Topology of Conical Intersection Seams and the Geometric Phase.

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

Frenkel exciton photodynamics of self-assembled monolayers of azobiphenyls.

We performed computational simulations of the photodynamics of a self-assembled monolayer (SAM) of an azobenzene derivative (azobiphenyl, ABPT) on a gold surface. An excitonic approach was adopted in a semiempirical framework, which allowed us to consider explicitly the electronic degrees of freedom of 12 azobenzene chromophores. The surface hopping scheme was used for nonadiabatic molecular dynamics simulations. According to our results for an all trans-ABPT SAM, the excitation energy transfer between different chromophores, very fast in the ππ∗ manifold, does not occur between nπ∗ states. As a consequence, the excitation transfer does not play an important role in the quenching of the azobenzene photoisomerization in the SAM (experimentally observed and reproduced by our calculations) which, instead, has to be attributed to steric effects.

Sampling initial positions and momenta for nuclear trajectories from quantum mechanical distributions.

We compare algorithms to sample initial positions and momenta of a molecular system for classical trajectory simulations. We aim at reproducing the phase space quantum distribution for a vibrational eigenstate, as in Wigner theory. Moreover, we address the issue of controlling the total energy and the energy partition among the vibrational modes. In fact, Wigner's energy distributions are very broad, quite at variance with quantum eigenenergies. Many molecular processes depend sharply on the available energy, so a better energy definition is important. Two approaches are introduced and tested: the first consists in constraining the total energy of each trajectory to equal the quantum eigenenergy. The second approach modifies the phase space distribution so as to reduce the deviation of the single mode energies from the correct quantum values. A combination of the two approaches is also presented.

Photochemistry in the strong coupling regime: A trajectory surface hopping scheme.

The strong coupling regime between confined light and organic molecules turned out to be promising in modifying both the ground state and the excited states properties. Under this peculiar condition, the electronic states of the molecule are mixed with the quantum states of light. The dynamical processes occurring on such hybrid states undergo several modifications accordingly. Hence, the dynamical description of chemical reactivity in polaritonic systems needs to explicitly take into account the photon degrees of freedom and nonadiabatic events. With the aim of describing photochemical polaritonic processes, in the present work, we extend the direct trajectory surface hopping scheme to investigate photochemistry under strong coupling between light and matter.

Delocalization effects in singlet fission: Comparing models with two and three interacting molecules.

We present surface hopping simulations of singlet fission in 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF). In particular, we performed simulations based on quantum mechanics/molecular mechanics (QM/MM) schemes in which either two or three ThBF molecules are inserted in the QM region and embedded in their MM crystal environment. Our aim was to investigate the changes in the photodynamics that are brought about by extending the delocalization of the excited states beyond the minimal model of a dimer. In the simulations based on the trimer model, compared to the dimer-based ones, we observed a faster time evolution of the state populations, with the largest differences associated with both the rise and decay times for the intermediate charge transfer states. Moreover, for the trimer, we predicted a singlet fission quantum yield of ∼204%, which is larger than both the one extracted for the dimer (∼179%) and the theoretical upper limit of 200% for the dimer-based model of singlet fission. Although our study cannot account for the effects of extending the delocalization beyond three molecules, our findings clearly indicate how and why the singlet fission dynamics can be affected.

Nonadiabatic dynamics simulations of singlet fission in 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene crystals.

We present simulations of the singlet fission dynamics in 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF), a thienoquinoid compound recently investigated experimentally by Kawata et al. The simulation model consisted of two ThBF molecules embedded in their crystal environment. The aim was to understand the singlet fission mechanism, and to predict the excited state lifetimes and the singlet fission quantum yield, hitherto unknown. The simulations were performed by the trajectory surface hopping approach with on-the-fly calculations of the electronic wave functions and energies by the semiempirical FOMO-CI method. We found that the initially photogenerated excitonic bright state decays to the lower dark state with a biexponential behaviour, essentially due to transitions to other close lying states. The dark state in turn decays with a lifetime of about 1 ps to the double triplet 1TT state, which is long-lived, as ascertained by performing a simulation with inclusion of the spin-orbit coupling. The singlet fission quantum yield is predicted to be close to the theoretical maximum of 200%. In view of using this thienoquinoid compound in photovoltaic devices, a major drawback is the low energy of the T1 state at its equilibrium geometry.

