The DDEC6 method is one of the most accurate and broadly applicable atomic population analysis methods. It works for a broad range of periodic and non-periodic materials with no magnetism, collinear magnetism, and non-collinear magnetism irrespective of the basis set type. First, we show DDEC6 charge partitioning to assign net atomic charges corresponds to solving a series of 14 Lagrangians in order. Then, we provide flow diagrams for overall DDEC6 analysis, spin partitioning, and bond order calculations. We wrote an OpenMP parallelized Fortran code to provide efficient computations. We show that by storing large arrays as shared variables in cache line friendly order, memory requirements are independent of the number of parallel computing cores and false sharing is minimized. We show that both total memory required and the computational time scale linearly with increasing numbers of atoms in the unit cell. Using the presently chosen uniform grids, computational times of $9 to 94 seconds per atom were required to perform DDEC6 analysis on a single computing core in an Intel Xeon E5 multiprocessor unit. Parallelization efficiencies were usually >50% for computations performed on 2 to 16 cores of a cache coherent node. As examples we study a B-DNA decamer, nickel metal, supercells of hexagonal ice crystals, six X@C 60 endohedral fullerene complexes, a water dimer, a Mn 12 -acetate single molecule magnet exhibiting collinear magnetism, a Fe 4 O 12 N 4 C 40 H 52 single molecule magnet exhibiting non-collinear magnetism, and several spin states of an ozone molecule. Efficient parallel computation was achieved for systems containing as few as one and as many as >8000 atoms in a unit cell. We varied many calculation factors (e.g., grid spacing, code design, thread arrangement, etc.) and report their effects on calculation speed and precision. We make recommendations for excellent performance. † Electronic supplementary information (ESI) available: ESI documentation includes a pdf le containing: the 14 charge partitioning Lagrangians (S1); spin partitioning Lagrangian and ow diagram (S2); equations for bond order analysis (S3); algorithm for total electron density grid correction (S4); table and description listing big arrays and in which modules they are allocated and deallocated (S5); table and description of computational parameters (S6); description of how to use the enclosed reshaping sub routines (S7); and description of how to use the enclosed spin functions (S8). Additionally ESI includes a zip format archive containing: the system geometries; Jmol readable xyz les containing DDEC6 NACs, atomic multipoles, electron cloud parameters, ASMs, SBOs, and r-cubed moments; DDEC6 bond orders and overlap populations; a Fortran module containing reshaping subroutines; and a Fortran module containing spin functions. See