### Task Track #2: Open-ended Scientific Discovery Task

#### Science domain: materials science
#### Science macro: first-principles materials design
#### Task name: maximizing the non-configurational partial molar entropy of oxygen-vacancy formation in nonstoichiometric oxides

#### Task description:

Screening for two-step thermochemical water splitting materials is overwhelmingly enthalpy-centric because non-configurational entropy is costly to compute and the maximum possible oxygen vacancy driven configurational entropy is similar for most oxides at a given δ. In this task, using first-principles methods we will look for materials that maximize the non-configurational partial molar entropy of oxygen vacancy formation (e.g., from electronic-multiplet, magnetic/spin, and vibrational sources) in search of a material that rivals or exceeds that of ceria while keeping the reduction enthalpy in the re-oxidation window of steam.

#### End goal:

Determine whether the non-configurational partial molar entropy of vacancy formation of any candidate exceeds that of ceria under the given constraints, and identify which entropy channel supplies it.

#### Evaluation metric:

Maximizing the non-configurational partial molar entropy of oxygen vacancy formation (J·mol O⁻¹·K⁻¹) serves as the continuous score, with the goal of getting close to or exceeding the value of ceria.

#### Simulation list:

This task will likely require extensive use of density functional theory (DFT) to calculate defect formation enthalpies and the vibrational component of the partial molar entropy. The electronic and spin/ magnetic entropy terms can be estimated using analytical methods or calculated using very computationally expensive (and specialized) DFT and related first-principles methods (like DMFT). For a search like this, the analytical route would likely be the better method choice.

#### Workflow:

At a very high level, compute the three non-configurational entropy channels across a defined ~20–40-composition series spanning f⁰→f¹ (Ce/Tb references), d⁰→d¹ (Ti, V), and spin-active/spin-crossover (Mn, Fe, Co) couples. Rank these by non-configurational entropy under the enthalpy and single-phase stability constraints. Top predictions could optionally be confirmed experimentally.

Relevant material property constraints (i.e., a material must satisfy these in addition to maximizing non-configurational partial molar entropy of oxygen vacancy formation):
- Reduction enthalpy in the re-oxidizable range (~2-4.5 eV/O)
- Stable/ single phase across the operating δ range
- Entropy evaluated at fixed δ = 0.05 (or as close as supercell choice allows) and per mol O

#### Constraint:

- Access to hpc resource
- Access to DFT software (e.g., VASP)
- `ase` python package
- `pymatgen` python package
- `mp-api` python package/ access to MP database

#### Dataset:

- No explicit dataset needs to be given, but the agent should evaluate the relevant literature when selecting structures to investigate