Coupled-Cluster in Real Space. 1. CC2 Ground State Energies Using Multiresolution Analysis

A framework to calculate CC2 approximated coupled-cluster ground state correlation energies in a multiresolution basis is derived and implemented into the MADNESS library. The CC2 working equations are formulated in first quantization which makes them suitable for real-space methods. The first quantized equations can be interpreted diagrammatically using the usual diagrams from second quantization with adjusted interpretation rules. Singularities arising from the nuclear and electronic potentials are regularized by explicitly taking the nuclear and electronic cusps into account. The regularized three- and six-dimensional cluster functions are represented directly on an adaptive grid. The resulting equations are free of singularities and virtual orbitals, which results in a low intrinsic scaling. Correlation energies close to the basis set limit are computed for small molecules. This work is the first step toward CC2 excitation energies in a multiresolution basis.