Symmetrization of the nuclear wavefunctions defined by the quantum trajectory dynamics

In a rigorous quantum-mechanical (QM) description of indistinguishable particles, the correct symmetry is often built-in into the form of an approximate wavefunction, with the electronic wavefunctions constructed as Slater determinants of the single-particle functions being the prime example. In contrast, when evaluating QM effects for the nuclei, often described by approximate wavefunctions of full dimensionality, the wavefunction symmetry can be included directly into calculation of expectation values. The straightforward implementation, however, may be impractical for a large system due to factorial scaling of particle permutations. In this work, the leading correction due to the wavefunction symmetrization within the quantum trajectory (QT) framework is presented. The correction is based on the non-symmetrized wavefunction evolved using QT dynamics with empirical friction, yielding the lowest energy states. Use of symmetry improves the accuracy and efficiency of this dynamics approach as shown on model systems of up to four dimensions.