An outstanding challenge in chemical
computation is the
many-electron
problem where computational methodologies scale prohibitively with
system size. The energy of any molecule can be expressed as a weighted
sum of the energies of two-electron wave functions that are computable
from only a two-electron calculation. Despite the physical elegance
of this extended “aufbau” principle, the determination
of the distribution of weightsgeminal occupationsfor
general molecular systems has remained elusive. Here we introduce
a new paradigm for electronic structure where approximate geminal-occupation
distributions are “learned” via a convolutional neural
network. We show that the neural network learns the N-representability conditions, constraints on the distribution for
it to represent an N-electron system. By training
on hydrocarbon isomers with only 2–7 carbon atoms, we are able
to predict the energies for isomers of octane as well as hydrocarbons
with 8–15 carbons. The present work demonstrates that machine
learning can be used to reduce the many-electron problem to an effective
two-electron problem, opening new opportunities for accurately predicting
electronic structure.