exec(stmt);

Msg 242, Level 16, State 3, Line 11
The conversion of a varchar data type to a datetime data type resulted in an out-of-range value.

select top 10 * from list where doc_date between '2015-04-01 00:00:00.000' and '2015-05-17 23:59:00.000'

select top 10 * from list where doc_date between '20150401 00:00:00.000' and '20150517 23:59:00.000'

declare @StartDate datetime = '2015-04-01 00:00:00.000' 
declare @EndDate datetime = '2015-05-17 23:59:00.000'

declare @Sql nvarchar(max) = N'
    select top 10 * 
    from dbo.list 
    where doc_date between @StartDate and @EndDate
';

declare @Params nvarchar(1000) = N'
    @StartDate datetime
  , @EndDate datetime
';    

exec sys.sp_executesql 
        @Sql
      , @Params
      , @StartDate = @StartDate
      , @EndDate = @EndDate;