rmatrix_data.m File Reference

Functions
input_files, every_nth_energy	input_files:every_nth_energy:Units:Input:Output:Input:final_state:initial_state:grid_vectors: (id dipole_tools,[every_nth_energy] id available,[Units] id show_states,[Input] id none,[Output] id Dyson_signs,[Input] final_state, initial_state, grid_vectors,[final_state] id state,[initial_state] id state,[grid_vectors] id grid_vectors)
n, 1	IMPORTANT:n_1:n_2:Input:phi:initial_state:final_state:grid_vectors: (id point,[n_1] gamma in case of NO2 coordinate,[n_2] ra in case of NO2 momentum_space_photodipoles,[Input] theta, phi, initial_state, final_state, grid_vectors theta,[phi] id electron,[initial_state] id state,[final_state] id state,[grid_vectors] id grid_vectors)
grid for internal	coordinate (bending angle in degrees in case of NO2) % grid_vectors
grid for internal	coordinate (asymmetric stretch in Bohr in case of NO2) % If grid_vectors
x, y, z	n_1:n_2:Input:final_stateF:grid_vectors:Output:n_1:n_2:Input:initial_state:grid_vectors:Output:n_1:n_2:Input:final_state:grid_vectors:Output:n_1:n_2:Source_files:Molecule:Max_L:N_energies:N_final_states:N_initial_states:N_angular_points:N_atoms:Final_states: (gamma in case of NO2 coordinate,[n_2] ra in case of NO2 final_state_dipoles,[Input] final_stateI, final_stateF, grid_vectors final_stateI,[final_stateF] id required,[grid_vectors] id index,[Output] x, y, z coordinates,[n_1] gamma in case of NO2 coordinate,[n_2] ra in case of NO2 initial_state_energy,[Input] initial_state, grid_vectors,[initial_state] id state,[grid_vectors] id index,[Output] n_1, n_2 coordinates,[n_1] gamma in case of NO2 coordinate,[n_2] ra in case of NO2 final_state_energy,[Input] final_state, grid_vectors,[final_state] id state,[grid_vectors] id index,[Output] n_1, n_2 coordinates,[n_1] gamma in case of NO2 coordinate,[n_2] ra in case of NO2 structures,[Source_files] id rmatrix_data,[Molecule] id molecule,[Max_L] id momentum,[N_energies] id energies,[N_final_states] id states,[N_initial_states] id states,[N_angular_points] id signs,[N_atoms] id centre,[Final_states] 3, N_final_states Final_states)
	disp (msg) else error('Expecting either one or two arguments on input.') end if not(iscell(input_files)) error('The argument input_files must be a cell vector') end obj.N_geometries
end if	not (ischar(input_files{geom, 1})) error('Path must be character') end msg
elseif	not (isequal(obj.Molecule, C)) disp(obj.Molecule) disp(C) error('Flag Molecule is not the same for all geometries.') end %Read the dimensions C
	N_energies_geom (geom)
	C (4)=0
if	not (isequal(ref, C)) disp(ref) disp(C) error('Dimension parameters are not the same for all geometries.') end end for i
	D (1:3, j)
if	not (is_ref_geom) if not(isequal(obj.Final_states
end Read the atom	coordinates (Bohr) for i
if is_ref_geom obj	Angular_grid_cartesian (1, i)
x obj	Angular_grid_cartesian (2, i)
y obj	Angular_grid_cartesian (3, i)
z obj	Angular_grid_cartesian (4, i)
obj	Xlm_precalculated (lm, i)
end end elseif	not (isequal(obj.Angular_grid_cartesian(:, i), C)) error('The angular grid is not the same for all geometries.') end end %Read the energy grid Energy_grid
Number and symmetry of the Dyson	orbital (only needed for book keeping so I know which Dysons were taken from the R-matrix files). flag
elseif	not (flag==obj.Dyson_orbitals{1, i, k}) % error('The Dyson orbital flags are not the same for all geometries.') end Dyson_signs
	fclose (fileID)
	energies (j, 1)
	map (geom)
end end	if (geom_has_energy) have_energy
end end	if (have_energy==true) obj.N_energies
	energies (obj.N_energies, 1)
	disp (strcat('Accepted energy:', str)) for geom
	disp (strcat('Dropping energy:', str)) end end obj.Electron_energies
obj	Electron_energies (1:obj.N_energies, 1)
Put the dipoles from the Dipoles_read structure to the obj Dipoles structure	disp ('Processing photodipoles arrays...') obj.Dipoles
obj	Dipoles (1:obj.N_lm, 1:3, e, f, in, geom)
end end end end	disp ('done')[obj.Internal_coordinates obj.Internal_coordinates_limits]
N_energies_geom(geom, 1)	zeros ()
end end if	map (i, 1)
