We have used a self-consistent pseudopotential method within local-density-functional theory to calculate the equilibrium ground state properties of transition metals Mo, Nb, and Zr. From our calculations, we obtain equilibrium lattice constants, cohesive energies, and bulk moduli which are in excellent agreement with the experiments;First principles frozen phonon calculations are then performed for the longitudinal (2/3,2/3,2/3) phonon in Mo, Nb, and bcc Zr as well as the H-point phonon in Mo and Nb. These calculations involve the precise evaluation of the total crystalline energy as a function of lattice displacement and yield phonon frequencies to within a few percent of the experimental values. Anharmonic terms are obtained with little additional effort and are found to be very important for causing the tendency toward the (omega)-phase instability in bcc Zr. These calculations allow a detailed analysis of the mechanisms causing phonon anomalies. They also provide first principle benchmarks at a few wavevectors where phenomenological models can be tested or their parameters determined;The validity of the adiabatic approximation is investigated for the Mo H-point phonon. Non-adiabatic effects are found to be small, while effects caused by the many-body renormalization of electronic states near the Fermi energy are found to be of the same order of magnitude as the discrepancy between experiment and the frozen phonon results;The microscopic interactions responsible for the vast frequency differences of the longitudinal (2/3,2/3,2/3) phonon in Mo, Nb, and Zr are analyzed by making use of the Hellmann-Feynman theorem. The stiffening of this mode as the electron per atom ratio increases from Nb to Mo is shown to arise from a development of directional bonding. The precipitous dip in this mode for the high temperature bcc phase of Zr is related to the d-electron screening, and the;tendency for this mode to go soft and cause a transformation to the (omega)-phase is also associated with details of the electronic structure; ('1)DOE Report IS-T-1065. This work was performed under Contract No. W-7405-Eng-82 with the U.S. Department of Energy.