// -*- coding: utf-8 -*-
//
// frequency_tensor.h
//
// @copyright Deepansh J. Srivastava, 2019-2021.
// Created by Deepansh J. Srivastava, Apr 11, 2019.
// Contact email = srivastava.89@osu.edu
//
#include "frequency/spatial_orientation_tensor_components.h"
#include "frequency/spin_transition_functions.h"
// =====================================================================================
// First-order nuclear shielding frequency tensor components
// =====================================================================================
/**
* The frequency tensors (FT) components from the first-order perturbation expansion of
* the nuclear shielding Hamiltonian, in a given frame, @f$\mathcal{F}@f$, described by
* the Euler angles @f$\Theta = [\alpha, \beta, \gamma]@f$ are
* @f[
* {\Lambda'}_{0,0}^{(\sigma)} &= \mathcal{R'}_{0,0}^{(\sigma)}(\Theta)
* ~~ \mathbb{p}(i, j),~\text{and} \\
* {\Lambda'}_{2,n}^{(\sigma)} &= \mathcal{R'}_{2,n}^{(\sigma)}(\Theta)
* ~~ \mathbb{p}(i, j),
* @f]
* where @f$\mathcal{R'}_{0,0}^{(\sigma)}(\Theta)@f$ and
* @f$\mathcal{R'}_{2,n}^{(\sigma)}(\Theta)@f$ are the spatial orientation functions in
* frame @f$\mathcal{F}@f$, and @f$\mathbb{p}(i, j)@f$ is the spin transition function
* for @f$\left|i\right> \rightarrow \left|j\right>@f$ transition.
*
* @param Lambda_0 A pointer to an array of length 1, where the frequency component from
* @f${\Lambda'}_{0,0}^{(\sigma)}@f$ is stored.
* @param Lambda_2 A pointer to a complex array of length 5, where the frequency
* components from @f${\Lambda'}_{2,n}^{(\sigma)}@f$ is stored ordered as
* @f$\left[{\Lambda'}_{2,n}^{(\sigma)}\right]_{n=-2}^2@f$.
* @param omega_0_delta_iso_in_Hz The isotropic chemical shift in Hz
* (@f$\omega_0\delta_\text{iso}/2\pi@f$).
* @param omega_0_zeta_sigma_in_Hz The shielding anisotropy quantity in Hz
* (@f$\omega_0\zeta_\sigma/2\pi@f$) defined using Haeberlen convention.
* @param eta The shielding asymmetry, @f$\eta_\sigma \in [-1,1]@f$, defined using
* Haeberlen convention.
* @param Theta A pointer to an array of Euler angles, in radians, of length 3, ordered
* as @f$[\alpha, \beta, \gamma]@f$.
* @param mf The spin quantum number of the final energy state.
* @param mi The spin quantum number of the initial energy state.
*/
static inline void FCF_1st_order_nuclear_shielding_tensor_components(
double *restrict Lambda_0, void *restrict Lambda_2,
const double omega_0_delta_iso_in_Hz, const double omega_0_zeta_sigma_in_Hz,
const double eta, const double *Theta, const float mf, const float mi) {
// Spin transition function
double transition_fn = STF_p(mf, mi);
// Return if the transition is zero
if (transition_fn == 0.0) {
// zero the R0 and R2 components before populating with shielding components
*Lambda_0 = 0.0;
vm_double_zeros(10, (double *)Lambda_2);
return;
}
// Spatial orientation function
sSOT_1st_order_nuclear_shielding_tensor_components(
Lambda_0, Lambda_2, omega_0_delta_iso_in_Hz, omega_0_zeta_sigma_in_Hz, eta,
Theta);
// frequency component function from the zeroth-rank irreducible tensor.