interpolate for the given internal_coordinates if	not (obj.Have_interpolant) error('Interpolation requested but not possible since the interpolant could not be const ructed.') end n_gamma = size([grid_vectors{2}],2)
number of gamma values else	error ('On input the size of the cell array grid_vectors must be either 1 or 3.') end if final _state > obj.N_final_states||final _state<=0error('On input final _state was out of range.') end if initial_state > obj.N_initial_states||initial_state<=0error('On input initial_state was out of range.') end if geom = [grid_vectors{1}]
end if nargin nargin< 2 error('Expecting either 1 or 2 parameters on input.') end if final_state > obj N_final_states final_state<=0 error('On input final_state was out of range.') end if n_coords==0 geom=1;%no interpolation;use the geometry with index 1 elseif n_coords==2 geom=0;%interpolate for the given internal_coordinates if not(obj.Have_interpolant) error('Interpolation requested but not possible since the interpolant could not be constructed.') end n_gamma=size([grid_vectors{1}], 2);%number of gamma values n_ra=size([grid_vectors{2}], 2);%number of gamma values else error('On input the size of the cell array grid_vectors must be either 1 or 3.') end %Check the range of the internal_coordinates if geom==0 if not(n_coords==size(obj.Internal_coordinates_limits, 2)) error('The number of supplied grid vectors for the nuclear coordinates does not equal the actual number of nuclear coordinates.') end for i=1:n_coords vectors=[grid_vectors{i}];n=size([grid_vectors{i}], 2);for j=1:n if vectors(j)< obj.Internal_coordinates_limits(1, i) disp(num2str(vectors(j))) disp(num2str(obj.Internal_coordinates_limits(1, i))) error('On input internal coordinate was too small.') end if vectors(j) > obj	Internal_coordinates_limits (2, i) disp(num2str(vectors(j))) disp(num2str(obj.Internal_coordinates_limits(1
end if nargin nargin< 2 error( 'Expecting either 1 or 2 parameters on input.') end if final_state > obj N_final_states final_state<=0 error( 'On input final_state was out of range.') end if n_coords==0 geom=1;%no interpolation;use the geometry with index 1 elseif n_coords==2 geom=0;%interpolate for the given internal_coordinates if not(obj.Have_interpolant) error( 'Interpolation requested but not possible since the interpolant could not be constructed.') end n_gamma=size([grid_vectors{1}], 2);%number of gamma values n_ra=size([grid_vectors{2}], 2);%number of gamma values else error( 'On input the size of the cell array grid_vectors must be either 1 or 3.') end %Check the range of the internal_coordinates if geom==0 if not(n_coords==size(obj.Internal_coordinates_limits, 2)) error( 'The number of supplied grid vectors for the nuclear coordinates does not equal the actual number of nuclear coordinates.') end for i=1:n_coords vectors=[grid_vectors{i}];n=size([grid_vectors{i}], 2);for j=1:n if vectors(j)< obj.Internal_coordinates_limits(1, i) disp(num2str(vectors(j))) disp(num2str(obj.Internal_coordinates_limits(1, i))) error( 'On input internal coordinate was too small.') end if vectors(j) > obj i	error ('On input internal coordinate was too large.') end end end end if geom
	e (1:n_gamma, 1:n_ra)
if nargin< 6||nargin >	disp (nargin) error('The number of input parameters(excluding the object itself) must be either 5 or 6.') end if n_coords
Take the real spherical harmonic from the precalculated buffer where possible otherwise calculate it for the point given if found	Xlm (1, lm)
end else Include interpolation accross geometries interpolation in	energy (1D) and geometry(2D) for each of the x
end else Output is a	matrix (3, n_en, n_en, n_en) corresponding to the x
end end end end end end Auxiliary functions needed to evaluate the dipoles in the momentum basis	methods (Static, Hidden) function r
end if t1< t2 tmax=t1;else tmax=t2;end if abs(M) > J	abs (N) > J r=0
end note that the meaning of theta and phi is swapped since xyz_to_tp uses the Mathematical convention for spherical	coordinates (theta is azimuthal angle, phi is the polar angle)! function[t

