Approximate variational coupled cluster theories
This thesis presents a new family of single-determinantal ab initio electronic structure\ud models ideal for the black-box computational investigation of molecular phenomena.\ud These theories mimic Variational Coupled Cluster and achieve an approximately\ud fulfilled variational upper bound property on the exact ground-state\ud Schrodinger energy eigenvalue, while not exceeding the limiting computational\ud complexity of the well-known CCSD method, and without sacrificing any other\ud advantageous methodological property. In particular, these Approximate Vari-\ud ational Coupled Cluster Theories are formulated through the minimization of a\ud rigorously extensive and orbitally-invariant functional that treats certain limiting\ud systems exactly. Unlike CCSD and related methods, for which it is extremely\ud problematic, these theories are highly robust to the breakdown of the Hartree-\ud Fock approximation that occurs when the single Slater determinant of minimal\ud energy becomes an inadequate qualitative description of the true electronic wavefunction.\ud Furthermore, presented results suggest that when the essential physics of\ud strong non-dynamic correlation is captured by a near-variational ansatz, remaining\ud dynamic correlation effects may be legitimately included perturbatively, with\ud implications for the design of future electronic structure models because the failure\ud of methods such as CCSD(T) to describe the dissociation of multiple bonds\ud may be ascribed to the inadequate non-variational description of the electronic\ud structure at the CCSD level, and not to a breakdown of perturbation theory;\ud Optimized-Orbital Quasi-Variational Coupled Cluster Doubles with a perturbative\ud treatment of triple excitations (OQVCCD(T)) is capable of predicting a\ud physically correct and quantitatively accurate potential energy curve for diatomic\ud nitrogen, N2, which has not been achieved, at the time of writing, by any other\ud practical (O(o2v4)-iterative O(o3v4)-non-iterative) method based on Restricted\ud Hartree-Fock theory. The method is demonstrated to be additionally suitable for\ud the black-box description of singlet multiradicals through application to model\ud hydrogen chains.
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