Contains functions for calculations of Moessbauer spectra parameters. More...

Data Types
type	moessbauer_d_density

Functions/Subroutines
subroutine	moessbauer_extract_data (system, m_atom, l_dens, s_dens, p_dens, atoms_array, unit_cell)
	Given the system node, the metal atom and the ligand density matrix, optionally returns the following data: More...

real function	moessbauer_is (s_dens)
	Calculate Moessbauer isomer shift The unversal formula for IS reads as follows. More...

real function	moessbauer_qs_from_efg (efg)
	Calculates Moessbauer quadrupole splitting. More...

real function, dimension(6)	moessbauer_p_atom_efg (p_dens)
	Calculates the p-electron contribution to the EFG tensor for the given atom based on the provided p density matrix. Returns the EFG tensor values in the order xx, yy, zz, xy, xz, yz. More...

real function, dimension(6)	moessbauer_d_atom_efg (d_dens)
	Calculates the d-electron contribution to the EFG tensor for the given atom based on the provided d density matrix. Returns the EFG tensor values in the order xx, yy, zz, xy, xz, yz. More...

real function, dimension(6)	moessbauer_ligand_efg (unit_cell, atom, atoms_array)
	Calculates the ligand contribution to the EFG tensor for the given atom based on the provided effective charges. Returns the EFG tensor values in the order xx, yy, zz, xy, xz, yz. More...

real function, dimension(6)	moessbauer_quadrupole_potential (r)
	Returns the values \( V_{ab} = \frac{3 r_a r_b - δ_{ab} * r^2}{r^5} \) as an array, in the order xx, yy, zz, xy, xz, yz. More...

real function, dimension(:), allocatable	moessbauer_qs_temperature_dependence (m_atom, p_dens, d_energies, d_densities, atoms_array, unit_cell, t_start, t_end, t_step)
	Returns an array values of quadrupole splitting on the given atom in the given temperature range. More...

Variables
real, parameter, private	sf_sp = 0.68

real, parameter, private	sf_d = 0.68

real, parameter, private	sf_g = 10.1

real, parameter, private	fe57m_gamma = 14413 / AtomicUnitOfEnergy2EV

real, parameter, private	fe57nuc_delr_over_r = -1.8e-3

real, parameter, private	fe57nuc_r = 3.75e-5 / Bohr2Angstrom

real, parameter, private	fe57nuc_q = 0.160

real, parameter, private	fe_z = 26

real, parameter, private	fe_4s_0 = 6.2501

real, parameter, private	fe_rm3_3d = 4.978801 / Bohr2Angstrom**3

real, parameter, private	fe_rm3_4p = 1.697 / Bohr2Angstrom**3

real, parameter, private	fe_is_coef = 0.8 * Pi * (1e3speedOfLightmpsec / Fe57m_gamma) Fe_Z * (Fe57nuc_R*2) Fe57nuc_delR_over_R(Fe_4s_0*2)

real, parameter, private	fe_qs_coef = 0.5 * (1e3speedOfLightmpsec / Fe57m_gamma) Bohr2Angstrom * (1e-8 * Fe57nuc_Q)

Detailed Description

Contains functions for calculations of Moessbauer spectra parameters.

Warning: Currently works only if the metal atom supplied is Fe

Author: Dmitrii Raenko

Date: Mar 2023

Todo:: Add printing of EFG tensors from different sources.

Function/Subroutine Documentation

◆ moessbauer_d_atom_efg()

real function, dimension(6) moessbauer::moessbauer_d_atom_efg ( type(oneelectronicelement), dimension(5,5), intent(in) d_dens )

Calculates the d-electron contribution to the EFG tensor for the given atom based on the provided d density matrix. Returns the EFG tensor values in the order xx, yy, zz, xy, xz, yz.

◆ moessbauer_extract_data()

subroutine moessbauer::moessbauer_extract_data	(	type(node), intent(inout)	system,
		type(particle), intent(in), pointer	m_atom,
		type(oneelectronicelement), dimension(:,:), intent(in), allocatable	l_dens,
		real, intent(out), optional	s_dens,
		type(oneelectronicelement), dimension(3,3), intent(out), optional	p_dens,
		type(particle_ptr), dimension(:), intent(out), optional, allocatable	atoms_array,
		type(unitcell), intent(out), optional, pointer	unit_cell
	)

Given the system node, the metal atom and the ligand density matrix, optionally returns the following data:

Parameters

[out,optional]	s_dens Density matrix element on the s-orbital of the given atom
[out,optional]	p_dens The density matrix on the p-orbitals of the given atom
[out,optional]	atoms_array The array of all the atoms in the system
[out,optional]	unit_cell pointer to the unit cell of the system

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◆ moessbauer_is()

real function moessbauer::moessbauer_is ( real, intent(in) s_dens )

Calculate Moessbauer isomer shift The unversal formula for IS reads as follows.

\[ IS = \frac{4\pi}{5} Z e^2 R^2 \frac{\Delta R}{R} \left| \Psi (0) \right|^2 \]

Since \( \left| \Psi (0) \right|^2 = ( \frac{1}{2 \sqrt{\pi}} R(0) )^2 * P_{4s} \) , the \( 4\pi \) cancels, and we are left only with 1/5 in the following formula:

\[ IS (\frac{\mathrm{mm}}{\mathrm{sec}}) = \frac{1}{5} \frac{c}{E_{\gamma}} Z e^2 R^2 \frac{\Delta R}{R} \left| \Psi (0) \right|^2 \]

Furthermore, we calculate the IS with respect to the free Fe atom \( 4s^2 3d^6 \), so the 4s density is shifted by -2.0

◆ moessbauer_ligand_efg()

real function, dimension(6) moessbauer::moessbauer_ligand_efg	(	type(unitcell), intent(in), pointer	unit_cell,
		type(particle), intent(in), pointer	atom,
		type(particle_ptr), dimension(:), intent(in), allocatable	atoms_array
	)

Calculates the ligand contribution to the EFG tensor for the given atom based on the provided effective charges. Returns the EFG tensor values in the order xx, yy, zz, xy, xz, yz.

