Solution of rate equation

[yudeng]

Dear Prof. Henkelman,

After I get the reaction barrier and the corresponding rate constant through cineb, how can I solve the first order reaction rate equation ( as shown in the attachment)? Can it be solved by the Sympy.solve module implemented in Python?

Unfortunately, when I use Python to solve the problem, I always get no solution.
Can you give me some advice?

Thank you very much.

yours
Yu

[graeme]

Dear Yu,
Unfortunately, I think this is outside the scope of my support in this forum. I do deal with these issues with my own graduate students, but here, I just want to make sure that you can calculate barriers with our VTST methods. I hope that your advisor can provide some guidance in terms of solving the rate equations. If you are really stuck, we could collaborate to sort this out, but I can't just look at these equations and suggest a reason why there is a problem solving them.
Graeme

[yudeng]

Ok, thank you Professor! I'll discuss it with my advisor again.

[yudeng]

Dear Prof. Henkelman,

I am sorry to bother you again.
Could you give me any references on solving rate equations for me to learn?
I have been confused about this problem for a long time.
Although I can solve rate equations at present, I can't get the same results as the corresponding reference, for example, J. Phys. Chem. C 2014, 118, 6706−6718.

Thank you very much.

yours
Yu

[jaganmsp]

Hi Yu,

I am Jagannath, graduate student from Dr. Henkelman's group. I think the issues you are having are mostly mathematical (and/or computational) because solving rate equations is nothing but solving a set of differential equations. Maybe you can search for "Solving system of differential equations" then you can find resources related to solving them analytically or numerically. There are also types of system of differential equations (like linear/non-linear or ordinary/partial, you need to figure out what kind of differential equations you want to solve). I personally prefer Mathematica to do this because it can solve them analytically and numerically, you can try using this (if your university has access to it) or any other open source codes/languages. Also, if you are having issues with solving all the 6 equations in parallel why not start with smaller systems (like an easier problem which has only 2 differential equations) and then try to work on your system of interest.

Jagannath

[yudeng]

Hi Jagannath,

Thank you for your reply very much.
I can numerically solve differential equations with some codes, but I can't get the same results as in the reference J. Phys. Chem. C 2014, 118, 6706−6718. I'm not sure whether it's my fault or there's a mistake in this reference.

yours
Yu

[jaganmsp]

I am not sure about that. Maybe check with the corresponding (or first) author for that paper?