{ "cells": [ { "cell_type": "markdown", "id": "74563bf4", "metadata": {}, "source": [ "# Understanding DARR with simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "7c8f9d66", "metadata": {}, "source": [ "While SLEEPY is mainly intended for predicting relaxation behavior or observing the influence of relaxation on a spin-system, it is also useful for simplifying other experiments by replacing diffusion-like behavior resulting from many spins with an artificial diffusion term in the Liouvillian. For example, some NMR experiments rely on spin-diffusion within the dense $^1$H network to induce broadening on heteronuclei which then drives spin-diffusion among the heteronuclei. The prime examples of this are the Proton-Driven Spin-Diffusion experiment (PDSD) and the Dipolar Assisted Rotational Resonance (DARR) experiments.\n", "\n", "DARR is the homonuclear ($^{13}$C-$^{13}$C) transfer of longitudinal magnetization, enabled by broadening of the Rotary Resonance (R$^2$) condition. Broadening of the R$^2$ condition is achieved via reintroduction of a heteronuclear dipole coupling ($^1$H-$^{13}$C) to the homonuclear spins by satisfying the Rotary Resonance Recoupling (R$^3$) condition.\n", "\n", "We will achieve a DARR transfer by artificially broadening the $^1H$ line using relaxation settings in SLEEPY. Note that it is also possible to introduce a large number of $^1$H spins (10) which will also give rise to the required broadening. The latter approach has been demonstrated in [SpinEvolution](https://spinevolution.com/) by Veshtort and Griffin.\n", "\n", "We will take several steps to piece together the DARR experiment.\n", "\n", "**A. Static experiments**\n", "1. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins have the same resonance frequency (resonant transfer).\n", "2. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins have different resonance frequencies and have an intrinsic linewidth due to $T_2$.\n", "3. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins have different resonance frequencies and have an intrinsic linewidth induced by coupling to $^1$H.\n", "**B. Experiments under MAS**\n", "1. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins are separated by the rotor frequency.\n", "2. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins have resonance frequencies not separated by the rotor frequency, but have an intrinsic linewidth due to $T_2$.\n", "3. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins have resonance frequencies not separated by the rotor frequency, but have an intrinsic linewidth induced by coupling to $^1$H.\n", "4. Simulate $^{13}$C–$^{13}$C transfer occuring via homonuclear dipole couplings, where the two spins have resonance frequencies not separated by the rotor frequency, but have an intrinsic linewidth induced by coupling to $^1$H, which is broadened by satisfying the DARR condition.\n", "\n", "**References**\n", "\n", "*DARR:* \n", "\n", "K. Takegoshi, S. Nakamura, T. Terao. [*Chem. Phys. Lett.*](http://dx.doi.org/10.1016/S0009-2614%2801%2900791-6), **2001**, 344, 631-637.\n", "\n", "K. Takegoshi, S. Nakamura, T. Terao. [*J. Chem. Phys.*](https://doi.org/10.1063/1.1534105), **2003**, 118, 2325-2341.\n", "\n", "*Simulating DARR*\n", "\n", "M. Veshtort, R.G. Griffin. [*J. Chem. Phys.*](https://doi.org/10.1063/1.3635374), **2011**, 135, 134509.\n", "\n", "*Rotary Resonance Recoupling:*\n", "\n", "T.G. Oas, R.G. Griffin, M.H. Levitt. [*J. Chem. Phys.*](https://doi.org/10.1063/1.455191) **1988**, 89, 692-695.\n", "\n", "*Rotational Resonance:*\n", "\n", "D.P. Raleigh, M.H. Levitt, R.G. Griffin. [*Chem. Phys. Lett.*](https://doi.org/10.1016/0009-2614(88)85051-6), **1988**, 146, 71-76.\n", "\n", "\n", "E.R. Andrew, S. Clough, L.F. Farnell, T.D. Gledhill, I. Roberts. [*Phys. Letters*](https://doi.org/10.1016/0031-9163(66)91274-1), **1966**, 21, 505-506.\n", "\n", "E.R. Andrew, A. Bradbury, R.G. Eades, V.T. Wynn. [*Phys. Letters*](https://doi.org/10.1016/0031-9163(63)90123-9), **1963**, 4, 99." ] } , { "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": "9a3aef71", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2, "id": "02a834c3", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "ebd1fe32", "metadata": {}, "source": [ "## A. Static Experiments" ] }, { "cell_type": "markdown", "id": "9846042f", "metadata": {}, "source": [ "### 1) Transfer between coupled spins with same resonance frequency" ] }, { "cell_type": "code", "execution_count": 3, "id": "aaf56fd2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "delta(C–C) = 972.6 Hz\n" ] } ], "source": [ "#C-C dipole, 2.5 Angstrom distance\n", "dCC=sl.Tools.dipole_coupling(.25,'13C','13C',)\n", "print(f'delta(C–C) = {dCC:.1f} Hz')\n", "\n", "# Build the spin-system (two nuclei, no MAS, dipole coupled with no chemical shift)\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','13C'],vr=0,pwdavg=sl.PowderAvg('zcw232'))\n", "ex.set_inter('dipole',i0=0,i1=1,delta=dCC)\n", "\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "Dt=1/50000 #20 microsecond timestep (we'll use 10 kHz MAS later with 5 steps per rotor