Energy Selection in Nonadiabatic Transitions.

In this work we investigate whether and how a molecule undergoing a nonadiabatic transition can show different energy mean values and distributions in the two electronic states that are populated. We analyze three models, of which models I and II mimick the limiting cases of almost adiabatic and almost diabatic regimes, respectively, and are solvable by first-order perturbation theory. Model III represents realistically the photodissociation of a diatomic molecule and is treated numerically. The three models provide a consistent picture of the energy selection effect. For a typical avoided crossing, the wavepacket component that undegoes the transition between the two adiabatic states has a larger mean value of energy than the other component, both for upward and for downward transitions. The analysis of model II shows that the Landau-Zener rule can be deduced in a fully quantum mechanical way. We believe that the energy selection effect can be observed experimentally in the photodissociation of diatomic molecules. The effect should be particularly relevant for wavepackets endowed with a broad energy spectrum, as the result of excitation with ultrashort light pulses.

Decoding the Molecular Basis for the Population Mechanism of the Triplet Phototoxic Precursors in UVA Light-Activated Pyrimidine Anticancer Drugs.

The photosensitization of DNA by thionucleosides is a promising photo-chemotherapeutic treatment option for a variety of malignancies. DNA metabolization of thionated prodrugs can lead to cell death upon exposure to a low dose of UVA light. The exact mechanisms of thionucleoside phototoxicity are still not fully understood. In this work, we have combined femtosecond broadband transient absorption experiments with state-of-the-art molecular simulations to provide mechanistic insights into the ultrafast and efficient population of the triplet state in the UVA-activated pyrimidine anticancer drug 4-thiothymine. The triplet state is thought to act as a precursor to DNA lesions and the reactive oxygen species responsible for 4-thiothymine photocytotoxicity. The electronic-structure and mechanistic results presented in this contribution reveal key molecular design criteria that can assist in developing alternative chemotherapeutic agents that may overcome some of the primary deficiencies of classical photosensitizers.

Surface hopping investigation of benzophenone excited state dynamics.

We present a simulation of the photodynamics of benzophenone for the first 20 ps after n →π* excitation, performed by trajectory surface hopping calculations with on-the-fly semiempirical determination of potential energy surfaces and electronic wavefunctions. Both the dynamic and spin-orbit couplings are taken into account, and time-resolved fluorescence emission is also simulated. The computed decay time of the S1 state is in agreement with experimental observations. The direct S1→ T1 intersystem crossing (ISC) accounts for about 2/3 of the S1 decay rate. The remaining 1/3 goes through T2 or higher triplets. The nonadiabatic transitions within the triplet manifold are much faster than ISC and keep the population of T1 at about 3/4 of the total triplet population, and that of the other states (mainly T2) at 1/4. Two internal coordinates are vibrationally active immediately after n →π* excitation: one is the C[double bond, length as m-dash]O stretching and the other one is a combination of the conrotatory torsion of phenyl rings and of bending involving the carbonyl C atom. The period of the torsion-bending mode coincides with oscillations in the time-resolved photoelectron spectra of Spighi et al. and substantially confirms their assignment.

Potential energy surfaces for the HBr(+) + CO2 → Br + HOCO(+) reaction in the HBr(+) (2)Π3/2 and (2)Π1/2 spin-orbit states.

Quantum mechanical (QM) + molecular mechanics (MM) models are developed to represent potential energy surfaces (PESs) for the HBr(+) + CO2 → Br + HOCO(+) reaction with HBr(+) in the (2)Π3/2 and (2)Π1/2 spin-orbit states. The QM component is the spin-free PES and spin-orbit coupling for each state is represented by a MM-like analytic potential fit to spin-orbit electronic structure calculations. Coupled-cluster single double and perturbative triple excitation (CCSD(T)) calculations are performed to obtain "benchmark" reaction energies without spin-orbit coupling. With zero-point energies removed, the "experimental" reaction energy is 44 ± 5 meV for HBr(+)((2)Π3/2) + CO2 → Br((2)P3/2) + HOCO(+), while the CCSD(T) value with spin-orbit effects included is 87 meV. Electronic structure calculations were performed to determine properties of the BrHOCO(+) reaction intermediate and [HBr⋯OCO](+) van der Waals intermediate. The results of different electronic structure methods were compared with those obtained with CCSD(T), and UMP2/cc-pVTZ/PP was found to be a practical and accurate QM method to use in QM/MM direct dynamics simulations. The spin-orbit coupling calculations show that the spin-free QM PES gives a quite good representation of the shape of the PES originated by (2)Π3/2HBr(+). This is also the case for the reactant region of the PES for (2)Π1/2 HBr(+), but spin-orbit coupling effects are important for the exit-channel region of this PES. A MM model was developed to represent these effects, which were combined with the spin-free QM PES.

