Variational Particle Number Approach for Rational Compound Design

Lilienfeld, O. Anatole von; Lins, Roberto D.; Röthlisberger, Ursula

doi:10.1103/physrevlett.95.153002

Cited by 132 publications

(176 citation statements)

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“…Alchemical changes and potentials involving fractional nuclear charges are commonly used for two, often related, purposes: either for the evaluation of free energy differences between different compounds, for example, using thermodynamic integration, [21] DF ¼ R dk h@E=@ki; or for obtaining a set of gradients with dimension of N I indicating the response of the system to a variation in nuclear charge on every site. [19,22] In practice, we can calculate such changes through interpolation of nuclear charges in any basis set that is converged for all values of an interpolating order parameter, k. For plane-wave pseudopotential implementations, the same can be accomplished by interpolation of pseudopotentials that replace the explicit treatment of the core electrons. [23][24][25][26][27][28] The use of a plane-wave basis set is advantageous because it is independent of atomic position and type, and will not introduce Pulay forces.…”

Section: Molecular Grand-canonical Ensemble Theorymentioning

confidence: 99%

“…To offer a rigorous framework for explicit changes in fZ I g, molecular grand-canonical ensemble DFT was introduced, [17] relying to a significant degree on preceding work. [18,19] Only a brief summary is given here, for more details, the reader is referred to the original contributions.…”

Section: Molecular Grand-canonical Ensemble Theorymentioning

confidence: 99%

“…Consequently, we dub l p ðR I Þ the molecular ' 'alchemical potential' ' of atom I. [19] Interpolating pseudopotentials…”

Section: Molecular Grand-canonical Ensemble Theorymentioning

confidence: 99%

“…Weigend et al [46] were probably the first to propose such an application in the context of predicting stability in binary atom clusters. Independently, it was applied to drug binding energies within a QM/MM study, [19] demonstrated for hydrogen-bonded complexes, interconverting methane, ammonia, water, and hydrogenfluoride while bound to formic acid, [22] and applied to the molecular Fukui function for tuning highest occupied molecular orbital (HOMO) eigenvalues of boron/nitride derivatives of benzene. [20] In Ref.…”

Section: Design Applicationsmentioning

confidence: 99%

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First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Lilienfeld

2013

Int J of Quantum Chemistry

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A well‐defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we give an introduction to an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand‐canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via “alchemical” interpolations involving fractional nuclear charges in the electronic Hamiltonian. We address Taylor expansions in CCS, property nonlinearity, improved predictions using reference compound pairs, and the ounce‐of‐gold prize challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. These relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schrödinger equation. © 2013 Wiley Periodicals, Inc.

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Section: Molecular Grand-canonical Ensemble Theorymentioning

confidence: 99%

Section: Molecular Grand-canonical Ensemble Theorymentioning

confidence: 99%

“…Consequently, we dub l p ðR I Þ the molecular ' 'alchemical potential' ' of atom I. [19] Interpolating pseudopotentials…”

Section: Molecular Grand-canonical Ensemble Theorymentioning

confidence: 99%

Section: Design Applicationsmentioning

confidence: 99%

See 2 more Smart Citations

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Lilienfeld

2013

Int J of Quantum Chemistry

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139

160

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“…The choice for the particular form and nature of v depends, of course, on the problem at hand. Data-centered methods 2,3 and basis-functions expansions 4,5 are among the most popular choices in materials science although neural-network approaches for inverting intermolecular potentials also have been reported in the literature. 6 Cluster expansion ͑CE͒ ͑Ref.…”

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confidence: 99%

Structure-property maps and optimal inversion in configurational thermodynamics

et al. 2010

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Cluster expansions of first-principles density-functional databases in multicomponent systems are now used as a routine tool for the prediction of zero-and finite-temperature physical properties. The ability of producing large databases of various degrees of accuracy, i.e., high-throughput calculations, makes pertinent the analysis of error propagation during the inversion process. This is a very demanding task as both data and numerical noise have to be treated on equal footing. We have addressed this problem by using an analysis that combines the variational and evolutionary approaches to cluster expansions. Simulated databases were constructed ex professo to sample the configurational space in two different and complementary ways. These databases were in turn treated with different levels of both systematic and random numerical noise. The effects of the crossvalidation level, size of the database, type of numerical imprecisions on the forecasting power of the expansions were extensively analyzed. We found that the size of the database is the most important parameter. Upon this analysis, we have determined criteria for selecting the optimal expansions, i.e., transferable expansions with constant forecasting power in the configurational space ͑a structure-property map͒. As a by-product, our study provides a detailed comparison between the variational cluster expansion and the genetic-algorithm approaches. I. RATIONAL DESIGN, STRUCTURE-PROPERTY MAPS, AND TARGETING PHYSICAL PROPERTIESRational design of molecular systems and solid-state materials relies on the knowledge of the effective potentials or interactions to tailor motifs with favorable properties. In a combinatorial high-throughput approach the task is, in principle, simple: To solve the Schrödinger equation for all viable conformations and combinations of a list of candidate components. In practice, however, this is unfeasible due the astronomical size of the chemical space ͑i.e., the set of all spatial and chemical conformations available to the system͒ that must be scanned to optimize a target property. 1 Constructing maps that relate structure to physical properties is at the core of rational design strategies. This approach looks for correlations between a set of measurements ͑experimental observations and/or quantum-mechanical calculations͒ of an observable F and a potential-energy surface V. In a practical fashion, the functional map replaces the true V dependence of F͓V͔ with a functional f͑v͒ through a suitable transformation from V to a set of key variables v = ͑v 1 , ... ,v N ͒. Members of the potential energy surface are thus characterized by different v's. The choice for the particular form and nature of v depends, of course, on the problem at hand. Data-centered methods 2,3 and basis-functions expansions 4,5 are among the most popular choices in materials science although neural-network approaches for inverting intermolecular potentials also have been reported in the literature. 6 Cluster expansion ͑CE͒ ͑Ref. 7-9͒ is the method of choice to...

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Interaction of Molecules with Surfaces

2019

Molecular Interactions

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Variational Particle Number Approach for Rational Compound Design

Cited by 132 publications

References 31 publications

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Structure-property maps and optimal inversion in configurational thermodynamics

Interaction of Molecules with Surfaces

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