> After that, the PDE is non-linear and non-separable, so. you have to resort to numeric methods. But the computational demands are very heavy, and even with to

> After that, the PDE is non-linear and non-separable, so. you have to resort to numeric methods. But the computational demands are very heavy, and even with today’s machines you can only get up to ~10 valence electrons Well as you mention, many of the models can be simplified at levels. For example regular QM and solid state physics like semiconductor assume nuclei’s are essentially stable compared to electrons. Applying this and other simplifications allowed us to build amazing semiconductors tech for example. DFT lets us estimate far more chemical interactions than pure QM, much less full QFT. However fundamentally knowing the core rules doesn’t help us predict complex scenarios. Personally I don’t see it as too different to the halting problem in CS. It doesn’t prevent us from creating and understanding amazing things. Actually I’m quite excited the rise of AI in quantum chemistry. These AI models can learn complex rules to simplify calculations like physicists figured out by hand, but can scale it out absurdly. > Yes you have Pauli exclusion principle, Hund's rule, based on QFT, but there are exceptions, and I never got a good explanation it doesn't apply to the entire compound (or the entire object, or the entire universe) It’s not clear to me exactly what you meant, but usually quantum tunneling and other effects are limited by decoherence. Yes an electron in your body can tunnel to say the moon. It’s just absurdly unlikely as the number of other electrons it would possibly interact with first is staggeringly large. Even in a single molecule evolved for tunneling like chlorophyll, the probabilities of tunneling outside a few key paths quickly become too small to represent with 64bit floating point numbers. I did the computations in my physics days, and it was challenging to compute.