# Quartic anharmonicity of rattlers in Ba₈Ga₁₆Ge₃₀ — self-consistent phonon and thermal-conductivity data

Input and output data for:

> T. Tadano and S. Tsuneyuki,
> *"Quartic Anharmonicity of Rattlers and Its Effect on Lattice Thermal Conductivity of Clathrates
> from First Principles"*, **Phys. Rev. Lett. 120, 105901 (2018)** —
> [doi:10.1103/PhysRevLett.120.105901](https://doi.org/10.1103/PhysRevLett.120.105901)
> — preprint [arXiv:1710.00311](https://arxiv.org/abs/1710.00311)

The dataset covers the 54-atom type-I clathrate Ba₈Ga₁₆Ge₃₀ (*Pm-3n*) at **five lattice constants**
(−2 %, opt., +2 %, +4 %, +6 %). Anharmonic force constants up to **sixth order** were obtained by
compressive sensing (LASSO); vibrational frequencies were renormalised by **self-consistent phonon
(SCPH) theory**; lattice thermal conductivity was then computed from the Peierls–Boltzmann equation
within the relaxation-time approximation.

Software: **VASP** (forces), **ALAMODE** (`alm` / `anphon`, development build `ALAMODE_priv`).

**Companion dataset.** The harmonic force constants used here come from the earlier study
T. Tadano, Y. Gohda and S. Tsuneyuki, *Phys. Rev. Lett.* **114**, 095501 (2015); see §2.6.

---

## 1. Which files reproduce the published numbers

| Published quantity | Paper | This dataset | File |
|---|---|---|---|
| κ_L at 300 K, SCP+BTE, opt. lattice constant | 0.97 W/mK | **0.967085** | `06_bte/results/kl_scph999_cell0_boundary2500_iso.dat` |
| κ_L at 300 K, conventional BTE | 0.58 W/mK | **0.579661** | `06_bte/results/kl_bte_cell0_boundary2500_iso.dat` |
| Anharmonic IFCs "up to the sixth order" | — | FC2–FC6 present, FC7 absent | `04_force_constants/lasso_published/*.xml.xz` |
| Five lattice constants −2 / opt / +2 / +4 / +6 % | — | 10.737 / 10.954 / 11.173 / 11.392 / 11.611 Å | `01_structure/` |
| SCPH solved at Γ only | — | `KMESH_SCPH = 1 1 1` | `05_scph/*/input_scph2.txt` |
| κ_L on a 9×9×9 q-grid | — | `*_999.kl`, `&kpoint 2 / 9 9 9` | `06_bte/*/input_BTE*.txt` |
| 140 training configurations | — | 140 × 54 rows | `03_training_data/disp_random_0.dat` |
| AIMD sampling temperature | 300 K *(SI typo)* | **800 K** — see §2.7 | `03_training_data/` |
| ENCUT 320 eV, 4×4×4 MP, PAW-PBE | — | ✓ | `02_dft_reference/` |

---

## 2. Read this before using the data

The working directory this came from contains three campaigns — a 2016 pilot, the 2017 production
run, and a Nov–Dec 2017 revision — plus 2018–2024 follow-on projects. Picking files by name or by
date alone gives the wrong answer in several distinct ways (§2.1–2.4). §2.5–2.7 record three further
things a user needs to know before comparing this data against the paper.

### 2.1 The published curves include boundary and isotope scattering

Two variants of every curve exist in `06_bte/results/`. Only the `_boundary2500_iso` files
(2500 nm boundary scattering + isotope scattering) reproduce the paper:

| At 300 K | plain | `_boundary2500_iso` | paper |
|---|---|---|---|
| SCP+BTE, cell0 | 1.024 | **0.967** | 0.97 |
| conventional BTE, cell0 | 0.613 | **0.580** | 0.58 |

Both are shipped. Use the `_boundary2500_iso` ones for anything compared against the paper.

### 2.2 The 100–1000 K conductivity files were re-run in 2019 — those are NOT the published ones

In the source `BTE/cellV/` directories, the SCPH temperatures 0, 100, 200 … 1000 K were **all
recomputed on 2019-02-25/28 and 2019-03-18** for a later study; only the 10–90 K files survive from
July 2017. The 2019 rerun gives κ(300 K) = 1.006 W/mK for cell0, which matches neither published
number.

