In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) [F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)]. The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large molecules, the number of amplitudes to be determined is reduced by a factor of 10(5)-10(6) relative to a canonical CCSD calculation on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a number of fifth order scaling steps that eventually rendered the method computationally expensive for large molecules (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below 8800 basis functions and >450 atoms. In all larger test calculations done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calculation, provided no approximations have been introduced in the latter. Thus, based on the present development reliable CCSD calculations on large molecules with unprecedented efficiency and accuracy are realized.

An efficient and near linear scaling pair natural orbital based local coupled cluster method

Fragmentation Methods: A Route to Accurate Calculations on Large Systems Mark S. Gordon,* Dmitri G. Fedorov, Spencer R. Pruitt, and Lyudmila V. Slipchenko Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States

Fragmentation methods: a route to accurate calculations on large systems.

https://chemistry.mdma.ch/hiveboard/rhodium/pdf/indole.synth.review.1994-99.pdf

Recent developments in indole ring synthesis—methodology and applications

More than 20 years ago, we published in Chemical Reviews a paper entitled “Intermolecular Interactions between Medium-Sized Systems. Nonempirical and Empirical Calculations of Interaction Energy: Successes and Failures”. The situation in calculations of noncovalent interactions at that time can be best characterized by the question we posed at the very beginning of the review: “Can quantum chemistry describe vdW (van der Waals; today we call it noncovalent) interactions as successfully as covalent interactions?” Our answer then was “unambiguously yes”. We had good reason for an optimistic “yes” since we presented the first coupledcluster calculations including triple excitations for a (at that time) large complexsthe water dimer. We stressed the importance of the triple excitations for noncovalent interactions, and in the section called Prospects, we wrote that “significant progress is highly desirable with beyond-SCF methods, where new, more accurate and efficient procedures are developed”. In this respect we were right, and in the past 20 years, we have witnessed an enormous growth of interest in the fast and accurate calculation of intermolecular interactions. What is the reason for such an interest, or more generally, why are noncovalent interactions so relevant in modern research? Is it the mere existence of noncovalent complexesmore » in the gas and liquid phases? Certainly not. The answer should be sought in the role that noncovalent interactions are playing in both bio- and nanostructures.« less

Stabilization and structure calculations for noncovalent interactions in extended molecular systems based on wave function and density functional theories.

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Sparse maps--A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory.

An exponential multireference wave-function Ansatz is formulated. In accordance with the state universal coupled-cluster Ansatz of Jeziorski and Monkhorst [Phys. Rev. A 24, 1668 (1981)] the approach uses a reference specific cluster operator. In order to achieve state selectiveness the excitation- and reference-related amplitude indexing of the state universal Ansatz is replaced by an indexing which is based on excited determinants. There is no reference determinant playing a particular role. The approach is size consistent, coincides with traditional single-reference coupled cluster if applied to a single-reference, and converges to full configuration interaction with an increasing cluster operator excitation level. Initial applications on BeH2, CH2, Li2, and nH2 are reported.

An exponential multireference wave-function Ansatz.

A general fully automated implementation of the incremental scheme for molecules and embedded clusters in the framework of the coupled cluster singles and doubles theory is presented. The code can be applied to arbitrary order of the incremental expansion and is parallelized in a master/slave structure. The authors found that the error in the total correlation energy is lower than 1kcal∕mol with respect to the canonical CCSD calculation if the incremental series is truncated in a proper way.

Fully automated implementation of the incremental scheme: application to CCSD energies for hydrocarbons and transition metal compounds.

New algorithms for an individually selecting MR-CI program

Initial applications of an exponential multi-reference wavefunction ansatz

The regioselectivity of the biradical cyclization of enyne-carbodiimides 1 can easily be controlled by variation of R1 at the alkyne terminus. Attachment of a hydrogen atom (R1 =H) leads to C2 -C7 cyclization and formation of biradical 2, whereas C2 -C6 cyclization to provide biradical 3 is observed with R1 =Me3 Si or Ph.

Two Novel Thermal Biradical Cyclizations in Theory and Experiment: New Synthetic Routes to 6H-Indolo[2,3-b]quinolines and 2-Aminoquinolines from Enyne-Carbodiimides.

Michael Hanrath

Papers

An exponential multireference wave-function Ansatz.

Fully automated implementation of the incremental scheme: application to CCSD energies for hydrocarbons and transition metal compounds.

New algorithms for an individually selecting MR-CI program

Initial applications of an exponential multi-reference wavefunction ansatz

Two Novel Thermal Biradical Cyclizations in Theory and Experiment: New Synthetic Routes to 6H-Indolo[2,3-b]quinolines and 2-Aminoquinolines from Enyne-Carbodiimides.