Concise Physical Chemistry

c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

342 QUANTUM MOLECULAR MODELING

The energy output of this simplified file is the same as the more complicated

File 20.7.

TOTAL ENERGY= -1.0934083240

Optimizing from a bond length estimate that is 10% in error leads to

E =-1.0938179551

which is different by about 0.25 kcal mol−^1 (slightly lower).

Problem 20.1

Find the energy of a particle in a one-dimensional box of lengthl. by the variational

method. Take
(x)=Asinnπx/las a trial function. Note that the Hamiltonian is

−(
^2 / 2 m)(∂^2 /∂x^2 ).

Problem 20.2

Electron diffraction studies yield two different Cl Cl distances (not bonded) in 1,2-

dichloroethane CH 2 Cl CH 2 Cl. Explain why this is so. What influence does this fact

have on molecular structure and energy calculations like MM and G3(MP2)?

Problem 20.3

The benzene molecule can be modeled as a potential well with a square planar bottom

0.400 nm on each side containing six 2pπelectrons (ignoring all the other electrons

in the molecule). What is the degeneracy of the occupied orbitals and what is the

degeneracy of the first two virtual orbitals according to this model? In what respect

does this model fail to represent the true levels of the benzene molecule?

Problem 20.4

Given the model proposed in Problem 20.3, what is the minimum energy required to

promote a ground state electron to its first excited state? What is the wavelength of

electromagnetic radiation that will supply this energy? Is this in the visible region?

Is benzene colored?

Problem 20.5

(a) Add a basis function of your own to the STO-2G basis set so as to create

your personal STO-3G linear combination. Use a graphing program to plot

your function, call itφmySTO-3G=f(r). STO-3G calculations were used at

the research level until the 1990s.