Solution to quantum chemistry problems using a phase-fitting, singularly P-stable, cost-effective two-step approach with disappearing phase-lag derivatives up to order 5

The phase lag and its first, second, third, fourth, and fifth derivatives are all accounted for in a phase-fitting method. The new system uses the fewest possible function evaluations per integration step (FEvs) to achieve the highest possible algebraic order (AOR) and is hence P-stable. PF5DPFN2SPS is the symbol for the new method. The proposed method can be used for many different problems with periodic and/or oscillating solutions. We used the unique approach to the well-known problem in quantum chemistry posed by Schrödinger-type coupled differential equations. The new method is part of the economic algorithms since it uses 5 FEvs at each stage to achieve a 12 AOR.