{ "cells": [ { "cell_type": "markdown", "id": "eeb120d6", "metadata": {}, "source": [ "# Contact shift" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "d5199d16", "metadata": {}, "source": [ "The contact shift occurs due to an isotropic hyperfine coupling between an electron and a nucleus, where the electron relaxes quickly compared to the size of the coupling. The result is that the coupling is averaged away, and therefore only a single peak appeals. Due to the electron polarization, however, the apparent shift of the nucleus is altered, according to:\n", "\n", "$$\n", "\\begin{equation}\n", "\\Delta_{CS}=\\frac{A_{iso}}{2}*P_{e-}\n", "\\end{equation}\n", "$$\n", "\n", "where $A_{iso}$ is the size of the isotropic hyperfine coupling, and $P_{e-}$ is the electron polarization. Then, the size of the contact shift is dependent on temperature, since it depends on the electron polarization.\n", "\n", "Correct calculation of the contact shift, and the more complex [pseudo-contact shift](../Chapter5/Ch5_PseudoContactShift.ipynb) requires correct thermalization of coherences, achieved in SLEEPY via Lindblad thermalization.$^1$\n", "\n", "[1] C. Bengs, M. Levitt. [*J. Magn. Reson.*](https://doi.org/10.1016/j.jmr.2019.106645), **2020**, 310,106645." ] } , { "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": "markdown", "id": "26112167", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2, "id": "1687131c", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "af54186c", "metadata": {}, "source": [ "## Build the spin-system" ] }, { "cell_type": "markdown", "id": "73641d12", "metadata": {}, "source": [ "To observe the contact shift, we just need an electron-nuclear system with an isotropic hyperfine coupling (i.e. $A_{xx}=A_{yy}=A_{zz}$). We may use the above formula to predict the size of the contact shift." ] }, { "cell_type": "code", "execution_count": 3, "id": "e7a61f58", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We expect a contact shift of -112.55 Hz\n" ] } ], "source": [ "ex=sl.ExpSys(v0H=850,Nucs=['13C','e-'],T_K=298)\n", "Aiso=5000\n", "ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=Aiso,Ayy=Aiso,Azz=Aiso)\n", "print(f'We expect a contact shift of {Aiso/2*ex.Peq[1]:.2f} Hz')" ] }, { "cell_type": "markdown", "id": "5a03f55a", "metadata": {}, "source": [ "## Define the Liouvillian, simulate without relaxation" ] }, { "cell_type": "markdown", "id": "405a3082", "metadata": {}, "source": [ "We will run two simulations. In the first, there will be no relaxation present, just thermal polarization. In the latter, we'll add electron $T_1$ (and $T_2$, to keep physical behavior).\n", "\n", "Note that to get the correct thermal polarization of the $S^\\alpha I_x$ and $S^\\beta I_x$, we have to start at thermal polarization and apply a $\\pi$/2 pulse." ] }, { "cell_type": "code", "execution_count": 4, "id": "6ed562f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "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": [ "# No relaxation\n", "L=ex.Liouvillian() #Liouville object\n", "\n", "# Define the sequence\n", "Dt=1/4000/2 #Short enough time step for 8000 Hz spectral width\n", "seq=L.Sequence(Dt=Dt)\n", "\n", "# Create density matrix, prepare with pi/2 pulse\n", "no_rlx=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Upi2=L.Udelta('13C',np.pi/2,np.pi/2)\n", "Upi2*no_rlx\n", "\n", "# Run and plot spectrum\n", "no_rlx.DetProp(seq,n=512)\n", "_=no_rlx.plot(axis='kHz',FT=True,apodize=True)" ] }, { "cell_type": "markdown", "id": "7e865591", "metadata": {}, "source": [ "Indeed, we get two peaks for each state of the electron, but they have different amplitudes due to the electron polarization." ] }, { "cell_type": "markdown", "id": "e0fa652e", "metadata": {}, "source": [ "## Add relaxation" ] }, { "cell_type": "markdown", "id": "6028e082", "metadata": {}, "source": [ "Here, we add fast $T_1$ and $T_2$ relaxation. We need the electrons to recover to their thermal equilibrium, so we use `L.add_relax(Type='recovery')` to thermalize the system. " ] }, { "cell_type": "code", "execution_count": 5, "id": "830a7116", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->2\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Now add T1 relaxation\n", "L.add_relax(Type='T1',i=1,T1=1e-6)\n", "L.add_relax(Type='T2',i=1,T2=1e-9)\n", "L.add_relax(Type='recovery')\n", "\n", "# Define the sequence\n", "Dt=1/8000 #Short enough time step for 8000 Hz spectral width\n", "seq=L.Sequence(Dt=Dt)\n", "\n", "# Create density matrix, prepare with pi/2 pulse\n", "rlx=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Upi2=L.Udelta('13C',np.pi/2,np.pi/2)\n", "Upi2*rlx\n", "\n", "# Run\n", "rlx.DetProp(seq,n=512)\n", "\n", "# Plot\n", "fig,ax=plt.subplots(1,2,figsize=[8,4])\n", "no_rlx.plot(axis='kHz',FT=True,apodize=True,ax=ax[0])\n", "rlx.plot(axis='kHz',FT=True,apodize=True,ax=ax[0])\n", "ax[0].legend(('No relaxation','With