Learn Hardcore Dutch: Ik heb per ongeluk de deur open gelaten.

Dutch uses hebben (not zijn) as the perfect auxiliary for transitive verbs like laten and for the separable verb openlaten. You only use zijn with a limited set of mostly intransitive motion/change verbs (e.g., Ik ben gevallen). Here, the verb affects an object (de deur), so it takes heb: Ik heb … gelaten.

What verb form is gelaten?

It’s the past participle of the irregular verb laten. Principal parts:

Infinitive: laten
Present: ik laat
Simple past: ik liet
Past participle: gelaten

Why is it written open gelaten here? Would opengelaten also be correct?

Both are correct in this sentence:

Ik heb de deur open gelaten.
Ik heb de deur opengelaten. With a full noun (de deur), you can treat open as a resultative adjective (open gelaten) or use the separable verb openlaten (opengelaten). With a pronoun object, however, Dutch strongly prefers the solid form: Ik heb hem opengelaten (not really: hem open gelaten).

Why do the non-finite verb forms come at the end of the clause?

Main clauses follow Verb-Second: the finite verb (heb) sits in second position, and the rest of the verb cluster goes to the clause-final position:

Subject + finite verb early: Ik heb …
Object and complements in the middle: … de deur …
Separable particle + participle at the end: … open gelaten.

Where can I place per ongeluk?

Common, natural options include:

Ik heb per ongeluk de deur open gelaten.
Ik heb de deur per ongeluk open gelaten.
Per ongeluk heb ik de deur open gelaten. (fronting for emphasis) Putting it at the very end is unusual: ?Ik heb de deur open gelaten per ongeluk.

Is open part of the verb or an adjective here?

It can be analyzed either way:

As part of the separable verb openlaten: opengelaten.
As a resultative adjective (state of the object) with the verb laten: open gelaten. Both analyses yield idiomatic Dutch; with a pronoun object, the verb analysis is preferred: hem opengelaten.

How does it change with a pronoun object?

Use the solid participle:

Ik heb hem opengelaten. (referring to a masculine de-word like de deur)
Ik heb ’m opengelaten. (colloquial) Avoid Ik heb hem open gelaten in standard Dutch.

How would this look in a subordinate clause?

Subordinate clauses send the whole verb cluster to the end. You’ll hear both orders:

… dat ik per ongeluk de deur open heb gelaten.
… dat ik per ongeluk de deur open gelaten heb. Both are accepted; the first is slightly more common.

Can I use the simple past instead of the perfect?

Yes, especially in narratives:

Ik liet per ongeluk de deur open. In everyday Dutch (NL), the present perfect is more common for past events, but the simple past is fine and a bit more neutral in Belgian Dutch.

What about open laten staan? Is that different?

Ik heb de deur open gelaten = you left it open (didn’t close it).
Ik heb de deur open laten staan = you let it remain standing open (adds the posture verb staan, often used to stress continued state). Both are common; the latter is a bit more descriptive/colloquial.

Is openhouden an option here?

Different meaning:

Ik heb de deur opengehouden = you kept/held the door physically open (e.g., for someone).
Ik heb de deur open gelaten/opengelaten = you left it open (you didn’t close it).
Choose based on intent.

Why de deur and not het deur?

Because deur is a common-gender (de-) noun: de deur. With a pronoun object, you’d use hem: Ik heb hem opengelaten.

Is it per ongeluk or perongeluk?

Standard spelling is two words: per ongeluk. The one-word form perongeluk is a common mistake. Near-synonyms include per vergissing and the more formal per abuis.

How do I negate this?

Place niet before the resultative or the verb phrase:

Ik heb de deur niet open gelaten. (I didn’t leave the door open.) If you want to deny intention, use expres/opzettelijk:
Ik heb de deur niet expres open gelaten. (I didn’t leave it open on purpose.)

Why isn’t there a te before any verb here?

After laten, Dutch uses a bare infinitive (no te): laten + infinitive (e.g., laten staan, laten doen). In open gelaten, open is a resultative adjective, so there’s no extra infinitive at all; gelaten is just the participle of laten.

Could I use achterlaten to say this?

You’ll hear it, but it’s heavier and less idiomatic for doors:

?Ik heb de deur open achtergelaten.
Native speakers strongly prefer open gelaten/opengelaten (or open laten staan). Achterlaten fits better with people or things you “leave behind” somewhere.

Any quick pronunciation tips?

deur: the eu is a rounded vowel like French “deux” [øː].
gelaten: initial g is the Dutch guttural [ɣ]/; -la- has a long aa [aː].
per ongeluk: stress usually on on-: per Óngeluk.
Final b in heb stays voiced ([b]), not [p].