Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone.

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ ab initio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

What is the Mechanism of H3+ Formation from Cyclopropane?

We examine the possibility that three hydrogen atoms in one plane of the cyclopropane dication come together in a concerted "ring-closing" mechanism to form H3+, a crucial cation in interstellar gas-phase chemistry. Ultrafast strong-field ionization followed by disruptive probing measurements indicates that the formation time of H3+ is 249 ± 16 fs. This time scale is not consistent with a concerted mechanism, but rather a process that is preceded by ring opening. Measurements on propene, an isomer of cyclopropane, reveal the H3+ formation time to be 225 ± 13 fs, a time scale similar to the H3+ formation time in cyclopropane. Ab initio molecular dynamics simulations and the fact that both dications share a common potential energy surface support the ring-opening mechanism. The reaction mechanism following double ionization of cyclopropane involves ring opening, then H-migration, and roaming of a neutral H2 molecule, which then abstracts a proton to form H3+. These results further our understanding of complex interstellar chemical reactions and gas-phase reaction dynamics relevant to electron ionization mass spectrometry.

Ultrafast internal conversion and photochromism in gas-phase salicylideneaniline.

Salicylideneaniline (SA) is an archetypal system for excited-state intramolecular proton transfer (ESIPT) in non-planar systems. Multiple channels for relaxation involving both the keto and enol forms have been proposed after excitation to S1 with near-UV light. Here, we present transient absorption measurements of hot gas-phase SA, jet-cooled SA, and SA in Ar clusters using cavity-enhanced transient absorption spectroscopy (CE-TAS). Assignment of the spectra is aided by simulated TAS spectra, computed by applying time-dependent complete active space configuration interaction (TD-CASCI) to structures drawn from nonadiabatic molecular dynamics simulations. We find prompt ESIPT in all conditions followed by the rapid generation of the trans keto metastable photochrome state and fluorescent keto state in parallel. Increasing the internal energy increases the photochrome yield and decreases the fluorescent yield and fluorescent state lifetime observed in TAS. In Ar clusters, internal conversion of SA is severely hindered, but the photochrome yield is unchanged. Taken together, these results are consistent with the photochrome being produced via the vibrationally excited keto population after ESIPT.

Linear and Nonlinear Optical Processes Controlling S2 and S1 Dual Fluorescence in Cyanine Dyes.

We report on the changes in the dual fluorescence of two cyanine dyes IR144 and IR140 as a function of viscosity and probe their internal conversion dynamics from S2 to S1 via their dependence on a femtosecond laser pulse chirp. Steady-state and time-resolved measurements performed in methanol, ethanol, propanol, ethylene glycol, and glycerol solutions are presented. Quantum calculations reveal the presence of three excited states responsible for the experimental observations. Above the first excited state, we find an excited state, which we designate as S1', that relaxes to the S1 minimum, and we find that the S2 state has two stable configurations. Chirp-dependence measurements, aided by numerical simulations, reveal how internal conversion from S2 to S1 depends on solvent viscosity and pulse duration. By combining solvent viscosity, transform-limited pulses, and chirped pulses, we obtain an overall change in the S2/S1 population ratio of a factor of 86 and 55 for IR144 and IR140, respectively. The increase in the S2/S1 ratio is explained by a two-photon transition to a higher excited state. The ability to maximize the population of higher excited states by delaying or bypassing nonradiative relaxation may lead to the increased efficiency of photochemical processes.

An accurate, non-empirical method for incorporating decoherence into Ehrenfest dynamics.

In mixed quantum-classical nonadiabatic molecular dynamics methods, the anchoring of the electronic wave function to a single nuclear geometry results in both quantitative and qualitative errors in the dynamics. In the context of both Ehrenfest and trajectory surface hopping methods, methods for incorporating decoherence are widely used to eliminate these errors. However, the accuracy of these methods often depends strongly on the parameterization of the decoherence time and/or other related quantities. Here, we present a refinement of the recently introduced collapse to a block (TAB) scheme for incorporating decoherence into Ehrenfest dynamics. The proposed approach incorporates an approximation to the history of the population dynamics and treats the coherence decay as Gaussian, rather than exponential. This method uses parameters that can be obtained from first principles, rather than empirical fitting. Application to one-dimensional models indicates excellent agreement with numerically exact simulations. We also introduce a second refinement to the TAB method: a robust linear least-squares algorithm for determining collapse probabilities.

