Mixed Ramp–Gaussian Basis Sets

McKemmish, Laura K.; Gilbert, Andrew T. B.; Gill, Peter M. W.

doi:10.1021/ct500615m

Cited by 19 publications

(22 citation statements)

References 72 publications

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“…Empirically, we find that modelling concentric R G shell-pairs with high Gaussian exponents is most challenging, necessitating careful selection of both fitting metric and model basis set; we have discussed this case in detail. 17 Modelling of non-concentric shell-pairs is more forgiving of fitting metric and model basis set, though more careful selection of these will enable shorter model lengths whilst retaining accuracy. Improvements to this procedure will improve the short-range timings, but have no influence on the timings for long-range integrals.…”

Section: Simplifying and Modelling Basis-function-pairsmentioning

confidence: 99%

“…Modification of this code to the anti-Coulomb metric as discussed in Ref. 17 should be a priority of future code development. Fortunately, the modelling subsection of the code is quite modular and improvements to the modelling process can be done without influencing other subsections of the code.…”

Section: R-31g Vs 6-31g Timings With No Screeningmentioning

confidence: 99%

“…Even though chemistry occurs in the valence region (and is described by the "3" and "1" basis functions), 6 Gaussian primitives are required to describe the core adequately. This author and collaborators recently proposed 17 the use of a novel type of basis function, the ramp, to describe electron distribution in the core region of atoms. A ramp with degree n and radius 1 is given by…”

Section: Introductionmentioning

confidence: 99%

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Efficient calculation of integrals in mixed ramp-Gaussian basis sets

McKemmish

2015

The Journal of Chemical Physics

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Algorithms 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.

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Section: Simplifying and Modelling Basis-function-pairsmentioning

confidence: 99%

Section: R-31g Vs 6-31g Timings With No Screeningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient calculation of integrals in mixed ramp-Gaussian basis sets

McKemmish

2015

The Journal of Chemical Physics

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“…al. 50 proposed a fundamentally new type of basis set, named mixed ramp-Gaussian basis sets, that have the potential to revolutionise our ability to computationally model core-electrons. These basis sets retain Gaussians to describe the valence electron distribution, but use a new type of basis function, the ramp (denoted by R) 51,52 , which has an electron-nuclear cusp, to describe the core-electron distribution.…”

Section: Introductionmentioning

confidence: 99%

Mixed Ramp-Gaussian Basis Sets for Core-Dependent Properties: STO-RG and STO-R2G for Li-Ne

2020

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Peer-reviewed publication https://doi.org/10.1071/CH19466The traditional Gaussian basis sets used in modern quantum chemistry lack an electron-nuclear cusp, and hence struggle to accurately describe core electron properties. A recently introduced novel type of basis set, mixed ramp-Gaussians, introduce a new primitive function called a ramp function which addresses this issue.This paper introduces three new mixed ramp-Gaussian basis sets -STO-R, STO-RG and STO-R2G, made from a linear combination of ramp and Gaussian primitive functions -which are derived from the single-core-zeta Slater basis sets for the elements Li to Ne. This derivation is done in an analogous fashion to the famous STO-nG basis sets. The STO-RG basis functions are found to outperform the STO-3G basis functions and STO-R2G outperforms STO-6G, both in terms of wavefunction fit and other key quantities such as the one-electron energy and the electron-nuclear cusp.The second part of this paper performs preparatory investigations into how standard all-Gaussian basis sets can be converted to ramp-Gaussian basis sets through modifying the core basis functions. Using a test case of the 6-31G basis set for carbon, we determined that the second Gaussian primitive is less important when fitting a ramp-Gaussian core basis function directly to an all-Gaussian core basis function than when fitting to a Slater basis function. Further, we identified the basis sets that are single-core-zeta and thus should be most straightforward to convert to mixed ramp-Gaussian basis sets in the future.

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“…This has allowed to treat large systems of chemical or biological significance containing hundreds of electrons and, at the same time, obtain very accurate results for small systems which are intensively studied spectroscopically. Introduction of general explicitly correlated methods [1][2][3], reliable extrapolation techniques [4][5][6][7][8][9], general coupled cluster theories [10,11], and new or improved one-electron basis sets [12][13][14][15][16][17][18][19][20][21][22] made the so-called spectroscopic accuracy (few cm −1 or less) achievable for many small molecules.…”

Section: Introductionmentioning

confidence: 99%

Calculation of Araki-Sucher correction for many-electron systems

2017

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In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

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Mixed Ramp–Gaussian Basis Sets

Cited by 19 publications

References 72 publications

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Mixed Ramp-Gaussian Basis Sets for Core-Dependent Properties: STO-RG and STO-R2G for Li-Ne

Calculation of Araki-Sucher correction for many-electron systems

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