Multi-Level Protocol for Mechanistic Reaction Studies Using Semi-Local Fitted Potential Energy Surfaces.

In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT.

The unfavorable scaling () of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.

Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2).

Building upon our previously published work [P. Pinski and F. Neese, J.

Communication: Exact analytical derivatives for the domain-based local pair natural orbital MP2 method (DLPNO-MP2).

Electron correlation methods based on pair natural orbitals (PNOs) have gained an increasing degree of interest in recent years, as they permit energy calculations to be performed on systems containing up to many hundred atoms, while maintaining chemical accuracy for reaction energies. We present an approach for taking exact analytical first derivatives of the energy contributions in the simplest method of the family of Domain-based Local Pair Natural Orbital (DLPNO) methods, closed-shell DLPNO-MP2. The Lagrangian function contains constraints to account for the relaxation of PNOs.

Multilevel Approaches within the Local Pair Natural Orbital Framework.

The linear-scaling local coupled cluster method DLPNO-CCSD(T) allows calculations on systems containing hundreds of atoms to be performed while reproducing canonical CCSD(T) energies typically with chemical accuracy (<1 kcal/mol). The accuracy of the method is determined by two main truncation thresholds that control the number of electron pairs included in the CCSD iterations and the size of the pair natural orbital virtual space for each electron pair, respectively. While the results of DLPNO-CCSD(T) calculations converge smoothly toward their canonical counterparts as the thresholds are tightened, the improved accuracy is accompanied by a fairly steep increase of the computational cost.

SparseMaps-A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals.

In this work, we present a linear scaling formulation of the coupled-cluster singles and doubles with perturbative inclusion of triples (CCSD(T)) and explicitly correlated geminals. The linear scaling implementation of all post-mean-field steps utilizes the SparseMaps formalism [P. Pinski et al.

SparseMaps--A systematic infrastructure for reduced-scaling electronic structure methods. IV. Linear-scaling second-order explicitly correlated energy with pair natural orbitals.

We present a formulation of the explicitly correlated second-order Møller-Plesset (MP2-F12) energy in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the domain based local pair-natural orbital-MP2 (DLPNO-MP2) method by us recently [Pinski et al.

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

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.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data.

Reactive Many-Body Expansion for a Protonated Water Cluster.

We generalize the standard many-body expansion technique that is used to approximate the total energy of a molecular system to enable the treatment of chemical reactions by quantum chemical techniques. By considering all possible assignments of atoms to monomer units of the many-body expansion and associating suitable weights with each, we construct a potential energy surface that is a smooth function of the nuclear positions. We derive expressions for this reactive many-body expansion energy and describe an algorithm for its evaluation, which scales polynomially with system size, and therefore will make the method feasible for future condensed phase simulations.