*Lambda_0 *= transition_fn;
// frequency component function from the second-rank irreducible tensor.
cblas_dscal(10, transition_fn, (double *)Lambda_2, 1);
}
// =====================================================================================
// First-order electric quadrupolar frequency tensor components
// =====================================================================================
/**
* The frequency tensor (FT) components from the first-order perturbation expansion of
* electric quadrupole Hamiltonian, in a given frame, @f$\mathcal{F}@f$, described by
* the Euler angles @f$\Theta = [\alpha, \beta, \gamma]@f$ are
* @f[
* {\Lambda'}_{2,n}^{(q)} = \mathcal{R'}_{2,n}^{(q)}(\Theta) ~~ \mathbb{d}(i, j),
* @f]
* where @f$\mathcal{R}_{2,n}^{(q)}(\Theta)@f$ are the spatial orientation functions in
* frame @f$\mathcal{F}@f$, and @f$\mathbb{d}(i, j)@f$ is the spin transition function
* for @f$\left|i\right> \rightarrow \left|j\right>@f$ transition.
*
* @param Lambda_2 A pointer to a complex array of length 5, where the frequency
* components from @f${\Lambda'}_{2,n}^{(q)}@f$ is stored ordered as
* @f$\left[{\Lambda'}_{2,n}^{(q)}\right]_{n=-2}^2@f$.
* @param spin The spin quantum number, @f$I@f$.
* @param Cq_in_Hz The quadrupole coupling constant, @f$C_q@f$, in Hz.
* @param eta The quadrupole asymmetry parameter, @f$\eta_q \in [0, 1]@f$.
* @param Theta A pointer to an array of Euler angles, in radians, of length 3, ordered
* as @f$[\alpha, \beta, \gamma]@f$.
* @param mf The spin quantum number of the final energy state.
* @param mi The spin quantum number of the initial energy state.
*/
static inline void FCF_1st_order_electric_quadrupole_tensor_components(
void *restrict Lambda_2, const double spin, const double Cq_in_Hz, const double eta,
const double *Theta, const float mf, const float mi) {
// Spin transition function
double transition_fn = STF_d(mf, mi);
// Return if the transition is zero
if (transition_fn == 0.0) {
// zero the R2 components before populating with quad components
vm_double_zeros(10, (double *)Lambda_2);
return;
}
// Spatial orientation function
sSOT_1st_order_electric_quadrupole_tensor_components(Lambda_2, spin, Cq_in_Hz, eta,
Theta);
// frequency component function from the second-rank irreducible tensor.
cblas_dscal(10, transition_fn, (double *)Lambda_2, 1);
}
// =====================================================================================
// Second-order electric quadrupolar frequency tensor components
// =====================================================================================
/**
* The frequency tensor (FCF) components from the second-order perturbation expansion of
* electric quadrupole Hamiltonian, in a given frame, @f$\mathcal{F}@f$, described by
* the Euler angles @f$\Theta = [\alpha, \beta, \gamma]@f$, are
* @f[
* {\Lambda'}_{0,0}^{(qq)} &= \mathcal{R'}_{0,0}^{(qq)}(\Theta)
* ~~ \mathbb{c}_0(i, j), \\
* {\Lambda'}_{2,n}^{(qq)} &= \mathcal{R'}_{2,n}^{(qq)}(\Theta)
* ~~ \mathbb{c}_2(i, j),~\text{and} \\
* {\Lambda'}_{4,n}^{(qq)} &= \mathcal{R'}_{4,n}^{(qq)}(\Theta)
* ~~ \mathbb{c}_4(i, j),
* @f]
* where @f$\mathcal{R'}_{0,0}^{(qq)}(\Theta)@f$,
* @f$\mathcal{R'}_{2,n}^{(qq)}(\Theta)@f$, and, @f$\mathcal{R'}_{4,n}^{(qq)}(\Theta)@f$
* are the spatial orientation functions in frame @f$\mathcal{F}@f$, and
* @f$\mathbb{c}_k(i, j)@f$ are the composite spin transition functions for
* @f$\left|i\right> \rightarrow \left|j\right>@f$ transition.
*
* @param Lambda_0 A pointer to an array of length 1, where the frequency
* component from @f${\Lambda'}_{0,0}^{(qq)}@f$ is stored.
* @param Lambda_2 A pointer to a complex array of length 5, where the frequency
* components from @f$\Lambda_{2,n}^{(qq)}@f$ are stored ordered as
* @f$\left[{\Lambda'}_{2,n}^{(qq)}\right]_{n=-2}^2@f$.
* @param Lambda_4 A pointer to a complex array of length 9, where the frequency
* components from @f${\Lambda'}_{4,n}^{(qq)}@f$ are stored ordered as
* @f$\left[{\Lambda'}_{4,n}^{(qq)}\right]_{n=-4}^4@f$.
