Arbitrary-Order Derivatives of Quantum Chemical Methods via Automatic Differentiation.

Herein, we present for the first time a general methodology for obtaining arbitrary-order nuclear coordinate derivatives of electronic energies derived from quantum chemistry methods. By leveraging modern advances in automatic differentiation software, we demonstrate that exact derivatives can be obtained for any method. This innovation completely bypasses the issues associated with the computational stability of applying numerical differentiation methods and dispenses the need to derive challenging formulae for analytic energy derivatives. We describe a freely available and open-source software implementation of our scheme and demonstrate its use in obtaining exact nuclear derivatives of energies from Hartree-Fock theory, second-order Møller-Plesset perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. Our sample computations include up to sextic derivatives and span a variety of test systems with up to 100 basis functions, confirming the viability of this scheme for a wide range of applications. Many of the results obtained have hitherto been unobtainable by exact means due to a lack of higher-order derivative formulae. The details of our implementation and possible further developments are discussed.

Characterization of the 2-methylvinoxy radical + O2 reaction: A focal point analysis and composite multireference study.

Vinoxy radicals are involved in numerous atmospheric and combustion mechanisms. High-level theoretical methods have recently shed new light on the reaction of the unsubstituted vinoxy radical with O2. The reactions of 1-methylvinoxy radical and 2-methylvinoxy radical with molecular oxygen have experimental high pressure limiting rate constants, k∞, 5-7 times higher than that of the vinoxy plus O2 reaction. In this work, high-level ab initio quantum chemical computations are applied to the 2-methylvinoxy radical plus O2 system, namely, the formation and isomerization of the 1-oxo-2-propylperoxy radical, the immediate product of O2 addition to the 2-methylvinoxy radical. Multireference methods were applied to the entrance channel. No barrier to O2 addition could be located, and more sophisticated treatment of dynamic electron correlation shows that the principal difference between O2 addition to the vinoxy and 2-methylvinoxy radicals is a larger steric factor for 2-methylvinoxy + O2. This is attributed to the favorable interaction between the incoming O2 molecule and the methyl group of the 2-methylvinoxy radical. Via the focal point approach, energetics for this reaction were determined, in most cases, to chemical accuracy. The coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy and Hartree-Fock energies were independently extrapolated to the complete basis set limit. A correction for the effect of higher excitations was computed at the CCSDT(Q)/6-31G level. Corrections for the frozen-core approximation, the Born-Oppenheimer approximation, the nonrelativistic approximation, and the zero-point vibrational energy were included. From the 1-oxo-2-propylperoxy radical, dissociation to reactants is competitive with the lowest energy isomerization pathway. The lowest energy isomerization pathway ultimately forms acetaldehyde, CO, and ·OH as the final products.

The addition of methanol to Criegee intermediates.

Bimolecular reactions involving stabilized Criegee intermediates (SCI) have been the target of many studies due to the role these molecules play in atmospheric chemistry. Recently, kinetic rates for the addition reaction of the simplest SCI (formaldehyde oxide) and its methylated analogue (acetone oxide) with methanol were reported both experimentally and theoretically. We re-examine the energy profile of these reactions by employing rigorous ab initio methods. Optimized CCSD(T)/ANO1 geometries are reported for the stationary points along the reaction path. Energies are obtained at the CCSD(T)/CBS level of theory. Contributions of full triple and quadruple excitations are computed to assess the convergence of this method. Rate constants are obtained using conventional canonical transition state theory under the rigid rotor harmonic oscillator approximation and with the inclusion of a one-dimensional hindered rotor treatment. These corrections for internal rotations have a significant impact on computed kinetic rate constants. With this approach, we compute rate constants for the addition of methanol to formaldehyde oxide (H2COO) and acetone oxide [(CH3)2COO] at 298.15 K as (1.2 ± 0.8) × 10-13 and (2.8 ± 1.3) × 10-15 cm3 s-1, respectively. Additionally, we investigate the temperature dependence of the rate constant, concluding that the transition state barrier height and tunneling contributions shape the qualitative behaviour of these reactions.

PES-Learn: An Open-Source Software Package for the Automated Generation of Machine Learning Models of Molecular Potential Energy Surfaces.

We introduce a free and open-source software package (PES-Learn) which largely automates the process of producing high-quality machine learning models of molecular potential energy surfaces (PESs). PES-Learn incorporates a generalized framework for producing grid points across a PES that is compatible with most electronic structure theory software. The newly generated or externally supplied PES data can then be used to train and optimize neural network or Gaussian process models in a completely automated fashion. Robust hyperparameter optimization schemes designed specifically for molecular PES applications are implemented to ensure that the best possible model for the data set is fit with high quality. The performance of PES-Learn toward fitting a few semiglobal PESs from the literature is evaluated. We also demonstrate the use of PES-Learn machine learning models in carrying out high-level vibrational configuration interaction computations on water and formaldehyde.

