Alchemical Normal Modes Unify Chemical Space

Based on thermodynamic integration we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any arbitrary reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas as the most generic reference, and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this choice affords exact and unambiguous definitions of energies and electron densities of AIMs We illustrate the approach for neutral iso-electronic diatomics (CO, N2, BF), various small molecules with different electronic hybridisation states of carbon (CH4, C2H6, C2H4, C2H2, HCN), and for all the possible BN doped mutants connecting benzene to borazine (C2nB3−nN3−nH6, 0 ≤ n ≤ 3). Analysis of the numerical results obtained suggests that APDFT based AIMs enable meaningful and new interpretations of molecular energies and electron densities.

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“…Second and higher order alchemical estimates were studied in Refs. [27,[47][48][49][50][51]. Insertion of µ I in Eq.…”

Section: A Theorymentioning

confidence: 99%

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

Rudorff

Lilienfeld

2019

J. Phys. Chem. B

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“…Here, the energy of the perturbed system (Δ E 0 | λ = 1 ) is the sum of the energy of the reference system (Δ E 0 | λ = 0 ) and terms involving alchemical derivatives, where the nth derivative is represented by

\partial_{λ}^{n} normalΔ E^{0}

. APDFT has been used in several diverse applications such as for predicting molecular reaction energetics, 22 deprotonation energies, 23 and properties of BN‐doped variants of benzene, coronene, fullerene, and graphene 24‐26 . APDFT has also been tested for predicting material properties of bulk transition metals, 27 semiconductor band gaps and stability, 26,28 and molecular adsorptions on nanoparticles and extended surfaces 22,24,29,30 .…”

Section: Introductionmentioning

confidence: 99%

“…APDFT has been used in several diverse applications such as for predicting molecular reaction energetics, 22 deprotonation energies, 23 and properties of BN‐doped variants of benzene, coronene, fullerene, and graphene 24‐26 . APDFT has also been tested for predicting material properties of bulk transition metals, 27 semiconductor band gaps and stability, 26,28 and molecular adsorptions on nanoparticles and extended surfaces 22,24,29,30 . The majority of these applications have used the Taylor series expression truncated to first order, which thus assigns a linear relationship between the energy perturbation and the alchemical derivatives of the reference shown in Equation ).

\partial_{λ} normalΔ E^{0} = \sum_{I} normalΔ μ_{nI} \partial_{λ} N_{I} - \sum_{I} normalΔ F_{I} \partial_{λ} R_{I} + normalΔ μ_{e} \partial_{λ} N_{e}

…”

Section: Introductionmentioning

confidence: 99%

Machine learning corrected alchemical perturbation density functional theory for catalysis applications

et al. 2020

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Alchemical perturbation density functional theory (APDFT) has promise for enabling computational screening of hypothetical catalyst sites. Here, we analyze errors in first order APDFT calculation schemes for binding energies of CH x , NH x , OH x , and OOH adsorbates over a range of different coverages on hypothetical alloys based on a Pt(111) reference system. We then train three different support vector regression machine learning models that correct systematic APDFT prediction errors for each of the three classes of carbon, nitrogen, and oxygen based adsorbates. While uncorrected first order APDFT alone approximates accurate adsorbate binding energies on up to 36 hypothetical alloys based on a single Kohn-Sham DFT calculation on a 3 × 3 unit cell for Pt(111), the machine learning-corrected APDFT extends this number to more than 20,000 and provides a recipe for developing other machine learning-based APDFT models. K E Y W O R D S adsorption, binding energies, high throughput screening 1 | INTRODUCTION Many efforts in computational catalysis are focused on screening materials for innovative catalysts that promote high chemical activity. 1-3 Descriptors for catalyst activity, for example, an adsorbate binding

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“…Here, the energy of the perturbed system (∆E 0 | λ=1 ) is the sum of the energy of the reference system (∆E 0 | λ=0 ) and terms involving alchemical derivatives, where the nth derivative is represented by ∂ n λ ∆E 0 . APDFT has been used in several diverse applications such as for predicting molecular reaction energetics, [22] deprotonation energies, [23] and properties of BN-doped variants of benzene, coronene, fullerene, and graphene [24,25,26]. APDFT has also been tested for predicting material properties of bulk transition metals, [27] semiconductor band gaps and stability, [26,28] and molecular adsorptions on nanoparticles and extended surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…APDFT has been used in several diverse applications such as for predicting molecular reaction energetics, [22] deprotonation energies, [23] and properties of BN-doped variants of benzene, coronene, fullerene, and graphene [24,25,26]. APDFT has also been tested for predicting material properties of bulk transition metals, [27] semiconductor band gaps and stability, [26,28] and molecular adsorptions on nanoparticles and extended surfaces. [22,24,29,30] The majority of these applications have used the Taylor series expression truncated to first order, which thus assigns a linear relationship between the energy perturbation and the alchemical derivatives of the reference shown in Eq.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Models Correct Systematic Errors in Alchemical Perturbation Density Functional Theory Applications to Catalysis

Griego¹,

Zhao²,

Saravanan³

et al. 2020

Preprint

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Alchemical perturbation density functional theory (APDFT) has great promise for enabling rapid and accurate computational screening of hypothetical catalyst sites, but first order approximations are unsatisfactorily inaccurate when alchemical derivatives are large. In this work, we analyze errors in first order APDFT calculation schemes for binding energies of CHx, NHx, OHx, and OOH adsorbates over a range of different coverages on hypothetical alloys based on a Pt(111) reference system. We then construct feature vectors by fingerprinting the dopant locations in the alloy and then use a data set of about 11,100 data points to train three different support vector regression machine learning models that correct systematic APDFT prediction errors for each of the three classes of carbon, nitrogen, and oxygen based adsorbates. While uncorrected first order APDFT alone can approximate reasonably accurate adsorbate binding energies on up to 36 hypothetical alloys based on a single Kohn-Sham DFT calculation on a 3 × 3 unit cell for Pt(111), the machine learning-corrected APDFT in principle extends this number to more than 20,000 and provides a recipe for developing other machine learning models to aid future high throughput screening studies.

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Alchemical Normal Modes Unify Chemical Space

Cited by 31 publications

References 58 publications

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

Machine learning corrected alchemical perturbation density functional theory for catalysis applications

Machine Learning Models Correct Systematic Errors in Alchemical Perturbation Density Functional Theory Applications to Catalysis

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