Phase-fitting, singularly P-stable, cost-effective two-step approach to solving problems in quantum chemistry with vanishing phase-lag derivatives up to order 6

A phase-fitting approach allows vanishing for not only the phase lag but also its first, second, third, fourth, fifth, and sixth derivatives to be considered. The new technique is dubbed economical method because it uses the maximum possible algebraic order (AOR) while simultaneously performing the fewest possible function evaluations (FEvs). The formula for this innovative method is PF6DPFN2SPS. The proposed technique is P-Stable (i.e. infinitely periodic). The proposed approach can be used to solve a variety of problems with periodic and/or oscillating solutions. To address the intractable nature of Schrödinger-type coupled differential equations in quantum chemistry, we adopted this unique approach. The new strategy is classified as a economic algorithm since it uses 5FEvs at each step to achieve a 12AOR. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.