HVAC remote management and air purification system comprised of an online cloud-based downloadable software platform for the monitoring, collection and transmission of diagnostic data collected from local HVAC and air purification system equipment utilizing artificial intelligence (AI) for optimizing energy efficiency, enthalpy, and air quality based on continual sensor data collection, indoor air quality (IAQ), and outdoor air quality measurement and operating parameters such as operating hours and scheduled run-time, system geographic location including altitude, efficiency rating, refrigerant type, metering type, manufacturer model and serial number; electronic communications systems comprised of downloadable communications software for transmitting HVAC system communications via alerts, text messages, emails, voice assistants, monitor displays, thermostat displays and fault indicator displays; system comprised of HVAC sensors for measuring and monitoring energy efficiency and air quality certification based on sensor data collection; Computer application software downloadable on to a smart mobile phone or tablet for displaying sensor measurements for HVAC systems for measuring and monitoring air quality, energy efficiency and air quality certification