# First-principles lattice thermal conductivity of Ba₈Ga₁₆Ge₃₀ and the guest-free framework Ga₁₆Ge₃₀

Input and output data for:

> T. Tadano, Y. Gohda and S. Tsuneyuki,
> *"Impact of Rattlers on Thermal Conductivity of a Thermoelectric Clathrate: A First-Principles Study"*,
> **Phys. Rev. Lett. 114, 095501 (2015)** — [doi:10.1103/PhysRevLett.114.095501](https://doi.org/10.1103/PhysRevLett.114.095501)
> — preprint [arXiv:1412.5723](https://arxiv.org/abs/1412.5723)

The dataset covers the type-I clathrate Ba₈Ga₁₆Ge₃₀ (BGG, 54 atoms/cell, *Pm-3n*) and the
hypothetical guest-free framework □₈Ga₁₆Ge₃₀ (GG, 46 atoms/cell), which together isolate the
effect of the Ba rattlers on the lattice thermal conductivity κ_L. The empty type-I germanium
clathrate Ge46 (46 atoms/cell, a = 10.735 Å, separately relaxed) is also included: it is the third
curve in Fig. 2 of the paper.

> **How the guest-free system was obtained — read this first.**
> There are **no separate DFT calculations for GG**, and none are missing from this deposit.
> Ba acts as an electron donor that completes the sp³ framework, so DFT on the empty cage is not
> meaningful; as the paper puts it, *"one cannot perform first-principles calculations directly on
> the fictitious material GG"*. Instead, GG force constants were obtained from the **same
> Ba₈Ga₁₆Ge₃₀ supercell calculations** by restricting the fit to the configurations in which only
> host-framework atoms are displaced, and setting every force-constant term involving Ba to zero.
> The lattice constant is unchanged (a = 10.954 Å). BGG and GG therefore share identical
> framework–framework force constants by construction, which is what makes the comparison a clean
> measurement of the rattlers' effect.
>
> Consequently `90_raw_dft/` contains only 54-atom Ba₈Ga₁₆Ge₃₀ runs — that is correct and complete
> for both systems. §3.1 documents the derivation and how to re-check it.

Software: **VASP 5.3.3** (forces) and **ALAMODE 0.9.2** (force constants, phonons, BTE/RTA).

---

## 1. Which files reproduce the published numbers

The paper reports κ_L at 100 K. Every published value is reproduced by the files below:

| Published quantity | Paper | This dataset | File |
|---|---|---|---|
| κ_L (BGG, 6×6×6 q-grid, *a* = 10.954 Å) | 0.78 W/mK | **0.7761** | `05_bte_results/BGG_cell0/BGG_666_submit2.kl` |
| κ_L (BGG, experimental lattice constant) | 1.35 W/mK | **1.3502** | `05_bte_results/BGG_cell-2/BGG_666_submit2.kl` |
| κ_L (GG, 8×8×8 q-grid) | 18.94 W/mK | **18.9463** | `05_bte_results/GG_cell0/GG_888_submit2.kl` |
| κ_L (Ge46, 8×8×8 q-grid) — third curve of Fig. 2 | — | 57.5874 | `05_bte_results/Ge46/Ge46_888_submit2.kl` |
| Symmetrically inequivalent harmonic / cubic IFCs (BGG) | 320 / 384 | **320 / 384** | `04_force_constants/BGG_cell0/alm_anharm.log` |
| Plane-wave cutoff, k-mesh | 320 eV, 4×4×4 MP | ✓ | `02_dft_reference/INCAR`, `KPOINTS` (Ge46 used its own; see `INCAR.Ge46_*`) |
| Lattice constant | 10.95 Å | 20.70 Bohr = 10.954 Å | `01_structure/BGG_cell0_a10.954.POSCAR` |

The reduced-lattice-constant calculation (`BGG_cell-2`, 20.29 Bohr = 10.737 Å, −2 %) is what the
paper refers to as "the experimental lattice constant" (quoted there as 10.76 Å).

