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chem8950 – 1.

$ 20.99
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H = = ?
2. Evaluate the following using Wick’s theorem for graphs. Fully simplify your answer assuming the indices refer to a basis of canonical Hartree-Fock spin-orbitals.
hΦabcijk|Fc C3|Φi = ?
3. (a) Explain how to get from the projected CCD Schr¨odinger equation
Ec tijab = hΦabij |Hc exp(T2)|Φi Hc = Fc + Vc (1)
to the working equation for CCD amplitudes
tijab = (Eabij)−1hΦabij |Vc exp(T2)|ΦiL (2)
assuming a canonical Hartree-Fock reference.
(b) Write out an algorithm to numerically solve equation 2.
Extra Credit: Derive the following interpretation rule in your own words:
Each open cycle in a graph contributes ( to the normal-ordered product of operators, where p and q label the free ends and hi is the number of hole contractions in the cycle. A closed cycle (loop) contributes (−)hi+1.

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