The PPP model - a minimal viable parametrisation of conjugated chemistry for modern computing applications

TL;DR

The paper argues that the Pariser-Parr-Pople (PPP) Hamiltonian provides a minimal, practical parametrisation for conjugated π-electron chemistry, balancing computability with the essential physics of electron correlation. It traces the historical development from Hückel theory to PPP, outlines the theoretical justification for ZDO and semi-empirical parameters, and demonstrates PPP’s ongoing relevance through model-exact studies, benchmarking, and applications in singlet fission and inverted singlet–triplet gaps. The authors highlight how PPP enables insights into large, strongly correlated systems, supports high-throughput inverse design, and offers a promising path for early quantum-computing chemistry applications (e.g., QPE+PPP) due to its sparsity and reduced Hilbert space. Overall, PPP remains a versatile, benchmark-friendly framework that informs both fundamental understanding and practical design of advanced conjugated materials, with potential to bridge classical and quantum computational approaches.

Abstract

The semi-empirical Pariser-Parr-Pople (PPP) Hamiltonian is reviewed for its ability to provide a minimal model of the chemistry of conjugated $π$-electron systems, and its current applications and limitations are discussed. From its inception, the PPP Hamiltonian has helped in the development of new computational approaches in instances where compute is constrained due to its inherent approximations that allow for an efficient representation and calculation of many systems of chemical and technological interest. The crucial influence of electron correlation on the validity of these approximations is discussed, and we review how PPP model exact calculations have enabled a deeper understanding of conjugated polymer systems. More recent usage of the PPP Hamiltonian includes its application in high-throughput screening activities to the inverse design problem, which we illustrate here for two specific fields of technological interest: singlet fission and singlet-triplet inverted energy gap molecules. Finally, we conjecture how utilizing the PPP model in quantum computing applications could be mutually beneficial.

Figures (6)

• Figure 1: Schematic illustration of orbitals that can form $\sigma$-bonds (blue) and $\pi$-bonds (purple) in benzene
• Figure 2: Illustration of the different model Hamiltonians on benzene. For each model, all interactions with respect to a specific $\pi$-orbital (highlighted in purple) are depicted. In the Hückel Hamiltonian, only hopping terms (dark blue) are included. In the Hubbard model, an on-site interaction term (purple) is added for each site. By also including parametrized interactions between nearest neighbours (solid green) and optionally also next-nearest neighbours (dashed green), one obtains the extended Hubbard Hamiltonian. In the PPP model, interaction terms between all sites are included (teal), and the interaction strength is scaled based on the inter-atomic distance between the sites.
• Figure 3: trans-polyacetylene (top) and poly(para-phenylene-vinylene) (bottom)
• Figure 4: Inverse design problem, adapted from Ref. green_inverse_2022
• Figure 5: Schematic illustration of the SF process (adapted from Ref. smith_singlet_2010) and the InveST mechanism (adapted from Ref. pollice_organic_2021)