KRONOS User Guide

KRONOS (Kohn-Residual Optimized Numerics Over Silicon) is a research-grade plane-wave DFT engine for computing ground-state total energy, electronic density, Kohn-Sham eigenvalues, and ionic forces for periodic crystalline systems.

1. Quick Start

Dependencies

Required: C++20 compiler (GCC 11+, Clang 14+), CMake 3.20+, FFTW3, BLAS, LAPACK, yaml-cpp. Optional: libxc 6.0+ (built-in LDA fallback if absent), HDF5, MPI.

# Ubuntu/Debian
sudo apt install build-essential cmake libfftw3-dev libblas-dev liblapack-dev libyaml-cpp-dev

# macOS
brew install cmake fftw yaml-cpp

Build and Run

cmake -B build -S .
cmake --build build -j$(nproc)
cd build && ctest --output-on-failure   # run tests

# First calculation
./build/src/kronos examples/si_bulk.yaml > si_result.json

GPU builds use -DKRONOS_GPU_BACKEND=cuda, -DKRONOS_GPU_BACKEND=hip, or -DKRONOS_GPU_BACKEND=metal (Apple Silicon, fp32 research tier -- see Section 2 note).

2. YAML Input File Reference

KRONOS enforces strict schema validation -- unknown keys cause a hard error. Five top-level sections are recognized: system, calculation, convergence, pseudopotentials, and hardware.

Complete Example

system:
  lattice:                        # 3x3 matrix, rows are lattice vectors (Angstrom)
    - [0.0, 2.7155, 2.7155]
    - [2.7155, 0.0, 2.7155]
    - [2.7155, 2.7155, 0.0]
  atoms:
    - {symbol: Si, position: [0.00, 0.00, 0.00]}   # fractional coordinates
    - {symbol: Si, position: [0.25, 0.25, 0.25]}

calculation:
  type: scf                       # scf | relax | bands | dos
  ecutwfc: 30.0                   # plane-wave cutoff (Ry), range 10-500
  ecutrho: 120.0                  # density cutoff (Ry), >= 4*ecutwfc; omit for auto
  kpoints: [4, 4, 4, 0, 0, 0]    # [nk1, nk2, nk3, shift1, shift2, shift3]
  xc: LDA_PZ                     # LDA_PZ | LDA_PW | PBE | PBEsol
  smearing: gaussian              # none | gaussian | marzari-vanderbilt | fermi-dirac
  degauss: 0.01                   # smearing width (Ry)
  spin: false                     # enable spin polarization

pseudopotentials:
  Si: pseudopotentials/Si.pz-vbc.UPF

convergence:
  energy: 1e-6                    # SCF energy threshold (Ry)
  density: 1e-6                   # SCF density threshold
  max_scf_steps: 100              # max iterations (hard limit: 200)
  force: 1e-3                     # force threshold for relax (Ry/bohr)

hardware:
  use_gpu: false
  gpu_backend: none               # none | cuda | hip | metal
  apple_fast_mode: false          # Apple-only: opt-in fp32 fast path (NOT validation-grade)
  mpi_tasks: 1

Field Reference

Field	Type	Default	Allowed Values	Description
system.lattice	3x3 float	required	det > 0	Lattice vectors in Angstrom (rows)
system.atoms[].symbol	string	required	element symbol	Atomic species
system.atoms[].position	3-float	required	fractional coords	Crystal coordinates, ideally in [0,1)
calculation.type	string	scf	scf, relax, bands, dos	Calculation type
calculation.ecutwfc	float	required	10 -- 500	Wavefunction cutoff (Ry)
calculation.ecutrho	float	4*ecutwfc	>= 4*ecutwfc	Density cutoff (Ry)
calculation.kpoints	6-int	[1,1,1,0,0,0]	grid >= 1, shift 0/1	Monkhorst-Pack grid + shift
calculation.xc	string	LDA_PZ	LDA_PZ, LDA_PW, PBE, PBEsol	XC functional
calculation.smearing	string	none	none, gaussian, marzari-vanderbilt, fermi-dirac	Occupation smearing
calculation.degauss	float	0.01	> 0	Smearing width (Ry)
calculation.spin	bool	false	true/false	Spin polarization
convergence.energy	float	1e-8	> 0	Energy tolerance (Ry)
convergence.density	float	1e-9	> 0	Density tolerance
convergence.max_scf_steps	int	100	1 -- 200	Max SCF iterations
convergence.force	float	1e-3	> 0	Force tolerance (Ry/bohr)
pseudopotentials.<El>	string	required	file path	Path to UPF v2 file
hardware.use_gpu	bool	false	true/false	Enable GPU
hardware.gpu_backend	string	none	none, cuda, hip, metal	GPU backend
hardware.apple_fast_mode	bool	false	true/false	Apple Metal only: opt-in fp32 fast path. NOT validation-grade; see note below.
hardware.mpi_tasks	int	1	>= 1	MPI task count

Every atomic species in system.atoms must have a matching pseudopotentials entry. Pseudopotential paths resolve relative to the current working directory.

