add compatibility with simpson scipy function

dynaphopy/analysis/thermal_properties.py

@@ -42,7 +42,7 @@ def n(temp, freq):
     total_energy = np.nan_to_num([dos[i] * h_bar * freq * (0.5 + n(temperature, freq))
                                  for i, freq in enumerate(frequency)])
 
-    total_energy = simps(total_energy, frequency) * N_a / 1000  # KJ/K/mol
+    total_energy = simps(total_energy, x=frequency) * N_a / 1000  # KJ/K/mol
     return total_energy
 
 
@@ -52,7 +52,7 @@ def get_free_energy(temperature, frequency, dos):
                                  for i, freq in enumerate(frequency)])
 
     free_energy[0] = 0
-    free_energy = simps(free_energy, frequency) * N_a / 1000  # KJ/K/mol
+    free_energy = simps(free_energy, x=frequency) * N_a / 1000  # KJ/K/mol
     return free_energy
 
 
@@ -64,7 +64,7 @@ def n(temp, freq):
     free_energy_c = np.nan_to_num([dos[i] * -h_bar/2 *shift*(n(temperature, freq) + 1 / 2.)
                                    for i, freq in enumerate(frequency)])
 
-    free_energy_c = simps(free_energy_c, frequency) * N_a / 1000 # KJ/K/mol
+    free_energy_c = simps(free_energy_c, x=frequency) * N_a / 1000 # KJ/K/mol
     return free_energy_c
 
 
@@ -81,7 +81,7 @@ def n(temp, freq):
 
     free_energy_c = free_energy_1 - free_energy_2
 
-    free_energy_c = simps(free_energy_c, frequency) * N_a / 1000 # KJ/K/mol
+    free_energy_c = simps(free_energy_c, x=frequency) * N_a / 1000 # KJ/K/mol
     return free_energy_c
 
 
@@ -93,7 +93,7 @@ def coth(x):
     entropy = np.nan_to_num([dos[i]*(1.0 / (2. * temperature) * h_bar * freq * coth(h_bar * freq / (2 * k_b * temperature))
                                      - k_b * np.log(2 * np.sinh(h_bar * freq / (2 * k_b * temperature))))
                              for i, freq in enumerate(frequency)])
-    entropy = simps(entropy, frequency) * N_a # J/K/mol
+    entropy = simps(entropy, x=frequency) * N_a # J/K/mol
     return entropy
 
 # Alternative way to calculate entropy (not used)
@@ -105,7 +105,7 @@ def n(temp, freq):
     entropy = np.nan_to_num([dos[i] * k_b * ((n(temperature, freq) + 1) * np.log(n(temperature, freq) + 1)
                                              - n(temperature, freq) * np.log(n(temperature, freq)))
                          for i, freq in enumerate(frequency)])
-    entropy = simps(entropy, frequency) * N_a # J/K/mol
+    entropy = simps(entropy, x=frequency) * N_a # J/K/mol
     return entropy
 
 
@@ -116,7 +116,7 @@ def z(temp, freq):
 
     c_v = np.nan_to_num([dos[i] * k_b * pow(z(temperature, freq), 2) * np.exp(z(temperature, freq)) / pow(np.exp(z(temperature, freq)) - 1, 2)
                          for i, freq in enumerate(frequency)])
-    c_v = simps(c_v, frequency) * N_a # J/K/mol
+    c_v = simps(c_v, x=frequency) * N_a # J/K/mol
 
     return c_v