* @param spin The spin quantum number, @f$I@f$.
* @param Cq_in_Hz The quadrupole coupling constant, @f$C_q@f$, in Hz.
* @param eta The quadrupole asymmetry parameter, @f$\eta_q \in [0, 1]@f$.
* @param v0_in_Hz The Larmor frequency, @f$\nu_0@f$, in Hz.
* @param Theta A pointer to an array of Euler angles, in radians, of length 3,
* ordered as @f$[\alpha, \beta, \gamma]@f$.
* @param mf The spin quantum number of the final energy state.
* @param mi The spin quantum number of the initial energy state.
*/
static inline void FCF_2nd_order_electric_quadrupole_tensor_components(
double *restrict Lambda_0, void *restrict Lambda_2, void *restrict Lambda_4,
const double spin, const double v0_in_Hz, const double Cq_in_Hz, const double eta,
const double *Theta, const float mf, const float mi) {
// Composite spin transition functions
double cl_value[3];
STF_cL(cl_value, mf, mi, spin);
// Spatial orientation function
sSOT_2nd_order_electric_quadrupole_tensor_components(
Lambda_0, Lambda_2, Lambda_4, spin, v0_in_Hz, Cq_in_Hz, eta, Theta);
// frequency component function from the zeroth-rank irreducible tensor.
*Lambda_0 *= cl_value[0];
// frequency component function from the second-rank irreducible tensor.
cblas_dscal(10, cl_value[1], (double *)Lambda_2, 1);
// frequency component function from the fourth-rank irreducible tensor.
cblas_dscal(18, cl_value[2], (double *)Lambda_4, 1);
}
// =====================================================================================
// First-order J-coupling frequency tensor components (weakly coupling limit)
// =====================================================================================
/**
* The frequency tensor (FT) components from the first-order perturbation expansion of
* the J-coupling Hamiltonian (weak coupling limit), in a given frame,
* @f$\mathcal{F}@f$, described by the Euler angles @f$\Theta = [\alpha, \beta,
* \gamma]@f$ are
* @f[
* {\Lambda'}_{0,0}^{(J)} &= \mathcal{R'}_{0,0}^{(J)}(\Theta)
* ~~ \mathbb{d}_{IS}(m_{i_I}, m_{i_S}, m_{f_I}, m_{f_S}),
* ~\text{and} \\
* {\Lambda'}_{2,n}^{(J)} &= \mathcal{R'}_{2,n}^{(J)}(\Theta)
* ~~ \mathbb{d}_{IS}(m_{i_I}, m_{i_S}, m_{f_I}, m_{f_S}),
* @f]
* where @f$\mathcal{R'}_{0,0}^{(J)}(\Theta)@f$ and
* @f$\mathcal{R'}_{2,n}^{(J)}(\Theta)@f$ are the spatial orientation functions in frame
* @f$\mathcal{F}@f$, and @f$\mathbb{d}_{IS}(m_{i_I}, m_{i_S}, m_{f_I}, m_{f_S})@f$ is
* the spin transition function for @f$\left|m_{i_I}, m_{i_S}\right> \rightarrow
* \left|m_{f_I}, m_{f_S}\right>@f$ transition.
*
* @param Lambda_0 A pointer to an array of length 1, where the frequency
* component from @f${\Lambda'}_{0,0}^{(J)}@f$ is stored.
* @param Lambda_2 A pointer to a complex array of length 5, where the frequency
* components from @f${\Lambda'}_{2,n}^{(J)}@f$ is stored ordered as
* @f$\left[{\Lambda'}_{2,n}^{(J)}\right]_{n=-2}^2@f$.
* @param J_iso_in_Hz The isotropic J-coupling, @f$J_\text{iso}@f$, in Hz.
* @param J_aniso_in_Hz The J-coupling anisotropy, @f$\zeta_J@f$, in Hz and
* defined using Haeberlen convention.
* @param J_eta The J-coupling anisotropy asymmetry parameter, @f$\eta_J \in
* [-1,1]@f$, defined using Haeberlen convention.
* @param Theta A pointer to an array of Euler angles of length 3 ordered as
* @f$[\alpha, \beta, \gamma]@f$.