Note on apple_fast_mode: Setting hardware.apple_fast_mode: true (or passing --apple-fast-mode on the CLI) enables the Apple Silicon Metal GPU path. Because Apple's Metal Shading Language has no double type, all GPU computations run in fp32. This is intentionally opt-in and NOT validation-grade: the validation test suite refuses to run in this mode. Use it for local development and iteration speed only; use CUDA or HIP for science-grade results. GPU builds: -DKRONOS_GPU_BACKEND=metal requires Xcode.app (macOS 13+) with the Metal toolchain — CLT-only installs are insufficient.

3. Example Calculations

Si Bulk SCF (Semiconductor)

system:
  lattice:
    - [0.0, 2.7155, 2.7155]
    - [2.7155, 0.0, 2.7155]
    - [2.7155, 2.7155, 0.0]
  atoms:
    - {symbol: Si, position: [0.0, 0.0, 0.0]}
    - {symbol: Si, position: [0.25, 0.25, 0.25]}
calculation:
  type: scf
  ecutwfc: 30.0
  xc: LDA_PZ
  kpoints: [4, 4, 4, 0, 0, 0]
pseudopotentials:
  Si: pseudopotentials/Si.pz-vbc.UPF
convergence:
  energy: 1e-6
  max_scf_steps: 100

FCC primitive vectors a/2*(0,1,1), a/2*(1,0,1), a/2*(1,1,0) with a = 5.431 A. Two basis atoms at (0,0,0) and (1/4,1/4,1/4). No smearing needed for this semiconductor.

QE Validation (Si diamond, celldm(1)=10.20)

system:
  lattice:
    - [0.0, 2.69880378, 2.69880378]
    - [2.69880378, 0.0, 2.69880378]
    - [2.69880378, 2.69880378, 0.0]
  atoms:
    - {symbol: Si, position: [0.0, 0.0, 0.0]}
    - {symbol: Si, position: [0.25, 0.25, 0.25]}
calculation:
  type: scf
  ecutwfc: 18.0
  xc: LDA_PZ
  kpoints: [4, 4, 4, 1, 1, 1]
  smearing: none
pseudopotentials:
  Si: pseudopotentials/Si.pz-vbc.UPF
convergence:
  energy: 1e-8
  max_scf_steps: 100

Reproduces QE example01: shifted 4x4x4 MP grid, ecutwfc=18 Ry. Reference total energy: -15.8445 Ry. KRONOS achieves agreement to ~0.02 Ry (gap due to symmetry reduction differences).

Metal: Cu FCC with Smearing

system:
  lattice:
    - [0.0, 1.805, 1.805]
    - [1.805, 0.0, 1.805]
    - [1.805, 1.805, 0.0]
  atoms:
    - {symbol: Cu, position: [0.0, 0.0, 0.0]}
calculation:
  type: scf
  ecutwfc: 50.0
  xc: PBE
  kpoints: [8, 8, 8, 1, 1, 1]
  smearing: marzari-vanderbilt
  degauss: 0.02
pseudopotentials:
  Cu: pseudopotentials/Cu.pbe-dn-kjpaw_psl.1.0.0.UPF

Metals require smearing and denser k-grids. Marzari-Vanderbilt ("cold") smearing converges faster than Gaussian for metallic systems.

Geometry Relaxation

Set type: relax and tighten the force threshold:

calculation:
  type: relax
  ecutwfc: 30.0
  xc: PBE
  kpoints: [4, 4, 4, 0, 0, 0]
convergence:
  energy: 1e-8
  force: 1e-4
  max_scf_steps: 100

The BFGS optimizer iterates SCF cycles until all forces fall below the threshold.

4. Convergence Strategy

Choosing ecutwfc

Start with the pseudopotential's recommended cutoff and increase in 5-10 Ry steps. Stop when total energy changes by less than 1 meV/atom. Typical values: sp-bonded (Si, C): 20-40 Ry; d-electron metals (Fe, Cu): 40-60 Ry; first-row elements (O, N, F): 50-80 Ry.

Choosing the k-point Grid

Start at 4x4x4, double each dimension until energy converges to 1 meV/atom. Metals need 8x8x8 or finer. Shifted grids (shift=[1,1,1]) converge faster for cubic systems by avoiding high-symmetry points.

Smearing for Metals

System type	Smearing	degauss
Insulator/semiconductor	none	--
Simple metal	marzari-vanderbilt	0.01-0.02 Ry
Magnetic metal	fermi-dirac	0.01 Ry

Verify insensitivity to degauss by varying it by a factor of 2. A large smearing_energy in the output indicates degauss is too high.

