A Laplace-transformed second-order Moller-Plesset perturbation theory (MP2) method is presented, which allows to achieve linear scaling of the computational effort with molecular size for electronically local structures. Also for systems with a delocalized electronic structure, a cubic or even quadratic scaling behavior is achieved. Numerically significant contributions to the atomic orbital (AO)-MP2 energy are preselected using the so-called multipole-based integral estimates (MBIE) introduced earlier by us [J. Chem. Phys. 123, 184102 (2005)]. Since MBIE provides rigorous upper bounds, numerical accuracy is fully controlled and the exact MP2 result is attained. While the choice of thresholds for a specific accuracy is only weakly dependent upon the molecular system, our AO-MP2 scheme offers the possibility for incremental thresholding: for only little additional computational expense, the numerical accuracy can be systematically converged. We illustrate this dependence upon numerical thresholds for the calculation of intermolecular interaction energies for the S22 test set. The efficiency and accuracy of our AO-MP2 method is demonstrated for linear alkanes, stacked DNA base pairs, and carbon nanotubes: e.g., for DNA systems the crossover toward conventional MP2 schemes occurs between one and two base pairs. In this way, it is for the first time possible to compute wave function-based correlation energies for systems containing more than 1000 atoms with 10 000 basis functions as illustrated for a 16 base pair DNA system on a single-core computer, where no empirical restrictions are introduced and numerical accuracy is fully preserved.
The dissociation of ligands from proteins and other biomacromolecules occurs over a wide range of timescales. For most pharmaceutically relevant inhibitors, these timescales are far beyond those that are accessible by conventional molecular dynamics (MD) simulation. Consequently, to explore ligand egress mechanisms and compute dissociation rates, it is necessary to enhance the sampling of ligand unbinding. Random Acceleration MD (RAMD) is a simple method to enhance ligand egress from a macromolecular binding site that does not require the user to choose a ligand egress reaction coordinate. It thus enables the unbiased exploration of ligand egress routes. Furthermore, the RAMD procedure can be used to compute the relative residence times of ligands. When combined with a machine-learning analysis of protein-ligand interaction fingerprints (IFP), molecular features that affect ligand unbinding kinetics can be identified. Here, we describe the implementation of RAMD in GROMACS 2020, which provides significantly improved computational performance, with scaling to large molecular systems. For the automated analysis of RAMD results, we developed MD-IFP, a set of tools for the generation of IFPs along unbinding trajectories and for their use in the exploration of ligand dynamics. We demonstrate that the analysis of ligand dissociation trajectories by mapping them onto the IFP space enables the characterization of ligand dissociation routes and metastable states. The combined implementation of RAMD and MD-IFP provides a computationally efficient and freely available workflow that can be applied
We derive rigorous multipole-based integral estimates (MBIE) in order to account for the distance dependence occurring in atomic-orbital (AO) formulations of electron correlation theory, where our focus is on AO-MP2 theory within a Laplace scheme. We find for the exact transformed integral products an extremely early onset of a linear-scaling behavior and a very small number of significant products. To preselect the significant integral products we adapt our MBIE method as rigorous upper bound. In this way it is possible to exploit the favorable scaling behavior observed and to reduce the scaling of estimated products asymptotically to linear, without sacrificing accuracy or reliability. By separating Coulomb- and exchange-type contractions only half-transformed integrals need to be computed. Furthermore, our scheme of rigorously preselecting transformed integral products via MBIE seems to offer particularly interesting perspectives for a direct formation of half- or fully transformed integrals by using multipole expansions and auxiliary basis sets.
Within an atomic-orbital-based (AO-based) formulation of second-order Møller-Plesset perturbation theory (MP2), we present a novel screening procedure which allows us to preselect numerically significant two-electron integrals more efficiently, especially for large basis sets. The screening is based on our recently introduced multipole-based integral estimates (MBIE) method [J. Chem. Phys., 2005, 123, 184102], that allows to exploit the 1/R(4) or 1/R(6) coupling between electronic charge distributions in transformed integral products within AO-MP2. In this way, linear scaling is attained with fully-controlled numerical accuracy. Furthermore, a parallel implementation of our linear-scaling AO-MP2 method is described, which also allows us to perform calculations with larger basis sets. First calculations reveal that for e.g. linear alkanes the scaling of the number of required transformed integral products is almost equal for 6-31G* and cc-pVTZ basis sets. Using the improved MBIE screening, the largest parallel calculation was performed for a ribozyme fragment consisting of 497 atoms and 5697 basis functions, while our largest AO-MP2 calculation was performed for a stacked DNA system (16 base pairs) comprising 1052 atoms and 10 674 basis functions on a single processor.
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