{
"cells": [
{
"cell_type": "markdown",
"id": "4b328fb5",
"metadata": {},
"source": [
"# Cross Effect"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "9e94048b",
"metadata": {},
"source": [
"The cross effect$^{1,2}$ is a powerful approach to DNP enhancement, where two coupled electrons with resonance frequencies separated by the nuclear Larmor frequency undergo a three-spin flip with the electron.\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"\\pm\\omega_n=\\omega_{e1}-\\omega_{e2}\n",
"\\end{equation}\n",
"$$\n",
"\n",
"Enhancement on the nucleus is induced if the polarization of the two electrons is different. This is achieved by applying a saturating field to the electrons, such that one becomes more saturated than the other.\n",
"\n",
"Most orientations of electron pairs in the sample do not match the above condition, however, magic angle spinning will bring most crystallites through the cross-effect matching condition at some point in the rotor period,$^3$ allowing cross effect to be an effective mechanism of enhancement. Other processes also occur: MAS will cause both electrons to get saturated at various points during the rotor period, and electron-electron transfer without involving the nucleus occurs when the two electrons have the same resonance frequency at some point during the rotor period. We investigate these various processes here.\n",
"\n",
"[1] A.V. Kessenikh, V.L. Luschikov, A.A. Manenkov, Y. Taran. *Sov. Phys. Solid State*, **1963**, 6, 321-329\n",
"\n",
"[2] C.F. Hwang, D.A. Hill. [*Phys. Rev. Lett.*](https://doi.org/10.1103/PhysRevLett.19.1011), **1967**, 19, 1011-1014.\n",
"\n",
"[3] K.R. Thurber, R. Tycko. [*J. Chem. Phys.*](https://doi.org/10.1063/1.4747449), **2012**, 137, 084508."
]
},
{
"cell_type": "markdown",
"id": "0f3b54cf",
"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": "c37f7428",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from time import time"
]
},
{
"cell_type": "markdown",
"id": "b389e326",
"metadata": {},
"source": [
"## Calculate a spectrum of one crystallite under MAS"
]
},
{
"cell_type": "markdown",
"id": "912da82a",
"metadata": {},
"source": [
"Something important to understand about cross-effect (and simulating it) is that by spinning the sample at a frequency much slower than the range of the electron resonance frequencies sampled during the rotor period, we do not average the electron resonance frequence. Instead, we sample many different frequencies. In our example here, the electron covers a range of frequencies about 600 MHz broad. This results in a broad spectrum of frequencies for single orientations.\n",
"\n",
"A few important points: \n",
"\n",
"1. In reality, the sampling of frequencies by MAS is continuous, but in simulation it is discretized. Then, narrow conditions may be missed in simulation that would be briefly met in reality. This can be dealt with by increasing the number of gamma angles, or by decreasing $T_2$ which should broaden conditions.\n",
"\n",
"2. A spectrum with many frequencies results from a single crystallite under MAS, although it is not phaseable. This is because different frequencies are sampled at different times during the rotor period, where the magnetization is not always starting along the x-axis, thus resulting in a varying phase.\n",
"\n",
"3. To obtain the full breadth of the spectrum, we spin faster than typical DNP experiments, and then sample many times in the rotor period (faster spinning allows us to sample less in one rotor period, yielding a faster simulation)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7d740c94",
"metadata": {},
"outputs": [],
"source": [
"# This is a trick to adjust the electron carrier frequency\n",
"# to be centered on the middle of the g-tensor\n",
"gxx,gyy,gzz=2.0021,2.0061,2.0094\n",
"sl.Constants['ge']=(gxx+gyy+gzz)/3"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "91a02d45",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 4->1\n",
"Prop: 10000 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": [
"ex=sl.ExpSys(v0H=250,Nucs='e-',LF=False,vr=100000,T_K=80,pwdavg='alpha0beta45',n_gamma=200)\n",