Convergence Checklist

1. Fix k-grid, converge ecutwfc (< 1 meV/atom change per step).
2. Fix ecutwfc, converge k-grid (< 1 meV/atom change per step).
3. For metals, verify results are insensitive to degauss.
4. For relaxation, use convergence.force <= 1e-4 Ry/bohr.
5. Compare energy components individually to catch cancellation of errors.

5. Pseudopotential Requirements

Supported Format

KRONOS requires UPF v2 (XML-based) norm-conserving pseudopotentials. The parser reads PP_HEADER, PP_R, PP_RAB, PP_LOCAL, PP_BETA, PP_DIJ, PP_RHOATOM, and PP_CHI sections. Fortran-style D exponents are handled automatically. Norm-conservation is validated on load. Ultrasoft and PAW are not yet supported (planned for v0.8).

Where to Download

• PseudoDojo (http://www.pseudo-dojo.org/) -- NC pseudopotentials with stringent validation. Use the "standard" accuracy UPF set.
• SSSP Library (https://www.materialscloud.org/discover/sssp) -- curated sets with recommended cutoffs per element.
• Quantum ESPRESSO -- ships validated pseudopotentials in pseudo/. The Si.pz-vbc.UPF used in examples comes from here.

Paths in pseudopotentials resolve relative to the working directory. Run KRONOS from the project root or use absolute paths.

6. Output Format

JSON Summary

Written to stdout. All energies in Rydberg (unless field name contains _ev). Forces in Ry/bohr. Eigenvalues in Ry per k-point.

{
  "calculation_type": "scf",
  "converged": true,
  "scf_steps": 6,
  "total_energy_ry": -15.84388657,
  "total_energy_ev": -215.5670586,
  "fermi_energy_ev": 6.683025046,
  "energy_components": {
    "kinetic_energy": 6.217669585,
    "hartree_energy": 1.079781174,
    "xc_energy": -4.817300104,
    "local_pp_energy": -4.994074776,
    "nonlocal_pp_energy": 3.569797306,
    "ewald_energy": -16.89975976,
    "smearing_energy": 0
  },
  "crystal": { "num_atoms": 2, "volume_bohr3": 265.30 },
  "forces": [[5.78e-19, 4.52e-19, 5.74e-19], [-5.78e-19, -3.79e-19, -5.06e-19]],
  "eigenvalues": [{"kpoint_index": 0, "values_ry": [-0.4117, 0.3419, ...]}],
  "timing": {"eigensolver": 69.7, "hamiltonian_apply": 30.0, "scf_step": 73.7}
}

When SCF does not converge, output is still written with "converged": false and partial results. The timing section reports wall-clock seconds for the eigensolver, Hamiltonian application (FFT + nonlocal), Ewald, forces, and total SCF time. HDF5 output (density, wavefunctions, restart data) is available when compiled with HDF5 support.

7. Troubleshooting

SCF Not Converging

• Increase ecutwfc for a better variational basis.
• Add a k-point shift or use a denser grid.
• For metals, enable smearing with appropriate degauss.
• KRONOS aborts if energy oscillates by > 1 Ry between steps -- check PP and lattice.
• Pulay/DIIS mixing (8-step history) is automatic; persistent oscillations signal input errors.

Negative Electron Density

Values below zero are clamped with a warning. If magnitude exceeds 1e-6, KRONOS aborts. Fix: increase ecutwfc or check PP compatibility.

Davidson Eigensolver Failure

If the Davidson residual exceeds 1e3, KRONOS auto-falls back to LOBPCG for that k-point. Subspace size is 3 * N_bands. Persistent failures indicate a poorly conditioned Hamiltonian.

UPF Parse Errors

Ensure UPF v2 format, norm-conserving type, and that the file is not truncated. Re-download from PseudoDojo or QE if parsing fails.

Common Error Messages

Error	Cause	Fix
ecutrho must be >= 4*ecutwfc	Explicit ecutrho too small	Remove ecutrho to auto-set, or increase it
Energy oscillation > 1 Ry	SCF diverging	Check PP and lattice vectors
Unknown key 'X'	Typo in YAML	Check field names in reference table
Missing entry for element 'X'	No PP for a species	Add element to pseudopotentials
Negative density > 1e-6	Numerical instability	Increase ecutwfc
ecutwfc: must be in range [10, 500]	Cutoff out of bounds	Use 10-500 Ry
system.lattice: determinant must be positive	Left-handed vectors	Reorder vectors so det > 0
Cannot open UPF file	Wrong path	Paths resolve from working directory
kpoints: must be a 6-element array	Format error	Use [nk1, nk2, nk3, sk1, sk2, sk3]