Generation of basis sets with high degree of fulfillment of the Hellmann‐Feynman theorem

Rico, J. Fernández; López, Rafael; Ema, I.; Ramı́rez, G.

doi:10.1002/jcc.20601

Cited by 10 publications

(7 citation statements)

References 31 publications

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“…[80] An advantage for using machine learning models to do this is that long-range forces calculated from densitybased machine learning models converge much quicker with respect to training cluster size compared to forcebased models. [25] While the aug-cc-pvdz basis set used to train the model in this work is not large enough to fulfill the requirements for accurate Hellmann-Feynman forces, [81,82] the accuracy of the machine learning electron densities suggests that with more complete basis sets the model could be directly applied for ab initio molecular dynamics.…”

Section: Additional Applications For the Machine Learning Modelmentioning

confidence: 99%

Predicting quantum-accurate electron densities for DNA with equivariant neural networks

Lee¹,

Rackers

Bricker³

2022

Preprint

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One of the fundamental limitations of accurately modeling biomolecules like DNA is the inability to perform quantum chemistry calculations on large molecular structures. We present a machine learning model based on an equivariant Euclidean Neural Network framework to obtain quantum-accurate electron densities for arbitrary DNA structures that are much too large for conventional quantum methods. The model is trained on representative B-DNA base pair steps that capture both base pairing and base stacking interactions. The model produces accurate electron densities for arbitrary B-DNA structures with typical errors of less than 1%. Crucially, the error does not increase with system size, which suggests that the model can extrapolate to large DNA structures with negligible loss of accuracy. The model also generalizes well to other DNA structural motifs such as the A- and Z-DNA forms, despite being trained on only B-DNA configurations. We show that this machine learning electron density model can be used to calculate electrostatic potentials of DNA with quantum accuracy. These electrostatic potentials produce more accurate results compared to classical force fields and do not show the usual deficiencies at short range. Lastly, the model is used to calculate electron densities of several large-scale DNA structures, and we show that the computational scaling for this model is linear.

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Section: Additional Applications For the Machine Learning Modelmentioning

confidence: 99%

Predicting quantum-accurate electron densities for DNA with equivariant neural networks

Lee¹,

Rackers

Bricker³

2022

Preprint

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“…We follow the strategy of Rico et al [25] in constructing the HF optimized basis sets. This approach relies on the observation that the Pulay force can be reduced with a basis that accurately reproduces its own spatial derivatives with respect to nuclear coordinates [29,30].…”

Section: Hellmann-feynman Optimized Basis Setmentioning

confidence: 99%

“…Pioneering work by Rico et al [25] has demonstrated that specially optimized basis sets can suppress the Pulay force. In their proof of principle work, Rico et al showed that atom-centered Slater-type orbital basis sets constructed to be flexible enough to describe the derivative of the wave function |∂Ψ/∂ R I afford noticeably attenuated Pulay forces.…”

Section: Introductionmentioning

confidence: 99%

Accurate Hellmann-Feynman forces with optimized atom-centered Gaussian basis sets

Pathak¹,

Rackers²,

López³

et al. 2022

Preprint

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The Hellmann-Feynman (HF) theorem provides a way to compute forces directly from the electron density, affording an approach to calculating forces of large systems with machine learning (ML) models that predict electron density. The primary issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upwards of 10 eV/Ang in forces. In this work, we construct specialized atom-centered Gaussian basis sets to reduce the Pulay force, and demonstrate the basis sets' effectiveness in computing accurate HF forces. We find that HF forces computed using the σNZHF (N = Single, Double, Triple) basis sets developed in this work yield comparable accuracy to forces computed with the Pulay term using size matched cc-pVNZ [1] and pcseg-N [2] basis sets for water clusters and pcseg-N and aug-pcseg-N basis sets for DNA fragments. Our results illustrate that the σNZHF basis sets yield HF forces with state-of-the-art accuracy, paving a clear path forwards for accurate and efficient calculations of forces for large systems using the HF theorem and ML densities.

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“…As remarked in the introduction, integrals of the first type are needed for the calculation of derivatives [11] of the electron energy and density, as well as for the analysis of the basis set stability [10]. An example of these integrals is reported in Table I.…”

Section: Computational Testsmentioning

confidence: 99%

“…Though particular expressions for these conventional integrals are known from other procedures, the present method has the advantage of giving their master formula, which enables to obtain nonconventional integrals such as multipolar moments associated to fragments of two-center charge distributions or overlap integrals containing derivatives of STO. The former is useful for computing atomic multipoles, electrostatic potentials of molecules, or molecular interactions [9], and the latter, in the study of basis sets stability [10], and in the calculation of the derivatives of electronic energy [11], nonadiabatic coupling matrix elements [12], and so forth.…”

Section: Introduction Imentioning

confidence: 99%

Auxiliary functions for molecular integrals with Slater‐type orbitals. II. Gauss transform methods

Ema

López

Fernández

et al. 2007

Int J of Quantum Chemistry

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ABSTRACT:The Gauss transform of Slater-type orbitals is used to express several types of molecular integrals involving these functions in terms of simple auxiliary functions. After reviewing this transform and the way it can be combined with the shift operator technique, a master formula for overlap integrals is derived and used to obtain multipolar moments associated to fragments of two-center distributions and overlaps of derivatives of Slater functions. Moreover, it is proved that integrals involving two-center distributions and irregular harmonics placed at arbitrary points (which determine the electrostatic potential, field and field gradient, as well as higher order derivatives of the potential) can be expressed in terms of auxiliary functions of the same type as those appearing in the overlap. The recurrence relations and series expansions of these functions are thoroughly studied, and algorithms for their calculation are presented. The usefulness and efficiency of this procedure are tested by developing two independent codes: one for the derivatives of the overlap integrals with respect to the centers of the functions, and another for derivatives of the potential (electrostatic field, field gradient, and so forth) at arbitrary points.

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Generation of basis sets with high degree of fulfillment of the Hellmann‐Feynman theorem

Cited by 10 publications

References 31 publications

Predicting quantum-accurate electron densities for DNA with equivariant neural networks

Predicting quantum-accurate electron densities for DNA with equivariant neural networks

Accurate Hellmann-Feynman forces with optimized atom-centered Gaussian basis sets

Auxiliary functions for molecular integrals with Slater‐type orbitals. II. Gauss transform methods

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