Molecular wavefunctions calculated with basis sets supplemented with higher-order functions show a smooth increase in the degree of d-function involvement from a polarizing role in main group compounds of normal valency to a genuine valence-orbital role in hypervalent compounds; compounds of second-row elements, especially when bonded to electronegative elements, often use d-functions in a marginal valence role. d-Functions contribute to molecular wavefunctions predominantly in bonding; atomic population terms are very small. The absence of orthogonality constraints (the d-functions are nodeless) facilitates the use of dπ-functions to reduce excessive charge disparity built up in the σ-network. Although exponents may he no greater than those found for normal valency compounds, d-function supplementation is often indispensable for the description of the bonding in hypervalent compounds in many of which more than one set of gaussian d-functions may be needed.