Morokuma scheme

One method that has proven to be particularly useful for the analysis of molecule/surface interactions is the constrained space orbital variation (CSOV) scheme originally proposed by Bagus and Hermann [30,31]. As does the Morokuma scheme, it allows for a decomposition of the total SCF or DFT interaction energy into its different contributions by calculating only energy quantities, and not as do most other decomposition schemes by analyzing electronic densities or wave functions. The CSOV analysis consists of several consecutive steps which can be roughly characterized as follows ... 

In the original Morokuma scheme [15], the matrix of Hamiltonian interaction elements (Fock matrix) and the overlap matrix in the secular equation ... 

Two possible routes are envisioned for X = B in Scheme 7-21. The authors favored a path involving the oxidative addition of the S-B bond to Pd(0), insertion of the alkyne into the Pd-S bond followed by C-B bond-forming reductive elimination. On the other hand, Morokuma et al. studied the mechanism of the addition of HSB(0CH2)2 (99) to acetylene (C2H2) using Pd(PH3)2 (100) as a catalyst to produce 101 using hybrid density functional calculations (Eq. 7.62) [5]. 

Scheme 8-2 Intermediate in the hydrozirconation of ethylene proposed by Morokuma and coworkers based on ah initio MO calculations...

Kitaura K, Morokuma K (1976) A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation. Int J Quantum Chem 10 325... 

The theoretical studies were carried out employing the ONIOM scheme developed by Morokuma and collaborators (18). This approach can be of great... 

Early determinations of RSE values employed unrestricted Hartree-Fock (UHF) theory in combination with 3-21G [9] or 4-31G [10] basis sets to evaluate the RSE according to Eq. 1. The appropriate consideration of correlation effects, the avoidance of spin contamination, and the treatment of thermochemical corrections have in detail been studied in the following, in particular by Bauschlicher [11], Coote [12-14], Morokuma [15-18], and Radom [19-25]. Highly accurate RSE and BDE results can be obtained with high level compound methods such as the G2 [26-30] and G3 [31-34] schemes (and variants thereof [11,15-18]), as well as extrapolation methods such as the CBS schemes [35,36], Wl, or W2 [37-39]. Generally, the accurate... 

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

Subsequently, Humbel, Sieber, and Morokuma (1996) generalized the IMOMM optuniza-tion scheme to the case where two different levels of QM theory were used instead of a QM/MM approach, and Svensson, Humbel, and Morokuma (1996) examined the relative efficacy of different combinations of levels for prototype problems. Corchado and Truhlar (1998) later proposed a refinement of that methodology to improve computed vibrational frequencies and Rickard et al. (2003) showed that a combination of MP2 and HF theories permits the calculation of high-quality NMR chemical shifts within the high-level system. 

K. Kitaura and K. Morokuma, Int.. Quantum Chem., 10, 325 (1976). A New Energy Decomposition Scheme for Molecular Interactions Within the Hartree-Fock Approximation. 

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