**The July-2017 production values survive only in `06_bte/results/*.dat`**, which is therefore the
authoritative record of Fig. 2. This release ships those curves plus the surviving July-2017 `.kl`
files, and excludes every 2019 rerun and every `*.kl_coherent` file.

### 2.3 Two LASSO fits exist; only the sixth-order one is published

| | **Published** | Exploratory |
|---|---|---|
| File | `BGG_FPMD800K_random*_lasso1.xml` (one per volume) | `BGG_lasso1.xml` |
| Orders present | FC2–**FC6** — matches the paper | FC4–**FC10** (`NORDER = 9`) |
| Location here | `04_force_constants/lasso_published/` | not shipped (1.1 GB, superseded) |

The cross-validation study in `04_force_constants/lasso_crossval/` (`input_alm*.txt`, `cv1–5.log`,
`cvscore.dat`, minimum CV score at α = 5.71638×10⁻⁵) belongs to the **exploratory tenth-order fit**.
It documents how the regularisation parameter was chosen, but it is not the fit that produced the
published force constants — and its α over-shrinks the sixth-order model. The sixth-order model has
been recovered by refitting and is documented in
`04_force_constants/lasso_published/input_alm_6th_order.reconstructed.txt`; see §6.

### 2.4 The +4 % volume uses a different filename

`cell+4__BGG_FPMD800K_random_lasso1.xml.xz` — **no `2`** — while the other four volumes are
`…random2…`. This matches `FCSXML` in `06_bte/cell+4/input_BTE*.txt`. The names are preserved
exactly as used; do not "correct" them.

### 2.5 The source tree used symlinks; this release does not

In the source, `BTE/cellV/*.xml` were 94 relative symlinks into `scph/cellV/newfc2/` and
`lasso/cellV/`. Everything here was copied with `cp -pL`, so every file is real data.
`MANIFEST.tsv` records the resolved source path for each.

### 2.6 The harmonic force constants are shared with the 2015 dataset

`04_force_constants/harmonic/BGG_cell0_harm.xml` (md5 `e7449a66ed686d5707d749472e8f8959`) is a
2016-05-16 refit of the harmonic IFCs of Ba₈Ga₁₆Ge₃₀, produced *for this study*. It is byte-identical
to a file present in the PRL 114, 095501 (2015) working directory — where it is deliberately
**excluded**, because that paper used the earlier 2014 fit (`BGG_cell0_harm0.02.xml`,
md5 `10b0877d7db3dc71f7236e970bc3e552`). The two deposits are consistent: same file, different
papers, and each ships the one its own paper used. `INCAR` and `KPOINTS` are likewise byte-identical
between the two studies (INCAR md5 `2fca39a52e1951797cf31788c5bacb55`).

### 2.7 The AIMD temperature was 800 K — the Supplemental Material says 300 K in error

The Supplemental Material of the paper states that the training snapshots were sampled from ab
initio molecular dynamics at **300 K**. That is a typo. The actual sampling temperature was
**800 K**, confirmed by the author. The data are consistent with 800 K in two independent ways:

- every file produced by that fit is named `…FPMD800K…`;
- the surviving training set has per-species mean-square displacements of
  ⟨u²⟩ = 0.277 / 0.118 / 0.104 Å² for Ba / Ga / Ge. Matched against the harmonic ⟨u²⟩(T) curve in
  `05_scph/cell0/dos30.msd` this gives T ≈ 760–860 K — near 800 K and nowhere near 300 K.
  (That estimate extrapolates a harmonic curve tabulated only to 141 K, so it is indicative
  rather than exact, but the discrepancy with 300 K is far larger than the uncertainty.)

Everything else in the SI description holds: 140 snapshots from the +4 % cell, an extra 0.1 Å random
displacement on every atom, and 140 × 5 = 700 DFT calculations in total. Use **800 K** when
describing or reproducing this dataset.

### Excluded as post-publication
`SQS/` (Sep 2018); `disp/cell0/to_Holger*` (Jul 2018 export); all `*.kl_coherent`; the Feb–Mar 2019
`.kl` reruns; `scph/*/newfc2` files dated 2020-06; `PM_*.bands`, `No-PM_*.bands`, `Boson_peak_*`,
`compute_diff.py` (2019–2024).

