Fig. 4: Calculations on benzene.
From: Towards the ground state of molecules via diffusion Monte Carlo on neural networks
a Atomic structure of the benzene molecule and representative electron positions39. Small balls represent electrons, with spin indicated by their colors, and larger balls represent nuclei. The electron pointed by the blue arrow is an arbitrarily chosen one for nodal set visualization in b and c. Rods are drawn to connect the nucleus with electrons nearby. b and c The log-scaled magnitude of unnormalized FermiNet wavefunctions for a benzene molecule. Each slice is generated by moving a single spin-up electron in the square [−5 a.u., 5 a.u.]2 on X–Y plane while fixing all other electrons in the representative positions shown in a. The dark curves are the nodes and the orange points are the fixed spin-up electrons projected onto X–Y plane. The moving electron for b and c corresponds to the one pointed by the blue arrow on the bottom C–H bond in a. b shows a slice for a 4-layer FermiNet while c is for a 3-layer FermiNet. d Ground state energy of benzene molecule. “L3” and “L4” stand for neural networks with 3 and 4 layers, respectively. The CCSD(T) result coincides with our best DMC result with the 4-layer network. e The trend of node difference to final state in the training process together with the ones for VMC and DMC energy for a benzene molecule using a 3-layer FermiNet. f The linear trend between the node difference and the DMC energy difference to final state. The points correspond to different intermediate training steps and the dashed line is fitted using least square.
