Photostability via sloped conical intersections: a computational study of the pyrene radical cation

The photophysics of the pyrene radical cation, a polycyclic aromatic hydrocarbon (PAH) and a possible source of diffuse interstellar bands (DIBs), is investigated by means of hybrid molecular mechanics-valence bond (MMVB) force field and multiconfigurational CASSCF and CASPT2 ab initio methods. Potential energy surfaces of the first three electronic states D 0, D 1, and D 2 are calculated. MMVB geometry optimizations are carried out for the first time on a cationic system; the results show good agreement with CASSCF optimized structures, for minima and conical intersections, and errors in the energy gaps are no larger than those found in our previous studies of neutral systems. The presence of two easily accessible sloped D 1/D 2 and D 0/D 1 conical intersections suggests the pyrene radical cation is highly photostable, with ultrafast nonradiative decay back to the initial ground state geometry predicted via a mechanism similar to the one found in the naphthalene radical cation.     

Photostability via sloped conical intersections: a computational study of the excited states of the naphthalene radical cation

On the basis of an extensive ab initio electronic structure study of the ground and excited-state potential energy surfaces of the naphthalene radical cation (N*+), we propose a mechanism for its ultrafast nonradiative relaxation from the second excited state (D2) down to the ground state (D0), which could explain the experimentally observed photostability [Zhao, L.; Lian, R.; Shkrob I. A.; Crowell, R. A.; Pommeret, S.; Chronister, E. L.; Liu, A. D.; Trifunac, A. D. J. Phys. Chem. A., 2004, 108, 25]. The proposed photophysical relaxation pathway involves internal conversion from the D2 state down to the D0 state via two consecutive, accessible, sloped conical intersections (CIs). The two crossings, D0/D1 and D1/D2, are characterized at the complete active space self-consistent field (CASSCF) level. At this level of theory, the D0/D1 crossing is energetically readily accessible, while the D1/D2 CI appears too high in energy to be involved in internal conversion. However, the inclusion of dynamic correlation effects, via single point CASPT2 calculations including excitations out of the valence pi- and sigma-orbitals, lowers the D0 and D2 state energies with respect to D1. Extrapolations at the CASPT2 level predict that the D1/D2 crossing is then significantly lower in energy than with CASSCF indicating that with a higher-level treatment of dynamic correlation it may be energetically accessible following vertical excitation to D2. N*+ is proposed as one of the species contributing to a series of diffuse infrared absorption bands originating from interstellar clouds. Understanding the mechanism for photostability in the gas phase, therefore, has important consequences for astrophysics.     

Mechanism of efficient firefly bioluminescence via adiabatic transition state and seam of sloped conical intersection

Firefly emission is a well-known efficient bioluminescence. However, the mystery of the efficient thermal generation of electronic excited states in firefly still remains unsolved, particularly at the atomic and molecular levels. We performed SA-CASSCF(12,12)/6-31G* and CASPT2(12,12)/6-31G*//SA-CASSCF(12,12)/6-31G* calculations to elucidate the reaction mechanism of bioluminescence from the firefly dioxetanone in the gas phase. Adiabatic transition state (TS) for the O-O bond cleavage and the minimum energy conical intersection (MECI) were located and characterized. The unique topology of MECI featuring a seam of a sloped conical intersection for the firefly dioxetanone, which was uncovered for the first time, emerges along the reaction pathway to provide a widely extended channel to diabatically access the excited-state from the ground state.     