---

## 3. Directory layout

```
01_structure/          POSCAR / POSCAR.orig / CONTCAR for the five lattice constants
02_dft_reference/      INCAR, KPOINTS, POTCAR.spec, PES job script
03_training_data/      two 140-configuration displacement-force sets for the LASSO fit
                       (AIMD at 800 K on the +4 % cell + 0.1 A random displacements; see §2.7)
04_force_constants/
    harmonic/          BGG_cell0_harm.xml  - shared with the 2015 dataset (§2.6)
    lasso_published/   the five sixth-order IFC files, xz-compressed, + CHECKSUMS.txt, cluster
                       patterns, and the reconstructed ALM input recovered by refitting
    lasso_crossval/    tenth-order cross-validation study: input_alm*.txt, cv1-5.log, cvscore.dat
05_scph/cellV/         SCPH inputs and logs; newfc2/ holds the renormalised FC2 files
                       BGG_SCPHV_offdiag_{T}K.xml for T = 0...1000 K that feed the BTE
06_bte/cellV/          anphon inputs, run logs, surviving July-2017 *.kl and *.kl_spec
06_bte/conventional/   mode-resolved .result behind the conventional-BTE curve (cell0 only;
                       see its README.txt - three volumes removed for size, regenerable)
06_bte/results/        >> the published Fig. 2 curves <<
07_pes_T2g/cellV/      frozen-phonon PES scans along the T2g (and T1g) rattling coordinate
08_linewidth/cellV/    Nov-Dec 2017 revision: mode-resolved linewidths, SCPH bands vs temperature
90_raw_dft/            vasprun.xml and OUTCAR archives for the PES scans, per volume
MANIFEST.tsv           path, size, md5, original path, original mtime for every file
```

Total ≈ 914 MB. The five force-constant files are the bulk of the science content: 1.1 GB of XML
compressed to 65 MB.

### Using the force constants

The bulky files are xz-compressed (`xz -9e`) rather than gzip/bzip2, which roughly halves the
deposit: the five force-constant files go from 11.2 MB each to 5.7 MB, and the raw-DFT archives
from 25 MB to 7 MB in total. Every compressed file was verified to decompress to the md5 recorded
in `CHECKSUMS.txt` / `MANIFEST.tsv`. Nothing was removed to meet the size limit.


```bash
cd 04_force_constants/lasso_published
xz -dk cell0__BGG_FPMD800K_random2_lasso1.xml.xz
md5 -r cell0__BGG_FPMD800K_random2_lasso1.xml   # compare against CHECKSUMS.txt
```
ALAMODE reads the plain XML. The `cellV__` prefix is added here to keep the five volumes distinct in
one directory; strip it if you want the original filename.

---

## 4. Which files correspond to which figure

| Figure | Content | Files |
|---|---|---|
| **1** | Phonon dispersion along Γ–X, PES of the T2g rattling mode, displacement pattern | `07_pes_T2g/cellV/{disp,force,energy}_pes*.dat` (PES); `05_scph/cellV/*.bands` and `08_linewidth/cellV/BGG_band_*K.bands` (SCPH dispersion vs temperature) |
| **2** | κ_L versus temperature and volume, SCP+BTE vs conventional BTE, vs experiment | `06_bte/results/kl_scph999_cellV[_boundary2500_iso].dat` and `kl_bte_cellV[_boundary2500_iso].dat` — **use the `_boundary2500_iso` variants** (§2.1) |
| **3** | Spectral thermal conductivity κ_L(ω) at several temperatures and lattice constants | `06_bte/cellV/*_999.kl_spec` (produced with `KAPPA_SPEC = 1`) |

Note on Fig. 2: the conventional-BTE curve exists for four volumes only — `cell+6` was added later
(Aug 2017) and has an SCP+BTE curve but no conventional counterpart.

---

## 5. Reproducing the results

The chain, per volume V:

```bash
# 1. anharmonic IFCs (already provided; the LASSO fit itself is the step documented in §6)
xz -dk 04_force_constants/lasso_published/cellV__BGG_FPMD800K_random*_lasso1.xml.xz

# 2. SCPH renormalisation of the harmonic force constants, Gamma point, T = 0...1000 K
cd 05_scph/cellV
anphon input_scph2.txt > scph.log        # SELF_OFFDIAG = 1  -> BGG_SCPHV_offdiag_{T}K.xml
#    (input_scph1.txt is the SELF_OFFDIAG = 0 comparison)

# 3. thermal conductivity on a 9x9x9 q-grid, using the SCPH-renormalised FC2 at temperature T
cd ../../06_bte/cellV
anphon input_BTE300.txt > BTE_300K_999.log    # FCSXML = LASSO IFCs, FC2XML = SCPH FC2 at 300 K
#    -> BGG_SCPHV_offdiag_300K_999.kl

# 4. published curve: take the diagonal (kappa at the same T the SCPH was solved at),
#    with boundary (2500 nm) and isotope scattering applied  -> 06_bte/results/*.dat
```

`ISOTOPE = 2` in the anphon inputs; the boundary correction was applied with ALAMODE's
`analyze_phonons.py` result analyzer (v1.0.4, recorded in the header of each `kl_bte_*.dat`).

