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Alpha Helix Geometry

Describes the precise angles and spacing within an alpha-helical structure, determined by hydrogen bonding patterns.
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The statement of the theorem

Let ri\mathbf{r}_i be the position vector of the ii-th residue's Cα\text{C}\alpha atom. The geometry of an α\alpha-helix is defined by the constraints on the backbone dihedral angles (ϕi,ψi)(\phi_i, \psi_i) and the hydrogen bonding pattern C(i)−H⋯O(i+4)\text{C}(i) - \text{H} \cdots \text{O}(i+4). Specifically, the ideal geometry requires: \n\nϕi≈−57∘ and ψi≈−47∘\phi_i \approx -57^{\circ} \text{ and } \psi_i \approx -47^{\circ} \n\nFurthermore, the hydrogen bond constraint dictates that the distance d(C(i),O(i+4))d(\text{C}(i), \text{O}(i+4)) and the angle ∠(C(i)−H(i)−O(i+4))\angle(\text{C}(i) - \text{H}(i) - \text{O}(i+4)) must approximate the ideal values for a stable hydrogen bond, ensuring a pitch P≈5.4 A˚P \approx 5.4 \text{ \AA} and a rise per residue h≈1.5 A˚h \approx 1.5 \text{ \AA}.
Source: Wikipedia