Polarized pump-probe measurements of electronic motion via a conical intersection

Polarized femtosecond pump-probe spectroscopy is used to observe electronic wavepacket motion for vibrational wavepackets centered on a conical intersection. After excitation of a doubly degenerate electronic state in a square symmetric silicon naphthalocyanine molecule, electronic motions cause a approximately 100 fs drop in the polarization anisotropy that can be quantitatively predicted from vibrational quantum beat modulations of the pump-probe signal. Vibrational symmetries are determined from the polarization anisotropy of the vibrational quantum beats. The polarization anisotropy of the totally symmetric vibrational quantum beats shows that the electronic wavepackets equilibrate via the conical intersection within approximately 200 fs. The relationship used to predict the initial electronic polarization anisotropy decay from the asymmetric vibrational quantum beat amplitudes indicates that the initial width of the vibrational wavepacket determines the initial speed of electronic wavepacket motion. For chemically reactive conical intersections, which can have 1000 times greater stabilization energies than the one observed here, the same theory predicts electronic equilibration within 2 fs. Such electronic movements would be the fastest known chemical processes.     

Efficient photochemical merocyanine-to-spiropyran ring closure mechanism through an extended conical intersection seam. A model CASSCF/CASPT2 study

A mechanism of the thermal and photochemical bleaching of merocyanine to spiropyran is proposed on the basis of CASSCF/CASPT2 calculations on the 6-(2-propenyliden)cyclohexadienone model system. Our results suggest that this photochemical transformation takes place in two steps. First, the initially pumped 1(pi-pi) S2 undergoes radiationless decay to 1(n-pi) S1 via an extended S2/S1 conical intersection seam that runs approximately parallel to the trans-to-cis isomerization coordinate, a few kilocalories per mole higher in energy. Thus, S2 --> S1 internal conversion is possible at all values of the S2 trans-to-cis reaction coordinate. Second, on the S1 potential energy surface, there is a barrierless ring closure reaction path from the S1 cis minimum that leads to a peaked S1/S0 conical intersection where the deactivation to the ground state takes place. The inertia of the moving nuclei then drives the system toward the ground-state minimum of the 2H-chromene product. Thus, the extended seam topology of the S2/S1 conical intersection and the coordinate of the branching space of the S1/S0 conical intersection are essential to explain the efficiency and high speed of this reaction.     

Dihydroazulene/vinylheptafulvene photochromism: a model for one-way photochemistry via a conical intersection

Dihydroazulene (DHA)/vinylheptafulvene (VHF) photochromism has been investigated by studying the isomerization of 1,2,3,8a,9-pentahydrocyclopent[a]azulene-9,9-dicarbonitrile through complete active space-self consistent field calculations on the ground (S(0)) and first excited (S(1)) states of smaller model compounds. In each case, the S(1) reaction coordinate is characterized by a transition structure for adiabatic ring opening, connecting a DHA-like intermediate to a much more stable VHF-like structure. This VHF-like structure is not a real S(1) minimum but a crossing (i.e., a conical intersection) between the excited- and ground-state potential energy surfaces. The existence of such a crossing is consistent with the lifetime of approximately 600 fs recently measured for the DHA-like intermediate on S(1) (Ern, J.; Petermann, M.; Mrozek, T.; Daub, J.; Kuldova, K.; Kryschi, C. Chem. Phys. 2000, 259, 331-337). The shape of the crossing is also crucial; it not only explains the fact that the quantum yield approaches 1.0 for the forward DHA --> VHF reaction, but also the lack of any fluorescence or photochemical back-reaction from VHF. These findings are supported by ab initio direct dynamics calculations. This work suggests that calculating and understanding the topology of excited-state potential energy surfaces will be useful in designing photochromic molecules.     

Stairway to the conical intersection: a computational study of the retinal isomerization