**Excluded because it is regenerable** — re-run the step shown, do not expect these in the deposit:
`*.scph_dymat`, `*.scph_fc2_correction`, `*.scph_bands` (4.8 GB, step 2 restart/output files);
the SCPH `*.result` files (≈2.3 GB, step 3). Of the *conventional* `.result` files only cell0's
is shipped, in `06_bte/conventional/` — it is the provenance of the headline published value; the
other three volumes' were removed to meet the repository size limit and are regenerable by the
step-3 command (see `06_bte/conventional/README.txt`); `*.V3.*` three-phonon matrix elements (3.3 GB); `*.evec` (782 MB); `*.apr`.

---

## 6. Known gaps

- **The LASSO run that produced the published force constants was not documented — the model has
  been recovered by refitting.** No ALM input or log in the source tree carries
  `PREFIX = BGG_FPMD800K_random2_lasso1`. The model was reconstructed and validated against the
  published XML; see `04_force_constants/lasso_published/input_alm_6th_order.reconstructed.txt`
  for the settings and the evidence. In brief: `NORDER = 5`, `NBODY = 2 3 3 2 2`, cutoffs equal to
  columns 1–4 of the surviving tenth-order input, harmonic part fixed to `BGG_cell0_harm.xml`.
  A refit reproduces the published cubic force constants with r = 0.9991 and a median ratio of
  0.998 on significant terms, and reproduces the FC2 and FC3 term counts exactly.
  **The regularisation strength is the one thing not recovered**: nothing records it, and the
  published file corresponds to the weakly regularised limit (α ≲ 3×10⁻⁸), *not* the
  α = 5.71638×10⁻⁵ cross-validation optimum in `lasso_crossval/`, which belongs to the tenth-order
  model. Bit-exact reproduction is impossible regardless: no surviving ALM build supports the 2017
  `MODE = lasso` syntax (oldest available is 1.3.0; the fit used 1.0.0RC).
- **Two of the five training sets survive, not one.** `03_training_data/` holds two independent
  140-configuration displacement-force sets — `disp_random_0.dat` and `disp_random.dat` are
  different data despite their identical size (no configuration is shared between them). Both
  reproduce the published cell0 cubic force constants at r = 0.9991; `disp_random_0` matches
  slightly better (median ratio 0.998 vs 0.982), so it is most likely the cell0 set and
  `disp_random` the one behind the differently-named `…random_lasso1` fit used for +4 %.
  The sets for the remaining volumes are not preserved.
- **`06_bte/cellV/` is incomplete by design**: the July-2017 `.kl` files survive only for SCPH
  temperatures 10–90 K (§2.2). The full published temperature range lives in `06_bte/results/`.
- `cell0_OUTCAR.tar.xz` and the other OUTCAR archives contain one stray entry named plainly
  `outcars/OUTCAR`, a leftover from the working directory. The per-configuration files are named
  `OUTCAR_T2g.<n>` / `OUTCAR.<n>` and correspond one-to-one with the `vasprun*.xml` files.
- **Three of the four conventional-BTE `.result` files were removed to meet the repository size
  limit** (22.9 MB each). Only cell0's is kept, since that is the volume the paper quotes. The
  published curves derived from all four are shipped in full in `06_bte/results/`, and
  `06_bte/conventional/README.txt` gives the exact command to regenerate any of them. This is the
  only place where data was dropped for size rather than for provenance reasons — everything else
  was kept and simply compressed harder (see §3).
- `POTCAR` files are **not** included; see `02_dft_reference/POTCAR.spec`.

---

## 7. Licence and citation

Data: **CC BY 4.0** (see `LICENSE`). If you use this dataset, please cite both the paper and this
deposit — see `CITATION.cff`.

ALAMODE is developed by T. Tadano and is available at <https://github.com/ttadano/alamode>.
