General Description of The Theory
The complexity of equations and the corresponding computer codes, as well as the cost of the computation increases sharply with the highest level of excitation. For many applications the sufficient accuracy may be obtained with CCSD, and the more accurate (and more expensive) CCSD(T) is often called "the gold standard of quantum chemistry" for its excellent compromise between the accuracy and the cost for the molecules near equilibrium geometries. More complicated coupled-cluster methods such as CCSDT and CCSDTQ are used only for high-accuracy calculations of small molecules. The inclusion of all n levels of excitation for the n-electron system gives the exact solution of the Schrödinger equation within the given basis set, within the Born–Oppenheimer approximation (although schemes could also be drawn up to work without the BO approximation with great cost).
One possible improvement to the standard coupled-cluster approach is to add terms linear in the interelectronic distances through methods such as CCSD-R12. This improves the treatment of dynamical electron correlation by satisfying the Kato cusp condition and accelerates convergence with respect to the orbital basis set. Unfortunately, R12 methods invoke the resolution of the identity which requires a relatively large basis set in order to be a good approximation.
The coupled-cluster method described above is also known as the single-reference (SR) coupled-cluster method because the exponential ansatz involves only one reference function . The standard generalizations of the SR-CC method are the multi-reference (MR) approaches: state-universal coupled cluster (also known as Hilbert space coupled cluster), valence-universal coupled cluster (or Fock space coupled cluster) and state-selective coupled cluster (or state-specific coupled cluster).
Read more about this topic: Coupled Cluster
Famous quotes containing the words general, description and/or theory:
“What journeyings on foot and on horseback through the wilderness, to preach the gospel to these minks and muskrats! who first, no doubt, listened with their red ears out of a natural hospitality and courtesy, and afterward from curiosity or even interest, till at length there “were praying Indians,” and, as the General Court wrote to Cromwell, the “work is brought to this perfection that some of the Indians themselves can pray and prophesy in a comfortable manner.””
—Henry David Thoreau (1817–1862)
“The type of fig leaf which each culture employs to cover its social taboos offers a twofold description of its morality. It reveals that certain unacknowledged behavior exists and it suggests the form that such behavior takes.”
—Freda Adler (b. 1934)
“The great tragedy of science—the slaying of a beautiful theory by an ugly fact.”
—Thomas Henry Huxley (1825–1895)