Toward Chemical Accuracy with Shallow Quantum Circuits: A Clifford-Based Hamiltonian Engineering Approach.

Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on a variational quantum eigensolver and hardware-efficient ansatz, our method designs the Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree-Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, (3) imposes negligible overhead for classical processing and does not require additional quantum resources, and (4) is compatible with any circuit topology. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.

Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression.

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning.

This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree-Fock computations. A MOB pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of MOs. The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant derivative kernel for Gaussian process regression (GPR) is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly accurate models for both dipole moments and energies on water and 14 small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering GPR scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with the literature results, MOB-ML provides the best test mean absolute errors of 4.21 mD and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110 000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.

New Stable and Fast Ring-Polymer Molecular Dynamics for Calculating Bimolecular Rate Coefficients with an Example of OH + CH4.

The accurate and efficient calculation of the rate coefficients of chemical reactions is a key issue in the research of chemical dynamics. In this work, by applying the dimension-free ultrastable Cayley propagator, the thermal rate coefficients of a prototypic high dimensional chemical reaction OH + CH4 → H2O + CH3 in the temperature range of 200 to 1500 K are investigated with ring polymer molecular dynamics (RPMD) on a highly accurate full-dimensional potential energy surface. Kinetic isotope effects (KIEs) for three isotopologues of the title reaction are also studied. The results demonstrate excellent agreement with experimental data, even in the deep tunneling region. Especially, the Cayley propagator shows a high calculation efficiency with little loss of accuracy. The present results confirmed the applicability of the RPMD method, particularly the speed-up using a Cayley propagator, in theoretical calculations of bimolecular reaction rates.

Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space.

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [ J. Chem. Theory Comput. 2019, 15, 6668] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantages of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and exhibiting improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering are further combined with scalable Gaussian process regression (GPR) or linear regression (LR) to learn molecular energies accurately by generating a local regression model in each cluster. Among all four combinations of regressors and clustering methods, GMM combined with scalable exact GPR (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized data sets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over other training protocols for MOB-ML, i.e., supervised regression clustering combined with GPR (RC/GPR) and GPR without clustering. GMM/GPR also provides the best molecular energy predictions compared with ones from the literature on the same benchmark data sets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in wall-clock training time compared with scalable exact GPR with a training size of 6500 QM7b-T molecules.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states.

Molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. The application of Nesbet's theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different datasets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending the MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone-backbone interaction dataset to an accuracy of 0.28 kcal/mol.

A generalized class of strongly stable and dimension-free T-RPMD integrators.

Recent work shows that strong stability and dimensionality freedom are essential for robust numerical integration of thermostatted ring-polymer molecular dynamics (T-RPMD) and path-integral molecular dynamics, without which standard integrators exhibit non-ergodicity and other pathologies [R. Korol et al., J. Chem. Phys. 151, 124103 (2019) and R. Korol et al., J. Chem. Phys. 152, 104102 (2020)]. In particular, the BCOCB scheme, obtained via Cayley modification of the standard BAOAB scheme, features a simple reparametrization of the free ring-polymer sub-step that confers strong stability and dimensionality freedom and has been shown to yield excellent numerical accuracy in condensed-phase systems with large time steps. Here, we introduce a broader class of T-RPMD numerical integrators that exhibit strong stability and dimensionality freedom, irrespective of the Ornstein-Uhlenbeck friction schedule. In addition to considering equilibrium accuracy and time step stability as in previous work, we evaluate the integrators on the basis of their rates of convergence to equilibrium and their efficiency at evaluating equilibrium expectation values. Within the generalized class, we find BCOCB to be superior with respect to accuracy and efficiency for various configuration-dependent observables, although other integrators within the generalized class perform better for velocity-dependent quantities. Extensive numerical evidence indicates that the stated performance guarantees hold for the strongly anharmonic case of liquid water. Both analytical and numerical results indicate that BCOCB excels over other known integrators in terms of accuracy, efficiency, and stability with respect to time step for practical applications.

Regulation of Electronic Structure of Graphene Nanoribbon by Tuning Long-Range Dopant-Dopant Coupling at Distance of Tens of Nanometers.

Long-range dopant-dopant coupling in graphene nanoribbon (GNR) has been under intensive study for a very long time. Using a newly developed dopant central insertion scheme (DCIS), we performed first-principles study on multiple H, O, OH, and FeN4 dopants in long (up to 1000 nm) GNRs and found that, although potential energy of the dopant decays exponentially as a function of distance to the dopant, GNR's electronic density of states (DOS) exhibits wave-like oscillation modulated by dopants separated at a distance up to 100 nm. Such an oscillation strongly infers the purely quantum mechanical resonance states constrained between double quantum wells. This has been unambiguously confirmed by our DCIS study together with a one-dimensional quantum well model study, leading to a proof-of-principle protocol prescribing on-demand GNR-DOS regulation. All these not only reveal the underlining mechanism and importance of long-range dopant-dopant coupling specifically reported in GNR, but also open a novel highway for rationally optimizing and designing two-dimensional materials.