A large-scale implementation of the complete active space self-consistent field (CASSCF) method is presented. The active space is described using the variational two-electron reduced-density-matrix (v2RDM) approach, and the algorithm is applicable to much larger active spaces than can be treated using configuration-interaction-driven methods. Density fitting or Cholesky decomposition approximations to the electron repulsion integral tensor allow for the simultaneous optimization of large numbers of external orbitals. We have tested the implementation by evaluating singlet-triplet energy gaps in the linear polyacene series and two dinitrene biradical compounds. For the acene series, we report computations that involve active spaces consisting of as many as 50 electrons in 50 orbitals and the simultaneous optimization of 1892 orbitals. For the dinitrene compounds, we find that the singlet-triplet gaps obtained from v2RDM-driven CASSCF with partial three-electron N-representability conditions agree with those obtained from configuration-interaction-driven approaches to within one-third of 1 kcal mol(-1). When enforcing only the two-electron N-representability conditions, v2RDM-driven CASSCF yields less accurate singlet-triplet energy gaps in these systems, but the quality of the results is still far superior to those obtained from standard single-reference approaches.

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

Variational two-electron reduced-density-matrix (2-RDM) methods can provide a referenceindependent description of the electronic structure of strongly correlated molecules and materials. These methods represent one of few ways of performing large active-space-based computations that are beyond the scope of conventional configuration-interaction-based approaches. However, implementations of the method are quite rare, making it difficult for the quantum chemistry community to assess the utility of the approach. Here, we discuss an open-shell implementation of the variational 2-RDM method and explore its ability to describe different spin states in several model systems, including linear hydrogen chains and linear acenes. The largest calculations considered are comparable to complete-active-space computations with 50 electrons in 50 orbitals..

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