* @param mIf The spin quantum number of the final energy state of site @f$I@f$.
* @param mIi The spin quantum number of the initial energy state of site
* @f$I@f$.
* @param mSf The spin quantum number of the final energy state of site @f$S@f$.
* @param mSi The spin quantum number of the initial energy state of site
* @f$S@f$.
*/
static inline void FCF_1st_order_weak_J_coupling_tensor_components(
double *restrict Lambda_0, void *restrict Lambda_2, const double J_iso_in_Hz,
const double J_aniso_in_Hz, const double J_eta, const double *Theta,
const float mIf, const float mIi, const float mSf, const float mSi) {
// Spin transition function
double transition_fn = STF_dIS(mIf, mIi, mSf, mSi);
// Return if the transition is zero
if (transition_fn == 0.0) {
// zero the R0 and R2 components before populating with shielding components
*Lambda_0 = 0.0;
vm_double_zeros(10, (double *)Lambda_2);
return;
}
// Spatial orientation function
sSOT_1st_order_weakly_coupled_J_tensor_components(Lambda_0, Lambda_2, J_iso_in_Hz,
J_aniso_in_Hz, J_eta, Theta);
// frequency component function from the zeroth-rank irreducible tensor.
*Lambda_0 *= transition_fn;
// frequency component function from the second-rank irreducible tensor.
cblas_dscal(10, transition_fn, (double *)Lambda_2, 1);
}
// =====================================================================================
// First-order Weakly coupled Magnetic Dipole frequency in the PAS.
// =====================================================================================
/**
* The frequency tensor (FT) components from the first-order perturbation expansion of
* the direct dipolar coupling Hamiltonian (weak coupling limit), in a given frame,
* @f$\mathcal{F}@f$, described by the Euler angles @f$\Theta = [\alpha, \beta,
* \gamma]@f$ are
* @f[
* {\Lambda'}_{2,n}^{(d)} = \mathcal{R'}_{2,n}^{(d)}(\Theta)
* ~~ \mathbb{d}_{IS}(m_{i_I}, m_{i_S}, m_{f_I}, m_{f_S}),
* @f]
* where @f$\mathcal{R'}_{2,n}^{(d)}(\Theta)@f$ are the spatial orientation functions in
* frame @f$\mathcal{F}@f$, and @f$\mathbb{d}_{IS}(m_{i_I}, m_{i_S}, m_{f_I},
* m_{f_S})@f$ is the spin transition function for @f$\left|m_{i_I}, m_{i_S}\right>
* \rightarrow \left|m_{f_I}, m_{f_S}\right>@f$ transition.
*
* @param Lambda_2 A pointer to a complex array of length 5, where the frequency
* components from @f${\Lambda'}_{2,n}^{(d)}@f$ is stored ordered as
* @f$\left[{\Lambda'}_{2,n}^{(d)}\right]_{n=-2}^2@f$.
* @param D_in_Hz The dipolar coupling, @f$D@f$, in Hz.
* @param Theta A pointer to an array of Euler angles of length 3 ordered as
* @f$[\alpha, \beta, \gamma]@f$.
* @param mIf The spin quantum number of the final energy state of site @f$I@f$.
* @param mIi The spin quantum number of the initial energy state of site @f$I@f$.
* @param mSf The spin quantum number of the final energy state of site @f$S@f$.
* @param mSi The spin quantum number of the initial energy state of site @f$S@f$.
*/
static inline void FCF_1st_order_weak_dipolar_coupling_tensor_components(
void *restrict Lambda_2, const double D_in_Hz, const double *Theta, const float mIf,
const float mIi, const float mSf, const float mSi) {
// Spin transition function
double transition_fn = STF_dIS(mIf, mIi, mSf, mSi);
// Return if the transition is zero
if (transition_fn == 0.0) {
// zero the R0 and R2 components before populating with shielding components
vm_double_zeros(10, (double *)Lambda_2);
return;
}
// Spatial orientation function
sSOT_1st_order_weakly_coupled_dipolar_tensor_components(Lambda_2, D_in_Hz, Theta);
// frequency component function from the second-rank irreducible tensor.
cblas_dscal(10, transition_fn, (double *)Lambda_2, 1);
}
