With the help of spherical tensor expression, an irreducible calculus of a Lth-rank macroscopic susceptibility chi for a polar liquid crystal (PLC) of biaxial and chiral molecules written as the average of molecular hyperpolarizability tensor beta associated with their spherical orientational order parameters < Y-lm > (0 <= l <= L) is presented. Comprehensive formulas of L = 1, 2 have been obtained and the latter explains the optical activity and spontaneous splay texture observed in bent-core PLC. The expression of L = 3 specifies for the molecules with D-2 symmetry which can be applied to analyze the nonlinear optical second harmonic generation (SHG) observed in proteins, peptides, and double-stranded DNA at interfaces. (C) 2012 Elsevier B.V. All rights reserved.