In this paper the electrical characteristics of metal oxide semiconductor (MOS) capacitors with high-k gate dielectric are investigated with quantum mechanical models. Both the self-consistent Schrödinger-Poisson (SP) model and the density gradient (DG) model are solved simultaneously to study quantum confinement effects (QCEs) for MOS capacitors. A computationally efficient parallel eigenvalue solution algorithm and a robust monotone iterative (MI) finite volume (FV) scheme for the SP and DG models are systematically proposed and successfully implemented on a Linux cluster, respectively. With the developed simulator, we can extract the effective gate oxide thickness from capacitance voltage (C-V) measurements for TaN and Al gate NMOS capacitors with ZrO2 and SiO2 gate dielectric materials. We found that quantization effects of 5.0 nm ZrO2 MOS samples cannot be directly equivalent to commonly quoted effects of 1.5 nm SiO2 MOS samples. Achieved benchmarks are also included to demonstrate excellent performances of the proposed computational techniques.