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  1. Conical intersections play a critical role in excited-state dynamics of polyatomic molecules because they govern the reaction pathways of many nonadiabatic processes. However, ultrafast probes have lacked sufficient spatial resolution to image wave-packet trajectories through these intersections directly. Here in this paper, we present the simultaneous experimental characterization of one-photon and two-photon excitation channels in isolated CF 3I molecules using ultrafast gas-phase electron diffraction. In the two-photon channel, we have mapped out the real-space trajectories of a coherent nuclear wave packet, which bifurcates onto two potential energy surfaces when passing through a conical intersection. In the one-photon channel, we havemore » resolved excitation of both the umbrella and the breathing vibrational modes in the CF 3 fragment in multiple nuclear dimensions. These findings benchmark and validate ab initio nonadiabatic dynamics calculations.« less
  2. Here, the spin-restricted ensemble-referenced Kohn-Sham (REKS) method is based on an ensemble representation of the density and is capable of correctly describing the non-dynamic electron correlation stemming from (near-)degeneracy of several electronic configurations. The existing REKS methodology describes systems with two electrons in two fractionally occupied orbitals. In this work, the REKS methodology is extended to treat systems with four fractionally occupied orbitals accommodating four electrons and self-consistent implementation of the REKS(4,4) method with simultaneous optimization of the orbitals and their fractional occupation numbers is reported. The new method is applied to a number of molecular systems where simultaneous dissociationmore » of several chemical bonds takes place, as well as to the singlet ground states of organic tetraradicals 2,4-didehydrometaxylylene and 1,4,6,9-spiro[4.4]nonatetrayl.« less
  3. We recently outlined an efficient multi-tiered parallel ab initio excitonic framework that utilizes time dependent density functional theory (TDDFT) to calculate ground and excited state energies and gradients of large supramolecular complexes in atomistic detail – enabling us to undertake non-adiabatic simulations which explicitly account for the coupled anharmonic vibrational motion of all the constituent atoms in a supramolecular system. Here we apply that framework to the 27 coupled bacterio-chlorophyll-a chromophores which make up the LH2 complex, using it to compute an on-the-fly nonadiabatic surface-hopping (SH) trajectory of electronically excited LH2. Part one of this article is focussed on calibratingmore » our ab initio exciton Hamiltonian using two key parameters: a shift δ, which corrects for the error in TDDFT vertical excitation energies; and an effective dielectric constant ε, which describes the average screening of the transition-dipole coupling between chromophores. Using snapshots obtained from equilibrium molecular dynamics simulations (MD) of LH2, we tune the values of both δ and ε through fitting to the thermally broadened experimental absorption spectrum, giving a linear absorption spectrum that agrees reasonably well with experiment. In part two of this article, we construct a time-resolved picture of the coupled vibrational and excitation energy transfer (EET) dynamics in the sub-picosecond regime following photo-excitation. Assuming Franck–Condon excitation of a narrow eigenstate band centred at 800 nm, we use surface hopping to follow a single nonadiabatic dynamics trajectory within the full eigenstate manifold. Consistent with experimental data, this trajectory gives timescales for B800→B850 population transfer (τ B800→B850) between 650–1050 fs, and B800 population decay (τ 800→) between 10–50 fs. The dynamical picture that emerges is one of rapidly fluctuating LH2 eigenstates that are delocalized over multiple chromophores and undergo frequent crossing on a femtosecond timescale as a result of the atomic vibrations of the constituent chromophores. The eigenstate fluctuations arise from disorder that is driven by vibrational dynamics with multiple characteristic timescales. The scalability of our ab initio excitonic computational framework across massively parallel architectures opens up the possibility of addressing a wide range of questions, including how specific dynamical motions impact both the pathways and efficiency of electronic energy-transfer within large supramolecular systems.« less
  4. Here, we present a reduced scaling formulation of the state specific complete active space second-order perturbation method (CASPT2) requiring O( N 4) operations and O( N 2) memory for a fixed active space, where N is proportional to system size. Motivated by the properties of the Kronecker sum, we introduce the supporting subspace technique (SST), which decomposes the CASPT2 linear equations into two parts: a single-reference MP2 energy term using dressed orbitals, plus a reduced linear system with dimension scaling as O( N 2). Together with Laplace quadrature, the SST allows us to reformulate CASPT2 using a MP2 energy computationmore » and Fock builds. By further applying the tensor hyper-contraction (THC) approximation, the MP2-like term can be computed with O( N 4) operations, and the remainder can be solved with O( N 3) operations using the preconditioned conjugate gradient method. This is the first application of THC in the context of multi-reference methods. We also developed an efficient implementation of the method by utilizing graphical processing units and exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method against conventional CASPT2 for reactions in the gas phase. We apply the new method to Menshutkin S N2 reactions in carbon nanotubes, demonstrating the feasibility of CASPT2 calculations with O(100) atoms.« less