cycle)\n", "seq=L.Sequence().add_channel('13C',t=Dt)\n", "\n", "# Initial density matrix/detection operator for spectrum\n", "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 4, "id": "cc8c7c55", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->4\n" ] } ], "source": [ "rho_spec.clear()\n", "_=rho_spec.DetProp(seq,n=5000)" ] }, { "cell_type": "code", "execution_count": 5, "id": "b5b213d8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_spec.plot(FT=True,apodize=True)\n", "_=ax.set_xlim([-1,1])" ] }, { "cell_type": "code", "execution_count": 6, "id": "3fc2b05f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->6\n" ] }, { "data": { "text/plain": [ "Density Matrix/Detection Operator\n", "rho0: S0z\n", "detect[0]: S0z\n", "detect[1]: S1z\n", "Current time is 12000.000 microseconds\n", "600 time points have been recorded\n", "\n", "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho_zz.clear()\n", "rho_zz.DetProp(seq,n=600)" ] }, { "cell_type": "code", "execution_count": 7, "id": "d0fb745d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "69ea7535", "metadata": {}, "source": [ "Above, we see the spectrum, which has a characteristic Pake-pattern, resulting from the dipole coupling between the two spins. Because the two spins have identical resonance frequencies, they mix, allowing the transfer of z-magnetization from one spin ($S_{0z}$) to the other spin ($S_{1z}$).\n", "\n", "We can investigate the Hamiltonian driving this transfer more closely by plotting it." ] }, { "cell_type": "code", "execution_count": 8, "id": "54e46f23", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=L.H[0].plot(mode='re')" ] }, { "cell_type": "markdown", "id": "478ee87b", "metadata": {}, "source": [ "Spin magnetization transfers because the $|1/2,-1/2\\rangle$ and $|-1/2,1/2\\rangle$ states mix. This may also be observed in the Liouvillian, made easier to see by zooming in on the correct set of states:" ] }, { "cell_type": "code", "execution_count": 9, "id": "c437f6c7", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax=plt.subplots(1,2)\n", "L.plot(ax=ax[0],mode='abs',colorbar=False)\n", "L.plot(block=4,ax=ax[1],mode='abs',colorbar=False)\n", "_=fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "89ce9c44", "metadata": {}, "source": [ "We see in the reduced space that $S_1^\\alpha S_2^\\beta$ is driven into the zero- and double-quantum coherences by the dipole coupling, and subsequently arrives in $S_1^\\beta S_2^\\alpha$, which is a transfer of magnetization from spin 1 to spin 2." ] }, { "cell_type": "markdown", "id": "6ac32742", "metadata": {}, "source": [ "### 2) Transfer between coupled spins with different resonance frequency" ] }, { "cell_type": "markdown", "id": "b205ef97", "metadata": {}, "source": [ "In the next step, we consider what happens if the two spins are separate by a few ppm (10 ppm, resulting in a 10x150=1500 Hz separation). " ] }, { "cell_type": "code", "execution_count": 10, "id": "88f12e66", "metadata": {}, "outputs": [], "source": [ "# We keep working with the previous spin-system, so we just need to add the chemical shifts\n", "ex.set_inter('CS',i=0,ppm=5)\n", "ex.set_inter('CS',i=1,ppm=-5)\n", "\n", "# The following components need to be rebuilt for the new edited spin-system\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "Dt=1/50000 #20 microsecond timestep (we'll use 10 kHz MAS later with 5 steps per rotor cycle)\n", "seq=L.Sequence().add_channel('13C',t=Dt)\n", "\n", "# Initial density matrix/detection operator for spectrum\n", "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 11, "id": "8f15cbb8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->4\n" ] } ], "source": [ "rho_spec.clear()\n", "_=rho_spec.DetProp(seq,n=5000)" ] }, { "cell_type": "code", "execution_count": 12, "id": "a686ef2f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=rho_spec.plot(FT=True,apodize=True,axis='ppm')\n", "_=ax.set_xlim([-15,15])" ] }, { "cell_type": "markdown", "id": "e0079bee", "metadata": {}, "source": [ "Now, we observe to separated Pake-patterns, separated by roughly 10 ppm." ] }, { "cell_type": "code", "execution_count": 13, "id": "a6203c1d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->6\n" ] } ], "source": [ "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=6000)" ] }, { "cell_type": "code", "execution_count": 14, "id": "c1b66438", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "2c3e1c6c", "metadata": {}, "source": [ "The separation in resonance frequency quenches the transfer between spins. This can be understood by observing the impact on the Hamiltonian. While the dipole coupling is not gone, it is now smaller than the difference in chemical shift, so that the states no longer mix." ] }, { "cell_type": "code", "execution_count": 15, "id": "f9589c88", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=L[50].H[0].plot(mode='re')" ] }, { "cell_type": "markdown", "id": "15d0081c", "metadata": {}, "source": [ "However, what would happen if some $T_2$ broadening is introduced to the two spins, such that there is a small amount of overlap?" ] }, { "cell_type": "code", "execution_count": 