In the case of numerical differentiation using a step length of δx = 10–3 Å, the difference in Hessian values between some of the displaced systems was smaller than the numerical precision, thus illustrating one of the problems of this approach. This can be illustrated by the anharmonic correction to the vibrational frequency of the 91 mode which is positive, whereas anharmonic corrections are generally expected to be negative, as is obtained in the analytic approach and when a step length of δx = 10–2 Å is used in the numerical differentiation approach. The anharmonic corrections to the vibrational frequencies of the high-frequency modes appear less sensitive to this problem. The analytic approach does not depend on the energy difference between slightly displaced systems and is therefore free from this source of numerical error.