Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-02-21 |
| Journal | Journal of Chemical Theory and Computation |
| Authors | James McClain, Qiming Sun, Garnet KinâLic Chan, Timothy C. Berkelbach |
| Institutions | Princeton University, University of Chicago |
| Citations | 241 |
| Analysis | Full AI Review Included |
6CCVD Technical Documentation: Advanced Electronic Structure Analysis of Covalent Semiconductors via Coupled-Cluster Theory
Section titled â6CCVD Technical Documentation: Advanced Electronic Structure Analysis of Covalent Semiconductors via Coupled-Cluster TheoryâReference Paper: McClain, J., Sun, Q., Chan, G. K.-L., & Berkelbach, T. C. (2017). Gaussian-based coupled-cluster theory for the ground state and band structure of solids.
Executive Summary
Section titled âExecutive SummaryâThis paper validates the use of highly accurate, wave function-based computational methods (Equation-of-Motion Coupled-Cluster theory with Single and Double excitations, EOM-CCSD) to predict the fundamental electronic and structural properties of prototypical covalent semiconductors: diamond and silicon. The findings provide critical theoretical benchmarks for designing next-generation diamond-based devices.
- Methodological Validation: First application of canonical Gaussian-based coupled-cluster theory for calculating ground-state properties (lattice constant, bulk modulus, cohesive energy) and excited-state band structure of three-dimensional solids.
- High Accuracy Results: Predicted indirect band gaps for Diamond (5.37 eV) and Silicon (1.19 eV) show excellent agreement (within 0.1 eV) with zero-point-corrected experimental values (5.45-5.50 eV and 1.17 eV, respectively).
- Structural Fidelity: CCSD calculations accurately predicted the lattice constants and bulk moduli for both materials, confirming the robust treatment of correlated electron effects crucial for structural integrity.
- Computational Scale: Calculations achieved unprecedented scale for this level of theory, handling up to 256 electrons in 2,176 orbitals using large triple-zeta valence basis sets (TZVP) and extensive k-point sampling (up to 4x4x4 Brillouin zone mesh).
- Material Relevance: The highly accurate determination of the 5.37 eV indirect band gap affirms the ultra-wide bandgap nature of diamond, essential for UV optics, high-power electronics, and quantum computing substrates.
- 6CCVD Value Proposition: This research confirms that realizing the theoretical performance of diamond requires ultra-high purity, low-defect Single Crystal Diamond (SCD) material, precisely matching 6CCVDâs core manufacturing expertise.
Technical Specifications
Section titled âTechnical SpecificationsâThe following table summarizes the key structural and electronic properties calculated using the highest level of theory and basis sets presented (CCSD/EOM-CCSD with TZVP basis, extrapolated to the thermodynamic limit $N_{k} \to \infty$ where applicable).
| Parameter | Value (Diamond, C) | Value (Silicon, Si) | Unit | Context |
|---|---|---|---|---|
| Material Structure | Cubic Fd<sub>3</sub>m | Cubic Fd<sub>3</sub>m | N/A | Paradigmatic covalent semiconductors. |
| Crystal Lattice Constant (CCSD) | 3.539 | 5.393 | Ă | Experimental: 3.553 Ă (C), 5.421 Ă (Si). |
| Bulk Modulus (CCSD) | 463 | 103 | GPa | High stiffness confirmed for Diamond. |
| Cohesive Energy (CCSD) | 7.04 | 4.15 | eV/atom | Energy required to separate the solid into atoms. |
| Indirect Band Gap (EOM-CCSD) | 5.37 | 1.19 | eV | Excellent agreement with experimental T=0 K values. |
| Computational Basis Set | TZVP (Triple-Zeta Valence Polarized) | TZVP | N/A | 17 orbitals per atom used for the highest accuracy runs. |
| Maximum System Size | 256 | 256 | Electrons | Canonical CCSD run using 4x4x4 k-point mesh. |
| Maximum Orbital Count | 2,176 | 2,176 | Orbitals | Used in the largest 4x4x4 Brillouin zone sampling. |
| Reference Temperature | 300 | 300 | K | Experimental lattice constants used for structural inputs. |
Key Methodologies
Section titled âKey MethodologiesâThe theoretical framework relies on sophisticated quantum chemistry methods adapted for periodic boundary conditions using Gaussian-based crystalline atomic orbitals (AOs).
- Mean-Field Initialization (HF): Initial calculations performed using Hartree-Fock (HF) theory to establish a closed-shell reference determinant ($\mid\Phi\rangle$). This involved solving the HF equation using integrals adapted for periodic systems, managing divergent Coulomb terms using Ewald summation techniques.
