How do I query two relationship fields where one relationship MUST be empty?

Question

I have two relationship fields. I am trying to query all entries where the first field is related to a particular element and the second field is related to nothing. Here is how I thought it would work but it doesn't.

$criteria->relatedTo = ['and',
[
    'targetElement' => anElementId,
    'field'         => 'relationshipOne'
],
[
    'targetElement' => null, // also tried ":empty:"
    'field'         => 'relationshipTwo'
]];

Answer 1

Splitting the criteria up like this works.

$criteria->relatedTo = [
    'targetElement' => anElementId,
    'field'         => 'relationshipOne'
];
$criteria->relationshipTwo = ':empty:';

Thanks to @carlcs in the Craft Slack channel.