Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

Abstract

A linear-scaling local second-order Møller–Plesset (MP2) method is presented for high-spin open-shell molecules based on restricted open-shell (RO) reference functions. The open-shell local MP2 (LMP2) approach inherits the iteration- and redundancy-free formulation and the completely integral-direct, OpenMP-parallel, and memory and disk use economic algorithms of our closed-shell LMP2 implementation. By utilizing restricted local molecular orbitals for the demanding integral transformation step and by introducing a novel long-range spin-polarization approximation, the computational cost of RO-LMP2 approaches that of closed-shell LMP2. Extensive benchmarks were performed for reactions of radicals, ionization potentials, as well as spin-state splittings of carbenes and transition-metal complexes. Compared to the conventional MP2 reference for systems of up to 175 atoms, local errors of at most 0.1 kcal/mol were found, which are well below the intrinsic accuracy of MP2. RO-LMP2 computations are presented for challenging protein models of up to 601 atoms and 11 000 basis functions, which involve either spin states of a complexed iron ion or a highly delocalized singly occupied orbital. The corresponding runtimes of 9–15 h obtained with a single, many-core CPU demonstrate that MP2, as well as spin-scaled MP2 and double-hybrid density functional methods, become widely accessible for open-shell systems of unprecedented size and complexity.

Basis set truncation corrections for improved frozen natural orbital CCSD(T) energies

“…One common feature of recent local correlation methods is the compression of the MO basis using orbital or orbital pair specific NOs. For instance, in our LNO family of methods [12,48,69,[78][79][80][81][82], all of the above correlation energy expressions can be decomposed into electron (or orbital) specific contributions:…”

“…where method M can refer to MP2 [80][81][82], CCSD [48,79], (T) [12,48,69], or even higher orders of CC theory [48,78]. For instance, for M=MP2, the correlation energy of Eq.…”

Coupled Cluster Benchmark of New DFT and Local Correlation Methods: Mechanisms of Hydroarylation and Oxidative Coupling Catalyzed by Ru(II, III) Chloride Carbonyls

“…Recently developed local correlation methods, such as DLPNO-CCSD(T) (domain localized pair natural orbital CCSD(T)) of Neese and coworkers, 15,16 PNO-LCCSD(T) (pair natural orbital, localized CCSD(T)) of Werner and co-workers, 17 and LNO-CCSD(T) of Nagy and Kaĺlay, 18,19 scale almost linearly with system size in the large-molecule limit and, at least for main-group systems, provide similar accuracy to the corresponding canonical calculations (in addition to the original papers, 17,18 it has been shown by Neese and co-workers 20 and by our group 21 ). For open-shell systems, several implementations aside from DLPNO-CCSD(T) have likewise been published, to wit: PNO-L methods, 22 LNO-CCSD(T) 23 (not yet available in MRCC 24 as of the time of writing), and the open-shell incremental methods of Dolg, Tew, and Friedrich. 25,26 Recently, benchmark studies of the performance of density functionals for transition-metal problems, using DLPNO-CCSD(T) for calibration, have started appearing for reaction energies 27 and barrier heights.…”

Recent Advances in First-Principles Based Molecular Dynamics

“…The optimal parallelization method depends on the level of theory used as well as on the basis set employed. Some recent examples of high-performance implementations can be found in refs − , for CCSD, MP2 and DFT calculations, respectively. Here, we will focus instead on the recently implemented multiscale simulation framework MiMiC.…”