On the Theoretical Determination of Photolysis Properties for Atmospheric Volatile Organic Compounds

Volatile organic compounds (VOCs) are ubiquitous atmospheric molecules that generate a complex network of chemical reactions in the troposphere, often triggered by the absorption of sunlight. Understanding the VOC composition of the atmosphere relies on our ability to characterize all of their possible reaction pathways. When considering reactions of (transient) VOCs with sunlight, the availability of photolysis rate constants, utilized in general atmospheric models, is often out of experimental reach due to the unstable nature of these molecules. Here, we show how recent advances in computational photochemistry allow us to calculate in silico the different ingredients of a photolysis rate constant, namely, the photoabsorption cross-section and wavelength-dependent quantum yields. The rich photochemistry of tert-butyl hydroperoxide, for which experimental data are available, is employed to test our protocol and highlight the strengths and weaknesses of different levels of electronic structure and nonadiabatic molecular dynamics to study the photochemistry of (transient) VOCs.

Ground-state geometry of tBHP was optimized at the MP2/aug-cc-pVDZ level, if not stated otherwise. Peroxide bond length (O−O) is challenging to predict accurately, and MP2 is known to provide a good compromise 23-25 (see Table S1). It is important to note that O−O bond length has a large impact on vertical excitation energies towards OH dissociative states (Table S2 and Table S3).
Photoabsorption cross-sections were calculated with the nuclear ensemble approach 26 based on a harmonic Wigner distribution in the ground electronic state. Harmonic vibra-S2 tional frequencies at the ground-state minimum were evaluated with the NumForce script within the Turbomole package. For the Wigner distribution, we assume that the molecule is in the ground vibrational state for all its modes. Temperature effects (e.g. room temperature) may excite low frequency modes, which in first approximation are considered to not significantly alter the absorption cross-sections (and photolysis quantum yields). 27 In total, 500 initial conditions were sampled, and the electronic transitions (excitation energies and oscillator strengths) were computed with different electronic-structure methods (Fig. S4). The lowest three excited singlet states were considered. The spectral transitions were broadened with Lorentzians using a phenomenological broadening of 0.05 eV.
Trajectory surface hopping 28 simulations were performed with the SHARC 2.1 code 29,30 coupled to BAGEL electronic structure package. Four electronic states were considered.
Nonadiabatic couplings were obtained by using the wavefunction overlap scheme, and kinetic energy was adjusted by rescaling the nuclear velocity vector following a successful hop. Electronic populations were corrected by the energy-based decoherence correction of Granucci and Persico. 31 The nuclear dynamics time step was 0.5 fs, with 25 substeps for propagation of the electronic quantities. 500 initial conditions (nuclear configurations and momenta) were randomly sampled from the Wigner distribution as described above. However, since each of the initial conditions can be initiated from any of the 3 excited states, there are 1500 unique initial conditions for the dynamics. 100 trajectories were initiated in each narrow energy window defined in Fig. 2 (i.e., in the excited state which falls within the energy window) based on random sampling, except for the lowest energy window where only 58 initial conditions could be sampled. Only a small number of trajectories had to be discarded from the analysis (Table S4) due to discontinuities in the total classical energy. However, if energy discontinuity occurs after the the dissociation limit was passed and the outcome of the photolysis was unambiguous, the trajectory was kept in the analysis.
Most trajectories were 30 fs long, which is a sufficient time for photodissociation to take place, while only a small number had to be extended to a longer time scale (up to 100 fs).

S3
The standard deviations of photolysis quantum yields were estimated following Persico and Granucci. 32 Molecular structures and orbitals were visualized with VMD 1.9.1 program. 33 Fig. 4 in the main text.  Figure S5: Energy profile for an exemplary trajectory following the OH photodissociation channel. Note that a sharp change in the S 4 potential energy appears as n σ * OH state is destabilized and the doubly excited state (n σ * OO ) falls down in energy. Figure S6: Energy profiles for exemplary trajectories following the H photodissociation channel and ending up in (a) an excited state and (b) the ground state. Excited-state H dissociation occurs for 85% of the trajectories. S12 Figure S7: Energy profile for an exemplary trajectory following the O+H photodissociation channel. Figure S8: Energy profile for an exemplary trajectory following the O photodissociation channel. A movie for this trajectory is available. We note that the H roaming motion is likely related to the initial excitation to a nσ * OH state (i.e., different from the n σ * OH state), a higher energy state which occasionally falls down in energy as a result of nuclear distortions.

S14
Comments on the appropriateness of TSH to study the photody-

namics of tBHP
We would like to note here the importance of considering the approximations of the TSH method for performing nonadiabatic molecular dynamics. TSH employs a swarm of independent classical trajectories hopping between electronic states to describe the nonadiabatic dynamics of nuclei. 28,32 As a result of its approximations, TSH is believed to perform well for nonadiabatic processes involving simple (and single) crossings between electronic states leading to a rapid decay towards the ground electronic state. We carefully checked that the excited-state of tBHP was fulfilling these requirements and observed rapid decays of the excited molecules towards the ground state -without recrossings between pair of electronic states -building up confidence in the result of the TSH dynamics. We would like to note here that we also observed a few cases (in particular for the photodynamics initiated from the high-energy windows) where a TSH trajectory would spend time in an extended region of coupling between electronic states (see the energy proximity between S 3 and S 2 in the left panel of Fig. S9). Extended coupling regions are notorious for challenging the approximations of TSH. 31,32 Hence, we compared for such a run the result of TSH and that of the method coined ab initio multiple spawning (AIMS), using in both cases the same level of electronic-structure theory (SA(4)-CASSCF(10/8)/def2-SVPD). AIMS makes a step closer to quantum dynamics by representing the dynamics of nuclear wavepackets by a swarm of coupled trajectory basis functions (TBFs, moving multidimensional Gaussian functions). 37,38 The number of these TBFs can be increased as needed in nonadiabatic regions. The AIMS simulations presented here were performed with the Molpro quantum chemistry package. 39 The dynamics of the first TBF in an AIMS calculation of tBHP (initiated in S 3 ) is depicted on the left panel of Fig. S9 (plain line). The energy gap between S 3 and S 2 is reduced multiple times during the short-time dynamics depicted here, resulting in a stepwise transfer of population towards S 2 . The population decay as depicted by AIMS for this particular initial condition is shown in the right panel of Fig. S9 (red line). TSH (50 averaged runs, all S15 starting from the same initial condition as AIMS) shows a faster decay of the S 3 population -a process that can be related to the overcoherence of the TSH method 32 -but importantly both methods agree for the fact the S 3 population is transferred towards S 2 within less than 8 fs. Figure S9: Comparison between TSH and AIMS for a given initial condition showing an extended coupling region (both simulations were performed at the SA(4)-CASSCF(10/8)/def2-SVPD level of theory). Left panel: energy profile for the first trajectory basis function (TBF1) of an AIMS run evolving on S 3 and spawning new TBFs in S 2 at times indicated by red circles. Right panel: comparison between the population trace for the excited electronic state S 3 with AIMS (red line) and TSH (purple line) for the initial condition depicted in the left panel. The TSH result is obtained by averaging over 50 TSH runs with the same initial condition but different seed for the random number generator, allowing for an adequate sampling of the stochastic nonadiabatic transitions. S16