McKemmish, Laura K.2015-07-062015-07-060021-9606http://hdl.handle.net/1885/14218Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RampItUp. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.14 pages© 2015 AIP Publishing LLC.http://www.sherpa.ac.uk/romeo/issn/0021-9606/..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 6/07/15)2015-04-0210.1063/1.49163142015-12-10