  5. Hydrogen bonds are fundamental to biological systems and are regularly found in networks implicated in folding, molecular recognition, catalysis, and allostery. Given their ubiquity, we asked the fundamental questions of whether, and to what extent, hydrogen bonds within networks are structurally coupled. To address these questions, we turned to three protein systems, two variants of ketosteroid isomerase and one of photoactive yellow protein. We perturbed their hydrogen bond networks via a combination of site-directed mutagenesis and unnatural amino acid substitution, and we used 1H NMR and high-resolution X-ray crystallography to determine the effects of these perturbations on the lengths ofmore » the two oxyanion hole hydrogen bonds that are donated to negatively charged transition state analogs. Perturbations that lengthened or shortened one of the oxyanion hole hydrogen bonds had the opposite effect on the other. The oxyanion hole hydrogen bonds were also affected by distal hydrogen bonds in the network, with smaller perturbations for more remote hydrogen bonds. Across 19 measurements in three systems, the length change in one oxyanion hole hydrogen bond was propagated to the other, by a factor of –0.30 ± 0.03. This common effect suggests that hydrogen bond coupling is minimally influenced by the remaining protein scaffold. The observed coupling is reproduced by molecular mechanics and quantum mechanics/molecular mechanics (QM/MM) calculations for changes to a proximal oxyanion hole hydrogen bond. However, effects from distal hydrogen bonds are reproduced only by QM/MM, suggesting the importance of polarization in hydrogen bond coupling. These results deepen our understanding of hydrogen bonds and their networks, providing strong evidence for long-range coupling and for the extent of this coupling. In conclusion, we provide a broadly predictive quantitative relationship that can be applied to and can be further tested in new systems.« less
  6. Here, we present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix–vector product formation enables calculations with configuration spaces as large as 30 electronsmore » in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 10 16 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2–5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.« less
  7. The excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene (BD), has long been the subject of controversy due to its strong coupling, ultrafast time scales and the difficulties that theory faces in describing the relevant electronic states in a balanced fashion. Here we apply Ab Initio Multiple Spawning (AIMS) using state-averaged complete active space multistate second order perturbation theory [SA-3-CAS(4/4)-MSPT2] which describes both static and dynamic electron correlation effects, providing a balanced description of both the initially prepared bright 1 1B u (ππ*) state and non-adiabatically coupled dark 2 1A g state of BD. Importantly, AIMS allows formore » on-the-fly calculations of experimental observables. We validate our approach by directly simulating the time resolved photoelectron-photoion coincidence spectroscopy results presented in Paper I [A. E. Boguslavskiy et al., J. Chem. Phys. 148, 164302 (2018)], demonstrating excellent agreement with experiment. Our simulations reveal that the initial excitation to the 1 1B u state rapidly evolves via wavepacket dynamics that follow both bright- and dark-state pathways as well as mixtures of these. In order to test the sensitivity of the AIMS results to the relative ordering of states, we considered two hypothetical scenarios biased toward either the bright 1B u or the dark 2 1A g state. In contrast with AIMS/SA-3-CAS(4/4)-MSPT2 simulations, neither of these scenarios yields favorable agreement with experiment. Thus, we conclude that the excited state non-adiabatic dynamics in BD involves both of these ultrafast pathways.« less
  8. The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1B u (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans’ correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us tomore » report the direct observation of the famously elusive S 1(2 1A g) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 1 1B u and 2 1A g states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S 2(1 1B u) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1B u surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. Lastly, in Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.« less
    Cited by 2
  9. Here, the Born–Oppenheimer approximation underlies much of chemical simulation and provides the framework defining the potential energy surfaces that are used for much of our pictorial understanding of chemical phenomena. However, this approximation breaks down when the dynamics of molecules in excited electronic states are considered. Describing dynamics when the Born–Oppenheimer approximation breaks down requires a quantum mechanical description of the nuclei. Chemical reaction dynamics on excited electronic states is critical for many applications in renewable energy, chemical synthesis, and bioimaging. Furthermore, it is necessary in order to connect with many ultrafast pump–probe spectroscopic experiments. In this review, we providemore » an overview of methods that can describe nonadiabatic dynamics, with emphasis on those that are able to simultaneously address the quantum mechanics of both electrons and nuclei. Such ab initio quantum molecular dynamics methods solve the electronic Schrödinger equation alongside the nuclear dynamics and thereby avoid the need for precalculation of potential energy surfaces and nonadiabatic coupling matrix elements. Two main families of methods are commonly employed to simulate nonadiabatic dynamics in molecules: full quantum dynamics, such as the multiconfigurational time-dependent Hartree method, and classical trajectory-based approaches, such as trajectory surface hopping. In this review, we describe a third class of methods that is intermediate between the two: Gaussian basis set expansions built around trajectories.« less
    Cited by 6

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