Laplace-Transform Fixed-Sparsity Local Møller−Plesset Perturbation Theory

Local correlation methods reduce steep scaling of electron correlation by discarding negligible contributions while retaining controllable accuracy. Building on recent advances in this domain, particularly the development of a single-threshold local second-order Møller-Plesset (MP2) theory that recovers canonical correlation energies while achieving linear scaling, we extend the scope and applicability of the so-called fixed sparsity approach for local correlation by virtue of the Laplace transform ansatz of Almöf. We will discuss theoretical and numerical aspects of Laplace transform fixed-sparsity local Møller-Plesset theory, which is iteration-free and uses orthogonal virtual orbitals. We will showcase how our Laplace transformed fixed-sparsity provides a platform for the development of more advanced techniques, with a particular focus on triples correlation energy in fourth-order Møller-Plesset theory, the original guide-rail for the definition of refernce methods CCSD[T] and the "gold standard" of single-reference quantum chemistry, CCSD(T).