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45403-AC6
Development of Partially Spin-Restricted Geminal Model for Studies of Transition Metal Compounds
The work on partial spin restriction is a part of long term research in formulation and implementation of computationally inexpensive model that incorporates important multireference effects. We construct such a model out of correlated two-electron functions, or geminals.
The geminal model developed prior to this grant was used in either spin-restricted, or spin-unrestricted formulations. Unfortunately, either one was found to be not accurate enough for the description of transition metal compounds. We have realized that geminal framework enables formulation of an intermediate case of partial spin restriction. The developed mathematical formalism reveals that partial spin restriction is a natural way to couple spins in geminal functions. We therefore argue that partial spin restriction should be used in generalized valence bond (GVB) functions. It is computationally inexpensive, and it reduces spin contamination of optimized wavefunctions. Combined with perturbative treatment of dynamic correlation, it yields a model that describes transition metal hydrides with the accuracy comparable to the accuracy of main group hydrides. Analysis of perturbative amplitudes shows that partially spin restricted geminal wavefunction incorporates all leading multireference effects.
Next, we realized that it is possible to eliminate remaining spin contamination in variational, size consistent, and computationally inexpensive way. This is due to localization of spin contamination on individual geminals. It enables the grouping of all possible spin couplings in the reference wavefunction (an exponentially large space) into a much smaller polynomial space of basis functions relevant for spin pure wavefunctions. While each basis function may contain a very large number of terms, there exist a computationally straightforward procedure to evaluate all relevant matrix elements for one- and two-electron operators.
We have coded the procedure into a development version of Q-Chem program and applied it to a set of chemically relevant models (a hydrogen cluster, FeH diatomic, O2 molecule, and bond-breaking in carbon monoxide). The model is shown to purify even strong spin contamination varitaionally. Interestingly, in the case of H4 cluster in square configuration it yields delocalized geminals that, combined with spin purification procedure, reproduce the exact wavefunction.
The partially spin restricted geminal model combined with spin purification procedure it, to our knowledge, the only one that yield pure spin wavefunctions in a rigorously size consistent way. Together with better than O(N5) scaling with system size and absence of adjustable parameters, it has a promising future in computational chemistry.
The spin purification procedure is computationally inexpensive, which prompts us to focus on partial re-optimization of spin-purified wavefunctions. We plan to complete this work in the second year of this grant, and to test it on the wide range of chemical systems, with the focus on transition metal chemistry.