CAS without SCF-Why to use CASCI and where to get the orbitals.

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree-Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Finally, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials.

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

Decoherence-corrected Ehrenfest molecular dynamics on many electronic states.

Decoherence corrections increase the accuracy of mixed quantum-classical nonadiabatic molecular dynamics methods, but they typically require explicit knowledge of the potential energy surfaces of all occupied electronic states. This requirement renders them impractical for applications in which large numbers of electronic states are occupied. The authors recently introduced the collapse to a block (TAB) decoherence correction [M. P. Esch and B. G. Levine, J. Chem. Phys. 152, 234105 (2020)], which incorporates a state-pairwise definition of decoherence time to accurately describe dynamics on more than two electronic states. In this work, TAB is extended by introduction of a scheme for efficiently computing a small number of approximate eigenstates of the electronic Hamiltonian, eliminating the need for explicit knowledge of a large number of potential energy surfaces. This adaptation of TAB for dense manifolds of states (TAB-DMS) is systematically improvable by increasing the number of computed approximate eigenstates. Application to a series of one-dimensional model problems demonstrates that TAB-DMS can be accurate when even a very modest number of approximate eigenstates are computed (four in all models tested here). Comparison of TAB simulations to exact quantum dynamical simulations indicates that TAB is quite accurate so long as the decoherence correction is carefully parameterized.

State-pairwise decoherence times for nonadiabatic dynamics on more than two electronic states.

Independent trajectory (IT) nonadiabatic molecular dynamics simulation methods are powerful tools for modeling processes involving transitions between electronic states. Incorporation and refinement of decoherence corrections into popular IT methods, e.g., Ehrenfest dynamics and trajectory surface hopping, is an important means of improving their accuracies. In this work, we identify a new challenge in the development of such decoherence corrections; when a system exists in a coherent superposition of three or more electronic states, coherences may decay unphysically when the decoherence correction is based on decoherence times assigned on a state-wise basis. As a solution, we introduce decoherence corrected Ehrenfest schemes based on decoherence times assigned on a state-pairwise basis. By application of these methods to a set of very simple one-dimensional model problems, we show that one of these state-pairwise methods ("collapse to a block") correctly describes the loss of coherence between all pairs of states in our multistate model problems, whereas a method based on a state-wise description of coherence loss does not. The new one-dimensional models introduced here can serve as useful tests for other decoherence correction schemes.

Electronic and Structural Comparisons between Iron(II/III) and Ruthenium(II/III) Imide Analogs.

