01 May (10 points) Explain in your own words i) the purpose of the Variation principle, ii) what in the
(10 points) Explain in your own words i) the purpose of the Variation principle, ii) what in the
wavefunction is being varied, and iii) why the Variation principle never predicts an energy that is
lower than the true energy (assuming that the exact Hamiltonian is used).
2. (10 points) Show that the secular determinant written in Equation 10D.7 has solutions
1
E
S
? ?
?
?
?
?
for the case when ?A = ?B = ?.
3. (10 points) Using the information found in Example 10B.1, i) show that the normalization constant
for
? ?
of H2 is 1.10. ii) Explain why this constant is expected to be larger than the normalization
constant for
? ?
of H2. iii) Furthermore, explain why neither normalization constant is equal to
1 2
as we have seen previously when adding normalized wavefunctions.
4. (10 points) Write the total wavefunction (space*spin) of the triplet excited state of H2 in terms of
the molecular orbitals
? ?
and
? ?
. Be sure to include all appropriate space and spin combinations.
5. (25 points) Consider the molecular orbitals that form the ?-bonds in acetylene H–C?C–H.
i) Write expressions for the linear combinations of atomic orbitals that form the ?-bonds in the
acetylene molecule in terms of the coefficients and the atomic orbitals. ii) Write the secular
equations and a single secular determinant corresponding to these ? molecular orbitals (recall that
there are two ?-bonds in the acetylene molecule). iii) Use the secular determinant to solve for the
energies of the ? molecular orbitals. iv) Sketch the molecular orbital energy level diagram for the ?
molecular orbitals of acetylene. Add the appropriate number of electrons that are involved in ?-
bonding to the diagram. Verify that your diagram predicts the correct number of ?-bonds in the
molecule. v) Use the data in the table below and your molecular orbital diagram to calculate the
Homework Problem Set #9 (Variation and Hückel Methods) 1. (10 points) Explain in your own words i) the purpose of the Variation principle, ii) what in the wavefunction is being varied, and iii) why the Variation principle never predicts an energy that is lower than the true energy (assuming that the exact Hamiltonian is used). ??? 2. (10 points) Show that the secular determinant written in Equation 10D.7 has solutions E? ? 1?S for the case when ? = ? = ?. A B 3. (10 points) Using the information found in Example 10B.1, i) show that the normalization constant for ? of H is 1.10. ii) Explain why this constant is expected to be larger than the normalization 2 ? constant for ? of H . iii) Furthermore, explain why neither normalization constant is equal to 2 ? 12 as we have seen previously when adding normalized wavefunctions. 4. (10 points) Write the total wavefunction (space*spin) of the triplet excited state of H in terms of 2 the molecular orbitals ? and ? . Be sure to include all appropriate space and spin combinations. ?? 5. (25 points) Consider the molecular orbitals that form the ?-bonds in acetylene H–C?C–H. i) Write expressions for the linear combinations of atomic orbitals that form the ?-bonds in the acetylene molecule in terms of the coefficients and the atomic orbitals. ii) Write the secular equations and a single secular determinant corresponding to these ? molecular orbitals (recall that there are two ?-bonds in the acetylene molecule). iii) Use the secular determinant to solve for the energies of the ? molecular orbitals. iv) Sketch the molecular orbital energy level diagram for the ? molecular orbitals of acetylene. Add the appropriate number of electrons that are involved in ?- bonding to the diagram. Verify that your diagram predicts the correct number of ?-bonds
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Order Now” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.