"ex.set_inter('g',i=0,gxx=gxx,gyy=gyy,gzz=gzz,euler=[0,0,0])\n",
"\n",
"L=ex.Liouvillian()\n",
"L.add_relax('T2',i=0,T2=50e-6,OS=True)\n",
"L.add_relax('T1',i=0,T1=250e-6,OS=True,Thermal=True)\n",
"\n",
"seq=L.Sequence()\n",
"\n",
"rho=sl.Rho('ex','ep')\n",
"rho.DetProp(seq,n=10000,n_per_seq=10000)\n",
"\n",
"_=rho.plot(FT=True,axis='MHz')"
]
},
{
"cell_type": "markdown",
"id": "be051171",
"metadata": {},
"source": [
"Then, we obtain a broad spectrum from the single orientation, but its phase is random. We can plot the power spectrum to get a better view (there is no built-in function for this, but it is trivial to obtain, since the Fourier-transformed spectrum is in `rho.FT`). Note that this does not yield the static spectrum; this would require an average over $\\beta$-angles."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "80db205a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots()[1]\n",
"rho.apodize=True\n",
"rho.apod_pars['LB']=200000\n",
"ax.plot(rho.v_axis*1e6,np.abs(rho.FT[0]))\n",
"_=ax.set_xlabel(r'\\nu / MHz')"
]
},
{
"cell_type": "markdown",
"id": "17464051",
"metadata": {},
"source": [
"## Cross-effect events as a function of the rotor cycle"
]
},
{
"cell_type": "markdown",
"id": "fb163f0a",
"metadata": {},
"source": [
"### Build the System"
]
},
{
"cell_type": "markdown",
"id": "7d5684e7",
"metadata": {},
"source": [
"It is also important to put the nucleus, but not the electrons, in the lab frame for cross-effect to occur. Some broadening on the electrons is also important, since the cross-effect condition is otherwise too narrow and will be missed during the rotor period.\n",
"\n",
"In the first simulation, we will just look at one rotor period to observe the cross-effect transfer. Note that $T_2$ relaxation added to the nucleus should be applied with the orientation-specific option (`OS=True`), since the nucleus is tipped away from the z-axis. If this is not used, some of the $T_2$ relaxation will be applied to the nuclear polarization.\n",
"\n",
"We take some parameters from Thurber and Tycko.$^3$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "05fc7487",
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"# Note that I have adjusted n_gamma large enough that the enhancement does\n",
"# not change with further increases\n",
"ex=sl.ExpSys(v0H=250,Nucs=['e-','e-','1H'],LF=[False,False,True],\n",
" vr=5000,T_K=80,pwdavg='alpha0beta45',n_gamma=1000)\n",
"delta=18e6\n",
"ex.set_inter('hyperfine',i0=0,i1=2,Axx=-delta/2,Ayy=-delta/2,Azz=delta)\n",
"ex.set_inter('g',i=0,gxx=gxx,gyy=gyy,gzz=gzz,euler=[0,0,0])\n",
"ex.set_inter('g',i=1,gxx=gxx,gyy=gyy,gzz=gzz,euler=[0,75*np.pi/180,0])\n",
"ex.set_inter('dipole',i0=0,i1=1,delta=sl.Tools.dipole_coupling(1.33,'e-','e-'),euler=[0,77*np.pi/180,0])\n",
"\n",
"L=ex.Liouvillian()\n",
"\n",
"L.add_relax('T2',i=0,T2=4e-6)\n",
"L.add_relax('T2',i=1,T2=4e-6)\n",
"_=L.add_relax('T2',i=2,T2=0.2e-3,OS=True)"
]
},
{
"cell_type": "markdown",
"id": "040c0d51",
"metadata": {},
"source": [
"### Run the simulation"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "4853fbe1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Prop: 1000 steps per every 1 rotor period\n"
]
}
],
"source": [
"seq=L.Sequence().add_channel('e',v1=500e3,voff=-50e6)\n",
"\n",
"ON=sl.Rho('Thermal',['S0z','S1z','1Hz'])\n",
"_=ON.DetProp(seq,n=1000,n_per_seq=1000)"
]
},
{
"cell_type": "markdown",
"id": "e9e5d883",
"metadata": {},
"source": [
"### Plot the results"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "47f5c351",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(2,2,figsize=[9,9])[1].flatten()\n",
"ON.plot(axis='us',det_num=2,ax=ax[0])\n",
"ON.plot(axis='us',det_num=[0,1],ax=ax[1])\n",
"i=np.argmax(np.abs(np.diff(ON.I[2]))) #Find the largest change in the nuclear polarization\n",
"ON.plot(axis='us',det_num=[0,1],ax=ax[2])\n",
"w=10\n",
"h=.001\n",
"ax[2].set_xlim(ON.t_axis[[i-w,i+w]]*1e6)\n",
"ax[2].set_ylim(ON.I[0][i].real+np.array([-h,h]))\n",
"ON.plot(axis='us',det_num=[0,1],ax=ax[3])\n",
"ax[3].set_xlim(ON.t_axis[[i-w,i+w]]*1e6)\n",
"ax[3].set_ylim(ON.I[1][i].real+np.array([-h,h]))\n",
"\n",
