{
"cells": [
{
"cell_type": "markdown",
"id": "f8aa4fa1",
"metadata": {},
"source": [
"# $T_1$ and Nuclear Overhauser Effect"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "58f5c650",
"metadata": {},
"source": [
"We previously simulated $T_1$ and NOE in [solution state](../Chapter2/Ch2_T1_NOE.ipynb). In solution NMR, our motion should result in full averaging of the anisotropic interactions. In contrast, in solid-state NMR, no tumbling occurs, so anisotropic interactions remain and influence the resulting spectrum. This also means that different orientations in the sample undergo relaxation with different rate constants. We will characterize this behavior here, and how it depends on the presence or absence of magic angle spinning."
]
}
,
{
"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": "19c91baa",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "11f82007",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "74ca2366",
"metadata": {},
"source": [
"## $T_1$ anisotropy under static conditions"
]
},
{
"cell_type": "markdown",
"id": "998eb3b3",
"metadata": {},
"source": [
"### Build the system\n",
"We use a two-spin $^1$H–$^{15}$N system, with parameters for the H–N in a protein backbone. We include a 1 ns correlation time, and recovery to thermal equilibrium (`L.add_relax('DynamicThermal')`)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "592a432f",
"metadata": {},
"outputs": [],
"source": [
"delta=sl.Tools.dipole_coupling(.102,'15N','1H')\n",
"hop=40*np.pi/180\n",
"ex0=sl.ExpSys(v0H=600,Nucs=['15N','1H'],vr=0,LF=True,pwdavg=7)\n",
"ex0.set_inter('CSA',i=0,delta=113,euler=[0,23*np.pi/180,0])\n",
"ex0.set_inter('dipole',i0=0,i1=1,delta=delta)\n",
"ex1=ex0.copy()\n",
"ex1.set_inter('CSA',i=0,delta=113,euler=[[0,23*np.pi/180,0],[0,hop,0]])\n",
"ex1.set_inter('dipole',i0=0,i1=1,delta=delta,euler=[0,hop,0])\n",
"\n",
"L=sl.Liouvillian(ex0,ex1)\n",
"L.kex=sl.Tools.twoSite_kex(1e-9)\n",
"_=L.add_relax('DynamicThermal')"
]
},
{
"cell_type": "markdown",
"id": "aea832e2",
"metadata": {},
"source": [
"### Propagate and plot"
]
},
{
"cell_type": "markdown",
"id": "fe47cc40",
"metadata": {},
"source": [
"We assume the system starts out with the $^{15}$N spin having been saturated, but thermal polarization on the $^1$H. Note that if a thermalized Liouvillian is used, then the initial magnetization is automatically scaled by the polarization of the system."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "40898b79",
"metadata": {},
"outputs": [],
"source": [
"seq=L.Sequence(Dt=1e-2)\n",
"U=seq.U()\n",
"rho=sl.Rho('1Hz','15Nz')\n",
"\n",
"_=rho.DetProp(U,n=10000)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "f82d8069",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=rho.plot(axis='s')\n",
"_=ax.plot(ax.get_xlim(),np.ones(2)*ex0.Peq[0],color='black',linestyle=':')"
]
},
{
"cell_type": "markdown",
"id": "259940cb",
"metadata": {},
"source": [
"Then, the $^{15}$N magnetization relaxes towards its thermal equilibrium. Note that we observe both a fairly fast component at the beginning ($T_1$~1 s), but also a much slower component, with $T_1$ on the order of 10 s.\n",
"\n",
"We can analyze the multiexponentiality precisely with SLEEPY, as done below."
