# Broad Broadening line spectrum with voigt profile ```python import numpy as np import matplotlib.pyplot as plt from TRXASprefitpack import gen_theory_data plt.rcParams["figure.figsize"] = (14,10) ``` ## basic defintion of gen_theory_data ```python help(gen_theory_data) ``` Help on function gen_theory_data in module TRXASprefitpack.mathfun.broad: gen_theory_data(e: numpy.ndarray, peaks: numpy.ndarray, A: float, fwhm_G: float, fwhm_L: float, peak_factor: float, policy: Union[str, NoneType] = 'shift') -> numpy.ndarray voigt broadening theoretically calculated lineshape spectrum Args: e: energy A: scaling parameter fwhm_G: full width at half maximum of gaussian shape (unit: same as energy) fwhm_L: full width at half maximum of lorenzian shape (unit: same as energy) peak_factor: Peak factor, its behavior depends on policy. policy: Policy to match discrepency between experimental data and theoretical spectrum. * 'shift' : Default option, shift peak position by peak_factor * 'scale' : scale peak position by peak_factor Returns: numpy ndarray of voigt broadened theoritical lineshape spectrum ## Define line spectrum Which has three peaks at 2833, 2835, 2838 eV with ratio 2:4:1 ```python peaks = np.array([[2833, 2], [2835, 4], [2838, 2]]) ``` ```python e = np.arange(2830,2845, 0.01) ``` ## Gaussian broadening 1. fwhm_G = 1 eV 2. fwhm_G = 2 eV 3. fwhm_G = 3 eV ```python gau_broad_1eV = gen_theory_data(e, peaks, 1, 1, 0, 0) # Note voigt profile with fwhm_L = 0 is gaussian gau_broad_2eV = gen_theory_data(e, peaks, 1, 2, 0, 0) # Note voigt profile with fwhm_L = 0 is gaussian gau_broad_3eV = gen_theory_data(e, peaks, 1, 3, 0, 0) # Note voigt profile with fwhm_L = 0 is gaussian ``` ```python plt.plot(e, gau_broad_1eV, label='gaussian broadening fwhm_G: 1 eV') plt.plot(e, gau_broad_2eV, label='gaussian broadening fwhm_G: 2 eV') plt.plot(e, gau_broad_3eV, label='gaussian broadening fwhm_G: 3 eV') plt.legend() plt.show() ``` ![png](broad_files/broad_9_0.png) ## Lorenzian broadening 1. fwhm_L = 1 eV 2. fwhm_L = 2 eV 3. fwhm_L = 3 eV ```python loren_broad_1eV = gen_theory_data(e, peaks, 1, 0, 1, 0) # Note voigt profile with fwhm_G = 0 is lorenzian loren_broad_2eV = gen_theory_data(e, peaks, 1, 0, 2, 0) # Note voigt profile with fwhm_G = 0 is lorenzian loren_broad_3eV = gen_theory_data(e, peaks, 1, 0, 3, 0) # Note voigt profile with fwhm_G = 0 is lorenzian ``` ```python plt.plot(e, loren_broad_1eV, label='lorenzian broadening fwhm_L: 1 eV') plt.plot(e, loren_broad_2eV, label='lorenzian broadening fwhm_L: 2 eV') plt.plot(e, loren_broad_3eV, label='lorenzian broadening fwhm_L: 3 eV') plt.legend() plt.show() ``` ![png](broad_files/broad_12_0.png) ## voigt broadening 1. fwhm_G = 1.5eV, fwhm_L = 0.5eV 2. fwhm_G = 1.0eV, fwhm_L = 1.0eV 3. fwhm_G = 0.5eV, fwhm_L = 1.5eV ```python voigt_broad_1 = gen_theory_data(e, peaks, 1, 1.5, 0.5, 0) voigt_broad_2 = gen_theory_data(e, peaks, 1, 1.0, 1.0, 0) voigt_broad_3 = gen_theory_data(e, peaks, 1, 0.5, 1.5, 0) ``` ```python plt.plot(e, voigt_broad_1, label='voigt broadening fwhm_G: 1.5 eV, fwhm_L: 