S-atomic orbitals

In Chapter 3,1 discussed the construction of simple LCAO-MOs for the hydrogen fflolecule-ion, starting from 1 s atomic orbitals on the hydrogen centres. Thus, we constructed LCAO-MO approximations to the two lowest energy molecular orbitals as... 

Figure 1.17 Molecular orbitals of H2- Combination of two hydrogen 1 s atomic orbitals leads to two H2 molecular orbitals. The lower-energy, bonding MO is filled, and the higher-energy, antibonding MO is unfilled.

Electron density plots for the 1, 2, and 3 S atomic orbitals of the hydrogen atom. The vertical... 

As two hydrogen atoms approach each other, the overlap of their 1 S atomic orbitals increases. The wave... 

A pair of sp hybrid orbitais forms by interacting an s atomic orbital and one p atomic orbital. The two hybrids point in opposite directions. 

A cr orbital can be formed either from two s atomic orbitals, or from one s and one p atomic orbital, or from two p atomic orbitals having a collinear axis of symmetry. The bond formed in this way is called a a bond. A n orbital is formed from two p atomic orbitals overlapping laterally. The resulting bond is called a n bond. For example in ethylene (CH2=CH2), the two carbon atoms are linked by one a and one n bond. Absorption of a photon of appropriate energy can promote one of the n electrons to an antibonding orbital denoted by n. The transition is then called Ti —> 7i. The promotion of a a electron requires a much higher energy (absorption in the far UV) and will not be considered here. 

Principle quantum number n Orbital angular momentum quantum number / Magnetic quantum number nil Spin quantum number s Atomic orbital designation... 

Figure 2.7 The (top) a1 and (bottom) b2 group orbitals formed from the 1 s atomic orbitals of the two hydrogen atoms of the water molecule...

Figure 3.6 The molecular orbital diagram for the combination of two identical 1 s atomic orbitals...

The molecule of hydrogen fluoride, HF, belongs to the Coov point group. The hydrogen atom uses its 1 s atomic orbital to make bonding and antibonding combinations with the 2pz orbital of the fluorine atom, the z... 

The values of ioni/ulion energies and atomic sizes are influenced by retain islic dlccls that, for valence electrons, increase with the value of 1 /. and become sufficiently important in the elements of the 6lh period (C s Rn) to explain largely their chemical differences from the elements of the 5lli period (Rh- Xe). The initial relativistic effect is to cause a decrease in the radius of the 1 s atomic orbital of Ihe atom. The I mass of the electron in the Is orbital becomes higher as the nuclear charge increases because the velocity of the electron increases. 

Work through the Molecular Orbital Theory tutorial in eChapter 7.13, which illustrates the formation of sigma molecular orbitals from s atomic orbitals, p Orbitals will also form sigma orbitals when they overlap head-on. Follow the examples given for the s orbitals and predict how p orbitals will form sigma molecular orbitals. 

For the integrations in ab initio calculations we need the actual mathematical form of the spatial functions, and the hydrogenlike expressions are Slater functions [1]. For atomic and some molecular calculations Slater functions have been used [3]. These vary with distance from where they are centered as exp(-constant.r), where r is the radius vector of the location of the electron, but for molecular calculations certain integrals with Slater functions are very time-consuming to evaluate, and so Gaussian functions, which vary as exp(-constant.r2) are almost always used a basis set is almost always a set of (usually linear combinations of) Gaussian functions [4]. Very importantly, we are under no theoretical restraints about their precise form (other than that in the exponent the electron coordinate occurs as exp(-constant.r2)). Neither are we limited to how many basis functions we can place on an atom for example, conventionally carbon has one 1 s atomic orbital, one 2s, and three 2p. But we can place on a carbon atom an inner and outer Is basis function, an inner and outer 2s etc., and we can also add d functions, and even f (and g ) functions. This freedom allows us to devise basis sets solely with a view to getting... 

Baetzold used extended Hiickel and complete neglect of differential overlap (CNDO) procedures for computing electronic properties of Pd clusters (102, 103). It appeared that Pd aggregates up to 10 atoms have electronic properties that are different than those of bulk palladium. d-Holes are present in small-size clusters such as Pd2 (atomic configuration 4dw) because the diffuse s atomic orbitals overlap strongly and form a low-energy symmetric orbital. In consequence, electrons occupy this molecular orbital, leaving a vacant d orbital. For a catalytic chemist the most important aspect of these theoretical studies is that the electron affinity calculated for a 10-atom Pd cluster is 8.1 eV. This value, compared to the experimental work function of bulk Pd (4.5 eV), means that small Pd clusters would be better than bulk metal as electron acceptors. 

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