3502_HWkey8 - Chem 3502/5502 Physical Chemistry II (Quantum...

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Chem 3502/5502 Physical Chemistry II (Quantum Mechanics) 3 Credits Fall Semester 2009 Laura Gagliardi Answers to Homework Set 8 From lecture 29: What is the value of P 52 for water after the first SCF step (i.e., at cycle 2)? By what percentage did it change compared to the initial guess? By what percentage did the total energy change for this same step? We must evaluate P "# = 2 a " i a # i i occupied $ for λ = 5 and σ = 2 using the occupied MO coefficients after the first SCF step which were given in the lecture notes as Occupied MO coefficients at cycle 2. 1 2 3 4 5 1 .994123 -.233041 .000000 -.103527 .000000 2 .026666 .834174 .000000 .541326 .000000 3 .000000 .000000 .000000 .000000 1.000000 4 .000000 .000000 .608401 .000000 .000000 5 -.004400 -.131110 .000000 .774771 .000000 6 -.006039 .156851 .443140 -.279656 .000000 7 -.006039 .156851 -.443140 -.279656 .000000 As there are 5 occupied MOs, we will sum over all 5 the product of a 5 i with a 2 i . So, for MO 1 we have –0.004400 times 0.026666. For MO 2, –0.131110 times 0.834174. For MO 3, 0 times 0. For MO 4, 0.774771 times 0.541326. And, for MO 5, 0 times 0 again. If we sum the three non-zero products and multiply by 2 (see equation above) we obtain
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This note was uploaded on 12/18/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.

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3502_HWkey8 - Chem 3502/5502 Physical Chemistry II (Quantum...

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