Excited-state Surfaces Research Articles

Excitation energies from time-dependent generalized valence bond method

A generalized valence bond perfect-pairing (GVB-PP) wavefunction has been extensively used in computational chemistry methods due to its multiconfigurational character, which captures in an inexpensive way static electron correlation. GVB-PP has been mostly applied to ground states and not much is known about its performance in predicting electronic spectra of molecules. Here, we present the formalism based on the time-dependent linear response theory which provides excitation energies from the GVB-PP ground-state wavefunction. The accuracy of the excitation energy dissociation curves parallels that of the TD-HF method around ground-state equilibrium geometries of the investigated molecules. For stretched-bond molecules, when TD-HF breaks down, the proposed TD-GVB method remains reliable. TD-GVB may therefore serve as a useful and inexpensive tool for exploring potential energy surfaces of excited states of molecules.

Communication: Coherences observed in vivo in photosynthetic bacteria using two-dimensional electronic spectroscopy.

Energy transfer through large disordered antenna networks in photosynthetic organisms can occur with a quantum efficiency of nearly 100%. This energy transfer is facilitated by the electronic structure of the photosynthetic antennae as well as interactions between electronic states and the surrounding environment. Coherences in time-domain spectroscopy provide a fine probe of how a system interacts with its surroundings. In two-dimensional electronic spectroscopy, coherences can appear on both the ground and excited state surfaces revealing detailed information regarding electronic structure, system-bath coupling, energy transfer, and energetic coupling in complex chemical systems. Numerous studies have revealed coherences in isolated photosynthetic pigment-protein complexes, but these coherences have not been observed in vivo due to the small amplitude of these signals and the intense scatter from whole cells. Here, we present data acquired using ultrafast video-acquisition gradient-assisted photon echo spectroscopy to observe quantum beating signals from coherences in vivo. Experiments were conducted on isolated light harvesting complex II (LH2) from Rhodobacter sphaeroides, whole cells of R. sphaeroides, and whole cells of R. sphaeroides grown in 30% deuterated media. A vibronic coherence was observed following laser excitation at ambient temperature between the B850 and the B850(∗) states of LH2 in each of the 3 samples with a lifetime of ∼40-60 fs.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections.

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.

Excited-state surfaces of ethylene from the B13 strong-correlation density functional

The energy surfaces of the ground and low-lying excited states of ethylene are challenging tests of multi-reference electronic structure methods. A variety of multi-reference wavefunction theories have been applied to this problem and the ensuing photochemistry has been well studied. Density-functional methods, however, have been less successful. In this work, the ‘B13’ strong-correlation density functional is used to generate multi-reference orbitals for the computation of the three lowest-lying singlet states. We explore the states and energies as a function of torsion angle, and as a function of the pyramidalisation angle with respect to the twisted orthogonal structure. The former features an avoided crossing at the orthogonal structure; the latter a Cs slice through a conical intersection. Both features are well reproduced by our B13 method.

From roaming atoms to hopping surfaces: mapping out global reaction routes in photochemistry.

The photodissociation of small molecules occurs upon irradiation by ultraviolet or visible light, and it is a very important chemical process in Earth's atmosphere, in the atmospheres of other planets, and in interstellar media. Photodissociation is an important method used to thoroughly investigate the fundamental issues of chemical reactivity. Photodissociation involves molecules and reaction fragments moving over ground- and excited-state potential surfaces (PESs). Molecules can move on a single PES (adiabatic pathway) or can cross over from one PES to another (nonadiabatic pathways). For a full theoretical understanding of a photodissociation mechanism, all of the important nonadiabatic and adiabatic pathways must be determined. This is not an easy task. We have developed an efficient computational method, called the global reaction route mapping (GRRM) strategy, that allows a theoretical exploration of ground- and excited-state PESs and their crossing seams in an automatic manner. In this Perspective, we summarize our approaches and present examples of their application together with newly determined chemical insights. These include the complex photodissociation mechanism of the formaldehyde molecule, the exclusive excited-state roaming dynamics of the nitrate radical, and all product channels and conformational memory in the photodissociation of the formic acid molecule. Finally, perspectives for the theoretical design of photofunctional molecules are discussed.

