{ "cells": [ { "cell_type": "markdown", "id": "36ce9c1e", "metadata": {}, "source": [ "# Pseudo-Contact Shift" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "dfce1ff4", "metadata": {}, "source": [ "In the previous section, we investigated the [contact shift](../Chapter5/Ch5_ContactShift.ipynb), which results from an isotropic hyperfine coupling to a fast-relaxing electron. However, if the coupling is dipolar in nature, then we instead have a pseudo-contact shift. Under static conditions, the pseudo-contact shift appears just from a dipolar hyperfine coupling, but under tumbling or MAS, this vanishes unless the electron has an anisotropic g-tensor. We show how to simulate this effect here." ] } , { "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": "99ad0a48", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 2, "id": "17688bfe", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "sl.Defaults['verbose']=False" ] }, { "cell_type": "markdown", "id": "18006f4f", "metadata": {}, "source": [ "The shift in the NMR peak due to an isotropic coupling to a polarized electron is known as the contact shift. The pseudo-contact shift, on the other hand, results from the anisotropic part of the coupling to the electron. The anisotropic hyperfine coupling's Hamiltonian has an average of zero when sampling all orientations, however. This means that isotropic tumbling or MAS would in principal remove the hyperfine coupling (MAS may leave spnning sidebands), even if the electron is polarized. Another factor comes in, however, which is the fact that the $g_{xz}$ and $g_{yz}$ components of the electron g-tensor may be large enough to tilt the electron's quantization axis away from the magnetic field's *z*-axis, such that MAS or isotropic tumbling no longer results in a complete averaging of the hyperfine Hamiltonian. Furthermore, the electron's polarization becomes orientation-dependent, which also hinders complete averaging of the pseudo-contact shift." ] }, { "cell_type": "markdown", "id": "9b25d271", "metadata": {}, "source": [ "## Pseudo-contact shift without g-anisotropy\n", "Without MAS or motion to average the coupling, a pseudo-contact shift (PCS) appears without g-tensor anisotropy, although the average shift is zero. We start by simulating this case, showing the PCS under static conditions, and under tumbling or MAS." ] }, { "cell_type": "markdown", "id": "ee8c1b00", "metadata": {}, "source": [ "### Build the system" ] }, { "cell_type": "code", "execution_count": 3, "id": "8a838743", "metadata": {}, "outputs": [], "source": [ "delta=sl.Tools.dipole_coupling(1,'e-','13C') #10 Angstroms from electron\n", "gxx=gyy=gzz=2\n", "g_euler=[0,2*np.pi/5,0]\n", "\n", "ex=sl.ExpSys(v0H=600,vr=0,Nucs=['13C','e-'],T_K=100,LF=False,pwdavg=9)\n", "ex.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz)\n", "\n", "L=ex.Liouvillian()" ] }, { "cell_type": "markdown", "id": "68d0a978", "metadata": {}, "source": [ "### Spectrum without relaxation" ] }, { "cell_type": "markdown", "id": "95e64e6f", "metadata": {}, "source": [ "First, we just simulate the Pake pattern resulting from the dipolar hyperfine coupling without relaxation. We start from thermal equilibrium, in order to be able to see the asymmetry of the Pake pattern due to electron polarization. If we just start from '13Cx', no polarization is included on the