Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Recently developed explicitly correlated local coupled-cluster methods [PNO-LCCSD(T)-F12] are reviewed. Extensive benchmarks for reaction energies and intermolecular interaction energies are presented, in which the convergence of the results with respect to all local approximations is studied. The explicit correlation treatment (F12) is shown to be essential to minimize basis set incompleteness errors, as well as errors caused by domain approximations. Generally, the errors of relative energies due to local approximations can be reduced to below 1 kcal/mol. The methods are well parallelized, and using small computer clusters with 100-200 computing cores, calculations for systems with 100-200 atoms using augmented triple-ζ basis sets can be carried out within a few hours of elapsed time. Recommendations are made on how such calculations should be carried out, how the accuracy can be tested, and which computational resources are required. This article is categorized under: Electronic Structure Theory> Ab Initio Electronic Structure Methods Software> Quantum Chemistry K E Y W O R D S explicit correlation, coupled cluster, local correlation, pair natural orbitals 1 | INTRODUCTIONThe coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)] is considered the gold standard of quantum chemistry for computing energies and other properties of molecules. Often, the accuracy is comparable or even better than that of experimental data, and chemical accuracy (1 kcal/mol or better for relative energies) can be achieved, provided that the system under consideration is of single-reference character, that is, the Hartree-Fock (HF) Slater determinant dominates the total wave function expansion. However, in its traditional canonical form, the application of the CCSD(T) method is limited to rather small systems (20-30 atoms) due to the steep increase of the computational effort with system size: The central processing unit (CPU) time scales as O N 7 el

The three central phenomena of cuprate superconductors are linked by a common doping p*, where the enigmatic pseudogap phase ends, around which the superconducting phase forms a dome, and at which the resistivity exhibits an anomalous linear dependence on temperature as T → 0 (ref. 1). However, the

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.