Rule: The be to + infinitive construction, particularly when it means 'possibility', does not accept all verbs as the following infinitive.
Examples of errors:
(1) Regarding literature in general it is clearly to be seen that only trivial novels fail to show the interrelationship between art and reality.
(2), Often there is to be heard about wars and increasing armament.
(3) But the reader can also learn about crime which is not to be visible at first sight.
(4) The unemployment of school-leavers will cause social problems that are hardly to be imagined.
(5) Homosexuals work in almost every type of job, but it is to be supposed that there are no homosexuals working in factories.
(6) This is something not easily to be achieved.
Rule 2.7.2 applies to some of the examples listed in 2.7.1 as well. Even with a passive infinitive, It is to be said that... (meaning 'It must be said that...') is not a very likely expression. On the other hand, It is to be remembered/regretted/lamented that... is perfectly acceptable, so there are obviously restrictions on which verbs can enter into this construction as infinitives. These restrictions are much greater when the construction has the meaning of 'possibility', as in (l)-(6), perhaps limiting the verbs which can occur as infinitive in this case to a very few, such as see, hear, and find. Because of these stronger restrictions on be to + infinitive meaning 'possibility', a sentence like
The car is not to be repaired.
would be understood to mean only 'The car must not be repaired', and not 'The car cannot be repaired'. (In German, where the equivalent construction occurs much more freely with the meaning 'possibility Das Auto ist nicht zu reparieren is ambiguous.)
The choice of verb as infinitive is not the only restriction on this construction. As (1) and (2) show, be to + infinitive does not readily accept extraposition and there constructions; compare:
Lilacs are not to be seen everywhere.
Rumors are to be heard on campus about you.
On the other hand, there seem to be fewer restrictions on the construction in questions than in statements. With deny as infinitive, for example, a sentence like the following can mean only 'obligation' or 'future':
It is to be denied that racial discrimination still exists.
= It should/will be denied...
As a question, though, the 'possibility' interpretation is also possible:
How is it to be denied?
= How should/will/can it be denied?