Polynomial extrapolation of response ('z-vector') elements is shown to reduce the cost of correlated-wavefunction, classical ab initio molecular dynamics. Demonstrations with resolution-of-the-identity Moller-Plesset perturbation theory (RI-MP2) show that the number of response equation iterations is reduced by a factor of 2-3, thereby enabling accelerated MP2 dynamics. Coupled with previously demonstrated Fock matrix extrapolation, the combined iterative SCF and z-vector calculations are reduced to a minority share of the total calculation. Though demonstrated for MP2, these methods can also be generalized to higher levels of electron correlation or excited state methods. (C) 2010 Elsevier B.V. All rights reserved.