Quantum Mechanical Treatment of Variable Molecular Composition: From 'Alchemical' Changes of State Functions to Rational Compound Design

Chang, K. Y. Samuel; Lilienfeld, O. Anatole von

doi:10.2533/chimia.2014.602

Cited by 14 publications

(19 citation statements)

References 79 publications

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“…We believe that such a high degree of accuracy is possible due to cancellation of the higher order non-linear effects, present in the electron density response, when considering relative energies. Similar to analogous compositional changes in small molecules we observe the most advantageous cancellation (resulting in highest predictive power) when inter converting elements appear late in the periodic table and when considering only vertical changes 38,40 . Also, the choice of reference salt, i.e.…”

Section: Resultssupporting

confidence: 60%

“…If treated separately, linear regression models would achieve even superior correlation coefficients and mean absolute errors. Similar observations have also been made in the case of alchemical predictions of covalent bond stretching in molecules 38,40 Fig. 5 also indicates that results differ for the alchemical prediction of the NaF lattice scan: While the alchemical prediction of the dissociative tail of NaF exhibits excellent linear correlation with the DFT numbers, the repulsive wall is not accounted for.…”

Section: Example 2: Nacl → Nax and Meclsupporting

confidence: 74%

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Alchemical screening of ionic crystals

Solovyeva

Lilienfeld

2016

Phys. Chem. Chem. Phys.

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We introduce alchemical perturbations as a rapid and accurate tool to estimate fundamental structural and energetic properties in pure and mixed ionic crystals. We investigated formation energies, lattice constants, and bulk moduli for all sixteen iso-valence-electron combinations of pure pristine alkali halides involving elements Me ∈ {Na, K, Rb, Cs} and X ∈ {F, Cl, Br, I}. For rock salt, zinc-blende, and cesium chloride symmetry, alchemical Hellmann-Feynman derivatives, evaluated along lattice scans of sixteen reference crystals, have been obtained for coupling to all respective 16 × 15 target crystals. Mean absolute errors (MAEs) are on par with the density functional theory level of accuracy for energies and bulk moduli. The predicted lattice constants are less accurate but reproduce qualitative trends. The reference salt NaCl affords the most accurate alchemical estimates of relative energies (MAE < 40 meV per atom). The best predictions of lattice constants are based on NaF as a reference salt (MAE < 0.5 Å), accounting only for qualitative trends. The best reference salt for the prediction of bulk moduli is CsCl (MAE < 0.4 × 10 dynes cm). The alchemical predictions distinguish competing rock salt and cesium chloride phases in binary and ternary solid mixtures with CsCl. Using pure RbI as a reference salt, they reproduce the reversal of the rock salt/cesium chloride stability trend for binary MeXCsCl as well as for ternary MeX(Me'Y)CsCl mixtures.

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Section: Resultssupporting

confidence: 60%

Section: Example 2: Nacl → Nax and Meclsupporting

confidence: 74%

Alchemical screening of ionic crystals

Solovyeva

Lilienfeld

2016

Phys. Chem. Chem. Phys.

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“…As a result, the Taylor expansion for this system is not convergent at λ = 1, similar to well known cases in Møller-Ploesset theory. [66][67][68] For asymmetric alchemical interpolations, as exemplified for the following examples in this study, as well as in previous studies, 11,17,20,32 the energy is typically smooth in all λ values, and derivative based expansions are expected to converge. (1) , second order truncated Taylor series calculated by coupled perturbed ∆E (2) CP , and second order truncated Taylor series calculated by independent particle approximation ∆E (2) IPA are plotted as black circles, red squares, blue open triangles, and blue filled triangles respectively.…”

Section: Alchemical Stretching Of H +mentioning

confidence: 60%

“…Numerical estimations of covalent bond stretching of small molecules are presented and discussed in Sec. III: Extending previous work on alchemical perturbation, 19,20,32 we discuss alchemical energy derivatives with respect to vertical transmutation, interpolating only the identity of the atoms while keeping the geometry fixed. Estimates of single, double and triple bonds are included as an application.…”

Section: Introductionmentioning

confidence: 99%

Fast and accurate predictions of covalent bonds in chemical space

Chang

Fias²,

Ramakrishnan

et al. 2016

The Journal of Chemical Physics

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We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated $\sigma$ bonding to hydrogen, as well as $\sigma$ and $\pi$ bonding between main-group elements, occurring in small sets of iso-valence-electronic molecular species with elements drawn from second to fourth rows in the $p$-block of the periodic table. Numerical evidence suggests that first order estimates of covalent bonding potentials can achieve chemical accuracy if (i) the alchemical interpolation is vertical (fixed geometry), (ii) involves molecules containing elements in the third and fourth row of the periodic table, and (iii) a reference geometry is optimized. In this case, changes in the bonding potential become near-linear in coupling parameter, resulting in analytical predictions with very high accuracy ($\sim$1 kcal/mol). Second order estimates deteriorate the prediction. If initial and final molecules differ not only in composition but also in geometry, all estimates become substantially worse, with second order being slightly more accurate than first order. The independent particle approximation to the second order perturbation performs poorly when compared to the coupled perturbed or finite difference approach. Taylor series expansions up to fourth order of the potential energy curve of highly symmetric systems indicate a finite radius of convergence, as illustrated for the alchemical stretching of H$_2^+$. Numerical results are presented for covalent bonds to hydrogen in 12 molecules with 8 valence electrons; (ii) main-group single bonds in 9 molecules with 14 valence electrons; (iii) main-group double bonds in 9 molecules with 12 valence electrons; (iv) main-group triple bonds in 9 molecules with 10 valence electrons; (v) H$_2^+$ single bond with 1 electron

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“…[9][10][11] A fundamentally different, but also highly promising approach has been von Lilienfeld's Alchemical Coupling approach. [12][13][14][15][16][17][18] In this ansatz, two iso-electronic molecules in CCS are alchemically coupled through interpolation of their external potentials (i.e. the potential acting on the electrons) in the Hamiltonian.…”

Section: Iintroductionmentioning

confidence: 99%