Insight into the mechanisms of luminescence of aminobenzonitrile and dimethylaminobenzonitrile in polar solvents. An ab initio study.

The dual fluorescence of 4-(dimethylamino)benzonitrile (DMABN) has been intensively studied in the last decades, but surprisingly there is not any detailed theoretical study of its photochemistry in polar solvents. In this work, we rationalize the different luminescent behavior of 4-aminobenzonitrile (ABN) and DMABN in acetonitrile by a computational study developed at the CASSCF/CASPT2 level and using the Polarized Continuum Model to reproduce the solvent environment. We present here the critical geometries, energies, and connections between the potential energy surfaces of the low-lying excited states: the locally excited state (LE) and several intramolecular charge transfer states (ICT). The computational results show that the topology of the potential energy surfaces (PES) does not change substantially when the effect of a polar solvent is included, in comparison with the gas phase. For DMABN, though, polar solvents stabilize preferentially the ICT states in such a way that the different interplay with the LE state induces strong qualitative changes in the photochemistry of this compound. Specifically, the planar ICT (PICT) species located on the S2 surface in the gas phase is, in acetonitrile, located on the S1 surface. that is, at the geometry of the PICT minimum, the LE state is higher in energy than the ICT. Now LE and PICT minima are practically degenerate and, given that both correspond to first excited state species, emission can take place from both of them. However, the twisted ICT (TICT) species is still the most favored thermodynamically so it is expected that this species would be preferentially populated. On the other hand, for ABN the equilibrium lies in favor of LE, as the TICT species was found at a much higher energy with a low reaction barrier toward LE. This explains why dual fluorescence cannot be observed in ABN, even in polar solvents.

Valence-bond non-equilibrium solvation model for a twisting monomethine cyanine.

We propose and analyze a two-state valence-bond model of non-equilibrium solvation effects on the excited-state twisting reaction of monomethine cyanines. Suppression of this reaction is thought responsible for environment-dependent fluorescence yield enhancement in these dyes. Fluorescence is quenched because twisting is accompanied via the formation of dark twisted intramolecular charge-transfer (TICT) states. For monomethine cyanines, where the ground state is a superposition of structures with different bond and charge localizations, there are two possible twisting pathways with different charge localizations in the excited state. For parameters corresponding to symmetric monomethines, the model predicts two low-energy twisting channels on the excited-state surface, which leads to a manifold of TICT states. For typical monomethines, twisting on the excited state surface will occur with a small barrier or no barrier. Changes in the solvation configuration can differentially stabilize TICT states in channels corresponding to different bonds, and that the position of a conical intersection between adiabatic states moves in response to solvation to stabilize either one channel or the other. There is a conical intersection seam that grows along the bottom of the excited-state potential with increasing solvent polarity. For monomethine cyanines with modest-sized terminal groups in moderately polar solution, the bottom of the excited-state potential surface is completely spanned by a conical intersection seam.

Peroxyacetyl radical: electronic excitation energies, fundamental vibrational frequencies, and symmetry breaking in the first excited state.

Peroxyacetyl radical [CH3C(O)O2] is among the most abundant peroxy radicals in the atmosphere and is involved in OH-radical recycling along with peroxyacetyl nitrate formation. Herein, the ground (X̃) and first (Ã) excited state surfaces of cis and trans peroxyacetyl radical are characterized using high-level ab initio methods. Geometries, anharmonic vibrational frequencies, and adiabatic excitation energies extrapolated to the complete basis-set limit are reported from computations with coupled-cluster theory. Excitation of the trans conformer is found to induce a symmetry-breaking conformational change due to second-order Jahn-Teller interactions with higher-lying excited states. Additional benchmark computations are provided to aid future theoretical work on peroxy radicals.

Photodesorption of water from rutile(110): ab initio calculation of five-dimensional potential energy surfaces of ground and excited electronic states and wave packet studies.

In this paper, we report on our results concerning the interaction of water with titanium dioxide in its rutile modification. The (110) surface is modelled by an embedded Ti9O18Mg7(14+) cluster. We present up to five-dimensional potential energy surfaces for the water molecule on this surface and include the dissociation of one hydrogen atom. The electronic ground state as well as one electronically excited state is included. To deal with the multi-configurational character of the wave function, we use the complete active space self-consistent field (CASSCF) approach. The resulting potential energy surfaces are fitted by means of an artificial neural network. As a first example of quantum dynamical studies based on our potential surfaces, we present results on the photodesorption of water from rutile(110).

