MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller–Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.

Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r: The 2-groupoid of 2dimensional fully extended r-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced Spin r 2 -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the r-th power of their Serre automorphisms. For r = 1 we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r = 2.To construct examples, we explicitly describe Spin r 2 -homotopy fixed points in the equivariant completion of any symmetric monoidal 2category. We also show that every object in a 2-category of Landau-Ginzburg models gives rise to fully extended spin TQFTs, and that half of these do not factor through the oriented bordism 2-category.

We give a combinatorial model for r-spin surfaces with parametrised boundary based on [Nov]. The r-spin structure is encoded in terms of Z r -valued indices assigned to the edges of a polygonal decomposition. With the help of this model we count the number of mapping class group orbits on r-spin surfaces with parametrised boundary and fixed r-spin structure on each boundary component, extending (and giving a different proof of) results in [Ran, GG].We use the combinatorial model to give a state sum construction of two-dimensional topological field theories on r-spin surfaces. We show that an example of such a topological field theory computes the Arf-invariant of an r-spin surface as introduced in [Ran, GG]. This implies in particular that the r-spin Arf-invariant is constant on orbits of the mapping class group, providing an alternative proof of that fact.

We give a combinatorial model for r-spin surfaces with parameterized boundary based on Novak (“Lattice topological field theories in two dimensions,” Ph.D. thesis, Universität Hamburg, 2015). The r-spin structure is encoded in terms of Zr-valued indices assigned to the edges of a polygonal decomposition. This combinatorial model is designed for our state-sum construction of two-dimensional topological field theories on r-spin surfaces. We show that an example of such a topological field theory computes the Arf-invariant of an r-spin surface as introduced by Randal-Williams [J. Topol. 7, 155 (2014)] and Geiges et al. [Osaka J. Math. 49, 449 (2012)]. This implies, in particular, that the r-spin Arf-invariant is constant on orbits of the mapping class group, providing an alternative proof of that fact.

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group G associated to outer automorphisms of G, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted G-bundles, and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted G-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, which is again two-dimensional Yang-Mills theory but with gauge group given by an extension of G by outer automorphisms. With the help of the orbifold completion of the topological defect bicategory of two-dimensional Yang-Mills theory, we describe the reverse orbifold using a Wilson line defect for the discrete gauge symmetry. We present our results using two complementary approaches: in the lattice regularisation of the path integral, and in the functorial approach to area-dependent quantum field theories with defects via regularised Frobenius algebras.

No abstract