---

## 2. Read this before using the data

The working directories these files came from contained **two complete calculation campaigns**
plus later reruns. Selecting files by date alone yields the *wrong* dataset. Four specific hazards
were identified and resolved; only the published campaign is shipped here.

### 2.1 Two campaigns — only the second one is published

| | First submission (superseded) | **Published (this dataset)** |
|---|---|---|
| File prefix | `*_new`, plain `*_666` / `*_444` | **`*_submit2`** |
| Dates | Feb–Aug 2014 | **Dec 2014 – Jan 2015** |
| ALAMODE | 0.9.0 | **0.9.2** |
| IFCs read from | `.info` (Feb 2014 fit) | **`.xml` (Dec 4 2014 re-fit)** |
| Non-zero harmonic IFCs (BGG / GG) | 9210 / 6450 | **28674 / 22038** |
| BZ integration | `ISMEAR=0` (Lorentzian) | **`ISMEAR=-1` (tetrahedron)** |
| κ_L (BGG) at 100 K | 0.6776 | **0.7761** |

The harmonic force constants were re-fitted on 2014-12-04 without a distance cutoff, which is
why the published harmonic IFC set is roughly three times denser. The cubic IFC model is
unchanged between campaigns (77952 / 12396 non-zero terms).

The first-submission κ_L curves are kept in `07_convergence/` **for the record only** — they are
clearly named `*_firstsubmission.kl` and must not be used as the paper's results.

### 2.2 The BGG κ_L file was overwritten by a post-hoc isotope run

The paper considers three-phonon scattering only (`ISOTOPE = 0` in every published run log).
On 2014-12-10 the no-isotope result was moved aside to `BGG_666_submit2.kl_bak` at 21:25, and a
rerun **with** isotope scattering overwrote `BGG_666_submit2.kl` at 21:53.

In this release the naming is corrected:

- `05_bte_results/BGG_cell0/BGG_666_submit2.kl` — **published**, no isotope (was `.kl_bak`)
- `05_bte_results/BGG_cell0/BGG_666_submit2_with_isotope.kl` — the post-hoc variant, **not** in the paper

The difference is small (0.7761 → 0.7694 W/mK at 100 K) but the published curve is the former.

### 2.3 Three input files were overwritten in 2016 and have been reconstructed

Later, unrelated work overwrote some input files in place. Each was rebuilt from the verbatim
input echo in the corresponding Dec-2014 log, which is shipped alongside it. Reconstructed files
are named `*.reconstructed.txt` and carry a header explaining their origin:

| Reconstructed file | Rebuilt from | Overwritten by |
|---|---|---|
| `04_force_constants/BGG_cell{0,-2}/input_alm_{harmonic,cubic}.reconstructed.txt` | `alm_harm.log`, `alm_anharm.log` | 2016-05-16 re-fit |
| `05_bte_results/BGG_cell0/input_BTE.reconstructed.txt` | `anphon_run.log1`–`log6` | 2014-12-10 isotope rerun |
| `06_phonon_properties/BGG_cell0/input_linewidth.reconstructed.txt` | `BGG_W202020_submit2.log` | 2016-01-17 Grüneisen run |

The `&position` block in the reconstructed ALM inputs was verified byte-identical to the 2014
POSCAR actually used for the DFT runs, and to the structure echoed in the Dec-2014 ALM log.
The guest-free ALM input (`04_force_constants/GG_cell0/input_alm.txt`) survived untouched and is
shipped as-is.

**Where the 2016 re-fit went.** The 2016-05-16 harmonic re-fit excluded here
(`BGG_cell0_harm.xml`, md5 `e7449a66ed686d5707d749472e8f8959`) was not stray work: it was made for
the follow-up study T. Tadano and S. Tsuneyuki, *Phys. Rev. Lett.* **120**, 105901 (2018), which uses
it as the harmonic starting point for self-consistent phonon calculations, and it is shipped in that
paper's companion dataset. Each deposit therefore carries the harmonic force constants its own paper
used — `BGG_cell0_harm0.02.xml` (md5 `10b0877d7db3dc71f7236e970bc3e552`) here, the 2016 re-fit there.
The two are not interchangeable. `INCAR` and `KPOINTS` are byte-identical between the two studies.

