{"cells":[{"cell_type":"markdown","metadata":{},"source":["## Implementation notes\n\n"]},{"cell_type":"markdown","metadata":{},"source":["This notebook has been used in a classroom setting\n\n- show the shape of Morse potential\n- illustrate connections between Morse parameters and molecular parameters (equilibrium bond length, bond strength)\n\n"]},{"cell_type":"markdown","metadata":{},"source":["## Comparing Morse potentials of several diatomics\n\n"]},{"cell_type":"markdown","metadata":{},"source":["General form for (simple) harmonic potential\n$$ V(r) = \\frac{1}{2}k(r-r_e)^2$$\n\nGeneral form for the [Morse potential](https://en.wikipedia.org/wiki/Morse_potential)\n\n$$V_m(r)= De \\left [ 1 − e^{−β(r−r_e)} \\right ] ^{2} $$\nwhere $\\alpha = \\sqrt{k/2D_e}$\n\nThe independent variable is $r-r_e$.\n\n"]},{"cell_type":"markdown","metadata":{},"source":["## Python Environment\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import matplotlib.pyplot as plt\n%matplotlib inline\nfrom matplotlib import style\n# style.use(\"seaborn-talk\")\nimport numpy as np\n\nfrom scipy.constants import hbar\nfrom scipy.constants import Planck as h\nfrom scipy.constants import Boltzmann as kB"]},{"cell_type":"markdown","metadata":{},"source":["## Task: Use the Morse potential to model bonds in diatomic molecules.\n\n"]},{"cell_type":"markdown","metadata":{},"source":["**Plan:** Calculate and plot the Morse potential for several diatomic molecules in a series. \n\nVm() takes molecular parameters from a textbook or NIST Webbook. Eho and Eaho calculate the classical harmonic and quantum anharmonic energy levels, respectively.\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["def Vm(r, re, k, D):\n \"Morse potential at r given spectroscopic constants\"\n\n alpha = np.sqrt(k/(2*D))\n return D * (1 - np.exp(-alpha*(r - re)))**2\n\ndef Eho(nu, v=0):\n \"\"\"Harmonic oscillator energy (J) of vibrational level v.\n nu is frequency in s^-1\"\"\"\n\n return h*nu*(v+1/2)\n\ndef Eaho(nu, v, D0):\n \"\"\"Anharmonic energy (J) of vibrational level v.\n nu=frequency (s^-1)\n D0=depth (J/molec)\"\"\"\n\n De = D0 + Eho(nu, 0)\n return h*nu*(v+1/2) - (h*nu)**2 / (4*De) * (v+1/2)**2"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":""},"metadata":{},"output_type":"display_data"}],"source":["pm = 1e-12 # picometer/meter conversion\nr = np.linspace(50*pm, 500*pm, 500) # internuclear separation, m\n\n# HCl spectroscopic parameters from Engle & Reid, 3rd, Table 19.3 \nre = 127.5 * pm # equilbrium separation, m\nD0 = 7.17e-19 # dissociation energy from E0, J/molecule\nk = 516 # force constant, N/m\nnu = 8.97e13 # frequency, Hz\nzpe = Eho(nu, 0) # zero-point energy, J\nHCl = [re, k, D0+zpe] # list of parameters to pass to Vm()\nV_HCl = Vm(r, *HCl) # Morse potential for HCl\n\nplt.plot(r, V_HCl, label=\"HCl\")\nplt.xlabel('r/m'); plt.ylabel('V(r)')\nplt.ylim(0, 1e-18)\nplt.legend()\n\n# plot some vibrational energy levels on Morse curve\nvlevels = np.arange(25)\nElevels = Eaho(nu, vlevels, D0)\n\nfor level in Elevels:\n xmin = r[np.where(V_HCl < level)][0]\n xmax = r[np.where(V_HCl < level)][-1]\n plt.hlines(level, xmin, xmax)"]},{"cell_type":"markdown","metadata":{},"source":["Note the energy is in J/molecule. For comparison, recall what region of the EM spectrum excites vibrational transitions. Also, compare to the energy available at room temperature. Is it likely an HCl molecule with be in an excited state at room temp?\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":"4.141945559999999e-21"}],"source":["kB * 300 # T in K; result in J"]},{"cell_type":"markdown","metadata":{},"source":["Repeat for other hydrogen halides.