]
},
{
"cell_type": "markdown",
"id": "8bb300bf",
"metadata": {},
"source": [
"### Histogram of all rate constants present"
]
},
{
"cell_type": "markdown",
"id": "e4b428b9",
"metadata": {},
"source": [
"SLEEPY gives us the ability to extract individual rate constants from propagators, given a starting density matrix, via the `rho.extract_decay_rates` function. This function has a few modes, but the `'wt_rates'` mode yields a list of rate constants and their corresponding amplitudes, weighted according to the powder average weighting (other modes offer, for example, an averaged weight for each element of the powder average, the average over the full powder average, or a list of rate constants for each element of the powder average; type `help(rho.extract_decay_rates)` for details).\n",
"\n",
"Once we have the rates and amplitudes, we can create a histogram for each weight. Note this is slightly more complex than a usual histogram, because the rate constants have amplitudes associated with them, so we cannot just count up the rate constants in a bin, rather, we need to add together the amplitudes for all rate constants in a bin.\n",
"\n",
"We can also calculate the average rate constant from the rates and amplitudes, shown on the plot."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b25505f2",
"metadata": {},
"outputs": [],
"source": [
"def histogram(R1,A,bins=None,ax=None):\n",
" if bins is None:\n",
" bins=np.linspace(np.log(R1.min()),np.log(R1.max()),25)\n",
" \n",
" db=bins[1]-bins[0]\n",
" \n",
" i=np.digitize(np.log(R1),bins)-1\n",
" h=np.zeros(len(bins))\n",
" for k in range(i.max()+1):\n",
" h[k]=A[k==i].sum()\n",
" \n",
" if ax is None:\n",
" ax=plt.subplots()[1]\n",
" alpha=1\n",
" color=plt.get_cmap('tab10')(0)\n",
" else:\n",
" alpha=.5 \n",
" color='red'\n",
" ax.bar(bins,h,width=(bins[2]-bins[1])*.9,alpha=alpha,color=color)\n",
" ax.set_xticks(bins[np.arange(5)*5])\n",
" ax.set_xticklabels([f'{10**bins[k:k+2].mean()*1e3:6.2f}' for k in range(0,25,5)])\n",
" ax.set_xlabel(r'$R_1*1e3$ / s$^{-1}$')\n",
" ax.set_ylabel('Intensity')\n",
" \n",
" return bins,ax"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "82004894",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rho.reset()\n",
"\n",
"# Calculate a weighted histogram\n",
"R1_static,A_static=rho.extract_decay_rates(U,mode='wt_rates')\n",
"bins,ax=histogram(R1_static,A_static)\n",
"\n",
"R1_avg_static=(R1_static*A_static).sum()/A_static.sum()\n",
"\n",
"ax.text(bins[1],4.5e-7,fr'$\\langle R_1\\rangle_{{static}}$: {R1_avg_static:.2f} $s^{{-1}}$')\n",
"_=ax.legend(('static','MAS'))"
]
},
{
"cell_type": "markdown",
"id": "1b561c2b",
"metadata": {},
"source": [
"We see that an extremely broad range of $R_1$ rate constants are obtained, covering several orders of magnitude. These correspond to both different orientations in the powder average, and also different rate constants depending if the dipolar and CSA relaxation are constructive or destructive (see [Trosy Effects](../Chapter2/Ch2_TROSY.ipynb)). \n",
"\n",
"We now repeat the above calculation, but under magic angle spinning conditions. Note that while we may change `ex0.vr`, we have to take care to clear the Liouvillian cache, also add `n_gamma`, which is set to 1 under static conditions. Newer users may prefer to rebuild the experimental system (`ex0`,`ex1`) and the Liouvillian from scratch, in order to automatically obtain the SLEEPY default settings and avoid mistakes."
]
},
{
"cell_type": "markdown",
"id": "c61f0496",
"metadata": {},
"source": [
"## $T_1$ anisotropy under MAS conditions"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "156e4213",
"metadata": {},
"outputs": [],
"source": [
"ex0.vr=10000\n",
"ex0.n_gamma=30\n",
"L.clear_cache()\n",
"\n",
"ex0.pwdavg=4\n",
"\n",
"seq=L.Sequence()\n",
"U=seq.U()**100\n",
"rho=sl.Rho('1Hz','15Nz')\n",
"\n",
"_=rho.DetProp(U,n=2000)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "05933d65",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_=rho.plot(axis='s')\n",
"_=ax.plot(ax.get_xlim(),np.ones(2)*ex0.Peq[0],color='black',linestyle=':')"
]
},
{
"cell_type": "markdown",
"id": "3c17a026",
"metadata": {},
"source": [
"The resulting curve appears much less multiexponential than obtained from static conditions, although indeed it is still multiexponential. \n",
"\n",
"We extract the distribution of relaxation rates for the MAS experiment below, and compare to the distribution under static conditions."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "bde27b0c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rho.reset()\n",
"R1_mas,A_mas=rho.extract_decay_rates(U,mode='wt_rates')\n",
"\n",
"_,ax=histogram(R1_static,A_static,bins=bins)\n",
"\n",
"_,ax=histogram(R1_mas,A_mas,bins=bins,ax=ax)\n",
"R1_avg_mas=(A_mas*R1_mas).sum()/A_mas.sum()\n",
"\n",
"ax.text(bins[1],4.5e-7,fr'$\\langle R_1\\rangle_{{static}}$: {R1_avg_static:.2f} $s^{{-1}}$')\n",
"ax.text(bins[1],6e-7,fr'$\\langle R_1\\rangle_{{MAS}}$: {R1_avg_mas:.2f} $s^{{-1}}$')\n",
"\n",
"ax.legend(('static','MAS'))\n",
"ax.set_xlabel(r'$R_1$ / s$^{-1}$')\n",
"_=ax.set_ylabel('Signal')"
]
},
{
"cell_type": "markdown",
"id": "79406519",
"metadata": {},
"source": [
"Indeed, the distribution of rate constants under MAS conditions is significantly narrower than under static conditions, although a distribution is still present. The reduction of the breadth of the distribution comes from the fact that as the sample is rotated, different relaxation rate constants are sampled throughout the rotor period, resulting in an average rate constant. However, the rotation does not bring the individual crystallites rate constant resulting from an average over *all* orientations.\n",
"\n",
"Although the width of the distribution changes, its average does not, where both calculations yield $\\langle R_1\\rangle$=0.66 s (the average $R_1$ must stay the same, the average $T_1$ may, on the other hand, change due to the different distribution width)."
