A statistical mechanics inspired formulation for the second virial coefficient (B-2) correlation is presented. We revisit the formula proposed some 40 years ago based on the simple square-well potential (Hirschfelder, J. O.; Curtis, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley: New York, 1964). To account for polar and anisotropic effects, we reformulate in terms of an anisotropic square-well potential that also depends on the Euler angles of orientation of the moleulces. A new mean-field second virial formula is derived. Only four parameters are needed in the correlation: i.e., the repulsive volume, B-r, the attractive (range) volume, V-a, the interaction energy (well depth), e, and a temperature correction factor, D-t, due to anisotropy. For some 40 chemicals, such as methane, ethane, propane (hydrocarbons), CO, CO2, oxygen, nitrogen, hydrogen, and water vapor, high accuracy in the correlation is achieved: most deviations are within 1-5% for the gases studied from low temperatures to temperatures above the Boyle temperature. The parameters Br, Va, E, and Dt can be expressed in terms of the critical volume, critical temperature, and acentric factor. Comparison with similar industrial correlations (e.g., Hayden, J. G.; O'Connell, J. P. Ind. Eng. Chem. Process Des. Dev. 1975,14,209; Tsonopoulos, C. AIChE J. 1974, 20, 263) shows that the present approach is generally more accurate.