Improved Local-Mode Zero-Point-Energy Conservation Scheme for Quasiclassical Trajectories.

We present an improvement of the local-pair zero-point-energy (LP-ZPE) scheme of Mukherjee and Barbatti. The new approximation is called the improved LP-ZPE scheme or iLP-ZPE. This scheme can produce trajectories that do not have unphysical leaking of zero-point energy from high-frequency spectator modes into low-frequency modes. We illustrate the method with a successful direct dynamics application to the Ne···HF van der Waals molecule. The method is well suited for direct dynamics calculations because it does not require costly evaluations of local Hessians or instantaneous normal modes along the trajectories.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2.

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

Parametrically Managed Activation Function for Fitting a Neural Network Potential with Physical Behavior Enforced by a Low-Dimensional Potential.

Machine-learned representations of potential energy surfaces generated in the output layer of a feedforward neural network are becoming increasingly popular. One difficulty with neural network output is that it is often unreliable in regions where training data is missing or sparse. Human-designed potentials often build in proper extrapolation behavior by choice of functional form. Because machine learning is very efficient, it is desirable to learn how to add human intelligence to machine-learned potentials in a convenient way. One example is the well-understood feature of interaction potentials that they vanish when subsystems are too far separated to interact. In this article, we present a way to add a new kind of activation function to a neural network to enforce low-dimensional constraints. In particular, the activation function depends parametrically on all of the input variables. We illustrate the use of this step by showing how it can force an interaction potential to go to zero at large subsystem separations without either inputting a specific functional form for the potential or adding data to the training set in the asymptotic region of geometries where the subsystems are separated. In the process of illustrating this, we present an improved set of potential energy surfaces for the 14 lowest 3A' states of O3. The method is more general than this example, and it may be used to add other low-dimensional knowledge or lower-level knowledge to machine-learned potentials. In addition to the O3 example, we present a greater-generality method called parametrically managed diabatization by deep neural network (PM-DDNN) that is an improvement on our previously presented permutationally restrained diabatization by deep neural network (PR-DDNN).

ChemPotPy: A Python Library for Analytic Representations of Potential Energy Surfaces and Diabatic Potential Energy Matrices.

Constructing analytic representations of global and semiglobal potential energy surfaces is difficult and can be laborious, and it is even harder when one needs coupled potential energy surfaces and their electronically nonadiabatic couplings. When accomplished, however, the resulting potential functions are a valuable resource. To facilitate the convenient use of potentials that have been developed, we provide a collection of existing surfaces in a library with consistent units and formats. A potential energy surface library of this type, namely PotLib, was built more than 20 years ago. However, that library only provided pristine Fortran subroutines for each potential energy surface, and therefore, it is not as user-friendly as would be desirable. Here, we report the creation of ChemPotPy, a CHEMical library of POTential energy surfaces in PYthon. ChemPotPy is a user-friendly library for analytic representation of single-state and multistate potential energy surfaces and couplings. A given entry in the library contains an analytic potential energy function or analytic functions for a set of coupled potential energy surfaces, and depending on the case, it may also include analytic or numerical gradients, nonadiabatic coupling vectors, and/or diabatic potential energy matrices and their gradients. Only three inputs, namely, the chemical formula of the system, the name of the potential energy surface or surface set, and the Cartesian geometry, are required. ChemPotPy uses the same units for input and output quantities of all surfaces and surface sets to facilitate general interfaces with the dynamics programs. The initial version of the library contains 338 entries, and we anticipate that more will be added in the future.

Semiclassical Trajectory Studies of Reactive and Nonreactive Scattering of OH(A 2 Σ+ ) by H2 Based on an Improved Full-Dimensional Ab Initio Diabatic Potential Energy Matrix.

We present a new full-dimensional diabatic potential energy matrix (DPEM) for electronically nonadiabatic collisions of OH(A 2 Σ+ ) with H2 , and we calculate the probabilities of electronically adiabatic inelastic collisions, nonreactive quenching, and reactive quenching to form H2 O+H. The DPEM was fitted using a many-body expansion with permutationally invariant polynomials in bond-order functions to represent the many-body part. The dynamics calculations were carried out with the fewest-switches with time uncertainty and stochastic decoherence (FSTU/SD) semiclassical trajectory method. We present results both for head-on collisions (impact parameter b equal to zero) and for a full range of impact parameters. The results are compared to experiment and to earlier FSTU/SD and quantum dynamics calculations with a previously published DPEM. The various theoretical results all agree that nonreactive quenching dominates reactive quenching, but there are quantitative differences between the two DPEMs and between the b=0 results and the all-b results, especially for the probability of reactive quenching.

Diabatic States of Molecules.

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Direct coherent switching with decay of mixing for intersystem crossing dynamics of thioformaldehyde: The effect of decoherence.