Variables
	__pad0__
	n_1
	__pad1__
	__pad2__
is given then	grid_vectors
is given then	initial_stateF
is given then cell array of size corresponding to the number of internal nuclear coordinates If the grid_vectors are not given then the dipoles are evaluated for geometry with index	Output
	__pad3__
	symmetry
spin	Final_states
spin for each	geometry
spin for each the internal nuclear coordinates In case of NO2	ninternal = 2 corresponding to the gamma
spin for each the internal nuclear coordinates In case of NO2 ra coordinates This array is only constructed if N_geometries	Internal_coordinates_limits
spin for each the internal nuclear coordinates In case of NO2 ra coordinates This array is only constructed if N_geometries	n = j
spin for each the internal nuclear coordinates In case of NO2 ra coordinates This array is only constructed if N_geometries where n is the number of internal nuclear coordinates At the moment n can be either or This array is only constructed if N_geometries	Angular_grid_cartesian = zeros(4,obj.N_angular_points)
spin for each the internal nuclear coordinates In case of NO2 ra coordinates This array is only constructed if N_geometries where n is the number of internal nuclear coordinates At the moment n can be either or This array is only constructed if N_geometries containing the grid points(x, y, z, w) defining the angular grid. %Angular_grid_spherical elseif	nargin
	msg = strcat('Accepting energies in steps of:',num2str(en_step))
obj	Source_files = input_files
obj	Have_interpolant = false
	Dipoles_read = cell(obj.N_geometries,1)
	Energy_grid = cell(obj.N_geometries,1)
	N_energies_geom = zeros(obj.N_geometries,1)
angular	grid
angular etc All other geometries must contain the same data for the reference values if	geom
else	is_ref_geom = 0
	C = fgetl(fileID)
if is_ref_geom obj	Molecule = C
Number of electron energies for this geometry if is_ref_geom obj	Max_L = C(1)
obj	N_lm = C(2)
obj	N_final_states = C(3)
obj	N_angular_points = C(5)
obj	N_atoms = C(6)
obj	N_initial_states = C(7)
Declarations obj	Initial_states = cell(3,obj.N_initial_states,obj.N_geometries)
obj	Atoms = cell(2,obj.N_atoms,obj.N_geometries)
	x
	y
	z
w obj	Angular_grid_spherical = zeros(3,obj.N_angular_points)
	theta = obj.Angular_grid_spherical(1,i)
	phi = obj.Angular_grid_spherical(2,i)
w obj	Xlm_precalculated = zeros(obj.N_lm,obj.N_angular_points)
obj	Dyson_orbitals = cell(2,obj.N_final_states,obj.N_initial_states,obj.N_geometries)
we omit the energy grid from the check since we determine the common set of energy points at the end	ref = [obj.Max_L
	D = fscanf(fileID,'%e',1)
	row
relative state number within its spin space symmetry	Ssym = strcat(' Symmetry = ',num2str(C(2)))
state symmetry	Sspin = strcat(' Spin = ',num2str(C(3)))
for	j
end for	i
quadrature weight note that theta and phi are swapped since xyz_to_tp uses the Mathematical convention for spherical	coordinates [obj.Angular_grid_spherical(2, i) obj.Angular_grid_spherical(1, i)] = obj.xyz_to_tp(obj.Angular_grid_cartesian(1,i),obj.Angular_grid_cartesian(2,i),obj.Angular_grid_cartesian(3,i))
Precalculate	Xlm = zeros(1,obj.N_lm)
	lm = 0
for	l
Read the Dyson orbital signs evaluated on the angular grid for	k
	Dnum = strcat(' Dyson orbital number = ',num2str(C(1)))
	Dsym = strcat(' Dyson orbital symmetry = ',num2str(C(2)))
end end Read the partial wave photoionization dipoles	Re = fscanf(fileID,'%e',obj.N_lm*3*N_energies_geom(geom,1)*obj.N_final_states*obj.N_initial_states)
	Im = fscanf(fileID,'%e',obj.N_lm*3*N_energies_geom(geom,1)*obj.N_final_states*obj.N_initial_states)
	all_energies = [Energy_grid{1,1}]
	energies = zeros(n,1)
if obj N_geometries Find the common set of energy	points
if obj N_geometries Find the common set of energy use the grid for geometry as the set of starting common points	energy_map = zeros(n,obj.N_geometries,'int32')
obj	N_energies = 0
	test = [Energy_grid{geom,1}]
	geom_has_energy = false
	break
else	have_energy = false
	str = num2str(energies(i,1))
for	in
Generate the griddedInterpolant for all dipole matrix	elements
Generate the griddedInterpolant for all dipole matrix energies and Dyson orbital	signs [obj.D_lm_xyz obj.Dipoles_initial obj.Dipoles_final obj.Energies_initial obj.Energies_final obj.Dyson_interpolant obj.Have_interpolant] = obj.construct_dipole_interpolant
obj	Electron_energies = energies(1:n,1)
obj	Dipoles = [Dipoles_read{geom,1}]
obj	D_lm_xyz = cell(obj.N_lm,3,obj.N_final_states,obj.N_initial_states)
	X = zeros(obj.N_energies,1)
	V = zeros(obj.N_energies,1)
	ref_grid = [Energy_grid{geom,1}]
end end end end end obj	Max_energy = max(obj.Electron_energies(:))
obj	Min_energy = min(obj.Electron_energies(:))
end function show_states(obj) disp(strcat( 'Molecule else	n_coords = 0
no	interpolation
number of gamma values	n_ra = size([grid_vectors{2}],2)
else	s = zeros(obj.N_angular_points,n_gamma,n_ra)
end end end function	e
end end function	d
for	xyz
list of energies	n_en = size(energies,2)
else	dinterp = zeros(obj.N_lm,3,n_en,n_en,n_en)
end	found = 0
end else Output is a z dipole components evaluated for the n_en *n_en *n_en points in the	energy
end else Output is a z dipole components evaluated for the n_en *n_en *n_en points in the	gamma
	t1 = J-N
	t2 = J+M
	t3 = M-N
if t3	tmin = t3
return end	S =sin(beta/2)
	tmp1 =sqrt(factorial(J+M)*factorial(J-M)*factorial(J+N)*factorial(J-N))
for	t
end	r = tmp
end note that the meaning of theta and phi is swapped since xyz_to_tp uses the Mathematical convention for spherical	p
	fact = sqrt(x*x + y*y)