### 2.4 The guest-free cubic force constants existed in only one copy

`GG_cell0_anharm.xml` had been regenerated in the fitting directory on 2016-01-26 with ALAMODE
0.9.6, producing a file that differs from the published one in the trailing digits and in its
section structure. The published file (ALAMODE 0.9.2, 2014-12-05) survived in the BTE working
directory only. The correct file is shipped here:

```
04_force_constants/GG_cell0/GG_cell0_anharm.xml   md5 = 19e2de7553a4e3a0a137559ddf33511e
```

Anything hashing to `dfb716dbbd213fc110f3f59bd3986d8d` is the 2016 regeneration, not the paper's.

**Ge46 has exactly the same problem.** `disp/Ge46/alm/Ge46_anharm.xml` was regenerated on
2015-12-23; the published file (2014-12-05) survived only in the BTE working directory and is what
is shipped here:

```
04_force_constants/Ge46/Ge46_anharm.xml           md5 = d4b8517129e65a50131b73fc15ea7925
```

### 2.5 The raw-DFT archives are dated after publication but contain 2014 data

`90_raw_dft/*.tar.gz` carry a 2015-06-05 mtime because that is when the loose VASP outputs were
archived. Their contents are the February 2014 production runs. `MANIFEST.tsv` records the
original path and mtime of every file so this remains auditable.

---

## 3. Directory layout and training data

```
01_structure/          POSCAR/CONTCAR for BGG (a=10.954 and 10.735 Å), the GG framework
                       geometry, Ge46, and the fully relaxed BGG cell (a=10.927 Å, 2012)
02_dft_reference/      INCAR, KPOINTS, POTCAR.spec, VASP job scripts
03_training_data/      displacement-force training sets fed to ALM (see 3.1)
                         BGG_cell0/  GG_cell0/  BGG_cell-2/  Ge46/
04_force_constants/    harmonic + cubic IFCs (.xml, .fcs), ALM inputs and logs
                         BGG_cell0/  GG_cell0/  BGG_cell-2/  Ge46/
05_bte_results/        RTA thermal conductivity (.kl), full mode-resolved output (.result),
                       anphon inputs, logs and job scripts
                         BGG_cell0/  BGG_cell-2/  GG_cell0/  Ge46/
06_phonon_properties/  phonon bands, group velocities, atom-projected DOS, participation
                       ratio, 20x20x20 phonon linewidths and three-phonon phase space, plus
                         groupvelocity/              Fig. 4(b)
                         V3_anharmonic_interaction/  Fig. 4(a) inputs and logs
                         mode_lifetime/              Fig. 4(c)
07_convergence/        q-grid convergence series and the superseded first-submission kappa_L
90_raw_dft/            raw VASP vasprun.xml and OUTCAR archives
                         BGG_cell0  36 harmonic + 252 cubic   (54-atom, covers GG too)
                         BGG_cell-2 36 harmonic   (cubic runs were never archived)
                         Ge46       24 harmonic +  96 cubic   (46-atom)
MANIFEST.tsv           path, size, md5, original path and original mtime for every file
```

### 3.1 Training sets and how GG is derived from BGG

All forces come from one set of 54-atom Ba₈Ga₁₆Ge₃₀ supercell calculations:

| Source runs (`cell0`) | Configurations |
|---|---|
| harmonic, single displacement, 0.02 Å | 36 |
| cubic, dual displacement, 0.04 Å | 252 |

| Fit | Cell | Configurations used (`NDATA`) | Files |
|---|---|---|---|
| BGG harmonic | 54 atoms | 18 (0.02 Å subset of the 36) | `BGG_cell0/disp,force_harm0.02.dat` |
| BGG cubic | 54 atoms | 288 (all 36 + all 252) | `BGG_cell0/disp_total.{disp,force}_au` |
| GG harmonic | 46 atoms | 12 | `GG_cell0/disp,force_harm_wo_Ba_0.02.dat` |
| GG cubic | 46 atoms | 84 (24 + 60) | `GG_cell0/disp_wo_Ba_total.{disp,force}_au` |