"for a,title in zip(ax,[r'$^1$H','e-',r'e$_0$ (zoom)',r'e$_1$ (zoom)']):\n",
" a.set_ylim(a.get_ylim())\n",
" a.set_title(title)\n",
" a.plot(ON.t_axis[i]*1e6*np.ones(2),a.get_ylim(),color='grey',linestyle=':')\n",
"ax[0].figure.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "cfe01aa7",
"metadata": {},
"source": [
"In the above plots, we can see where cross effect occurs based on where the $^1$H polarization changes (upper left). The largest such event is marked by a dashed line in all plots. In the upper right plot, we see the behavior of the two electrons. The first event in this plot is partial saturation of $\\langle S_{1z}\\rangle$. This is followed closely by an exchange of magnetization between the two electrons, where $\\omega_{e1}=\\omega_{e2}$. Next, saturation of $\\langle S_{0z}\\rangle$ occurs, followed by the first cross effect event, marked by a dashed line. This event is zoomed in on in the lower two plots. A second cross-effect event occurs next. The final event is further saturation of $\\langle S_{1z}\\rangle$.\n",
"\n",
"We can continue with this system, adding $T_1$ relaxation to the spins, and propagating over many rotor periods to see the net buildup of polarization."
]
},
{
"cell_type": "markdown",
"id": "286daa35",
"metadata": {},
"source": [
"## Polarization build up over many rotor cycles"
]
},
{
"cell_type": "markdown",
"id": "31747aab",
"metadata": {},
"source": [
"### Add $T_1$ relaxation\n",
"Don't forget to use `OS=True` to ensure correct relaxation of the mixed nuclear states. We also need thermalization for DNP enhancement to occur (`Thermal=True`)."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "044a2155",
"metadata": {},
"outputs": [],
"source": [
"L.add_relax('T1',i=0,T1=250e-6,OS=True,Thermal=True)\n",
"L.add_relax('T1',i=1,T1=250e-6,OS=True,Thermal=True)\n",
"_=L.add_relax('T1',i=2,T1=10,OS=True,Thermal=True)"
]
},
{
"cell_type": "markdown",
"id": "f5b5b493",
"metadata": {},
"source": [
"### Run the simulation"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "81f88031",
"metadata": {},
"outputs": [],
"source": [
"seq=L.Sequence().add_channel('e',v1=500e3,voff=-150e6)\n",
"ON=sl.Rho('Thermal',['S0z','S1z','1Hz'])\n",
"_=ON.DetProp(seq,n=500)"
]
},
{
"cell_type": "markdown",
"id": "0d9ca030",
"metadata": {},
"source": [
"### Plot the results"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "e0cb335c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_=ON.plot(det_num=2)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "8174dec4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Enhancement: -258\n"
]
}
],
"source": [
"print(f'Enhancement: {ON.I[-1][-1].real/ex.Peq[-1]:.0f}')"
]
},
{
"cell_type": "markdown",
"id": "eddfae61",
"metadata": {},
"source": [
"A significant nuclear enhancement is achieved. However, it is interesting to note what happens if the electron saturation is removed, since the cross-effect condition is still met during the rotor cycle, even without microwaves."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "85b03799",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 64->24\n"
]
}
],
"source": [
"seq=L.Sequence()\n",
"OFF=sl.Rho('Thermal',['S0z','S1z','1Hz'])\n",
"_=OFF.DetProp(seq,n=500)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "a4a9fcba",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_=OFF.plot(det_num=2)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "fe4db141",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Apparent enhancement: -503\n"
]
}
],
"source": [
"print(f'Apparent enhancement: {ON.I[-1][-1].real/OFF.I[-1][-1].real:.0f}')"
]
},
{
"cell_type": "markdown",
"id": "fe0cbbef",
"metadata": {},
"source": [
"The $^1$H polarization is depleted when no microwave irradiation is applied. \n",
"\n",
"Then, if the enhancement is determined by comparing on and off signal, we will significantly overestimate the enhancement. This effect can be understood by noting that even without microwave irradiation, the cross effect condition is periodically met, and if the electrons are not at their own thermal equilibrium at that point, then polarization can be lost from the nucleus."
