Symmetries and the Intrinsic Dimensionality of Chemical Space

Guido Falk von Rudorff

The vastness of chemical space renders it challenging to make fundamental statements of its properties. Using quantum alchemy, a perturbative approach to estimating quantities for similar systems of the same quantum chemistry calculation, we can obtain closed form expressions for property estimates for small volumes in chemical space. For energies, we obtain approximate symmetries which must hold true for all conceivable systems of certain structural properties. While the formal dimensionality of solving Schrödinger’s equation is three spatial degrees of freedom and one nuclear charge per atom, we often find the effective dimensionality to be lower. Using the quantum alchemy picture, we estimate the intrinsic dimensionality of the molecular energy, its scaling with system size, and deviation from equilibrium structures. This allows to estimate the best achievable data efficiency in models.

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