We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problemswith numerous highly correlated orbitals. To exploit the advantagesof TTNS a novel algorithm is designed to optimize the tree tensornetwork topology based on quantum information theory and entanglement.The superior performance of the TTNS method is illustrated on theionic-neutral avoided crossing of LiF. It is also shown that the avoidedcrossing of LiF can be localized using only ground state properties,namely one-orbital entanglement.
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