Reinterpretation of the electronic absorption spectrum of the methylene amidogen radical (H2CN).

The peculiar electronic absorption spectrum of H2CN has been of great interest to experiment. Herein, this system is studied extensively by applying theoretical methods to the ground and low-lying excited electronic states. Employing a large breadth of high-level ab initio computations, including coupled cluster [CCSD(T) and CCSDT(Q)] and multireference configuration interaction [MRCISD+Q] methods, we comprehensively demonstrate that the most recent experimental and theoretical interpretations of the electronic spectrum of H2CN are in error. The previous assignments of the two broad features in the spectrum as the origin 000 (∼35 050 cm-1) and 402 (∼35 600 cm-1) B̃ 2A1←X̃ 2B2 transitions are both found to be incorrect. The presently reported transition energies suggest that the higher energy band near 35 600 cm-1 is the true origin band. Additionally, from the computed anharmonic vibrational frequencies of the X̃ 2B2 and B̃ 2A1 states, we show that this ∼550 cm-1 band spacing cannot be attributed to a simple vibronic transition, as claimed by the 402 assignment. Possible alternative explanations for the appearance of the lower intensity band near 35 050 cm-1 are discussed.

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development.

Psi4NumPy demonstrates the use of efficient computational kernels from the open-source Psi4 program through the popular NumPy library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Furthermore, several reference codes have been integrated into Jupyter notebooks, allowing background, underlying theory, and formula information to be associated with the implementation. Psi4NumPy tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementations also demonstrate the power of the hybrid C++/Python programming approach employed by the Psi4 program.

The Structure and Cl-O Dissociation Energy of the ClOO Radical: Finally, the Right Answers for the Right Reason.

The chlorine peroxy radical (ClOO) has historically been a highly problematic system for theoretical studies. In particular, the erratic ab initio predictions of the Cl-O bond length reported in the literature thus far exhibit unacceptable errors with respect to the experimental structure. In light of the widespread disagreement observed, we present a careful and systematic investigation of the ClOO geometry toward the basis set and correlation limits of single reference ab initio theory, employing the cc-pVXZ (X = D, T, Q, 5, 6) basis sets extrapolated to the complete basis set limit and coupled cluster theory through single, double, triple, and perturbative quadruple excitations [CCSDT(Q)]. We demonstrate a considerable sensitivity of the Cl-O bond length to both electron correlation and basis set size. The CCSDT(Q)/CBS structure is found to be re(ClO) = 2.082, re(OO) = 1.208, and θe(ClOO) = 115.4°, in remarkable agreement with Endo's semi-experimentally determined values re(ClO) = 2.084(1), re(OO) = 1.206(2), and θe(ClOO) = 115.4(1)°. Moreover, we compute a Cl-O bond dissociation energy of 4.77 kcal mol-1, which is likewise in excellent agreement with the most recent experimental value of 4.69 ± 0.10 kcal mol-1.

Radicals derived from acetaldehyde and vinyl alcohol.

Vinyl alcohol and acetaldehyde are isoelectronic products of incomplete butanol combustion. Along with the radicals resulting from the removal of atomic hydrogen or the hydroxyl radical, these species are studied here using ab initio methods as complete as coupled cluster theory with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)], with basis sets as large as cc-pV5Z. The relative energies provided herein are further refined by including corrections for relativistic effects, the frozen core approximation, and the Born-Oppenheimer approximation. The effects of anharmonic zero-point vibrational energies are also treated. The syn conformer of vinyl alcohol is predicted to be lower in energy than the anti conformer by 1.1 kcal mol-1. The alcoholic hydrogen of syn-vinyl alcohol is found to be the easiest to remove, requiring 84.4 kcal mol-1. Five other radicals are also carefully considered, with four conformers investigated for the 1-hydroxyvinyl radical. Beyond energetics, we have conducted an overhaul of the spectroscopic literature for these species. Our results also provide predictions for fundamental modes yet to be reported experimentally. To our knowledge, the ν3 (3076 cm-1) and ν4 (2999 cm-1) C-H stretches for syn-vinyl alcohol and all but one of the vibrational modes for anti-vinyl alcohol (ν1-ν14) are yet to be observed experimentally. For the acetyl radical, ν6 (1035 cm-1), ν11 (944 cm-1), ν12 (97 cm-1), and accounting for our changes to the assignment of the 1419.9 cm-1 experimental mode, ν10 (1441 cm-1), are yet to be observed. We have predicted these unobserved fundamentals and reassigned the experimental 1419.9 cm-1 frequency in the acetyl radical to ν4 rather than to ν10. Our work also strongly supports reassignment of the ν10 and ν11 fundamentals of the vinoxy radical. We suggest that the bands assigned to the overtones of these fundamentals were in fact combination bands. Our findings may be useful in constructing improved combustion models of butanol and in spectroscopically characterizing these molecules further.