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Merge pull request #5 from utf/joss-review
Fix typos
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README.md

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0. Prepare a sequence of atomic structure models with displacements that interpolate between two defect configurations (e.g. a site vacancy in charge states q=0 and q=+1).
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Run single-point energy calculations on these structures, and extract the total energies. Scripts for preprocessing may be found in `script`.
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1. Find a best fit for the energy calculations of the deferomed structures (`potential`) to generate potential energy surfaces (PES).
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1. Find a best fit for the energy calculations of the deformed structures (`potential`) to generate potential energy surfaces (PES).
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Solve the 1D Schrödinger equation for each PES to obtain their phonon (nuclear) wavefunctions.
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3. Constructe configuration coordinate (`conf_coord`) to calculate the wavefunction overlap between each PES,
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3. Construct configuration coordinate (`conf_coord`) to calculate the wavefunction overlap between each PES,
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which forms part of the temperature-dependent capture coefficient.
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![schematics](https://github.com/WMD-group/CarrierCapture.jl/blob/master/schematics/carrier_capture_sketch.png?raw=true "schematics")
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> The electronic matrix element frequently causes feelings of discomfort (Stoneham, 1981)
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The capture of electrons or holes by point defects in a crystalline materials requires the consideration of a number of factors including the coupling between electronic and vibrational degrees of freeedom. Many theories and approximations have been developed to describe the reaction kinetics.
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The capture of electrons or holes by point defects in a crystalline materials requires the consideration of a number of factors including the coupling between electronic and vibrational degrees of freedom. Many theories and approximations have been developed to describe the reaction kinetics.
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The capture coefficient between an initial and final state for this computational set up is given by (eq. 22 in [Alkauskas and coworkers](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.075202)):
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docs/src/index.md

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0. Prepare a sequence of atomic structure models with displacements that interpolate between two defect configurations (e.g. a site vacancy in charge states q=0 and q=+1).
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Run single-point energy calculations on these structures, and extract the total energies. Scripts for preprocessing may be found in `script`.
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1. Find a best fit for the energy calculations of the deferomed structures (`potential`) to generate potential energy surfaces (PES).
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1. Find a best fit for the energy calculations of the deformed structures (`potential`) to generate potential energy surfaces (PES).
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Solve the 1D Schrödinger equation for each PES to obtain their phonon (nuclear) wavefunctions.
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3. Constructe configuration coordinate (`conf_coord`) to calculate the wavefunction overlap between each PES,
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3. Construct configuration coordinate (`conf_coord`) to calculate the wavefunction overlap between each PES,
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which forms part of the temperature-dependent capture coefficient.
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![schematics](https://github.com/WMD-group/CarrierCapture.jl/blob/master/schematics/carrier_capture_sketch.png?raw=true "schematics")

docs/src/usage.md

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## 1. Preparation
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Before `CarrierCapture`, you need to calculate potential energy surfaces of atomic vibrations (one-dimensional Configuration Coordinate diagram; `1D-CC`) and _e-ph_ coupling matrix element (`W_if`). Prepare a sequence of structures with displacements which interpolate between two defect states. Run single-point energy calculations on these structures, and extract the total energies. Scripts for preprocessing can be found in `/script` which require a python library [`pymatgen`](http://pymatgen.org).
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Before `CarrierCapture`, you need to calculate potential energy surfaces of atomic vibrations (one-dimensional Configuration Coordinate diagram; `1D-CC`) and _e-ph_ coupling matrix element (`W_if`). Prepare a sequence of structures with displacements which interpolate between two defect states. Run single-point energy calculations on these structures, and extract the total energies. Scripts for preprocessing can be found in `/script` which require the [`pymatgen`](http://pymatgen.org) python library.
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1. **Generate `1D-CC`**
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1. Calculate equilibirum geometries and total energies of defective supercells with charge states `q`(initial) and `q±1`(final) denoted `Conf.(q)` and `Conf.(q±1)`, respectively.
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1. Calculate equilibrium geometries and total energies of defective supercells with charge states `q`(initial) and `q±1`(final) denoted `Conf.(q)` and `Conf.(q±1)`, respectively.
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2. Generate interpolated and extrapolated structures between `Conf.(q)` (`POSCAR_i`) and `Conf.(q±1)` (`POSCAR_f`). You may use `gen_cc_struct.py`:
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disp_dir_f
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```
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3. Run total-energy calculations for each structures. Example of the directory tree (`template` contains all input files for DFT calculations. Make sure DFT-program write wavefunctions (e.g. `LWAVE=.TRUE.` in `VASP`) for [the next stage `W_if`](#wif)):
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3. Run total-energy calculations for each structure. Example of the directory tree (`template`) contains all input files for DFT calculations. Make sure DFT-program writes wavefunctions (e.g. `LWAVE=.TRUE.` in `VASP`) for [the next stage `W_if`](#wif)):
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```bash
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├── 00_q2q±1
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│   │   ├── ...
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```
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You can submit jobs for all calculations using a following script in a high-performace computer with a batch system.
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You can submit jobs for all calculations using a following script in a high-performance computer with a batch system.
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```bash
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#!/bin/bash -l
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2. **Calcuate _e-ph_ coupling matrix element `W_if`** <a name="wif"></a>
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You already have eigenvalues, wave functions and configurations. Read [Work by Alkauskas and coworkers](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.075202) carefully.
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You already have eigenvalues, wavefunctions and configurations. Read [Work by Alkauskas and coworkers](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.075202) carefully.
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1. Find initial and final eigenvalues (`ϵ_i` and `ϵ_f`).
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paper/paper.md

