# Ramping it up : mixed ramp-gaussian basis sets

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2015

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McKemmish, Laura Kelly

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For decades, all-Gaussian basis sets have dominated molecular quantum chemistry, despite some of their less desirable properties. In particular, gaussian basis functions cannot describe the nuclear-electron cusp and consequently large numbers of high exponents gaussians are present in core basis functions to try to describe the inner core electron distribution adequately. This is despite the fact that core electron distribution changes little in response to changing molecular environments and is not an important contribution to chemical energetics that chemists are generally interested in (reaction energies, ionisation energies, isomerisation energies and so on). The principal reason for the dominance of gaussian basis sets is that accurate evaluation of two-electron integral evaluation in these basis sets is far quicker than for other competing types of basis sets. This thesis seeks to change this. We reintroduce a ramp basis function, which has a non-zero nuclearelectron cusp and can therefore describe the inner core accurately and efficiently. This ramp function has compact support, which greatly reduces the difficulty of two-electron integral evaluation, but means it cannot describe valence electron distributions. Thus, gaussian basis functions are added to describe valence electrons to form a mixed ramp-gaussian basis set. To simplify the development of this new class of basis set, we modify only the core basis function in 6-31G (6-31+G) to produce R-31G (R-31+G). These novel rampified basis sets have very similar chemistry to their parent basis sets in atoms and molecules in Hartree-Fock (HF), density functional theory (DFT) and Moller-Plesset 2 Theory (MP2) calculations. The mixed ramp-gaussian basis sets are vastly better than their parent basis sets at predicting electron density at the nucleus and in fact gives better performance than cc-pVQZ. Faster HF, DFT and MP2 calculations in large molecules would increase the speed of the most common types of computational chemistry calculations in the world. This thesis provides strong evidence that mixed ramp-Gaussian basis sets are a viable way to get these faster calculations without compromising chemical accuracy. A preliminary integral evaluation program, RampItUp, was developed in this thesis that calculates all one- and two-electron ramp-containing integrals for a mixed ramp-Gaussian basis set with S-ramps, sand p-gaussians. With the main caveat that two-electron screening is not performed in either basis set, the Fock build time for R-31+G is faster than in 6-31+G by about 10% for large linear molecules, e.g. fatty acids, with more than 20 heavy atoms. This demonstrates that fast integral evaluation is possible. This thesis provides strong justification for the inclusion of ramp-gaussian basis sets into mainstream quantum chemistry packages to allow the full benefits of these new type of basis sets to be experienced by the field as a whole.

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Thesis (PhD)

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Open Access

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## DOI

10.25911/5d5153d25e971