# How can I plot this function?

I'm trying to plot this function without any success, any help is more than welcome. The function f contains a sum of integral which depends on T and then the function g is a derivative of the function f Thank you very much.

An = 10^-10;
amu = 1.660539 10^-27 ;
μ = 132.905451/2 amu;
Subscript[N, a] = 6.0221409 10^23;
m = 4 μ;
Subscript[ω, e] = 28.8918*100;
r = 5.3474208 An;
c = 2.99792 10^8;
h = 6.6260755  10^-34;
De = 2722.28*100*h*c;
hbar = h/(2 π);
kb = 1.38064852 10^-23;
R = 8.314511;
λ = (hbar α)^2/(2 μ);
a = μ/(hbar α)^2 De (Exp[2 α r] - 1);
b = 1/2 (1 - Sqrt[
1 + (8 μ De (Exp[α r] + 1)^2)/(hbar α)^2]);
Subscript[k, 1] = a/b - b/2;
v = 207;
Subscript[k, 2] = a/(v + 1 + b) - (v + 1 + b)/2;
Subscript[A,1] = -π c Subscript[ω, e] r Sqrt[(2 μ)/De]
Exp[-π c Subscript[ω, e] r Sqrt[(2 μ)/De]];
α = π c Subscript[ω, e] Sqrt[(2 μ)/De] + 1/r (1 - Log[1 + Log[1 + Subscript[A, 1]]]/(2 + Log[1 + Subscript[A, 1]])) Log[1 + Subscript[A, 1]];
f[T_] := 2 Sum[
NIntegrate[
Exp[-(1/(kb T)) (De - λ (a/(x + b) - (x + b)/2)^2)] Cos[
2 π i x], {x, 0, v + 1}, Method -> "LocalAdaptive"], {i, 1,
20}];
g[T_] := kb T^2 D[Log[f[T]], T];
Plot[g[T], {T, 0, 100}]

• Before you can plot the function, you need to make sure it works... Try g[1], which just falls over
– ktm
Commented Nov 20, 2019 at 17:12

## 1 Answer

Clear["Global*"]

An = 10^-10;
amu = 1.660539 10^-27;
μ = 132.905451/2 amu;
Subscript[N, a] = 6.0221409 10^23;
m = 4 μ;
Subscript[ω, e] = 28.8918*100;
r = 5.3474208 An;
c = 2.99792 10^8;
h = 6.6260755 10^-34;
De = 2722.28*100*h*c;
hbar = h/(2 π);
kb = 1.38064852 10^-23;
R = 8.314511;
λ = (hbar α)^2/(2 μ);
a = μ/(hbar α)^2 De (Exp[2 α r] - 1);
b = 1/2 (1 -
Sqrt[1 + (8 μ De (Exp[α r] + 1)^2)/(hbar α)^2]);
Subscript[k, 1] = a/b - b/2;
v = 207;
Subscript[k, 2] = a/(v + 1 + b) - (v + 1 + b)/2;
Subscript[A, 1] =
-π c Subscript[ω, e] r Sqrt[(2 μ)/De];
Exp[-π c Subscript[ω, e] r Sqrt[(2 μ)/De]];
α = π c Subscript[ω, e] Sqrt[(2 μ)/De] +
1/r (1 - Log[1 + Log[1 + Subscript[A, 1]]]/
(2 + Log[1 + Subscript[A, 1]]))*
Log[1 + Subscript[A, 1]];

f[T_?NumericQ] := 2 Sum[
NIntegrate[
Exp[-(1/(kb T))*
(De - λ (a/(x + b) - (x + b)/2)^2)]*
Cos[2 π i x], {x, 0, v + 1},
Method -> "LocalAdaptive"], {i, 1, 20}];

Needs["NumericalCalculus"]

g[T_?NumericQ] := kb T^2 ND[Log[f[t]], t, T];

Module[{y},
Plot[{Re[y = g[T]], Im@y}, {T, 0, 100},
PlotLegends -> Placed[{Re, Im}, {0.25, 0.25}]]]


• Thank you very much Commented Nov 21, 2019 at 4:53