Atoms electron distribution

In quantum mechanics, we think of each atom or molecule as having its own wave functions that describe the distribution of its electrons. The expected basis of interaction is that two atoms or molecules react to each other as dipoles, each atom s or molecule s dipolar electric field shining out as 1/r3 with distance r from the center. This dipole interaction averages to zero when taken over the set of electron positions predicted for the isolated atoms. However, when the isolated-atom electron distributions are... 

As was emphasized before (cf. Chapter 3), a molecule is not simply a collection of its constituting atoms. Rather, it is a system of atomic nuclei and a common electron distribution. Nevertheless, in describing the electronic structure of a molecule, the most convenient way is to approximate the molecular electron distribution by the sum of atomic electron distributions. This approach is called the linear combination of atomic orbitals (LCAO) method. The orbitals produced by the LCAO procedure are called molecular orbitals (MOs). An important common property of the atomic and molecular orbitals is that both are one-electron wave functions. Combining a certain number of one-electron atomic orbitals yields the same number of one-electron molecular orbitals. Finally, the total molecular wave function is the... 

Because of the proton s chemical importance and its favorable characteristics for NMR detection, the overwhelming bulk of experimental investigation and correlation of chemical shifts has been centered on the proton. However, the situation regarding the determination of proton shielding anisotropies has been unsatisfactory in many respects. Similarly, the field of ab initio theoretical calculations of proton shielding tensors has, until very recently, enjoyed little success. Both these factors are related to the fact that the proton chemical shifts are comparatively small and hence influenced strongly by secondary factors such as neighboring-atom electron distribution and medium effects. 

A molecule is defined as a system of atomic nuclei and a common electron distribution. However, describing the electronic structure of molecules is done by approximating the molecular electron distribution by the sum of atomic electron distributions. This approach is known as the Linear combination of atomic orbitals... 

The same periodic function results from optimization on a golden spiral with a variable convergence angle of Art In — 1), which describes a spherical standing wave with nodes at n. Analysis of the wave structure shows that it correctly models the atomic electron distribution for all elements as a function of the golden ratio and the Bohr radius, uq. Normalization of the wave structure into uniform spherical units simulates atomic activation, readily interpreted as the basis of electronegativity and chemical affinity. 

The atomic scattering factors are the Fourier transforms of the spherical atomic electron distributions. They are considered as known from quantum-chemical calculations. The site occupation parameters may assume values different from unity if the structure is disordered. The Debye-Waller factors allow for the atomic thermal motions. They are functions of the atomic displacement parameters W. Omitting the atom index n and representing the Miller indices and lengths of the reciprocal lattice vectors by and a, respectively ... 

We note thaL for molecular systems, the atomic electron distributions are largely unaffected by the formation of chemical bonds. We may therefore first concentrate our attention on atomic systems, seeking a set of simple analytical functions suitable for expansions of orbitals in many-electron atoms. Once such functions have been found, we may generalize our procedure to polyatomic molecules by introducing a separate basis of AOs for each atom in the molecule, being careful to include in our basis any additional functions that may be needed to describe the molecular bonding. 

To complete the construction of the STO-fcG basis sets, we must specify the Slater exponents to be used for the orbitals. One solution would be to use exponents optimized in separate atomic calculations for each STO-AG set. The resulting exponents are similar for all k and also close to the exponents of Clementi and Raimondi (5.67 for Is, 1.61 for 2s and 1.57 for 2p in the carbon atom), optimized for single STOs in atoms [2], In practice, for the first-row atoms, the atomic exponents of Clementi and Raimondi are used for the K shell. For the L shell, however, a set of standard molecular exponents (obtained from calculations on small molecules) is used - recognizing that, in a molecular environment, the optimum exponents for the valence shells differ somewhat from their atomic values. For the carbon atom, an exponent of 1.72 is used for the 2s and 2p orbitals. For the hydrogen Is orbital, the exponent is 1.24. Thus, the hydrogen exponent differs substantially from its atomic value, reflecting a significant contraction of the atomic electron distribution in a molecular environment. 

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