HW_5.pdf - ChE 554 HW 5 Due Sunday:59 pm E Term 2020 1 Explain the following a What is the electron density b What is a functional c What is the

HW_5.pdf - ChE 554 HW 5 Due Sunday:59 pm E Term 2020 1...

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ChE 554 E Term 2020 HW 5 Due: Sunday June 21, 11:59 pm 1. Explain the following. a. What is the electron density? b. What is a functional? c. What is the exchange-correlation functional? 2. Evaluate the following functionals. F[g] = ∫ ࠵?(࠵?)࠵?࠵? ( , G[g] = ) * )+ * ; ࠵? = 1 a. g(x) = x 4 , F[g] = ?, G[g] = ? b. g(x) = sin(-x), F[g] = ?, G[g] = ? c. g(x) = exp(-a · x 2 ), F[g] = ?, G[g] = ? 3. Explain the difference between GGA, meta-GGA, and Hybrid exchange-correlation functionals. Give examples of each. 4. Water molecules in solution tend to form clusters, such as dimers (two water molecules interacting), trimers (three water molecules interacting), or larger clusters. For this problem you are to find the binding energy between water molecules in dimers and trimers. First model a single water molecule. Then model two water molecules together. You should consider modeling an H atom from one water molecule interacting with an O atom of the other water molecule. A typical O---H distance in liquid water is about X Å. The binding
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