The potential-energy surface of the first excited state of the 11-cis-retinal protonated Schiff base (PSB11) chromophore has been studied at the density functional theory (DFT) level using the time-dependent perturbation theory approach (TDDFT) in combination with Becke's three-parameter hybrid functional (B3LYP). The potential-energy curves for torsion motions around single and double bonds of the first excited state have also been studied at the coupled-cluster approximate singles and doubles (CC2) level. The corresponding potential-energy curves for the ground state have been calculated at the B3LYP DFT and second-order M?ller-Plesset (MP2) levels. The TDDFT study suggests that the electronic excitation initiates a turn of the beta-ionone ring around the C6-C7 bond. The torsion is propagating along the retinyl chain toward the cis to trans isomerization center at the C11=C12 double bond. The torsion twist of the C10-C11 single bond leads to a significant reduction in the deexcitation energy indicating that a conical intersection is being reached by an almost barrierless rotation around the C10-C11 single bond. The energy released when passing the conical intersection can assist the subsequent cis to trans isomerization of the C11=C12 double bond. The CC2 calculations also show that the torsion barrier for the twist of the retinyl C10-C11 single bond adjacent to the isomerization center almost vanishes for the excited state. Because of the reduced torsion barriers of the single bonds, the retinyl chain can easily deform in the excited state. Thus, the CC2 and TDDFT calculations suggest similar reaction pathways on the potential-energy surface of the excited state leading toward the conical intersection and resulting in a cis to trans isomerization of the retinal chromophore. According to the CC2 calculations the cis to trans isomerization mechanism does not involve any significant torsion motion of the beta-ionone ring.     

Optimal control of ultrafast cis-trans photoisomerization of retinal in rhodopsin via a conical intersection

Optimal control simulation is applied to the cis-trans photoisomerization of retinal in rhodopsin within a two-dimensional, two-electronic-state model with a conical intersection [S. Hahn and G. Stock, J. Phys. Chem. B 104, 1146 (2000)]. For this case study, we investigate coherent control mechanisms, in which laser pulses work cooperatively with a conical intersection that acts as a "wave-packet cannon." Optimally designed pulses largely consist of shaping subpulses that prepare a wave packet, which is localized along a reaction coordinate and has little energy in the coupling mode, through multiple electronic transitions. This shaping process is shown to be essential for achieving a high target yield although the envelopes of the calculated pulses depend on the local topography of the potential-energy surfaces around the conical intersection and the choice of target. The control mechanisms are analyzed by considering the motion of reduced wave packets in a nuclear configuration space as well as by snapshots of probability current-density maps.     

Infrared spectra at a conical intersection: vibrations of methoxy

The J = 0 infrared spectrum of methoxy is theoretically calculated for the ground X?(2)E state using a quartic potential energy force field, and the quadratic dipole moment expansion is calculated ab initio at the CCSD(T) level of theory and cc-pVTZ basis. Writing these expansions with vibronic operators whose symmetry properties are defined with respect to C(3v) rotation greatly simplifies these calculations. With minor adjustments to the force field, excellent agreement with experiment is found for both the transition energies of CH(3)O and those of CD(3)O. The role of Jahn-Teller and Fermi coupling is illustrated by scaling these terms by a parameter δ that varies from 0 to 1. Plotting the eigenvalues as a function of δ yields a correlation diagram connecting the harmonic eigenvalues to those of the fully coupled problem. The spectrum for CH(3)O is determined using a combination of Davidson and Lanczos iteration schemes. The spectral features are found to be dominated by Jahn-Teller effects, but direct Fermi coupling and indirect potential couplings have important roles. The origin of the complexities in the CH stretch region are discussed.     

CASSCF calculations for photoinduced processes in large molecules: Choosing when to use the RASSCF, ONIOM and MMVB approximations

In this article, we compare and contrast the RASSCF, ONIOM and MMVB electronic structure methods for calculating relaxation paths on potential energy surfaces of the excited states of large molecules, and for locating any resulting conical intersections at which nonadiabatic decay can take place. Each method is treated here as an approximation to CASSCF, which we choose as our reference level of theory, but which becomes prohibitively expensive computationally for large molecules. Both MMVB and ONIOM are hybrid computational methods – combining different levels of theory in an energy plus derivatives calculation at a particular molecular geometry – but they differ fundamentally in that MMVB is a hybrid-atom method, whereas ONIOM is a hybrid-molecule method. We explain this distinction through four representative applications: the photostability of pyracylene (studied with CASSCF, RASSCF, MMVB); large geometry changes in the singlet excited states of triangulene (studied with MMVB); a model for interstitial nickel defects in a synthetic diamond lattice (studied with ONIOM CAS:UFF); and the photochemical [4 + 4] cycloaddition of cyclohexadiene to naphthalene (studied with ONIOM CAS:MMVB). We show that each method is more appropriate for a particular type of photochemical problem. This article is part perspective, part review, and contains new results for three multi-state or photoinduced processes in complex systems.     

