{
"cells": [
{
"cell_type": "markdown",
"id": "85b01b75",
"metadata": {},
"source": [
"# Experimental Settings and Spin-System Definition"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "5f38a3fc",
"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": "0d830fa5",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "8a7f1ffd",
"metadata": {},
"source": [
"## Defining nuclei and experimental conditions"
]
},
{
"cell_type": "markdown",
"id": "4b9838e2",
"metadata": {},
"source": [
"The experimental system defines the magnetic field, the nuclei in the spin-system, the spinning rate, the temperature, the rotor angle, the powder average, and the number of gamma angles calculated during one rotor period. Except for the field and nuclei, these all have default values and only need to be provided if other values are needed.\n",
"\n",
"- `v0H`: The magnetic field strength, given as the $^1$H frequency in MHz (required, unless `B0` provided)\n",
"- `B0`: The magnetic field strength in Tesla (required, unless `v0H` provided)\n",
"- `Nucs`: List of nuclei, with mass number followed by atomic symbol ('1H','13C','2H', etc.). Electrons may also be included via 'e-'. To obtain a high-spin electron, start with e and follow with the spin. For example, specifying 'e1' would give an electron with spin 1, and 'e3/2' or 'e1.5' would produce an electron with spin-3/2.\n",
"- `T_K`: Temperature in Kelvin. Only used if relaxation to thermal equilibrium is used (thermalization), or the density matrix (rho) is initialized with the \"thermal\" option. Default is 298 K.\n",
"- `vr`: Spinning frequency in Hz (only used if anisotropic interactions provided). Default is 10000\n",
"- `rotor_angle`: Rotor angle, in radians. Default is the magic angle\n",
"- `n_gamma` Number of gamma angles calculated per rotor period. For string-specified powder averages (i.e. not JCP59 or grid), this is also the number of gamma angles in the powder average. Default is 100\n",
"- `pwdavg`: Type of powder average. Type sl.PowderAvg.list_powder_types to see options (Most powder averages are taken from [SIMPSON](https://inano.au.dk/about/research-centers-and-projects/nmr/software/simpson)). If an integer is provided, then this yields the [JCP59](https://doi.org/10.1063/1.1680590) powder average, with higher integers yielding more angles. Default is 3 (JCP59 with 99 angles). Note that if 'alpha0beta0','alpha0beta90', or 'alpha0beta45' are used, then the powder average will automatically switch to gamma_encoded mode, so that only one angle is simulated (otherwise, gamma_encoded defaults to False). This behavior can be overridden by the user simply by setting `gamma_encoded=True` or `gamma_encoded=False`. \n",
"- `LF`: Specifiy whether each spin should be simulated in the lab frame. Can be provided as a single boolean, e.g. False sets all spins in the rotating frame, or as a list the same length as Nucs, which puts some spins in the lab frame and some in the rotating frame (useful, e.g. for DNP experiments such as solid-effect/cross-effect where the electrons should be in the rotating frame, but the nucleus in the lab frame)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "daccb4bf",
"metadata": {},
"outputs": [],
"source": [
"ex=sl.ExpSys(v0H=600,Nucs=['1H','13C'],vr=10000,T_K=298,\n",
" rotor_angle=np.arccos(np.sqrt(1/3)),n_gamma=100,\n",
" pwdavg=3,LF=[False,False])"
]
},
{
"cell_type": "markdown",
"id": "5b5e83fb",
"metadata": {},
"source": [
"Typing `ex` at the command line will return a description of the experimental setup."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "3f397200",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-spin system (1H,13C)\n",
"B0 = 14.092 T (600.000 MHz 1H frequency)\n",
"rotor angle = 54.736 degrees\n",
"rotor frequency = 10.0 kHz\n",
"Temperature = 298 K\n",
"Powder Average: JCP59 with 99 angles\n",
"Interactions:\n",
"\n",
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ex"
]
},
{
"cell_type": "markdown",
"id": "434e1e08",
"metadata": {},
"source": [