Excited-state wavepacket and potential reconstruction by coherent anti-Stokes Raman scattering

Among the major challenges in the chemical sciences is controlling chemical reactions and deciphering their mechanisms. Since much of chemistry occurs in excited electronic states, in the last three decades scientists have employed a wide variety of experimental techniques and theoretical methods to recover excited-state potential energy surfaces and the wavepackets that evolve on them. These methods have been partially successful but generally do not provide a complete reconstruction of either the excited state wavepacket or potential. We have recently proposed a methodology for reconstructing excited-state molecular wavepackets and the corresponding potential energy surface [Avisar and Tannor, Phys. Rev. Lett., 2011, 106, 170405]. In our approach, the wavepacket is represented as a superposition of the set of vibrational eigenfunctions of the molecular ground-state Hamiltonian. We assume that the multidimensional ground-state potential surface is known, and therefore these vibrational eigenfunctions are known as well. The time-dependent coefficients of the basis functions are obtained by experimental measurement of the resonant coherent anti-Stokes Raman scattering (CARS) signal. Our reconstruction strategy has several significant advantages: (1) the methodology requires no a priori knowledge of any excited-state potential. (2) It applies to dissociative as well as to bound excited-state potentials. (3) It is general for polyatomics. (4) The excited-state potential surface is reconstructed simultaneously with the wavepacket. Apart from making a general contribution to the field of excited-state spectroscopy, our method provides the information on the excited-state wavepacket and potential necessary to design laser pulse sequences to control photochemical reactions.

Assessment of Franck-Condon Methods for Computing Vibrationally Broadened UV-vis Absorption Spectra of Flavin Derivatives: Riboflavin, Roseoflavin, and 5-Thioflavin.

We address the performance of the vertical and adiabatic Franck-Condon (VFC/AFC) approaches combined with time-independent or time-dependent (TI/TD) formalisms in simulating the one-photon absorption spectra of three flavin compounds with distinct structural features. Calculations were done in the gas phase and in two solvents (water, benzene) for which experimental reference measurements are available. We utilized the independent mode displaced harmonic oscillator model without or with frequency alteration (IMDHO/IMDHO-FA) and also accounted for Duschinsky mixing effects. In the initial validation on the first excited singlet state of riboflavin, the range-separated functionals, CAM-B3LYP and ωB97xD, showed the best performance, but B3LYP also gave a good compromise between peak positions and spectral topology. Large basis sets were not mandatory to obtain high-quality spectra for the selected systems. The presence of a symmetry plane facilitated the computation of vibrationally broadened spectra, since different FC variants yield similar results and the harmonic approximation holds rather well. Compared with the AFC approach, the VFC approach performed equally well or even better for all three flavins while offering several advantages, such as avoiding error-prone geometry optimization procedures on excited-state surfaces. We also explored the advantages of curvilinear displacements and of a Duschinsky treatment for the AFC spectra in cases when a rotatable group is present on the chromophore. Taken together, our findings indicate that the combination of the VFC approach with the TD formalism and the IMDHO-FA model offers the best overall performance.

Validity of Linear Response Theory for Time-Dependent Fluorescence in Staphylococcus Nuclease

We report a theoretical study on the relaxation dynamics of Staphylococcus nuclease following photon excitation. Molecular dynamics simulations were implemented for both ground state and excited state surface of Trp140. Over the course of 40 ns ground state simulation, a structural transition was observed from one isomeric protein configuration to another. No obvious isomerization process was exhibited in the excited state simulations. Using linear response theory and direct nonequilibrium approach, time-dependent Stokes shift, as well as its time-infinity value, was evaluated for both ground state isomers. Comparison between these methods exhibits severe disagreement. The nonequilibrium simulations show the similar relaxation dynamics as the excited state linear response approach, whereas they severely differ from the ground state linear response evaluation. Further examination reveals that the isomerization process breaks the characteristics of the energy gap histogram from Gaussian statistics. We also made the comparison between the experimental and simulation results. The significant inertial decay, in theory, is absent in the experiment. The ground state linear response evaluation provides a better agreement with the experimental results among all three approaches.