0.5 eV') plt.plot(e, voigt_broad_2, label='voigt broadening fwhm_G: 1.0 eV, fwhm_L: 1.0 eV') plt.plot(e, voigt_broad_3, label='voigt broadening fwhm_G: 0.5 eV, fwhm_L: 1.5 eV') plt.legend() plt.show() ``` ![png](broad_files/broad_15_0.png) ## peak shift To see how peak shift afftects broadened spectrum, set fwhm_G = fwhm_L = 1.0 eV ```python voigt_broad_peak_shift0 = gen_theory_data(e, peaks, 1, 1.0, 1.0, 0) voigt_broad_peak_shiftm5 = gen_theory_data(e, peaks, 1, 1.0, 1.0, -5) voigt_broad_peak_shift5 = gen_theory_data(e, peaks, 1, 1.0, 1.0, 5) ``` ```python plt.plot(e, voigt_broad_peak_shift0, label='peak_shift: 0 eV') plt.plot(e, voigt_broad_peak_shiftm5, label='peak_shift: -5 eV') plt.plot(e, voigt_broad_peak_shift5, label='peak_shift: 5 eV') plt.legend() plt.show() ``` ![png](broad_files/broad_18_0.png) peak_shift moves spectrum to -peak_shift. ## Intensity scaling To see how intensity scaling afftects spectrum fix fwhm_G=fwhm_L=1.0 eV and peak_shift=0 1. A: 0.5 2. A: 1.0 3. A: 2.0 ```python voigt_broad_scale_half = gen_theory_data(e, peaks, 0.5, 1.0, 1.0, 0) voigt_broad_scale1 = gen_theory_data(e, peaks, 1, 1.0, 1.0, 0) voigt_broad_scale2 = gen_theory_data(e, peaks, 2, 1.0, 1.0, 0) ``` ```python plt.plot(e, voigt_broad_scale_half, label='A(scale): 0.5') plt.plot(e, voigt_broad_scale1, label='A(scale): 1.0') plt.plot(e, voigt_broad_scale2, label='A(scale): 2.0') plt.legend() plt.show() ``` ![png](broad_files/broad_22_0.png) ## Peak position scaling Different from electron-excited spectrum, one can match theoretically calculated vibrational spectrum (IR, Raman) to experimental one by uniformly scaling peak position of theoretically calculated peaks ``gen_thoery_data`` scales peak position instead of shifting by setting ``policy`` argument to ``scale`` ```python thy_ir_peak = np.array([[235, 661, 917, 1181, 1298, 1348, 1501, 1688, 3172, 3178, 3195 , 618, 826, 1036, 1175, 1200, 1394, 1433, 1501, 1597, 3181, 3208 , 92, 388, 484, 746, 892, 962] , [1.284, 0.803, 1.7269, 4.6578, 8.2517, 4.191, 1.2156, 6.8394, 10.9014, 16.4984, 73.323 , 8.1709, 0.0041, 3.9287, 1.2982, 1.6477, 4.005, 0.5812, 1.8711, 4.4402, 3.00e-04, 77.3937 , 0.8536, 0.0804, 12.81, 59.6901, 55.4987, 6.1347]]) thy_ir_peak = thy_ir_peak.T nu = np.arange(200, 3500, 1) fwhm_G = 15 # cm-1 pos_scale_1 = gen_theory_data(nu, thy_ir_peak, 1, fwhm_G, 0, 0.95, policy='scale') pos_scale_2 = gen_theory_data(nu, thy_ir_peak, 1, fwhm_G, 0, 1, policy='scale') pos_scale_3 = gen_theory_data(nu, thy_ir_peak, 1, fwhm_G, 0, 1.05, policy='scale') ``` ```python plt.plot(nu, pos_scale_1, label='peak scale: 0.95') plt.plot(nu, pos_scale_2, label='peak scale: 1') plt.plot(nu, pos_scale_3, label='peak scale: 1.05') plt.legend() plt.xlim(300, 2000) plt.ylim(0, 4.0) plt.show() ``` ![png](broad_files/broad_25_0.png) ```python plt.plot(nu, pos_scale_1, label='peak scale: 0.95') plt.plot(nu, pos_scale_2, label='peak scale: 1') plt.plot(nu, pos_scale_3, label='peak scale: 1.05') plt.legend() plt.xlim(2950, 3500) plt.ylim(0, 6) plt.show() ``` ![png](broad_files/broad_26_0.png)