Abstract
The necessary theory to construct different direct orbital optimization schemes in the framework of the spin-projected Hartree-Fock (spin-PHF) method for systems with an even number of electrons and for the proper characterization of the pertinent spin-PHF solutions is developed using the formalism of second quantization. The treatment is based on a unitary transformation of a reference DODS (different orbitals for different spins) Slater determinant. The energy expectation value corresponding to the transformed DODS Slater determinant is expanded in a Taylor series about the reference DODS Slater determinant, including second-order terms. On the basis of this expansion we propose several direct iterative approaches to optimize the spin-PHF energy expectation value: for example, implementations of steepest descent and conjugated gradient techniques, and Newton–Raphson, Fletcher, and limited configuration interaction approaches. The analysis of the second-order term in the Taylor series expansion of the spin-PHF energy expectation value about a spin-PHF solution is used to define stability conditions for spin-PHF solutions. Explicit expressions are reported for all matrix elements between different spin-projected DODS Slater determinants appearing in the treatment.
| Original language | English |
|---|---|
| Pages (from-to) | 239-264 |
| Number of pages | 26 |
| Journal | INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY |
| Volume | 30 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1986 |