Accurate correlated electronic structure methods involve a significant amount of computations and can be only employed to small molecular systems. For example, the coupled-cluster singles, doubles, and perturbative triples model (CCSD(T)), which is known as the ``gold standard" of quantum chemistry for its accuracy, usually can treat molecules with 20-30 atoms. To extend the reach of accurate correlated electronic structure methods to larger molecular systems, we work towards two directions: parallel computing and reduced-cost/scaling approaches. Parallel computing can utilize more computational resources to handle systems that demand more substantial computational efforts. Reduced-cost/scaling approaches, which introduce approximations to the existing electronic structure methods, can significantly reduce the amount of computation and storage requirements. In this work, we introduce a new distributed-memory massively parallel implementation of standard and explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) with canonical bigO{N^6} computational complexity ( C. Peng, J. A. Calvin, F. Pavov{s}evi'c, J. Zhang, and E. F. Valeev, textit{J. Phys. Chem. A} 2016, textbf{120}, 10231.), based on the TiledArray tensor framework. Excellent strong scaling is demonstrated on a multi-core shared-memory computer, a commodity distributed-memory computer, and a national-scale supercomputer. We also present a distributed-memory implementation of the density-fitting (DF) based CCSD(T) method. (C. Peng, J. A. Calvin, and E. F. Valeev, textit{in preparation for submission}) An improved parallel DF-CCSD is presented utilizing lazy evaluation for tensors with more than two unoccupied indices, which makes the DF-CCSD storage requirements always smaller than those of the non-iterative triples correction (T). Excellent strong scaling is observed on both shared-memory and distributed-memory computers equipped with conventional Intel Xeon processors and the Intel Xeon Phi (Knights Landing) processors. With the new implementation, the CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even more massive computations possible on leadership-class computing resources. The inclusion of F12 correction to the CCSD(T) method makes it converge to basis set limit much more rapidly. The large-scale parallel explicitly correlated coupled-cluster program makes the accurate estimation of the coupled-cluster basis set limit for molecules with 20 or more atoms a routine. Thus, it can be used rigorously to test the emerging reduced-scaling coupled-cluster approaches. Moreover, we extend the pair natural orbital (PNO) approach to excited states through the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. (C. Peng, M. C. Clement, and E. F. Valeev, textit{submitted}) We simulate the PNO-EOM-CCSD method using an existing massively parallel canonical EOM-CCSD program. We propose the use of state-averaged PNOs, which are generated from the average of the pair density of excited states, to span the PNO space of all the excited states. The doubles amplitudes in the CIS(D) method are used to compute the state-averaged pair density of excited states. The issue of incorrect states in the state-averaged pair density, caused by an energy reordering of excited states between the CIS(D) and EOM-CCSD, is resolved by simply computing more states than desired. We find that with a truncation threshold of
10−7, the truncation error for the excitation energy is already below 0.02 eV for the systems tested, while the average number of PNOs is reduced to 50-70 per pair. The accuracy of the PNO-EOM-CCSD method on local, Rydberg and charge transfer states is also investigated.
macroqc is a quantum chemistry software package designed for high-accuracy electronic structure computations and large-scale molecular simulations. The macroqc framework provides efficient implementations of energies and analytic gradients for a wide range of many-body perturbation theory and coupled-cluster (CC) methods. In particular, the analytic gradient implementations of second-order Møller-Plesset perturbation theory (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] exhibit excellent computational performance, even in comparison with established commercial quantum chemistry programs. In addition to conventional correlated methods, macroqc incorporates several advanced capabilities, including molecular fragmentation techniques for ground and excited state molecular systems and density-fitted analytic gradients. The software also supports interoperability with selected external packages through a flexible plugin framework, allowing developers to construct customized interfaces and extensions. The notable features of macroqc are the linear-scaling systematic molecular fragmentation (LSSMF) and the cluster-in-molecule (CIM) approaches, which enable the application of high-level post-Hartree-Fock approaches to large molecular systems that would otherwise be computationally prohibitive. Furthermore, the new machine learning (ML) library enables the integration of data-driven approaches into quantum chemical workflows, providing efficient tools for developing and applying ML-based models for molecular property prediction and electronic structure computations. With its combination of efficient implementations, advanced theoretical methods, and extensible design, macroqc is expected to serve as a useful platform for a broad range of computational chemistry applications.