The photo-orientation of azobenzene in viscous solutions, simulated by a stochastic model.

We report a computational study of the photo-orientation kinetics in a viscous solution of azobenzene in ethylene glycol, under irradiation with linearly polarized light. The development of anisotropy and its interplay with photoisomerization are simulated by a stochastic model. A distinctive feature of the model is that it takes into account the photo-orientation angular distributions, specific for each isomer, obtained by nonadiabatic dynamics simulations at the molecular level. We find that the anisotropy, as measured by optical absorption dichroism, does not necessarily increase monotonously with time. As expected, the photo-orientation turns out to be strongly coupled with photoisomerization, but the latter is not a mandatory ingredient of this phenomenon: we predict that any chromophore undergoing large amplitude geometry relaxation during its excited state dynamics can develop anisotropy under suitable conditions.

Interplay of radiative and nonradiative transitions in surface hopping with radiation-molecule interactions.

We implemented a method for the treatment of field induced transitions in trajectory surface hopping simulations, in the framework of the local diabatization scheme, especially suited for on-the-fly dynamics. The method is applied to a simple one-dimensional model with an avoided crossing and compared with quantum wavepacket dynamics. The results show the importance of introducing a proper decoherence correction to surface hopping, in order to obtain meaningful results. Also the energy conservation policy of standard surface hopping must be revised: in fact, the quantum wavepacket energetics is well reproduced if energy absorption/emission is allowed for in the hops determined by radiation-molecule coupling. To our knowledge, this is the first time the issues of decoherence and energy conservation have been analyzed in depth to devise a mixed quantum-classical method for dynamics with molecule-field interactions.

Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories.

In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH.

Dynamics of acetone photodissociation: a surface hopping study.

We present on the fly surface hopping simulations of the dynamics of photoexcited acetone in the n → π* band, taking into account both the spin-orbit and the dynamic couplings and allowing for the C-C bond dissociation. The S0, S1, T1 and T2 states were considered and the propagation time was 50 ps. According to the simulation results, after excitation to S1 both Internal Conversion (IC) to S0 and InterSystem Crossing (ISC) to T1 or T2 take place at comparable rates; T2 plays an important role and the simultaneous treatment of the spin-orbit and dynamic couplings is shown to be mandatory to describe the photodynamics. We propose a mechanism that explains the observed fast and slow decay rates of the S1 state of acetone.

Theoretical study of the chemiluminescence of the Al + H2O reaction.

We performed surface hopping simulations of Al + H(2)O collisions by a direct semiempirical method, reproducing the conditions of previous beam-gas experiments. We observed the formation of the HAlOH species, that dissociates to AlOH + H after a lifetime of about 0.6 ps. This species undergoes nonadiabatic transitions to its first excited state and is responsible for chemiluminescence in the visible range, while the Al-H(2)O complex emits in the infrared. The computed emission band in the visible is red-shifted with respect to the experimental one, because of slight inaccuracies of the potential energy surfaces. However, collisions with more water molecules and exciplex formation with excited Al((2)S, (4)P) atoms may also contribute to the short wavelength emission, as we show by accurate ab initio calculations.

Dual photoisomerization mechanism of azobenzene embedded in a lipid membrane.

The photoisomerization of chromophores embedded in biological environments is of high importance for biomedical applications, but it is still challenging to define the photoisomerization mechanism both experimentally and computationally. We present here a computational study of the azobenzene molecule embedded in a DPPC lipid membrane, and assess the photoisomerization mechanism by means of the quantum mechanics/molecular mechanics surface hopping (QM/MM-SH) method. We observe that while the trans-to-cis isomerization is a slow process governed by a torsional mechanism due to the strong interaction with the environment, the cis-to-trans mechanism is completed in sub-ps time scale and is governed by a pedal-like mechanism in which both weaker interactions with the environment and a different geometry of the potential energy surface play a key role.

