Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results.

Quantum chemistry provides chemists with invaluable information, but the high computational cost limits the size and type of systems that can be studied. Machine learning (ML) has emerged as a means to dramatically lower the cost while maintaining high accuracy. However, ML models often sacrifice interpretability by using components such as the artificial neural networks of deep learning that function as black boxes. These components impart the flexibility needed to learn from large volumes of data but make it difficult to gain insight into the physical or chemical basis for the predictions. Here, we demonstrate that semiempirical quantum chemical (SEQC) models can learn from large volumes of data without sacrificing interpretability. The SEQC model is that of density-functional-based tight binding (DFTB) with fixed atomic orbital energies and interactions that are one-dimensional functions of the interatomic distance. This model is trained to ab initio data in a manner that is analogous to that used to train deep learning models. Using benchmarks that reflect the accuracy of the training data, we show that the resulting model maintains a physically reasonable functional form while achieving an accuracy, relative to coupled cluster energies with a complete basis set extrapolation (CCSD(T)*/CBS), that is comparable to that of density functional theory (DFT). This suggests that trained SEQC models can achieve a low computational cost and high accuracy without sacrificing interpretability. Use of a physically motivated model form also substantially reduces the amount of ab initio data needed to train the model compared to that required for deep learning models.

A Density Functional Tight Binding Layer for Deep Learning of Chemical Hamiltonians.

Current neural networks for predictions of molecular properties use quantum chemistry only as a source of training data. This paper explores models that use quantum chemistry as an integral part of the prediction process. This is done by implementing self-consistent-charge Density-Functional-Tight-Binding (DFTB) theory as a layer for use in deep learning models. The DFTB layer takes, as input, Hamiltonian matrix elements generated from earlier layers and produces, as output, electronic properties from self-consistent field solutions of the corresponding DFTB Hamiltonian. Backpropagation enables efficient training of the model to target electronic properties. Two types of input to the DFTB layer are explored, splines and feed-forward neural networks. Because overfitting can cause models trained on smaller molecules to perform poorly on larger molecules, regularizations are applied that penalize nonmonotonic behavior and deviation of the Hamiltonian matrix elements from those of the published DFTB model used to initialize the model. The approach is evaluated on 15 700 hydrocarbons by comparing the root-mean-square error in energy and dipole moment, on test molecules with eight heavy atoms, to the error from the initial DFTB model. When trained on molecules with up to seven heavy atoms, the spline model reduces the test error in energy by 60% and in dipole moments by 42%. The neural network model performs somewhat better, with error reductions of 67% and 59%, respectively. Training on molecules with up to four heavy atoms reduces performance, with both the spline and neural net models reducing the test error in energy by about 53% and in dipole by about 25%.

Constant size descriptors for accurate machine learning models of molecular properties.

Two different classes of molecular representations for use in machine learning of thermodynamic and electronic properties are studied. The representations are evaluated by monitoring the performance of linear and kernel ridge regression models on well-studied data sets of small organic molecules. One class of representations studied here counts the occurrence of bonding patterns in the molecule. These require only the connectivity of atoms in the molecule as may be obtained from a line diagram or a SMILES string. The second class utilizes the three-dimensional structure of the molecule. These include the Coulomb matrix and Bag of Bonds, which list the inter-atomic distances present in the molecule, and Encoded Bonds, which encode such lists into a feature vector whose length is independent of molecular size. Encoded Bonds' features introduced here have the advantage of leading to models that may be trained on smaller molecules and then used successfully on larger molecules. A wide range of feature sets are constructed by selecting, at each rank, either a graph or geometry-based feature. Here, rank refers to the number of atoms involved in the feature, e.g., atom counts are rank 1, while Encoded Bonds are rank 2. For atomization energies in the QM7 data set, the best graph-based feature set gives a mean absolute error of 3.4 kcal/mol. Inclusion of 3D geometry substantially enhances the performance, with Encoded Bonds giving 2.4 kcal/mol, when used alone, and 1.19 kcal/mol, when combined with graph features.

