In this research, we derive equations for solving for the stationary points of the DLPNO-CCSD Lagrangian, in the t1-transformed formalism introduced earlier and as currently implemented in the Psi4 quantum chemistry software package. These lambda equations in the local pair natural orbital basis allow for the evaluation of CCSD(T)Λ energetics with linear-scaling computational effort, also known as the asymmetric triples correction. This DLPNO-CCSD(T)Λ method allows for accurate triples contributions to be computed for larger molecules, especially in cases that CCSD(T) is known to be insufficient, such as with multireference systems and bond-breaking systems. We showcase the accuracy of our code on reaction energies, barrier heights, and noncovalent interaction energies. Also showcased are the capabilities of our code by evaluating DLPNO-CCSD(T)Λ energetics on large noncovalent dimers up to 112 atoms, as well as a rhodium catalyst complex containing 66 atoms.

In this work, we implement a local pair natural orbital-based coupled-cluster method through the full treatment of quadruple excitations (CCSDTQ). The domain-based local pair natural orbital (DLPNO) approach, which has successfully been applied to lower levels of coupled-cluster theory, is utilized in our algorithm, and thus our algorithm is called DLPNO-CCSDTQ. For simplicity in the working equations and in the implementation, we t1-dress the two-electron integrals as well as Fock matrix elements. Our method can recover CCSDTQ-CCSDT and CCSDTQ-CCSDT(Q) energy differences on the order of 0.01-0.05 kcal mol-1, even at a loose quadruples natural orbital (QNO) occupation number cutoff of 3.33 × 10-6. To highlight the capabilities of our code and its potential future applications, we showcase computations that would be intractable with canonical CCSDTQ, such as the benzene dimer, (H2O)17, and adamantane. With sufficient computing resources, computations up to 15 heavy atoms (40 atoms overall) may be feasible for fully bonded 3D systems.

Although popular throughout the 1990s and early 2000s, interest in Al2H2 suddenly diminished, leaving an unresolved chasm between theory and experiment for over 20 years. Our computations reconcile the two, unveiling evidence for the unidentified but earlier observed Al2H2 butterfly global minimum in matrix IR. We confirm the experimental IR assignments of the cyclic and monobridged structures. The critical ingredient in our case is the b2 symmetry Al-H stretching frequency predicted here to be 1096 cm-1. This feature was observed at 1090 cm-1 by Andrews et al., but never identified. Andrews et al. also assigned a feature at 1647 cm-1 to the linear structure of Al2H2. However, this is unlikely, as we do not find the linear structure to be an equilibrium geometry. CCSD(T) geometries and energies for four neutral Al2H2 isomers in this work are computed at the highest levels of theory among theoretical investigations in the literature. For final energetic predictions, basis sets as large as augmented quadruple zeta were used, as were theoretical methods as advanced as CCSDT(Q). We also report Al2H2 VPT2 fundamental frequencies for the first time. In addition, two anionic structures are investigated at the same levels of theory, the butterfly ground state and monobridged local minimum, which have never been characterized. We conclude that these anion structures could be identified in future mass-selected gas-phase spectroscopy experiments.

We present an efficient, asymptotically linear-scaling implementation of the canonically O(N^8) coupled-cluster method with singles, doubles, and full triples excitations (CCSDT) method. We apply the domain-based local pair natural orbital (DLPNO) approach for computing CCSDT amplitudes. Our method, called DLPNO-CCSDT, uses the converged coupled-cluster amplitudes from a preceding DLPNO-CCSD(T) computation as a starting point for the solution of the CCSDT equations in the local natural orbital basis. To simplify the working equations, we t1-dress our two-electron integrals and Fock matrices, allowing our equations to take on the form of CCDT. With appropriate parameters, our method can recover more than 99.99% of the total canonical CCSDT correlation energy. In addition, we demonstrate that our method consistently yields sub-kJ mol^-1 errors in relative energies when compared to canonical CCSDT, and, likewise, when computing the difference between CCSDT and CCSD(T). Finally, to highlight the low scaling of our algorithm, we present timings on linear alkanes (up to 30 carbons and 730 basis functions) and water clusters (up to 131 water molecules and 3144 basis functions).

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.