Function Documentation

abs()

end if t1< t2 tmax=t1;else tmax=t2;end if abs(M) > J abs ( N )

pure virtual

Angular_grid_cartesian() [1/4]

if is_ref_geom obj Angular_grid_cartesian	(	1	,
		i	)

Angular_grid_cartesian() [2/4]

x obj Angular_grid_cartesian	(	2	,
		i	)

Angular_grid_cartesian() [3/4]

y obj Angular_grid_cartesian	(	3	,
		i	)

Angular_grid_cartesian() [4/4]

z obj Angular_grid_cartesian	(	4	,
		i	)

C()

C ( 4 )

pure virtual

coordinate() [1/2]

grid for internal coordinate

(

asymmetric stretch in Bohr in case of

NO2

)

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coordinate() [2/2]

grid for internal coordinate

(

bending angle in degrees in case of

NO2

)

coordinates() [1/2]

end Read the atom coordinates

(

Bohr

)

coordinates() [2/2]

end note that the meaning of theta and phi is swapped since xyz_to_tp uses the Mathematical convention for spherical coordinates	(	theta is azimuthal	angle,
		phi is the polar	angle )

D()

D	(	1:3	,
		j	)

Dipoles()

obj Dipoles	(	1:obj.	N_lm,
		1:3	,
		e	,
		f	,
		in	,
		geom	)

disp() [1/6]

end end end end disp

(

'done'

)

disp() [2/6]

Put the dipoles from the Dipoles_read structure to the obj Dipoles structure disp

(

'Processing photodipoles arrays...'

)

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disp() [3/6]

disp(msg) else disp

(

msg

)

Initial value:

= 1:obj.N_geometries
 
                %The first geometry will be used as a reference one
                %for the energy

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disp() [4/6]

if nargin< 6||nargin > disp

(

nargin

)

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disp() [5/6]

disp

(

strcat( 'Accepted energy:', str)

)

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disp() [6/6]

disp

(

strcat( 'Dropping energy:', str)

)

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e()

e	(	1:n_gamma	,
		1:n_ra	)

