Cluster-in-Molecule Approach with Explicitly Correlated Methods for Large Molecules

Efficient Computational Strategies of the Cluster-in-Molecule Local Correlation Approach for Interaction Energies of Large Host-Guest Systems

We propose a heterogeneously accelerated reduced cluster-in-molecule (CIM) local correlation approach for calculating host-guest interaction energies. The essence of this method is to compute only the clusters that make significant contributions to the interaction energies while approximately neglecting those clusters with smaller contributions. Benchmark calculations at the CIM resolution-of-identity second-order Mo̷ller-Plesset perturbation (CIM-RI-MP2) or CIM spin-component-scaled RI-MP2 (CIM-SCS-RI-MP2) levels, involving three medium-sized protein-ligand structures, demonstrate that the reduced CIM method achieves over 48% time savings without compromising accuracy, as the interaction energy error remains within 0.5 kcal/mol compared to the full CIM method. To further enhance cluster computation efficiency, we developed a heterogeneous parallel version of the CIM-(SCS-)RI-MP2 method. It achieves over 93% internode parallel efficiency and over 98% multi-GPU card parallel efficiency for the tested large complexes. Ultimately, the hardware-accelerated reduced CIM-(SCS-)RI-MP2 method is applied to calculate the interaction energies of six protein-ligand systems, ranging from 913 to 1425 atoms. Remarkably, the method requires only 4.3-22.8% of the clusters to achieve accurate results, and under the condition of using only a single node, the wall time is within 2 days. Additionally, the reduced CIM domain-based local pair natural orbital coupled cluster with singles, doubles, and perturbative triples [CIM-DLPNO-CCSD(T)] method is successfully applied to the calculation of a 1425-atom protein-ligand system. These computations demonstrate the capability of a specific electronic structure to accurately calculate interaction energies for large host-guest systems.

Local Wave Function Embedding: Correlation Regions in PNO-LCCSD(T)-F12 Calculations

Many chemical reactions affect only a rather small number of bonds, leaving the largest part of the chemical and geometrical structure of the molecules nearly unchanged. In this work we extended the previously proposed region method [J. Chem. Phys. 128, 144106 (2008)] to PNO-LCCSD(T)-F12. Using this method, we investigate whether accurate reaction energies for larger systems can be obtained by correlating only the electrons in a region of localized molecular orbitals close to the reaction center at high-level (PNO-LCCSD(T)-F12). The remainder is either treated at lower level (PNO-LMP2-F12) or left uncorrelated (Hartree-Fock frozen core). It is demonstrated that indeed the computed reaction energies converge rather quickly with the size of the correlation regions toward the results of the full calculations. Typically, 2-3 bonds from the reacting atoms need to be included to reproduce the results of the full calculations to within ±0.2 kcal/mol. We also computed spin-state energy differences in a large transition metal complex, where a factor of 15 in computation time could be saved, still yielding a result that is within ±0.1 kcal/mol of the one obtained in a full PNO-LCCSD(T)-F12 calculation.

Analytical Gradient Using Cluster-in-Molecule RI-MP2 Method for the Geometry Optimizations of Large Systems

We present an efficient analytical energy gradient algorithm for the cluster-in-molecule resolution-of-identity second-order Møller-Plesset perturbation (CIM-RI-MP2) method based on the Lagrange multiplier method. Our algorithm independently constructs the Lagrangian formalism within each cluster, avoiding the solution of the coupled-perturbed Hartree-Fock (CPHF) equation for the whole system. Due to this feature, the computational cost of the CIM-RI-MP2 gradients is much lower than that of other local MP2 algorithms. Benchmark calculations of several molecules containing up to 312 atoms demonstrate the general applicability of our CIM-RI-MP2 gradient algorithm. The optimized structure of a 244-atom molecule using the CIM-RI-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure. A single-point gradient calculation conducted for a molecular cage containing 972 atoms and 9612 basis functions takes 48 h on 25 nodes, utilizing a total of 600 CPU cores. The present CIM-RI-MP2 gradient program is applicable for obtaining the optimized geometries of large systems with hundreds of atoms.