Hi chrisapo!

Questions are always appreciated! Sorry for the delayed reply.

**Regarding: the random choice of initial conditions**

The algorithm to compute ground states via imaginary time propagation of the MCTDH-X working equations is generally very insensitive to the choice of initial conditions.

However, there are some pitfalls. For instance, when initial state (determined by coefficients and orbitals) has **exactly zero** overlap with the ground state that is sought.

The motivation for the random choice of initial conditions is to guarantee that the overlap with any possible state is finite. This random choice typically makes the initial steps of the integration a bit slower.

**Regarding orthonormality**: the orbitals (working as well as natural) should always be strictly orthonormal. For hand-given-orbitals, this is ensured by a Gram-Schmidt orthonormalization.

During real-time evolution, orthonormality is a property that follows from the projection operator in the equations of motion and the unitarity of the Hamiltonian.

During imaginary-time evolution, the orthonormality is guaranteed by a Gram-Schmidt orthonormalization at every integration step.

Hope that helps!