Electron_energies()

obj Electron_energies	(	1:obj.	N_energies,
		1	)

energies() [1/2]

energies	(	j	,
		1	)

energies() [2/2]

energies	(	obj.	N_energies,
		1	)

energy()

end else Include interpolation accross geometries interpolation in energy

(

1D

)

error() [1/2]

end if nargin nargin< 2 error('Expecting either 1 or 2 parameters on input.') end if final_state > obj N_final_states final_state<=0 error('On input final_state was out of range.') end if n_coords==0 geom=1;%no interpolation;use the geometry with index 1 elseif n_coords==2 geom=0;%interpolate for the given internal_coordinates if not(obj.Have_interpolant) error('Interpolation requested but not possible since the interpolant could not be constructed.') end n_gamma=size([grid_vectors{1}], 2);%number of gamma values n_ra=size([grid_vectors{2}], 2);%number of gamma values else error('On input the size of the cell array grid_vectors must be either 1 or 3.') end %Check the range of the internal_coordinates if geom==0 if not(n_coords==size(obj.Internal_coordinates_limits, 2)) error('The number of supplied grid vectors for the nuclear coordinates does not equal the actual number of nuclear coordinates.') end for i=1:n_coords vectors=[grid_vectors{i}];n=size([grid_vectors{i}], 2);for j=1:n if vectors(j)< obj.Internal_coordinates_limits(1, i) disp(num2str(vectors(j))) disp(num2str(obj.Internal_coordinates_limits(1, i))) error('On input internal coordinate was too small.') end if vectors(j) > obj i error

(

'On input internal coordinate was too large.'

)

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error() [2/2]

number of gamma values else error ( 'On input the size of the cell array grid_vectors must be either 1 or 3.' ) = [grid_vectors{1}]

finalpure virtual

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fclose()

fclose

(

fileID

)

if() [1/2]

end end if

(

geom_has_energy

)

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if() [2/2]

end end if

(

have_energy

= =true

)

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IMPORTANT:n_1:n_2:Input:phi:initial_state:final_state:grid_vectors:()

n, 1 IMPORTANT:n_1:n_2:Input:phi:initial_state:final_state:grid_vectors: ( id point, [n_1] gamma in case of NO2 coordinate, [n_2] ra in case of NO2 momentum_space_photodipoles, [Input] theta,phi,initial_state,final_state,grid_vectors theta, [phi] id electron, [initial_state] id state, [final_state] id state, [grid_vectors] id grid_vectors )

virtual

input_files:every_nth_energy:Units:Input:Output:Input:final_state:initial_state:grid_vectors:()

input_files, every_nth_energy input_files:every_nth_energy:Units:Input:Output:Input:final_state:initial_state:grid_vectors: ( id dipole_tools, [every_nth_energy] id available, [Units] id show_states, [Input] id none, [Output] id Dyson_signs, [Input] final_state,initial_state,grid_vectors , [final_state] id state, [initial_state] id state, [grid_vectors] id grid_vectors )

virtual

Internal_coordinates_limits()

end if nargin nargin< 2 error( 'Expecting either 1 or 2 parameters on input.') end if final_state > obj N_final_states final_state<=0 error( 'On input final_state was out of range.') end if n_coords==0 geom=1;%no interpolation;use the geometry with index 1 elseif n_coords==2 geom=0;%interpolate for the given internal_coordinates if not(obj.Have_interpolant) error( 'Interpolation requested but not possible since the interpolant could not be constructed.') end n_gamma=size([grid_vectors{1}], 2);%number of gamma values n_ra=size([grid_vectors{2}], 2);%number of gamma values else error( 'On input the size of the cell array grid_vectors must be either 1 or 3.') end %Check the range of the internal_coordinates if geom==0 if not(n_coords==size(obj.Internal_coordinates_limits, 2)) error( 'The number of supplied grid vectors for the nuclear coordinates does not equal the actual number of nuclear coordinates.') end for i=1:n_coords vectors=[grid_vectors{i}];n=size([grid_vectors{i}], 2);for j=1:n if vectors(j)< obj.Internal_coordinates_limits(1, i) disp(num2str(vectors(j))) disp(num2str(obj.Internal_coordinates_limits(1, i))) error( 'On input internal coordinate was too small.') end if vectors(j) > obj Internal_coordinates_limits	(	2	,
		i	)

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map() [1/2]

map

(

geom

)

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map() [2/2]

end end if map	(	i	,
		1	)

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matrix()

end else Output is a matrix	(	3	,
		n_en	,
		n_en	,
		n_en	)

methods()

end end end end end end Auxiliary functions needed to evaluate the dipoles in the momentum basis methods	(	Static	,
		Hidden	)

