Proton transfer is a fundamental process in many chemical and biological systems. A wellknown example is the proton transfer through the hydrogen bond network in liquid water, which accounts for the anomalously high mobility of protons in aqueous systems. Sharedproton systems, in which a proton is shared between two closed-shell molecular fragments, are prototypical models to further understand proton transfer in condensed phases. For example, a proton equally shared by two water molecules, known as the Zundel ion, is considered to be one of the fundamental structural motifs in the proton transfer process in water and has been extensively studied for many years. A significant challenge in the theoretical treatment of proton transfer comes from the quantum nature of protons. In conventional quantum chemistry methods, nuclei are treated as classical particles. However, because of the low mass of protons, their nuclear quantum effects (NQEs) can not be ignored in many cases. For instance, proton delocalization and proton tunneling substantially influence structure and dynamics of water. In enzymes, strong hydrogen bonds and associated NQEs play a crucial role in lowering activation barriers and facilitating rapid and efficient chemical transformations. Many theoretical methods have been developed to incorporate NQEs, mainly including quantum dynamics methods, path-integral approaches, and multicomponent quantum chemistry methods. Recently, constrained nuclear-electronic orbital density functional theory (CNEO-DFT) was developed within the multicomponent quantum chemistry framework and has been shown to efficiently and accurately describe vibrational modes involving hydrogen atoms. Unlike other multicomponent quantum chemistry methods, the CNEO framework is based on the key physical fact that, while quantum nuclei have density distributions in space similar to electrons, yet they are much more localized than those of electrons. Therefore, nuclear expectation positions can be used to represent the classical positions for nuclei. As such, the treatment of nuclei in CNEO is both quantum and classical, which is achieved by introducing constraints on nuclear expectation positions in the Lagrangian of multicomponent systems. The total energy minimized under these constraints leads to the CNEO energy surfaces. The CNEO energy surface is analogous to the Born-Oppenheimer potential energy surface, but is an effective energy surface with NQEs incorporated. Both analytic gradients and analytic Hessian of the CNEO enengy surface have been developed, making it possible to incorporate NQEs, especially nuclear quantum delocalization effects, into structural optimization, transition state search, and molecular dynamics simulations. In particular, the combination of CNEO with molecular dynamics (CNEO-MD) has significantly expanded its range of applications. Tests on a series of molecular systems demonstrated that CNEO-MD provides an accurate description of molecular vibrational frequencies, particularly for those vibrational modes involving hydrogen atoms. Furthermore, CNEO shows great promise for hydrogen atom transfer reactions, which gives accurate rate constants but with computational costs comparable to conventional DFT-based transition state theory. In previous studies on molecular vibrations with CNEO-DFT, interactions between electrons and protons were limited to mean-field Coulomb interactions, while electron-proton correlations were neglected. Therefore, the impact of electron-proton correlations in CNEO-DFT on vibrational spectra awaits systematic studies, especially since it was well known that electron-proton correlations can be crucial in the accurate description of proton densities and protonic affinities in conventional NEO-DFT. In this paper, we address this question by systematically investigating a series of shared-proton systems. Specially, we This paper is organized as follows. A brief review of the basic concepts and theoretical formulation of CNEO-DFT will be presented in Sec. II to ensure the paper self-contained.