"Note that we have used the default values, so the same system may be obtained while omitting all the defaults:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b0c5089e",
"metadata": {},
"outputs": [],
"source": [
"ex=sl.ExpSys(v0H=600,Nucs=['1H','13C'])"
]
},
{
"cell_type": "markdown",
"id": "81e54f71",
"metadata": {},
"source": [
"## Defining Interactions\n",
"Once the experimental settings and spin-system is set, we may add interactions. This is achieved by running\n",
"```\n",
"ex.set_inter(...)\n",
"```\n",
"For every interaction, we have to specify the spins involved. For an N-spin system, this is specified with an index (spin-field) or indices (spin-spin) referring to the spin at the corresponding position in Nucs. Note we use python convention of indexing from 0 to N-1. For spin-field interactions, we specify \"i\", and for spin-spin interactions, we specify \"i0\" and \"i1\". The available interactions are:\n",
"\n",
"- dipole: Specify `delta` (the full anisotropy in Hz, which is 2x the definition used by SIMPSON). Optionally specify an asymmetry, `eta` (unitless) and the euler angles, `euler` as a 3-element (alpha,beta,gamma) list in radians.\n",
"- J: Specify `J` in Hz.\n",
"- CS: Isotropic chemical shift, specify in ppm (use `ppm=...`) or in Hz (use `Hz=...`). \n",
"- CSA: Chemical shift anisotropy. Specify delta in ppm (`delta=...`) or in Hz (`deltaHz=...`). eta and the euler angles are optional.\n",
"- hyperfine: Specify `Axx`, `Ayy`, and `Azz`. If all entries are equal, will be treated as an isotropic interaction. `euler` may be optionally provided.\n",
"- quadrupole: Specify `delta` in Hz. Note that this is not the peak-to-peak splitting, but rather the tensor anisotropy (as is always the case in SLEEPY). `DelPP` can be alternatively be provided to directly specify the peak-to-peak splitting (integer spin: distance between the inner two peaks, half-integer spin: distance between the central peak and the first peak). Optionally specify `eta` and `euler`.\n",
"- g: Electron g-tensor. Specify `gxx`, `gyy`, and `gzz`, and optionally `euler`.\n",
"- ZeroField: Electron zero-field. Specify `D` and optionally `E` (both in Hz), and optionally `euler`.\n",
"\n",
"Note that `euler` may be replaced with `euler_d` to input the angles in degrees instead of radians."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "37a3f08b",
"metadata": {},
"outputs": [],
"source": [
"ex=sl.ExpSys(v0H=600,Nucs=['1H','13C'],pwdavg='rep678')\n",
"delta=sl.Tools.dipole_coupling(.109,'1H','13C') #Calculate H-C dipole for 1.05 Angstrom distance\n",
"ex.set_inter('dipole',i0=0,i1=1,delta=delta,euler=[0,np.pi/4,0]) #H-C dipole coupling\n",
"ex.set_inter('CSA',i=1,delta=100,eta=1) #13C CSA\n",
"_=ex.set_inter('CS',i=0,ppm=10) #1H isotropic chemical shift"
]
},
{
"cell_type": "markdown",
"id": "4d208179",
"metadata": {},
"source": [
"We can view the shape of a tensor with the `ex.plot_inter()` function. Note that this results in a scatter plot, where the number of points is determined by the powder average. What is shown is the magnitude (as distance from the origin) and phase (as color). For the $n=0$ component, only real values are possible, so we only see positive (red) and negative (blue)."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "1d2963d6",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig=plt.figure(figsize=[15,8])\n",
"ax=[fig.add_subplot(1,5,k+1,projection='3d') for k in range(5)]\n",
"for k,a in enumerate(ax):ex.plot_inter(0,n=k-2,ax=a)"
]
},
{
"cell_type": "markdown",
"id": "1a143b95",
"metadata": {},
"source": [
"Note, if we try to plot an isotropic term, we just obtain a sphere."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "148e2ce8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_=ex.plot_inter(2,n=0)"
]
},
{
"cell_type": "markdown",
"id": "4efffa81",
"metadata": {},
"source": [
"When setting an interaction, ex returns itself. This lets us string together multiple commands, for example, the following line will achieve the same interactions as above. Note that if an interaction is defined twice for the same spin or spins, the former definition will be overwritten."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "b87474a6",
