Efficient calculation of integrals in mixed ramp-Gaussian basis sets

McKemmish, Laura K.

doi:10.1063/1.4916314

Cited by 10 publications

(14 citation statements)

References 74 publications

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“…ramp-ramp shell-pairs and thus dramatically reduces the complexity of two-electron integrals. [15] In combination with modelling ramp-Gaussian shell pairs as a linear combination of ramps, it has been demonstrated that calculation times of ramp-Gaussian basis sets can be competitive with or slightly faster than similar all-Gaussian basis sets [15] for low-angular momentum basis sets.…”

Section: Basis Sets and Core Chemistrymentioning

confidence: 99%

Introducing Pseudoramps and Mixed Ramp-Gaussian Jensen Basis Sets for Better Nuclear Densities

Cox

McKemmish

2021

Aust. J. Chem.

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Gaussian basis sets dominate quantum chemistry but struggle to model near-core electron densities and thus nuclear magnetic resonance (NMR) spectral properties. Mixed ramp-Gaussian (RG) basis sets show significant promise for these core properties due to the inclusion of a ramp-function with a non-zero nuclear-electron cusp. To enable quicker testing of the potential of RG basis sets for core chemistry, here we approximate ramps as a large linear combination of Gaussians called pseudoramps, thus enabling standard quantum chemistry packages to be used to approximate RG basis set results. We produce and test rampified general-purpose segmented Jensen basis sets. These basis sets retain the valence chemistry of their parent all-Gaussian basis sets, as desired, but unfortunately fail to show significantly improved performance in core chemistry. Crucially, for NMR spinspin couplings (the most promising potential application of RG basis sets), general-purpose basis sets are so poorly performing that results cannot be interpreted. For chemical shifts, P-ramps are likely required for improved performance. We conclude that the use of pseudoramps to test the performance of ramp-Gaussian basis sets is extremely helpful, decoupling methodology development and evaluation from implementation, but that more sophisticated basis set optimisation will be required to identify potential advantages of ramp-Gaussian basis sets over all-Gaussian basis sets.

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Section: Basis Sets and Core Chemistrymentioning

confidence: 99%

Introducing Pseudoramps and Mixed Ramp-Gaussian Jensen Basis Sets for Better Nuclear Densities

Cox

McKemmish

2021

Aust. J. Chem.

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“…In analogy, the differentials present in Eq. (13) are rewritten as (16) where ∇ Q is the gradient operator andẐ lm (∇ Q ) are the (real) spherical harmonic gradient operators [111]. Heuristically, they are obtained by taking an explicit expression for Z lm (r) and replacing all Cartesian coordinates with the corresponding differentials.…”

Section: A Generalised Mcmurchie-davidson Schemementioning

confidence: 99%

“…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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“…The support of the function is chosen as 1 Bohr because this enables two-centre ramp-ramp shell pairs to be avoided in most practical calculations (as bond lengths between non-hydrogen atoms are typically greater than 2 Bohr). This choice dramatically decreases the complexity of the twoelectron integrals and enables calculation times with ramp-Gaussian basis sets to be competitive with all-Gaussian basis sets 53 . In this paper, the degree of the ramp, n, is constrained to be an integer, as this makes two-electron integrals easier and avoids unbound derivatives at r = 1 Bohr.…”

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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Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Cited by 10 publications

References 74 publications

Introducing Pseudoramps and Mixed Ramp-Gaussian Jensen Basis Sets for Better Nuclear Densities

Introducing Pseudoramps and Mixed Ramp-Gaussian Jensen Basis Sets for Better Nuclear Densities

Calculation of Araki-Sucher correction for many-electron systems

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

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