## 1 Introduction  
The direct synthesis of hydrogen peroxide (DS) has been under investigation as an alternative to the anthraquinone process [1] for more than 15 years [2; 3; 4]. The anthraquinone process is the most affordable for large-scale productions, which include also the H\({}_{2}\)O\({}_{2}\) synthesis step of the integrated HPPO (Hydrogen peroxide-Propylene Oxide) process by BASF/Dow [5]. However, the use of H\({}_{2}\)O\({}_{2}\) in the large-scale chemical manufacturing is still limited and the most common down-stream applications of H\({}_{2}\)O\({}_{2}\) generally require dilute solutions of H\({}_{2}\)O\({}_{2}\). In spite of this H\({}_{2}\)O\({}_{2}\) from the anthraquinone process must be extracted in water and concentrated up to ca 70%, \(w/w\) in order to store and transport it. This makes hydrogen peroxide much more expensive than it would be otherwise and raises safety concerns about the handling of the concentrated solutions. For this reason, alternative processes for the on-demand, small-scale, on-site production of diluted solutions of H\({}_{2}\)O\({}_{2}\) have been taken into account and the DS seems to be particularly promising. Many authors stress that most of the down-stream applications of H\({}_{2}\)O\({}_{2}\) produced upon the on-site, on-demand DS would require small-scale plants, with a reduced risk of operation and a much lower CAPEX too. However, the handling of H\({}_{2}\)/O\({}_{2}\) mixtures would be a major safety issue; moreover wide-spread diffusion of small scale DS plants would require an extended network for H\({}_{2}\) transportation, another safety issue, or local facilities for its production. Particularly interesting results have been obtained so far by [PERSON] and co-workers, who were able to implement a DS protocol leading to the production of H\({}_{2}\)O\({}_{2}\) solutions in MeOH up to ca 9% (\(w/w\)) concentration [6]. For this purpose, they used catalytic supports bearing acidic groups (e.g., SO\({}_{3}\)H) and covalently functionalized with Br. Among these supports ion-exchange resins like Lewatit K2641 play an important role [7; 8; 9]. However, [PERSON]'s catalysts require relatively high pressure (up to 5 MPa) and the selectivity (calculated on H\({}_{2}\)) is around 50%. The problem of selectivity if of paramount importance in the DS, although its reaction scheme is relatively simple, with only two reagents (H\({}_{2}\), O\({}_{2}\)), two products (H\({}_{2}\)O\({}_{2}\), H\({}_{2}\)O) and four steps (Figure 1). In fact, the activation of H\({}_{2}\) and O\({}_{2}\) over active metals (palladium or alloys thereof) generally leads to both H\({}_{2}\)O\({}_{2}\) and H\({}_{2}\)O, which is much more thermodynamically stable. In particular, it is very difficult to obtain a high selectivity and a relatively high concentration of H\({}_{2}\)O\({}_{2}\) in the final mixture. A low selectivity is at the same time an economic and a safety issue. On the one hand, with a little selective catalyst a high proportion of H\({}_{2}\) is transformed into valueless water; on the other one, a relatively high H\({}_{2}\) partial pressure should be employed to form appreciable amounts of H\({}_{2}\)O\({}_{2}\). However, this is not recommended because H\({}_{2}\)/O\({}_{2}\) mixtures have a very large explosion range [10]: for this reason, the DS is generally carried out with a H\({}_{2}\)/O\({}_{2}\) ratio below its lower limit. [PERSON] and coworkers were among the first to report a catalytic activity well exceeding 90%, with an AuPd catalyst supported on activated carbon pre-treated with an oxidizing acid [11]. In spite of these successes the commercial application of the DS is still an open challenge. At the same time, it is a fascinating scientific question, too, which was addressed by several research groups around the world [3; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21].