To examine structural and electronic differences between iron and ruthenium imido complexes, a series of compounds was prepared with different phosphine basal sets. The starting material for the ruthenium complexes was Ru(NAr/Ar*)(PMe3)3 (Ru1/Ru1*), where Ar = 2,6-(iPr)2C6H3 and Ar* = 2,4,6-(iPr)3C6H2, which were prepared from cis-RuCl2(PMe3)4 and 2 equiv of LiNHAr/Ar*. The starting materials for the iron complexes were the analogous Fe(NAr/Ar*)(PMe3)3 species (Fe1/Fe1*), which were not isolated but could be generated in situ from FeCl2, PMe3, and LiNHAr/Ar*. With both iron and ruthenium, the PMe3 starting materials underwent phosphine replacement with chelating ligands to give new group 8 imido complexes in the +2 oxidation state. Addition of 1,2-bis(diphenylphosphino)ethane (dppe) to M1/M1* gave Ru(NAr/Ar*)(PMe3)(dppe) and Fe(NAr/Ar*)(PMe3)(dppe). Addition of 1,2-bis(dimethylphosphino)ethane (dmpe) provided Ru(NAr/Ar*)(dmpe)2. A triphos ligand, {P(Me)2CH2}3SitBu (tP3), was also examined. Addition of tP3 to Fe1 provided Fe(NAr)(tP3) (Fe4), but a similar reaction with Ru1 only gave intractable materials. Oxidation of Fe4 with AgSbF6 gave {Fe(NAr)(tP3)}+SbF6- (Fe4a). Oxidation of Ru2 with AgSbF6 gave the unstable cation {Ru(NAr)(PMe3)(dppe)}+, which dimerized in the presence of acetonitrile via C-C bond formation at the aryl group C4 positions, affording {Ru(NAr)(PMe3)(NCMe)(dppe)}2+. This suggested that there was substantial radical character in the imide π system on oxidation and that an aromatic group substituted at the 4-position might provide greater stability. The cations {Fe(NAr*)(PMe3)(dppe)}+ (Fe2a*), {Ru(NAr*)(PMe3)(dppe)}+ (Ru2a*), and Fe4a were examined by EPR spectroscopy, which suggested differences in electronic structure depending on the metal and ligand set. CASPT2 calculations on model systems for Ru2a* and Fe2a* suggested that the large differences in electronic structure are related to the energy gap between the π-antibonding HOMO and the π-bonding HOMO-1. Both the geometry of the phosphines, which is slightly different between the iron and ruthenium analogs, and the metal center seem to contribute to this energetic difference.

Locality of conical intersections in semiconductor nanomaterials.

A predictive theory connecting atomic structure to the rate of recombination would enable the rational design of semiconductor nanomaterials for optoelectronic applications. Recently our group has demonstrated that the theoretical study of conical intersections can serve this purpose. Here we review recent work in this area, focusing on the thesis that low-energy conical intersections in nanomaterials share a common feature: locality. We define a conical intersection as local if (a) the intersecting states differ by the excitation of an electron between spatially local orbitals, and (b) the intersection is accessed when the energies of these orbitals are tuned by local distortions of the geometry. After illustrating the locality of the conical intersection responsible for recombination at dangling bond defects in silicon, we demonstrate the locality of low-energy conical intersections in cases where locality may be a surprise. First, we demonstrate the locality of low-energy self-trapped conical intersections in a pristine silicon nanocrystal, which has no defects that one would expect to serve as the center of a local intersection. Second, we demonstrate that the lowest energy intersection in a silicon system with two neighboring dangling bond defects localizes to a single defect site. We discuss the profound implications of locality for predicting the rate of recombination and suggest that the locality of intersections could be exploited in the experimental study of recombination, where spectroscopic studies of molecular models of defects could provide new insights.

A Conical Intersection Perspective on the Low Nonradiative Recombination Rate in Lead Halide Perovskites.

The utility of optoelectronic materials can be greatly reduced by the presence of efficient pathways for nonradiative recombination (NRR). Lead halide perovskites have garnered much attention in recent years as materials for solar energy conversion, because they readily absorb visible light, are easy to synthesize, and have a low propensity for NRR. Here we report a theoretical study of the pathways for NRR in an archetypal lead halide perovskite: CsPbBr3. Specifically, we identified a set of conical intersection (CIs) in both a molecule-sized cluster model (Cs4PbBr6) and nanoparticle model (Cs12Pb4Br20) of the CsPbBr3 surface. The energies of the minimal energy CIs, corrected for both dynamical electron correlation and spin-orbit coupling, are well above the bulk band gap of CsPbBr3, suggesting that these intersections do not provide efficient pathways for NRR in this material. Analysis of the electronic structure at these intersections suggests that the ionic nature of the bonds in CsPbBr3 may play a role in the high energy of these CIs. The lowest-energy intersections all involve charge transfer over long distances, whether it be across a dissociated bond or between neighboring unit cells.

A discontinuous basis enables numerically exact solution of the Schrödinger equation around conical intersections in the adiabatic representation.

