Physical Chemistry , 1st ed.

Example 13.11 Determine whether the following integrals are exactly zero or might be nonzero strictly from symmetry consideratio ...

Solution The following table is taken from the Rh(3)character table: EC iS   1 sDg(0) 1 1 1 1 1  2 sDg(0) 1 1 1 1 1 EM o ...

Character tables and the GOT are crucial elements in determining a proper SALC of atomic orbitals. The first step is to identify ...

Do this for all irreducible representations of the point group. This will yield a large number of linear combinations. Inspect ...

A 1 ^14 (2sO 2 sO 2 sO 2 sO) A 1  4 1 (2px,O 2 px,O 2 px,O 2 px,O) A 1 ^14 (2py,O^2 py,O^2 py,O^2 py,O) A ...

where the individual hydrogens andtheir electrons are labeled as either 1 or 2. (It is important to keep track of the labels 1 a ...

overall antisymmetric wavefunction. The following summarizes the properties, which can easily be verified: spatial 1 2 [1sH1(1 ...

is not a bad approximation.) For the energy of the ground state of H 2 ,one needs to evaluate EH 2 ^12  6 [1sH1(1)  1 sH2(2) ...

wavefunctions are different. The integrals involve not only electron 1 on H1 and electron 2 on H2, but electron 1 on H2and elect ...

makes use of atomic orbitals of the valence-bonding sort. We will assume dur- ing this discussion that the bonding that occurs b ...

The wavefunction  1 is a hybrid orbital, composed of one part sorbital and three parts porbital. The other three hybrid orbital ...

These three orbitals have the relative spatial orientation shown in Figure 13.25. They are all in the same plane and make 120° a ...

for a pure sp^3 hybrid orbital). However, in most cases a “pure” hybrid orbital can be assumed and acts as a good enough approxi ...

bitals onto each other (for an overall contribution of 0). The total contribu- tion to the character is 2, so that d2. The co ...

Therefore, the four sp^3 hybrid orbitals can bond with any other molecular or- bital or set of molecular orbitals that have eith ...

13.1.In your own words, explain why an object that has more symmetry elements is said to have “higher symmetry” than an object w ...

13.20.Identify the point group of the wavefunctions of the following molecules. (a)Hydrogen chloride, HCl (b)Sulfur dioxide, SO ...

13.7 Great Orthogonality Theorem 13.39.Reduce the following reducible representations using the great orthogonality theorem. (a) ...

13.60.Using an appropriate software graphics package, in- put the forms of the sand phydrogen-like wavefunctions (from Chapter 1 ...

14 461461 V IRTUALLY EVERYTHING WE KNOW about matter comes from the interaction of matter with electromagnetic radiation. In its ...