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n_1:n_2:Input:final_stateF:grid_vectors:Output:n_1:n_2:Input:initial_state:grid_vectors:Output:n_1:n_2:Input:final_state:grid_vectors:Output:n_1:n_2:Source_files:Molecule:Max_L:N_energies:N_final_states:N_initial_states:N_angular_points:N_atoms:Final_states:()

x, y, z n_1:n_2:Input:final_stateF:grid_vectors:Output:n_1:n_2:Input:initial_state:grid_vectors:Output:n_1:n_2:Input:final_state:grid_vectors:Output:n_1:n_2:Source_files:Molecule:Max_L:N_energies:N_final_states:N_initial_states:N_angular_points:N_atoms:Final_states: ( gamma in case of NO2 coordinate, [n_2] ra in case of NO2 final_state_dipoles, [Input] final_stateI,final_stateF,grid_vectors final_stateI, [final_stateF] id required, [grid_vectors] id index, [Output] x,y,z coordinates, [n_1] gamma in case of NO2 coordinate, [n_2] ra in case of NO2 initial_state_energy, [Input] initial_state,grid_vectors , [initial_state] id state, [grid_vectors] id index, [Output] n_1,n_2 coordinates, [n_1] gamma in case of NO2 coordinate, [n_2] ra in case of NO2 final_state_energy, [Input] final_state,grid_vectors , [final_state] id state, [grid_vectors] id index, [Output] n_1,n_2 coordinates, [n_1] gamma in case of NO2 coordinate, [n_2] ra in case of NO2 structures, [Source_files] id rmatrix_data, [Molecule] id molecule, [Max_L] id momentum, [N_energies] id energies, [N_final_states] id states, [N_initial_states] id states, [N_angular_points] id signs, [N_atoms] id centre, [Final_states] 3,N_final_states Final_states )

virtual

N_energies_geom()

N_energies_geom

(

geom

)

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not() [1/7]

elseif not

(

flag

= =obj.Dyson_orbitals{1, i, k}

)

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not() [2/7]

if not(is_ref_geom) if not

(

is_ref_geom

)

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not() [3/7]

end if not

(

ischar(input_files{geom, 1})

)

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not() [4/7]

end end elseif not

(

isequal(obj.Angular_grid_cartesian(:, i), C)

)

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not() [5/7]

elseif not

(

isequal(obj.Molecule, C)

)

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not() [6/7]

if not

(

isequal(ref, C)

)

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not() [7/7]

interpolate for the given internal_coordinates if not

(

obj.

Have_interpolant

)

const = size([grid_vectors{2}],2)

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orbital()

Number and symmetry of the Dyson orbital

(

only needed for book keeping so I know which Dysons were taken from the R-matrix

files

)

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Xlm()

Take the real spherical harmonic from the precalculated buffer where possible otherwise calculate it for the point given if found Xlm	(	1	,
		lm	)

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Xlm_precalculated()

obj Xlm_precalculated	(	lm	,
		i	)

zeros()

N_energies_geom(geom, 1) zeros ( )

virtual

Variable Documentation

__pad0__

__pad0__

__pad1__

__pad1__

__pad2__

__pad2__

__pad3__

__pad3__

all_energies

all_energies = [Energy_grid{1,1}]

Angular_grid_cartesian

obj Angular_grid_cartesian = zeros(4,obj.N_angular_points)

Angular_grid_spherical

w obj Angular_grid_spherical = zeros(3,obj.N_angular_points)

Atoms

obj Atoms = cell(2,obj.N_atoms,obj.N_geometries)

break

break

C

C = fgetl(fileID)

coordinates

quadrature weight note that theta and phi are swapped since xyz_to_tp uses the Mathematical convention for spherical coordinates[obj.Angular_grid_spherical(2, i) obj.Angular_grid_spherical(1, i)] = obj.xyz_to_tp(obj.Angular_grid_cartesian(1,i),obj.Angular_grid_cartesian(2,i),obj.Angular_grid_cartesian(3,i))

D

D = fscanf(fileID,'%e',1)

d

d

Initial value:

= final_state_dipoles(obj,final_stateI,final_stateF,grid_vectors)
            
            if nargin == 4
                if not(iscell(grid_vectors))
                    error('On input grid_vectors must a cell array.')
                end
                n_coords = size(grid_vectors,2)

D_lm_xyz

end end obj D_lm_xyz = cell(obj.N_lm,3,obj.N_final_states,obj.N_initial_states)

dinterp

else dinterp = zeros(obj.N_lm,3,n_en,n_en,n_en)

Dipoles

obj Dipoles = [Dipoles_read{geom,1}]

Dipoles_read

Dipoles_read = cell(obj.N_geometries,1)

Dnum

Dnum = strcat(' Dyson orbital number = ',num2str(C(1)))

Dsym

Dsym = strcat(' Dyson orbital symmetry = ',num2str(C(2)))