"metadata": {},
"outputs": [],
"source": [
"_=ex.set_inter('dipole',i0=0,i1=1,delta=delta,euler=[0,np.pi/4,0]).set_inter('CSA',i=1,delta=100,eta=1).\\\n",
" set_inter('CS',i=0,ppm=10)"
]
},
{
"cell_type": "markdown",
"id": "5c470cf4",
"metadata": {},
"source": [
"If we type 'ex' at the command line, we will obtain a description of the experimental system"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "7a09f56f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-spin system (1H,13C)\n",
"B0 = 14.092 T (600.000 MHz 1H frequency)\n",
"rotor angle = 54.736 degrees\n",
"rotor frequency = 10.0 kHz\n",
"Temperature = 298 K\n",
"Powder Average: rep678 with 67800 angles\n",
"Interactions:\n",
"\tdipole between spins 0,1 with arguments:\n",
"\t\t(delta=46656.37,euler=[0.00,45.00,0.00])\n",
"\tCSA on spin 1 with arguments: (delta=100.00,eta=1.00)\n",
"\tCS on spin 0 with arguments: (ppm=10.00)\n",
"\n",
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ex"
]
},
{
"cell_type": "markdown",
"id": "4d53cec5",
"metadata": {},
"source": [
"## Functions and contents of ExpSys"
]
},
{
"cell_type": "markdown",
"id": "da751d78",
"metadata": {},
"source": [
"The ExpSys object, `ex`, contains various useful pieces of information (both to the user, and the program). For example:\n",
"\n",
"- `ex.B0`: Magnetic field\n",
"- `ex.Nucs`: Nuclei/electrons in spin-system\n",
"- `ex.S`: Spins of nuclei in spin-system\n",
"- `ex.Peq`: Thermal polarization of spins in spin-system (based on Larmor frequency only)\n",
"- `ex.gamma`: Gyromagnetic ratio of spins in spin-system\n",
"- `ex.v0`: Larmor frequency of spins in spin-system\n",
"- `ex.vr`: Rotor frequency\n",
"- `ex.taur`: Rotor period\n",
"- `ex.rotor_angle`: Rotor angle\n",
"- `ex.inter`: List of all interactions entered\n",
"\n",
"It also contains a number of functions\n",
"\n",
"- `ex.copy`: Returns a copy of ex (useful for building exchange calculations, where interactions may change due to exchange, but things like the field, Nuclei, etc. should remain fixed)\n",
"- `ex.Hamiltonian`: Returns a Hamiltonian object for the spin-system\n",
"- `ex.Liouvillian`: Returns a Liouvillian object for the spin-system\n",
"\n",
"Finally, it contains important objects\n",
"\n",
"- `ex.pwdavg`: Powder average object for the spin-system. Note, if all interactions are isotropic, when a Liouvillian or Hamiltonian is created, the powder average will be replaced with a 1-element powder-average\n",
"- `ex.Op`: Spin-operator object, which contains the spin-operators for the spin-system"
]
},
{
"cell_type": "markdown",
"id": "e3548d2d",
"metadata": {},
"source": [
"## The powder average"
]
},
{
"cell_type": "markdown",
"id": "669e8cfa",
"metadata": {},
"source": [
"The powder average can be changed, by simply replacing the powder average object (can be generated from `sl.PowderAvg`). One may also simply provide the string for the desired powder average, or the quality factor for the 'JCP59' powder average, although this does not allow one to provide further arguments. Note that this needs to be done before calculating propagators.\n",
"```\n",
"ex.pwdavg=sl.PowderAvg('rep144',gamma_encoded=True)\n",
"ex.pwdavg='rep144' #We cannot specifying gamma encoding this way\n",
"```\n",
"Both would set the powder average to a repulsion powder average with 144 alpha and beta angles. Setting gamma_encode to True will skip the average over gamma_angles, which speeds up some calculations considerably, but will return incorrect results for pulse sequences that are not gamma encoded (e.g. REDOR).\n",
"\n",
"One can also specify simply\n",
"```\n",
"ex.pwdavg='rep144'\n",
"```\n",
"although in this approach, it is not possible to specify gamma encoding (will yield `gamma_encoded=False`).\n",
"\n",
"The powder average object contains useful information about how to execute the powder average. For example:\n",
"- `pwdavg.PwdType` : Type of powder average used\n",
"- `pwdavg.N` : Number of angles in the powder average\n",
"- `pwdavg.alpha` : alpha angles\n",
"- `pwdavg.beta` : beta angles\n",
"- `pwdavg.gamma` : gamma angles\n",
