{ "cells": [ { "cell_type": "markdown", "id": "cf0672bd", "metadata": {}, "source": [ "# Short Examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "b7f35a16", "metadata": {}, "source": [ "The following notebook shows some simulations that can be done in just a few lines of code. These are intended to familiarize you with the basics of setting up SLEEPY simulations." ] }, { "cell_type": "markdown", "id": "8d434c7e", "metadata": {}, "source": [ "## Setup" ] } , { "cell_type": "code", "execution_count": 0, "metadata": {"tags": [ "remove-cell" ]}, "outputs": [], "source": [ "# SETUP SLEEPY\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " !pip install sleepy-nmr" ] }, { "cell_type": "code", "execution_count": 2, "id": "dcef0a0b", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "9d2dcb53", "metadata": {}, "source": [ "## 1D Spectrum in Exchange\n", "Two peaks, separated by 10 ppm, with a correlation time of exchange of 1 ms." ] }, { "cell_type": "code", "execution_count": 3, "id": "7a8f1cdf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 8->2\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ex0=sl.ExpSys(v0H=600,Nucs='13C')\n", "ex1=ex0.copy()\n", "ex0.set_inter('CS',i=0,ppm=5)\n", "ex1.set_inter('CS',i=0,ppm=-5)\n", "\n", "L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=1e-3))\n", "seq=L.Sequence(Dt=1/3000) #1/(2*10 ppm*150 MHz)\n", "\n", "rho=sl.Rho('13Cx','13Cp')\n", "rho.DetProp(seq,n=4096)\n", "_=rho.plot(FT=True,axis='ppm')" ] }, { "cell_type": "markdown", "id": "6c3cd160", "metadata": {}, "source": [ "## $T_1$ relaxation in solid-state NMR\n", "$^{13}$C $T_1$ relaxation in solid-state NMR, due to a 30$^\\circ$ reorientation of the H–C dipole coupling, occuring with a correlation time of 1 ns." ] }, { "cell_type": "code", "execution_count": 4, "id": "c50a2d3c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ex0=sl.ExpSys(v0H=600,Nucs=['13C','1H'],vr=10000,LF=True) #T1 occurs only due to terms in the lab frame\n", "ex1=ex0.copy()\n", "ex0.set_inter('dipole',i0=0,i1=1,delta=44000)\n", "ex1.set_inter('dipole',i0=0,i1=1,delta=44000,euler=[0,30*np.pi/180,0])\n", "\n", "L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=1e-9))\n", "seq=L.Sequence() #Defaults to 1 rotor period\n", "\n", "rho=sl.Rho('13Cz','13Cz')\n", "rho.DetProp(seq,n=10000*10) #10 seconds\n", "_=rho.plot(axis='s')" ] }, { "cell_type": "markdown", "id": "7ce810ca", "metadata": {}, "source": [ "## $T_{1\\rho}$ relaxation\n", "$^{13}$C $T_{1\\rho}$ relaxation in solid-state NMR, due to a 30$^\\circ$ reorientation of the H–C dipole coupling, occuring with a correlation time of 100 ns." ] }, { "cell_type": "code", "execution_count": 5, "id": "9cb4104c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 32->16\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ex0=sl.ExpSys(v0H=600,Nucs=['13C','1H'],vr=10000)\n", "ex1=ex0.copy()\n", "ex0.set_inter('dipole',i0=0,i1=1,delta=44000)\n", "ex1.set_inter('dipole',i0=0,i1=1,delta=44000,euler_d=[0,30,0])\n", "\n", "L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=1e-7))\n", "seq=L.Sequence().add_channel('13C',v1=25000) #Defaults to 1 rotor period\n", "\n", "rho=sl.Rho('13Cx','13Cx')\n", "rho.DetProp(seq,n=1500) #100 ms\n", "_=rho.plot()" ] }, { "cell_type": "markdown", "id": "1b30602f", "metadata": {}, "source": [ "## Chemical Exchange Saturation Transfer\n", "CEST is useful when a system has a major and minor population, the minor being invisible in the spectrum. However, applying a saturating field to the minor population will still be effective in saturating the major population, so that we may sweep the frequency of the saturating field to find the minor population's resonance frequency.\n", "\n", "In this simple example, we'll just monitor the total z-magnetization, although in the real experiment we would integrate the peak with high population (also possible in SLEEPY, but requires additional steps to acquire the full direct dimension and integrate over the correct peak)." ] }, { "cell_type": "code", "execution_count": 6, "id": "46bd1d15", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ex0=sl.ExpSys(v0H=600,Nucs='13C')\n", "ex1=ex0.copy()\n", "ex0.set_inter('CS',i=0,Hz=750)\n", "ex1.set_inter('CS',i=0,Hz=-750)\n", "\n", "L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=1e-1,p1=.95)) #5% population 2\n", "L.add_relax('T1',i=0,T1=1)\n", "L.add_relax('T2',i=0,T2=.1)\n", "L.add_relax('recovery')\n", "seq=L.Sequence(Dt=.5) #1/(2*10 ppm*150 MHz)\n", "\n", "rho=sl.Rho('13Cz','13Cz')\n", "voff0=np.linspace(-1500,1500,101)\n", "\n", "for voff in voff0:\n", " rho.reset()\n", " seq.add_channel('13C',v1=50,voff=voff)\n", " (seq*rho)()\n", "ax=rho.plot()\n", "ax.set_xticks(np.linspace(0,101,11))\n", "ax.set_xticklabels(voff0[np.linspace(0,100,11).astype(int)]/1000)\n", "_=ax.set_xlabel(r'$\\nu_{off}$ / kHz')" ] }, { "cell_type": "markdown", "id": "8fde5cac", "metadata": {}, "source": [ "## Contact shift\n", "The contact shift comes from the hyperfine coupling between a fast-relaxing electron and a nucleus. While the fast relaxing electron averages the splitting, the peak itself shifts due to polarization of the electron.\n", "\n", "We'll run the simulation as a function of temperature, where lower temperatures yield a higher shift (and more signal). Note that realistically, we wouldn't expect the electron relaxation times to remain fixed with the varying temperature." ] }, { "cell_type": "code", "execution_count": 7, "id": "4edd91bc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->2\n", "State-space reduction: 16->2\n", "State-space reduction: 16->2\n", "State-space reduction: 16->2\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=None\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','e']).set_inter('hyperfine',i0=0,i1=1,Axx=1e5,Ayy=1e5,Azz=1e5)\n", "for T in [50,100,200,400]:\n", " ex.T_K=T\n", " L=ex.Liouvillian()\n", " L.add_relax('T1',i=1,T1=1e-9)\n", " L.add_relax('T2',i=1,T2=1e-10)\n", " L.add_relax('recovery')\n", "\n", " seq=L.Sequence(Dt=5e-5)\n", "\n", " rho=sl.Rho('13Cx','13Cp')\n", " ax=rho.DetProp(seq,n=2048).plot(FT=True,ax=ax)" ] }, { "cell_type": "markdown", "id": "5b37fbe0", "metadata": {}, "source": [ "## Spinning sidebands (one liner)\n", "The last simulation is a little bit just for fun, but also to demonstrate some of the convenience of object-oriented programming in SLEEPY. We simulate $^{13}$C spinning sidebands resulting from chemical shift anisotropy. However, we set up the whole simulation in a single (broken) line of code and plot the result.\n", "\n", "Compare to Herzfeld/Berger figure 2c.$^1$\n", "\n", "[1] J. Herzfeld, A.E. Berger. [*J.Chem. Phys.*](https://doi.org/10.1063/1.440136) **1980**, 73, 6021-6030." ] }, { "cell_type": "code", "execution_count": 8, "id": "4ec19b0b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 4->1\n", "Prop: 20 steps per every 1 rotor period\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=sl.Rho('31Px','31Pp').DetProp(\n", " sl.ExpSys(B0=6.9009,Nucs='31P',vr=2060).set_inter('CSA',i=0,delta=-104,eta=.56).\\\n", " Liouvillian().Sequence(),\n", " n=4096,n_per_seq=20).plot(FT=True,axis='kHz',apodize=True)" ] } ], "metadata": { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 5 }