Molecules many-electron, application

Noncovalent interactions such as van der Waals, hydrogen bonding, n-n stacking and electrostatic interactions have been widely used to hybridize pristine nanocarbons via ex situ approaches. The major advantage of this route is that the nanocarbons do not require modification prior to hybridization and their structure remains undisturbed, an important factor in many electronic applications. The strength of hybridization is weaker compared to covalent interactions but the synthetic process is generally simpler. Noncovalent attachment of small molecules to nanocarbons is often used to change the surface chemistry for subsequent ex situ or in situ hybridization. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

The well balanced electronic and coordinative unsaturation of their Ru(II) center accounts for the high performance and the excellent tolerance of these complexes toward an array of polar functional groups. This discovery has triggered extensive follow up work and carbenes 1 now belong to the most popular metathesis catalysts which set the standards in this field [3]. Many elegant applications to the synthesis of complex target molecules and structurally diverse natural products highlight their truely remarkable scope. 

Reduced-Density-Matrix Mechanics. With Application to Many-Electron Atoms and Molecules,... 

D. A. Mazziotti, Variational reduced-density-matrix method using three-particle N-represent-ability conditions with application to many-electron molecules. Phys. Rev. A 74, 032501 (2006). 

D. A. Mazziotti, First-order semidefinite programming for the direct determination of two-electron reduced density matrices with application to many-electron atoms and molecules. J. Chem. Phys. 121, 10957 (2004). 

T. Yanai and G. K. L. Chan, Canonical transformation theory for dynamic correlations in multireference problems, in Reduced-Density-Matrix Mechanics With Application to Many-Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134 (D.A. Mazziotti, ed.), Wiley, Hoboken, NJ, 2007. 

J. Paldus, J. Cizek, and 1. Shavitt, Correlation problems in atomic and molecular systems. IV. Extended coupled-pair many-electron theory and its application to the BHs molecule. Phys. Rev. A 5, 50 (1972). 

REDUCED-DENSITY-MATRIX MECHANICS WITH APPLICATION TO MANY-ELECTRON ATOMS AND MOLECULES... 

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