We evaluate the effect of electronic decoherence on intersystem crossing in the photodynamics of thioformaldehyde. First, we show that the state-averaged complete-active-space self-consistent field electronic structure calculations with a properly chosen active space of 12 active electrons in 10 active orbitals can predict the potential energy surfaces and the singlet-triplet spin-orbit couplings quite well for CH2S, and we use this method for direct dynamics by coherent switching with decay of mixing (CSDM). We obtain similar dynamical results with CSDM or by adding energy-based decoherence to trajectory surface hopping, with the population of triplet states tending to a small steady-state value over 500 fs. Without decoherence, the state populations calculated by the conventional trajectory surface hopping method or the semiclassical Ehrenfest method gradually increase. This difference shows that decoherence changes the nature of the results not just quantitatively but qualitatively.

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.

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.

Direct diabatization and analytic representation of coupled potential energy surfaces and couplings for the reactive quenching of the excited 2Σ+ state of OH by molecular hydrogen.

We have employed extended multiconfiguration quasidegenerate perturbation theory, fourfold-way diabatic molecular orbitals, and configurational uniformity to develop a global three-state diabatic representation of the potential energy surfaces and their couplings for the electronically nonadiabatic reaction OH* + H2 → H2O + H, where * denotes electronic excitation to the A 2Σ+ state. To achieve sign consistency of the computed diabatic couplings, we developed a graphics processing unit-accelerated algorithm called the cluster-growing algorithm. Having obtained consistent signs of the diabatic couplings, we fit the diabatic matrix elements (which consist of the diabatic potentials and the diabatic couplings) to analytic representations. Adiabatic potential energy surfaces are generated by diagonalizing the 3 × 3 diabatic potential energy matrix. The comparisons between the fitted and computed diabatic matrix elements and between the originally computed adiabatic potential energy surfaces and those generated from the fits indicate that the current fit is accurate enough for dynamical studies, and it may be used for quantal or semiclassical dynamics calculations.

Extended Hamiltonian molecular dynamics: semiclassical trajectories with improved maintenance of zero point energy.

It is well known that classical trajectories, even if they are initiated with zero point energy (ZPE) in each mode (trajectories initiated this way are commonly called quasiclassical trajectories), do not maintain ZPE in the final states. The energy of high-frequency modes will typically leak into low-frequency modes or relative translation of subsystems during the time evolution. This can lead to severe problems such as unphysical dissociation of a molecule, production of energetically disallowed reaction products, and unphysical product energy distributions. Here a new molecular dynamics method called extended Hamiltonian molecular dynamics (EHMD) is developed to improve the ZPE problem in classical molecular dynamics. In EHMD, two images of a trajectory are connected by one or more springs. The EHMD method is tested with the Henon-Heiles Hamiltonian in reduced and real units and with a Hamiltonian with quartic anharmonicity in real units, and the method is found to improve zero-point maintenance as intended.

Doubly Excited Character or Static Correlation of the Reference State in the Controversial 21Ag State of trans-Butadiene?

Butadiene is the simplest polyene and has long served as a model system for many chemical and spectroscopic properties. However, this small molecule has presented significant challenges to theoretical chemistry. The 21Ag state, which is dark but photochemically important, is a prime source of this difficulty. Previous studies attributed the notorious difficulty in treating this state to strong double excitation character of the 21Ag state, which prevents the application of linear response (LR) methods. Therefore, one would require methods with much higher computational cost, especially for the analogues of this state in longer polyenes, and consequently studies of longer polyenes are very limited. In the present work, we argue that the difficulty stems more significantly from the inherently multiconfigurational character of the ground state. In addition, we validate the possibility of employing LR time-dependent density functional theory to investigate such a state with reasonable accuracy.

Dual-Functional Tamm-Dancoff Approximation with Self-Interaction-Free Orbitals: Vertical Excitation Energies and Potential Energy Surfaces near an Intersection Seam.

Recently we have developed the dual-functional Tamm-Dancoff approximation (DF-TDA) method. DF-TDA is an alternative to linear-response time-dependent density functional theory (LR-TDDFT) with the advantage of providing a correct double-cone topology of S1/S0 conical intersections. In the DF-TDA method, we employ different functionals, which are denoted G and F, for orbital optimization and Hamiltonian construction. We use the notation DF-TDA/G:F. In the current work, we propose that G be the same as F except for having 100% Hartree-Fock exchange. We use the notation F100 to denote functional F with this modification. A motivation for this is that functionals with 100% Hartree-Fock exchange are one-electron self-interaction-free. Here we validate the use of F100/M06 to compute vertical excitation energies and the global potential energy surface of ammonia near a conical intersection to further validate the F100 method for photochemical problems.

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.

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.

