QuTree: A tree tensor network package.

We present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer.

Vibronically and spin-orbit coupled diabatic potentials for X(P) + CH4 → HX + CH3 reactions: General theory and application for X(P) = F(2P).

An approach to systematically construct vibronically and spin-orbit coupled diabatic potential energy surfaces (PESs) for X(P) + CH4 → HX + CH3 reactions is proposed. Permutational symmetry and permutational invariants of the S4 group and its S3 and S2 × S2 subgroups are used to construct a diabatic model which properly describes the reaction starting from reactants to products. As a first example, the approach is applied to the construction of diabatic potentials for the F(2P) + CH4 → HF + CH3 reaction. The description of the entrance channel relies on a set of vibronically and spin-orbit coupled diabatic PESs previously developed by Westermann et al. [Angew. Chem., Int. Ed. 53, 1122 (2014)]. The same set of diabatic electronic states is also used in the transition state region and all four exit channels. There the lowest adiabatic PES derived from the diabatic model reproduces the CSBB-PES of Czakó et al. [J. Chem. Phys. 130, 084301 (2009)]. Interesting aspects of the newly developed diabatic potential matrix and the corresponding adiabatic PESs are discussed.

Vibronically and spin-orbit coupled diabatic potentials for X(2P) + CH4 → HX + CH3 reactions: Neural network potentials for X = Cl.

Vibronically and spin-orbit (SO) coupled diabatic potentials for the Cl(2P) + CH4 → HCl + CH3 reaction are constructed based on a recently developed approach [T. Lenzen and U. Manthe, J. Chem. Phys. 150, 064102 (2019)]. Diabatic potentials and couplings describing the entrance channel of the reaction are obtained based on ab initio data using a diabatization by an ansatz scheme. A detailed investigation of the electronic structure in the entrance channel using multireference configuration interaction (MRCI), coupled cluster [CCSD/CCSD(T)], and SO-MRCI calculations is presented. Neural networks using permutationally invariant polynomials as inputs are employed to represent the elements of the diabatic potential energy matrix. The same set of diabatic states is also used in the transition state region and all four exit channels. Here, the lowest adiabatic potential energy surface (PES) derived from the diabatic model is chosen to reproduce an adiabatic PES recently developed by Li and Guo. The accuracy of the resulting PES is evaluated, and the properties of the newly developed coupled diabatic potentials are analyzed in detail.

Neural network based coupled diabatic potential energy surfaces for reactive scattering.

An approach for the construction of vibronically coupled potential energy surfaces describing reactive collisions is proposed. The scheme utilizes neural networks to obtain the elements of the diabatic potential energy matrix. The training of the neural network employs a diabatization by the Ansatz approach and is solely based on adiabatic electronic energies. Furthermore, no system-specific symmetry consideration is required. As the first example, the H2+Cl→H+HCl reaction, which shows a conical intersection in the entrance channel, is studied. The capability of the approach to accurately reproduce the adiabatic reference energies is investigated. The accuracy of the fit is found to crucially depend on the number of data points as well as the size of the neural network. 5000 data points and a neural network with two hidden layers and 40 neurons in each layer result in a fit with a root mean square error below 1 meV for the relevant geometries. The coupled diabatic potential energies are found to vary smoothly with the coordinates, but the conical intersection is erroneously represented as a very weakly avoided crossing. This shortcoming can be avoided if symmetry constraints for the coupling potential are incorporated into the neural network design.