Yes, certain nouns can have an attribute in the form of a zu infinitive or an infinitival construction with a zu infinitive. For instance:
- die Angst(,) zu verlieren (= the fear of losing) : Er hatte Angst(,) zu verlieren. Die Angst(,) zu verlieren(,) war groß.
- der Versuch, den Mount Everest zu besteigen (= the attempt to summit the Mount Everest) : Sie machte den Versuch, den Mount Everest zu besteigen. Beim Versuch, den Mount Everest zu besteigen, starb sie. Sie starb beim Versuch, den Mount Everest zu besteigen.
There is no connector involved. The infinitive (infinitival construction) immediately follows the noun.
Defining the class of nouns that are capable of such behaviour is non-trivial; you correctly identify two such nouns, Versuch and Kapazität. At any rate, the property is largely semantic in nature, apparently with a substantial degree of stability across languages. Schmid (2000: 293), in a study of English, observes (examples in squared brackets not in original):
Infinitives have been found as postmodifiers or complements of the following types of nouns:
- directive and commissive nouns in the linguistic domain [eg: order, request, command; suggestion, proposal];
- volitional nouns in the mental domain [eg: wish, aim, plan];
- nouns expressing permission, obligation, ability and dynamic modality related to the possibility, likelihood and necessity of
events [eg: permission, right, freedom; licence, option];
- eventive nouns, especially those producing 'Attempt' uses [eg: attempt, effort];
- circumstantial nouns related to the manner of events [eg: way, approach, method]
As best as I can tell, all the examples above would work the same way in German: die Aufforderung zu schweigen; der Wunsch zu fliegen; etc. Apparently in German there are additional types of nouns that would have to be added to the list. Using Schmid's terminology, for instance, additional noun types from the "mental domain" (besides "volitional nouns") would be covered, namely "creditive nouns" (belief, assumption) and "emotive nouns" (fear, regret, surprise). As you can see in the very first example I gave in this answer (die Angst zu verlieren), these are not expressed with an infinitive in English. I am not aware if a similarly detailed study exists for German (perhaps Restle 2006, but that seems to be unpublished).
With respect to German in particular, it has been pointed out that the relevant nouns are "particularly those derived from a verb and/or that express an attitude or a feeling" (Rapp and Wöllstein 2013: 345; my translation). That sounds straightforward, but, to be fair, the devil is in the detail (of which there seem to be many). On the other hand, depending on your native tongue, there is a good chance you can make fairly accurate inferences.
Hans-Jörg Schmid (2000), English Abstract Nouns as Conceptual Shells, De Gruyter; David Restle (2006), Kontrollnomina: Eine Untersuchung zum Verhalten attributiver Infinitivkonstruktionen im Deutschen, habilitation thesis, Universität München; Irene Rapp and Angelika Wöllstein (2013), "Satzwertige zu-Infinitivkonstruktionen", in: Jörg Meibauer et al, Satztypen des Deutschen, De Gruyter (freely available via ids-pub.bsz-bw.de).