I believe you meant "not" rather than "now".
However, your first example is also non-deterministic. Here's the proof.
Create table dbo.SalesOrderHeader (RN INT IDENTITY(1,1),SomeDate DATETIME);
GO
ALTER TABLE dbo.SalesOrderHeader ADD WhichDay AS datepart(day,'20180131') PERSISTED;
Msg 4936, Level 16, State 1, Line 1
Computed column 'WhichDay' in table 'SalesOrderHeader' cannot be persisted because the column is non-deterministic.
--Jeff Moden
Change is inevitable... Change for the better is not.