Dyson_orbitals

end obj Dyson_orbitals = cell(2,obj.N_final_states,obj.N_initial_states,obj.N_geometries)

e

e

Initial value:

= final_state_energy(obj,final_state,grid_vectors)
             
            if nargin == 3
                if not(iscell(grid_vectors))
                    error('On input grid_vectors must a cell array.')
                end
                n_coords = size(grid_vectors,2)

Electron_energies

obj Electron_energies = energies(1:n,1)

elements

Generate the griddedInterpolant for all dipole matrix elements

energies

energies = zeros(n,1)

energy

end else Output is a z dipole components evaluated for the n_en* n_en* n_en points in the energy

Energy_grid

Energy_grid = cell(obj.N_geometries,1)

energy_map

if obj N_geometries Find the common set of energy use the grid for geometry as the set of starting common points energy_map = zeros(n,obj.N_geometries,'int32')

fact

fact = sqrt(x*x + y*y)

Final_states

end obj Final_states

Initial value:

{2,i}: energy (in H) of the final state.
    %              Final_states{3,i}: array of dimensions (3,N_final_states) containing the three components of the dipole couplings between the i-th state and all other final states.
    %Initial_states: cell array of dimensions (3,N_initial_states). The data in the cells is of the same type but this time for the bound initial states.
    %Dyson_orbitals: cell array of dimensions (2,N_final_states,N_initial_states)
    %               Dyson_orbitals(1,f,i): string containing the label for the Dyson orbital corresponding to the initial state i and the final state f.
    %               Dyson_orbitals(2,f,i): array of dimension (N_angular_points,1) containing the signs of the Dyson orbitals evaluated on the angular grid.
    %Atoms: cell array of dimensions (2,N_atoms).
    %       Atoms{1,i}: vector (3,1) containing the coordinates (in Bohr) of the i-th atom.
    %       Atoms{2,i}: string containing the name of the i-th atom.
    %Internal_coordinates: array of dimensions(ninternal,N_geometries) containing

found

end found = 0

gamma

end else Output is a z dipole components evaluated for the n_en* n_en* n_en points in the gamma

geom

end end end end if geom

Initial value:

== 1
                    is_ref_geom = 1

geom_has_energy

geom_has_energy = false

geometry

spin for each geometry

grid

angular grid

grid_vectors

is given then grid_vectors

Initial value:

{3} must be present too.
    %                     If only grid_vectors{1} is given then the photodipoles are evaluated for geometry with index 1.
    %
    %       Output: complex(3,n_en,n_1,n_2)
    %       -------
    %       Photoelectron dipoles (x,y,z) evaluated for the given combination of initial and final states and photoelectron emission direction.
    %       n_en: size of the energy grid.
    %       n_1: size of the grid for internal coordinate 1 (gamma in case of NO2).
    %       n_2: size of the grid for internal coordinate 2 (ra in case of NO2).
    %       The photoelectron dipoles are evaluated interpolating the partial wave dipole matrix elements on the grid of energies and nuclear coordinates.
    %
    %       initial_state_dipoles
    %       =====================
    %
    %       Input: (initial_stateI,initial_stateF,grid_vectors)
    %       ------
    %       initial_stateI

have_energy

else have_energy = false

Have_interpolant

obj Have_interpolant = false

i

end else Output is a z dipole components evaluated for the n_en* n_en* n_en points in the ra space for i

Initial value:

= 1:obj.N_final_states
                    C = fscanf(fileID,'%d',3)

Im

Im = fscanf(fileID,'%e',obj.N_lm*3*N_energies_geom(geom,1)*obj.N_final_states*obj.N_initial_states)

in

for in

Initial value:

= 1:obj.N_initial_states
                        for f = 1:obj.N_final_states
                            for e = 1:obj.N_energies
                                i = energy_map(e,geom)

initial_stateF

is given then initial_stateF

Initial_states

end obj Initial_states = cell(3,obj.N_initial_states,obj.N_geometries)

Internal_coordinates_limits

spin for each the internal nuclear coordinates In case of NO2 ra coordinates This array is only constructed if N_geometries Internal_coordinates_limits

interpolation

no interpolation

is_ref_geom

else is_ref_geom = 0

j

for j

Initial value:

=1:obj.N_initial_states
                        C = fscanf(fileID,'%e',3)

k

Read the Dyson orbital signs evaluated on the angular grid for k

Initial value:

= 1:obj.N_initial_states
                    for i = 1:obj.N_final_states
                        C = fscanf(fileID,'%d',2)

l

for l

Initial value:

