Realisation of semi-empirical electronic structure theory on a field-programmable gate array

High-throughput quantum-chemical calculations underpin modern molecular modelling, materials discovery, and machine-learning workflows, yet even semi-empirical methods become restrictive when many molecules must be evaluated. Here we report an integrated FPGA realisation of semi-empirical electronic structure theory, implementing as a proof of principle Extended Hückel Theory (EHT) and non-self-consistent Density Functional Tight Binding (DFTB0). Our design performs Hamiltonian construction and diagonalisation on the FPGA device through a streaming dataflow, enabling deterministic execution without host intervention. Separately, a stand-alone DFTB0 Hamiltonian generator isolates the performance of streaming Hamiltonian construction from diagonalisation. On a mid-range Artix-7 FPGA, the DFTB0 Hamiltonian generator delivers, for the larger systems considered, more than four times the throughput of an unbatched C++ implementation and generally around twice that of a batched implementation on a contemporary server-class CPU, while achieving over two orders of magnitude higher energy efficiency than the unbatched CPU implementation. Improvements in eigensolver design, memory capacity, and extensions to nuclear gradients and excited states could further expand capability.