroscopy that this reaction is complete within a few hundred picoseconds and suggest that isomerization occurs along a conical intersection seam formed by the ground-state and excited-state potential energy surfaces.

Selective Excitation of Atomic-Scale Dynamics by Coherent Exciton Motion in the Non-Born-Oppenheimer Regime

Time-domain investigations of the nonadiabatic coupling between electronic and vibrational degrees of freedom have focused primarily on the formation of electronic superpositions induced by atomic motion. The effect of electronic nonstationary-state dynamics on atomic motion remains unexplored. Here, phase-coherent excitation of the two lowest electronic transitions in semiconducting single-walled carbon nanotubes by broadband <5-fs pulses directly triggers coherent exciton motion along the axis of the nanotubes. Optical pump-probe spectroscopy with sub-10-fs time resolution reveals that exciton motion selectively excites the high-frequency G mode coherent phonon, in good agreement with results obtained from time-domain ab initio simulations. This observed phenomenon arises from the direct modulation of the C-C interatomic potential by coherent exciton motion on a time scale that is commensurate with atomic motion. Our results suggest the possibility of employing light-field manipulation of electron densities in the non-Born-Oppenheimer regime to initiate selective atomic motion.

Low-lying excited-states of 5-benzyluracil

A numerical study is reported concerning the first and second singlet excited-states of 5-benzyluracil using the multireference self-consistent field (state-averaged CASSCF) method. The vertical excitation energies of low-lying excited-states were characterized using the SA-CASSCF method, as well as using higher-level methods, such as CASPT2, MRCI and EOM-CCSD. The local minima and conical intersections found on the potential energy surfaces (PESs) were characterized in terms of molecular geometry and natural population analysis. Different relaxation pathways on the PESs are identified and discussed by comparing with the similar pathways found for the individual monomers of uracil and benzene. The molecule can be thought of as a model system for the study of crosslink reaction between DNA and proteins induced by UV light.

Ultrafast above-threshold dynamics of the radical anion of a prototypical quinone electron-acceptor

Quinones feature prominently as electron acceptors in nature. Their electron-transfer reactions are often highly exergonic, for which Marcus theory predicts reduced electron-transfer rates because of a free-energy barrier that occurs in the inverted region. However, the electron-transfer kinetics that involve quinones can appear barrierless. Here, we consider the intrinsic properties of the para-benzoquinone radical anion, which serves as the prototypical electron-transfer reaction product involving a quinone-based acceptor. Using time-resolved photoelectron spectroscopy and ab initio calculations, we show that excitation at 400 and 480 nm yields excited states that are unbound with respect to electron loss. These excited states are shown to decay on a sub-40 fs timescale through a series of conical intersections with lower-lying excited states, ultimately to form the ground anionic state and avoid autodetachment. From an isolated electron-acceptor perspective, this ultrafast stabilization mechanism accounts for the ability of para-benzoquinone to capture and retain electrons.

Ultrafast Excited-State Dynamics of ortho-Terphenyl and 1,2-Diphenylcyclohexene: The Role of "Ethylenic Twisting" in the Nonadiabatic Photocyclization of Stilbene Analogs

Nonadiabatic photocyclization is the fundamental step underlying photoswitching and light-assisted bond formation within diarylethylenes, yet the details of the nuclear dynamics leading to cyclization remain unclear. We have examined the ultrafast excited-state dynamics of o-terphenyl (OTP) and 1,2-diphenylcyclohexene (DPCH) in solution to determine how variation in structural constraints impacts the course of nonadiabatic photocyclization specifically in stilbenoids. Measured spectral dynamics reflect cyclization through a S1-to-S0 transition for both systems on picosecond time scales, with excited-state decay appreciably faster for DPCH versus OTP. Supportive ab initio calculations reveal a higher energetic penalty in OTP versus DPCH for reaching the lowest-energy conical intersection from the S1 minimum; this penalty is associated primarily with twisting about the carbon-carbon bond that bridges terminal phenyl groups, a structural change that has a critical role in nonadiabatic cis-trans isomerization of diarylethylenes. Findings provide a new experimental perspective on the elusive nuclear dynamics underlying cis-stilbene photocyclization.

Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework

The delocalized, anticorrelated component of pigment vibrations can drive nonadiabatic electronic energy transfer in photosynthetic light-harvesting antennas. In femtosecond experiments, this energy transfer mechanism leads to excitation of delocalized, anticorrelated vibrational wavepackets on the ground electronic state that exhibit not only 2D spectroscopic signatures attributed to electronic coherence and oscillatory quantum energy transport but also a cross-peak asymmetry not previously explained by theory. A number of antennas have electronic energy gaps matching a pigment vibrational frequency with a small vibrational coordinate change on electronic excitation. Such photosynthetic energy transfer steps resemble molecular internal conversion through a nested intermolecular funnel.

