## 1 Introduction  
Two-dimensional zinc oxide (2D ZnO) is a novel promising material for catalytic, sensing, energy storage, and optoelectronics applications [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. The great potential of this graphene-like wide-band-gap material mainly originates from its unique properties, which can even outperform those of bulk ZnO [11]. For example, the fact that the 2D ZnO has an atomically thick, flat surface implies that all surficial atoms are available for the interaction with foreign atoms or molecules, making this material catalytically active and extremely sensitive to external stimuli. Therefore, during the last ten years, intensive research efforts have been devoted to the synthesis and theoretical investigation of the ZnO monolayer [12; 13; 14; 15]. A combination of 2D ZnO with graphene in a synergistic manner is a promising and effective strategy to extend the initial functionality of 2D ZnO through designing van der Waals (vdW) 2 DZnO/graphene heterostructures with improved optical and charge transfer properties [16; 17; 18]. [PERSON] and [PERSON] [18] demonstrated the remarkable advantages associated with integrating ZnO and graphene in a heterostructure. One notable benefit is the significantly prolonged carrier relaxation time compared to ZnO in isolation, resulting in enhanced carrier mobility, electrical conductivity, and electronic thermal conductivity within the heterostructure. Moreover, the heterostructure exhibits approximately five-times-higher lattice thermal conductivity than ZnO alone. Additionally, [PERSON] et al. [17] reported a remarkable 87% improvement in UV-light photosensing in a 2D ZnO/graphene heterostructure under a compressive strain. In this regard, it is crucially important to comprehend the fundamental properties of 2 DZnO/graphene heterostructures, especially considering a realistic structure of 2D ZnO that may include point defects, such as oxygen vacancies or substitutional defects. Given that defect engineering is an important strategy for tailoring the properties of two-dimensional materials [19; 20], achieving an in-depth understanding of the effects of different types of defects in 2D ZnO on the electronic, contact, and catalytic properties of the 2 DZnO/graphene heterostructure is highly demanded. Despite the previous research that provided insights into the mechanisms underlying the formation of point defects and their effect on the selected properties of 2D ZnO supported by graphene [21; 22; 23; 24; 25], some issues related to spin-dependent electronic and contact properties, as well the catalytic properties of defective 2 DZnO/graphene heterostructures, still need to be resolved. More specifically, spin selectivity effects on defect-engineered 2 DZnO/graphene systems and the hydrogen evolution reaction (HER) in these heterogeneous vdW heterostructures have been poorly investigated. To demonstrate the potential of defect engineering for optimizing 2 DZnO/graphene heterostructure properties for specific applications, two representative types of points defects are investigated in this work: neutral oxygen vacancies and Fe substitutional atoms. This paper aims to provide a comprehensive theoretical framework for understanding the impact of defects in 2D ZnO supported by graphene on its physical properties, and to guide the design of future experiments for optimizing its functionalities for specific applications. The influence of a wide range of defects, including Fe substitutional defects and oxygen vacancies, on the electronic band structure and contact and charge transfer properties of the 2D ZnO/graphene heterostructure are explored by employing state-of-the-art spin-polarized GGA-PBE+U-D2 calculations. The catalytic activity of defect-engineered 2D ZnO/graphene heterostructures towards the hydrogen evolution reaction is in special focus.