]
},
{
"cell_type": "markdown",
"id": "68ec78d6",
"metadata": {},
"source": [
"## Several rotor cycles without microwaves\n",
"We simulate several rotor cycles without microwaves to observe the trajectory of the nuclear and electronic magnetization."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "6dd85e7d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 64->24\n",
"Prop: 200 steps per every 1 rotor period\n"
]
}
],
"source": [
"OFF=sl.Rho('Thermal',['S0z','S1z','1Hz'])\n",
"_=OFF.DetProp(seq,n=1000,n_per_seq=200)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "72c6fecf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(2,2,figsize=[9,9])[1].flatten()\n",
"OFF.plot(axis='us',det_num=2,ax=ax[0])\n",
"OFF.plot(axis='us',det_num=[0,1],ax=ax[1])\n",
"i=np.argmax(np.abs(np.diff(OFF.I[2]))) #Find the largest change in the nuclear polarization\n",
"OFF.plot(axis='us',det_num=[0,1],ax=ax[2])\n",
"w=10\n",
"h=.00001\n",
"ax[2].set_xlim(OFF.t_axis[[i-w,i+w]]*1e6)\n",
"ax[2].set_ylim(OFF.I[0][i].real+np.array([-h,h]))\n",
"OFF.plot(axis='us',det_num=[0,1],ax=ax[3])\n",
"ax[3].set_xlim(OFF.t_axis[[i-w,i+w]]*1e6)\n",
"ax[3].set_ylim(OFF.I[1][i].real+np.array([-h,h]))\n",
"\n",
"for a,title in zip(ax,[r'$^1$H','e-',r'e$_0$ (zoom)',r'e$_1$ (zoom)']):\n",
" a.set_ylim(a.get_ylim())\n",
" a.set_title(title)\n",
" a.plot(OFF.t_axis[i]*1e6*np.ones(2),a.get_ylim(),color='grey',linestyle=':')\n",
"ax[0].figure.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "8faab166",
"metadata": {},
"source": [
"Above, we see that although no saturating field is applied to the electron, the electron polarization still varies throughout the rotor period. This is partly because the thermal equilibrium for the electron polarization changes throughout the rotor period, which is observed as slow variation of the electron polarization (it is important to use `OS=True` and `Thermal=True` to obtain this behavior), and secondly because when the electrons having matching frequencies, they exchange polarization. Then, due to different electron polarizations, the nucleus will lose polarization when the cross effect condition is matched.\n",
"\n",
"Interestingly, this does not lead to an immediate depletion of nuclear polarization; that comes after the first rotor period.\n",
"\n",
"We should note: setting `rho=sl.Rho(rho0='Thermal',...)` sets polarization for each orientation of the rotor separately based on the full Hamiltonian, if thermalization is done with `OS=True` (if orientation-specific thermalization is not applied, then the average polarization is used). However, this may not be equilibrium for the system under spinning, and indeed, the system may not have a true equilibrium once spinning, since sometimes polarizations are continuously varying throughout the rotor period."
]
}
],
"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
}