electron." ] }, { "cell_type": "code", "execution_count": 4, "id": "8b773c24", "metadata": {}, "outputs": [], "source": [ "Dt=0.00002\n", "seq=L.Sequence(Dt=Dt)\n", "Upi2=L.Udelta('13C',phi=np.pi/2,phase=np.pi/2) #pi/2 along y\n", "\n", "no_rlx=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Upi2*no_rlx\n", "_=no_rlx.DetProp(seq,n=100)" ] }, { "cell_type": "code", "execution_count": 5, "id": "bbeedfba", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "no_rlx.apod_pars['LB']=300\n", "_=no_rlx.plot(FT=True,apodize=True)" ] }, { "cell_type": "markdown", "id": "0840e4d5", "metadata": {}, "source": [ "### Spectrum with relaxation" ] }, { "cell_type": "code", "execution_count": 6, "id": "a1bcdc26", "metadata": {}, "outputs": [], "source": [ "L.clear_relax()\n", "L.add_relax(Type='T1',i=1,T1=1e-7)\n", "L.add_relax(Type='T2',i=1,T2=1e-12)\n", "L.add_relax(Type='recovery')\n", "\n", "rlx=sl.Rho(rho0='Thermal',detect='13Cp')\n", "\n", "Upi2*rlx\n", "_=rlx.DetProp(seq,n=100)" ] }, { "cell_type": "code", "execution_count": 7, "id": "4b68060c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rlx.apod_pars['LB']=300\n", "ax=rlx.plot(FT=True,apodize=True)\n", "no_rlx.plot(FT=True,apodize=True,ax=ax)\n", "_=ax.legend(('With relaxation','No relaxation'))" ] }, { "cell_type": "markdown", "id": "11f0f121", "metadata": {}, "source": [ "Then, we see that the Pake pattern collapses to the average of the two sides of the pattern. However, the average of the pseudo-contact shift is zero, and can be removed with moderate spinning, as shown below. Note that we change the powder average since the large number of angles are not required for MAS.\n", "\n", "We re-initialize the experimental system (`ex`), since a number of settings get changed when adding MAS." ] }, { "cell_type": "code", "execution_count": 8, "id": "9cc4a303", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ex=sl.ExpSys(v0H=600,vr=5000,Nucs=['13C','e-'],T_K=100,LF=False,pwdavg=3)\n", "ex.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz)\n", "\n", "L=ex.Liouvillian()\n", "Upi2=L.Udelta('13C',np.pi/2,np.pi/2)\n", "seq=L.Sequence()\n", "\n", "rho=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Upi2*rho\n", "rho.DetProp(seq,n=1024)\n", "\n", "ax=rho.plot(FT=True,apodize=True)\n", "_=ax.set_xlim([-.5,.5])" ] }, { "cell_type": "markdown", "id": "1d5ebd33", "metadata": {}, "source": [ "Then, if include magic-angle spinning, the influence of the pseudo-contact shift is removed. Similarly, if the system undergoes isotropic tumbling, the pseudo-contact shift vanishes. We allow the system to hop around a tetrahedral geometry to mimic this behavior." ] }, { "cell_type": "code", "execution_count": 9, "id": "e74cf5c1", "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,vr=0,Nucs=['13C','e-'],T_K=100,LF=False,pwdavg='alpha0beta0')\n", "ex0.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex0.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz)\n", "\n", "L=sl.Tools.SetupTumbling(ex0,q=1,tc=1e-9) #This creates a system hopping around a tetrahedral geometry\n", "\n", "L.add_relax(Type='T1',i=1,T1=1e-7)\n", "L.add_relax(Type='T2',i=1,T2=1e-12)\n", "L.add_relax(Type='recovery')\n", "\n", "Upi2=L.Udelta('13C',np.pi/2,np.pi/2)\n", "seq=L.Sequence(Dt=1/1000)\n", "\n", "rho=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Upi2*rho\n", "rho.DetProp(seq,n=1024)\n", "\n", "rho.plot(FT=True,apodize=True)\n", "_=ax.set_xlim([-500,500])" ] }, { "cell_type": "markdown", "id": "92d3c4b7", "metadata": {}, "source": [ "## Pseudo-contact shift with g-anisotropy" ] }, { "cell_type": "markdown", "id": "f6862716", "metadata": {}, "source": [ "Above, we saw that the pseudo-contact shift vanishes with MAS or isotropic motion. However, if a g-anisotropy is included, then the pseudo-contact shift reappears.