relaxation'))\n", "no_rlx.plot(axis='Hz',FT=True,apodize=True,ax=ax[1])\n", "rlx.plot(axis='Hz',FT=True,apodize=True,ax=ax[1])\n", "ax[1].set_xlim(1000,-1000)\n", "ax[1].set_ylim(ax[1].get_ylim())\n", "ax[1].plot(Aiso/2*ex.Peq[1]*np.ones(2),ax[1].get_ylim(),color='grey',linestyle=':')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "bcca2104", "metadata": {}, "source": [ "Indeed, the resulting contact shift is exactly where expected (-112 Hz), as marked with the dashed line." ] }, { "cell_type": "markdown", "id": "c7d5ba5a", "metadata": {}, "source": [ "Without relaxation, we obtain two peaks at $\\pm$2500 Hz, with the peak at -2500 Hz being slightly higher in amplitude, due to the higher electron polarization for that state. When electron $T_1$ relaxation is included, the two peaks get averaged together, weighted according to their amplitude, yielding the peak at -112 Hz. " ] }, { "cell_type": "markdown", "id": "2cdd9525", "metadata": {}, "source": [ "## Sweep the temperature\n", "An interesting effect with the contact shift is its dependence on temperature. As we increase temperature, the peak gets smaller due to less polarization on the spin, and the contact shift is decreased, since the electron polarization is decreased." ] }, { "cell_type": "code", "execution_count": 6, "id": "a96b1bbb", "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", "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Dt=1/4000 #Short enough time step for 4000 Hz spectral width\n", "seq=L.Sequence(Dt=Dt)\n", "\n", "ax=plt.figure().add_subplot(111)\n", "T=np.logspace(np.log10(20),np.log10(200),8)\n", "for T_K in T:\n", " ex.T_K=T_K\n", " \n", " rho.clear()\n", " Upi2*rho\n", " rho.DetProp(seq,n=4096)\n", " \n", " rho.plot(FT=True,apodize=True,ax=ax,axis='kHz')\n", "ax.figure.set_size_inches([6,4])\n", "_=ax.legend([f'T = {T_K:.0f} K' for T_K in T])" ] }, { "cell_type": "markdown", "id": "1ceb8f8e", "metadata": {}, "source": [ "Note that the contact shift has the same dependence on magnetic field as a normal chemical shift: the hyperfine coupling remains fixed with field, but the electron polarization grows linearly with field (in the high-temperature approximation)" ] }, { "cell_type": "code", "execution_count": 7, "id": "d4996be3", "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", "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": [ "ex.T_K=200\n", "rho=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Dt=1/1000 #Short enough time step for 4000 Hz spectral width\n", "\n", "fig,ax=plt.subplots(1,2)\n", "fig.set_size_inches([9,4])\n", "\n", "B00=np.linspace(5,30,6)\n", "for B0 in B00:\n", " ex=sl.ExpSys(B0=B0,Nucs=['13C','e-'],T_K=298)\n", " ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=Aiso,Ayy=Aiso,Azz=Aiso)\n", " L=ex.Liouvillian()\n", " L.add_relax(Type='T1',i=1,T1=1e-6)\n", " L.add_relax(Type='T2',i=1,T2=1e-9)\n", " L.add_relax(Type='recovery')\n", " seq=L.Sequence(Dt=Dt)\n", " Upi2=L.Udelta('13C',phi=np.pi/2,phase=np.pi/2)\n", " \n", " rho.clear()\n", " Upi2*rho\n", " rho.DetProp(seq,n=4096)\n", " \n", " rho.plot(FT=True,apodize=True,ax=ax[0],axis='kHz')\n", " rho.plot(FT=True,apodize=True,ax=ax[1],axis='ppm')\n", "\n", "ax[0].legend([f'B0 = {B0:.0f} T' for B0 in B00])\n", "ax[0].set_xlim([0.5,-0.5])\n", "ax[1].set_xlim([5,-5])\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "91db0688", "metadata": {}, "source": [ "If the temperature approaches 0 K, then the electron is no longer in the high-temperature approximation, and therefore the contact shift is no longer linear with the field, as demonstrated below." ] }, { "cell_type": "code", "execution_count": 10, "id": "96b046ef", "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", "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": [ "rho=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Dt=1/5000/2 #Short enough time step for 4000 Hz spectral width\n", "\n", "\n", "fig,ax=plt.subplots(1,2)\n", "fig.set_size_inches([9,4])\n", "\n", "B00=np.linspace(5,30,6)\n", "for B0 in B00:\n", " ex=sl.ExpSys(B0=B0,Nucs=['13C','e-'],T_K=10)\n", " ex.set_inter(Type='hyperfine',i0=0,i1=1,Axx=Aiso,Ayy=Aiso,Azz=Aiso)\n", " L=ex.Liouvillian()\n", " L.add_relax(Type='T1',i=1,T1=1e-6)\n", " L.add_relax(Type='T2',i=1,T2=1e-9)\n", " L.add_relax(Type='recovery')\n", " seq=L.Sequence(Dt=Dt)\n", " Upi2=L.Udelta('13C',phi=np.pi/2,phase=np.pi/2)\n", " \n", " rho.clear()\n", " Upi2*rho\n", " rho.DetProp(seq,n=4096)\n", " rho.plot(FT=True,apodize=True,ax=ax[0],axis='kHz')\n", " rho.plot(FT=True,apodize=True,ax=ax[1],axis='ppm')\n", " \n", "ax[0].legend([f'B0 = {B0:.0f} T' for B0 in B00])\n", "ax[0].set_xlim([3,-3])\n", "ax[1].set_xlim([20,-20])\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "e9692756", "metadata": {}, "source": [ "The contact shift only occurs where an isotropic hyperfine coupling is present, so no through-space contact shift occurs. On the other hand, the dipolar-modulated pseudocontact shift, discussed in the next [section](Ch5_PseudoContactShift.ipynb), can induce a similar effect." ] } ], "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 }