Solving the vibrational Schrödinger equation in the neighborhood of conical intersections in the adiabatic representation is a challenge. At the intersection point, first- and second-derivative nonadiabatic coupling matrix elements become singular, with the singularity in the second-derivative coupling (diagonal Born-Oppenheimer correction) being non-integrable. These singularities result from discontinuities in the vibronic functions associated with the individual adiabatic states, and our group has recently argued that these divergent matrix elements cancel when discontinuous adiabatic vibronic functions sum to a continuous total nonadiabatic wave function. Here we describe the realization of this concept: a novel scheme for the numerically exact solution of the Schrödinger equation in the adiabatic representation. Our approach is based on a basis containing functions that are discontinuous at the intersection point. We demonstrate that the individual adiabatic nuclear wave functions are themselves discontinuous at the intersection point. This proves that discontinuous basis functions are essential to any tractable method that solves the Schrödinger equation around conical intersections in the adiabatic representation with high numerical precision. We establish that our method provides numerically exact results by comparison to reference calculations performed in the diabatic representation. In addition, we quantify the energetic error associated with constraining the density to be zero at the intersection point, a natural approximation. Prospects for extending the present treatment of a two-dimensional model to systems of higher dimensionality are discussed.

Substituent effects on H3 + formation via H2 roaming mechanisms from organic molecules under strong-field photodissociation.

Roaming chemical reactions are often associated with neutral molecules. The recent findings of roaming processes in ionic species, in particular, ones that lead to the formation of H3 + under strong-field laser excitation, are of considerable interest. Given that such gas-phase reactions are initiated by double ionization and subsequently facilitated through deprotonation, we investigate the strong-field photodissociation of ethanethiol, also known as ethyl mercaptan, and compare it to results from ethanol. Contrary to expectations, the H3 + yield was found to be an order of magnitude lower for ethanethiol at certain laser field intensities, despite its lower ionization energy and higher acidity compared to ethanol. In-depth analysis of the femtosecond time-resolved experimental findings, supported by ab initio quantum mechanical calculations, provides key information regarding the roaming mechanisms related to H3 + formation. Results of this study on the dynamics of dissociative half-collisions involving H3 +, a vital cation which acts as a Brønsted-Lowry acid protonating interstellar organic compounds, may also provide valuable information regarding the formation mechanisms and observed natural abundances of complex organic molecules in interstellar media and planetary atmospheres.

Time-resolved signatures across the intramolecular response in substituted cyanine dyes.

The optically populated excited state wave packet propagates along multidimensional intramolecular coordinates soon after photoexcitation. This action occurs alongside an intermolecular response from the surrounding solvent. Disentangling the multidimensional convoluted signal enables the possibility to separate and understand the initial intramolecular relaxation pathways over the excited state potential energy surface. Here we track the initial excited state dynamics by measuring the fluorescence yield from the first excited state as a function of time delay between two color femtosecond pulses for several cyanine dyes having different substituents. We find that when the high frequency pulse precedes the low frequency one and for timescales up to 200 fs, the excited state population can be depleted through stimulated emission with efficiency that is dependent on the molecular electronic structure. A similar observation at even shorter times was made by scanning the chirp (frequencies ordering) of a femtosecond pulse. The changes in depletion reflect the rate at which the nuclear coordinates of the excited state leave the Franck-Condon (FC) region and progress towards achieving equilibrium. Through functional group substitution, we explore these dynamic changes as a function of dipolar change following photoexcitation. Density functional theory calculations were performed to provide greater insight into the experimental spectroscopic observations. Complete active space (CAS) self-consistent field and CAS second order perturbation theory calculated potential energy surfaces tracking twisting and pyramidalization confirm that the steeper potential at the FC region leads to the observation of faster wave packet dynamics.

Complete active space configuration interaction from state-averaged configuration interaction singles natural orbitals: Analytic first derivatives and derivative coupling vectors.

