Ab-initio calculation of energy

Ab initio calculation of energy changes accompanying distortions of the dioxathiaazapentalene cation (8) showed structure (8) not to have the lowest energy but to be rather a transition state between the two valence bond structures (9) and (10). This process corresponds to an in-plane bend parallel to the 3c,4e-hypervalent bond at sulfur. An out-of-plane bend about the SN bond also leads to an energy minimum but this is at a much higher level and is therefore less realistic <91PS(55)35>. 

Ab initio calculation of energy changes accompanying distortions of the dioxathiaazapentalene cation showed structure (254) to be a transition state between the two valence bond structures (253a) and (253b). 

This chapter deals with silyl-substituted carbocations. In Section II results of quantum chemical ab initio calculations of energies and structures of silyl-substituted carbocations are summarized1. Throughout the whole chapter results of ab initio calculations which relate directly to the experimental observation of silyl-substituted carbocations and their reactions are reviewed. Section m reports on gas phase studies and Section IV on solvolytic investigations of reactions which involve silyl-substituted carbocation intermediates and transition states. Section V summarizes the structure elucidation studies on stable silyl-substituted carbocations. It includes ultra-fast optical spectroscopic methods for the detection of transient intermediates in solution, NMR spectroscopic investigations of silyl-substituted carbocations in superacids and non-nucleophilic solvents, concomitant computational studies of model cation and X-ray crystallography of some silyl-substituted carbocations which can be prepared as crystals of salts. 

The key process in the HF ab initio calculation of energies and wavefunctions is calculation of the Fock matrix, i.e. of the matrix elements Frs (Section 5.2.3.6.2). Equation (5.63) expresses these in terms of the basis functions and the operators //core, J and K, but the J and K operators (Eqs. 5.28 and 5.31) are themselves functions of the MO s i// and therefore of the c s and the basis functions Fock matrix to be efficiently calculated from the coefficients and the basis functions without explicitly evaluating the operators J and K after each iteration. This formulation of the Fock matrix will now be explained. 

The ab initio calculations of energy on fully minimized structures give high accuracy with the basis sets employed. However, one must simplify the system in order to conserve computer time in a judicious manner so as to preserve the main features of interest. It would be prohibitive in time to compute the structure of Q and R and their exchange intermediates. It took about 35-40 hours of actual supercomputer time to obtain the results for the saturated five- and six-... 

The two current ways of carrying out the "direct" ab initio calculations of energies or forces have come to be known as the "frozen phonon" method and the force constant method. In the former approach, the atoms are displaced in a given phonon mode and the phonon frequency is calculated either form the energy E = (i/2)kx2 or the force F= -kx. In this case both E and F provide exactly equivalent information and Frozen phonon calculations have prooved very successful and have been applied to many modes in Ge, GaAs, ... 

AB INITIO CALCULATIONS OF ENERGIES FOR CONVERSIONS OF NITROGEN DIOXIDE DIMMERS... 

Stumpf, R. and SchefBer, M. (1996). Ab initio calculations of energies and selfdiffusion on flat and stepped surfaces of A1 and their unphcations on crystal growth, Phys. Rev. B 53, 4958-4973. 

Several studies have been made by Vanderbilt et al. [17] on Ihe ab initio calculation of energy of the domain wall having a narrow width of Ihe... 

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