Angular momentum entanglement of molecular interactions for quantum computing using solid harmonic Gaussian orbitals

For quantum chemistry simulations, its molecular integral package is a crucial part of any quantum chemistry program. Unfortunately, efficient calculations of molecular integrals using quantum computers remain a big challenge. Solid harmonic Gaussian orbitals (SHGOs) are angular momentum eigenfunctions and can apply to calculate angular momentum entanglement of molecular integrals using quantum computers. Vector-coupling and vector-uncoupling schemes of quantum angular momenta correspond to unitary Clebsch-Gordan transformations to manipulate angular momentum entanglement of molecular interactions. The addition of quantum angular momentum and the product of Gaussian orbitals simultaneously apply to transform molecular multi-center interactions to one-center interactions, reducing the degree of entanglement using the orthonormality of SHGOs. This transformation also leads to simple analytical molecular integrals, revealing angular momentum entanglement interactions under nuclear and electron Coulomb fields. The molecular angular momentum entanglement provides quantum constraint to limit multipole interactions of Coulomb fields, resulting in highly efficient calculations of molecular integrals using quantum circuits of unitary and cascading Clebsch-Gordan transformations in quantum computers.