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◆ moessbauer_p_atom_efg()

real function, dimension(6) moessbauer::moessbauer_p_atom_efg ( type(oneelectronicelement), dimension(3,3), intent(in) p_dens )

Calculates the p-electron contribution to the EFG tensor for the given atom based on the provided p density matrix. Returns the EFG tensor values in the order xx, yy, zz, xy, xz, yz.

◆ moessbauer_qs_from_efg()

real function moessbauer::moessbauer_qs_from_efg ( real, dimension(6), intent(in) efg )

Calculates Moessbauer quadrupole splitting.

Parameters

[in]

EFG

Electric field gradient tensor, in the form of an array corresponding to components xx, yy, zz, xy, xz, yz The formula for QS reads as follows:

\[ QS (\frac{\mathrm{mm}}{\mathrm{sec}}) = \frac{c}{E_{\gamma}} \frac{eQV_{zz}}{2} \sqrt{1+\frac{\eta^2}{3}} \]

where \( \eta = \frac{|V_{xx}| - |V_{yy}|}{V_{zz}} \) and \( |V_{yy}| \leq |V_{xx}| \leq |V_{zz}| \) are are the main components of the EFG tensor

◆ moessbauer_qs_temperature_dependence()

real function, dimension(:), allocatable moessbauer::moessbauer_qs_temperature_dependence	(	type(particle), intent(in), pointer	m_atom,
		type(oneelectronicelement), dimension(3,3), intent(in)	p_dens,
		real, dimension(:), intent(in)	d_energies,
		type(moessbauer_d_density), dimension(:), intent(in)	d_densities,
		type(particle_ptr), dimension(:), intent(in), allocatable	atoms_array,
		type(unitcell), intent(in), pointer	unit_cell,
		real, intent(in)	t_start,
		real, intent(in)	t_end,
		real, intent(in)	t_step
	)

Returns an array values of quadrupole splitting on the given atom in the given temperature range.

Parameters

[in]	m_atom	Pointer to atom on which QS is calculated
[in]	p_dens	Density matrix of the d-atom's p-shell
[in]	d_energies	Energies of the d-shell states on m_atom
[in]	d_densities	One-electronic density matrices correspoding to d_energies
[in]	atoms_array	`particle_ptr` array of all unit cell atoms
[in]	unit_cell	The system's unit cell
[in]	t_start,t_end,t_step	Temperature range parameters

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◆ moessbauer_quadrupole_potential()

real function, dimension(6) moessbauer::moessbauer_quadrupole_potential ( type(vector), intent(in) r )

Returns the values \( V_{ab} = \frac{3 r_a r_b - δ_{ab} * r^2}{r^5} \) as an array, in the order xx, yy, zz, xy, xz, yz.

Variable Documentation

◆ fe57m_gamma

real, parameter, private moessbauer::fe57m_gamma = 14413 / AtomicUnitOfEnergy2EV

private

◆ fe57nuc_delr_over_r

real, parameter, private moessbauer::fe57nuc_delr_over_r = -1.8e-3

private

◆ fe57nuc_q

real, parameter, private moessbauer::fe57nuc_q = 0.160

private

◆ fe57nuc_r

real, parameter, private moessbauer::fe57nuc_r = 3.75e-5 / Bohr2Angstrom

private

◆ fe_4s_0

real, parameter, private moessbauer::fe_4s_0 = 6.2501

private

◆ fe_is_coef

real, parameter, private moessbauer::fe_is_coef = 0.8 * Pi * (1e3*speedOfLightmpsec / Fe57m_gamma) * Fe_Z * (Fe57nuc_R**2) * Fe57nuc_delR_over_R*(Fe_4s_0**2)

private

◆ fe_qs_coef

real, parameter, private moessbauer::fe_qs_coef = 0.5 * (1e3*speedOfLightmpsec / Fe57m_gamma) * Bohr2Angstrom * (1e-8 * Fe57nuc_Q)

private

◆ fe_rm3_3d

real, parameter, private moessbauer::fe_rm3_3d = 4.978801 / Bohr2Angstrom**3

private

◆ fe_rm3_4p

real, parameter, private moessbauer::fe_rm3_4p = 1.697 / Bohr2Angstrom**3

private

◆ fe_z

real, parameter, private moessbauer::fe_z = 26

private

◆ sf_d

real, parameter, private moessbauer::sf_d = 0.68

private

◆ sf_g

real, parameter, private moessbauer::sf_g = 10.1

private

◆ sf_sp

real, parameter, private moessbauer::sf_sp = 0.68

private

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ moessbauer_d_atom_efg()

◆ moessbauer_extract_data()

◆ moessbauer_is()

◆ moessbauer_ligand_efg()

◆ moessbauer_p_atom_efg()

◆ moessbauer_qs_from_efg()

◆ moessbauer_qs_temperature_dependence()

◆ moessbauer_quadrupole_potential()

Variable Documentation

◆ fe57m_gamma

◆ fe57nuc_delr_over_r

◆ fe57nuc_q

◆ fe57nuc_r

◆ fe_4s_0

◆ fe_is_coef

◆ fe_qs_coef

◆ fe_rm3_3d

◆ fe_rm3_4p

◆ fe_z

◆ sf_d

◆ sf_g

◆ sf_sp