\n", "\n", "It is not sufficient to add the g-anisotropy in the rotating frame. The g-anisotropy induces a pseudo-contact shift because it changes the quantization axis of the electron away from the $z-$axis of the lab frame, *and* because the electron polarization varies as a function of the g-tensor orientation. The former effect is only induced if the computation is performed in the lab frame. In this case, we need to be careful not to forget to downmix the resulting signal. One may try also simulating in the rotating frame, to separate contributions from electron tilting and variation of the electron polarization.\n", "\n", "The latter effect is only induced if we correctly implement relaxation. Since the electron quantization axis is no longer along *z*, then $T_1$ and $T_2$ relaxation need to be applied along the tilted axes, and the polarization needs to be readjusted depending on the g-tensor orientation. This requires using the `OS=True` option, along with the `Thermal=True` option for $T_1$ relaxation. \n", "\n", "We furthermore note that the electron $T_1$ must be faster than the tumbling: otherwise, the electron does not return to its quantization axis quickly enough to induce the pseudo-contact shift.\n", "\n", "We use hopping around the 'rep10' powder average to mimic tumbling. This will not perfectly reproduce the solution-state PCS, partly because it does not include motion around the $\\gamma$ angle, and also because not enough angles are included. Nonetheless, it is a good demonstrate of the PCS concept and its general behavior." ] }, { "cell_type": "markdown", "id": "2ff99866", "metadata": {}, "source": [ "### Pseudo-contact shift with isotropic hopping" ] }, { "cell_type": "code", "execution_count": 10, "id": "af4197d9", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gxx,gyy,gzz=1,1,4\n", "ex0=sl.ExpSys(v0H=600,vr=0,Nucs=['13C','e-'],T_K=298,LF=True,pwdavg='alpha0beta0')\n", "ex0.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex0.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz)\n", "\n", "L=sl.Tools.SetupTumbling(ex0,q=2,tc=5e-9) #This creates a system hopping around a tetrahedral geometry\n", "\n", "L.add_relax(Type='T1',i=1,T1=1e-10,OS=True,Thermal=True)\n", "L.add_relax(Type='T2',i=1,T2=1e-10,OS=True)\n", "\n", "Upi2=L.Udelta('13C',np.pi/2,np.pi/2)\n", "seq=L.Sequence(Dt=1/1000)\n", "\n", "rho=sl.Rho(rho0='Thermal',detect='13Cp')\n", "Upi2*rho\n", "rho.DetProp(seq,n=1024)\n", "rho.downmix()\n", "\n", "ax=rho.plot(FT=True,apodize=True)" ] }, { "cell_type": "markdown", "id": "fe5a0510", "metadata": {}, "source": [ "We can repeat the above calculation with decreasing temperature, to verify that the simulated PCS increases with decreasing temperature." ] }, { "cell_type": "markdown", "id": "c3941c68", "metadata": {}, "source": [ "### Temperature dependence" ] }, { "cell_type": "code", "execution_count": 