Spin-free quantum chemistry

The use of the conventional spin formulation in conjunction with a spin-free Hamiltonian HSF merely assures symmetry adaptation to a given spin-free permutational symmetry [Asp] without recourse to group theory. In fact, one may symmetry adapt to a given spin-free permutational symmetry without recourse to spin. This is the motivation behind the Spin-Free Quantum Chemistry series.107-116 In this spin-free formulation one uses a spatial electronic ket which is symmetry adapted to a given spin-free permutational symmetry by the application of an appropriate projector. The Pauli-allowed partitions are given by eq. (2-12) and the correspondence with spin by eqs. (2-14) and (2-15). Finally, since in this formulation [Asp] is the only type of permutational symmetry involved, we suppress the superscript SF on [Asp],... 

F. A. Matsen, Adv. Quant. Chem. 1, 59 (1964). Spin-Free Quantum Chemistry. 

The most general many-electronic wavefunction in spin-free quantum chemistry, which should be a spin eigenfunction and share anti-symmetry of electron indices, is of the form,... 

In spin-free quantum chemistry, matrix elements of a spin-independent... 

In the first volume of Advances in Quantum Chemistry [1] I published an article called Spin-Free Quantum Chemistry. Since then I have broadened this concept considerably and have changed the name of the subject to "freeon dynamics". The word "freeon1 means "free-of-spin" and not the common refrigerant. Freeon dynamics is a viable alternative (for light atoms and for molecules with light atoms) to the more-conventional fermion dynamics. The raison d etre for freeon dynamics is that it is conceptually and computationally simpler than fermion dynamics and so is consistent with Ockham s razor ... 

This approach is used in a spin-free context by F. A. Matsen in the paper which introduced the idea of spin-free methods Spin-Free Quantum Chemistry in Advances in Quantum Chemistry, 1, 59, (1964). Matsen uses a rather austere aigebraic method, dispensing with the spin factors from the very start. 

The above equivalence confirms that, with a spinless Hamiltonian, we may obtain the same energy expectation value either (i) by expanding (7.4.1) in terms of determinants and then using the rules in Section 3.3 or (ii) by using a linear combination of purely spatial functions (7.4.6) of appropriate symmetry. The second approach is essentially that of spin-free quantum chemistry (Matsen, 1964), which is considered in more detail in later sections. In the present case a first-principles argument will lead to the required matrix-element expressions. 

This leads to a spin-free formulation of quantum chemistry. The formulas for matrix elements of this type sure discussed in detail elsewhere. 

Like electron spin, the valence state of an atom has no meaning in terms of free-atom wave functions. Like spin it could be added on by an ad hoc procedure, but this has never been achieved beyond the qualitative level. All conventional methods of quantitative quantum chemistry endeavour to simulate atomic behaviour in terms of free-atom functions. 

In many cases, the conventional spin formulation of quantum chemistry could be replaced by a spin-free formulation using the permutation symmetry properties of a -electron system (see 12>). However, it is then necessary to have recourse to the complete theory of permutation groups. 

Implementations of the spin-free DKH Hamiltonian exist by now for many standard quantum chemistry packages like Molecule-Sweden, Columbus, Turbomole, Molcas and Nwchem. The method has also been implemented in several programs for the calculation of periodic structures, in particular crystals (Boettger 1998b Fehrenbach and Schmidt 1997 Geipel and Hess 1997). 

In our early calculations we followed the procedure outlined in Quantum Chemistry. The wavefunctions were constructed from large basis sets of eigenfunctions of S, symmetry adapted to ) . More recently we have employed the spin-free formulation. Most of the states studied are the lower states of a particular symmetry type, in which case we minimize with respect... 

Eqs. (l)-(3), (13), and (19) define the spin-free CGWB-AIMP relativistic Hamiltonian of a molecule. It can be utilised in any standard wavefunction based or Density Functional Theory based method of nonrelativistic Quantum Chemistry. It would work with all-electron basis sets, but it is expected to be used with valence-only basis sets, which are the last ingredient of practical CGWB-AIMP calculations. The valence basis sets are obtained in atomic CGWB-AIMP calculations, via variational principle, by minimisation of the total valence energy, usually in open-shell restricted Hartree-Fock calculations. In this way, optimisation of valence basis sets is the same problem as optimisation of all-electron basis sets, it faces the same difficulties and all the experience already gathered in the latter is applicable to the former. 

So far we have made no mention of relativistic effects, apart from a development in terms of pseudospinors rather than pseudoorbitals. Since the intended use of most pseudopotentials is in code based on a nonrelativistic formulation of quantum chemistry, the separation of the spin-free and spin-orbit terms is essential. Two approaches are again possible. 

---