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# Author contributions
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[Sunghyun Kim](https://github.com/frssp) wrote the majority of the code base with contributions from [Samanth N. Hood](https://github.com/PaleBlueSam). [Lucy D. Whalley](https://github.com/lucydot) and [Puck van Gerwen](https://github.com/puckvg) performed detailed code testing and contributed to the example and test suite. All authors along with [Aron Walsh](https://github.com/aronwalsh) made decisions about code design and feature implementation. This manuscript was written with input from all co-authours.
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[Sunghyun Kim](https://github.com/frssp) wrote the majority of the code base with contributions from [Samanth N. Hood](https://github.com/PaleBlueSam). [Lucy D. Whalley](https://github.com/lucydot) and [Puck van Gerwen](https://github.com/puckvg) performed detailed code testing and contributed to the example and test suite. All authors along with [Aron Walsh](https://github.com/aronwalsh) made decisions about code design and feature implementation. This manuscript was written with input from all co-authors.
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# Acknowledgements
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src/Brooglie.jl

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Solve the potential `V`(x,y,z,...) in a grid xᵢ ∈ [`a`,`b`], discretized in `N`
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steps.
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The particle is asumed to have mass `m` (by default 1, a electron mass).
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The particle is assumed to have mass `m` (by default 1, a electron mass).
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The function will return the `nev` first energy levels (in Hartree[^1])
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and its normalized eigenfunctions.

src/CaptureRate.jl

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## Fields
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- `name` -- the name of a configuration coordinate.
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- `V1` and `V2` -- the initial and fianal `potential`s.
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- `V1` and `V2` -- the initial and final `potential`s.
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- `W` -- the e-ph coupling matrix element.
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- `g` -- the degeneracy.
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- `temperature` -- the temperature range where `capt_coeff` is calculated.
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"""
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calc_overlap!(cc::conf_coord; cut_off = 0.25, σ = 0.025)
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Calculate phonon overlap between phonon wave functions 'potenrial.χ'.
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Calculate phonon overlap between phonon wave functions 'potential.χ'.
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If energy difference is larger then the cutoff (eV) `abs(cc.V1.ϵ[i] - cc.V2.ϵ[j]) > cut_off`,
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the overlap will not be calculated.
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Delta functions are replaced by a Gaussians function with widths `σ`.
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Delta functions are replaced by Gaussian functions with widths `σ`.
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"""
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function calc_overlap!(cc::conf_coord; cut_off = 0.25, σ = 0.025)
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Q₀ = cc.V1.Q0
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"""
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calc_capt_coeff!(cc::conf_coord, V::Float64, temperature)
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Calculte the capture coefficient `cc.capt_coeff` as a function of `temperature` which is a `UnitRange`.
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Calculate the capture coefficient `cc.capt_coeff` as a function of `temperature` which is a `UnitRange`.
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`V` is a volume where the electron-phonon coupling matrix element `cc.W` is calculated.
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The lowest thermal occupation number of the eigenstate must be lower than `occ_cut_off = 1E-5`.
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# importing parameters
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"""
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Depreciated.
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Construct `conf_coord` from two potentials `pot_i` (initila) and 'pot_f' (final) and configure dictionalry `cfg`.
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Construct `conf_coord` from two potentials `pot_i` (initial) and 'pot_f' (final) and configure dictionary `cfg`.
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"""
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function cc_from_dict(pot_i, pot_f, cfg::Dict)::conf_coord
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cc = conf_coord(pot_i, pot_f)

src/Potential.jl

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- `QE_data` -- the (n X 2) DataFrame of data points (Q vs Energy).
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- `E0`, `Q0` -- the minimum point of the potential [`Q0`, `E0`].
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- `func_type` -- the type of fitting function ("bspline", "spline", "harmonic", "polyfunc", "morse_poly", "morse").
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- `params` -- the list of hyper paramters for the fitting function.
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- `params` -- the list of hyper parameters for the fitting function.
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- `Q`, `E` -- `Q` and `E`=`func(Q, p_opt; params)`.
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- `nev` -- the number of eigenvalues to be evaluated.
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- `ϵ` -- the list of eigenvalues
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Polynomial function;
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`y = E₀ + Σ coeffs[i].* (x .- Q₀) .^(i-1)`.
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- `poly_order`: the maximum order of polynomials.
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- `p0`: the initial paramters for the fitting function.
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- `p0`: the initial parameters for the fitting function.
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## Example
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- Spline fit
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Construct `potential` from `QE_data` and configure dictionalry `cfg`.
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Construct `potential` from `QE_data` and configure dictionary `cfg`.
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function get_bspline(Qs, Es)
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# Qs, Es have to be equally-spaced (Range)
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src/paramScan.jl

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a_i: first parameter of the Morse potential of the initial state
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a_f: first parameter of the Morse potential of the final state
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b_i: second parameter of the Morse potential of the initial state
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b_f: seond parameter of the Morse potential of the final state
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b_f: second parameter of the Morse potential of the final state
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Q0 : horizontal shift between the PES', in amu^0.5 Å^-1
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E0 : vertical shift between the PES', in eV
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