Beta sheets are illustrated as such in most diagrams, where:
- In an antiparallel β-sheet, the polypeptide strands are arranged such that a $\ce{C=O}$ and an $\ce{NH}$ from adjacent strands face each other, and the $\ce{H}$ forms an H-bond with the $\ce{O}$, with $\ce{C=O**HN}$ all lying on the same plane.
- In a parallel β-sheet, the strands are literally parallel, and so the H-bond formed has to form a sort of angle, where the $\ce{C=O}$ and $\ce{NH}$ no longer lie on the same plane (when viewed from the perspective of the diagram).
Most explanations explain the stronger bond strength by stating the obvious from the diagram: that the "hydrogen bonds are aligned directly opposite each other, making for stronger and more stable bonds." (taken from chem libretexts, https://chem.libretexts.org/Bookshelves/Biological_Chemistry/Supplemental_Modules_(Biological_Chemistry)/Proteins/Protein_Structure/Secondary_Structure%3A_-Pleated_Sheet)
This seems intuitive, but my issue arises when considering some orbital geometry: in a peptide bond, the $\ce{C}$, $\ce{N}$ and $\ce{O}$ have orbitals with ${sp^2}$ hybridization, meaning that bond pairs/lone pairs are organized in a trigonal planar orientation around each of those atoms. As a consequence of this, one can also observe that all the atoms illustrated in the diagram should lie on the same plane, making things rather easy to visualize.
However, if one considers that the 2 lone pairs and one bond pair in the $\ce{O}$ atoms are orientated in a trigonal planar fashion, then shouldn't the ideal, strongest, H-bond is orientated at an angle (specifically $\pu{{60}^\circ}$) relative to the $\ce{C=O}$ bond? Now, if I observe the diagram again, it seems this $\pu{{60}^\circ}$ H-bond angle is better fulfilled in the parallel strand than in the antiparallel one. So shouldn't the H-bond in the parallel strand, theoretically, be stronger?
A possible explanation would be that the bond length in parallel strands would be longer, thereby weakening it. But that's not how most textbooks explain it, so what am I missing out here?