Machine learning has recently been introduced into the arsenal of tools that are available to computational chemists. In the past few years, we have seen an increase in the applicability of these tools on a plethora of applications, including the automated exploration of a large fraction of the chemical space, the reduction of repetitive computational tasks, the detection of outliers on large databases, and the acceleration of molecular simulations. An attractive application of machine learning in molecular electronic structure theory is the “recycling” of molecular wave functions for faster and more accurate completion of complex quantum chemical calculations. Along these lines, we have developed hybrid quantum chemical/machine learning workflows that utilize information from low-level wave functions for the accurate prediction of higher-level wave functions. The data-driven coupled-cluster (DDCC) family of methods is discussed in this article together with the importance of the inclusion of physical properties in such hybrid workflows. After a short introduction to the philosophy and the capabilities of DDCC, we present our recent progress in extending its applicability to larger and more complex molecular structures and data sets. A significant advantage offered by DDCC is its transferability, with respect to different molecular systems and different excitation levels. As we show here, predicted wave functions at the coupled-cluster singles and doubles level of theory can be used for the accurate prediction of the perturbative triples of the CCSD(T) scheme. We conclude with some personal considerations with respect to future directions related to the development of the next generation of such hybrid quantum chemical/machine learning models.
Machine learning has recently been introduced into the arsenal of tools that are available to computational chemists. In the past few years, we have seen an increase in the applicability of these tools on a plethora of applications, including the automated exploration of a large fraction of the chemical space, the reduction of repetitive computational tasks, the detection of outliers on large databases, and the acceleration of molecular simulations. An attractive application of machine learning in molecular electronic structure theory is the “recycling” of molecular wave functions for faster and more accurate completion of complex quantum chemical calculations. Along these lines, we have developed hybrid quantum chemical/machine learning workflows that utilize information from low-level wave functions for the accurate prediction of higher-level wave functions. The data-driven coupled-cluster (DDCC) family of methods is discussed in this article together with the importance of the inclusion of physical properties in such hybrid workflows. After a short introduction to the philosophy and the capabilities of DDCC, we present our recent progress in extending its applicability to larger and more complex molecular structures and data sets. A significant advantage offered by DDCC is its transferability, with respect to different molecular systems and different excitation levels. As we show here, predicted wave functions at the coupled-cluster singles and doubles level of theory can be used for the accurate prediction of the perturbative triples of the CCSD(T) scheme. We conclude with some personal considerations with respect to future directions related to the development of the next generation of such hybrid quantum chemical/machine learning models.
Computational cost limits the applicability of post-Hartree–Fock methods such as coupled-cluster on larger molecular systems. The data-driven coupled-cluster (DDCC) method applies machine learning to predict the coupled-cluster two-electron amplitudes ( t 2 ) using data from second-order perturbation theory (MP2). One major limitation of the DDCC models is the size of training sets that increases exponentially with the system size. Effective sampling of the amplitude space can resolve this issue. Five different amplitude selection techniques that reduce the amount of data used for training were evaluated, an approach that also prevents model overfitting and increases the portability of data-driven coupled-cluster singles and doubles to more complex molecules or larger basis sets. In combination with a localized orbital formalism to predict the CCSD t 2 amplitudes, we have achieved a 10-fold error reduction for energy calculations.
Solving the coupled-cluster (CC) equations is a cost-prohibitive process that exhibits poor scaling with system size. These equations are solved by determining the set of amplitudes ( t ) that minimize the system energy with respect to the coupled-cluster equations at the selected level of truncation. Here, a novel approach to predict the converged coupled-cluster singles and doubles (CCSD) amplitudes, thus the coupled-cluster wave function, is explored by using machine learning and electronic structure properties inherent to the MP2 level. Features are collected from quantum chemical data, such as orbital energies, one-electron Hamiltonian, Coulomb, and exchange terms. The data-driven CCSD (DDCCSD) is not an alchemical method because the actual iterative coupled-cluster equations are solved. However, accurate energetics can also be obtained by bypassing solving the CC equations entirely. Our preliminary data show that it is possible to achieve remarkable speedups in solving the CCSD equations, especially when the correct physics are encoded and used for training of machine learning models.
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 train- ing 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.
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 review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal/mol uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods are also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10–100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1–2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.
In the field of quantum machine learning (QML), parametrized quantum circuits (PQCs)─constructed using a combination of fixed and tunable quantum gates─provide a promising hybrid framework for tackling complex machine learning problems. Despite numerous proposed applications, there remains limited exploration of data sets relevant to quantum chemistry. In this study, we investigate the potential benefits and limitations of PQCs on two chemically meaningful data sets: (1) the BSE49 data set, containing bond separation energies for 49 different classes of chemical bonds, and (2) a data set of water conformers, where coupled-cluster singles and doubles (CCSD) wave functions are predicted from lower-level electronic structure methods using the data-driven coupled-cluster (DDCC) approach. We construct a comprehensive set of 168 PQCs by combining 14 data encoding strategies with 12 variational ansätze, and evaluate their performance on circuits with 5 and 16 qubits. Our initial analysis examines the impact of circuit structure on model performance using state-vector simulations. We then explore how circuit depth and training set size influence model performance. Finally, we assess the performance of the best-performing PQCs on current quantum hardware, using both noisy simulations ("fake" backends) and real quantum devices. Our findings underscore the challenges of applying PQCs to chemically relevant problems that are straightforward for classical machine learning methods but remain nontrivial for quantum approaches.