16, "id": "44679c0a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->6\n" ] } ], "source": [ "L.add_relax(Type='T2',i=0,T2=.002)\n", "L.add_relax(Type='T2',i=1,T2=.002)\n", "\n", "seq=L.Sequence().add_channel('13C',t=100*Dt) # Transfer is a lot slower, so take bigger steps\n", "\n", "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=500)" ] }, { "cell_type": "code", "execution_count": 17, "id": "d0fb75b4", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot(axis='ms')" ] }, { "cell_type": "markdown", "id": "18f98aaf", "metadata": {}, "source": [ "As we see, the transfer is reintroduced, although it is considerably slower, and no longer coherent. " ] }, { "cell_type": "markdown", "id": "453fe511", "metadata": {}, "source": [ "### 3) Transfer between coupled spins with different resonance frequency, coupled to a flipping $^1$H\n", "\n", "We often refer to $^{13}C$-$^{13}C$ transfer without a field applied to $^1$H as Proton-Driven Spin-Diffusion (PDSD). But what does this transfer have to do with protons? It turns out that the broadening required for the transfer may be provided indirectly by a coupling to $^1$H that undergoes flipping.\n", "\n", "For this experiment, then, we need to add another spin. We'll add a one-bond H–C dipole coupling to one of the two $^{13}$C. We start without flipping on the $^1H$, but then introduce it in a subsequent step." ] }, { "cell_type": "code", "execution_count": 18, "id": "907f763e", "metadata": {}, "outputs": [], "source": [ "dHC=sl.Tools.dipole_coupling(.11,'1H','13C')\n", "\n", "# Build the spin-system (two nuclei, no MAS, dipole coupled with no chemical shift)\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','13C','1H'],vr=0,pwdavg=sl.PowderAvg('zcw232'))\n", "ex.set_inter('dipole',i0=0,i1=1,delta=dCC)\n", "ex.set_inter('dipole',i0=0,i1=2,delta=dHC,euler=[0,np.pi/4,0]) \n", "#Couplings usually shouldn't be colinear\n", "\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "Dt=1/50000 #20 microsecond timestep (we'll use 10 kHz MAS later with 5 steps per rotor cycle)\n", "seq=L.Sequence().add_channel('13C',t=Dt)\n", "\n", "# Initial density matrix/detection operator for spectrum\n", "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 19, "id": "e62a5b7a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 64->8\n", "State-space reduction: 64->12\n" ] } ], "source": [ "seq=L.Sequence().add_channel('13C',t=Dt) # Transfer is a lot slower, so take bigger steps\n", "\n", "rho_spec.clear()\n", "rho_spec.DetProp(seq,n=15000)\n", "\n", "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=500*100)" ] }, { "cell_type": "code", "execution_count": 20, "id": "f8bc7c06", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho_spec.apod_pars['LB']=1000\n", "_=rho_spec.plot(FT=True,apodize=True)" ] }, { "cell_type": "code", "execution_count": 21, "id": "e3a946aa", "metadata": {}, "outputs": [ { "data": { "image/png": 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YCKSAae6+OFM1iYjIzjL5GgHu/irwarN5Dzab/inw00zWISIirdN/FouI7CebN2/mqquuIi8vjyOOOIKzzjqro0sCMnxFICISdfX19cTjcXJycrj22mu55ZZbuPLKKwFYtGhRm9dTVlZGv379MlJju64IzOzrZjYwI5WIiHQiy5Yt41vf+hZjx45lxYoVJJNJ3nnnHc4444zGNscee2yb15eXl8eXv/xl3nrrLdz37bvo23xFYGbjgR+nH/OzfVqFiMg+8oM/L2Hppop9us5xQ3vzvS8cvdt21dXVPPfcc0yfPh1358Ybb2ThwoX06tULgHPPPZfjjjuOSy65hOuuu47TTz+9zTWsWLGCGTNmcN9993H77bdz7bXXcsMNNzB06NA97leD9lwR3AR8G7hur7cqItIJDRkyhOnTpzNt2jTmzJnDzTff3BgCADNmzOCFF16gT58+TJo0iZdeeonq6mquv/56brnlFp566qlW152VlcVFF13Eiy++yKxZs1i9ejUjRoxg7ty5e113m64IzKw7cCFwDHCmmU1099l7vXURkX2sLX+5Z8rzzz/P9OnTufTSS5k6dSrXX389I0eObFxuZkycOJGJEydSVlbGwoULqays5PLLL+cLX/gCV155JVdffTXr1q3j4YcfZs2aNZgZTz75JADl5eU8++yzPProo3Tt2pXp06czfvz4va67rVcElwEz3b0OeJRwdSAiIk2cf/75PPvss8yePZs+ffowZcoUzj33XNauXcvMmTOpr68HoKioiNmzZ3PeeedRWFjI8OHhQxiysrIAGDlyJDfddBNZWVn8/ve/B+Caa67hxBNPZPXq1Tz++OPMmjWL66+/nuzs7L2uu62vEdwE/Gv651eBX5lZT3ev2usKREQ6mQEDBnDnnXdy5513MnfuXLKysnj++ef56le/Ss+ePenevTv33HMPp512GgUFBRQWFnL88ceTSqUAWLt2Ld///vd54IEHyMnJAeCKK67gscceo0uXff9mT9vdq8/pewb81t2vbTLvG8ACd39rn1e0G3l5eZ6fn7+/Nysin2LLli3jqKOO6ugy9kh1dTV33HEH2dnZTJw4kauvvppx48ZxwQUXkJOTwze/+U369+/frnW2tD/MbL6757XUfrfR4u7bgWubzftlu6oSEZEW5eTk8Oijj+4wb+nSpa20zoy2vlicDXwVmEj4KOnZwAPurg//FhE5wLV1sOlxoBL4bXp6KvAE8KVMFCUiIvtPW4NgrLs3vU/A22a2IBMFiYjI/tXWt49+aGanNkyY2SnAnMyUJCIi+1NbrwhOAa4zs/Xp6RHAMjNbBLi77/1/NIiISIdoaxBMymgVIiLSYdoaBIcCRxPeMbTU3d/OXEkiIrI/7TIIzGwY8CIQA+YDBlxhZj8BLnX3jZkvUUREMml3VwT3Ef5f4LGmM83sOuB3wJQM1SUiIvvJ7t41NK55CAC4++PAkRmpSESkkzpQb1WZ1dJMMzuotWUiIvKJznCryj+b2cNmltMwI/3zg4RPIRURkRZ0pltVfhu4F1hnZusI7xoaCfwB+Pd9WomIyL4w4y7Y0va/tNvkkGNh8o932+xAvVXlLoPA3ePAv5rZfwKHE941VODuNXu9ZRGRTmbIkCGMHz+eadOmceSRO7+MOmPGDObMmcPLL7/MpEmTeOKJJxg/fjw//OEPKS8v5/nnn2913Q23qrzooosoLi7m7rvvZsSIEbz77rtMmDBhr+re7f8RmFkPYIy7L2gybwSQ1NtHReRTpw1/uWfKntyq8pJLLmH69Olcfvnlje0+jbeqjAMvNn2dAJgGDNnrrYuIdCJ7cqvKlnzqblXp7nEz+1/gSuCR9NXAIHfXbcJERFrQnltVtmR/36qyrZ8+Og24Mf3zdYQb2IuIyG5MmDCB4cOH8/DDD7Nq1SoWLFjA3LlzG4eCSktLue222/jwww+59957Abjwwgvp378/9957L9u2bQPg4osvzkgIQBs/a8jdPzYzzOwIwk1pJmakGhGRiBkwYAAPPvjgDvP2960q23pFADCdcGWw0N3LMlSPiIjsZ+0JgueA4wiBICIinUSbg8Dda9y9j7u/0dbHmNkkM1tuZgVmdtcu2p1sZkkzu7y1NiIikhntuSJoFzPLAu4HJgPjgKlmNq6Vdj8BZmaqFhHp/Pb1xy4cqPZkP2QsCIAJhP9CXu3u9cAztPyx1f8HeAEoymAtItKJZWdnU1paGvkwcHdKS0vb/b8FmXkvUjAM2NBkupBw7+NG6RvfXAqcDZzc2orM7FbgVoARI0bs80JF5MCWm5tLYWEhxcXFHV1Kh8vOziY3N7ddj8lkEFgL85rH9a+A77h70qyl5ukHuT8EPASQl5cX7cgXkZ107dqV0aNHd3QZB6xMBkEhMLzJdC6wqVmbPOCZdAgMBC40s4S7v5TBukREpIlMBsE8YIyZjQY2AlcBX27awN0bI9zMHgNeUQiIiOxfGQsCd0+Y2R2EdwNlAY+4+xIzuy29/MFdrkBERPaLTF4R4O6v0uxOZq0FgLvfkMlaRESkZZl8+6iIiBwAFAQiIhGnIBARiTgFgYhIxCkIREQiTkEgIhJxCgIRkYhTEIiIRJyCQEQk4hQEIiIRpyAQEYk4BYGISMQpCEREIk5BICIScQoCEZGIUxCIiEScgkBEJOIUBCIiEacgEBGJOAWBiEjEKQhERCJOQSAiEnEKAhGRiFMQiIhEnIJARCTiFAQiIhGnIBARiTgFgYhIxCkIREQiTkEgIhJxGQ0CM5tkZsvNrMDM7mph+dVmtjD99a6ZHZfJekREZGcZCwIzywLuByYD44CpZjauWbM1wBnuPh64B3goU/WIiEjLMnlFMAEocPfV7l4PPANMadrA3d9197L05HtAbgbrERGRFmQyCIYBG5pMF6bnteYmYEZLC8zsVjPLN7P84uLifViiiIhkMgishXneYkOzswhB8J2Wlrv7Q+6e5+55gwYN2ocliohIlwyuuxAY3mQ6F9jUvJGZjQemAZPdvTSD9YiISAsyeUUwDxhjZqPNrBtwFfBy0wZmNgJ4EbjW3VdksBYREWlFxq4I3D1hZncAM4Es4BF3X2Jmt6WXPwh8FxgA/M7MABLunpepmkREZGfm3uKw/adWXl6e5+fnd3QZIiIHFDOb39of2vrPYhGRiFMQiIhEnIJARCTiFAQiIhGnIBARiTgFgYhIxCkIREQiTkEgIhJxCgIRkYhTEIiIRJyCQEQk4hQEIiIRpyAQEYk4BYGISMQpCEREIk5BICIScQoCEZGIUxCIiEScgkBEJOIUBCIiEacgEBGJOAWBiEjEKQhERCJOQSAiEnEKAhGRiFMQiIhEnIJARCTiFAQiIhGnIBARiTgFQQN3SCXD99XvQCq1/7bbVCoJNdvC/NJVYV55IVSXtH9dzVVuab1NrCJ8r9kGdVWhXV1VmFeyEpLx3W+/qQ1zoa5yx3nx2h2nKzZDdWn71rs7rfUvUfdJfxrUVYX93dTujvvu9nHzdg3fU8mw7ngs7OM91Xz7DedtS1KpnftcXw2J+h3nJer2vJ5YRehPKhXW3Xz7bd1fu9JwPjZVsXnH6Y0fQPGKHefVV4fHue/c592pr4GqovBzPLb79g3Pj3gtbN/Qvm0BJBPhe0M/q4qhtizMb1h3Q5sM6JKxNX8ala2Fp6eGE8QOgpOuh/cehNO+Gn5xbZwPoybCov+Bk24IJ9fYyaHtx6/AEZPgoz/Cef8FHz4JB/eDQWNhw/tw9KWw9E9w+Hnw1/8b1l1dDNl94OD+kEpAVrewru3rYfkMGHZC2O6VT8G7v4Y+I6BbD5j7EJz7A3jje5D3z5D/CHTNgf6jwy/lm2bCCzdD7smw8q9h2/P/AN17wqAjw3b6jYQu2ZA7IfSnphQ25sNnvxZOrHg19B0Js34GX3oMnr4STr09bCtnUKj/rXvgmhfhyS/CYedAn1wYeESof+7v4bQ7QlgNPDzsx5NvgiX/C/1GhX0yciKMnQTLXoHDzoJ37oUv/Br+fCeM/Tws/wtkdYdz/jNs94rH4fmb4KgvwIqZYXs9+odj13to2C8jJ0LFRhh2YjiOmxeEX0ajTofa7SHEr3wCZnwHzv5PePFmGPW5sN+LlsF5P4DXvwvXvABPXArD8iBeE/ZJzsBwnC99KNSWezIUvAlDjoM5v4IeAyBWDv0Pg1NuhXfvg8PPhXVz4My7YeGzIbT75MLHf4F/+tfQ5szvwBvfh2OvgIO6wII/wjnfhTf/C65+AZ66DI65PARnbRkcezmsfy+cP91y4NAz4W8/gdO/DrN+Cqd+FWb9d9gvh54FhfPC+j58Ek79Crz/+3Ae11fD/EfhvHvgvd/BBT8K502fYTDoKFg5EyZ+E2b/IuyjtX8Px6NLNpx4bTg3S5bDkV8AT8G4i+GDx2HA4fDub2DCrbDqbShdCed+P/Tx6ufhxVtDPfOmw4BDw7H+8ImwH/MfDceuaCmMOA16DwOz8FyrLoYTrwttT7oRZv8ynAsf/AHGXhgCr3wDjDkP5vwaTvkKvP8AnHwzzJsW9sflj8Ir34CLfwv/c0OosXgZrPk79BwcztXew2D5q+H5vOwV+PzPw7l56Bmw7t3wvNi8AGpK4LLp8NJXYOozsPSl0PdYRejzgMPh7z+H6/8ctjX4aCjMD+fT0V8Mz9ULfhjO7ezeYV8NPQGWvRyeI917hf09cAwseDqcQ7N/CV98OKyv9zAwwvPthGvC8b3hL+HY7mPm+yKxW1u52STg10AWMM3df9xsuaWXXwjUADe4+we7WmdeXp7n5+e3v5j6avjR0PY/TkTk0yLvJrjoF3v0UDOb7+55LS3L2NCQmWUB9wOTgXHAVDMb16zZZGBM+utW4IFM1UNpQcZWLSKyX3z+5xlZbSaHhiYABe6+GsDMngGmAEubtJkCPO7hsuQ9M+trZkPcffPOq9tLDWOKN78VLksHjwtjj2Vr4ZjLwiXv8VPD5df4q8JlanlheMzQ48PlWd+R4bJv+/pwWfvBY3DUlHD5PGAM1G4LQzADx8KMf4PJ/x0uBwePC2P8q99JDxf8NlzCr3wjXKYf3B+2LoZxl4TL89pt0GtIuIrZujhcAq/8K+TmwZbF0OuQMK675H8h70Z4+qowvLT279B3RBiu2r4+DKPMmwZHXAAVm6D/oaFfa/4Gp9wG8x8Lw0p1lZDVNQxfHdwvDE9k9w3T8Vo4uC9s+igse+2uMDRWVwlVW8Ml7oKnQ19f/264hP/4L3DIsWG/zfoZTLkPtiyCoSeG/tRXhzoGHx3WX1MC/UZ/UsPyGXDk52H5a3DkhbDqrTAscMxl8M6P4dzvhUvoYy6DZH3oW5/cMCQy+Sfwp9vDpfnAI6CiMAyXLXgGJtwS2vYcHLbfb3QYCsruE4Z1TrgmrG/VW/C5b4XhttNuD0N+PfpDn+Ghz117wAs3wXV/ghWvhWGWrtnhHMsZFIaKxl8BmxfCYWdDKg7b1kBdRRhOqNkGvYeEocg1fw9DAvOmwXFTYea/w5Dx4VzYvi7s39fuDr8A3v0NjP6nT17HOv//haGroSfA5o9CP7seHNZ/UBZsWRiGoiq3hOHCTR+G9Wz+KJyjmz4I+/WQY8MwzoRbwj6ccEsY3uwxIAyNFubDKf8Cz14b9kfOoHDcuvcK+2PkZ2HNrLC/k3VhnSUrwrkw66dwwrXhOVK+EY66CBa/AMdfHfpz0o1hWKhrdjgOHz0dhu/e+AEcfk44z/sOD7W8eU9YVrk57POti6CkIDyHT7gmHNveQ0JtJSvDvnrj+zDx67DkpXBOLXg6PP6zX4PXvweXPQwfPgUjTg3HuL46PPc+fDIMdRbOC/2qqwx/TPYcDF26h/3ac3B4rlQVhWGvf9wX+lWyPAzpxWPhGOfdGOo477/glW+Gc6JHf5j7cDhf3/5RGEIqeCNsK14ThlyPvCgM5/YaAolYGMY02+e/GiGDQ0Nmdjkwyd1vTk9fC5zi7nc0afMK8GN3n52efhP4jrvnN1vXrYQrBkaMGHHSunXr2l/Q+vfCgbrw59Br8B72SkTkwLSroaFMXhG0FF3NU6ctbXD3h4CHILxGsEfVjDg1fImIyA4y+fbRQmB4k+lcYNMetBERkQzKZBDMA8aY2Wgz6wZcBbzcrM3LwHUWnAqUZ+T1ARERaVXGhobcPWFmdwAzCW8ffcTdl5jZbenlDwKvEt46WkB4++iNmapHRERaltF/KHP3Vwm/7JvOe7DJzw7cnskaRERk1/QREyIiEacgEBGJOAWBiEjEKQhERCIuox86lwlmVgzswb8WAzAQaMPnOXcq6nM0qM/RsDd9Hunug1pacMAFwd4ws/zW/sW6s1Kfo0F9joZM9VlDQyIiEacgEBGJuKgFwUMdXUAHUJ+jQX2Ohoz0OVKvEYiIyM6idkUgIiLNKAhERCIuMkFgZpPMbLmZFZjZXR1dz75gZsPN7G0zW2ZmS8zszvT8/mb2upmtTH/v1+Qxd6f3wXIzu6Djqt87ZpZlZh+m73LX6fucvo3r82b2cfp4nxaBPn8jfV4vNrOnzSy7s/XZzB4xsyIzW9xkXrv7aGYnmdmi9LLfmLXznpbu3um/CB+DvQo4FOgGLADGdXRd+6BfQ4AT0z/3AlYA44D/Bu5Kz78L+En653HpvncHRqf3SVZH92MP+/5N4I/AK+npTt1n4A/AzemfuwF9O3OfgWHAGuDg9PRzwA2drc/APwEnAoubzGt3H4G5wGmEuz7OACa3p46oXBFMAArcfbW71wPPAFM6uKa95u6b3f2D9M+VwDLCE2gK4RcH6e+XpH+eAjzj7nXuvoZwH4gJ+7XofcDMcoHPA9OazO60fTaz3oRfGNMB3L3e3bfTifuc1gU42My6AD0Idy/sVH1291nAtmaz29VHMxsC9Hb3f3hIhcebPKZNohIEw4ANTaYL0/M6DTMbBZwAvA8M9vSd3tLfP5Nu1ln2w6+AbwOpJvM6c58PBYqBR9PDYdPMLIdO3Gd33wj8DFgPbCbcvfCvdOI+N9HePg5L/9x8fptFJQhaGi/rNO+bNbOewAvA1929YldNW5h3QO0HM7sIKHL3+W19SAvzDqg+E/4yPhF4wN1PAKoJQwatOeD7nB4Xn0IYAhkK5JjZNbt6SAvzDqg+t0FrfdzrvkclCAqB4U2mcwmXmQc8M+tKCIGn3P3F9Oyt6ctF0t+L0vM7w344HbjYzNYShvjONrMn6dx9LgQK3f399PTzhGDozH0+F1jj7sXuHgdeBD5L5+5zg/b2sTD9c/P5bRaVIJgHjDGz0WbWDbgKeLmDa9pr6XcGTAeWufsvmix6Gbg+/fP1wJ+azL/KzLqb2WhgDOFFpgOGu9/t7rnuPopwHN9y92vo3H3eAmwws7HpWecAS+nEfSYMCZ1qZj3S5/k5hNfAOnOfG7Srj+nho0ozOzW9r65r8pi26ehXzffjq/MXEt5Vswr4j46uZx/1aSLhEnAh8FH660JgAPAmsDL9vX+Tx/xHeh8sp53vLPi0fQFn8sm7hjp1n4Hjgfz0sX4J6BeBPv8A+BhYDDxBeLdMp+oz8DThNZA44S/7m/akj0Beej+tAu4j/akRbf3SR0yIiERcVIaGRESkFQoCEZGIUxCIiEScgkBEJOIUBCIiEacgEGkm/UmfX91Nm9+b2en7qyaRTFIQiOysL7DLIABOAd7LfCkimacgENnZj4HDzOwjM/tp84VmdhSwwt2TzeY/ZmYPpO8RsdrMzkh/3vwyM3ss3SYr3W5x+vPjv7FfeiSyC106ugCRT6G7gGPc/fhWlk8GXmtlWT/gbOBi4M+Ez0a6GZhnZscT7o0xzN2PgTAMtc+qFtlDuiIQab8LaD0I/uzh3/UXAVvdfZG7p4AlwChgNXComf3WzCYBu/q0WJH9QkEg0g5m1gPo6+6tfbpjXfp7qsnPDdNd3L0MOA54B7idHW+uI9IhNDQksrNKwq0/W3IW8PaertjMBgL17v6Cma0CHtvTdYnsKwoCkWbcvdTM5qRvKD7D3f+tyeLJhPsB7KlhhDuNNVyN370X6xLZJ/TpoyLtYGYfAKd4uFmKSKegIBARiTi9WCwiEnEKAhGRiFMQiIhEnIJARCTiFAQiIhGnIBARibj/DwqaZcl0zCarAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "acb343e5", "metadata": {}, "source": [ "The $^1$H dipole coupling alone is insufficient to drive a transfer, but if the $^1$H undergoes flipping due to spin diffusion, then the transfer occurs." ] }, { "cell_type": "code", "execution_count": 22, "id": "760b4d02", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 64->8\n", "State-space reduction: 64->12\n" ] } ], "source": [ "L.add_relax(Type='SpinDiffusion',i=2,k=300) #Spin-diffusion on 1H\n", "\n", "rho_spec.clear()\n", "rho_spec.DetProp(seq,n=15000)\n", "\n", "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=50000)" ] }, { "cell_type": "code", "execution_count": 23, "id": "95fdd057", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_spec.plot(FT=True,apodize=True)" ] }, { "cell_type": "code", "execution_count": 24, "id": "24d578a1", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "c1bdc7e8", "metadata": {}, "source": [ "## B. Magic-Angle Spinning Experiments" ] }, { "cell_type": "markdown", "id": "8d27c735", "metadata": {}, "source": [ "Previously, we found that two dipole-coupled spins with the same chemical shift resulted in transfer of longitudinal magnetization between them. Here, we test if the same principle applies under magic angle spinning (10 kHz)." ] }, { "cell_type": "markdown", "id": "84a55332", "metadata": {}, "source": [ "### 1) Transfer when two spins are separated by the rotor frequency" ] }, { "cell_type": "code", "execution_count": 25, "id": "e2fa8e17", "metadata": {}, "outputs": [], "source": [ "# Build the spin-system (two nuclei, no MAS, dipole coupled with no chemical shift)\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','13C'],vr=10000)\n", "ex.set_inter('dipole',i0=0,i1=1,delta=dCC)\n", "\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "seq=L.Sequence() #Sequence defaults to 1 rotor period when spinning\n", "\n", "# Initial density matrix/detection operator for spectrum\n", "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 26, "id": "97a2f887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->4\n", "State-space reduction: 16->6\n" ] } ], "source": [ "rho_spec.DetProp(seq,n=15000)\n", "_=rho_zz.DetProp(seq,n=1000)" ] }, { "cell_type": "code", "execution_count": 27, "id": "8b453fe2", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_spec.plot(FT=True,apodize=True)" ] }, { "cell_type": "code", "execution_count": 28, "id": "0564bcd3", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "7246ee19", "metadata": {}, "source": [ "Magic angle spinning quenches the transfer by averaging the dipole coupling to zero. On the other hand, if the spins are separated by the MAS frequency (i.e. the $R^2$ condition), the coupling is reintroduced" ] }, { "cell_type": "code", "execution_count": 29, "id": "0853b224", "metadata": {}, "outputs": [], "source": [ "DelCS=10000/(600*sl.Tools.NucInfo('13C')/sl.Tools.NucInfo('1H'))\n", "ex.set_inter('CS',i=0,ppm=DelCS/2)\n", "ex.set_inter('CS',i=1,ppm=-DelCS/2)\n", "\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "seq=L.Sequence() #Sequence defaults to 1 rotor period when spinning\n", "\n", "# Initial density matrix/detection operator for spectrum\n", "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 30, "id": "adc4c8d0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->4\n", "Prop: 2 steps per every 1 rotor period\n" ] } ], "source": [ "_=rho_spec.DetProp(seq,n=5000,n_per_seq=2)" ] }, { "cell_type": "code", "execution_count": 31, "id": "5549fe7e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_spec.plot(FT=True,apodize=True)" ] }, { "cell_type": "markdown", "id": "5d8e80d4", "metadata": {}, "source": [ "Matching the rotational resonance condition distorts the spectrum by reintroducing the dipole coupling. " ] }, { "cell_type": "code", "execution_count": 32, "id": "65497e57", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->6\n" ] } ], "source": [ "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=100)" ] }, { "cell_type": "code", "execution_count": 33, "id": "d6e43510", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "03de2621", "metadata": {}, "source": [ "The rotational resonance condition induces a transfer, but it also distorts the spectrum, and furthermore can only be matched