"- `pwdavg.weight` : weight to use when summing the powder average\n",
"- `pwdavg.gamma_encoded` : Boolean, determines whether averaging over gamma is skipped (cannot be set except at initialization, or when running pwdavg.set_pwd_type)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "2e9cb00e",
"metadata": {},
"outputs": [],
"source": [
"_=ex.pwdavg.set_powder_type('rep256')"
]
},
{
"cell_type": "markdown",
"id": "71bc4d26",
"metadata": {},
"source": [
"Typing `ex.pwdavg` at the command line will provide basic information about the powder average"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "f3d8be00",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Powder Average\n",
"Type:\trep256 with 25600 angles\n",
"\n",
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ex.pwdavg"
]
},
{
"cell_type": "markdown",
"id": "58cb3d13",
"metadata": {},
"source": [
"The powder average can also be plotted. By default, this plots the $\\alpha$ and $\\beta$ angles, but can be switched to $\\beta$ and $\\gamma$ angles by setting beta_gamma to True"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "d9f8f9e1",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_=ex.pwdavg.plot()"
]
},
{
"cell_type": "markdown",
"id": "1739ec78",
"metadata": {},
"source": [
"## The Spin Operators"
]
},
{
"cell_type": "markdown",
"id": "8b19e109",
"metadata": {},
"source": [
"The spin operators are used to build the Hamiltonian for a given spin system. They are found in `ex.Op`, although one can also create a spin-operators from `sl.SpinOp(...)`, with a list of spins as input. `ex.Op` contains basic information about the operators:\n",
"\n",
"- `ex.Op.N`: Number of spins\n",
"- `ex.Op.S`: Spin number\n",
"- `ex.Op.Mult`: Multiplicity of each spin (2*S+1)\n",
"- `ex.Hlabels`/`ex.Llabels`: $\\LaTeX$ labels for each spin state in Hilbert and Liouville space\n",
"- `ex.state_index`: List of states of each spin in the density matrix (used for spin-exchange)\n",
"\n",
"To access the spin matrices themselves, we first provide an index to go the desired spin, and then choose the spin matrix that we want:\n",
"\n",
"Possible matrices: `x`, `y`, `z`, `alpha`, `beta`, `m` ($I^-$), `p` ($I^+$), `eye` (identity matrix)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "d1607173",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[0. +0.j, 0. +0.j, 0.5+0.j, 0. +0.j],\n",
" [0. +0.j, 0. +0.j, 0. +0.j, 0.5+0.j],\n",
" [0.5+0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [0. +0.j, 0.5+0.j, 0. +0.j, 0. +0.j]])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ex.Op[0].x #Example: x operator for the 0th spin"
]
},
{
"cell_type": "markdown",
"id": "2a576770",
"metadata": {},
"source": [
"We also have access to the coherence order of each element of the matrix (`ex.Op[0].coherence_order`).\n",
"\n",
"Finally, we have access to the matrices for spherical tensors, via e.g. `ex.Op[0].T`. T can be be indexed to give the rank 0, rank 1, and rank 2 (if spin-1 or higher) operators. The resulting list contains the operators running from the lowest to highest index.\n",
"\n",
"So, `ex.Op[0].T[1][0]` returns $T_{1,-1}^{(0)}$, that is the rank $m=-1$ component of the rank-1 tensor for spin 0."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "450c79e7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0. +0.j, -0. +0.j, -0.70710678+0.j,\n",
" -0. +0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j,\n",
" -0.70710678+0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j,\n",
" -0. +0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j,\n",
" -0. +0.j]])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ex.Op[0].T[1][0] #eg m=-1 component of the rank-1 tensor for spin 0"
]
},
{
"cell_type": "markdown",
"id": "2d63c2a1",
"metadata": {},
"source": [