Effect of Initial Conditions Sampling on Surface Hopping Simulations in the Ultrashort and Picosecond Time Range. Azomethane Photodissociation as a Case Study.

We tested the effect of different ways of sampling the initial conditions in surface hopping simulations, with a focus on the initial energy distributions and on the treatment of the zero point energy (ZPE). As a test case, we chose the gas phase photodynamics of azomethane, which features different processes occurring in overlapping time scales: geometry relaxation in the excited state, internal conversion, photoisomerization, and fast and slow dissociation. The simulations, based on a semiempirical method, had a sufficiently long duration (10 ps) to encompass all of the above processes. We tested several variants of methods based on the quantum mechanical (QM) distributions of the nuclear coordinates q and momenta p, which yield, at least on the average over a large sampling set, the correct QM energy, namely the ZPE when starting from the ground vibrational state. We compared the QM samplings with the classical Boltzmann (CB) distribution obtained by a thermostated trajectory, whereby thermal effects are taken into account, but the ZPE is utterly ignored. We found that most QM and CB approaches yield similar results as to short time dynamics and decay lifetimes, whereas the rate of the ground state dissociation reaction CH3NNCH3 → CH3NN + CH3 is sharply affected by the sampling method. With QM samplings a large fraction of trajectories dissociate promply (<1 ps) after decay to the ground state and with rates of the order of 10-1 ps-1 after the first ps. Instead, the CB samplings yield a much smaller fraction of prompt dissociations and much lower rates at long times. We provided evidence that the ZPE "leaks" from high frequency modes to the reactive ones (N-C bond elongations), therefore unphysically increasing the dissociation rates with QM samplings. We show that an effective way to take into account the ZPE and to avoid the "leaking" problem is to add the ZPE to the potential energy surfaces as a function of the most relevant internal coordinates. Then, Boltzmann sampling can be done as usual, so this approach is suitable also for condensed state dynamics. In the tests we present here, the ZPE correction method yields dissociation rates intermediate between QM and uncorrected Boltzmann samplings.

Stochastic model for photoinduced anisotropy.

We present a stochastic model for the kinetics of photoinduced anisotropy in a sample of molecular chromophores that may undergo photoisomerization. It is assumed that the chromophores do not interact among them, but are embedded in a medium that slows down the rotational diffusion. The model makes use of data about the photoinduced reorientation of the single chromophore, its photoisomerization and its rotational diffusion, that are made available by molecular dynamics simulations. For the first time such molecular scale processes are computationally connected to the development of anisotropy in a large sample and on a long time scale. A test on azobenzene shows the potentiality of the method and the interplay between photoinduced anisotropy and photoisomerization.

Photo-orientation of axial molecules.

We examine the photo-orientation of molecules in a linearly polarized field and the ensuing optical anisotropy of a sample. We propose a theoretical model that considers both photoinduced reorientation and rotational diffusion, for the case of linear or axial molecules not interacting among them, as in dilute solutions in viscous media. We perform numerical simulations to highlight the dependence on the parameters of the molecular reorientation processes, on the intensity of the exciting light, and on the use of cross polarized pulses. As a realistic example we simulate the photo-orientation of azobenzene in ethylene glycol.

Semiempirical Hamiltonian for simulation of azobenzene photochemistry.

We present a semiempirical Hamiltonian that provides an accurate description of the first singlet and triplet potential energy surfaces of azobenzene for use in direct simulations of the excited-state dynamics. The parameterization made use of spectroscopic and thermochemical data and the best ab initio results available to date. Two-dimensional potential energy surfaces based on constrained geometry optimizations are presented for the states that are most relevant for the photochemistry of azobenzene, namely, S(0), S(1), and S(2). In order to run simulations of the photodynamics of azobenzene in hydrocarbons or hydroxylic solvents, we determined the interactions of methane and methanol with the azo group by ab initio calculations and fitted the interactions with a QM/MM interaction Hamiltonian.