Coupled-cluster methods accuracy

There is a variation on the coupled cluster method known as the symmetry adapted cluster (SAC) method. This is also a size consistent method. For excited states, a Cl out of this space, called a SAC-CI, is done. This improves the accuracy of electronic excited-state energies. 

Figures 11.9 and 11.10 compare the performance of the CCSD and CCSD(T) methods, based on either an RFIF or UHF reference wave function. Compared to the RMP plot (Figure 11.7), it is seen that the infinite nature of coupled cluster causes it to perform somewhat better as the reference wave function becomes increasingly poor. While the RMP4 energy curve follows the exact out to an elongation of 1.0A, the CCSD(T) has the same accuracy out to - 1.5 A. Eventually, however, the wrong dissociation limit of the RHF wave also makes the coupled cluster methods break down, and the energy starts to decrease.

MBPT starts with the partition of the Hamiltonian into H = H0 + V. The basic idea is to use the known eigenstates of H0 as the starting point to find the eigenstates of H. The most advanced solutions to this problem, such as the coupled-cluster method, are iterative well-defined classes of contributions are iterated until convergence, meaning that the perturbation is treated to all orders. Iterative MBPT methods have many advantages. First, they are economical and still capable of high accuracy. Only a few selected states are treated and the size of a calculation scales thus modestly with the basis set used to carry out the perturbation expansion. Radial basis sets that are complete in some discretized space can be used [112, 120, 121], and the basis... 

Kowalksi K, Piecuch P (2004) New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states. J Chem Phys 120 1715-1738. 

Molecular polarizabilities and hyperpolarizabilities are now routinely calculated in many computational packages and reported in publications that are not primarily concerned with these properties. Very often the calculated values are not likely to be of quantitative accuracy when compared with experimental data. One difficulty is that, except in the case of very small molecules, gas phase data is unobtainable and some allowance has to be made for the effect of the molecular environment in a condensed phase. Another is that the accurate determination of the nonlinear response functions requires that electron correlation should be treated accurately and this is not easy to achieve for the molecules that are of greatest interest. Very often the higher-level calculation is confined to zero frequency and the results scaled by using a less complete theory for the frequency dependence. Typically, ab initio studies use coupled-cluster methods for the static values scaled to frequencies where the effects are observable with time-dependent Hartree-Fock theory. Density functional methods require the introduction of specialized functions before they can cope with the hyperpolarizabilities and higher order magnetic effects. 

Working to similar levels of accuracy, Pawlowski et al have calculated the static and frequency-dependent linear polarizability and second hyperpolarizability of the Ne atom using coupled-cluster methods with first order relativistic corrections. Good agreement with recent experimental results is achieved. Klopper et al.s have applied an implementation of the Dalton code that enables... 

The restricted-unrestricted approach (RU) in [155] has been applied to calculate the isotropic hyperfine coupling constants of a sequence of organic radicals and transition metal compounds. In the case of organic compounds, both spin-restricted and unrestricted approaches could accurately describe the isotropic hyperfine coupling constants which matched the accuracy achieved by coupled cluster methods. The situation is different for transition metal compounds for which the overall quality of the RU results is slightly better than the corresponding unrestricted results (see Table 13), independently on the exchange-correlation functional used in calculations. 

Electronic correlation in extended systems remains a central problem despite impressive progress in recent years. For small systems a number of very powerful methods have reached a high degree of accuracy thanks to a combination of formal algebraic and numerical techniques. These include configuration interaction,1-5 propagator methods,2,4 5 many-body perturbation procedures,3-5 and coupled-cluster methods.4 For extended systems density functional methods6,7 dominate the scene. Certain forms of correlation are taken into account by such methods, but how and to what extent are still unclear.8... 

A particular variant of the coupled cluster method, called Fock-space or valence-universal [49,50], gave remarkable agreement with experiment for many transition energies of heavy atoms [51]. This success makes the scheme a useful tool for reliable prediction of the structure and spectrum of superheavy elements, which are difficult to access experimentally. A brief description of the method is given below. A more flexible scheme with higher accuracy and extended applicability, the intermediate Hamiltonian Fock-space coupled cluster approach, is shown in the next section. 

Ah initio quantum chemical calculations are primarily used to describe the electronic character of individual molecules in the gas phase. Quantum chemical methods can vary widely in their accuracy, depending on the specific approximations taken. Those most applicable to the study of ionic liquids are medium level methods such as DFT and MP2 [20]. Hartree-Fock(HF) level calculations may be carried out as a starting point or to obtain geometries but should be followed by calculations that include some level of electronic correlation. Higher level methods such as Coupled Cluster methods (ie CCSD(T)) are only just accessible, and will not be routine. They do however allow for an estimation of effects hard to recover with the lower level DFT and MP2 methods, such as dispersion, more dynamic correlation, and an estimation of other neglected effects (such as the stabilization afforded by mixing in excited electronic states). The method employed (HF< DFT < MP2 < CCSD(T)) and sophistication of the basis set used are typically used to indicate the quality of an ab initio quantum chemical calculation. 

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