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.
Reduced-scaling
methods are needed to make accurate and systematically
improvable coupled cluster linear response methods for the calculation
of molecular properties tractable for large molecules. In this paper,
we examine the perturbed pair natural orbital-based PNO++ approach
that creates an orbital space optimized for response properties derived
from a lower-cost field-perturbed density matrix. We analyze truncation
errors in correlation energies, dynamic polarizabilities, and specific
rotations from a coupled cluster singles and doubles (CCSD) reference.
We find that incorporating a fixed number of orbitals from the pair
natural orbital (PNO) space into the PNO++ methoda new method
presented here, the “combined PNO++” approachrecovers
accuracy in the CCSD correlation energy while preserving the well-behaved
convergence behavior of the PNO++ method for linear response properties.
The challenge of assigning the absolute stereochemical configuration to a chiral compound can be overcome via accurate ab initio predictions of optical rotation, a sensitive molecular property that is further complicated by solvent effects. The solvent's "chiral imprint"the transfer of the chirality from the solute to the surrounding achiral solventis explored here using conformational averaging and time-dependent densityfunctional theory. These complex solvent effects are taken into account via simple averaging over a molecular dynamics trajectory together with the explicit quantum mechanical consideration of the solvent molecules within the solute's cybotactic region and implicit modeling of the bulk solvent. We consider several axes along which the system's optical rotation varies, including the sampling of the dynamical trajectory, the quality of the one-electron basis set, and the use of continuum solvent models to account for bulk effects.
Advances in quantum computation for electronic structure,
and particularly
heuristic quantum algorithms, create an ongoing need to characterize
the performance and limitations of these methods. Here we discuss
some potential pitfalls connected with the use of hardware-efficient
Ansätze in variational quantum simulations of electronic structure.
We illustrate that hardware-efficient Ansätze may break Hamiltonian
symmetries and yield nondifferentiable potential energy curves, in
addition to the well-known difficulty of optimizing variational parameters.
We discuss the interplay between these limitations by carrying out
a comparative analysis of hardware-efficient Ansätze versus
unitary coupled cluster and full configuration interaction, and of
second- and first-quantization strategies to encode Fermionic degrees
of freedom to qubits. Our analysis should be useful in understanding
potential limitations and in identifying possible areas of improvement
in hardware-efficient Ansätze.
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