A Least-Squares Commutator in the Iterative Subspace Method for Accelerating Self-Consistent Field Convergence.

A least-squares commutator in the iterative subspace (LCIIS) approach is explored for accelerating self-consistent field (SCF) calculations. LCIIS is similar to direct inversion of the iterative subspace (DIIS) methods in that the next iterate of the density matrix is obtained as a linear combination of past iterates. However, whereas DIIS methods find the linear combination by minimizing a sum of error vectors, LCIIS minimizes the Frobenius norm of the commutator between the density matrix and the Fock matrix. This minimization leads to a quartic problem that can be solved iteratively through a constrained Newton's method. The relationship between LCIIS and DIIS is discussed. Numerical experiments suggest that LCIIS leads to faster convergence than other SCF convergence accelerating methods in a statistically significant sense, and in a number of cases LCIIS leads to stable SCF solutions that are not found by other methods. The computational cost involved in solving the quartic minimization problem is small compared to the typical cost of SCF iterations and the approach is easily integrated into existing codes. LCIIS can therefore serve as a powerful addition to SCF convergence accelerating methods in computational quantum chemistry packages.

Modeling Field-Induced Quenching in Poly(p-phenylene vinylene) Polymers and Oligomers.

Field-induced fluorescence quenching of poly(p-phenylene vinylene) (PPV) oligomers due to nonradiative relaxation through free electron-hole pair (FEHP) states is modeled using singles configuration interaction computations with the intermediate neglect of differential overlap Hamiltonian. The computations find FEHP states with energies that drop linearly with applied field and undergo avoided crossings with the fluorescent state. The coupling between the FEHP and fluorescent state, computed for multiple FEHP states on a variety of oligomer lengths, is found to depend primarily on the field strength required for the state to cross the fluorescent state. The rate of decay to these dark FEHP states is then calculated from Marcus theory, which is modified to take into account dielectric in addition to other bulk measurement considerations. The results predict that individual molecules go from being emissive to fully quenched over a small range of applied field strengths. Phenomenological introduction of inhomogeneous broadening for the energies of the FEHP states leads to a more gradual dependence on applied field. The fluorescence quenching mechanism considered here is found to be important for applied fields above about 1 MV cm(-1), which is similar in magnitude to those present in light-emitting diodes.

Brownian dynamics simulations of charge mobility on conjugated polymers in solution.

A model is developed for the mobility of a charge carrier along a conjugated polymer dissolved in solution, as measured by time-resolved microwave conductivity. Each unit cell of the polymer is assigned a torsional degree of freedom, with Brownian dynamics used to include the effects of solvent on the torsions. The barrier to torsional motion is substantially enhanced in the vicinity of the charge, leading to self-trapping of the charge onto a planarized region of the polymer chain. Within the adiabatic approximation used here, motion arises when regions of the polymer on either side of the charge fluctuate into planarity and the wavefunction spreads in the corresponding direction. Well-converged estimates for the mobility are obtained for model parameters where the adiabatic approximation holds. For the parameters expected for conjugated polymers, where crossing between electronic surfaces may lead to breakdown in the adiabatic approximation, estimates for the mobility are obtained via extrapolation. Nonadiabatic contributions from hopping between electronic surfaces are therefore ignored. The resulting mobility is inversely proportional to the rotational diffusion time, trot, of a single unit cell about the polymer axis in the absence of intramolecular forces. For trot of 75 ps, the long-chain mobility of poly(para-phenylene vinylene) is estimated to be between 0.09 and 0.4 cm(2)∕Vs. This is in reasonable agreement with experimental values for the polymer, however, the nonadiabatic contribution to the mobility is not considered, nor are effects arising from stretching degrees of freedom or breaks in conjugation.

Computational design of a light-driven molecular motor.