"However, what we usually need for building Hamiltonians is the rank-2 spherical tensors. For 1-spin tensors, these are obtained first by changing the mode of the spherical tensor to 'B0_LF', for example:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "56f96090",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[0. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [0. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [0.5+0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [0. +0.j, 0.5+0.j, 0. +0.j, 0. +0.j]]), array([[ 0.40824829+0.j, 0. +0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0.40824829+0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, -0.40824829+0.j,\n",
" -0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, -0. +0.j,\n",
" -0.40824829+0.j]]), array([[-0. +0.j, -0. +0.j, -0.5+0.j, -0. +0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j, -0.5+0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j, -0. +0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j, -0. +0.j]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]])]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ex.Op[0].T.set_mode('B0_LF')\n",
"ex.Op[0].T[2]"
]
},
{
"cell_type": "markdown",
"id": "cf973218",
"metadata": {},
"source": [
"For spin-spin interactions, we need to multiply the spin-operators together and also define whether both spins are in the rotating frame or lab frame. For example, if the first spin is in the lab frame and second in the rotating frame, we use:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "00f55232",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]),\n",
" array([[-0. +0.j, -0. +0.j, -0.25+0.j, -0. +0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j, 0.25-0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j, -0. +0.j],\n",
" [-0. +0.j, -0. +0.j, -0. +0.j, -0. +0.j]]),\n",
" array([[ 0.20412415+0.j, 0. +0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, -0.20412415+0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, -0.20412415+0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, 0. +0.j,\n",
" 0.20412415+0.j]]),\n",
" array([[ 0. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [ 0.25+0.j, 0. +0.j, 0. +0.j, 0. +0.j],\n",
" [ 0. +0.j, -0.25+0.j, 0. +0.j, 0. +0.j]]),\n",
" array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]])]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T2spin=ex.Op[0].T*ex.Op[1].T\n",
"T2spin.set_mode('LF_RF')\n",
"T2spin[2]"
]
},
{
"cell_type": "markdown",
"id": "e2180d84",
"metadata": {},
"source": [
"If both spins are in the rotating frame, then we need to define if this is a homonuclear ('homo') or heteronuclear ('het') interaction. If we compare the results, we see that off-diagonal terms emerge for the homonuclear interaction, but not for the heternuclear interaction."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "88a2e1b9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[ 0.20412415+0.j, 0. +0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, -0.20412415+0.j, -0.20412415+0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, -0.20412415+0.j, -0.20412415+0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, 0. +0.j,\n",
" 0.20412415+0.j]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]])]"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T2spin.set_mode('homo')\n",
"T2spin[2]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "a950f28c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[ 0.20412415+0.j, 0. +0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, -0.20412415+0.j, 0. +0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, -0.20412415+0.j,\n",
" 0. +0.j],\n",
" [ 0. +0.j, 0. +0.j, 0. +0.j,\n",
" 0.20412415+0.j]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]), array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]])]"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T2spin.set_mode('het')\n",
"T2spin[2]"
]
},
{
"cell_type": "markdown",
"id": "feebbd2e",
"metadata": {},
"source": [
"SLEEPY uses the full set of rank-2 spherical tensors (`T`) when operating in the lab frame, but just the rank-2, $m=0$ component in the rotating frame (rotating frame Hamiltonians are usually defined with the cartesian spin-operators in SLEEPY, although one could use the spherical tensors)."
]
}
],
"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",
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