A Numerical Method for the Efficient Calculation of Scattering Form Factors

Scintillating molecular crystals have emerged as prime candidates for directional dark matter detector targets. This anisotropy makes them exquisitely sensitive due to the daily modulation induced by the directional dark matter wind. However, predicting the interaction rate for arbitrary molecules requires accurate modeling of the many-body ground as well as excited states, a task that has been historically computationally expensive. Here, we present a theory and computational framework for efficiently computing dark matter scattering form factors for molecules. We introduce SCarFFF, a GPU-accelerated code to compute the fully three-dimensional anisotropic molecular form factor for arbitrary molecules. We use a full time-dependent density functional theory framework to compute the lowest-lying singlet excited states, adopting the B3YLP exchange functional and a double-zeta Gaussian basis set. Once the many-body electronic structure is computed, the form factors are computed in a small fraction of the time from the transition density matrix. We show that ScarFFF can compute the first 12 form factors for a molecule of 10 heavy atoms in approximately 5 seconds, opening the door to accurate, high-throughput material screening for optimal directional dark matter detector targets. Our code can perform the calculation in three independent ways, two semi-analytical and one fully numeric, providing optimised methods for every precision goal.