11, "id": "97059df9", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots()[1]\n", "seq=L.Sequence(Dt=1/5000)\n", "\n", "T=[10,50,100,200,298]\n", "for T_K in T:\n", " L.expsys.T_K=T_K\n", " \n", " rho.clear()\n", " Upi2*rho\n", " rho.DetProp(seq,n=1024)\n", " rho.downmix()\n", " \n", " rho.plot(FT=True,apodize=True,ax=ax)\n", "_=ax.legend([f'T = {T_K:.0f} K' for T_K in T])" ] }, { "cell_type": "markdown", "id": "7c55a391", "metadata": {}, "source": [ "Indeed, the expected temperature dependence is obtained. \n", "\n", "Note that the pseudo-contact shift depends on the electron's polarization and quantization axis changing for different orientations. If the electron $T_1$ is longer than the rate of reorientation (from tumbling or MAS), the pseudo-contact shift is reduced, because the electron does not have time to fully requilibrate at each new orientation. We repeat the above calculation with a longer electron $T_1$ to see the effects." ] }, { "cell_type": "markdown", "id": "cd5231c1", "metadata": {}, "source": [ "### Electron $T_1$ dependence" ] }, { "cell_type": "code", "execution_count": 12, "id": "07227463", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "L.clear_relax()\n", "L.add_relax(Type='T1',i=1,T1=1e-8,OS=True,Thermal=True)\n", "L.add_relax(Type='T2',i=1,T2=1e-10,OS=True)\n", "\n", "ax=plt.subplots()[1]\n", "seq=L.Sequence(Dt=1/5000)\n", "\n", "T=[10,50,100,200,298]\n", "for T_K in T:\n", " L.expsys.T_K=T_K\n", " \n", " rho.clear()\n", " Upi2*rho\n", " rho.DetProp(seq,n=1024)\n", " rho.downmix()\n", " \n", " rho.plot(FT=True,apodize=True,ax=ax)\n", "_=ax.legend([f'T = {T_K:.0f} K' for T_K in T])" ] }, { "cell_type": "markdown", "id": "51b3a65c", "metadata": {}, "source": [ "The magnitude of the PCS is reduced, since the electron does not recover to its thermal equilibrium quickly when hopping to a new orientation." ] }, { "cell_type": "markdown", "id": "51e72c45", "metadata": {}, "source": [ "### Orientation dependence of PCS" ] }, { "cell_type": "markdown", "id": "98ed058c", "metadata": {}, "source": [ "PCS has a complex orientation dependence, due to variation of the relative orientations of the g-tensor and hyperfine tensor, dependence on the location of the nuclear spin relative to the electron. Here, we calculate the size of the PCS for a 10 Angstrom distance as a function of the g-tensor orientation relative to the dipolar hyperfine coupling orientation." ] }, { "cell_type": "code", "execution_count": 13, "id": "5a6ebd06", "metadata": {}, "outputs": [], "source": [ "# Sweep euler angles\n", "sl.Defaults['verbose']=False\n", "SZ=[15,30]\n", "beta=np.linspace(0,np.pi/2,SZ[0])\n", "gamma=np.linspace(0,np.pi*2,SZ[1])\n", "N=beta.size*gamma.size\n", "\n", "beta,gamma=np.meshgrid(beta,gamma)\n", "shift=[]\n", "for k,(beta0,gamma0) in enumerate(zip(beta.reshape(np.prod(SZ)),gamma.reshape(np.prod(SZ)))):\n", " ex0=sl.ExpSys(v0H=600,Nucs=['13C','e-'],LF=True,vr=0,T_K=100,pwdavg=sl.PowderAvg('alpha0beta0')) #Electron-nuclear system\n", " ex0.