{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "0f3d07ef-5267-4715-9819-51aba110dce1", "metadata": {}, "outputs": [], "source": [ "import lmfit\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "2d951f03-8a2e-4941-b077-777a0a796e42", "metadata": {}, "source": [ "lavoreremo in unità atomiche:\n", "https://en.wikipedia.org/wiki/Atomic_units" ] }, { "cell_type": "code", "execution_count": 2, "id": "d6fb3614-9839-4969-9344-77e7f160e40f", "metadata": {}, "outputs": [], "source": [ "U_cm_1=5.2917721e-09\n", "U_c=137.036\n", "U_amu=1822.89\n", "U_h=2.0*np.pi\n", "U_angs=1.8897261\n", "U_eV=1/27.211386\n", "U_kJ_mol=1/2625.4996\n", "conv_v=U_cm_1*U_c*U_h\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "f36ff7a0-e882-48b6-8364-5fa0c1603bea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.009765046635958882, 0.019408985880292336)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w1_CO=2143.18*conv_v\n", "w2_CO=4259.78*conv_v\n", "mu_CO=(12.0+15.999)*U_amu\n", "w1_CO,w2_CO" ] }, { "cell_type": "code", "execution_count": 4, "id": "e861dd53-67a8-441e-8ec1-9ad91596cf05", "metadata": {}, "outputs": [], "source": [ "#livelli energetici, tratti da https://en.wikipedia.org/wiki/Morse_potential\n", "def energy_levels(alpha, De, mu):\n", " w0=alpha*np.sqrt(2*De/mu)\n", " wm_a=w0*(np.arange(3)+1/2)\n", " return wm_a-wm_a**2/4/De\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "adda19e6-fd9c-4328-86da-3b582b889703", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.00121278, 0.00340324, 0.0052802 ])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "energy_levels(4.0, 1e-2, mu_CO)" ] }, { "cell_type": "code", "execution_count": 6, "id": "24b17e30-a6a9-4b21-b240-847a3efcc4c5", "metadata": {}, "outputs": [], "source": [ "def obj_fun(parms, mu):\n", " wm_a=energy_levels(parms['alpha'].value, parms['De'].value, mu)\n", " w1=wm_a[1]-wm_a[0]\n", " w2=wm_a[2]-wm_a[0]\n", " return (w1-w1_CO)**2+(w2-w2_CO)**2" ] }, { "cell_type": "code", "execution_count": 7, "id": "518f9dc6-a912-4f99-92fb-a8962b620d3c", "metadata": {}, "outputs": [], "source": [ "parms_CO=lmfit.create_params(alpha=4.0, De=1.0e-2)" ] }, { "cell_type": "code", "execution_count": 8, "id": "87ae1f20-db9c-4257-8648-a1db33939fe6", "metadata": {}, "outputs": [], "source": [ "fit_result=lmfit.minimize(obj_fun, parms_CO, method='bfgs', args=[mu_CO],\n", " tol=1e-11)" ] }, { "cell_type": "code", "execution_count": 9, "id": "be25207b-3d8b-4f65-9984-f372186adc48", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Fit Result

Fit Statistics
fitting methodBFGS
# function evals414
# data points1
# variables2
chi-square 5.8989e-31
reduced chi-square 5.8989e-31
Akaike info crit.-65.6053787
Bayesian info crit.-69.6053787
Parameters
namevalueinitial valueminmaxvary
alpha 2.486840284.0 -inf infTrue
De 0.403310530.01 -inf infTrue
" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit_result" ] }, { "cell_type": "code", "execution_count": 10, "id": "0130328e-62d4-4499-bcc7-367f5359c976", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
Parameters
namevalueinitial valueminmaxvary
alpha 2.486840284.0 -inf infTrue
De 0.403310530.01 -inf infTrue
" ], "text/plain": [ "Parameters([('alpha', ), ('De', )])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit_result.params" ] }, { "cell_type": "code", "execution_count": 11, "id": "077093bf-738e-41a7-b079-6bd47eb4312a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(7.680403738808353e-16)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "obj_fun(fit_result.params, mu_CO)" ] }, { "cell_type": "code", "execution_count": 12, "id": "c5cd4df3-d86a-4433-9089-93e178396e1a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.00492797, 0.01469305, 0.02433695])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p=fit_result.params\n", "el=energy_levels(p['alpha'].value, p['De'].value, mu_CO)\n", "el" ] }, { "cell_type": "code", "execution_count": 13, "id": "bc9f3b33-d886-4433-a3fe-5b5aee62e966", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.float64(0.009765071278924427), 0.009765046635958882)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "el[1]-el[0], w1_CO" ] }, { "cell_type": "code", "execution_count": 14, "id": "55ecbada-efe8-45e0-bc5b-5b743e35ec9a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.float64(0.01940897320099334), 0.019408985880292336)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "el[2]-el[0], w2_CO" ] }, { "cell_type": "code", "execution_count": 15, "id": "70682c90-9bf8-4686-8be3-93d5b505ce32", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(4.6994469810158614)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p['alpha'].value*U_angs" ] }, { "cell_type": "code", "execution_count": 16, "id": "1bee6fc3-9c8c-4bef-be13-4e78d9924f5e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(1058.8916226475715)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p['De'].value/U_kJ_mol" ] }, { "cell_type": "code", "execution_count": 17, "id": "4c1a2261-aaf3-4d53-80fb-9024b8f0dcdc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(10.9746383796933)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p['De'].value/U_eV" ] }, { "cell_type": "markdown", "id": "8ea8e791-c962-4727-81dd-7d508dd536d6", "metadata": {}, "source": [ "## esercizi:\n", "1. aggiungete un grafico della curva di morse corrispondente\n", "2. applicate i parametri per HCl" ] }, { "cell_type": "code", "execution_count": null, "id": "d1a5a9f8-0c56-41c1-9a57-210a16c9250d", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }