A Single Reference Perturbation Theory beyond the Møller-Plesset Partition.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of electronic structures is crucial in chemistry.
• Existing methods for open-shell systems and multi-reference problems have limitations.
• Size extensivity is a key property for reliable computational methods.

Purpose of the Study:

• To propose a novel single-reference perturbation partition for ROHF and CASSCF.
• To assess the size extensivity of the new perturbation partition.
• To evaluate the accuracy of the new method by comparing it with established techniques.

Main Methods:

• Development of a new single-reference perturbation partition based on a sum of one-particle operators.
• Implicit definition of the operator for ROHF and CASSCF orbitals.
• Size extensivity tests using Hartree-Fock (HF), F2, and N2 with stretched bonds.
• Perturbation calculations for H2O, NH3, and CH4 using CASSCF orbitals.
• Comparison with Multi-Reference Configuration Interaction (MRCI), MRCI+Q, MRPT2, and MRPT3.
• Calculation of singlet-triplet separation for CH2 and SiH2 radicals.

Main Results:

• The proposed perturbation partition is implicitly defined and yields orbital energies.
• The first three-order energies calculated with the new partition demonstrate size extensivity.
• Perturbation calculations for H2O, NH3, and CH4 show good agreement with other advanced methods.
• The single-reference nature of the perturbation theory is confirmed by radical calculations.

Conclusions:

• The new single-reference perturbation partition is a valid and size-extensive approach for ROHF and CASSCF.
• This method offers a promising alternative for accurate electronic structure calculations in open-shell and multi-reference systems.
• The developed theory provides reliable results comparable to established high-level computational chemistry methods.