The IntelliGantt Web Part integrates with SharePoint Calendar Lists within the same SharePoint site.
A SharePoint site is typically created with a Calendar List called 'Calendar'.
To link a task with a Calendar event, first open the tool window by clicking on the blue circle at the very upper left of the IntelliGantt Web Part.
Click on the 'mini calendar' icon to create the event.
The new event is now in the Calendar. It's start and end dates are derived from the task's start and due dates.
The event can also link to the task by adding an lookup column called 'Task'. (Technical Details)
Back in the IntelliGantt Web Part, the task can also link to the event by adding a lookup column called 'Events'. (Technical Details)