Supplemental data for the letter "The origin of ferroelectric domain wall alignment with surface trenches in ultrathin films"

1) EnergyDifferenceTrenches.xml \(\rightarrow\) Total energy/energy difference data used used for Table I in the main text. Some further analysis of the different terms in the Kohn-Sham total energy is also included.

2) example_input \(\rightarrow\) all of the files needed to run a structural relaxation with CONQUEST. We take the example of the \(d = 1, \parallel ^{\text{centroid}}\)  + AFD film used in the main text. This folder includes:

• 1DeepCentroid_doubled.in \(\rightarrow\)fractional coordinates for the initial structure for the relaxation.
• Conquest_input \(\rightarrow\) a commented CONQUEST input file.
•  O.ion, Pb.ion and Ti.ion \(\rightarrow\) The SZP basis sets and pseudopotentials used in the main text.