elphy, short for electron-phonon anharmonicity, is a C
program to calculate free energies and forces for tight-binding models
on supercells, complemented with linear electron-phonon coupling and a
harmonic potential. It is a faster rewrite of the Python module
elphmod.md and thus primarily a driver for the
path-integral molecular-dynamics code i-PI. It is written in ANSI C
(C89/C99).
The following command compiles the program using GCC without optimization:
makeDifferent compilers and optimization flags can be selected:
make CC=icx CFLAGS=-O2LAPACK and BLAS with the standard LP64 interface are required.
The program accepts one, two, or three arguments:
elphy <data file>
elphy <data file> <socket>
elphy <data file> <init file> <radius>With one argument, it alternately reads atomic positions from standard input and writes energies and forces to standard output, both using the XYZ format.
With two arguments, it exchanges these quantities with i-PI through
its socket interface. <socket> is a host name
optionally followed by a colon and a port number, e.g.,
localhost:31415. If the port number is omitted or zero, a
UNIX socket is used for communication, otherwise an internet socket. The
address must match the information in the i-PI input file
input.xml.
With three arguments, it creates an <init file>
with initial atomic positions in the XYZ format for i-PI, adding random
displacements smaller than <radius>, and prints the
corresponding energies and forces.
The <data file> is defined below:
<temperature kT>
<number of electrons per unit cell>
<number of orbitals per unit cell>
<number of spins per orbital>
<strain>
A₀₀ A₀₁ A₀₂
A₁₀ A₁₁ A₁₂
A₂₀ A₂₁ A₂₂
a₀₀ a₀₁ a₀₂
a₁₀ a₁₁ a₁₂
a₂₀ a₂₁ a₂₂
<number of atoms per unit cell>
X₀ r₀₀ r₀₁ r₀₂ F₀₀ F₀₁ F₀₂
X₁ r₁₀ r₁₁ r₁₂ F₁₀ F₁₁ F₁₂
X₂ r₂₀ r₂₁ r₂₂ F₂₀ F₂₁ F₂₂
⋮
<number of lattice vectors>
R₀₀ R₀₁ R₀₂
R₁₀ R₁₁ R₁₂
R₂₀ R₂₁ R₂₂
⋮
<number of hopping parameters>
i₀ α₀ β₀ <0 α₀|H|Rᵢ₀ β₀>
i₁ α₁ β₁ <0 α₁|H|Rᵢ₁ β₁>
i₂ α₂ β₂ <0 α₂|H|Rᵢ₂ β₂>
⋮
<number of interatomic force constants>
j₀ x₀ y₀ ∂²E/[∂u(0, x₀) ∂u(Rⱼ₀, y₀)]
j₁ x₁ y₁ ∂²E/[∂u(0, x₁) ∂u(Rⱼ₁, y₁)]
j₂ x₂ y₂ ∂²E/[∂u(0, x₂) ∂u(Rⱼ₂, y₂)]
⋮
<number of electron-phonon matrix elements>
k₀ z₀ l₀ γ₀ δ₀ <0 γ₀|∂H/∂u(Rₖ₀, z₀)|Rₗ₀ δ₀>
k₁ z₁ l₁ γ₁ δ₁ <0 γ₁|∂H/∂u(Rₖ₁, z₁)|Rₗ₁ δ₁>
k₂ z₂ l₂ γ₂ δ₂ <0 γ₂|∂H/∂u(Rₖ₂, z₂)|Rₗ₂ δ₂>
⋮The indices i, j, k, l run over lattice vectors,
α, β, γ, δ over orbitals, and x, y, z over the
three Cartesian displacement directions for all atoms. All indices are
zero-based. All matrix elements <…> are single real
numbers. The primitive, position, and force vectors a, r, F
are given in Cartesian, the supercell and lattice vectors
A, R in integer crystal coordinates.
No unit conversions are performed, so any consistent energy and
length units can be used. However, i-PI expects energies and forces in
Hartree atomic units. The atom labels X are copied to the
<init file> and define the default masses.
Note that the interatomic force constants are assumed to be partially screened: They shall exclude the harmonic term of the electronic potential-energy surface. Any forces that the model may generate at zero displacements can be compensated by adding a force correction specified next to the atomic positions.
Lattice vectors and atomic positions are multiplied by 1 +
<strain> and the zero-displacement hopping parameters
and lattice energy adjusted accordingly.
make input.dat model=TaS2 (or graphene)
creates an example input file.make test verifies that the computed free energy and
forces are correct.make ipi lets elphy and i-PI perform a
structural relaxation together. The files generated by i-PI can be
cleaned up with make clean_ipi.make ipi_elphmod does the same job using
elphmod instead of elphy.make show displays an animation of the relaxation
process.The Python packages elphmod, ipi, and
matplotlib are required.
The method is described in the following paper: