Spline Interpolation: Finding the Charge Density of H2

[torehan]

Hi,

I have a 3D gridded ( Nx,Ny,Nz : integers, respectively, size of the grid in x,y and z direction ) which contains the charge distribution of an atom, say Hydrogen,
and I would like to simulate the charge density of another structure, in easiest case Hydrogen dimer. (H₂)

To accomplish my approach I must be capable of finding values of my data, I will call it $$\rho(\vec r)$$ from now on, continuously in all space. Spline interpolation comes to scene right now. And let me ask a quick question here,

• After a spline interpolation,in principle, I must have opportunity to evaluate the value of the function $$\rho(\vec r(x,y,z)) anywhere (arbitrary set of x,y and z ) in the space right?$$

$$<br /> If so, I can imitate the charge density of dimer (or any structure) as long as I know the distance between atoms in the structure.<br /> <br /> But still I'm not sure about the procedure, am I on the right path?<br /> <br /> Any wise comments will be fairly appreciated.<br /> <br /> -torehan$$

 

[lofgran]

Dear torehan,

Thank you for sharing your approach with us. It sounds like you have a solid understanding of the concept of spline interpolation and how it can be used to evaluate values of a function at arbitrary points in space.

To answer your question, yes, after performing a spline interpolation on your 3D gridded data, you should be able to evaluate the function \rho(\vec r) at any point in space. This is one of the main benefits of spline interpolation – it allows us to approximate and interpolate values of a function at any desired point, even if there are no data points at that location.

In terms of simulating the charge density of a dimer or any other structure, it is important to keep in mind that the accuracy of your simulation will depend on the quality of your data and the chosen interpolation method. It may be helpful to validate your results by comparing them to experimental data or other simulations.

Overall, it seems like you are on the right path and have a good understanding of how to approach this problem. I would recommend further researching and exploring different interpolation methods to ensure the best results for your specific application.

Best of luck with your research!