2f:Teb8,data_raw= [ { "y": 0.0624, "x": 48.8961 }, { "y": 3.7989, "x": 59.8105 }, { "y": 0.6819, "x": 82.0896 }, { "y": 3.6402, "x": 100.0766 }, { "y": 7.3408, "x": 126.8707 }, { "y": 0.0305, "x": 144.1426 }, { "y": 0.2887, "x": 202.2492 }, { "y": 50.8225, "x": 255.5271 }, { "y": 58.1423, "x": 259.45 }, { "y": 2.1249, "x": 277.5248 }, { "y": 8.0589, "x": 354.9531 }, { "y": 5.0614, "x": 472.2665 }, { "y": 1.0322, "x": 483.2614 }, { "y": 14.0249, "x": 770.9218 }, { "y": 1.4457, "x": 785.6352 }, { "y": 6.8015, "x": 824.8677 }, { "y": 67.7721, "x": 881.3717 }, { "y": 97.4698, "x": 922.4147 }, { "y": 153.4756, "x": 945.0484 }, { "y": 6.8097, "x": 978.1783 }, { "y": 15.0688, "x": 982.1986 }, { "y": 9.8045, "x": 1007.6604 }, { "y": 0.2747, "x": 1052.9094 }, { "y": 7.3005, "x": 1085.5383 }, { "y": 48.7789, "x": 1097.5763 }, { "y": 0.1291, "x": 1104.9296 }, { "y": 2.1185, "x": 1118.0461 }, { "y": 15.7291, "x": 1131.192 }, { "y": 27.2601, "x": 1142.8979 }, { "y": 3.1854, "x": 1194.2036 }, { "y": 26.6424, "x": 1218.7805 }, { "y": 10.262, "x": 1228.7351 }, { "y": 0.1316, "x": 1260.1022 }, { "y": 1.2941, "x": 1268.1 }, { "y": 8.202, "x": 1272.8092 }, { "y": 4.9362, "x": 1284.7259 }, { "y": 1.6633, "x": 1295.8257 }, { "y": 1.662, "x": 1297.8343 }, { "y": 10.6313, "x": 1336.774 }, { "y": 0.3324, "x": 1366.9425 }, { "y": 0.6184, "x": 1376.3751 }, { "y": 34.9051, "x": 1376.9607 }, { "y": 8.6875, "x": 1489.2456 }, { "y": 0.5533, "x": 1490.2035 }, { "y": 0.0729, "x": 1491.8127 }, { "y": 7.1556, "x": 1493.5091 }, { "y": 1.52, "x": 1494.2922 }, { "y": 0.2483, "x": 1500.2333 }, { "y": 45.0829, "x": 1543.0649 }, { "y": 33.1028, "x": 1543.4096 }, { "y": 171.4676, "x": 2791.5468 }, { "y": 200.9447, "x": 2791.714 }, { "y": 5.3061, "x": 2951.0599 }, { "y": 23.9265, "x": 2951.7737 }, { "y": 67.5693, "x": 2953.5669 }, { "y": 7.2541, "x": 2958.3694 }, { "y": 44.852, "x": 2962.3419 }, { "y": 307.0503, "x": 2966.2139 }, { "y": 36.9729, "x": 2978.7167 }, { "y": 139.8752, "x": 2980.0164 }, { "y": 103.5201, "x": 2995.3742 }, { "y": 87.4538, "x": 2996.156 }, { "y": 8.6212, "x": 3394.5751 }, { "y": 12.7016, "x": 3394.8984 }, { "y": 6.1278, "x": 3430.6333 }, { "y": 5.5263, "x": 3430.7316 } ]30:[] 2d:{"title":"Compute line for simulated IR Spectrum","cells":[{"id":0,"value":"# Compute line for simulated IR Spectrum","pinned":false,"hidden":false,"mode":"md"},{"id":15,"value":"Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\" },\n marks: [\n Plot.ruleY([0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"navy\"\n })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":160,"value":"In this tutorial I explain how to get from the data shown above to a normalized simulated IR spectrum. I'm going to normalize the y-axis (Intensity) to values between 0 and 1 and draw a line based on the Lorentzian function of each individual data point.\n\n## Lorentzian function\n\nThe Lorentzian function gives the shape of certain types of spectral lines. It is the singly peaked function given by:","pinned":false,"hidden":false,"mode":"md"},{"id":166,"value":"

\n \n L \n (\n x \n) \n \n = \n \frac{\n}{1} \n \n \frac{\n}{\n \frac{\n}{1} \n \n Γ \n} \n