ONIOM approach for non-adiabatic on-the-fly molecular dynamics demonstrated for the backbone controlled Dewar valence isomerization

Non-adiabatic on-the-fly molecular dynamics (NA-O-MD) simulations require the electronic wavefunction, energy gradients, and derivative coupling vectors in every timestep. Thus, they are commonly restricted to the excited state dynamics of molecules with up to ≈20 atoms. We discuss an approximation that combines the ONIOM(QM:QM) method with NA-O-MD simulations to allow calculations for larger molecules. As a proof of principle we present the excited state dynamics of a (6-4)-lesion containing dinucleotide (63 atoms), and especially the importance to include the confinement effects of the DNA backbone. The method is able to include electron correlation on a high level of theory and offers an attractive alternative to QM:MM approaches for moderate sized systems with unknown force fields.

Wave Packet Dynamics at an Extended Seam of Conical Intersection: Mechanism of the Light-Induced Wolff Rearrangement

Quantum dynamics calculations on a model surface based on CASPT2//CASSCF calculations are carried out to probe the traversal of a wave packet through an extended seam of conical intersection during the light-induced Wolff rearrangement of diazonaphtoquinone. The reaction is applied in the fabrication of integrated circuits. It consists of nitrogen elimination and ring rearrangement to yield a ketene. After excitation, the wave packet relaxes and reaches the extended seam. A fraction of the wave packet decays to the ground state at a region of the seam connected to a carbene intermediate, while the remaining part decays at a region leading to the ketene. The passage of the wave packet through the extended seam explains the competition between concerted ketene formation and a stepwise mechanism involving a carbene. The two primary photoproducts are formed in the first 100 fs of the simulation, in agreement with recent ultrafast spectroscopy measurements.

Time-resolved photoelectron spectroscopy from first principles: excited state dynamics of benzene

We use the ab initio multiple spawning (AIMS) method to follow the dynamics of benzene after excitation to the second singlet excited state (S2). The results are validated by comparison to potential energy surfaces including dynamical electron correlation effects. Time-resolved photoelectron spectra are computed and compared to experimental results. Simulations agree with experiment that there are both short-lived and long-lived components of the excited state population. We show that these components both originate from quenching through the same S2/S1 conical intersection and that the difference between them comes from their behavior immediately after decay to S1. This is presumed to be a function of the details of the way in which the S2/S1 intersection region is accessed; for example, the momentum distribution and the topology of the seam in the relevant region.

QUANTIZATION OF CHEMICAL REACTION: THE DYNAMIC CORRELATION DIAGRAM METHOD FREE FROM NONCROSSING RULE

Both Fukui's frontier orbital (FO) theory and Woodward–Hoffmann's orbital symmetry conservation (W–H) theory are based on the molecular orbital theory. However, there are some obvious inconsistencies between the two theories in explaining the electron movement. The process of chemical reactions has been explained by the potential surface analysis based on the time-independent Schrödinger equation. However, this approach is not always appropriate for describing unsteady states, because the variable of reaction coordinate should be time t by its very nature. When considering the time-scale of chemical reactions for molecules, there is inherent uncertainty in the energy levels for the midway state of chemical reactions owing to the Heisenberg uncertainty principle. The states which can be accurately described by quantum mechanics exist discontinuously in chemical reactions. Such quantization of chemical reactions solves all noncrossing problems. We also show that such an essential fact leads to new concepts and theories in chemical reactions such as stable molecule, elementary reaction and minimum deformation of orbital phases. Finally, taking the regularity in organic reactions as an example, we demonstrate that FO theory and W–H theory can be unified consistently by the universally applicable "dynamic correlation diagram method."

Quantum dynamics study of fulvene double bond photoisomerization: the role of intramolecular vibrational energy redistribution and excitation energy

The double bond photoisomerization of fulvene has been studied with quantum dynamics calculations using the multi-configuration time-dependent Hartree method. Fulvene is a test case to develop optical control strategies based on the knowledge of the excited state decay mechanism. The decay takes place on a time scale of several hundred femtoseconds, and the potential energy surface is centered around a conical intersection seam between the ground and excited state. The competition between unreactive decay and photoisomerization depends on the region of the seam accessed during the decay. The dynamics are carried out on a four-dimensional model surface, parametrized from complete active space self-consistent field calculations, that captures the main features of the seam (energy and locus of the seam and associated branching space vectors). Wave packet propagations initiated by single laser pulses of 5-25 fs duration and 1.85-4 eV excitation energy show the principal characteristics of the first 150 fs of the photodynamics. Initially, the excitation energy is transferred to a bond stretching mode that leads the wave packet to the seam, inducing the regeneration of the reactant. The photoisomerization starts after the vibrational energy has flowed from the bond stretching to the torsional mode. In our propagations, intramolecular energy redistribution (IVR) is accelerated for higher excess energies along the bond stretch mode. Thus, the competition between unreactive decay and isomerization depends on the rate of IVR between the bond stretch and torsion coordinates, which in turn depends on the excitation energy. These results set the ground for the development of future optical control strategies.