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How can we solve the state and behavior of many electron atom and many electron molecule and the chemical reaction quantum mechanically?

    I wonder how the electrons in a heavy atom or in a complex molecule behave.

Because all of the electrons in a complex system are suffering from the same common nuclear potential field.

Of course, the state and behavior of the nuclei are by themselves difficult problem to solve.

Since all of the electrons are equal, I don't understand why the ordinary textbooks repeat the axiomatic doctrine that an electron is in one of the systematicall classified state, like 1S or 2P etc.  Or am I wrong at some important point?

    As a basic research, I am working to make programs of Schroedinger eigenvalu problem and Schroedinger's time dependent equation.

But by the limit of the speed and memory capacity of the personal computer, I have to satisfy doing 2D-1B problem or 1D-2B problem.

For the above mentioned difficult problem to be solved by personal computer, it looks like to take a much time far beyond my life time.

At this time, I would like to comment only one thing.

    It is this. As lomg as the interaction potential function stays the same for all time, time developmental simulation shows that the system under computation returns necessarily to its initial state at some time sooner or later.  So, even if we could compose a collision simulation program for realistic 3 dimensional hydrogen atoms each of which is constituted from an electron and a proton, the simulation cannot yield the synthesized hydrogen molecule whatever the initial 12 variables wave function may be.

    Therefore, for me, it seems for us to have something another thing to make the computational chemical reaction happen.

    For example, a few years ago, I have ever succeeded to cause quantum mechanical transition in a computersimulation.

There, two things were absolutely necessary.  One thing is of course to obey the energy conservation law.  That is, the energy that one system gains must equal to the energy the other system loses.  The second thing was an artificially assumed ephemeral coupling interaction term.  Although I do not know yet the true character of the ephemeral couplingterm, if it is adjusted exactly, then it really works to cause the quantum mechanical transition.

    Thus I cannot but speculate third unknown thing other than the two chemical reagents that are the very players involved in a general chemical reaction.

    As a last word.  For any chemical problem, there must be involved many many electrons and nuclei.  How should we devise a way to solve such a many many electron-nuclei Schroedinger time-dpendent equation to simulate and understand a real chemical reaction?   

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