\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":""},"metadata":{},"output_type":"display_data"}],"source":["# parameters for HF\nre = 91.68*pm # m\nk = 966 # N/m\nD0 = 9.46e-19 # J/molecule\nnu = 1.24e14 # Hz\nzpe = Eho(0,nu) # J\nHF = (re, k, D0+zpe)\n\n# parms for HBr\nnu = 7.94e13\nzpe = Eho(0,7.94e13)\nHBr = [141.*pm, 412, 6.08e-19+zpe]\n\nnames = ['HF', 'HCl', 'HBr']\nfor name, parms in zip(names, (HF, HCl, HBr)):\n plt.plot(r, Vm(r, *parms), label=name)\nplt.legend()\nplt.ylim(0,1e-18)\nplt.xlabel('r/m'); plt.ylabel('V(r)/J');"]},{"cell_type":"markdown","metadata":{},"source":["Often these curves are plotted with $V(r\\rightarrow \\infty)=0$. It is reasonable to define [zero potential](https://en.wikipedia.org/wiki/Morse_potential#Potential_energy_function) anywhere, so separated atoms is a convenient choice for $V=0$.\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":""},"metadata":{},"output_type":"display_data"}],"source":["names = ['HF', 'HCl', 'HBr']\n\nfor name, parms in zip(names, (HF, HCl, HBr)):\n offset = Vm(1e-9, *parms) # arbitrarily large value for r\n plt.plot(r, Vm(r, *parms)-offset, label=name)\n plt.legend()\nplt.ylim(-1e-18,1e-18)\nplt.axhline(0,lw=1, color='k')\nplt.xlabel('r/m'); plt.ylabel('V(r)/J');"]},{"cell_type":"markdown","metadata":{},"source":["## Comparing double and triple bonds\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Predict the behavior of the potential curves for single, double, and triple bonds in molecules. Then plot them.\n\n"]},{"cell_type":"markdown","metadata":{},"source":["*Solution*\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["# values from ER3 Table 19.3\n# N2\nnu = 7.07e13 # Hz\nk = 2295 # Nm\nre = 109.8*pm # m\nD0 = 1.57e-18 + Eho(nu, 0) # J\nN2 = [re, k, D0]\n\n# O2 parameters\nO2 = [120.8*pm, 1177, 8.27e-19 + Eho(4.74e14, 0)]\n\n# CO parameters\nCO = [112.8*pm, 1902, 1.79e-18 + Eho(6.51e13, 0)]"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":""},"metadata":{},"output_type":"display_data"}],"source":["for name, parms in zip(['N$_2$','O$_2$','CO'],[N2, O2, CO]):\n plt.plot(r, Vm(r, *parms)-Vm(10e-10,*parms), label = name)\nplt.axhline(0, color='k', lw=1)\nplt.ylim(-2e-18, 1e-18)\nplt.legend()\nplt.xlabel('r/m')\nplt.ylabel('V(r)/J')\nplt.title(\"Morse curves for double- and triple-bonded diatomics\\n\");"]},{"cell_type":"markdown","metadata":{},"source":["## Questions\n\n"]},{"cell_type":"markdown","metadata":{},"source":["- Why do potentials have minima at different values of $r$?\n- What is the physical meaning of the depth of the potential well?\n- What is the physical meaning of the potentials approaching zero at large values of $r$?\n- What is the physical meaning of the potentials crossing zero at small values of $r$?\n- What determines the curvature (“steepness”) of the well?\n- How are vibrational frequency and bond strength related?\n- How are vibrational frequency and atomic mass related?\n\n"]},{"cell_type":"markdown","metadata":{},"source":["## Appendix\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Python tricks\n\n- Functions can have arguments with default values assigned in the function defintion. Arguments with default values must come after arguments without default values\n- Arguments can be passed to a function in many forms like lists or objects (see the list of molecular parameters above).\n- \\`\\*\\` arguments and **tuple unpacking** are handy when lots of arguments are being passed. Search terms for more information: “star arguments”, “kwarg python”, “tuple unpacking”.\n\n"]}],"metadata":{"org":null,"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.5.2"}},"nbformat":4,"nbformat_minor":0}