 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/58/a/i/solution

F (- h) = F (h)^{*}

F (h) = ∣ F (h) ∣ e^{i ϕ_{h}}

and pairing positive and negative indices gives

ρ (x) = F (0) + 2 \sum_{h = 1}^{\infty} ∣ F (h) ∣ cos (2 πh x - ϕ_{h}) .

The sign in the cosine follows from the supplied negative-sign Fourier-synthesis convention.

F (0)

is the mean electron density in the fractional-coordinate normalization.

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