Basis sets coupled-clusters

Fig. 1 An example of the time savings achieved when using additive corrections such as those employed in the ccCA methodology. When approximating a large basis set coupled cluster computation on the benzene molecule, a relative savings of almost two orders of magnitude in CPU time is achieved...

Evaluated with the aug-cc-pVTZ basis set. Coupled-cluster methods estimated via an addition of the difference between MP2 and coupled-cluster correlation energies with the aug-cc-pVDZ basis set to the MP2/aug-cc-pVTZ energies. 

Basis Sets Correlation Consistent Sets Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Density Functional Theory Applications to Transition Metal Problems G2 Theory Metal Complexes MpUer-Plesset Perturbation Theory Transition Metal Chemistry Transition Metals Applications. 

Cartesian coordinates system for locating points in space based on three coordinates, which are usually given the symbols x, y, z or i, j, k CBS (complete basis set) an ah initio method CC (coupled cluster) a correlated ah initio method CFF (consistent force field) a class of molecular mechanics force fields CFMM (continuous fast multipole method) a method for fast DFT calculations on large molecules... 

The structure of ozone is a well-known pathological case for electronic structure theory. Prior to the QCI and coupled cluster methods, it proved very difficult to model accurately. The following table summarized the results of geometry optimizations of ozone, performed at the MP2, QCISD and QCISD(T) levels using the 6-31G(d) basis set ... 

Specifically, if T] < 0.02, the CCSD(T) metliod is expected to give results close the full Cl limit for the given basis set. If is larger than 0.02, it indicates that the reference wave function has significant multi-determinant character, and multi-reference coupled cluster should preferentially be employed. Such methods are being developedbut have not yet seen any extensive use. 

In the next section we derive the Taylor expansion of the coupled cluster cubic response function in its frequency arguments and the equations for the required expansions of the cluster amplitude and Lagrangian multiplier responses. For the experimentally important isotropic averages 7, 7i and yx we give explicit expressions for the A and higher-order coefficients in terms of the coefficients of the Taylor series. In Sec. 4 we present an application of the developed approach to the second hyperpolarizability of the methane molecule. We test the convergence of the hyperpolarizabilities with respect to the order of the expansion and investigate the sensitivity of the coefficients to basis sets and correlation treatment. The results are compared with dispersion coefficients derived by least square fits to experimental hyperpolarizability data or to pointwise calculated hyperpolarizabilities of other ab inito studies. 

Table 3 Comparison of the dispersion coefficients for 7 and 7 for different basis sets and coupled cluster models.

If we compare results obtained with the same basis sets with the three coupled cluster models CCS, CC2 and CCSD, we find similar trends as observed in Refs. [22,45] The CCS model underestimates strongly the static hyperpolarizabilities and their dispersion. The results are usually of similar quality as those obtained with SCF. For methane, the CCS static hyperpolarizabilities are intermediate between the SCF and the CCSD values obtained in the same basis set. In Ref. [45] the CCS percentage dispersion contribution to the third harmonic generation (THG) hyperpolarizability of methane was found to be slightly smaller than for SCF, both underestimating significantly the dispersion obtained with the correlated coupled cluster models CC2 and CCSD. Accordingly the CCS dispersion coeflBcients listed in Table 3 are substantially smaller than the respective CCSD results obtained in the same basis sets. 

Comparing the last two entries in Figure 4.7, the all-electron Douglas-Kroll coupled cluster result for A te is in perfect agreement with the RPPA [156, 157]. Figure 4.8 shows the relativistic effects in dissociation energies. Here, relativistic effects are very sensitive to the level of electron correlation and basis sets used. RPPA... 

In this chapter, we will study the elementary reaction steps of these mechanisms focusing primarily on the anthraphos systems. This chapter begins with a description of the impact of different methods (coupled cluster, configuration interaction and various DFT functionals), different basis sets, and phosphine substituents on the oxidative addition of methane to a related Ir system, [CpIr(III)(PH3)Me]+. Then, it compares the elementary reaction steps, including the effect of reaction conditions such as temperature, hydrogen pressure, alkane and alkene concentration, phosphine substituents and alternative metals (Rh). Finally, it considers how these elementary steps constitute the reaction mechanisms. Additional computational details are provided at the end of the chapter. 

A. D. Boese, J. M. L. Martin, and W. Klopper, Basis set limit coupled cluster study of H bonded systems and assessment of more approximate methods. J. Phys. Chem. A 111, 11122 11133 (2007). 

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