Spin-coupled theory for 'N electrons in M orbitals' active spaces

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• Spin-Coupled (SC) theory is an ab initio valence bond (VB) approach.
• The original SC model provides a compact wave function comparable to CASSCF(N,N).
• Extension to N-in-M active spaces is needed for more complex systems.

Purpose of the Study:

• To extend Spin-Coupled (SC) theory to N-in-M active spaces (SC(N,M)).
• To demonstrate the utility of SC(N,M) for describing the electronic structure of aromatic cyclic ions.
• To assess the compactness and accuracy of SC(N,M) compared to CASSCF.

Main Methods:

• Development of the SC(N,M) wave function, involving products of nonorthogonal orbitals with flexible spin functions.
• Application of SC(N,M) to calculate the electronic structure of the cyclopentadienyl anion (C5H5–) using SC(6,5).
• Application of SC(N,M) to calculate the electronic structure of the tropylium cation (C7H7+) using SC(6,7).

Main Results:

• The SC(N,M) wave function is significantly more compact than CASSCF(N,M) (e.g., SC(6,7) has 35 CSFs vs. 490 for CASSCF(6,7)).
• SC(N,M) provides clear VB models for C5H5– and C7H7+ electronic structures, analogous to the benzene SC model.
• SC(N,M) recovers over 97% of correlation energy for C5H5– and over 95% for C7H7+ compared to CASSCF.

Conclusions:

• The SC(N,M) method successfully extends the benefits of SC theory to N ≠ M active spaces.
• SC(N,M) offers an accurate and computationally efficient alternative to CASSCF for studying electronic structures of complex molecules.
• This advancement provides valuable insights into the electronic properties of aromatic systems.