The workhorse method of computational materials science is undeniably density functional theory in the Kohn-Sham framework of approximate exchange and correlation energy functionals. However, the need for highly accurate predictions of ground and excited state properties in materials science motivates the further development and exploration of alternative as well as complementary techniques. Among these alternative approaches, quantum chemical wavefunction based theories and in particular coupled cluster theory hold the promise to fill a gap in the toolbox of computational materials scientists. Coupled cluster (CC) theory provides a compelling framework of approximate infinite-order perturbation theory in the form of an exponential of cluster operators describing the true quantum many-body effects of the electronic wave function at a computational cost that, despite being significantly more expensive than DFT, scales polynomially with system size. The hierarchy of size-extensive approximate methods established in the framework of CC theory achieves systematic improvability for many materials properties. This is in contrast to currently available density functionals that often suffer from uncontrolled approximations that limit the accuracy in the prediction of materials properties. In this tutorial-style review we will introduce basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the connection between coupled cluster theory and the random-phase approximation to bridge the gap between traditional quantum chemistry and many-body Green’s function theories that are widely-used in the field of solid state physics. We will discuss various approaches to improve the computational performance without compromising accuracy. These approaches include large-scale parallel design as well as techniques that reduce the prefactor of the computational complexity. A central part of this article discusses the convergence of calculated properties to the thermodynamic limit which is of significant importance for reliable predictions of materials properties and constitutes an additional challenge compared to calculations of large molecules. Furthermore we mention technical aspects of computer code implementations of periodic coupled cluster theories in different numerical frameworks of the one-electron orbital basis; the projector-augmented-wave formalism using a plane wave basis set and the numeric atom-centered-orbital with resolution-of-identity.
Many-body perturbation theories (MBPT) (both single and multireference), by design, are capable of representing electron correlation very well. However, the practical implementation of these methods for many-electron systems beyond a certain order is extremely difficult, if not impossible. For instance, there are hardly any calculations beyond third order at the multireference and fifth order at the single reference of perturbation theories. Thus, these methods are typically limited to systems where the higher-order electron correlation effect is not significant. A practical solution to this problem is the coupled cluster theory, which was first introduced by Coester [20] and Coester and Kümmel [21] in nuclear physics and was later adopted in the electron structure theory by Čížek [23, 106] and Paldus and Čížek [107]. The coupled-cluster (CC) theory is a non-perturbative all-order theory. This stateof-the-art theory has now been recognized as the basis of modern quantitative quantum chemistry and atomic physics for high-precision calculations. Its superior accuracy is rooted in the exponential ansatz for the wave function, which provides an energy expression that scales correctly with the number of electrons and under certain provisions leads to a faster convergence of the many-body expansion.
Coupled-cluster theory (CC) is a highly accurate and versatile method for simulating complex interactions within quantum systems. The extension of CC theory to model mixed electron-photon processes with quantum electrodynamics (QED) has improved our capability to predict cavity-modified chemistry, a field where photons are used as cost-effective and eco-friendly alternatives to catalyze/inhibit chemical reactions. However, calculations with CC methods, even without incorporating QED effects, are often prohibitively expensive. Simulations of larger systems require scalable infrastructures that exist for traditional CC methods but not for QED-CC methods. As such, we present a GPU-enabled, high-performance, open-source implementation of the quantum electrodynamics coupled-cluster method with single and double excitations (QED-CCSD) within the ExaChem quantum chemistry software package. ExaChem relies on the Tensor Algebra for Many-body Methods (TAMM) infrastructure: a parallel heterogeneous tensor library designed to achieve scalable performance on modern heterogeneous supercomputing platforms. We discuss theoretical foundations, algorithmic details, and numerical benchmarks to showcase the larger systems that ExaChem can simulate and how the integration of photonic degrees-of-freedom alters their ground-state properties.
We propose a streamlined combination of the transcorrelation (TC) and coupled cluster (CC) theory, which not only increases the convergence rate with respect to the basis set but also extends the applicability of the lowest-order CC approximations to strongly correlated systems. Using the three-dimensional uniform electron gas as a model for real periodic solids and highly accurate ground-state energies from the state-of-the-art quantum Monte Carlo methods as benchmark, we show that, with the correct physical insights incorporated, our TC-CC methods gain drastic improvements in accuracy compared with canonical CC methods, and the errors of our methods remain $\ifmmode\pm\else\textpm\fi{}0.001$ Hartree per electron (Ha/electron) across a wide range of densities. With the greatly improved efficiencies and the balanced and accurate performances at both low and high densities, our methods present great promise for applications on real solids with weak and strong correlations.