Multiple algorithms exist for calculating Coulomb (J) or exchange (K) contributions to Fock-like matrices, and it is beneficial to develop a framework that allows the seamless integration and combination of different J and K construction algorithms. In PSI4, we have implemented the "CompositeJK" formalism for this purpose. CompositeJK allows for the combination of any J and K construction algorithms for any quantum chemistry method formulated in terms of J-like or K-like matrices (including, but not limited to, Hartree-Fock and density functional theory) in a highly modular and intuitive fashion, which is simple to utilize for both developers and users. Using the CompositeJK framework, PSI4 was interfaced to the sn-LinK implementation in the GauXC library, adding the first instance of noncommercial graphics processing unit (GPU) support for the construction of Fock matrix elements to PSI4. On systems with hundreds of atoms, the interface to the CPU sn-LinK implementation displays a higher performance than all the alternative JK construction methods available in PSI4, with up to x2.8 speedups compared to existing PSI4 JK implementations. The GPU sn-LinK implementation, harnessing the power of GPUs, improves the observed performance gains to up to x7.0.

Here, 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).

The protein-ligand binding free energy is a central quantity in structure-based computational drug discovery efforts. Although popular alchemical methods provide sound statistical means of computing the binding free energy of a large breadth of systems, they are generally too costly to be applied at the same frequency as end point or ligand-based methods. By contrast, these data-driven approaches are typically fast enough to address thousands of systems but with reduced transferability to unseen systems. We introduce Dr Delta G-Net (or simply Dragnet), an equivariant graph neural network that can blend ligand-based and protein-ligand data-driven approaches. It is based on a 3D fingerprint representation of the ligand alone and in complex with the protein target. Dragnet is a global scoring function to predict the binding affinity of arbitrary protein-ligand complexes, but can be easily tuned via transfer learning to specific systems or end points, performing similarly to common 2D ligand-based approaches in these tasks. Dragnet is evaluated on a total of 28 validation proteins with a set of congeneric ligands derived from the Binding DB and one custom set extracted from the ChEMBL Database. In general, a handful of experimental binding affinities are sufficient to optimize the scoring function for a particular protein and ligand scaffold. When not available, predictions from physics-based methods such as absolute free energy perturbation can be used for the transfer learning tuning of Dragnet. Furthermore, we use our data to illustrate the present limitations of data-driven modeling of binding free energy predictions.

Following a formula found in the paper of Avramov, Iyengar, Lipman, and Nayak (2010) and ideas of Neeman and Khusyairi, we indicate that Grothendieck duality for finite tor-amplitude maps can be developed from scratch via the formula $f^! := \delta^*\pi_1^{\times}f^*$. Our strategy centers on the subcategory $\Gamma_{\Delta}(\mathrm{QCoh}(X \times X))$ of quasicoherent sheaves on $X \times X$ supported on the diagonal. By exclusively using this subcategory instead of the full category $\mathrm{QCoh}(X \times X)$ we give systematic categorical proofs of results in Grothendieck duality and reprove many formulas found in Neeman (2018). We also relate some results in Grothendieck duality with properties of the sheaf of (derived) Grothendieck differential operators.

By reading a standard formula for the ring of Grothendieck differential operators in a derived way, we construct a derived (sheaf of) ring of Grothendieck differential operators for Noetherian schemes $X$ separated and finite-type over a base $S$, when the map $X \to S$ is finite tor-amplitude. Using this ring of differential operators, we (re-)develop the theory of $D$-modules from scratch and show an equivalence of categories between $D$-modules using our definition and crystals over the infinitesimal site.

We present the working equations for a reduced-scaling method of evaluating the perturbative triples (T) energy in coupled-cluster theory, through the tensor hypercontraction (THC) of the triples amplitudes (tijkabc). Through our method, we can reduce the scaling of the (T) energy from the traditional O(N7) to a more modest O(N5). We also discuss implementation details to aid future research, development, and software realization of this method. Additionally, we show that this method yields submillihartree (mEh) differences from CCSD(T) when evaluating absolute energies and sub-0.1 kcal/mol energy differences when evaluating relative energies. Finally, we demonstrate that this method converges to the true CCSD(T) energy through the systematic increasing of the rank or eigenvalue tolerance of the orthogonal projector, as well as exhibiting sublinear to linear error growth with respect to system size.

Atomic charges are critical quantities in molecular mechanics and molecular dynamics, but obtaining these quantities requires heuristic choices based on atom-typing orrelatively expensive quantum mechanical methods to generate a density to be partitioned. Most machine learning efforts in this domain ignore total molecular charges,relying on overfitting and arbitrary rescaling in order to match the total system charge.Here we introduce the electron-passing neural network (EPNN), a fast, accurate neural network atomic charge partitioning model that conserves total molecular charge byconstruction. EPNNs predict atomic charges very similar to those obtained by partitioning quantum mechanical densities, but at such a small fraction of the cost that they can be easily computed for large biomolecules. Charges from this method may be useddirectly for molecular mechanics, as features for cheminformatics, or as input to anyneural network potential.