A new complete active space configuration interaction (CASCI) method was recently introduced that uses state-averaged natural orbitals from the configuration interaction singles method (configuration interaction singles natural orbital CASCI, CISNO-CASCI). This method has been shown to perform as well or better than state-averaged complete active space self-consistent field for a variety of systems. However, further development and testing of this method have been limited by the lack of available analytic first derivatives of the CISNO-CASCI energy as well as the derivative coupling between electronic states. In the present work, we present a Lagrangian-based formulation of these derivatives as well as a highly efficient implementation of the resulting equations accelerated with graphical processing units. We demonstrate that the CISNO-CASCI method is practical for dynamical simulations of photochemical processes in molecular systems containing hundreds of atoms.

A direct-compatible formulation of the coupled perturbed complete active space self-consistent field equations on graphical processing units.

We recently developed an algorithm to compute response properties for the state-averaged complete active space self-consistent field method (SA-CASSCF) that capitalized on sparsity in the atomic orbital basis. Our original algorithm was limited to treating small to moderate sized active spaces, but the recent development of graphical processing unit (GPU) based direct-configuration interaction algorithms provides an opportunity to extend this to large active spaces. We present here a direct-compatible version of the coupled perturbed equations, enabling us to compute response properties for systems treated with arbitrary active spaces (subject to available memory and computation time). This work demonstrates that the computationally demanding portions of the SA-CASSCF method can be formulated in terms of seven fundamental operations, including Coulomb and exchange matrix builds and their derivatives, as well as, generalized one- and two-particle density matrix and σ vector constructions. As in our previous work, this algorithm exhibits low computational scaling and is accelerated by the use of GPUs, making possible optimizations and nonadiabatic dynamics on systems with O(1000) basis functions and O(100) atoms, respectively.

The best of both Reps-Diabatized Gaussians on adiabatic surfaces.

When simulating nonadiabatic molecular dynamics, choosing an electronic representation requires consideration of well-known trade-offs. The uniqueness and spatially local couplings of the adiabatic representation come at the expense of an electronic wave function that changes discontinuously with nuclear motion and associated singularities in the nonadiabatic coupling matrix elements. The quasi-diabatic representation offers a smoothly varying wave function and finite couplings, but identification of a globally well-behaved quasi-diabatic representation is a system-specific challenge. In this work, we introduce the diabatized Gaussians on adiabatic surfaces (DGAS) approximation, a variant of the ab initio multiple spawning (AIMS) method that preserves the advantages of both electronic representations while avoiding their respective pitfalls. The DGAS wave function is expanded in a basis of vibronic functions that are continuous in both electronic and nuclear coordinates, but potentially discontinuous in time. Because the time-dependent Schrödinger equation contains only first-order derivatives with respect to time, singularities in the second-derivative nonadiabatic coupling terms (i.e., diagonal Born-Oppenheimer correction; DBOC) at conical intersections are rigorously absent, though singular time-derivative couplings remain. Interpolation of the electronic wave function allows the accurate prediction of population transfer probabilities even in the presence of the remaining singularities. We compare DGAS calculations of the dynamics of photoexcited ethene to AIMS calculations performed in the adiabatic representation, including the DBOC. The 28 fs excited state lifetime observed in DGAS simulations is considerably shorter than the 50 fs lifetime observed in the adiabatic simulations. The slower decay in the adiabatic representation is attributable to the large, repulsive DBOC in the neighborhood of conical intersections. These repulsive DBOC terms are artifacts of the discontinuities in the individual adiabatic vibronic basis functions and therefore cannot reflect the behavior of the exact molecular wave function, which must be continuous.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Defect-Induced Conical Intersections Promote Nonradiative Recombination.

We apply multireference electronic structure calculations to demonstrate the presence of conical intersections between the ground and the first excited electronic states of three silicon nanocrystals containing defects characteristic of the oxidized silicon surface. These intersections are accessible upon excitation at visible wavelengths and are predicted to facilitate nonradiative recombination with a rate that increases with decreasing particle size. This work illustrates a new framework for identifying defects responsible for nonradiative recombination.