C#, EF: How to get OUTER JOIN and EXISTS

EFOuterJoinAndExists.cs

/// <summary>
/// Queries the requisitions.
/// </summary>
public static IQueryable<Requisition> QueryRequisitions()
{
    var ctx = GetContext();

    var statusIdsQuery = ctx.OrderStatuses
        .Select(i => i.OrderStatusId);

    var orderIdsQuery = ctx.OrderDetails
        .Where(i => i.BusinessType == "R")
        .Select(i => i.OrderID);

    var rentalChildrenQuery = XavierContext.QueryRentalChildren()
        .Select(i => i.OrderId);

    var query = ctx.OrderHeaders
        .Include("OrderDetails")
        .Where(i => i.OrderId != null)
        .Where(i => i.RequisitionType == "R")
        .Where(i => statusIdsQuery.Contains(i.OrderStatusID))
        .Where(i => !orderIdsQuery.Contains(i.OrderId))
        .Where(i => i.IsRentalParent == false)
        .Where(i => !rentalChildrenQuery.Contains(i.OrderId))
        .OrderByDescending(i => i.OrderId)
        .Select(i => new Requisition
        {
            OrderId = i.OrderId,
            OrderNumber = i.OrderNumber,
            PONumber = i.PONumber,
            DepartmentName = ctx.Departments.FirstOrDefault(j => j.DepartmentID == i.DepartmentID).DepartmentName,
            CustomerName = i.CustomerName,
            CreatedDt = i.CreatedDt,
            PriorityFl = i.PriorityFl,
            OrderStatusDescription = ctx.OrderStatuses.FirstOrDefault(j => j.OrderStatusId == i.OrderStatusID).StatusDescription,
            CreatedBy = i.CreatedBy,
            OrderTotal = i.OrderDetails.Sum(j => j.TotalAmount)
        });

    return query;
}