Tethered Gaussian wavepackets for quantum dynamics simulations: Sticking together for better convergence

Standard Gaussian products are frequently employed as a basis to represent potential energy surfaces (PESs) or time-dependent wavefunctions. The effective "volume" of standard Gaussian products decreases as dimensionality f increases, meaning that rapidly growing basis sets are required to obtain accurate results as f grows. Here, we show that the flexibility inherent in Gaussian-based simulations allows development of new basis sets in which behavior at higher-dimensionality is improved. For the case of PES regression, we first show that recasting Gaussian basis functions in an "additive" form improves fitting convergence in higher-dimensional problems. Taking inspiration from these PES regression studies, we then propose two new Gaussian wavepacket (GWP) basis functions-stretched and tethered GWPs-for quantum dynamics simulations. When combined with careful choice of initial GWP conditions, we find that tethered GWP basis sets, in particular, improve convergence of predicted time-dependent observables compared to standard product GWPs. The new GWP basis sets proposed here are readily compatible with all previous GWP-based quantum dynamics strategies, opening a path toward more accurate predictions with smaller basis sets.