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.     

Towards experimental determination of conical intersection properties: a twin state based comparison with bound excited states

The energy and approximate structure of certain S(0)/S(1) conical intersections (CI) are shown computationally to be deducible from those of two bound states: the first triplet (T(1)), which is iso-energetic with the CI, and the second excited singlet state (S(2)). This is demonstrated for acepentalene (I) and its perfluoro derivative (II) using the twin state concept for three states systems and based on the fact that the triplet T(1) is almost degenerate with the CI. The stable S(2) (C(3v) configuration) state exhibits unusual exaltation of Jahn-Teller active degenerate mode-ν(JT) = 2058 cm(-1) (～500 cm(-1) higher than analogous e-mode of the symmetric (C(3v)) T(1) and the dianion I(-2) or any C-C vibration of the Jahn-Teller distorted (C(s)) ground state minimum). The acepentalene molecule, whose rigid structure and possibility to attain the relatively high symmetry C(3v) configuration, is a particularly suitable candidate for this purpose.     

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.     

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.     

Photostability via a sloped conical intersection: a CASSCF and RASSCF study of pyracylene

An extensive ab initio study of the ground- and excited-state potential energy surfaces of pyracylene is presented in this work. CASSCF calculations show that there is an accessible sloped S0/S1 conical intersection, which leads to ultrafast internal conversion and explains the observed photostability. RASSCF calculations (using a well-defined subset of the CASSCF configurations) are shown to be able to reproduce CASSCF results satisfactorily and will therefore be useful for larger systems where CASSCF is currently too expensive. MRCI and MRPT2 energy corrections are computed to assess the ionic character of the excited states. Finally, MMVB calculations are also benchmarked against CASSCF, to assess the reliability of this parametrized method for excited states of large conjugated polycyclic aromatic hydrocarbons.     

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.     

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.     

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.     

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.     

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.     

Solvent effects on the thioamide rotational barrier: an experimental and theoretical study.

The solvent effect on the C-N rotational barriers of N,N-dimethylthioformamide (DMTF) and N,N-dimethylthioacetamide (DMTA) has been investigated using ab initio theory and NMR spectroscopy. Selective inversion recovery NMR experiments were used to measure rotational barriers in a series of solvents. These data are compared to ab initio results at the G2(MP2) theoretical level. The latter are corrected for large amplitude vibrational motions to give differences in free energy. The calculated gas phase barriers are in very good agreement with the experimental values. Solvation effects were calculated using reaction field theory. This approach has been found to give barriers that are in good agreement with experiment for many aprotic, nonaromatic solvents that do not engage in specific interactions with the solute molecules. The calculated solution-phase barriers for the thioamides using the above solvents are also in good agreement with the observed barriers. The solvent effect on the thioamide rotational barrier is larger than that for the amides because the thioamides have a larger ground-state dipole moment, and there is a larger change in dipole moment with increasing solvent polarity. The transition-state dipole moments for the amides and thioamides are relatively similar. The origin of the C-N rotational barrier and its relation to the concept of amide "resonance" is examined.     

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.     

Principle and mechanism of direct porphyrin metalation: joint experimental and theoretical investigation

The direct metalation of tetraphenylporphyrin with bare metal atoms (Co and Zn) was studied with X-ray photoelectron spectroscopy, scanning tunneling microscopy, and temperature-programmed reaction measurements on ordered monolayer films of the molecules adsorbed on a Ag(111) surface. The mechanism of this novel type of surface reaction was investigated using density functional theory (DFT) calculations for the related gas-phase reactions of the unsubstituted porphyrin with the metals Fe, Co, Ni, Cu, and Zn. The reaction starts with the formation of an initial complex, in which the metal atom is coordinated by the intact unreduced porphyrin. This complex resembles the sitting-atop complex proposed for porphyrin metalation with metal ions in solution. In two subsequent steps, the pyrrolic hydrogen atoms are transferred to the metal atom, forming H2, which is eventually released. The activation barriers of the H-transfer steps vary for the different metal atoms. DFT calculations suggest that metalations with Fe, Co, and Ni show two-state reactivity, while those with Cu and Zn proceed on a single potential energy surface. For metalation with Zn, we calculated a barrier of the first hydrogen transfer step of 32.6 kcal mol(-1), in good agreement with the overall experimental activation energy of 31 kcal mol(-1).     

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry--presented here for the first time--is found to be the global minimum in the intersection space.     

Comparison of algorithms for conical intersection optimisation using semiempirical methods

We present a comparison of three previously published algorithms for optimising the minimum energy crossing point between two Born–Oppenheimer electronic states. The algorithms are implemented in a development version of the MNDO electronic structure package for use with semiempirical configuration interaction methods. The penalty function method requires only the energies and gradients of the states involved, whereas the gradient projection and Lagrange–Newton methods also require the calculation of non-adiabatic coupling terms. The performance of the algorithms is measured against a set of well-known small molecule conical intersections. The Lagrange–Newton method is found to be the most efficient, with the projected gradient method also competitive. The penalty function method can only be recommended for situations where non-adiabatic coupling terms cannot be calculated. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

We have previously shown how femtosecond angle- and energy-resolved photoelectron spectroscopy can be used to monitor quantum wavepacket bifurcation at an avoided crossing or conical intersection and also how a symmetry-allowed conical intersection can be effectively morphed into an avoided crossing by photo-induced symmetry breaking. The latter result suggests that varying the parameters of a laser to modify a conical intersection might control the rate of passage of wavepackets through such regions, providing a gating process for different chemical products. In this paper, we show with full quantum mechanical calculations that such optical control of conical intersections can actually be monitored in real time with femtosecond angle- and energy-resolved photoelectron spectroscopy. In turn, this suggests that one can optimally control the gating process at a conical intersection by monitoring the photoelectron velocity map images, which should provide far more efficient and rapid optimal control than measuring the ratio of products. To demonstrate the sensitivity of time-resolved photoelectron spectra for detecting the consequences of such optical control, as well as for monitoring how the wavepacket bifurcation is affected by the control, we report results for quantum wavepackets going through the region of the symmetry-allowed conical intersection between the first two (2)A' states of NO(2) that is transformed to an avoided crossing. Geometry- and energy-dependent photoionization matrix elements are explicitly incorporated in these studies. Time-resolved photoelectron angular distributions and photoelectron images are seen to systematically reflect the effects of the control pulse.     

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.     

Solvent effects on the photodissociation of formic acid: a theoretical study

Photodissociation of aqueous formic acid has been investigated with the CASSCF, DFT, and MR-CI methods. Solvent effects are considered as a combination of the hydrogen-bonding interaction from explicit H2O molecules and the effects from the bulk surrounding H2O molecules using the polarizable continuum model. It is found that the hydrogen-bonding effect from the explicit water in the complex is the major factor to influence properties of aqueous formic acid, while the bulk surrounding H2O molecules has a noticeable influence on the structures of the complex. The direct C-O bond fission along the S1 pathway is predicted to be an important channel upon photolysis of aqueous formic acid at 200 nm, which is consistent with experimental observation that aqueous formic acid dissociates predominantly into fragments of HCO and OH. The existence of a dark channel upon photolysis of aqueous formic acid at 200 nm is assigned as fast relaxation from the S1 Franck-Condon geometry to the T1/S1 intersection and subsequent S1-->T1 intersystem crossing process. S1-->S0 internal conversion followed by molecular elimination to CO+H2O is the most probable primary process for formation of carbon monoxide, which was observed with considerable yield upon photolysis of aqueous formic acid at 253.7 nm.