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We present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster theory. Our DLPNO-CCSDT(Q) algorithm uses converged doubles and triples amplitudes from a preceding DLPNO-CCSDT computation to compute the quadruples amplitude and energy in the quadruples natural orbital (QNO) basis. We demonstrate the compactness of the QNO space, showing that more than 95% of the (Q) correction can be recovered using relatively loose natural orbital cutoffs, compared to the tighter cutoffs used in pair and triples natural orbitals at lower levels of coupled-cluster theory. We also highlight the accuracy of our algorithm in the computation of relative energies, which yields deviations of sub-kJ mol−1 in relative energy compared to the canonical CCSDT(Q). Timings are conducted on a series of growing linear alkanes (up to 10 carbons and 608 basis functions) and water clusters (up to 49 water molecules and 2842 basis functions) to establish the asymptotic linear-scaling of our DLPNO-(Q) algorithm. 

We present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps associated with the CCSD(T) method are linear-scaling. In this work, we show that the t1-transformed Hamiltonian allows for a less complex algorithm when evaluating the local CCSD(T) energy without compromising efficiency or accuracy. Our algorithm yields sub-kJ mol−1 deviations for relative energies when compared with canonical CCSD(T), with typical errors being on the order of 0.1 kcal mol−1, using our TightPNO parameters. We extensively tested and optimized our algorithm and parameters for non-covalent interactions, which have been the most difficult interaction to model for orbital (PNO)-based methods historically. To highlight the capabilities of our code, we tested it on large water clusters, as well as insulin (787 atoms). 

From left to right and top to bottom, the five Ge₂H₂⁺structures are shown:trans, monobridged, butterfly, germylidene, and linear. 

Hypohalous acids (HOX) are a class of molecules that play a key role in the atmospheric seasonal depletion of ozone and have the ability to form both hydrogen and halogen bonds. The interactions between the HOX monomers (X = F, Cl, Br) and water have been studied at the CCSD(T)/aug-cc-pVTZ level of theory with the spin free X2C-1e method to account for scalar relativistic effects. Focal point analysis was used to determine CCSDT(Q)/CBS dissociation energies. The anti hydrogen bonded dimers were found with interaction energies of −5.62 kcal mol −1 , −5.56 kcal mol −1 , and −4.97 kcal mol −1 for X = F, Cl, and Br, respectively. The weaker halogen bonded dimers were found to have interaction energies of −1.71 kcal mol −1 and −3.03 kcal mol −1 for X = Cl and Br, respectively. Natural bond orbital analysis and symmetry adapted perturbation theory were used to discern the nature of the halogen and hydrogen bonds and trends due to halogen substitution. The halogen bonds were determined to be weaker than the analogous hydrogen bonds in all cases but close enough in energy to be relevant, significantly more so with increasing halogen size. 

Despite the interest in sulfur monoxide (SO) among astrochemists, spectroscopists, inorganic chemists, and organic chemists, its interaction with water remains largely unexplored. We report the first high level theoretical geometries for the two minimum energy complexes formed by sulfur monoxide and water, and we report energies using basis sets as large as aug-cc-pV(Q+d)Z and correlation effects through perturbative quadruple excitations. One structure of SO⋯H 2 O is hydrogen bonded and the other chalcogen bonded. The hydrogen bonded complex has an electronic energy of −2.71 kcal mol −1 and a zero kelvin enthalpy of −1.67 kcal mol −1 , while the chalcogen bonded complex has an electronic energy of −2.64 kcal mol −1 and a zero kelvin enthalpy of −2.00 kcal mol −1 . We also report the transition state between the two structures, which lies below the SO⋯H 2 O dissociation limit, with an electronic energy of −1.26 kcal mol −1 and an enthalpy of −0.81 kcal mol −1 . These features are much sharper than for the isovalent complex of O 2 and H 2 O, which only possesses one weakly bound minimum, so we further analyze the structures with open-shell SAPT0. We find that the interactions between O 2 and H 2 O are uniformly weak, but the SO⋯H 2 O complex surface is governed by the superior polarity and polarizability of SO, as well as the diffuse electron density provided by sulfur's extra valence shell.