We investigate tree tensor network states for quantum chemistry. Tree tensor
network states represent one of the simplest generalizations of matrix product
states and the density matrix renormalization group. While matrix product
states encode a one-dimensional entanglement structure, tree tensor network
states encode a tree entanglement structure, allowing for a more flexible
description of general molecules. We describe an optimal tree tensor network
state algorithm for quantum chemistry. We introduce the concept of
half-renormalization which greatly improves the efficiency of the calculations.
Using our efficient formulation we demonstrate the strengths and weaknesses of
tree tensor network states versus matrix product states. We carry out benchmark
calculations both on tree systems (hydrogen trees and \pi-conjugated
dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and
chromium dimer). In general, tree tensor network states require much fewer
renormalized states to achieve the same accuracy as matrix product states. In
non-tree molecules, whether this translates into a computational savings is
system dependent, due to the higher prefactor and computational scaling
associated with tree algorithms. In tree like molecules, tree network states
are easily superior to matrix product states. As an ilustration, our largest
dendrimer calculation with tree tensor network states correlates 110 electrons
in 110 active orbitals.Comment: 15 pages, 19 figure