The GG sets are **subsets of the BGG runs with the eight Ba rows deleted**. Of the 36 harmonic
runs, the 24 that displace only host atoms are kept (the 12 that displace Ba — patterns `1x`,
`3x`, `3y` — are dropped); of the 252 cubic runs, 60 are kept. The intermediate 54-row extractions
are shipped as `GG_cell0/subset54_*.{disp,force}_au` so the derivation can be checked directly:

```python
# every GG configuration equals a BGG configuration minus its 8 Ba rows
subset54_harm.force_au[cfg][8:]  ==  force_harm_wo_Ba_0.02.dat[cfg]
```

Verified here for all 12 harmonic configurations. The two extraction passes used marginally
different Bohr-radius constants (0.529177 vs 0.52917721 Å), so the values agree to a uniform
factor of 1 + 4×10⁻⁷ rather than bit-exactly. This is a unit constant, not different physics.

`xml_list.harmonic` / `xml_list.cubic` in each directory name the exact `vasprun.xml` files used,
and every one of them is present in `90_raw_dft/`.

Maximum displacement is 0.0200 Å in the harmonic set and 0.0400 Å in the cubic set, verified
directly from the shipped files.

**Total energies are not tabulated.** The `.energy` files in the source tree contain only `N/A`
placeholders — the extraction script never populated them — so they are not shipped. Per-configuration
energies can be read from `<i name="e_fr_energy">` in the raw `vasprun.xml` files in `90_raw_dft/`.

---

## 4. Which files correspond to which figure

| Figure | Content | Files |
|---|---|---|
| **1(a)** | Phonon dispersion and atom-projected DOS of BGG (solid) and GG (dotted) | `06_phonon_properties/BGG_cell0/BGG_phband_all.bands`, `GG_cell0/GG_phband_all.bands`; projected DOS `*_W202020_submit2.dos` (column headers give the `Ba/Ga/Ge` projections) |
| **1(b,c)** | Crystal structure and the two inequivalent Ba cages | `01_structure/BGG_cell0_a10.954.POSCAR` |
| **2** | κ_L(T) for BGG, GG and Ge46 | `05_bte_results/{BGG_cell0,GG_cell0,Ge46}/*_submit2.kl`, plus `BGG_cell-2/` for the experimental-lattice-constant curve |
| **3** | Phonon linewidths at 300 K; inset: three-phonon phase space W_q± | `06_phonon_properties/*/*_W202020_submit2.scatter` (phase space) and `*_W202020_300K_submit2.dat` (linewidths), 20×20×20 grid |
| **4(a)** | Magnitude of anharmonic (cubic) interaction of TA/LA modes at q = (0.1, 0, 0) | `06_phonon_properties/*/V3_anharmonic_interaction/` — `input_V3.txt`, `kslist.in` and run logs. **The V3 matrix-element dumps themselves (`*.V3.*.Z`, 1.1 GB) are not deposited**; re-run `anphon input_V3.txt` against the shipped IFCs to regenerate them. |
| **4(b)** | Squared group velocity of TA/LA modes, BGG vs GG, normalised by v_p² | `06_phonon_properties/*/groupvelocity/vel2_*2.dat` and the `modify_vel_*2.py` scripts that produced them, from `*_GX_vel.phvel` |
| **4(c)** | Phonon lifetimes of transverse/longitudinal modes at 300 K | `06_phonon_properties/*/mode_lifetime/` (mode-resolved anphon runs along [100]) and the full `05_bte_results/*/*.result` files |

