Write a function file U.m that returns the potential energy, U. Find the minimal energy for n = 3 using fminsearch in MATLAB. Try several initial guesses until you are convinced you have the absolute minimum.

Then use the Matlab command plot3 to plot the three atoms in the minimum energy configuration as circles, and connect all circles with line segments to view the conformed molecule.

It's given how the U.m could look like:

function out = U ( p_in )

% p_in is for the unknown values

% For N = 3, the unknown values are z_2, x_3, y_3,z_3 and for N=4, the unknown values are z_2 , x_3 , y_3 , z_3 , x_4 , y_4, z_4 etc

% p_fix are for the values that has fixed values

% Atom 1 is

p_fix (1) = 0.0; % x_1

p_fix (2) = 0.0; % y_1

p_fix (3) = 0.0; % z_1

% Atom 2 isbound to the z-axis

p_fix (4) = 0.0; % x_2

p_fix (5) = 0.0; % y_2

p = [ p_fix , p_inn ]; % All values in one vector

% now the x_1 = p(1) , y_1 = p (2) , z_1 = p (3) , x_2 = p (4) etc .

% One slice of the values of p is

p_x = p ([1:3: end ]) % This vector only oincludes the x-values

np = length ( p ) ; if ( mod ( np , 3) ~= 0)

error ('The length must be multible by 3')

end

%THE CODE TO FIND U (THE POTENTIAL ENERGY)

end

And it's given that the minimal energy can be found using the code

[p_out, f_min]=fminsearch(@U, p0)

(The lowest for N=3 is U=-3)

- ( - ) , ij = : - #j)? + : - 9) + - j2 . () - - ( - ) , ij = : - #j)? + : - 9) + - j2 . ()