Atomic functions

Once we have the measures, we have to apply them to chemical objects. Objects of interest to a chemist include molecules, reactions, mbrtures, spectra, patents, journal articles, atoms, functional groups, and complex chemical systems. Most frequently, the objects studied for similarity/dissimilarity are molecular structures. 

Substitution means the replacement of one or more hydrogen atoms in a given compound by some other kind of atom or group of atoms, functional or nonfunctional. In substitutive nomenclature, each substituent is cited as either a prefix or a suffix to the name of the parent (or substituting radical) to which it is attached the latter is denoted the parent compound (or parent group if a radical). 

Gaussian and other ab initio electronic structure programs use gaussian-type atomic functions as basis functions. Gaussian functions have the general form ... 

An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the... 

Six members of this series could be isolated in modest yields as highly air-sensitive, dark blue or dark purple crystalline solids for which analytical, spectroscopic, and single-crystal X-ray analyses were fully consistent with the side-on-biidged N2 structures shown in Scheme 102. These complexes show unusual structural features as well as a unique reactivity. An extreme degree of N = N bond elongation was manifested in rf(N-N) values of up to 1.64 A, and low barriers for N-atom functionalization allowed functionalization such as hydrogenation, hydrosilylation, and, for the first time, alkylation with alkyl bromides at ambient temperature. ... 

The beauty of bromide-mediated oxidations is that they combine mechanistic complexity with practical simplicity and, hence, utility. They involve an intricate array of electron transfer steps in which bromine atoms function as go-betweens in transfering the oxidizing power of peroxidic intermediates, via redox metal ions, to the substrate. Because the finer mechanistic details of these elegant processes have often not been fully appreciated we feel that their full synthetic potential has not yet been realized. Hence, we envision further practical applications in the future. 

The advantages of the momentum approach are not only limited to the opportunity for direct numerical calculations for chemical systems, but it also offers the prospect of selecting better bases of atomic functions on which rely almost all first principle quantum mechanical calculations. 

Relaxing the Einstein convention, sums over repeated Greek indices a = x,y,z are made explicit in this Section, to avoid misunderstanding whenever two couples of repeated indices a and / , with a < (3, appear in a formula, compare fo r (92) hereafter. Introducing a basis set x of atomic functions, for the second-order term one defines the expansion... 

Clementi, E. (1965) Tables of atomic functions, in Supplement to the paper Ab initio computations in atoms and molecules , IBMJ. Res. Develop., 9, 2-19. 

Each of these tin atoms acts as a Lewis acid, with two neighboring nitrogen atoms functioning as electron donors. The ten-membered ring folds up to generate a four-membered cycle bridged at the 1,3- and 2,4-positions. The structure, which can easily be deduced from high-resolution NMR spectra, is displayed in Fig. 14. 

Ab initio calculations usually begin with a solution of the Hartree-Fock equations, which assumes the electronic wavefunction can be written as a single determinant of molecular orbitals. The orbitals are described in terms of a basis set of atomic functions and the reliability of the calculation depends on the quality of the basis set being used. Basis sets have been developed over the years to produce reliable results with a minimum of computational cost. For example, double zeta valence basis sets such as 3-21G [15] 4-31G [16] and 6-31G [17] describe each atom in the molecule with a single core Is function and two functions for the valence s and p functions. Such basis sets are commonly used, as there appears to be a cancellation of errors, which fortuitously allows them to predict quite accurate results. 

H20, CH3OH-. . H20, CN-. . HzO, HCC-. . H20, HCOCT. . H20. The DFT(B3LYP) and the DFT(BLYP) results were in a fair agreement with the MP2 results. The root mean square deviation of the DFT and the MP2 complexation enthalpies amounted to 0.7 and 1.1 kcal/mol, for B3LYP and BLYP, respectively. From the basis set dependence of the DFT results, it was concluded that the nonlocal DFT calculations require diffuse atomic functions. 

The filled molecular orbitals beyond the crg and au that arise from combining the 2s atomic functions are (tcJ2 (-,J2 (.-r,]2. However, there is an empty antibonding orbital (designated as 7r or zr, ) on CN that can be shown as... 

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