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CHEM 550 Problem Set 7: Hartree-Fock Method, Spin Functions, and Atomic Spectroscopy - Pro, Assignments of Quantum Chemistry

University of Washington (UW) - SeattleQuantum Chemistry
Prof. David Ginger Jr

Problem set 7 for a chemistry course, which includes exercises on the hartree-fock method, spin functions, and atomic spectroscopy. Students are asked to write out wave functions for the first excited state of he atom, calculate the field strength of a 900mhz nmr, explain the hartree-fock method, and perform calculations for atomic emission spectroscopy and h2 molecule.

Typology: Assignments

Pre 2010

Uploaded on 03/11/2009

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CHEM 550 Problem Set #7
Problem Set 7A – Due Tue Nov 28 This set is NOT as long as it looks so don’t panic
Problem Set 7B – Due Mon Dec 4
(Note: Problem Set 8 Will be Due Fri Dec 8 (last day of lecture))
Levine Exercises:
10.18 Spin functions
Additional Problems
Spin
1) a) Write out all of the allowed wave functions for the first excited state of the He atom
as proper antisymmetric products of spatial and spin functions so that your functions
correspond to triplet states and to singlet states (identify which is which). Demonstrate
which are eigenfunctions of S
2total
and S
z-total
? What are the eigenvalues?
2) The Mhz value on an NMR is the frequency of electromagnetic radiation needed to
induce a transition between the upper and lower states of a proton in the NMR’s magnetic
field. Calculate the field strength of the 900Mhz wide-bore NMR that was installed at
PNNL in 2002 (http://www.pnl.gov/news/2002/02-08.htm) (now that’s a big magnet!)
Qualitative Material – Keep the Answers SHORT and CONCISE (2-3 sentences)
4) a) Explain why the Hartree-Fock SCF method doesn’t obtain the exact ground state
energy even though it incorporates an interelectron repulsion term into the Hamiltonian.
b) Explain why the energy of an orbital depend on l for electrons in atoms other than
hydrogen? Annotate your discussion with a sketch of the radial wave functions for 3s, 3p
and 3d.
c) Rationalize why, all other things being equal, parallel (unpaired) spins generally (not
always) produce states of lower energy than states with antiparallel (paired) (Hund’s rule)
d) Complete this sentence: Hartree-Fock is a variational theory that approximates the
wave function as a ___________________ using ____________________ as trial
functions. (I bet its been a long time since you had a fill-in-the-blank homework
problem—that’s my holiday gift to you!)
Freshman Chemistry Revisited
3) When UV radiation of wavelength 58.4 nm from a He lamp is directed on to a sample
of Krypton gas, electrons are ejected with a maximum speed of 1.59x10
6
m/s. What is
the ionization energy of Krypton?
pf2

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Download CHEM 550 Problem Set 7: Hartree-Fock Method, Spin Functions, and Atomic Spectroscopy - Pro and more Assignments Quantum Chemistry in PDF only on Docsity!

CHEM 550 Problem Set # Problem Set 7A – Due Tue Nov 28 This set is NOT as long as it looks so don’t panic Problem Set 7B – Due Mon Dec 4 (Note: Problem Set 8 Will be Due Fri Dec 8 (last day of lecture)) Levine Exercises: 10.18 Spin functions Additional Problems Spin

  1. a) Write out all of the allowed wave functions for the first excited state of the He atom as proper antisymmetric products of spatial and spin functions so that your functions correspond to triplet states and to singlet states (identify which is which). Demonstrate which are eigenfunctions of S^2 total and Sz-total? What are the eigenvalues?
  2. The Mhz value on an NMR is the frequency of electromagnetic radiation needed to induce a transition between the upper and lower states of a proton in the NMR’s magnetic field. Calculate the field strength of the 900Mhz wide-bore NMR that was installed at PNNL in 2002 (http://www.pnl.gov/news/2002/02-08.htm) (now that’s a big magnet!) Qualitative Material – Keep the Answers SHORT and CONCISE (2-3 sentences)
  3. a) Explain why the Hartree-Fock SCF method doesn’t obtain the exact ground state energy even though it incorporates an interelectron repulsion term into the Hamiltonian. b) Explain why the energy of an orbital depend on l for electrons in atoms other than hydrogen? Annotate your discussion with a sketch of the radial wave functions for 3s, 3p and 3d. c) Rationalize why, all other things being equal, parallel (unpaired) spins generally (not always) produce states of lower energy than states with antiparallel (paired) ( Hund’s rule ) d) Complete this sentence: Hartree-Fock is a variational theory that approximates the wave function as a ___________________ using ____________________ as trial functions. (I bet its been a long time since you had a fill-in-the-blank homework problem—that’s my holiday gift to you!) Freshman Chemistry Revisited
  4. When UV radiation of wavelength 58.4 nm from a He lamp is directed on to a sample of Krypton gas, electrons are ejected with a maximum speed of 1.59x10^6 m/s. What is the ionization energy of Krypton?

Problem Set 7B Levine Problems: 13.28 – review MO diagrams

Additional Problems:

  1. Atomic emission spectroscopy can be used to detect the presence of certain metals at very low concentration. The basic concept is simple enough, and you may have even done this in some form or another in a chemistry lab: heat the sample until it is hot enough to emit light and see what color the flame is glowing. Sodium makes the flame glow yellow because of an electronic transition from the (3p) 2 P3/2 to the (3s) 2 S1/2 level. Calculate the percentage of atoms in the relative populations of these levels in thermal equilibrium in flames at temperatures of 1500, 2500 and 3500K.

  2. This is one of my favorite problems of the whole quarter: Choose a MO wave-function for the H 2 +^ ground state using 1s-like orbitals with the exponent (nuclear charge) as the variational parameter (Levine eqns 13.43 and 13.44). Set up the coordinate system as suggested in lecture so that you won’t need to learn confocal elliptical coordinates.

2A) Evaluate the overlap integral (S) for the H 2 +^ MO wave function. 2B) Evaluate the Coulomb (Haa) and Exchange (Hab) integrals for H 2 +^ MO wave function. 2C) Using your results from 2 and 3, plot minimized E (as a function of the variational parameters, k) as a function of R for the H 2 +^ ion for the bonding and antibonding molecular orbitals. Optional: Plot E vs R for the orbitals with k=1. 2D) Use your calculation to find the equilibrium bond length, and the dissociation energy, of the H 2 +^ molecule. Use your calculation to find the energy required to excite the molecule from the n=0 to n=1 vibrational level.

Tips: Make sure you use the ‘assume’ command to tell the computer everything you know about parameters such as a 0 , RAB (are they positive, real, etc.) or you won’t get a correct answer.