Let me be a little less obtuse.
If I see a photograph of a perfect stranger who is smiling warmly for the camera, I'll think "that person is smiling"
If someone who knows the subject sees the same photograph, they will see the smile and fill in the missing data. They will know the subject is a generally outgoing and good-natured person. Then they will say... "Ah, that Johnny. He's such an outgoing and good-natured person"
The photo cannot communicate anything except the physical appearance of a subject. The viewer must fill in all of the rest.
Short answer? No. You cannot capture the 'soul' of a subject.
One more time: If you have a good rapport with your subject, they will relax and react 'naturally' to the camera. When that happens, you capture their normal expression... whether happy or sad. A viewer who knows the subject will see the same face they see when they interact with the subject under normal circumstances.
The viewer reacts positively to your picture because they see the subject just as they see the subject in actual life.
Bottom line: Get your subject to relax and be themselves for you. No mystery.