Nonlocal kinetic energy functionals by functional integration

At a Glance

Metadata	Details
Publication Date	2018-05-10
Journal	The Journal of Chemical Physics
Authors	Wenhui Mi, Alessandro Genova, Michele Pavanello
Institutions	Rutgers, The State University of New Jersey
Citations	77
Analysis	Full AI Review Included

Technical Documentation and Analysis: Nonlocal Kinetic Energy Functionals by Functional Integration

Executive Summary

This research introduces MGP, a highly accurate and computationally efficient nonlocal Kinetic Energy Density Functional (KEDF) designed for Orbital-Free Density Functional Theory (OF-DFT) simulations, providing critical tools for advanced material science research involving wide-bandgap semiconductors like MPCVD diamond.

Novel Functional: MGP (Mi-Genova-Pavanello) features a density-independent kernel derived through functional integration of the inverse Free Electron Gas (FEG) response function.
Kinetic Electron Term: Accuracy is significantly improved by augmenting the kernel with a “Kinetic electron” term, which corrects the long-range (low-q) behavior crucial for semiconductors and insulators.
High Accuracy Benchmark: MGP accurately reproduces bulk properties (equilibrium volume, bulk modulus, total energy) for both metallic (BCC, FCC) and highly challenging semiconducting phases (CD Silicon, nine III-V ZB semiconductors).
Energy Precision: MGP total equilibrium energies deviate from the rigorous Kohn-Sham DFT (KS-DFT) benchmark by less than 5 meV/cell across all tested Si and III-V compounds.
Superior Computational Efficiency: MGP is numerically stable, converging typically within 12 iterations, and maintains a computational cost similar to the highly efficient Wang-Teter (WT) functional—up to 1000 times faster than the highly accurate Huang-Carter (HC) KEDF for Silicon.
Relevance to Diamond: MGP’s proven ability to model covalent bonding and electron density in challenging wide-bandgap materials (Si, GaAs) makes it an essential tool for predicting and optimizing the properties of diamond (C), a superior Group IV semiconductor.

Technical Specifications

The following table summarizes the key performance metrics and computational parameters used or achieved during the benchmarking of the MGP functional:

Parameter	Value	Unit	Context
MGP Total Energy Deviation (Si)	< 5	meV/cell	Deviation from KS-DFT benchmark.
MGP Total Energy Deviation (III-V)	< 5	meV/cell	Deviation from KS-DFT benchmark.
MGP/HC V₀ Deviation (III-V)	< 2	%	Accuracy of Equilibrium Volume (V₀) relative to KS-DFT.
MGP/HC B₀ Deviation (III-V)	< 10	GPa	Accuracy of Bulk Modulus (B₀) relative to KS-DFT.
MGP Convergence Speed	~12	Iterations	Typical steps using truncated Newton minimization.
OF-DFT Grid Spacing (ATLAS)	0.2	Å	Real-space grid resolution used in OF-DFT calculations.
OF-DFT Kinetic Energy Cutoff	1600	eV	Used in PROFESS 3.0 for 1 meV/cell convergence.
KS-DFT Kinetic Energy Cutoff	800	eV	Used for bulk property simulations.
Electron Density Grid (ZB GaAs)	54 x 54 x 54	Grid Points	Real space density representation.
Electron Density Grid (CD Silicon)	36 x 36 x 36	Grid Points	Real space density representation.
MGP Kernel Parameters (CD Si, BLPS)	a=0.364, b=0.57	N/A	Optimal parameters for the Kinetic electron term.

Key Methodologies

The MGP functional was developed and benchmarked through a rigorous computational process combining theoretical derivation and extensive simulation against established Density Functional Theory (DFT) methods.

