Accelerating Excited-State Calculations of Large Systems with Restricted Boltzmann Machines

Accurate
excited-state electronic-structure calculations
for large
systems remain challenging due to the prohibitive cost of constructing
and screening the configuration space in conventional linear-response
approaches. Here, we present a generative machine-learning-accelerated
simplified Tamm–Dancoff approximation (gML-sTDA) method that
enables efficient excited-state calculations for large systems. The
key idea is to use restricted Boltzmann machines (RBM) as generative
models to learn the distribution of important singly excited Slater
determinants (SSDs) from previously calculated excited-state solutions
and to propose new relevant SSDs in an iterative way to avoid exhaustively
evaluating matrix elements over the huge configuration space. Benchmarks
on finite single-walled carbon nanotube models up to 1114 atoms (16,424
basis functions) show that gML-sTDA reproduces sTDA reference excitation
energies with mean absolute errors of ∼0.007–0.011 eV
and yields essentially identical absorption spectra while providing
substantial speedups. In particular, relative to the tight-threshold
sTDA reference protocol, the overall acceleration ratio approaches
∼40× for the largest nanotube and remains close to ∼9×
compared with the default-threshold sTDA-cut workflow. Additional
applications to a silicon quantum dot, a large black-phosphorus supercell,
and a rubrene cluster demonstrate consistent performance, with speedup
factors of 7.4, 4.5, and 9.8, respectively, compared to those of the
sTDA-cut. These results establish gML-sTDA as a practical and scalable
route to excited-state electronic structure calculations in large-scale
systems and provide an efficient starting point for applications requiring
repeated excited-state evaluations.