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", " ex0.set_inter('g',i=1,gxx=1,gyy=1,gzz=4,euler=[0,beta0,gamma0])\n", "\n", " L=sl.Tools.SetupTumbling(ex0,tc=1e-9,q=2) #1 ns tumbling\n", "\n", " L.add_relax(Type='T1',i=1,T1=1e-11,OS=True,Thermal=True)\n", " L.add_relax(Type='T2',i=1,T2=1e-11,OS=True)\n", "\n", " seq=L.Sequence(Dt=1e-4)\n", "\n", " rho=sl.Rho('Thermal','13Cp') #Generate initial state, detection operator\n", " Upi2=L.Udelta('13C',np.pi/2,np.pi/2)\n", " (Upi2*rho).DetProp(seq,n=800) #Propagate the system\n", " rho.downmix()\n", "\n", " i=np.argmax(rho.FT[0])\n", " shift.append(rho.v_axis[i])\n", " \n", "shift=np.array(shift).reshape([SZ[1],SZ[0]])" ] }, { "cell_type": "markdown", "id": "588fe89e", "metadata": {}, "source": [ "### 3D plot of the PCS magnitude" ] }, { "cell_type": "code", "execution_count": 14, "id": "982c278a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from copy import copy\n", "x=shift*np.sin(beta)*np.cos(gamma)\n", "y=shift*np.sin(beta)*np.sin(gamma)\n", "z=shift*np.cos(beta)\n", "\n", "ax=plt.figure(figsize=[8,8]).add_subplot(1,1,1,projection='3d')\n", "i=shift>0\n", "\n", "x0,y0,z0=copy(x),copy(y),copy(z)\n", "for q in [x0,y0,z0]:q[i]=0\n", "ax.plot_surface(x0,y0,z0,color='#801010')\n", "ax.plot_surface(-x0,-y0,-z0,color='#801010')\n", "\n", "x0,y0,z0=copy(x),copy(y),copy(z)\n", "for q in [x0,y0,z0]:q[~i]=0\n", "ax.plot_surface(x0,y0,z0,color=\"#0093AF\")\n", "ax.plot_surface(-x0,-y0,-z0,color=\"#0093AF\")\n", "\n", "\n", "# ax.plot_surface(x[~i],y[~i],z[~i])\n", "for q in ['x','y','z']:\n", " getattr(ax,f'set_{q}lim')([-500,500])\n", " getattr(ax,f'set_{q}label')(r'$\\delta_{PCS} / Hz$')" ] }, { "cell_type": "markdown", "id": "b7301429", "metadata": {}, "source": [ "Then, we see that the sign and magnitude of the PCS varies depending on the relative orientations of the dipolar and g-tensors, resulting in different PCS depending on the position of the nucleas relative to the electron. The resulting shape is slightly tilted– this effect only comes when calculating in the lab frame. In the rotating frame, the shape is aligned along the axes, highlighting the importance of including lab-frame terms." ] }, { "cell_type": "markdown", "id": "d145ad80", "metadata": {}, "source": [ "## Pseudo-contact Shift under MAS" ] }, { "cell_type": "markdown", "id": "481b1360", "metadata": {}, "source": [ "Finally, we investigate how the PCS manifests under magic angle spinning. Due to the anistropic g-tensor, the PCS cannot be spun out, and furthermore, different crystallites in the rotor will have different shifts, yielding a complex, rank-4 lineshape." ] }, { "cell_type": "markdown", "id": "87e37714", "metadata": {}, "source": [ "### Run the simulation" ] }, { "cell_type": "code", "execution_count": 15, "id": "ff36fbac", "metadata": {}, "outputs": [], "source": [ "delta=sl.Tools.dipole_coupling(1,'e-','13C') #10 Angstroms from electron\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','e-'],vr=6000,LF=True,T_K=200,pwdavg=4,n_gamma=30) #Electron-nuclear system\n", "ex.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex.set_inter('g',i=1,gxx=1,gyy=1,gzz=4)\n", " \n", "L=sl.Liouvillian(ex) #Generate a Liouvillian\n", "\n", "L.add_relax('T1',i=1,T1=1e-7,OS=True,Thermal=True) \n", "L.add_relax('T2',i=1,T2=1e-7,OS=True)\n", "\n", "seq=L.Sequence() #Generate an empty sequence\n", "\n", "rho200=sl.Rho('13Cx','13Cp') #Generate initial state, detection operator\n", "_=rho200.DetProp(seq,n=8000,n_per_seq=1) #Propagate the system" ] }, { "cell_type": "markdown", "id": "a0498327", "metadata": {}, "source": [ "### Plot the results" ] }, { "cell_type": "code", "execution_count": 16, "id": "baae75fe", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho200.downmix()\n", "ax=rho200.plot(FT=True) #Plot the