Coupled-cluster calculations

Coupled cluster calculations are similar to conhguration interaction calculations in that the wave function is a linear combination of many determinants. However, the means for choosing the determinants in a coupled cluster calculation is more complex than the choice of determinants in a Cl. Like Cl, there are various orders of the CC expansion, called CCSD, CCSDT, and so on. A calculation denoted CCSD(T) is one in which the triple excitations are included perturbatively rather than exactly. 

Coupled cluster calculations give variational energies as long as the excitations are included successively. Thus, CCSD is variational, but CCD is not. CCD still tends to be a bit more accurate than CID. 

The accuracy of these two methods is very similar. The advantage of doing coupled cluster calculations is that it is a size extensive method (see chapter 26). Often, coupled-cluster results are a bit more accurate than the equivalent... 

Correlated calculations, such as configuration interaction, DFT, MPn, and coupled cluster calculations, can be used to model small organic molecules with high-end workstations or supercomputers. These are some of the most accurate calculations done routinely. Correlation is not usually required for qualitative or even quantitative results for organic molecules. It is needed to obtain high-accuracy quantitative results. 

Since the singly excited determinants effectively relax the orbitals in a CCSD calculation, non-canonical HF orbitals can also be used in coupled cluster methods. This allows for example the use of open-shell singlet states (which require two Slater determinants) as reference for a coupled cluster calculation. 

Hess, B.A. and Kaldor, U. (2000) Relativistic all-electron coupled-cluster calculations on Au2 in the framework of the Douglas—Kroll transformation. Journal of Chemical Physics, 112, 1809-1813. 

Wesendrup, R., Laerdahl, J.K and Schwerdtfeger, P. (1999) Relativistic Effects in Gold Chemistry. VI. Coupled Cluster Calculations for the Isoelectronic Series AuPt , Au2 and AuHg. Joumul of Chemical Physics, 110, 9457-9462. 

Seth, M., Cooke, F., Pehssier, M., Heully J.-L. and Schwerdtfeger, P. (1998) The Chemistry of the Superheavy Elements II. The Stability of High Oxidation States in Group 11 Elements. Relativistic Coupled Cluster Calculations for the Fluorides of Cu, Ag, Au and Element 111. Journal of Chemical Physics, 109, 3935—3943. 

Botschwina, P, 1998, The Saddle Point of the Nucleophilic Substitution Reaction Cl- + CH3C1 Results of Large-Scale Coupled Cluster Calculations , Theor. Chem. Acc., 99, 426. 

Gauss, J., Stanton, J. F., 1996, Perturbative Treatment of Triple Excitations in Coupled Cluster Calculations of Nuclear Magnetic Shielding Constants , J. Chem. Phys., 104, 2574. 

The tautomerism of furoxan (l,2,5-oxadiazole-2-oxide) has been investigated by different computational methods comprising modern density functions as well as single-reference and multi-reference ab initio methods. The ring-opening process to 1,2-dinitrosoethylene is the most critical step of the reaction and cannot be treated reliably by low-level computations (Scheme 2). The existence of cis-cis-trans- 1,2-dinitrosoethylene as a stable intermediate is advocated by perturbational methods, but high-level coupled-cluster calculations identify this as an artifact <2001JA7326>. 

In Table 5 the insertion barrier at levels of theory higher than MP2 are also reported (runs 10-13). The MP3 and MP4 insertion barriers are both remarkably higher than the MP2 barrier. The CCSD insertion barrier also is quite larger than the MP2 barrier (5.2 kcal/mol above), but the perturbative inclusion of triple excitations in the couple cluster calculations reduces considerably the CCSD barrier, which is 8.7 kcal/mol (3.1 kcal/mol above the MP2 insertion barrier). The insertion barriers reported in Table 5 can be used to obtain a further approximation of the insertion barrier. In fact, the CCSD(T) barrier of 8.7 kcal/mol should be lowered by roughly 3 kcal/mol if... 

Single point coupled cluster calculations with inclusion of single, double and perturbatively connected triple excitations, CCSD(T) [102, 103], were performed on the B3LYP geometries. 

The prerequisites for high accuracy are coupled-cluster calculations with the inclusion of connected triples [e.g., CCSD(T)], either in conjunction with R12 theory or with correlation-consistent basis sets of at least quadruple-zeta quality followed by extrapolation. In addition, harmonic vibrational corrections must always be included. For small molecules, such as those contained in Table 1.11, such calculations have errors of the order of a few kJ/mol. To reduce the error below 1 kJ/mol, connected quadruples must be taken into account, together with anhar-monic vibrational and first-order relativistic corrections. In practice, the approximate treatment of connected triples in the CCSD(T) model introduces an error (relative to CCSDT) that often tends to cancel the... 

Another approach of this kind uses the approximate Brueckner orbitals from a so-called Brueckner doubles, coupled-cluster calculation [39, 40]. Methods of this kind are distinguished by their versatility and have been applied to valence ionization energies of closed-shell molecules, electron detachment energies of highly correlated anions, core ionization... 

The coupled cluster calculations involved in Wlc theory were carried out using MOLPRO 2002.3. (7P) (For the open-shell calculations on the constituent atoms, the definition of the open-shell CCSD and CCSD(T) energies in Ref. (20) was employed.) The density functional calculations were carried out using a modified version of Gaussian 98 rev. All (27), as were the Gn theory (22-24) and CBS-n (25) calculations. 

Recent microwave data for the potential interstellar molecule Sis is used together with high-level coupled-cluster calculations to extract an accurate equilibrium structure. Observed rotational constants for several isotopomers have been corrected for effects of vibration-rotation interaction subsequent least-squares refinements of structural parameters provide the equilibrium structure. This combined experimental-theoretical approach yields the following parameters for this C2v molecule re(SiSi) = 2.173 0.002A and 0e(SiSiSi) = 78.1 O.2 ... 

Noga, J., Valiron, P. Explicitly correlated R12 coupled cluster calculations for open shell systems. Chem. Phys. Lett. 2000, 324, 166-74. 

In order to use wave-function-based methods to converge to the true solution of the Schrodinger equation, it is necessary to simultaneously use a high level of theory and a large basis set. Unfortunately, this approach is only feasible for calculations involving relatively small numbers of atoms because the computational expense associated with these calculations increases rapidly with the level of theory and the number of basis functions. For a basis set with N functions, for example, the computational expense of a conventional HF calculation typically requires N4 operations, while a conventional coupled-cluster calculation requires N7 operations. Advances have been made that improve the scaling of both FIF and post-HF calculations. Even with these improvements, however you can appreciate the problem with... 

Curve 1(c) shows the results of a rather accurate coupled-cluster calculation, while Ciurve (d) shows those of full Cl calculations [10] (for all electrons outside a frozen Is core), in which about 250 000 Slater determinants were employed. 

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