for one pair of spins at a time. So, we move off the rotational resonance condition." ] }, { "cell_type": "code", "execution_count": 34, "id": "9da07d7e", "metadata": {}, "outputs": [], "source": [ "ex.set_inter('CS',i=0,ppm=-15) #Shift away from rotational resonance\n", "ex.set_inter('CS',i=1,ppm=15) #Shift away from rotational resonance\n", "\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "seq=L.Sequence() #Sequence defaults to 1 rotor period when spinning\n", "\n", "# Initial density matrix/detection operator for spectrum\n", "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 35, "id": "6fc5f251", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->4\n", "Prop: 2 steps per every 1 rotor period\n" ] } ], "source": [ "_=rho_spec.DetProp(seq,n=5000,n_per_seq=2)" ] }, { "cell_type": "code", "execution_count": 36, "id": "48e1704b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_spec.plot(FT=True,apodize=True)" ] }, { "cell_type": "markdown", "id": "bd7988ef", "metadata": {}, "source": [ "Away from rotational resonance, our spectrum looks nicer, but what happens to our transfer?" ] }, { "cell_type": "code", "execution_count": 37, "id": "065f576a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->6\n" ] } ], "source": [ "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=1500)" ] }, { "cell_type": "code", "execution_count": 38, "id": "0dc5d745", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "a2c86ca0", "metadata": {}, "source": [ "Not surprisingly, the transfer is quenched. It can be reintroduced by broadening of the $^{13}$C resonance" ] }, { "cell_type": "markdown", "id": "0b61167f", "metadata": {}, "source": [ "### 2) Transfer between spins away from rotary resonance, broadened by T$_2$" ] }, { "cell_type": "code", "execution_count": 39, "id": "89b10476", "metadata": {}, "outputs": [], "source": [ "L.clear_relax()\n", "L.add_relax(Type='T2',i=0,T2=.001)\n", "_=L.add_relax(Type='T2',i=1,T2=.001)" ] }, { "cell_type": "code", "execution_count": 40, "id": "15306889", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 16->6\n" ] } ], "source": [ "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=15000)" ] }, { "cell_type": "code", "execution_count": 41, "id": "d8ccfabc", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "0e9fde56", "metadata": {}, "source": [ "Then, can we achieve the same affect by coupling to a $^1$H?" ] }, { "cell_type": "markdown", "id": "ef3f3350", "metadata": {}, "source": [ "### 3) Transfer between spins away from rotary resonance, broadened by coupled $^1$H" ] }, { "cell_type": "code", "execution_count": 42, "id": "4e361cac", "metadata": {}, "outputs": [], "source": [ "# Build the spin-system (two nuclei, no MAS, dipole coupled with no chemical shift)\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','13C','1H'],vr=10000)\n", "ex.set_inter('dipole',i0=0,i1=1,delta=dCC)\n", "ex.set_inter('dipole',i0=0,i1=2,delta=dHC,euler=[0,np.pi/4,0])\n", "ex.set_inter('CS',i=0,ppm=15)\n", "ex.set_inter('CS',i=1,ppm=-15)\n", "\n", "# Liouvillian\n", "L=ex.Liouvillian()\n", "L.add_relax('SpinDiffusion',i=2,k=300)\n", "\n", "# Pulse sequence (no sequence- just a time step)\n", "seq=L.Sequence()\n", "\n", "# Initial density matrix/detection operator for transverse magnetization transfer\n", "rho_zz=sl.Rho(rho0='S0z',detect=['S0z','S1z'])" ] }, { "cell_type": "code", "execution_count": 43, "id": "fc1dc0ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 64->12\n" ] } ], "source": [ "_=rho_zz.DetProp(seq,n=15000)" ] }, { "cell_type": "code", "execution_count": 44, "id": "83b94474", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "1acf4cea", "metadata": {}, "source": [ "Some transfer occurs, although it is not particularly efficient. We finally want to understand what happens if we introduce a field on the $^1$H matching the rotary resonance recoupling (R$^3$) condition" ] }, { "cell_type": "markdown", "id": "b6c1d006", "metadata": {}, "source": [ "### Transfer between spins not on rotary resonance, broadened by irradiation of protons." ] }, { "cell_type": "markdown", "id": "efb7536b", "metadata": {}, "source": [ "First, we observe the $^{13}$C spectrum with $^1$H cw decoupling, first away from the rotary resonance recoupling condition, and then on the condition. Lines mark the resonance frequency of the first $^{13}$C and the distance to the corresponding rotational resonance condition." ] }, { "cell_type": "code", "execution_count": 45, "id": "1d5a58c4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 64->8\n", "Prop: 5 steps per every 1 rotor period\n" ] } ], "source": [ "rho_spec=sl.Rho(rho0='13Cx',detect='13Cp')\n", "_=rho_spec.DetProp(seq,n=5000,n_per_seq=5)" ] }, { "cell_type": "code", "execution_count": 46, "id": "7f55585b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_spec.plot(FT=True,apodize=True)" ] }, { "cell_type": "code", "execution_count": 47, "id": "2ce927a7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 64->16\n", "Prop: 5 steps per every 1 rotor period\n" ] } ], "source": [ "seq.add_channel('1H',v1=10000)\n", "rho_spec.clear()\n", "_=rho_spec.DetProp(seq,n=25000,n_per_seq=5)" ] }, { "cell_type": "code", "execution_count": 