A novel conical intersection topography and its consequences: the 1, 2 2A conical intersection seam of the vinoxy radical

A region of the 1, 2 2A seam of accidental conical intersections in the vinoxy radical exhibits a novel topography which has important consequences for both upper-state to lower-state and lower-state to upper-state nonadiabatic transitions. The impact of this topography on these nonadiabatic transitions is described. We also considered the possibility that this conical intersection seam provides a dynamical bottleneck to the photodissociation of vinoxy to H+ketene by facilitating nonadiabatic recrossing. Our analysis of the conical topographies and the proximity of the conical intersections to the transition state for dissociation to H+ketene does not support nonadiabatic recrossing as an effective dynamical bottleneck blocking the H+ketene channel.     

Solvent tuning of a conical intersection: direct experimental verification of a theoretical prediction

We report an ultrafast study of a merocyanine molecule, whose fluorescence lifetime was tuned by changing the solvent's polarity. A recent theoretical prediction that the fluorescence lifetime is considerably shortened upon lowering the polarity of the solvent, due to tuning of the conical intersection properties, is fully confirmed (Xu et al. J. Phys. Chem. A 2009, 113, 9779-9791). This constitutes a direct measurement of a previously predicted tunable property of a conical intersection.     

Kinetics of reductive N-O bond fragmentation: the role of a conical intersection

N-alkoxyheterocycles can act as powerful one-electron acceptors in photochemical electron-transfer reactions. One-electron reduction of these species results in formation of a radical that undergoes N-O bond fragmentation to form an alkoxy radical and a neutral heterocycle. The kinetics of this N-O bond fragmentation reaction have been determined for a series of radicals with varying substituents and extents of delocalization. Rate constants varying over 7 orders of magnitude are obtained. A reaction potential energy surface is described that involves avoidance of a conical intersection. A molecular basis for the variation of the reaction rate constant with radical structure is given in terms of the relationship between the energies of the important molecular orbitals and the reaction potential energy surface. Ab initio and density functional electronic structure calculations provide support for the proposed reaction energy surface.     

Dissipative dynamics of a system passing through a conical intersection: ultrafast pump-probe observables

The dynamics of a system incorporating a conical intersection, in the presence of a dissipative environment, is studied with the purpose of identifying observable ultrafast spectroscopic signatures. A model system consisting of two vibronically coupled electronic states with two nuclear degrees of freedom is constructed. Dissipation is treated by two different methods, Lindblad semigroup formalism and the surrogate Hamiltonian approach. Pump-probe experimental expectation values such as transient emission and transient absorption are calculated and compared to the adiabatic and diabatic population transfer. The ultrafast population transfer reflecting the conical intersection is not mirrored in transient absorption measurements such as the recovery of the bleach. Emission from the excited state can be suppressed on the ultrafast time scale, but the existence of a conical intersection is only one of the possible mechanisms that can provide ultrafast damping of emission.     

