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Optimization of nonlinear driving terms have become a useful tool for designing storage rings, especially modern light sources where the strong nonlinearity is dominated by the large chromatic effects of quadrupoles and strong sextupoles for chromaticity control. The Lie algebraic method is well known for computing such driving terms. However, it appears that there was a lack of explicit formulas in the public domain for such computation, resulting in uncertainty and/or inconsistency in widely used codes. This note presents explicit formulas for driving terms due to sextupoles and chromatic effects of quadrupoles, which can be considered as thin elements. The computation is accurate to the 4th-order Hamiltonian and 2nd-order in terms of magnet parameters. The results given here are the same as the APS internal note AOP-TN-2009-020. This internal nte has been revised and published here as a Light Source Note in order to get this information into the public domain, since both ELEGANT and OPA are using these formulas

Explicit formulas for 2nd-order driving terms due to sextupoles and chromatic effects of quadrupoles.