Problem

Metal atoms (Pt, Pd, Co) on graphitic carbon nitride (g-C$_3$N$_4$) photocatalysts shift optical absorption into the visible range.

Observable: Computed electronic structure and optical response for different dopants and doping sites
Question: What mechanism enables visible absorption—and how much structural detail can optical spectra actually constrain?

This was my second computational project. The goal was no longer just “get a band gap,” but to understand what information optical spectra do and do not encode about microscopic structure.

What I tried

Initial approach
Run DFT, compute band structures and dielectric functions, compare absorption spectra, claim insight.

That approach produced clean-looking spectra—but I couldn’t tell whether the differences were physically meaningful or artifacts of structure choice.

Problems became obvious quickly:

  1. Multiple doping sites exist for each metal—no single “correct” structure.
  2. PBE band gaps are wrong by $\sim1\ \mathrm{eV}$—could optical conclusions still be trusted?
  3. Finite supercells were required—was I seeing physics or finite-size effects?

So I backed up and reframed the problem.

How I reframed it

Instead of asking “which structure is best?”, I treated the problem as a forward mapping:

\[\text{structure} \;\rightarrow\; \text{electronic states} \;\rightarrow\; \text{optical response}\]

In polymeric, weakly ordered semiconductors like g-C$_3$N$_4$, this mapping is many-to-one.
Optical spectra are projections of electronic structure, not structural fingerprints.

The task became:

  • identify which optical features are robust to structural variation, and
  • recognize where inversion (spectrum $\rightarrow$ structure) becomes non-identifiable.

What I figured out

Why metal doping shifts absorption

The key mechanism is symmetry breaking, not fine energetic tuning.

Pristine g-C$_3$N$_4$ has relatively high symmetry at the electronic level. Many low-energy optical transitions are weak or forbidden by selection rules, limiting visible absorption.

Introducing metal dopants:

  • breaks local symmetry,
  • introduces metal $d$-character near the band edges, and
  • activates transitions that were previously forbidden or weak.

This is visible directly in the transition matrix elements.

At the independent-particle level, optical intensity depends on

\[\varepsilon_2(\omega) \propto \sum_{v,c,\mathbf{k}} \left| \langle \psi_c | \mathbf{r} | \psi_v \rangle \right|^2 \delta(\varepsilon_c - \varepsilon_v - \hbar\omega),\]

not on eigenvalues alone.

I verified the mechanism by:

  • computing transition dipole moments, not just band structures,
  • tracking how oscillator strength redistributed after doping,
  • comparing multiple dopants and multiple sites.

Result: Visible absorption enhancement is robust. It does not depend sensitively on the exact site or functional choice, because it originates from symmetry breaking rather than precise level alignment.

What survived structural variation

Across plausible configurations, several features were consistent:

  • near-UV absorption onset in pristine g-C$_3$N$_4$
  • dominance of $\pi \rightarrow \pi^*$ transitions
  • strong in-plane versus out-of-plane anisotropy
  • extension of absorption into the visible after metal doping

These define the material class, not a specific microscopic structure.

What I couldn’t determine

Which specific doping site dominates in real samples

I sampled $\sim10$–$20$ metal positions per dopant. All showed similar absorption onsets (within $\sim0.2$–$0.3\ \mathrm{eV}$).

I do not know which sites are actually occupied experimentally—nor whether multiple sites coexist.

Quantitative peak positions

PBE underestimates gaps by $\sim1\ \mathrm{eV}$.
While the symmetry-breaking argument is qualitative and robust, precise transition energies would require HSE06 or GW–BSE, which were not feasible at scale on our cluster.

Effect of real disorder

Experimental g-C$_3$N$_4$ is polycrystalline, partially polymerized, and compositionally variable. My models assume ideal periodicity. How much disorder reshapes the spectra beyond broadening remains uncertain.

What collapsed under inversion

Different structural perturbations produced nearly indistinguishable spectra once disorder and resolution were considered:

  • stacking and interlayer spacing
  • vacancy density versus termination
  • planar distortion versus electronic localization
  • band curvature changes versus apparent excitonic shifts
  • thickness versus intrinsic disorder

The dominant surviving quantity was the transition dipole moment,

\[\mathbf{d}_{vc} = \langle \psi_v | \mathbf{r} | \psi_c \rangle.\]

Peak positions alone could not uniquely constrain structure.

What I learned

Qualitative mechanisms can be robust even when quantitative predictions aren’t.

Symmetry breaking explains why metal doping helps. That insight survives functional choice, site ambiguity, and finite-size limitations.

But claiming which site or which dopant is optimal would be overclaiming without experimental structural constraints (e.g., EXAFS, XANES).

When to stop computing

More configurations, larger cells, and better functionals would not resolve a fundamentally non-identifiable inverse problem.

At some point, additional DFT just samples more structures—not necessarily the right ones.

What I’d do differently

  1. Collaborate with experimentalists upfront to constrain plausible sites
  2. Run a small number of HSE06 calculations for calibration
  3. Sample more aggressively only if claiming structure–property specificity
  4. State bounds on what optical spectra can and cannot determine earlier

Status: Ongoing project, no manuscript yet.

What I learned:
Computation is better at identifying mechanisms (symmetry breaking) than specific structures (exact doping sites). Optical spectra constrain families of admissible structures, not unique configurations.

Constraint analysis: /constraints/gcn-optical-transitions
Methods: DFT-PBE, DFT-HSE06, Optical response from DFT, Configuration sampling

Project date: Spring 2024 – Present
My experience level: Second computational project; learning excited-state modeling and where DFT optical predictions remain trustworthy.