results into the same axis\n", "_=ax.set_xlim([1.5,-1.5])" ] }, { "cell_type": "markdown", "id": "6eafc6ef", "metadata": {}, "source": [ "A complex lineshape is obtained, resulting from incomplete averaging of the rank-4 PCS tensor. As with isotropic hopping, decreasing the temperature will increasing the magnitude of the PCS, as shown below." ] }, { "cell_type": "markdown", "id": "7501a858", "metadata": {}, "source": [ "### Temperature dependence" ] }, { "cell_type": "code", "execution_count": 17, "id": "cdbbf4ad", "metadata": {}, "outputs": [], "source": [ "delta=sl.Tools.dipole_coupling(1,'e-','13C') #10 Angstroms from electron\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','e-'],vr=6000,LF=True,T_K=100,pwdavg=4,n_gamma=30) #Electron-nuclear system\n", "ex.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex.set_inter('g',i=1,gxx=1,gyy=1,gzz=4)\n", " \n", "L=sl.Liouvillian(ex) #Generate a Liouvillian\n", "\n", "L.add_relax('T1',i=1,T1=1e-7,OS=True,Thermal=True) #1 microsecond T1\n", "L.add_relax('T2',i=1,T2=1e-7,OS=True) #1 ns T2, required for physical system when T1 is present\n", "\n", "seq=L.Sequence() #Generate an empty sequence\n", "\n", "rho100=sl.Rho('13Cx','13Cp') #Generate initial state, detection operator\n", "_=rho100.DetProp(seq,n=8000,n_per_seq=1) #Propagate the system" ] }, { "cell_type": "code", "execution_count": 18, "id": "85bef36a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho100.downmix()\n", "ax=rho100.plot(FT=True) #Plot the results into the same axis\n", "rho200.plot(FT=True,ax=ax)\n", "ax.legend(('100 K','200 K'))\n", "_=ax.set_xlim([1.5,-1.5])" ] }, { "cell_type": "markdown", "id": "3cc11acc", "metadata": {}, "source": [ "The same tensor shape is obtained, but it is now twice as broad (it also has more signal from the lower temperature). \n", "\n", "Finally, we observe how the PCS tensor shape depends on the relative orientation of the dipolar- and g-tensors." ] }, { "cell_type": "markdown", "id": "94b4c00c", "metadata": {}, "source": [ "### Re-orient the g-tensor" ] }, { "cell_type": "code", "execution_count": 19, "id": "51bcb513", "metadata": {}, "outputs": [], "source": [ "delta=sl.Tools.dipole_coupling(1,'e-','13C') #10 Angstroms from electron\n", "ex=sl.ExpSys(v0H=600,Nucs=['13C','e-'],vr=6000,LF=True,T_K=200,pwdavg=4,n_gamma=30) #Electron-nuclear system\n", "ex.set_inter('hyperfine',i0=0,i1=1,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n", "ex.set_inter('g',i=1,gxx=1,gyy=1,gzz=4,euler=[0,np.pi/2,np.pi/5])\n", " \n", "L=sl.Liouvillian(ex) #Generate a Liouvillian\n", "\n", "L.add_relax('T1',i=1,T1=1e-7,OS=True,Thermal=True) \n", "L.add_relax('T2',i=1,T2=1e-7,OS=True)\n", "\n", "seq=L.Sequence() #Generate an empty sequence\n", "\n", "rho=sl.Rho('13Cx','13Cp') #Generate initial state, detection operator\n", "_=rho.DetProp(seq,n=8000,n_per_seq=1) #Propagate the system" ] }, { "cell_type": "markdown", "id": "8801ea21", "metadata": {}, "source": [ "### Plot the results" ] }, { "cell_type": "code", "execution_count": 20, "id": "865de3fb", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho.downmix()\n", "ax=rho.plot(FT=True) #Plot the results into the same axis\n", "_=ax.set_xlim([1.5,-1.5])" ] }, { "cell_type": "code", "execution_count": null, "id": "bddccb2e", "metadata": {}, "outputs": [], "source": [] } ], "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 }