Light-driven molecular motors may be useful for nanotechnology applications. The possibility of building such a motor based on the tolane framework is explored here. In the ground electronic state of tolane, the barrier to internal rotation is comparable to room temperature thermal energies, k(B)T. The barrier increases substantially in the excited state, causing the molecule to planarize after absorption of a photon. This tendency to planarize may be converted into unidirectional rotational motion by placing chiral substituents on the phenyl rings. A potential advantage of this class of motors is that they may undergo rapid, nanosecond scale rotation. Computational design of appropriate substituents was done using semiempirical quantum chemical methods, SAM1 for the ground electronic state coupled to INDO for the excitation energy. The torsional surfaces of the best candidate were then generated using ab initio DFT methods, which confirm that the molecule should undergo unidirectional rotation upon photoexcitation. The results provide a proof of principle for this class of motors; however, two aspects of the final candidate are nonideal. First, although the design goal was to use steric interactions between substituents to induce the rotation, decomposition of the interaction energy suggests attractive interactions play a role. Solvent interactions may interfere with these attractive interactions. Second, TDDFT calculations suggest that interactions between excited states lower the rotational driving force in the excited state.

Modeling outer-sphere disorder in the symmetry breaking of PPV.

Disorder plays an important role in the photophysics of conjugated polymers such as poly(para-phenylene vinylene) (PPV). The dipole moments measured by electroabsorption spectroscopy for a centrosymmetric system such as PPV provide a direct quantitative measure of disorder-induced symmetry breaking. Although inner-sphere (structural) disorder is present, outer-sphere (environmental) disorder dominates the symmetry breaking in PPV. This paper develops and compares six models of outer-sphere disorder that differ in their representation of the electrostatic environment of PPV in glassy solvents. The most detailed model is an all-atom description of the solvent glass and this model forms the basis for comparison of the less detailed models. Four models are constructed in which multipoles are placed at points on a lattice. These lattice models differ in the degree to which they include correlation between the lattice spacings and the orientations of the multipoles. A simple model that assigns random Gaussian-distributed electrostatic potentials to each atom in the PPV molecule is also considered. Comparison of electronic structure calculations of PPV in these electrostatic environments using the all-atom model as a benchmark reveals that dipole and quadrupole lattices provide reasonable models of organic glassy solvents. Including orientational correlation among the solvent molecules decreases the effects of outer-sphere disorder, whereas including correlation in the lattice spacings increases the effects. Both the dipole and quadrupole moments of the solvent molecules can have significant effects on the symmetry breaking and these effects are additive. This additivity provides a convenient means for predicting the effects of various glassy solvents based on their multipole moments. The results presented here suggest that electrostatic disorder can account for the observed symmetry breaking in organic glasses. Furthermore, the lattice models are in general agreement with the dipole and quadrupole lattice models used to explain the Poole-Frenkel behavior in charge transport through disordered organic materials.

Using Molecular Similarity to Develop Reliable Models of Chemical Reactions in Complex Environments.

The use of molecular similarity to develop reliable low-cost quantum mechanical models for use in quantum mechanical/molecular mechanical simulations of chemical reactions is explored, using the H + HF → H2 + F collinear reaction as a test case. The approach first generates detailed quantum chemical data for the reaction center in geometries and electrostatic environments that span those expected to arise during the molecular dynamics simulations. For each geometry and environment, both high- and low-level ab initio calculations are performed. A model is then developed to predict the high-level results using only inputs generated from the low-level theory. The inputs used here are based on principal component analysis of the low-level distributed multipoles, and the model is a simple linear regression. The distributed multipoles are monopoles, dipoles, and quadrupoles at each atomic center, and they summarize the electronic distribution in a manner that is comparable across basis set. The error in the model is dominated by extrapolation from small to large basis sets, with extrapolation from uncorrelated to correlated methods contributing much less error. A single regression can be used to make predictions for a range of reaction-center geometries and environments. For the trial collinear reaction, separate regressions were developed for the transition region and the entrance and exit channels. These models can predict the results of CCSD(T)/cc-pVTZ computations from HF/3-21G distributed multipoles, with an average error for the reaction energy profile of 0.69 kcal/mol.