]
},
{
"cell_type": "markdown",
"id": "0ce7974c",
"metadata": {},
"source": [
"## Methyl relaxation"
]
},
{
"cell_type": "markdown",
"id": "e17930f6",
"metadata": {},
"source": [
"In the next calculation, we investigate relaxation of a $^{13}$C nucleus and the surrounding $^1$H in a methyl group, due to the 3-site methyl hopping dynamics. Approximate methyl correlation time (30 ps) taken from HET-s.$^1$\n",
"\n",
"Methyl hopping represents a special case for exchange simulations, where when a methyl hop (120$^\\circ$ rotation) occurs, the new spin-system is identical to the old spin system, except for a change in the spin-indexing. Rather than introducing exchange, which increases the size of the Liouvillian, we may therefore induce exchange within the existing Liouvillian. This is done with the `L.add_SpinEx(...)` function, which requires as input the indices of the spins in exchange and the correlation time of the exchange process as arguments. The resulting Liouvillian is therefore $3\\times3=9$ times smaller than if exchange were added via multiple spin-systems in exchange.\n",
"\n",
"[1] K. Zumpfe, M. Berbon, B. Habenstein, A. Loquet, A.A. Smith. [*J. Am. Chem. Soc.*](https://doi.org/10.1021/jacs.3c12620), **2024**, 146, 8164-8178"
]
},
{
"cell_type": "markdown",
"id": "de660ec9",
"metadata": {},
"source": [
"### Build the system\n",
"We introduce a 4-spin, C-H-H-H system, with dipole couplings between all spins, and CSA on the $^{13}$C. Dipole couplings and euler angles are calculated from a tetrahedral geometry with the symmetry axis of the methyl group along the *z*-axis."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7172d621",
"metadata": {},
"outputs": [],
"source": [
"ex=sl.ExpSys(700,Nucs=['13C','1H','1H','1H'],LF=True,vr=0,pwdavg=5)\n",
"tetra=np.arccos(-1/3) #Tetrahedral angle (109.47 degrees)\n",
"dHC=0.109 #H-C bond length\n",
"dHH=2*dHC*np.sin(np.pi-tetra)*np.sin(np.pi/3) #H-H distance in tetrahedron\n",
"\n",
"deltaHC=sl.Tools.dipole_coupling(dHC,'1H','13C')\n",
"deltaHH=sl.Tools.dipole_coupling(dHH,'1H','1H')\n",
"ex.set_inter('CSA',i=0,delta=50,euler=[0,np.pi/2,0])\n",
"for k in range(1,4):\n",
" ex.set_inter('dipole',i0=0,i1=k,delta=deltaHC,euler=[0,np.pi-tetra,(k-1)*2*np.pi/3])\n",
" for j in range(k+1,4):\n",
" ex.set_inter('dipole',i0=k,i1=j,delta=deltaHH,euler=[0,np.pi/2,2*np.pi*(5/12+2/3*(k-3))])"
]
},
{
"cell_type": "markdown",
"id": "129cc9fd",
"metadata": {},
"source": [
"We add *spin-exchange*, rather than rebuilding the Liouville matrix three times. This approach is only valid if the exchange yields only swapping of positions of the spins.\n",
"\n",
"We also thermalize the Liouvillian, so that it recovers to thermal equilibrium, using `L.add_relax('DynamicThermal')`."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "b8e19456",
"metadata": {},
"outputs": [],
"source": [
"L=ex.Liouvillian()\n",
"L.add_SpinEx([1,2,3],tc=30e-12)\n",
"_=L.add_relax('DynamicThermal')"
]
},
{
"cell_type": "markdown",
"id": "8e52a504",
"metadata": {},
"source": [
"Below, we plot the resulting Liouvillian, and also the exchange matrix extracted from the Liouvillian. Note that for technical reasons, the spin-exchange matrix appears in the relaxation matrix (`Lrelax`), rather than in the exchange matrix (`Lex`).\n",
"\n",
"Vertical lines in the Liouvillian plot result from thermalization of the system. The exchange matrix (right), couples states where spins 1, 2, and 3 swap positions (either 1-2-3 goes to 2-3-1 or 3-1-2). For example, the state $|S_0^\\alpha S_1^+S_2^-S_3^\\beta\\rangle$ is coupled to the $|S_0^\\alpha S_1^-S_2^\\beta S_3^+\\rangle$ and $|S_0^\\alpha S_1^\\beta S_2^+S_3^-\\rangle$ states by the exchange matrix."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "7ae87a1a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig,ax=plt.subplots(1,2,figsize=[12,7])\n",