The aromaticity of pyracylene: an experimental and computational study of the energetics of the hydrogenation of acenaphthylene and pyracylene

In this work, the aromaticity of pyracylene (2) was investigated from an energetic point of view. The standard enthalpy of hydrogenation of acenaphthylene (1) to acenaphthene (3) at 298.15 K was determined to be minus sign(114.5 +/- 4.2) kJ x mol(-1) in toluene solution and minus sign(107.9 +/- 4.2) kJ x mol(-1) in the gas phase, by combining results of combustion and reaction-solution calorimetry. A direct calorimetric measurement of the standard enthalpy of hydrogenation of pyracylene (2) to pyracene (4) in toluene at 298.15 K gave -(249.9 plus minus 4.6) kJ x mol(-1). The corresponding enthalpy of hydrogenation in the gas phase, computed from the Delta(f)H(o)m(cr) and DeltaH(o)m(sub) values obtained in this work for 2 and 4, was -(236.0 +/- 7.0) kJ x mol(-1). Molecular mechanics calculations (MM3) led to Delta(hyd)H(o)m(1,g) = -110.9 kJ x mol(-1) and Delta(hyd)H(o)m(2,g) = -249.3 kJ x mol(-1) at 298.15 K. Density functional theory calculations [B3LYP/6-311+G(3d,2p)//B3LYP/6-31G(d)] provided Delta(hyd)H(o)m(2,g) = -(244.6 +/- 8.9) kJ x mol(-1) at 298.15 K. The results are put in perspective with discussions concerning the "aromaticity" of pyracylene. It is concluded that, on energetic grounds, pyracylene is a borderline case in terms of aromaticity/antiaromaticity character.     

Photochemicalsyn-anti isomerization of a Schiff base: A two-dimensional description of a conical intersection in formaldimine

The shape of theS ₀,S ₁, andT ₁ potential energy surfaces of formaldimine, CH₂=NH, is explored in the two-dimensional subspace defined by the twisting and linear inversion motions which correspond to the geometricalsyn-anti isomerization, using anab initio large-scale CI method. Minima in theS ₁ andT ₁ surfaces as well as aS ₀-S ₁ conical intersection are identified and the photoisomerization mechanism is discussed.     

Photochemical reaction mechanism of cyclobutanone: CASSCF study

The photochemical reaction channels of cyclobutanone have been studied at the CASSCF level with a 6‐31G* basis set. Starting from the n‐π* excited‐state (S₁) cyclobutanone, the three reactions can take place: decarbonylation (produce CO and cyclopropane or propylene), cycloelimination (produce ketene and ethylene), and ring expansion (produce oxacarbene). Our computation indicates that decarbonylation products CO and triplet trimethylene are formed on the triplet n‐π* excited state (T₁) in a stepwise way via a biradical intermediate after intersystem crossing (ISC) to T₁ from S₁. And, then, the triplet trimethylene undergoes a second ISC to the ground state (S₀) to produce the singlet trimethylene from which cyclopropane can be produced rapidly only overcoming a 1 to 2‐kcal/mol barrier while propylene can be formed as a secondary product. The cycloelimination products ketene and ethylene are formed on the S₀ in a concerted mechanism after internal conversion (IC) to S₀ from S₁ via a biradical conical intersection. The reaction channels corresponding to ring expansion on the S₀, T₁, and S₁ states have also been discussed, and the likeliest reaction path is that oxacarbene is formed on the ground state following S₁/S₀ internal conversion. The surface topology of cyclobutanone on the S₁ surface is characterized by a transition state separating the minimum from the S₁/S₀ conical intersection, which is consistent with the previous computations and can explain the wavelength dependence of the fluorescence emission yield. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

On the locus of points of conical intersection: seams near seams

The existence of a seam of conical intersection, the reference seam, does not rule out the existence of additional disjoint seams of conical intersection. These disjoint seams intersect the g-h planes of the reference seam, a region usually assumed to be devoid of intersections, potentially leading to unexpected points of degeneracy in close proximity to the original conical intersection. Here the authors show how the locus of these disjoint seams can be predicted employing a Hamiltonian derived from second-order perturbation theory. Dramatic differences between the g-h planes of the reference and disjoint seams are found and are expected to have a profound impact on nuclear dynamics. Numerical studies of both high symmetry (D(3h), C(3)H(3)) and low symmetry (C(2v), C(2)H(2)N) species are presented.