","pinned":false,"hidden":false,"mode":"html"},{"id":209,"value":"viewof gamma = Inputs.range([1, 1000], { label: \"gamma\", step: 1 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":196,"value":"single_distribution = {\n const points = 200;\n const step = 4000 / points;\n const half_gamma = gamma / 2;\n const x_0 = 0;\n\n function lorentz(x) {\n return (\n (1 / Math.PI) *\n (half_gamma / (Math.pow(x - x_0, 2) + Math.pow(half_gamma, 2)))\n );\n }\n\n const data = Array.from({ length: points }, (_, i) => {\n const x = -2000 + step * i;\n return {\n x,\n y: lorentz(x)\n };\n });\n\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":219,"value":"Plot.plot({\n marks: [\n Plot.ruleY([0]),\n Plot.lineY(single_distribution, { x: \"x\", y: \"y\", stroke: \"red\" }),\n Plot.ruleX([0], { strokeWidth: 4, stroke: \"#ccc\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":236,"value":"lines = {\n return data.map((d) => {\n const points = 200;\n const step = 4000 / points;\n return Array.from({ length: points }, (_, i) => {\n const x = step * i;\n const y = lorentz(x, d.x) * d.y;\n return {\n x,\n y\n };\n });\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":248,"value":"{\n const maxValues = lines.map((line) => Math.max(...line.map((d) => d.y)));\n return Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\" },\n marks: [\n Plot.ruleY([0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"#ccc\"\n }),\n ...lines.map((line, i) =>\n Plot.lineY(line, {\n x: \"x\",\n y: (d) => (d.y * data[i].y) / maxValues[i],\n stroke: \"red\"\n })\n )\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":280,"value":"sum_lines = {\n const data = new Array(200);\n for (let i = 0; i < 200; ++i) {\n let yAcc = 0;\n for (const line of lines) {\n yAcc += line[i].y;\n }\n data[i] = { x: lines[0][i].x, y: yAcc };\n }\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":284,"value":"Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\" },\n marks: [\n Plot.ruleY([0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"#ccc\"\n }),\n Plot.lineY(sum_lines, { x: \"x\", y: \"y\", stroke: \"red\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":290,"value":"normalized_sum_line = {\n const max = Math.max(...sum_lines.map((d) => d.y));\n\n return sum_lines.map((d) => {\n d.y = d.y / max;\n return d;\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":294,"value":"Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\", reverse: true },\n marks: [\n Plot.ruleY([1, 0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"#ccc\"\n }),\n Plot.lineY(normalized_sum_line, { x: \"x\", y: \"y\", stroke: \"red\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":157,"value":"---\n\n### Constants","pinned":false,"hidden":false,"mode":"md"},{"id":12,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs"},{"id":263,"value":"data = {\n const raw = Array.from({ length: data_raw.length });\n const max = Math.max(...data_raw.map(({ y }) => y));\n\n return data_raw.map((d) => {\n d.y = d.y / max;\n return d;\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":238,"value":"lorentz = function lorentz(x, x_0) {\n const half_gamma = gamma / 2;\n\n return (\n (1 / Math.PI) *\n (half_gamma / (Math.pow(x - x_0, 2) + Math.pow(half_gamma, 2)))\n );\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"1","titling":"auto"}