CCSD-T technique

This same quantity was calculated also using a coupled-cluster method, which includes single and double excitations, and a triple-excitation correction, the so-called CCSD-T technique. The results were found to be quire similar to the MP4 values for each basis set examined. The authors suggest that because of the small contributions from infinite summations, SDTQ-MBPT(4) is much more cost effective than is CCSD-T. 

The development of correlation schemes at the highest levels of theory (the CCSD(T) technique) allowed for very accurate DCB predictions of atomic properties for the heaviest elements up to Z=122 (see Chapter 2 in this book). Reliable electronic configurations were obtained assuring the position of the superheavy elements in the Periodic Table. Accurate ionization potentials, electron affinities and energies of electronic transitions (with the accuracy of below 0.01 eV) are presently available and can be used to assess the similarity between the heaviest elements and their lighter homologs in the Periodic Table. 

The only generally applicable methods are CISD, MP2, MP3, MP4, CCSD and CCSD(T). CISD is variational, but not size extensive, while MP and CC methods are non-variational but size extensive. CISD and MP are in principle non-iterative methods, although the matrix diagonalization involved in CISD usually is so large that it has to be done iteratively. Solution of the coupled cluster equations must be done by an iterative technique since the parameters enter in a non-linear fashion. In terms of the most expensive step in each of the methods they may be classified according to how they formally scale in the large system limit, as shown in Table 4.5. 

There are many computational investigations of transition metal oxides, see, e.g., the recent review by Harrison [7]. Some studies have included the whole sequence of 3d metal oxides. In one of these studies, Bauschlicher and Maitre [17], employed different high-level ab initio methods. It was found that ScO - MnO and CuO were well described by single-reference based techniques and that the CCSD(T) method gave spectroscopic constants (re, uje and D0) in good agreement with experiments. For FeO - NiO multi-reference based techniques (CASSCF/ICACPF) were necessary to get good results. 

Instead, practical methods involve a subset of possible Slater determinants, especially those in which two electrons are moved from the orbitals they occupy in the HF wavefunction into empty orbitals. These doubly excited determinants provide a description of the physical effect missing in HF theory, correlation between the motions of different electrons. Single and triple excitations are also included in some correlated ab initio methods. Different methods use different techniques to decide which determinants to include, and all these methods are computationally more expensive than HF theory, in some cases considerably more. Single-reference correlated methods start from the HF wavefunction and include various excited determinants. Important methods in inorganic chemistry include Mpller-Plesset perturbation theory (MP2), coupled cluster theory with single and double excitations (CCSD), and a modified form of CCSD that also accounts approximately for triple excitations, CCSD(T). 

On the theoretical side the H20-He systems has a sufficiently small number of electrons to be tackled by the most sophisticated quantum-chemical techniques, and in the last two decades several calculations by various methods of electronic structure theory have been attempted [77-80]. More recently, new sophisticated calculations appeared in the literature they exploited combined symmetry - adapted perturbation theory SAPT and CCSD(T), purely ab initio SAPT [81,82], and valence bond methods [83]. A thorough comparison of the topology, the properties of the stationary points, and the anisotropy of potential energy surfaces obtained with coupled cluster, Moller-Plesset, and valence bond methods has been recently presented [83]. 

The exponential ansatz given in Eq. [31] is one of the central equations of coupled cluster theory. The exponentiated cluster operator, T, when applied to the reference determinant, produces a new wavefunction containing cluster functions, each of which correlates the motion of electrons within specific orbitals. If T includes contributions from all possible orbital groupings for the N-electron system (that is, T, T2, . , T ), then the exact wavefunction within the given one-electron basis may be obtained from the reference function. The cluster operators, T , are frequently referred to as excitation operators, since the determinants they produce from fl>o resemble excited states in Hartree-Fock theory. Truncation of the cluster operator at specific substi-tution/excitation levels leads to a hierarchy of coupled cluster techniques (e.g., T = Ti + f 2 CCSD T T + T2 + —> CCSDT, etc., where S, D, and... 

The designed molecular complexes of the reactants, products, and transition states were optimized using the Becke3LYP functional of the DFT technique and the COSMO method. The used basis set is the same as in the previous in vacuo model. The single point energy determination was performed with the CCSD(T) method and the 6-31++G(d,p) basis set within the COSMO formalism. The active space contained all of the orbitals except those belonging to frozen core electrons (Is of the O and N atoms inner electrons of Pt and Cl were covered within the ECP approach). 

---