2026-08-13 –, Room 2
We implement the Pariser-Parr-Pople (PPP) Hamiltonian in a Julia package, PPP.jl. This method allows the extremely fast calculation of optical properties of molecules, by using a minimal set of fitted parameters to approximate the one and two-electron integrals. We machine-learn the parameters of our model within our Julia package, and work towards extending the PPP formalism to include a many-body parameterisation based on the Atomic Cluster Expansion (ACEPotentials.jl).
Semi-empirical methods achieve their celebrated computational efficiency through specific choices of basis set and empirically determined parameters approximating the one and two-electron integrals in the Hamiltonian. The Pariser-Parr-Pople (PPP) Hamiltonian uses a minimal basis set of pi-orbitals, including electron correlation with an effective pairwise approximation of the two-electron integrals. Using the PPP method one can quickly and accurately calculate excitation energies for conjugated pi-electron systems, including the inverted singlet-triplet energy gap of optical emitters (Bedogni et al. 2023). These calculations are much faster than high-level calculations, enabling large computational screens of inverted-gap molecules to identify organic light-emitting diode (OLED) candidates (Jorner et al. 2024).
To perform energy calculations with the PPP method, we present our dedicated Julia package, PPP.jl. For a given molecule, the self-consistent-field (SCF) method is employed to calculate the ground state energy. Next, a configuration interaction (CI) calculation is run on top of this to obtain singlet and triplet excitation energies, which are of the most interest.
Our package facilitates the testing of PPP models by generically defining a function for each empirical parameter. This way, the parametrisation of a given model can be specified in a new file, identified by its "model" abstract type. Further to this, a given PPP parameter may be characterised with other constants that can be machine-learned within our Julia package. We will present examples of machine-learned parameters, using PPP models from the literature as a starting point (see, e.g. Bedogni et al. 2023, Jorner et al. 2024, Zhang et al. 2011), together with their energy calculation results for a small set of conjugated hydrocarbons.
We work towards extending the PPP formalism by incorporating machine-learnt many-body physics into the parametrisation of the Hamiltonian. This can be done with the Atomic Cluster Expansion (ACE) method (see, e.g. Drautz 2019, Ortner 2023), making use of the ACEPotentials.jl package to model the effective electron repulsion integrals. By machine-learning the parameters of a fully quantum-mechanical model, one expects a strong inductive bias, enabling good generalisability to larger systems.
I am a first-year PhD student in the Frost Group at Imperial College London. I work on semi-empirical methods in electronic structure theory, focusing on the Hückel and Pariser-Parr-Pople (PPP) methods. For these, I am studying machine learning methods that can be used to optimise the empirical parameters.