Find all possible combinations of 2 vectores (spin) of a system with N atoms with pondered distance

Hello!

I wanna take a tridimensional system of atoms, calculate the distance between them and all possible combinations of spin.

I want to take note that with the and being the magnetic moment of i and j repectivelly, which ones could take the values -1 and 1 and the values of 1's must be equal to the number of -1's. Thus, i want to take note of the value of and for each atom and for all different values of the sum.

Hope, you can help me fixing this problem. I leave what I have attached.

Thanks

[Jan]

The posted code contains some bugs, e.g.

distance=zeros(length(A(:,1)),length(A(:,1)));

The number of parenthesis does not match. Using length is prone to bugs, because it uses the longer dimension automagically. Prefer:

distance = zeros(size(A, 1), size(A, 1));

What is your actual question? What is a "tridimensional system of atoms"? What is the wanted output?

[Miguel Cardoso]

I know that the code contain some bugs. Anyway the matrix A represent the position of the 16 atoms (row) on space x,y, z (column). The output should be the sum for all possible magmom's combinations.

For example:

I have 16 atoms and I want to try different combinations of spin

(...)

[Jan]

Again: What is the wanted output? If you have 16 atoms, what does "tridimensional" mean?

[Miguel Cardoso]

3D(tridimentional) space

X Y Z

A= atom 1 [ 0.000000000 0.000000000 0.000000000

atom 2 0.000000000 0.000000000 2.700000048

atom 3 0.000000000 2.700000048 0.000000000

atom 4 0.000000000 2.700000048 2.700000048

atom 5 2.700000048 0.000000000 0.000000000

atom 6 2.700000048 0.000000000 2.700000048

atom 7 2.700000048 2.700000048 0.000000000

atom 8 2.700000048 2.700000048 2.700000048

atom 9 1.350000024 1.350000024 1.350000024

atom 10 1.350000024 1.350000024 4.050000191

atom 11 1.350000024 4.050000191 1.350000024

atom 12 1.350000024 4.050000191 4.050000191

atom 13 4.050000191 1.350000024 1.350000024

atom 14 4.050000191 1.350000024 4.050000191

atom 15 4.050000191 4.050000191 1.350000024

atom 16 4.050000191 4.050000191 4.050000191]

As I said before I want to calculate the distance between each atom, assign the values and 1 (spin) to each atom and calculate all possible combinations of these values.

The output should be

My main problem is how can I assign these values to each atom, guarantee that all combinations are executed and regist all possible combinations.

Thank you for spending your time trying to help me.

Answer 1

[Guillaume]

You have to bear in mind that most of us probably don't work in the same field as you do. Last time I had to worry about atom spin was some 20 years ago... So make sure to explain yourself clearly. Giving us code with syntax errors, or matrices that are not valid syntax does not help.

I want to calculate the distance between each atom,

I assume euclidean distance. That's trivially done, in just one line.

A=[ 0.000000000         0.000000000         0.000000000
    0.000000000         0.000000000         2.700000048
    0.000000000         2.700000048         0.000000000
    0.000000000         2.700000048         2.700000048
    2.700000048         0.000000000         0.000000000
    2.700000048         0.000000000         2.700000048
    2.700000048         2.700000048         0.000000000
    2.700000048         2.700000048         2.700000048
    1.350000024         1.350000024         1.350000024
    1.350000024         1.350000024         4.050000191
    1.350000024         4.050000191         1.350000024
    1.350000024         4.050000191         4.050000191
    4.050000191         1.350000024         1.350000024
    4.050000191         1.350000024         4.050000191
    4.050000191         4.050000191         1.350000024
    4.050000191         4.050000191         4.050000191];

distance = sqrt(sum((permute(A, [1 3 2]) - permute(A, [3 1 2])) .^ 2, 3))

assign the values and 1 (spin) to each atom

That;s really not clear. Going by your +- diagram, I think you want to get all possible combinations of 8 atoms out of 16 (once you've chosen 8 positive spins, the others are negative). That's trivially done again however note that for 16 atoms, there are 12870 such combinations. For more atoms, it will easily get out of hands:

ncombs = nchoosek(size(A, 1), size(A, 1)/2);   %number of combinations. If it's too large the following line will take forever and may even lock your computer
pospin = nchoosek(1:size(A, 1), size(A, 1)/2); %each row is a unique combination of 8 out 16 atoms

We can fill a matrix of -1 and +1 easily from there:

spin = -ones(size(pospin, 1), size(A, 1));  %fill with negative spin
spin(sub2ind(size(spin), repmat((1:size(spin, 1))', 1, size(pospin, 2)), pospin)) = 1; %fill selected atoms with positive spin

calculate all possible combinations of these values.

What values? Again, taking a guess based on your equation:

%using dimensional notation introduced in R2018b, here. 
%in earlier versions, you'd have to call sum twice.
result = squeeze(sum(permute(spin, [3 2 1]) .* permute(spin, [2 3 1]) .* distance, [1 2]))

[Miguel Cardoso]

Thank you for your answer, it really helped me. I don't know if I was explaining well but what I was thinking is to sum all the distances between all atoms multiplied every single time by the spin of both for different configurations of spins.

[Guillaume]

"sum all the distances between all atoms multiplied every single time by the spin of both for different configurations of spins"

This is exactly what the last line does:

result = squeeze(sum(permute(spin, [3 2 1]) .* permute(spin, [2 3 1]) .* distance, [1 2]))

at once for all spin combinations.

[Miguel Cardoso]

Sure, thank you once again.