- Pseudopotentials and Basis Sets: Used Gaussian Type Hutter (GTH) norm-conserving pseudopotentials to remove core electrons, focusing only on the four valence electrons per atom. Single-particle basis sets included DZV (8 orbitals/atom), DZVP (13 orbitals/atom), and TZVP (17 orbitals/atom).
- Ground-State Correlation (CCSD): Electron correlation energy was calculated using Coupled-Cluster Singles and Doubles (CCSD) theory, which corrects for static and dynamic correlation errors inherent in the mean-field approximation.
- Excited-State Calculation (EOM-CCSD): Quasiparticle band structure and band gaps were determined using Equation-of-Motion CCSD (EOM-CCSD). This involved diagonalizing the effective Hamiltonian in the space of one-hole (IP) and one-particle (EA) charged excitations.
- Brillouin Zone Sampling: Calculations sampled the Brillouin zone using uniform $\Gamma$-centered k-point meshes (e.g., 3x3x3 and 4x4x4). Finite-size errors related to k-point sampling were corrected via extrapolation assuming a theoretical $N_{k}$-1/3 scaling to reach the thermodynamic limit.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe theoretical accuracy achieved in this research sets a high bar for the quality of physical diamond required for experimental validation and practical device engineering. 6CCVD is uniquely positioned to supply the materials needed to match these idealized computational models.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the high-purity, low-defect structure necessary for applications relying on the intrinsic 5.37 eV band gap of diamond, researchers need materials with minimal substitutional defects and nitrogen incorporation.
| Application Requirement | 6CCVD Recommended Material | Rationale |
|---|---|---|
| Ultra-Wide Bandgap / UV Optics | Optical Grade Single Crystal Diamond (SCD) | Highest material purity, lowest nitrogen content (typically < 1 ppb), and highest crystalline perfection to minimize in-gap states and maximize transparency at UV wavelengths. |
| High-Power Electronics Substrates | Electronic Grade SCD (Low Defect) | Essential for realizing diamondâs theoretical high breakdown voltage and thermal conductivity, closely matching the ideal lattice parameters studied. |
| Semiconducting/Conductive Diamond | Heavy Boron-Doped Diamond (BDD) | While the paper focuses on intrinsic properties, future work on device design requires customized $p$-type material supplied by 6CCVD in both SCD and PCD forms. |
Customization Potential
Section titled âCustomization PotentialâThe predictive power of EOM-CCSD calculation is only useful if the physical material can be precisely engineered to match design specifications. 6CCVD offers extensive customization capabilities critical for device fabrication:
- Custom Dimensions and Substrates: 6CCVD provides high-quality SCD and PCD plates/wafers up to 125 mm in diameter, accommodating advanced prototyping needs. Substrates are available up to 10 mm thick.
- Precision Thickness Control: We offer Single Crystal Diamond (SCD) layers with precise thickness control from 0.1 ”m up to 500 ”m, enabling the growth of thin films required for quantum and electronic applications.
- Metalization Services: To create functional electronic devices based on these theoretical structures, reliable contact layers are mandatory. 6CCVD offers in-house deposition of standard and custom metal stacks, including Ti, W, Au, Pt, Pd, and Cu, tailored to specific ohmic or Schottky contact requirements.
- Ultra-Smooth Polishing: Achieving predictable surface states for high-performance devices (especially for quantum emitters or electronic interfaces) requires exceptionally smooth surfaces. 6CCVD guarantees ultra-low roughness polishing: Ra < 1 nm for SCD and Ra < 5 nm for Inch-size PCD.
Engineering Support
Section titled âEngineering SupportâThe robust correlation methods detailed in this paper highlight the necessity of materials that perform close to the ideal limit. 6CCVDâs in-house PhD team provides authoritative guidance on material selection and processing, ensuring that supplied SCD/PCD meets the demanding requirements for correlated electronic structure projects, including:
- Minimizing defects that introduce charge traps or alter the effective band gap.
- Optimizing crystal orientation and thickness for specific electronic or optical devices.
- Consultation on doping levels for BDD applications derived from theoretical band structure modeling.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We present the results of Gaussian-based ground-state and excited-state equation-of-motion coupled-cluster theory with single and double excitations for three-dimensional solids. We focus on diamond and silicon, which are paradigmatic covalent semiconductors. In addition to ground-state properties (the lattice constant, bulk modulus, and cohesive energy), we compute the quasiparticle band structure and band gap. We sample the Brillouin zone with up to 64 k-points using norm-conserving pseudopotentials and polarized double- and triple-ζ basis sets, leading to canonical coupled-cluster calculations with as many as 256 electrons in 2176 orbitals.