## 5. Reproducing the results

ALAMODE 0.9.2 is required for bit-identical output; later versions change the last digits of the
fitted force constants (see §2.4).

```bash
# 1. Harmonic force constants
cd 04_force_constants/BGG_cell0
ln -s ../../03_training_data/BGG_cell0/{disp,force}_harm0.02.dat .
alm input_alm_harmonic.reconstructed.txt > harm.log     # -> BGG_cell0_harm0.02.xml
#    check: "Number of  HARMONIC FCs (nzero): 320"

# 2. Cubic force constants (harmonic part fixed via FC2XML)
ln -s ../../03_training_data/BGG_cell0/disp_total.{disp,force}_au .
alm input_alm_cubic.reconstructed.txt > anharm.log      # -> BGG_cell0_anharm.xml
#    check: "Number of   ANHARM3 FCs (nzero): 384"

# 3. Thermal conductivity (RTA, 6x6x6 q-grid)
cd ../../05_bte_results/BGG_cell0
ln -s ../../04_force_constants/BGG_cell0/BGG_cell0_anharm.xml .
mpirun anphon input_BTE.reconstructed.txt > run.log     # -> BGG_666_submit2.kl
#    check: kappa_xx(100 K) = 0.7761 W/mK
```

The guest-free case is identical with `GG_cell0` and an 8×8×8 q-grid (its ALM input survived and
is shipped verbatim); the reduced-lattice-constant case uses `BGG_cell-2` (`&cell` prefactor 20.29
instead of 20.7). Ge46 uses its own cell (`1.889` scale, a = 10.7347 Å) and an 8×8×8 q-grid — but
see §6: its ALM fitting input was not preserved.

Note: the RTA runs were executed as a sequence of restarts (`RESTART = 1`), which is why several
sequentially numbered logs (`anphon_run.log1`…`log6`) accompany a single result file.

---

## 6. Known gaps

- **No ALM fitting log survives for the `BGG_cell-2` December-2014 re-fit.** Only the February
  2014 log remains in the source directory and it describes the superseded fit, so it is not
  shipped. That the shipped `BGG_cell-2_*.xml` files (2014-12-04 / 12-07) belong to the published
  campaign is established independently: the BTE run log reports 28674 non-zero harmonic IFCs,
  matching the `cell0` December re-fit exactly. The reconstructed ALM inputs for `cell-2` are
  therefore derived from the `cell0` logs with only the lattice constant and file names changed.
- The 20×20×20 linewidth runs (`*_W202020_submit2`) were executed with ALAMODE **0.9.0** on
  2014-12-07, two days after the IFC re-fit, whereas the RTA runs used 0.9.2. Both read the same
  published IFC files (confirmed by their non-zero-IFC counts).
- **No ALM fitting inputs or logs survive for Ge46.** `disp/Ge46/alm/input_alm.txt` was overwritten
  on 2015-12-23 and the only surviving log (2014-10-20) is a `MODE = suggest` pattern-generation
  run, not the fit. No reconstruction is attempted here because there is no record to reconstruct
  from. The Dec-2014 IFC files and the full training data are shipped, so the fit can be redone,
  but the exact cutoffs and `NDATA` used in the published fit are not documented anywhere.
- **For `BGG_cell-2` only the harmonic raw DFT was archived.** The 252 cubic `vasprun.xml`/`OUTCAR`
  files for that lattice constant were never packed and no longer exist; the extracted
  displacement–force data (288 configurations) is complete, so the IFCs remain reproducible.
- The three-phonon matrix-element dumps (`*.V3.*.Z`, 1.1 GB) and the participation-ratio
  eigenvector dump (`*.apr`, 110 MB) are excluded as regenerable; see the Fig. 4(a) row in §4.
- `BGG_cell0_cubic_OUTCAR.tar.gz` contains one stray entry named plainly `outcars/OUTCAR`, a
  leftover from the original working directory. The 252 per-configuration files are named
  `OUTCAR.<tag>` and correspond one-to-one with the 252 `vasprun.xml` files.
- `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>.
