.. currentmodule:: mrsimulator.method.lib .. _mqvas_ref: Multi-quantum variable-angle spinning ------------------------------------- The following classes are used when simulating a multi-quantum variable-angle spinning spectrum which correlates the frequencies from the symmetric multiple-quantum transition to the central transition frequencies. The :math:p and :math:d pathways for the MQVAS methods are .. math:: p: &0 \rightarrow M \rightarrow -1 \\ d: &0 \rightarrow 0 \rightarrow 0 where :math:M is the multiple-quantum number. The value of :math:M depends on the spin quantum number, :math:I, and is listed in :numref:tb_mqvas. **Affine mapping** The resulting spectrum is sheared and scaled, such that the frequencies along the indirect dimension are given as .. math:: \langle \Omega\rangle_\text{MQ-VAS} = \frac{1}{1+\kappa}\Omega_{m, -m} + \frac{\kappa}{1+\kappa}\Omega_{1/2, -1/2}. Here, :math:\langle \Omega\rangle_\text{MQ-VAS} is the average frequency along the indirect dimension, :math:\Omega_{m, -m} and :math:\Omega_{1/2, -1/2} are the frequency contributions from the :math:|m\rangle \rightarrow |-m\rangle symmetric multiple-quantum transition and the central transition, respectively, and :math:\kappa is the shear factor. The values of the shear factor for various transitions are listed in :numref:tb_mqvas. .. cssclass:: table-bordered .. _tb_mqvas: .. list-table:: The table lists the multi-quantum transition associated with the spin :math:I, and the corresponding shear factor, :math:\kappa, used in affine mapping of the MQ-VAS methods. :widths: 20 40 20 20 :header-rows: 1 * - Spin - Symmetric multi-quantum transition - :math:M - :math:\kappa * - 3/2 - :math:\left(\frac{3}{2} \rightarrow -\frac{3}{2}\right) - :math:-3 - 21/27 * - 5/2 - :math:\left(-\frac{3}{2} \rightarrow \frac{3}{2}\right) - :math:3 - 114/72 * - 5/2 - :math:\left(\frac{5}{2} \rightarrow -\frac{5}{2}\right) - :math:-5 - 150/72 * - 7/2 - :math:\left(-\frac{3}{2} \rightarrow \frac{3}{2}\right) - :math:3 - 303/135 * - 7/2 - :math:\left(-\frac{5}{2} \rightarrow \frac{5}{2}\right) - :math:5 - 165/135 * - 7/2 - :math:\left(\frac{7}{2} \rightarrow -\frac{7}{2}\right) - :math:-7 - 483/135 * - 9/2 - :math:\left(-\frac{3}{2} \rightarrow \frac{3}{2}\right) - :math:3 - 546/216 * - 9/2 - :math:\left(-\frac{5}{2} \rightarrow \frac{5}{2}\right) - :math:5 - 570/216 * - 9/2 - :math:\left(-\frac{7}{2} \rightarrow \frac{7}{2}\right) - :math:5 - 84/216 .. _threeQ_vas_ref: Triple-quantum variable-angle spinning method ''''''''''''''''''''''''''''''''''''''''''''' .. autoclass:: ThreeQ_VAS :show-inheritance: :members: :inherited-members: BaseModel .. _fiveQ_vas_ref: Five-quantum variable-angle spinning method ''''''''''''''''''''''''''''''''''''''''''' .. autoclass:: FiveQ_VAS :show-inheritance: :members: :inherited-members: BaseModel .. _sevenQ_vas_ref: Seven-quantum variable-angle spinning method '''''''''''''''''''''''''''''''''''''''''''' .. autoclass:: SevenQ_VAS :show-inheritance: :members: :inherited-members: BaseModel