Erkale

Official Resources

• Homepage: https://github.com/susilehtola/erkale
• Documentation: https://github.com/susilehtola/erkale/wiki
• Source Repository: https://github.com/susilehtola/erkale
• License: GNU General Public License v2.0

Overview

Erkale is an open-source quantum chemistry program for Hartree-Fock and density functional theory calculations using Gaussian basis sets. Originally developed at the University of Helsinki, it focuses on computing X-ray properties including ground-state electron momentum densities, Compton profiles, X-ray absorption spectra (XAS), and X-ray Raman scattering spectra. Erkale has evolved to include advanced capabilities in basis set development and self-interaction corrected DFT.

Scientific domain: Molecules, X-ray spectroscopy, core-level physics, basis set development
Target user community: Researchers studying X-ray properties, spectroscopy, and those needing SIC-DFT or basis set optimization tools

Theoretical Methods

• Hartree-Fock (RHF, UHF, ROHF)
• Density Functional Theory (DFT)
• Gaussian Type Orbitals (GTOs) of arbitrary angular momentum
• Exchange-correlation via LibXC (600+ functionals)
• Self-Interaction Correction (SIC-DFT)
• Orbital localization methods (Foster-Boys, Pipek-Mezey, etc.)
• Core-level spectroscopy methods
• Basis set optimization algorithms

Capabilities (CRITICAL)

• Ground-state electronic structure
• X-ray absorption spectroscopy (XAS) simulation
• X-ray Raman scattering spectra
• Compton profiles
• Electron momentum densities
• Core-level excitations (K-edge, L-edge)
• Self-interaction corrected DFT
• Basis set completeness optimization
• Multiple orbital localization schemes
• Transition potential method
• Full core-hole approximation

Sources: GitHub repository, University of Helsinki, published papers

Key Strengths

X-ray Spectroscopy Focus:

• Native XAS simulation capabilities
• X-ray Raman scattering
• Compton profile calculations
• Core-level physics expertise
• Direct comparison with synchrotron experiments

Self-Interaction Correction:

• Perdew-Zunger SIC implementation
• Improved orbital energies
• Better description of localized states
• Corrected band gaps

Basis Set Development:

• Automatic basis set optimization
• Completeness-optimized basis sets
• Angular momentum extensions
• Contraction optimization

Modern Implementation:

• Object-oriented C++ design
• LibXC integration (600+ functionals)
• ADIIS/Broyden convergence accelerators
• Easy to understand and extend

Inputs & Outputs

• Input formats:

  • Native Erkale input files
  • XYZ coordinates
  • Basis set specifications (Gaussian format)

• Output data types:

  • Total energies
  • Orbital energies and coefficients
  • XAS spectra
  • Compton profiles
  • Electron momentum densities
  • Localized orbitals

Interfaces & Ecosystem

• LibXC integration:

  • Access to 600+ density functionals
  • LDA, GGA, meta-GGA, hybrid functionals
  • Range-separated hybrids

• Basis set libraries:

  • Standard Gaussian basis formats
  • Basis Set Exchange compatibility
  • Custom basis optimization

• Visualization:

  • Molden format output
  • Cube file generation
  • Standard plotting tools

Advanced Features

Core-Level Spectroscopy:

• Full core-hole approximation
• Transition potential method
• Core-valence separation
• Element-specific probing
• Comparison with experimental spectra

Orbital Localization:

• Foster-Boys localization
• Pipek-Mezey localization
• Edmiston-Ruedenberg
• Fourth-moment methods
• Intrinsic atomic orbitals

Basis Set Optimization:

• Completeness profiles
• Exponent optimization
• Polarization function addition
• Contraction schemes
• Element-specific tuning

SIC-DFT:

• Perdew-Zunger formulation
• Improved ionization potentials
• Better charge localization
• Reduced self-interaction error

Performance Characteristics

• Speed: Efficient for medium-sized systems
• Accuracy: High accuracy for spectroscopy
• System size: Molecules up to ~100 atoms
• Memory: Standard Gaussian code requirements
• Parallelization: OpenMP threading

Computational Cost

• DFT/HF: Standard Gaussian scaling
• XAS: Additional cost for core-hole calculations
• SIC: 2-3x overhead per iteration
• Typical: Desktop calculations for most molecules
• Large basis: Feasible with thousands of functions

Limitations & Known Constraints

• Periodicity: Molecular only (no periodic systems)
• System size: Best for small to medium molecules
• Forces: Limited geometry optimization
• User base: Specialized (X-ray spectroscopy)
• Documentation: Academic-level
• Dynamics: No molecular dynamics

Comparison with Other Codes

• vs Gaussian/ORCA: Erkale specialized for X-ray, general codes broader
• vs FLOSIC: Both have SIC-DFT, different implementations
• vs StoBe: Both X-ray focused, different methodologies
• Unique strength: X-ray spectroscopy, SIC-DFT, basis set development, open-source

Application Areas

X-ray Spectroscopy:

• K-edge XANES simulation
• L-edge spectra
• X-ray Raman scattering
• Comparison with synchrotron data
• Element-specific probing

Core-Level Physics:

• Core ionization potentials
• Chemical shifts
• Core-hole effects
• Auger processes

Electronic Structure:

• Ground-state calculations
• Orbital localization analysis
• Electron density analysis
• Bonding characterization

Basis Set Research:

• Completeness optimization
• New basis set development
• Polarization function design
• Contraction schemes

Best Practices

XAS Calculations:

• Use appropriate core-hole approximation
• Converge basis set for core region
• Compare with experimental calibration
• Account for relativistic effects for heavy elements

Basis Set Selection:

• Start with standard basis (cc-pVTZ)
• Add diffuse functions for Rydberg states
• Test core-region completeness
• Document basis choice

SIC Calculations:

• Start from converged standard DFT
• Monitor SIC energy convergence
• Check orbital localization
• Compare with experimental IPs

SCF Convergence:

• Use ADIIS for difficult cases
• Monitor energy convergence
• Level shifting if needed

Community and Support

• Open source GPL v2
• GitHub repository
• Academic publications
• Author-maintained (S. Lehtola)
• Active development

Verification & Sources

Primary sources:

1. GitHub: https://github.com/susilehtola/erkale
2. S. Lehtola et al., J. Comput. Chem. 33, 1572 (2012)
3. S. Lehtola, J. Chem. Theory Comput. publications

Secondary sources:

1. X-ray spectroscopy literature
2. Basis set optimization papers
3. SIC-DFT methodology papers

Confidence: VERIFIED - Active GitHub, published methodology

Verification status: ✅ VERIFIED

• Source code: OPEN (GitHub, GPL v2)
• Academic use: Published applications
• Documentation: Wiki and papers
• Active development: Recent commits
• Specialty: X-ray spectroscopy, SIC-DFT, basis set development