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.

A general method for the development of diabatic spin-orbit models for multi-electron systems.

Spin-orbit (SO) coupling can have significant effects on the quantum dynamics of molecular systems, but it is still difficult to account for accurately. One promising way to do this is to devise a diabatic SO model combined with the molecular potential energy. Few such models have been developed utilizing spatial and time-reversal symmetry.

Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation.

In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion.

The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation.

The multilayer multiconfigurational time-dependent Hartree (MCTDH) in optimized second quantization representation (oSQR) approach combines the tensor contraction scheme of the multilayer MCTDH approach with the use of an optimized time-dependent orbital basis. Extending the original work on the subject [U. Manthe and T.

On the multi-layer multi-configurational time-dependent Hartree approach for bosons and fermions.

A multi-layer multi-configurational time-dependent Hartree (MCTDH) approach using a second quantization representation (SQR) based on optimized time-dependent orbitals is introduced. The approach combines elements of the multi-layer MCTDH-SQR approach of Wang and Thoss, which employs a preselected time-independent orbital basis, and the MCTDH for bosons and multi-configuration time-dependent Hartree-Fock approaches, which do not use multi-layering but employ time-dependent orbital bases. In contrast to existing MCTDH-type approaches, the results of the present approach for a given number of configurations are not invariant with respect to unitary transformations of the time-dependent orbital basis.

Development of multi-mode diabatic spin-orbit models at arbitrary order.

The derivation of diabatic spin-orbit (SO) Hamiltonians is presented, which are expanded in terms of nuclear coordinates to arbitrary order including the treatment of multi-mode systems, having more than one mode of the same symmetry. The derivation is based on the microscopic Breit-Pauli SO operator and the consequent utilization of time reversal and spatial symmetry transformation properties of basis functions and coordinates. The method is demonstrated for a set of (2)E and (2)A1 states in C(3v)* (double group) symmetry, once for a 3D case of one a1 and one e mode and once for a 9D case of three a1 and three e coordinates.