48, "id": "fe11c668", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho_spec.apod_pars['LB']=500\n", "ax=rho_spec.plot(FT=True,apodize=True)\n", "ax.set_ylim([0,1])\n", "CS=-15*ex.v0[0]/1e9\n", "ax.plot([CS,CS],ax.get_ylim(),color='grey',linestyle=':')\n", "_=ax.plot([CS+10,CS+10],ax.get_ylim(),color='grey',linestyle=':')" ] }, { "cell_type": "code", "execution_count": 50, "id": "70471cc8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 64->24\n" ] } ], "source": [ "rho_zz.clear()\n", "_=rho_zz.DetProp(seq,n=15000)" ] }, { "cell_type": "code", "execution_count": 51, "id": "3e26c063", "metadata": {}, "outputs": [ { "data": { "image/png": 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/tOVQ32WuvfLSk5man05JXhpT89IpCZ/OS9MhJ4lrCgIZs7IDySwq8e5h6K8x2Mme2lZ21rRQWdfG3rpW9h5uZeuBJv60uYqOfmNDF2WlMjUv7eiwyEtnSl4axTkBBYWMawoCGZeyA8kDnqwG6OlxVDe3s/dwK3vrWqk83BsUbby7p47nNhygu+foq+nyM1IozglQnJPG5NwAk3O9gOh9npgdIFn3SsgYpSCQuJOQYEzM9hrv0hn5x6zv6u7hYGOQvYfb2F/fxoGGNvY3BDlQ30ZlXStv7aylKXj0+EkJ5u1VFOekMSUUDsW5aUzOCTAxFBRFmamkJCksZPRREIj0k5SYQEno0NBgmtu7OFB/JCD29043tLHlQGPfWNP9FWSkMCE7wMTsVCZmhZ5zAqFpb74gM1X3UUhUKQhETkBmahJzJmYxZ2LWgOudc9S3drKvvo3qpnYONQY51NjOoaYgVaHpzfsbqW5up/89nb17FxOzA0zoDYvsABOyUinMTKUoK5XCrFQKM1M0loSMCAWBiA/MjLyMFPIyUo67XVd3DzXNHaGgCHKoqT0UFF5YVNa18u6eOg73u1S2V1YgiaJMLxiKMr1wKMzsDYpQaISW6YS3DEZBIBJDSYkJff03HU97Vzc1zR3UNLVT3dROTXPvo4Pqpnaqm9vZcrCRmqZ2Gvudv+iVlZp0JDCyvHDIz0ihICOF/IxU8jKSKcjwluWlJ6ujwDiiIBAZA1KTEpmS652IHkqws5vaFi80egPDC48OqpvbqWnyuvl4ralm0NAAyElLpiC0V9MbGHl9wXH0dH5GCukpak7GKv3PiYwzgeTIQ6Ozu4e61g4Ot3RwuLmDw6Hp2uYO6lo7qG3poK6lg72HW3l/bz11LR109QzcUWUgOYH89BTyM709jNy0ZPLSk8lJ9/YwctOTyU1L8Z7TU8hNSyY7LVknxkcBBYFIHEtOTGBClndSOhLOORqDXV5w9D3aOdzS2e+5g921LdS3dtIY7DzmhHgvM++ej97A6A2P3PQUcsKmw8MjLz2FrEASCQqQEaMgEJGImRk5acnkpCUzszAjop/p7nE0tnVS39ZJXWsHDa2d1Ld1UNfiLatv7aC+9cj6nTUt1Ld2HPewlRl9deSkJZMdSCY7LYnsQGg+LZnsQJL3HFqfk5bUN60T50dTEIiIrxITjlxBNZPIwgO8K6oag13Ut3ZQ19pJQ1h4NISWNQY7aWzrpKGtk4ONwb7p9q5j7+EIl5KUEAqQpLCgGChMvGW9YZMVSCIzkDTuLttVEIjIqJSUmNB3Inq4gp3dNAW7aAx6wdDY1kljsCtsupPGtq6+6fpW71BWY9BbNth5kF4pSQlkpXqhkBVIIjM1iaxAMlmpSX1hkZnqBUdW3zbJoe2O/MxouTJLQSAi404gOZFAciJFWanD/lnnHG2d3aHQCIVJaO+jub2LpmDv48h8c7CLyrq2o5b1769qIGnJiX3BkRUKk8ywMOlbFgqOeZOymDvITYwnQ0EgIhLGzEhPSSI9JYniY/ssjIhzjmBnD03tnX1B0RTsornd2zNpDnaFAsMLjvBlVU3BI9t3dB11ov3Ln5jFt5adOjL/0DAKAhGREWZmpKUkkpaSyIST+ALf0+No7ez2AiPYRXZa8sgVGUZBICIySiUkGJmp3mEhTnDvJKL38e+lRURkLFAQiIjEOQWBiEicUxCIiMQ5BYGISJzzNQjMbJmZbTOzcjP79iDbfMLM3jezTWb2Fz/rERGRY/l2+aiZJQK/Bi4DKoF3zOxZ59zmsG1ygd8Ay5xze8xsgl/1iIjIwPzcIzgbKHfOVTjnOoDHgRX9trkBeNo5twfAOVflYz0iIjIAP4NgCrA3bL4ytCzcXCDPzP5sZuvN7JaBXsjM7jSzMjMrq66u9qlcEZH45GcQDDRqRP9emJKAM4ErgcuB75vZ3GN+yLkHnXOlzrnSoqKika9URCSO+dnFRCUwNWy+BNg/wDY1zrkWoMXM1gFLgO0+1iUiImH83CN4B5hjZjPNLAW4Dni23zb/AVxoZklmlg6cA2zxsSYREenHtz0C51yXmd0DvAAkAg875zaZ2V2h9Q8457aY2R+BDUAPsMo5t9GvmkRE5FjmBhtVepQqLS11ZWVlsS5DRGRMMbP1zrnSgdbpzmIRkTinIBARiXPDCgIz+x9mVuhXMSIiEn0RB4GZLQbuBW71rRoREYm64ewR3A58Exjw7l8RERmbIgoCM0sFrgB+C5Sb2VJfqxIRkaiJdI/gc8ALzrl24BG8vQMRERkHIg2C24HVoenngY+bWaY/JYmISDQNGQShMQP2O+feA3DOdQP34XUzLSIiY9yQXUw45+qBm/st+4VfBYmISHRF1NeQmQWAu4GleF1Jvwbc75wL+libiIhEQaSdzj0KNAH/LzR/PfDPwOf9KEpERKIn0iCY55xbEjb/ipl94EdBIiISXZFeNfSemZ3bO2Nm5wCv+1OSiIhEU6R7BOcAt5jZntD8NGCLmX0IOOfcYl+qExER30UaBMt8rUJERGIm0iA4BTgN74qhzc65V/wrSUREoum4QWBmU4CngSCwHjDgC2b2U+Aa59w+/0sUERE/DbVHcB/e/QJrwhea2S3Ab4AVPtUlIiJRMtRVQwv6hwCAc+5R4FRfKhIRkagaKggSB1poZgmDrRMRkbFlqCD4TzN7yMwyeheEph/A64VURETGuKGC4JtAA7DbzNabWRmwC2gE/tbn2kREJAqOe7LYOdcJ/K2ZfR+YjXfVULlzrjUaxYmIiP+GvI/AzNKBOc65D8KWTQO6dfmoiMjYF0lfQ53A0+HnCYBVQLE/JYmISDQNGQShw0P/DnwR+vYGipxzZT7XJiIiURBp76OrgNtC07fgDWAvIiLjQER9DTnntpoZZjYXb1Capf6WJSIi0RLpHgHAarw9gw3OuTqf6hERkSgbThA8ASzBCwQRERknIg4C51yrcy7HOfenSH/GzJaZ2TYzKzezbx9nu7PMrNvMro30tUVEZGQMZ49gWMwsEfg1sBxYAFxvZgsG2e6nwAt+1SIiIoPzLQiAs/HuQq5wznUAjzNwt9VfBZ4CqnysRUREBuFnEEwB9obNV4aW9QkNfHMNXid2gzKzO82szMzKqqurR7xQEZF45mcQ2ADLXL/5XwLfcs51H++FnHMPOudKnXOlRUVFI1WfiIgQ+ZjFJ6ISmBo2XwLs77dNKfC4mQEUAleYWZdz7hkf6xIRkTB+BsE7wBwzmwnsA64DbgjfwDk3s3fazNYAzykERESiy7cgcM51mdk9eFcDJQIPO+c2mdldofXHPS8gIiLR4eceAc655+k3ktlgAeCcu9XPWkREZGB+niwWEZExQEEgIhLnFAQiInFOQSAiMhb0dENXhy8v7evJYhGRuNfTA50tEGyE9iZobww9mvotCz0fsyy0XWcLXPgNuOQHI16igkBEZDDdnV4jHKz3HgM13sGGIw32MQ18aNkxnSoMICULAtmQmgWp2RDIhZypoWWh5dPO8+WfqSAQkfGrpyf0Lbsh9KgPm26Atvrjr+tsGfo9ktOPNN6pocY8c0JoPmxZalbokdNvWTakZEJC7I7UKwhEZHTr6YH2Bmirg9Y677n30dt4t9WHNeT1YQ36UN/GzWuQAzneN/BADuSfAmm5R+b71oW2C2/0U7MgMdnv34DvFAQiEh3OhRrt3ob8sNeAtx7utyw03bs8WA+uZ/DXTckMa7BzILsEJpzmTaflHr0uvHFPy/UOx8Twm/hooSAQkeHr/ZbeUgutNdBaCy2h577H4X6Nez0cr6Ph1GyvcU7Lh7Q87/h4emi6d1laXtiyPK9BHwffyGNNQSAi3mWJfQ14TahRPzxwI987PVijnpwO6QVHGu2cKYM35H3Lc9Wgx5CCQGQ8cg46mqG5ClqqoflQ2HS/59bD3rf7waTlQXohZBR6x89LzvKm0wtCywuOTKcXQEp69P6dMiIUBCJjRXjj3lwFLVX9pqtDz4e86a62AV7EvMY6cwJkFMGUM4408un5YdOhhj0tDxLVTIx3+h8WGQ3am6DpIDQdOM7zoSEa94mQWQRTzz3S0Pcuy5jgLUsvVMMux9BfhIifOttCDflgjXtouqP52J9NzoDsYsgq9g7HZE4MNfChRr13Or1AjbucFP31iJyo7k6vIW/YBw2V0FjpTTf2zu/zTqr2l5gKWZO8Bn7iQpjzqSPz4c+pWdH/N0lcUhCIDMQ579j7QA18byPfdJBjblZKzYGcEu9KmSlnes9Zk49u4NPywBunW2RUUBBIfHLOu7a9bhfU74H63VC3+8h0/R7oCh79M0lpXsOePQVmXXJkOmeKdxNTzhR9i5cxSUEg41dHCxzeGdbIhxr43ga/o+no7QO5kDcdiuZ5h2typ0Pu1FBjX6Jv8jJuKQhkbGtvhrqdULsDDlfA4R1e41+7A5oPHr1tcobX0OdOh5kXQu40bzpvujcdyInNv0EkxhQEMvp1tnkNe215qKGvgNoK77l/Y58xAQpmwexLvJuf8mdC3gzIneFdJ69v9CLHUBDI6NF6GGq2e4/qbUee6/dw1EnZzImQPwtmXwoFp4Qa/Fleo69j9CLDpiCQ6HLOu9qmanNYg/8R1GzzujvolRSAgjnelTen3wCFc6Fgttfop2bGrn6RcUhBIP7paIGqLXBok/eo2gyHNnpX6/QK5HonZ+cu8xr7onnec+40SEiMWeki8URBICfPOe+E7cEPjzT6hzZ5l2b2HtJJzoAJ82H+1TDxNG+66FSvGwQdtxeJKQWBDE9Pj3eS9sD73mP/+3Bgw5HeKy3BO15fvNg7pDNhgdfw507XACAio5SCQAbnnHelzv73Qg3++16j33v9fWKq18gv+hwUnw6TFnnf9JPTYli0iAyXgkCOCDbAvvVQWQZ734bKd7xhAsE7eTtpESz5otfoTz7dO7SjwURExjwFQbxyzrtqZ+9bXoO/9x2o3op3TN+8Rn7B1V6vl1POhMJ56uFSZJzSJzte9PR4V+3sfh12vQa73/CGIQTvyp2Ss2DhZ6Gk1Gv4dZetSNzwNQjMbBnwj0AisMo5d2+/9TcC3wrNNgNfds594GdNcaOn27uKZ/frsOt12PPGkcs2c6bBnMtg+vkw7Tzv5K5O5IrELd+CwMwSgV8DlwGVwDtm9qxzbnPYZjuBi5xzdWa2HHgQOMevmsa9hn2w42XvUfFnaDvsLc+bCadeCdOXwowLvGv0RURC/NwjOBsod85VAJjZ48AKoC8InHNvhG3/JlDiYz3jT0er941/x8tQ/pJ3dy54XTDMvRxOuRhmLPW6RxYRGYSfQTAF2Bs2X8nxv+3fDqwdaIWZ3QncCTBtWpx/m206BNvXwra13rf+rqB3Rc/08+GMm2HWJ71r93WTlohEyM8gGKglcgMsw8wuxguCpQOtd849iHfYiNLS0gFfY9xyzruaZ+sfvMZ/X5m3PHcanHmr12/+9PN17b6InDA/g6ASmBo2XwLs77+RmS0GVgHLnXMDDPAap6q2wManYdPT3k1dAJPPgE9+D+ZdoW/9IjJi/AyCd4A5ZjYT2AdcB9wQvoGZTQOeBm52zm33sZaxoXbHkca/arPXXcOMpXDu3V7jn10c6wpFZBzyLQicc11mdg/wAt7low875zaZ2V2h9Q8APwAKgN+Y9+22yzlX6ldNo1JbPWx8Et77Hex/11s27Ty44h+8DtqyJsa0PBEZ/8y5sXXIvbS01JWVlcW6jJPT0wM7/wLvPQZbn/NO+E5cCEuuh9Ou0VU+IjLizGz9YF+0dWdxNLXUwrv/BGWPQMMe747ej90MH7sJipfomL+IxISCIBoOfABvPegdAuoKwowL4bIfwbwrITkQ6+pEJM4pCPziHHz0Irz2C697h+R079DP2XfCxAWxrk5EpI+CYKT1dMOWZ+HVn3t9/eRMhU/9HXzsRkjLi3V1IiLHUBCMlJ4e77LPP/+9d91/wRz4zP2w6PPqs19ERjUFwclyDna8BH/6MRzc4F398/l/gvmf1uDrIjImKAhOxsGN8MJ3YOc6b0zezz4EC69Vl84iMqYoCE5EsNE7BPTWb70BXJb/XzjzNkhKiXVlIiLDpiAYrk3PwNpvQfMhr9O3S34A6fmxrkpE5IQpCCLVehie/1vY+JR389f1/+IN6SgiMsYpCCJR/hI8c7c3xu/F34Ol/1MDuYvIuKHW7Hh6emDdz7zzAUWnwo1PeHsDIiLjiIJgMG318PSX4KP/gsXXwVW/gJT0WFclIjLiFAQDadgHj33OuzHsyp9D6e3qEE5Exi0FQX9VW7wQCDbCTU/BKRfFuiIREV8pCMJVbYU1V0JCMvy3tTBpUawrEhHxnYKgV005PHo1JCTBbc9DwaxYVyQiEhUKAoDmanjsGq/n0Fv/oBAQkbiiIOhqh9/fBM1V3p7AhFNjXZGISFQpCP74Hdj7Jlz7iO4UFpG4FN/dZG5bC2Wr4bx7YOFnY12NiEhMxG8QtNTAf9wDExd5HceJiMSp+D009KcfQrAeVj4LSamxrkZEJGbic49g33p47zE4926YeFqsqxERian4DIJX/h7S8uGib8a6EhGRmIu/IKhcD+Uvwvn3QGpWrKsREYm5+AuCv/wU0vLg7DtjXYmIyKgQX0HQXA0fvQBnfUl7AyIiIfEVBBWveM/zlse2DhGRUSS+gmDHy95JYo0yJiLSJ76CoLIMpp8PCYmxrkREZNTwNQjMbJmZbTOzcjP79gDrzcx+FVq/wczO8K2Y7i6o2wmFc3x7CxGRsci3IDCzRODXwHJgAXC9mS3ot9lyYE7ocSdwv1/10LAHerogX11Mi4iE83OP4Gyg3DlX4ZzrAB4HVvTbZgXwqPO8CeSaWbEv1dRWeM8Fs315eRGRscrPIJgC7A2brwwtG+42mNmdZlZmZmXV1dUnVk1KBsy7UoeGRET68bPTORtgmTuBbXDOPQg8CFBaWnrM+ohMP897iIjIUfzcI6gEpobNlwD7T2AbERHxkZ9B8A4wx8xmmlkKcB3wbL9tngVuCV09dC7Q4Jw74GNNIiLSj2+HhpxzXWZ2D/ACkAg87JzbZGZ3hdY/ADwPXAGUA63AbX7VIyIiA/N1YBrn3PN4jX34sgfCph3wFT9rEBGR44uvO4tFROQYCgIRkTinIBARiXMKAhGROGfe+dqxw8yqgd0n+OOFQM0IluMH1XjyRnt9MPprHO31gWocrunOuaKBVoy5IDgZZlbmnCuNdR3HoxpP3mivD0Z/jaO9PlCNI0mHhkRE4pyCQEQkzsVbEDwY6wIioBpP3mivD0Z/jaO9PlCNIyauzhGIiMix4m2PQERE+lEQiIjEuXEZBGa2zMy2mVm5mX17gPVmZr8Krd9gZmeMwhpvDNW2wczeMLMlo6m+sO3OMrNuM7s2mvWF3nvIGs3sE2b2vpltMrO/jKb6zCzHzP7TzD4I1RfV3nfN7GEzqzKzjYOsHw2fk6FqjOnnJJIaw7aL2WdlSM65cfXA6/J6B3AKkAJ8ACzot80VwFq8EdLOBd4ahTWeD+SFppdHs8ZI6gvb7mW8HmavHYW/w1xgMzAtND9hlNX3v4GfhqaLgMNAShRr/DhwBrBxkPUx/ZxEWGPMPieR1hj29xCTz0okj/G4R3A2UO6cq3DOdQCPAyv6bbMCeNR53gRyzax4NNXonHvDOVcXmn0Tb/S2UVNfyFeBp4CqKNbWK5IabwCeds7tAXDORbPOSOpzQJaZGZCJFwRd0SrQObcu9J6DifXnZMgaY/w56a1hqN8jxPazMqTxGARTgL1h85WhZcPdxk/Dff/b8b6ZRcuQ9ZnZFOAa4AFiI5Lf4Vwgz8z+bGbrzeyWqFUXWX33AfPxhmf9EPiac64nOuVFJNafk+GK9uckIqPgszIkXwemiREbYFn/a2Qj2cZPEb+/mV2M9we+1NeK+r3tAMv61/dL4FvOuW7vC23URVJjEnAmcAmQBvzVzN50zm33uzgiq+9y4H3gk8As4EUze9U51+hzbZGK9eckYjH6nETql8T2szKk8RgElcDUsPkSvG9cw93GTxG9v5ktBlYBy51ztVGqDSKrrxR4PPSHXQhcYWZdzrlnolJh5P/PNc65FqDFzNYBS4BoBEEk9d0G3Ou8g8jlZrYTOBV4Owr1RSLWn5OIxPBzEqlYf1aGFuuTFCP9wAu3CmAmR07SndZvmys5+iTY26Owxml4YzmfPxp/h/22X0P0TxZH8jucD7wU2jYd2AgsHEX13Q/8KDQ9EdgHFEb59ziDwU/ExvRzEmGNMfucRFpjv+2i/lmJ5DHu9gicc11mdg/wAt6Z+oedc5vM7K7Q+gfwztxfgfcH1Ir3zWy01fgDoAD4TeibRJeLUi+GEdYXU5HU6JzbYmZ/BDYAPcAq59xxL/GLZn3AT4A1ZvYhXmP7Ledc1LosNrN/BT4BFJpZJfBDIDmsvph+TiKsMWafk2HUOOqpiwkRkTg3Hq8aEhGRYVAQiIjEOQWBiEicUxCIiMQ5BYGISJxTEIhEwMxyzezuIbb5rZldEK2aREaKgkAkMrnAcYMAOAev4zORMUVBIBKZe4FZobENftZ/pZnNB7Y757r7Lf+8mW0MjTmwLlrFigyHbigTiYCZzQCec84tHGT914F659zD/ZZ/CCxzzu0zs1znXL3vxYoMk/YIREbG5cAfB1j+Ol43El/C62pCZNRREIicJDNLB3Kdc8f0zOmcuwv4Hl4vnu+bWUG06xMZioJAJDJNQNYg6y4GXhlohZnNcs695Zz7AVDD0d06i4wKCgKRCDivn/vXQyd++58sXs7Ah4UAfmZmH4YGNl+H1x21yKiik8UiJ8nM3gXOcc51xroWkROhIBARiXM6NCQiEucUBCIicU5BICIS5xQEIiJxTkEgIhLnFAQiInHu/wNcX/tZRgY59QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=rho_zz.plot()" ] }, { "cell_type": "markdown", "id": "c3fbf0f2", "metadata": {}, "source": [ "Then, we see how broadening the C-C R$^2$ condition via recoupling the H–C dipole coupling with R$^3$ allows for C-C spin-diffusion to occur. This is also a convenient way to achieve the required broadening, since to recover an unbroadened spectrum, we must simply remove the field from the $^1$H channel (or better yet, apply heteronuclear decoupling)." ] } ], "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 }