Photoinduced oxidation of water in the pyridine-water complex: comparison of the singlet and triplet photochemistries.

It has recently been shown that low-lying dark charge-separated singlet excited states of nπ* and ππ* character exist in the hydrogen-bonded pyridine-water complex in addition to the familiar nπ* and ππ* excited states of the pyridine chromophore. The former have been shown to promote the transfer of a proton from water to pyridine, resulting in the pyridinyl-hydroxyl radical pair. In the present work, the potential-energy surfaces of the triplet excited states of the pyridine-water complex have been explored with the same ab initio electronic-structure methods (ADC(2), CASPT2). Minimum-energy reaction paths for excited-state H atom transfer, energy surfaces in the vicinity of the barrier for H atom transfer, as well as multistate surface crossings have been characterized. The photochemical reaction mechanisms on the singlet and triplet potential-energy surfaces are compared, and their relevance for photoinduced water oxidation with the pyridine chromophore are discussed.

Inverted substrate preferences for photochemical heterolysis arise from conical intersection control.

Heterolytic bond scission is a staple of chemical reactions. While qualitative and quantitative models exist for understanding the thermal heterolysis of carbon-leaving group (C-LG) bonds, no general models connect structure to reactivity for heterolysis in the excited state. CASSCF conical intersection searches were performed to investigate representative systems that undergo photoheterolysis to generate carbocations. Certain classes of unstabilized cations are found to have structurally nearby, low-energy conical intersections, whereas stabilized cations are found to have high-energy, unfavorable conical intersections. The former systems are often favored from photochemical heterolysis, whereas the latter are favored from thermal heterolysis. These results suggest that the frequent inversion of the substrate preferences for nonadiabatic photoheterolysis reactions arises from switching from transition-state control in thermal heterolysis reactions to conical intersection control for photochemical heterolysis reactions. The elevated ground-state surfaces resulting from generating unstabilized or destabilized cations, in conjunction with stabilized excited-state surfaces, can lead to productive conical intersections along the heterolysis reaction coordinate.

Photoisomerization among ring-open merocyanines. II. A computational study.

The photochemical isomerization of the trans-trans-cis to the trans-trans-trans isomer of the merocyanine form of 6-nitro BIPS, which has been studied with femtosecond transient absorption spectroscopy [S. Ruetzel, M. Diekmann, P. Nuernberger, C. Walter, B. Engels, and T. Brixner, J. Chem. Phys. 140, 224310 (2014)], is investigated using time-dependent density functional theory in conjunction with polarizable continuum models. Benchmark calculations against SCS-ADC(2) evaluate the applicability of the CAM-B3LYP functional. Apart from a relaxed scan in the ground state with additional computation of the corresponding excitation energies, which produces the excited-state surface vertical to the ground-state isomerization coordinate, a relaxed scan in the S1 gives insight into the geometric changes orthogonal to the reaction coordinate and the fluorescence conditions. The shape of the potential energy surface (PES) along the reaction coordinate is found to be highly sensitive to solvation effects, with the method of solvation (linear response vs. state-specific) being critical. The shape of the PES as well as the computed harmonic frequencies in the S1 minima are in line with the experimental results and offer a straightforward interpretation.

State-specific solvation effect on the intramolecular charge transfer reaction in solution: A linear-response free energy TDDFT method

State-specific solvation for constructing excited-state free energy surfaces in solution is discussed within the framework of reference interaction site model/time-dependent density functional theory. The self-consistency between the solute electron density and solvation structure is achieved using the linear-response free energy approach. The proposed method is applied to the intramolecular charge-transfer (ICT) state formation of 4-(N-pyrrolo)benzonitrile. The linear-response solvation method underestimates the ICT state severely, and the calculation predicts erroneously that the reaction is endergonic. Therefore, it is essential to apply the state-specific method when the transition density fails in describing the solute–solvent interaction upon excitation.

