Thermodynamic calculations for molecules with asymmetric internal rotors—application to 1,3-butadiene

Harnessing deep neural networks to solve inverse problems in quantum dynamics: machine-learned predictions of time-dependent optimal control fields

Inverse problems continue to garner immense interest in the physical sciences, particularly in the context of controlling desired phenomena in non-equilibrium systems. In this work, we utilize a series of deep neural networks for predicting time-dependent optimal control fields, E(t), that enable desired electronic transitions in reduced-dimensional quantum dynamical systems. To solve this inverse problem, we investigated two independent machine learning approaches: (1) a feedforward neural network for predicting the frequency and amplitude content of the power spectrum in the frequency domain (i.e., the Fourier transform of E(t)), and (2) a cross-correlation neural network approach for directly predicting E(t) in the time domain. Both of these machine learning methods give complementary approaches for probing the underlying quantum dynamics and also exhibit impressive performance in accurately predicting both the frequency and strength of the optimal control field. We provide detailed architectures and hyperparameters for these deep neural networks as well as performance metrics for each of our machine-learned models. From these results, we show that machine learning, particularly deep neural networks, can be employed as cost-effective statistical approaches for designing electromagnetic fields to enable desired transitions in these quantum dynamical systems.

Sulfate radical oxidation of aromatic contaminants: a detailed assessment of density functional theory and high-level quantum chemical methods

Advanced oxidation processes that utilize highly oxidative radicals are widely used in water reuse treatment. In recent years, the application of sulfate radical (SO₄˙^-) as a promising oxidant for water treatment has gained increasing attention. To understand the efficiency of SO₄˙^- in the degradation of organic contaminants in wastewater effluent, it is important to be able to predict the reaction kinetics of various SO₄˙^--driven oxidation reactions. In this study, we utilize density functional theory (DFT) and high-level wavefunction-based methods (including computationally-intensive coupled cluster methods), to explore the activation energies of SO₄˙^--driven oxidation reactions on a series of benzene-derived contaminants. These high-level calculations encompass a wide set of reactions including 110 forward/reverse reactions and 5 different computational methods in total. Based on the high-level coupled-cluster quantum calculations, we find that the popular M06-2X DFT functional is significantly more accurate for OH^- additions than for SO₄˙^- reactions. Most importantly, we highlight some of the limitations and deficiencies of other computational methods, and we recommend the use of high-level quantum calculations to spot-check environmental chemistry reactions that may lie outside the training set of the M06-2X functional, particularly for water oxidation reactions that involve SO₄˙^- and other inorganic species.

Zn Coordination Chemistry: Development of Benchmark Suites for Geometries, Dipole Moments, and Bond Dissociation Energies and Their Use To Test and Validate Density Functionals and Molecular Orbital Theory

We present nonrelativistic and relativistic benchmark databases (obtained by coupled cluster calculations) of 10 Zn-ligand bond distances, 8 dipole moments, and 12 bond dissociation energies in Zn coordination compounds with O, S, NH3, H2O, OH, SCH3, and H ligands. These are used to test the predictions of 39 density functionals, Hartree-Fock theory, and seven more approximate molecular orbital theories. In the nonrelativisitic case, the M05-2X, B97-2, and mPW1PW functionals emerge as the most accurate ones for this test data, with unitless balanced mean unsigned errors (BMUEs) of 0.33, 0.38, and 0.43, respectively. The best local functionals (i.e., functionals with no Hartree-Fock exchange) are M06-L and τ-HCTH with BMUEs of 0.54 and 0.60, respectively. The popular B3LYP functional has a BMUE of 0.51, only slightly better than the value of 0.54 for the best local functional, which is less expensive. Hartree-Fock theory itself has a BMUE of 1.22. The M05-2X functional has a mean unsigned error of 0.008 Å for bond lengths, 0.19 D for dipole moments, and 4.30 kcal/mol for bond energies. The X3LYP functional has a smaller mean unsigned error (0.007 Å) for bond lengths but has mean unsigned errors of 0.43 D for dipole moments and 5.6 kcal/mol for bond energies. The M06-2X functional has a smaller mean unsigned error (3.3 kcal/mol) for bond energies but has mean unsigned errors of 0.017 Å for bond lengths and 0.37 D for dipole moments. The best of the semiempirical molecular orbital theories are PM3 and PM6, with BMUEs of 1.96 and 2.02, respectively. The ten most accurate functionals from the nonrelativistic benchmark analysis are then tested in relativistic calculations against new benchmarks obtained with coupled-cluster calculations and a relativistic effective core potential, resulting in M05-2X (BMUE = 0.895), PW6B95 (BMUE = 0.90), and B97-2 (BMUE = 0.93) as the top three functionals. We find significant relativistic effects (∼0.01 Å in bond lengths, ∼0.2 D in dipole moments, and ∼4 kcal/mol in Zn-ligand bond energies) that cannot be neglected for accurate modeling, but the same density functionals that do well in all-electron nonrelativistic calculations do well with relativistic effective core potentials. Although most tests are carried out with augmented polarized triple-ζ basis sets, we also carried out some tests with an augmented polarized double-ζ basis set, and we found, on average, that with the smaller basis set DFT has no loss in accuracy for dipole moments and only ∼10% less accurate bond lengths.

An Efficient and Accurate Formalism for the Treatment of Large Amplitude Intramolecular Motion

We propose a general approach to describe large amplitude motions (LAM) with multiple degrees of freedom (DOF) in molecules or reaction intermediates, which is useful for the computation of thermochemical or kinetic data. The kinetic part of the LAM Lagrangian is derived using a Z-matrix internal coordinate representation within a new numerical procedure. This derivation is exact for a classical system, and the uncertainties on the prediction of observable quantities largely arise from uncertainties on the LAM potential energy surface (PES) itself. In order to rigorously account for these uncertainties, we present an approach based on Bayesian theory to infer a parametrized physical model of the PES using ab initio calculations. This framework allows for quantification of uncertainties associated with a PES model as well as the forward propagation of these uncertainties to the quantity of interest. A selection and generalization of some treatments accounting for the coupling of the LAM with other internal or external DOF are also presented. Finally, we discuss and validate the approach with two applications: the calculation of the partition function of 1,3-butadiene and the calculation of the high-pressure reaction rate of the CH₃ + H → CH₄ recombination.

Thermodynamic calculations for molecules with asymmetric internal rotors. II. Application to the 1,2-dihaloethanes

The thermodynamic properties of three halocarbon molecules relevant in atmospheric and public health applications are presented from ab initio calculations. Our technique makes use of a reaction path-like Hamiltonian to couple all the vibrational modes to a large-amplitude torsion for 1,2-difluoroethane, 1,2-dichloroethane, and 1,2-dibromoethane, each of which possesses a heavy asymmetric rotor. Optimized ab initio energies and Hessians were calculated at the CCSD(T) and MP2 levels of theory, respectively. In addition, to investigate the contribution of electronically excited states to thermodynamic properties, several excited singlet and triplet states for each of the halocarbons were computed at the CASSCF/MRCI level. Using the resulting potentials and projected frequencies, the couplings of all the vibrational modes to the large-amplitude torsion are calculated using the new STAR-P 2.4.0 software platform that automatically parallelizes our codes with distributed memory via a familiar MATLAB interface. Utilizing the efficient parallelization scheme of STAR-P, we obtain thermodynamic properties for each of the halocarbons, with temperatures ranging from 298.15 to 1000 K. We propose that the free energies, entropies, and heat capacities obtained from our methods be used to supplement theoretical and experimental values found in current thermodynamic tables.