Simulated evolution of fluorophores for light emitting diodes.

Organic light emitting diodes based on fluorophores with a propensity for thermally activated delayed fluorescence (TADF) are able to circumvent limitations imposed on device efficiency by spin statistics. Molecules with a propensity for TADF necessarily have two properties: a small gap between the lowest lying singlet and triplet excited states and a large transition dipole moment for fluorescence. In this work, we demonstrate the use of a genetic algorithm to search a region of chemical space for molecules with these properties. This algorithm is based on a flexible and intuitive representation of the molecule as a tree data structure, in which the nodes correspond to molecular fragments. Our implementation takes advantage of hybrid parallel graphics processing unit accelerated computer clusters to allow efficient sampling while retaining a reasonably accurate description of the electronic structure (in this case, CAM-B3LYP/6-31G(∗∗)). In total, we have identified 3792 promising candidate fluorophores from a chemical space containing 1.26 × 10(6) molecules. This required performing electronic structure calculations on only 7518 molecules, a small fraction of the full space. Several novel classes of molecules which show promise as fluorophores are presented.

Configuration interaction singles natural orbitals: an orbital basis for an efficient and size intensive multireference description of electronic excited states.

Multireference quantum chemical methods, such as the complete active space self-consistent field (CASSCF) method, have long been the state of the art for computing regions of potential energy surfaces (PESs) where complex, multiconfigurational wavefunctions are required, such as near conical intersections. Herein, we present a computationally efficient alternative to the widely used CASSCF method based on a complete active space configuration interaction (CASCI) expansion built from the state-averaged natural orbitals of configuration interaction singles calculations (CISNOs). This CISNO-CASCI approach is shown to predict vertical excitation energies of molecules with closed-shell ground states similar to those predicted by state averaged (SA)-CASSCF in many cases and to provide an excellent reference for a perturbative treatment of dynamic electron correlation. Absolute energies computed at the CISNO-CASCI level are found to be variationally superior, on average, to other CASCI methods. Unlike SA-CASSCF, CISNO-CASCI provides vertical excitation energies which are both size intensive and size consistent, thus suggesting that CISNO-CASCI would be preferable to SA-CASSCF for the study of systems with multiple excitable centers. The fact that SA-CASSCF and some other CASCI methods do not provide a size intensive/consistent description of excited states is attributed to changes in the orbitals that occur upon introduction of non-interacting subsystems. Finally, CISNO-CASCI is found to provide a suitable description of the PES surrounding a biradicaloid conical intersection in ethylene.

Polyatomic molecules under intense femtosecond laser irradiation.

Interaction of intense laser pulses with atoms and molecules is at the forefront of atomic, molecular, and optical physics. It is the gateway to powerful new tools that include above threshold ionization, high harmonic generation, electron diffraction, molecular tomography, and attosecond pulse generation. Intense laser pulses are ideal for probing and manipulating chemical bonding. Though the behavior of atoms in strong fields has been well studied, molecules under intense fields are not as well understood and current models have failed in certain important aspects. Molecules, as opposed to atoms, present confounding possibilities of nuclear and electronic motion upon excitation. The dynamics and fragmentation patterns in response to the laser field are structure sensitive; therefore, a molecule cannot simply be treated as a "bag of atoms" during field induced ionization. In this article we present a set of experiments and theoretical calculations exploring the behavior of a large collection of aryl alkyl ketones when irradiated with intense femtosecond pulses. Specifically, we consider to what extent molecules retain their molecular identity and properties under strong laser fields. Using time-of-flight mass spectrometry in conjunction with pump-probe techniques we study the dynamical behavior of these molecules, monitoring ion yield modulation caused by intramolecular motions post ionization. The set of molecules studied is further divided into smaller sets, sorted by type and position of functional groups. The pump-probe time-delay scans show that among positional isomers the variations in relative energies, which amount to only a few hundred millielectronvolts, influence the dynamical behavior of the molecules despite their having experienced such high fields (V/Å). High level ab initio quantum chemical calculations were performed to predict molecular dynamics along with single and multiphoton resonances in the neutral and ionic states. We propose the following model of strong-field ionization and subsequent fragmentation for polyatomic molecules: Single electron ionization occurs on a suboptical cycle time scale, and the electron carries away essentially all of the energy, leaving behind little internal energy in the cation. Subsequent fragmentation of the cation takes place as a result of further photon absorption modulated by one- and two-photon resonances, which provide sufficient energy to overcome the dissociation energy. The proposed hypothesis implies the loss of a photoelectron at a rate that is faster than intramolecular vibrational relaxation and is consistent with the observation of nonergodic photofragmentation of polyatomic molecules as well as experimental results from many other research groups on different molecules and with different pulse durations and wavelengths.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients.

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.