The introduction of machine-learning (ML) algorithms to quantum mechanics enables rapid evaluation of otherwise intractable expressions at the cost of prior training on appropriate benchmarks. Many computational bottlenecks in the evaluation of accurate electronic structure theory could potentially benefit from the application of such models, from reducing the complexity of the underlying wave function parameter space to circumventing the complications of solving the electronic Schrödinger equation entirely. Applications of ML to electronic structure have thus far been focused on learning molecular properties (mainly the energy) from geometric representations. While this line of study has been quite successful, highly accurate models typically require a "big data" approach with thousands of training data points. Herein, we propose a general, systematically improvable scheme for wave function-based ML of arbitrary molecular properties, inspired by the underlying equations that govern the canonical approach to computing the properties. To this end, we combine the established ML machinery of the t-amplitude tensor representation with a new reduced density matrix representation. The resulting model provides quantitative accuracy in both the electronic energy and dipoles of small molecules using only a few dozen training points per system.

We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schrödinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of 2 with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedupsof up to a factor of 14 in test simulations of water clustersare obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash–Karp integrator, provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge–Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.

The underlying reasons for the poor convergence of the venerated many-body expansion (MBE) for higher-order response properties are investigated, with a particular focus on the impact of basis set superposition errors. Interaction energies, dipole moments, dynamic polarizabilities, and specific rotations are computed for three chiral solutes in explicit water cages of varying sizes using the MBE including corrections based on the site–site function counterpoise (or “full-cluster” basis) approach. In addition, we consider other possible causes for the observed oscillatory behavior of the MBE, including numerical precision, basis set size, choice of density functional, and snapshot geometry. Our results indicate that counterpoise corrections are necessary for damping oscillations and achieving reasonable convergence of the MBE for higher order properties. However, oscillations in the expansion cannot be completely eliminated for chiroptical properties such as specific rotations due to their inherently nonadditive nature, thus limiting the efficacy of the MBE for studying solvated chiral compounds.

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We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schrödinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of two with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedups -of up to a factor of 14 in test simulations of water clusters -are obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash-Karp integrator provide an effective balance between computing costs and numerical stability. Finally, 1