This work analyzes a very subtle kind of energy metrics for Data Centers (DCs), namely productivity metrics which affect the global energy efficiency assessment in DC since they focus on the energy used for processing computing operations. By exploiting the available set of energy consumption data of operating systems in ENEA-DC, HPC-Cluster, the authors evaluated the energy consumed by different queues with several running applications. The queues energy waste has been calculated to provide an assessment for the ineffective use of computation-related energy load within the Cluster. This work shows an increment innovation beyond state-of-the-art for productivity metrics (e.g. useful work), and it will also help provide an invaluable insight into useful energy use and the use of enhanced sustainability metrics with the goal of driving a more sustainable DC. Additionally, sustainability concept in DC operations is driven by estimation of its indirect carbon emissions, which is shown in this work.