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For typical atoms and molecules, the Becke 1988 exchange functional improves exchange energies and commonly improves molecular energetics relative to exchange-only local density approximation, because it accounts for density gradients and corrects important nonuniformity errors. This is a general trend, not a theorem for every observable or system.

A comparison of total molecular predictions also depends on the correlation functional, basis, spin treatment and geometry. B88 is an exchange approximation, not by itself a complete specification of an exchange-correlation calculation.

$x_{\sigma }=|\nabla {\rho }_{\sigma }|/{\rho }_{\sigma }^{4/3}$ is a dimensionless reduced density gradient. It measures inhomogeneity relative to the local density scale, vanishes for a uniform gas, and allows a generalized gradient approximation correction to distinguish rapidly varying density from slowly varying density with the same local value.

The parameter $\beta$ controls the correction strength in the Becke 1988 exchange functional; it was fitted to atomic exchange energies. The large-gradient denominator simultaneously produces the intended asymptotic behavior, so its role is more constrained than an arbitrary multiplicative adjustment.^[ref]