Functional Derivation (MGP): The functional relies on constructing a nonlocal Kinetic Energy Density Functional (KEDF) potential, $v_{T_{NL}} [\rho] (r)$, by functionally integrating the second functional derivative of the noninteracting Kinetic energy, $\delta^{2} T_{s} / \delta \rho (r) \delta \rho (r’)$, along a linear density path (Hypercorrelation).
Imposing FEG Response: The kernel of the nonlocal functional is formulated to exactly reproduce the inverse Lindhard function, $G_{Lind}(\eta)$, in the Free Electron Gas (FEG) limit.
Kinetic Electron Augmentation: To ensure proper long-range behavior, essential for semiconductors/insulators, the kernel $\omega_{T_{NL}}(q)$ is modified by the “Kinetic electron” term: $\omega_{MGP} (q) = \omega_{T_{NL}} (q) + \text{erf}^{2} (q) (4\pi a / q^{2}) e^{-bq^{2}}$.
Computational Tools: Orbital-Free DFT calculations were executed using modified versions of the ATLAS⁴³ and PROFESS 3.0⁴⁴ packages.
Benchmark Materials: Calculations focused on Crystal Diamond (CD), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC) phases of Silicon, alongside nine common III-V Zinc Blende (ZB) semiconductors (e.g., GaAs, AlAs, InP).
Benchmark References: Results were compared against established KEDFs (WT, WGC, HC) and high-accuracy Kohn-Sham DFT (KS-DFT) benchmarks utilizing Optimal Effective Local Pseudopotentials (OEPP) and Bulk-Derived Local Pseudopotentials (BLPS).
Property Calculation: Bulk properties (Equilibrium Volume V₀, Minimum Energy E₀, Bulk Modulus B₀) were extracted by fitting total energy curves against the Murnaghan equation of state.

6CCVD Solutions & Capabilities

The MGP functional’s success in accurately modeling the challenging covalent bonds and long-range dielectric behavior in Silicon and III-V semiconductors represents a massive leap forward for materials engineering. This computational methodology is directly applicable to diamond (C), the ultimate wide-bandgap semiconductor. 6CCVD leverages its specialization in MPCVD diamond to provide the physical substrates required to validate and implement these advanced theoretical predictions.

Research Requirement	6CCVD Applicable Material	6CCVD Solution & Value Proposition
Wide-Bandgap Modeling	High-purity electronic materials for fundamental studies (analogous to CD Si/GaAs).	Optical Grade Single Crystal Diamond (SCD): We supply high-ppurity SCD wafers up to 500µm thickness, essential for experiments requiring the lowest defect density, enabling direct comparison with highly accurate DFT predictions like MGP.
Electrochemical/Doped Systems	Modeling heavily doped materials (e.g., Boron in diamond) requires precise density functional input.	Boron-Doped Diamond (BDD): 6CCVD produces tailored BDD films (SCD or PCD) with controlled doping levels. Use MGP to predict optimal BDD lattice constants (V₀) and bulk moduli (B₀); we supply the physical material for validation.
Large-Scale Simulations	Need for large systems (e.g., supercells up to 1024 atoms used in the paper) requires inch-size substrates for practical device testing.	Custom Dimensions & Polishing: We manufacture Polycrystalline Diamond (PCD) plates up to 125mm in diameter. Our advanced polishing achieves Ra < 5nm for inch-size PCD, meeting the strict surface requirements of high-performance electronic devices simulated via OF-DFT.
Interface/Contact Simulation	Testing the effects of custom contacts (e.g., Ti/Pt/Au) modeled computationally.	In-House Metalization: 6CCVD offers internal, custom deposition services for Au, Pt, Pd, Ti, W, and Cu contacts directly onto diamond surfaces, allowing seamless translation from theoretical interface modeling to physical device fabrication.
Material-Specific Optimization	Choosing the ideal material parameters (e.g., crystal orientation, thickness) for novel applications.	Expert Engineering Support: Our in-house PhD material scientists specialize in MPCVD growth and can translate MGP/KS-DFT results into optimal material specifications, ensuring the supplied SCD/PCD/BDD perfectly matches the calculated requirements for your project.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Since the seminal studies of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting kinetic energy, Ts[ρ], the subject of this work. The typical paradigm is to first approximate the energy functional and then take its functional derivative, δTs[ρ]δρ(r), yielding a potential that can be used in orbital-free DFT or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for Ts[ρ] is prescribed [which we dub Mi-Genova-Pavanello (MGP)] having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero “Kinetic electron” arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential is derived from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (body-centered cubic, face-centered cubic) and semiconducting (crystal diamond) phases of silicon as well as of III-V semiconductors. The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm. MGP’s computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.

Tech Support

Original Source

DOI: https://doi.org/10.1063/1.5023926

References

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