Valence

Part of the mental dictionary entry for a verb lists the complements or completions that a verb can and must have. A verb’s required and optional complements are frequently referred to as its “valence.”

Valence is a crucial part of a native speaker’s competence and something that has to be learned by learners of a foreign language, especially since a verb in the learner’s language often has a different valence from the corresponding verb in the target language.

For example, English to leave can be used with or without a direct object.

1. He left his wife.
2. He left the house.
3. He left at 10 o’clock.

But in German, verlassen must always have a direct object, and thus cannot be used to translate no. 3.

4. Er verließ seine Frau.
5. Er verließ das Haus.
6. Er verließ um zehn Uhr.*

Sentences that would not be uttered by native speakers–ungrammatical sentences–are marked *.

On the other hand, (weg)gehen can never have a direct object, and thus cannot be used to translate no. 1 or no. 2.

7. Er ging seine Frau weg.*
8. Er ging das Haus.*
9. Er ging um zehn Uhr weg.

Yet a dictionary would probably list both verlassen and (weg)gehen as being equivalent to to leave. 

A valence dictionary would list required and optional elements after each verb (in the following examples, optional elements are in parentheses).

to leave (+DO)
weggehen
verlassen + AkkObj.

But ordinary dictionaries do not include valence information in this way. You have to look for labels like v.i. and  v.t., and you have to look carefully at the full entry. For example, in a valence dictionary, we might write fahren (+AkkObj). In an orindary dictionary we might find fahren (1), v.t., to drive (a car, a train, etc.) . . .; (2) v.i., to drive.    

Prepositional Complements

For many verbs, in both German and English, part of the valence is one or more prepostional complements. For example, we can say:

10. She works.
11. She works eighty hours a week.
12. She works for Commerce Bank.
13. She works at Commerce Bank.
14. She is working on a novel.

The valence looks something like this:
work (+ for + OBJ [employer] OR + at + OBJ [place of employment] OR + on + OBJ [work product]).

In German, arbeiten is like to work in that it can be used with or without prepositional complements, but simply knowing the English and German prepositions does not really let you predict which prepositional complements arbeiten will take.

15. Sie arbeitet.
16. Sie arbeitet achtzig Stunden in der Woche.
17. Sie arbeitet bei der Deutschen Bank.
18. Sie arbeitet an einem Roman.

The valence looks something like this:
arbeiten (+ bei + DAT [employer, place of employment] OR + an + DAT [work product]).

Again, a good dictionary will include this information, but not in this form. You must look at the entry carefully and consider the various usage examples.

Verbs with prepositional complements are a problem for learners, because the choice of preposition depends on the verb’s valence and is often not predictable from the base meaning or translation of the preposition. Moreover, with the accusative/dative prepositions, the choice of case cannot be predicted from the basic rules for the use of the prepositions.

As a rule of thumb, when the spatial aspect has completely disappeared, auf and über are used with the accusative, all the others with the dative; however, it is sometimes debatable whether the spatial aspect has completely disappeared, and a number of exceptions or apparent exceptions occur.  

In the end, learners must simply memorize a large number of verb+preposition+case combinations. 

List of Verbs With Prepositonal Complements

Many textbooks and grammar books contain lists of verb+preposition combinations, sometimes alphabetically by verb, sometimes grouped by preposition. Probably none of these lists are complete, since a complete list of all the combinations currently in use in would no doubt run well into the hundreds. The following list is highly selective.  

1. abhängen (+ von + DAT) to depend on
2. Angst haben (+ vor + DAT) to be afraid of
3. arbeiten (+ an + DAT) to work (on)
4. ärgern (+ REFL +  über + ACC) to get angry about
5. basieren (+ auf + DAT) to be based on
6. beitragen (+ zu + DAT)  to contribute to
7. bestehen (+ auf + DAT) to insist on; (+ aus + DAT) to consist of
8. bitten (+ ACC + um + ACC) to ask for, to request
9. danken (+ DAT + für + ACC) to thank someone for something
10. denken (+ an + ACC) to think of
11. eingehen (+ auf + ACC) to go into
12. erinnern (+ REFL + an + ACC) to remember
13. erkennen ( + an + DAT) to recognize by
14. erkundigen (+ REFL + nach + DAT) to inquire about
15. freuen (+ REFL + auf + ACC) to look forward to ; (+ REFL + über + ACC) to be happy about.
16. gehören ( + zu + DAT) to belong to, as in “er gehört zu meinen besten Freunden” (he is one of my best friends), NOT used to express simple possesion.
17. gewöhnen (+ REFL + an + ACC) to get used to
18. glauben (+ an + ACC) to believe in
19. gratulieren (+ DAT + zu + DAT) to congratulate someone on
20. interessieren (+ REFL + für + ACC) to be interessted in
21. konzentrieren (+ REFL + auf + ACC) to concentrate on
22. leiden (+ an + DAT) to suffer from 
23. nachdenken (+ über + ACC) to think about 
24. reagieren (+ auf + ACC) to react to
25. rechnen (+ zu + DAT) to consider to be
26. sprechen (+ über + ACC) to talk about
27. sterben (+ an + DAT) to die of
28. übereinstimmen (+ mit + DAT) to agree with
29. verheiraten (+ REFL + mit + DAT) to marry
30. verlassen (+ REFL + auf + ACC) to rely on, have trust in
31. verlieben (+ in + ACC) to fall in love with
32. warten (+ auf + ACC) to wait for
33. werben (+ REFL + um + ACC) to apply for 
34. wundern (+ REFL + über + ACC) to be surprised / amazed by / about
35. zweifeln (+ an + DAT) to doubt, have doubts about (Ich zweifele an seinen Fähigkeiten = I doubt his abilities). 

Übungen
Übersetzen Sie ins Englische

1. Viele Kindere haben Angst vor dem Dunkel.
2. Er interessiert sich schon seit vielen Jahren für die äagyptische Kunst
3. Ich habe mich nach den Preisen erkundigt
4. Kafka ist an Tuberkulose gestorben
5. Wasser besteht aus Wasserstoff und Sauerstoff.
6. Dieses neue Buch trägt viel zu unserem Verständnis von den Ursachen des Ersten Weltkrieges bei.
7. Kleist wird manchmal zu den Romantikern gerechnet.
8. Der Täter wurde an seiner merkwürdigen Stimme erkannt.
9. Darf ich Ihnen zum Geburtstag gratulieren?
10. Du kannst dich auf mich verlassen.

Übersetzen Sie ins Deutsche

1. She is working on a new book.
2. I still remember my grandfather very well.
3. I thank you very much for the flowers.
4. She suffers from headaches.
5. May I ask you for five hundred marks?
6. My mother gets very angry about my clothes.
7. Are you looking forward to the vacation?
8. Have you gotten used to the climate yet?
9. We’re waiting for the bus.
10. I am writing to you to apply for the position as manager.