In this work we examine the consequences of incorporating the ab initio derived monomer potential-energy surface and nonlinear dipole surface of Partridge and Schwenke [J. Chem. Phys. 106, 4618 (1997)] into the previously developed TTM2-R model of Burnham [J. Chem. Phys. 116, 1500 (2002)] in order to develop a new, all-atom polarizable, flexible model for water (TTM2-F). We found that the use of the nonlinear dipole surface is essential in modeling the change in the internal geometry of interacting water molecules and, in particular, the increase in the internal H-O-H bend angle with cluster size. This is the first demonstration of a flexible model which shows an increase in the bending angle in clusters. An explanation for this behavior is presented using the concept of geometric polarizabilities. The model furthermore reproduces the n=2-6 cluster binding energies to within an RMS deviation of 0.05 kcal/mol per hydrogen bond with respect to the MP2 complete basis set estimates. Preliminary results for the liquid with the new model are also presented.