Fitting of Coupled Potential Energy Surfaces via Discovery of Companion Matrices by Machine Intelligence.

Fitting coupled potential energy surfaces is a critical step in simulating electronically nonadiabatic chemical reactions and energy transfer processes. Analytic representation of coupled potential energy surfaces enables one to perform detailed dynamics calculations. Traditionally, fitting is performed in a diabatic representation to avoid fitting the cuspidal ridges of coupled adiabatic potential energy surfaces at conical intersection seams. In this work, we provide an alternative approach by carrying out fitting in the adiabatic representation using a modified version of the Frobenius companion matrices, whose usage was first proposed by Opalka and Domcke. Their work involved minimizing the errors in fits of the characteristic polynomial coefficients (CPCs) and diagonalizing the resulting companion matrix, whose eigenvalues are adiabatic potential energies. We show, however, that this may lead to complex eigenvalues and spurious discontinuities. To alleviate this problem, we provide a new procedure for the automatic discovery of CPCs and the diagonalization of a companion matrix by using a special neural network architecture. The method effectively allows analytic representation of global coupled adiabatic potential energy surfaces and their gradients with only adiabatic energy input and without experience-based selection of a diabatization scheme. We demonstrate that the new procedure, called the companion matrix neural network (CMNN), is successful by showing applications to LiH, H3, phenol, and thiophenol.

Small Representative Databases for Testing and Validating Density Functionals and Other Electronic Structure Methods.

Broad and diverse sets of accurate data provide useful metrics for assessing the performance of new theoretical methods. However, assessing methods against large databases can be an arduous task. Here, we present 17 representative energetic databases, defined as small databases whose errors and error spreads are representative of larger databases and which therefore can serve as efficient benchmarks for developing and testing electronic structure methods and density functionals. In 15 cases, the representative databases have 6 entries while being representative of larger databases with 14-107 entries, and in the other two cases, they have 14 entries while being representative of larger databases with 418-455 entries. The mean unsigned error (MUE) of 100 electronic structure methods on a given representative database is typically within about 8% of the MUE on its parent database, and the root-mean-square error (RMSE) is typically within about 11% of the RMSE on the parent database. Thus, the representative databases are quite successful in indicating accuracy while maintaining good diversity. The databases include both main-group and transition-metal compounds and reactions, and they include bond energies, reaction energies, barrier heights, noncovalent interactions, ionization potentials, and absolute energies.

Kinetics and Mechanism of the Singlet Oxygen Atom Reaction with Dimethyl Ether.

We combine in situ laser spectroscopy, quantum chemistry, and kinetic calculations to study the reaction of a singlet oxygen atom with dimethyl ether. Infrared laser absorption spectroscopy and Faraday rotation spectroscopy are used for the detection and quantification of the reaction products OH, H2O, HO2, and CH2O on submillisecond time scales. Fitting temporal profiles of products with simulations using an in-house reaction mechanism allows product branching to be quantified at 30, 60, and 150 Torr. The experimentally determined product branching agrees well with master equation calculations based on electronic structure data and transition state theory. The calculations demonstrate that the dimethyl peroxide (CH3OOCH3) generated via O-insertion into the C-O bond undergoes subsequent dissociation to CH3O + CH3O through energetically favored reactions without an intrinsic barrier. This O-insertion mechanism can be important for understanding the fate of biofuels leaking into the atmosphere and for plasma-based biofuel processing technologies.

Quantitative kinetics reveal that reactions of HO2 are a significant sink for aldehydes in the atmosphere and may initiate the formation of highly oxygenated molecules via autoxidation.

Large aldehydes are widespread in the atmosphere and their oxidation leads to secondary organic aerosols. The current understanding of their chemical transformation processes is limited to hydroxyl radical (OH) oxidation during daytime and nitrate radical (NO3) oxidation during nighttime. Here, we report quantitative kinetics calculations of the reactions of hexanal (C5H11CHO), pentanal (C4H9CHO), and butanal (C3H7CHO) with hydroperoxyl radical (HO2) at atmospheric temperatures and pressures. We find that neither tunneling nor multistructural torsion anharmonicity should be neglected in computing these rate constants; strong anharmonicity at the transition states is also important. We find rate constants for the three reactions in the range 3.2-7.7 × 10-14 cm3 molecule-1 s-1 at 298 K and 1 atm, showing that the HO2 reactions can be competitive with OH and NO3 oxidation under some conditions relevant to the atmosphere. Our findings reveal that HO2-initiated oxidation of large aldehydes may be responsible for the formation of highly oxygenated molecules via autoxidation. We augment the theoretic studies with laboratory flow-tube experiments using an iodide-adduct time-of-flight chemical ionization mass spectrometer to confirm the theoretical predictions of peroxy radicals and the autoxidation pathway. We find that the adduct from HO2 + C5H11CHO undergoes a fast unimolecular 1,7-hydrogen shift with a rate constant of 0.45 s-1. We suggest that the HO2 reactions make significant contributions to the sink of aldehydes.

Direct Observation of Covalently Bound Clusters in Resonantly Stabilized Radical Reactions and Implications for Carbonaceous Particle Growth.

Based on quantum mechanically guided experiments that observed elusive intermediates in the domain of inception that lies between large molecules and soot particles, we provide a new mechanism for the formation of carbonaceous particles from gas-phase molecular precursors. We investigated the clustering behavior of resonantly stabilized radicals (RSRs) and their interactions with unsaturated hydrocarbons through a combination of gas-phase reaction experiments and theoretical calculations. Our research directly observed a sequence of covalently bound clusters (CBCs) as key intermediates in the evolution from small RSRs, such as benzyl (C7H7), indenyl (C9H7), 1-methylnaphthyl (1-C11H9), and 2-methylnaphthyl (2-C11H9), to large polycyclic aromatic hydrocarbons (PAHs) consisting of 28 to 55 carbons. We found that hydrogen abstraction and RSR addition drive the formation and growth of CBCs, leading to progressive H-losses, the generation of large PAHs and PAH radicals, and the formation of white smoke (incipient carbonaceous particles). This mechanism of progressive H-losses from CBCs (PHLCBC) elucidates the crucial relationship among RSRs, CBCs, and PAHs, and this study provides an unprecedentedly seamless path of observed assembly from small RSRs to large nanoparticles. Understanding the PHLCBC mechanism over a wide temperature range may enhance the accuracy of multiscale models of soot formation, guide the synthesis of carbonaceous nanomaterials, and deepen our understanding of the origin and evolution of carbon within our galaxy.

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.

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.

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory.

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear-electronic coupling in addition to accurately predicting Franck-Condon vertical excitations. In this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree-Fock exchange. These results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

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').

Supervised learning of a chemistry functional with damped dispersion.

Kohn-Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.