Rare Event Sampling Improves Mercury Instability Statistics

Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury’s orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10−4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.

Ab initio investigation on the low-lying states of LaX (X = Se, Sn, Sb)

Potential energy curves for the low-lying electronic states of the title molecules in their neutral and anionic forms have been calculated by means of the diffusion Monte Carlo method. The effect of different trial functionals has been investigated using single determinants constructed from density functional theory (DFT) orbitals with B3LYP, B3PW91, and M06-2X functions. Bond length, vibrational frequency, and electron affinity have also been numerically derived for the selected species and the ground state has been assigned. Spectroscopic parameters obtained are interpreted and compared to their isovalents, shedding some light on further investigations on the selected dimers.