"L.plot(ax=ax[0],colorbar=False)\n",
"L.plot('Lrelax',mode='re',ax=ax[1],colorbar=False)\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "44b2845f",
"metadata": {},
"source": [
"Now we observe the relaxation behavior of the spins, assuming all spins were saturated at the beginning of the measurement."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "6a9bac62",
"metadata": {},
"outputs": [],
"source": [
"rho=sl.Rho('zero',['S0z','S1z','S2z','S3z'])\n",
"\n",
"seq=L.Sequence(Dt=.1) #100 ms time step\n",
"U=seq.U()\n",
"_=rho.DetProp(U,n=100)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "a2843728",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_=rho.plot(axis='s')"
]
},
{
"cell_type": "markdown",
"id": "cf849239",
"metadata": {},
"source": [
"We observe a complex relaxation behavior, resulting from coupling of the $^1$H and $^{13}$C relaxation. If we calculate the histogram for this relaxation process, we obtain both positive and negative amplitudes, resulting from the initial buildup of the $^{13}$C relaxation above its thermal equilibrium, followed by decay back to thermal equilibrium. Note that this prevents from easily calculating a meaningful averaged relaxation rate constant."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "30380236",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rho.reset()\n",
"R1,A=rho.extract_decay_rates(U,mode='wt_rates')\n",
"\n",
"_,ax=histogram(R1,A)\n",
"\n",
"ax.set_xlabel(r'$R_1$ / s$^{-1}$')\n",
"_=ax.set_ylabel('Signal')"
]
},
{
"cell_type": "markdown",
"id": "0edd63e0",
"metadata": {},
"source": [
"We can get a less complex behavior by saturating the $^1$H during the recovery. Note that we must use irradiation in the lab-frame irradiation, which is possible with the `sl.LFrf` class."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "91c97238",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"LF calculation: |██████████████████████████████| 100% complete\n",
"Completed\n"
]
}
],
"source": [
"rho=sl.Rho('zero',['S0z','S1z','S2z','S3z'])\n",
"\n",
"seq=L.Sequence(Dt=0.1).add_channel('1H',v1=25000)\n",
"U=sl.LFrf(seq).U()\n",
"\n",
"_=rho.DetProp(U,n=100)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "a9c3e839",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rho.reset()\n",
"R1,A=rho.extract_decay_rates(U,mode='wt_rates')\n",
"\n",
"_,ax=histogram(R1,-A)\n",
" \n",
"R1_avg=(A*R1).sum()/A.sum()\n",
" \n",
"_=ax.text(3,6e-6,fr'$\\langle R_1\\rangle$: {R1_avg:.2f} s$^{{-1}}$')"
]
},
{
"cell_type": "markdown",
"id": "27ecbc76",
"metadata": {},
"source": [
"The distribution is narrowed, and negative components are eliminated. We plot the buildup, and compare the resulting curve to a monoexpential curve with the averaged relaxation rate constant."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "194c9dfe",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=rho.plot(axis='s',det_num=0)\n",
"ax.plot(rho.t_axis,rho.I[0][-1].real*(1-np.exp(-rho.t_axis*R1_avg)),color='black',linestyle=':')\n",
"_=ax.legend((r'Simulated decay',fr'Monoexponential decay, $R_1$={R1_avg:.2f} s$^{{-1}}$'))"
]
},
{
"cell_type": "markdown",
"id": "f1b2c97e",
"metadata": {},
"source": [
"By saturating the $^1$H, we get a narrower distribution of correlation times in the $^{13}$C recovery. Deviation from the monoexponential curve is fairly limited."
]
}
],
"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
}