Orbital-optimized coupled-cluster

Even though computers were an essential tool in quantum chemical calculations, the main challenge was the further development of methods and concepts to describe even more facets of chemistry and with higher accuracy. Methods that account for electron correlation were extended to be able to describe energy surfaces more reliably. Several variants of the CEPA Ansatz (CEPA-1, CEPA-2) were developed as well as the method of self-consistent electron pairs (SCEP). Formulations using canonical or localized orbitals (e.g., pair natural orbitals, PNO, as a kind of optimized virtual orbitals) were put forth. These methods were extensively used for two decades, primarily in Germany, until coupled cluster formulations became more popular. ... 

G. E. Scuseria and H. F. Schaefer, Chem. Phys. Lett., 142, 354 (1987). The Optimization of Molecular Orbitals for Coupled Cluster Wavefunctions. 

Such a basis set combines well with coupled-cluster wave functions to tend to converge in a consistent and predictable manner towards limits of the basis set and the theory. Calculation of the rotational g tensor and magnetizability involved use of rotational London orbitals [10]. Optimization, first order in derivatives of energy with respect to internuclear distances, yielded all reported geometric stmctures of... 

One of the main advantages of the Monte Carlo method of integration is that one can use any computable trial function, including those going beyond the traditional sum of one-body orbital products (i.e., linear combination of Slater determinants). Even the exponential ansatz of the coupled cluster (CC) method [27, 28], which includes an infinite number of terms, is not very efficient because its convergence in the basis set remains very slow. In this section we review recent progress in construction and optimization of the trial wavefunctions. 

Adamowicz, L. (2010). Optimized virtual orbital space (OVOS) in coupled-cluster calculations. Mol Phys. 108, pp. 3105-3112, doi 10.1080/ 00268976.2010.520752. 

There are numerous alternative methods that introduce electron correlation in the molecular calculations at a more precise level that can be profitably used. We mention here the MC-SCF approach (the acronym means that this is a variant of HF (or SCF) procedure starting fi om the optimization no more of a single antisymmetric orbital product, but of many different products, or configurations), the Coupled-Cluster theory, etc., all methods based on a MO description of single-electron functions. 

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