=0:obj.Max_L
                            for m=-l:l
                                lm = lm + 1

lm

lm = 0

Max_energy

end end end end end obj Max_energy = max(obj.Electron_energies(:))

Max_L

Number of electron energies for this geometry if is_ref_geom obj Max_L = C(1)

Min_energy

obj Min_energy = min(obj.Electron_energies(:))

Molecule

if is_ref_geom obj Molecule = C

msg

if obj N_geometries msg = strcat('Accepting energies in steps of:',num2str(en_step))

n

end end n = j

n_1

is given then cell array of size corresponding to the number of internal nuclear coordinates If the grid_vectors are not given then the dipoles are evaluated for geometry with index n_1

N_angular_points

obj N_angular_points = C(5)

N_atoms

obj N_atoms = C(6)

n_coords

use the geometry with index elseif n_coords = 0

n_en

list of energies n_en = size(energies,2)

N_energies

obj N_energies = 0

N_energies_geom

N_energies_geom = zeros(obj.N_geometries,1)

N_final_states

obj N_final_states = C(3)

N_initial_states

obj N_initial_states = C(7)

N_lm

obj N_lm = C(2)

n_ra

number of gamma values n_ra = size([grid_vectors{2}],2)

nargin

spin for each the internal nuclear coordinates In case of NO2 ra coordinates This array is only constructed if N_geometries where n is the number of internal nuclear coordinates At the moment n can be either or This array is only constructed if N_geometries containing the grid points (x,y,z,w) defining the angular grid. %Angular_grid_spherical elseif nargin

Initial value:

== 2
                en_step = round(every_nth_energy)

ninternal

spin for each the internal nuclear coordinates In case of NO2 ninternal = 2 corresponding to the gamma

Output

is given then cell array of size corresponding to the number of internal nuclear coordinates If the grid_vectors are not given then the dipoles are evaluated for geometry with index Output

p

end note that the meaning of theta and phi is swapped since xyz_to_tp uses the Mathematical convention for spherical p

Initial value:

= xyz_to_tp( x,y,z )
            p = acos(z)

phi

phi = obj.Angular_grid_spherical(2,i)

points

if obj N_geometries Find the common set of energy points

r

end r = tmp

Re

end end Read the partial wave photoionization dipoles Re = fscanf(fileID,'%e',obj.N_lm*3*N_energies_geom(geom,1)*obj.N_final_states*obj.N_initial_states)

ref

we omit the energy grid from the check since we determine the common set of energy points at the end ref = [obj.Max_L

ref_grid

ref_grid = [Energy_grid{geom,1}]

row

row

Initial value:

= initial state indices:
                    Snum = strcat(' Number = ',num2str(C(1)))

S

return end S =sin(beta/2)

s

else s = zeros(obj.N_angular_points,n_gamma,n_ra)

signs

Generate the griddedInterpolant for all dipole matrix energies and Dyson orbital signs[obj.D_lm_xyz obj.Dipoles_initial obj.Dipoles_final obj.Energies_initial obj.Energies_final obj.Dyson_interpolant obj.Have_interpolant] = obj.construct_dipole_interpolant

Source_files

obj Source_files = input_files

Sspin

state symmetry Sspin = strcat(' Spin = ',num2str(C(3)))

Ssym

relative state number within its spin space symmetry Ssym = strcat(' Symmetry = ',num2str(C(2)))

str

end else str = num2str(energies(i,1))

symmetry

symmetry

t

for t

Initial value:

=tmin:tmax
                tmp = tmp + ((-1)^t)*(tmp1/(factorial(J+M-t)*factorial(J-N-t)*factorial(t)*factorial(t+N-M)))*C^(2*J+M-N-2*t)*S^(2*t+N-M)

t1

t1 = J-N

t2

t2 = J+M

t3

t3 = M-N

test

test = [Energy_grid{geom,1}]

theta

theta = obj.Angular_grid_spherical(1,i)

tmin

else tmin = t3

tmp1

tmp1 =sqrt(factorial(J+M)*factorial(J-M)*factorial(J+N)*factorial(J-N))

V

V = zeros(obj.N_energies,1)

X

X = zeros(obj.N_energies,1)

x

x

Xlm

else Xlm = zeros(1,obj.N_lm)

Xlm_precalculated

w obj Xlm_precalculated = zeros(obj.N_lm,obj.N_angular_points)

xyz

end else for xyz

Initial value:

= 1:3
                   d(xyz,1) = FD(xyz,final_stateF)

y

end else Output is a y

z

z