Hydrogen atom s orbitals

Figure 5.8 Hydrogen atom s orbitals can donate electron density to adjacent cationic centers as can heteroatoms bearing lone electron pairs.

Let me stress that k represents a funetion of position r in the 3-D spaee, only the periodicity has a 1-D character. The function is a linear eombination of the hydrogen atom s orbitals. The coefficients of the linear combination depend exclusively on the value of k. Equation (9.28) tells... 

The solution to this problem has an exceptionally important role in quantum mechanics and especially in quantum chemistry. Firstly, this is a problem that can be solved analytically (though some special mathematical functions must be used). Secondly, the solution is of great importance for chemistry where the electronic orbits arise from the solution moreover the theory of the chemical bond has been worked out using the results. Thirdly, an empirically modified hydrogen atom s orbits are widely used generally for heavier atoms because there are no other ways of achieving results. 

Atomic Orbital. A function centered on an atom. Atomic orbitals typically closely resemble the solutions to the hydrogen atom (s, p, d.type orbitals). 

Studies of the electron distributions around outer atoms consistently show that hydrogen is always associated with two electrons (one pair). All other outer atoms always have eight electrons (four pairs). The reason for this regularity is that each atom in a molecule is most stable when its valence shell of electrons is complete. For hydrogen, this requires a single pair of electrons, enough to make full use of the hydrogen 1 S orbital. Any other atom needs four pairs of electrons, the maximum number that can be accommodated by an .S p valence shell. Details of these features can be traced to the properties of atoms (Chapter 8) and are discussed further in Chapter 10. 

Methane forms from orbital overlap between the hydrogen 1 S orbitals and the s hybrid orbitals of the carbon atom. 

To visualize bond formation by an outer atom other than hydrogen, recall the bond formation in HF. One valence p orbital from the fluorine atom overlaps strongly with the hydrogen 1 S orbital to form the bond. We can describe bond formation for any outer atom except H through overlap of one of its valence p orbitals with the appropriate hybrid orbital of the inner atom. An example is dichloromethane, CH2 CI2, which appears in Figure 10-11. We describe the C—H bonds by 5 -I S overlap, and we describe the C—Cl bonds by 5 - 3 p... 

This MO can be shown to have terminal lobes of the same phase, so that overlap between the hydrogen atom s Is orbital and both the terminal lobes of (38) s MO can be maintained in the T.S. (39) ... 

The spin of the radical is characterized by two spin quantum numbers, the total spin S and the component of the total spin along the z-axis M. The simplest type of radical has one unpaired electron, and hence S = and M = , where the sign of M indicates the orientation of the electron spin in the z-direction. The dissociated singlet molecule, described by the N + l)-electron wavefunction, consists of the radical and a hydrogen atom in orbital (j) at infinity, ... 

Similarly, in hydrogen cyanide, HCN, we assume that the carbon is sp-hybridized, since it is combined with only two other atoms, and is hence in a divalent state. One of the sp-hybrid orbitals overlaps with the hydrogen 1 s orbital, while the other overlaps end-to-end with one of Vr VP VP the three unhybridized p orbitals of the nitrogen atom. 

When one (or more) hydrogen atom(s) of the polyethylene monomeric unit is (are) replaced by a heteroatom, an aliphatic or an aromatic group, modifications are induced in the valence band spectrum new peaks, band shift and/or splitting, redistribution of the electronic population among the molecular orbitals will denote the new bonds created in the molecule. Similar effects will be observed for the insertion of heteroatom(s) between two carbon elements of the polymer skeleton. 

The value of an ns orbital close to the nucleus is higher than that of an np orbital of the same atom s orbitals are more penetrating than p orbitals of equal quantum munber n (recall that p orbitals have a node at the position of the nucleus). As a consequence, there is more negative charge to be taken into account for efifect (b) in the case of a p orbital. The same is true of d orbitals with respect to p orbitals of equal n. Figure 5.4 shows the radial probability distributions of the degenerate hydrogen-like 3s, 3p and 3d orbitals for the potassium atom. 

Identify the relationships among a hydrogen atom s energy levels, sublevels, and atomic orbitals. 

What sublevels are contained in the hydrogen atom s first four energy levels What orbitals are related to each s suhlevel and each p sublevel ... 

As you have seen, the Schrodinger equation may be written in spherical polar coordinates using the usual transformation. As a result, we can write a radial part and an angular part for the wavefunction ik. As an example, let s look at the wavefunction for the Is and 2pz orbitals in the hydrogen atom. These orbitals have the quantum numbers n = 1, l = 0, mg = 0 and n = 2, = 1, mg = 0, respectively. 

---