Can exact bond angles in cycloalkanes be calculated?

I know that bond angles in cycloalkanes are usually different from $$\ce{109.5}^{\circ}$$ as predicted by the VSEPR theory because of their shape, and a higher deviation will cause a higher ring strain. Can we calculate exact ring angles using ring strain, or other data?

• Yes, molecular orbital methods, which rely on quantum mechanics will produce accurate geometry. These are definitely not trivial calculations and so most non-experts will use commercial software. A standard method is called the Hartree-Fock self consistent field (SCF) approximation. Jul 13 '21 at 6:51

There may be experimental data for the specific cycloalkane in question, for example by a single-crystal diffraction analysis. Beside entries in the primary literature, there are databases with the relevant structure data including the atomic coordinates; the later ones may be used to calculate the angles in question.

If experimental data are not (yet) available, one may predict the geometry of the compound in question, and use these atom positions guessed to compute the angles in question. The accuracy of these predictions depends on the know-how implemented in these programs. For a quick prediction of smallish motifs seen in organic chemistry, you may draw such molecules, e.g. in MolCalc, run an optimization to yield one reasonable spatial arrangement of the atoms, and eventually measure distances and angles:

The geometry predicted may be (but need not be) the most stable one among all of the conformations of the molecule submitted. It requires insight in theory and practice with the relevant programs to gauge the results of these predictions, e.g., by comparison with other structures already described.

MolCalc serves as an interface to the programs in the background (GAMESS, JSmol) performing the computation at RHF/STO-3G (orbitals and orbital energies), or PM3 level (all the rest, including optimization of the geometry).

Jensen, J. H.; Kromann, J. C. The Molecule Calculator: A Web Application for Fast Quantum Mechanics-Based Estimation of Molecular Properties. J. Chem. Educ. 2013, 90, 1093–1095; doi 10.1021/ed400164n.

• Thanks for the recommendation. Your answer really helps and I'll accept that. Jul 13 '21 at 14:17