Molecular Dynamics of Methanol Monocation (CH3OH+) in Strong Laser Fields

Experimental studies by Yamanouchi and co-workers indicate that an intense 40 fs 800 nm laser pulse can cause CH3OH(+) to isomerizes during the pulse. The potential energy surfaces of methanol neutral, monocation, and singlet and triplet dication were explored using the CBS-APNO, CBS-QB3, CAM-B3LYP, and B3LYP levels of theory. Ab initio classical trajectories were calculated in the presence of a 2.9 × 10(14) W/cm(2) 800 nm laser field for methanol monocation on the ground state potential energy surface using the CAM-B3LYP/6-31G(d,p) level of theory. With only zero point energy, CH3OH(+) gained less than 15 kcal/mol from the 40 fs laser pulse, which was not enough to overcome any of the barriers for isomerization or fragmentation. To simulate extra energy deposited during the ionization process, 75, 100, and 125 kcal/mol of vibrational energy was added to the initial structures. After 400 fs, the distribution of product was CH2OH(+) + H (79-81%), HCOH(+) + H2 (9-13%), CH2OH2(+) (1-3%), CH3(+) + OH (1-3%), and CH2(+) + H2O (<0.5%). The estimated kinetic energy releases are in accord with experimental findings. Experimental results using a probe pulse to ionize CH3OH(+) to the dication showed substantial fraction C-O dissociation in both CH3OH(+) and CH2OH2(+) after the pulse. Because very few CH2OH2(+) → CH2(+) + H2O trajectories were seen in the simulation, the calculations suggest that some of the processes observed experimentally must occur on excited state surfaces or may be due to coupled nuclear-electron dynamics during the pump pulse.

Calculation of absorption spectra involving multiple excited states: Approximate methods based on the mixed quantum classical Liouville equation

We investigate the calculation of absorption spectra based on the mixed quantum classical Liouville equation (MQCL) methods. It has been shown previously that, for a single excited state, the averaged classical dynamics approach to calculate the linear and nonlinear spectroscopy can be derived using the MQCL formalism. This work focuses on problems involving multiple coupled excited state surfaces, such as in molecular aggregates and in the cases of coupled electronic states. A new equation of motion to calculate the dipole-dipole correlation functions within the MQCL formalism is first presented. Two approximate methods are then proposed to solve the resulted equations of motion. The first approximation results in a mean field approach, where the nuclear dynamics is governed by averaged forces depending on the instantaneous electronic states. A modification to the mean field approach based on first order moment expansion is also proposed. Numerical examples including calculation of the absorption spectra of Frenkel exciton models of molecular aggregates, and the pyrazine molecule are presented.

Competing adiabatic and nonadiabatic pathways in the cis–trans photoisomerization of cis-1,2-di(1-methyl-2-naphthyl)ethene. A zwitterionic twisted intermediate

Identical fluorescence lifetimes and spectra of cis- and trans-1,2-di(1-methyl-2-naphthyl)ethene reveal an adiabatic cis → trans photoisomerization pathway that accounts for a significant fraction of observed cis → trans photoisomerization quantum yields. The fluorescence quantum yields of both isomers decrease as the solvent is changed from methylcyclohexane to the more polarizable toluene or to the more polar acetonitrile and there is a corresponding increase in the photoisomerization quantum yield in the trans → cis direction. The pronounced solvent dependence of the contribution of the adiabatic pathway to cis → trans photoisomerization--methylcyclohexane (70%), toluene (45%), acetonitrile (31%)--is consistent with the participation of a zwitterionic twisted intermediate, (1)p*, on the singlet excited state surface which is stabilized as the polarizability and/or polarity of the solvent is increased. Solvent stabilization of (1)p* favours the nonadiabatic photoisomerization pathways of both isomers and diminishes the cis → trans adiabatic pathway.

Near-threshold photodissociation dynamics of CHCl3

Energy- and angle-resolved photofragment distributions for ground-state Cl ((2)P3/2) and spin-orbit excited Cl* ((2)P1/2) have been recorded using the velocity map imaging technique after photodissociation of chloroform at wavelengths of 193 and ∼235 nm. Translational energy distributions are rather broad and peak between 0.6 and 1.0 eV. The spin-orbit branching ratios [Cl*]/[Cl] are 1 and 0.3 at 193 and 235 nm, respectively, indicating the involvement of two or more excited state surfaces. Considering the anisotropy parameters and branching ratios collectively, we conclude that the reaction at 193 nm takes place predominantly on the (1)Q1 surface, while the (3)Q1 surface gains importance at lower dissociation energies around 235 nm.