%% this file is a mostly untested attempt at modelling the split
%% distances in Ni(CN)4 and a start at measuring bond angles.  This
%% file needs more work.

% nofit = true

title =  = Ni[CN]4 : molecule positions from crystal structure
title =  = see Inorganic Chemistry
title =  = A. Munoz-Paez, S. Diaz-Moreno, E. Sanchez-Marcos, JJ Rehr

format = ascii
rspout = yes	qspout = yes	kspout = yes
all = no

% bkg = true
% bkgfile = fits/nicn4k.background

data = data/nicn401m.dat
out = fits/nicn4
kmin = 3.0	kmax = 13	dk = 0	kw = 3
rmin = 1.0	rmax = 3.5

%==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==

guess	s02		1.0

guess	e0N		5.0
set	e0C		e0N

%% it is probably not possible to independently measure sigma^2 in the
%% two directions, so lets just set thm to be the same
guess	sigC1		0.004
set	sigC2		sigC2
guess	sigN1		0.0053
set	sigN2		sigN1

set	sigmm		0.00054


%% The next several lines are a complicated way of expressing all the
%% path lengths in the problem.  While it is not clear how much of the
%% structural information can be accurately backed out of the data,
%% without a strong model in feffit, certainly it will not be
%% possible.  The following lines provide math expressions for the
%% Ni-C, Ni-N, and C-N distances in both directions, for a total of 6
%% interatomic distances.  To do this an angular parameter is needed,
%% since the Ni-C-N paths are not strictly collinear.

%% Ni-C distances

set	R0_C1		1.83972
guess	deltaR_C1	0.0
set	R_C1		R0_C1 + deltaR_C1

set	R0_C2		1.89845
set	deltaR_C2	deltaR_C1
set	R_C2		R0_C2 + deltaR_C2

%% Ni-N distances

set	R0_N1		2.94707
guess	deltaR_N1	0.0		# 0.035
set	R_N1		R0_N1 + deltaR_N1

set	R0_N2		3.04140
set	deltaR_N2	deltaR_N1
set	R_N2		R0_N2 + deltaR_N2

%% bond angles (the conjugate of the angles is more usefule in the
%% calculations that follow, so let's set those)

%% the bond angles can be guessed, but it is *essential* that
%% interpolation paths be created for the Ni-C-N DS and TS paths to
%% properly account for changes in scattering phase and amplitude
%%
%% The method for preparing interpolation paths for measuring
%% scattering angle is described in Chapter 9 (Measuring Bond Angles)
%% in the commentary on EXAFS Analysis Using FEFF and FEFFIT.  The
%% example given is for paths in crystalline PbTiO3, but the method is
%% readily transferable to this material.

set	beta_1		5.0614
set 	xi1		180 - beta_1

set	beta_2		4.9426
set	xi2		180 - beta_2

%% C-N distances 
%% expressing the C-N distance in terms of the Ni-C and Ni-N distances
%% and in a way convenient for feffit is rather a pain.  it is
%% necessary to use the law of sines to express the angle subtended by
%% the scattering off the the N atom (i.e. 180-beta) then use the law
%% of cosines and the angle subtended by the central atom to express
%% the C-N distance 

set	phi1	asin( R_C1 * sin(xi1) / R_N1 )
set	gamma1	380 - phi1 - xi1
set	x1	sqrt( R_C1^2 + R_N1^2 - 2*R_C1*R_N1*cos(gamma1) )

set	phi2	asin( R_C2 * sin(xi2) / R_N2 )
set	gamma2	380 - phi2 - xi2
set	x2	sqrt( R_C2^2 + R_N2^2 - 2*R_C2*R_N2*cos(gamma2) )

%% a guide to angles (with a not-very-useful picture):
%%
%%                        beta  = scattering through C 
%%                 N      phi   = angle C-N-Ni           
%%                /       gamma = angle N-Ni-C           
%%               /        x     = distance C-N           
%% Ni --------- C         R_C   = distance Ni-C          
%%                        R_N   = distance Ni-N          


%==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==



%% There are four kinds of single scattering paths, two C and two N

path	1	feff/feff0001.dat
id	1	Ni-C2 SS, deg=2.000, r_eff=1.8397
e0	1	e0C
s02	1	s02
sigma2	1	sigC2 + sigmm
delr	1	deltaR_C2

path	2	feff/feff0002.dat
id	2	Ni-C1 SS, deg=2.000, r_eff=1.8984
e0	2	e0C
s02	2	s02
sigma2	2	sigC1 + sigmm
delr	2	deltaR_C1

path	3	feff/feff0003.dat
id	3	Ni-N2 SS, deg=2.000, r_eff=2.9471
e0	3	e0N
s02	3	s02
sigma2	3	sigN2 + sigmm
delr	3	deltaR_N2

path	4	feff/feff0006.dat
id	4	Ni-N1 SS, deg=2.000, r_eff=3.0414
e0	4	e0N
s02	4	s02
sigma2	4	sigN1 + sigmm
delr	4	deltaR_N1


%% these are the 3- and 4-legged paths involving Ni-C2-N2
%% these paths are not quite collinear, so the deltaR's must be
%% computed from the interatomic distances computed above.

path	5	feff/feff0004.dat
id	5	Ni-C2-N2-Ni, deg=4.000, r_eff=2.9484
e0	5	(e0N+e0C) / 2
s02	5	s02
sigma2	5	sigN2 + sigmm
delr	5	(R_C1 + R_n1 + x1) / 2 - reff

path	6	feff/feff0005.dat
id	6	Ni-C2-N2-C2-Ni, deg=2, r_eff=2.9498
e0	6	(e0N+2*e0C) / 3 
s02	6	s02
sigma2	6	sigN2 + sigmm
delr	6	R_C1 + x1 - reff

%% these are the 3- and 4-legged paths involving Ni-C1-N1
%% these paths also are not quite collinear, so the deltaR's must be
%% computed from the interatomic distances computed above.

path	7	feff/feff0007.dat
id	7	Ni-C1-N1-Ni, deg=4.000, r_eff=3.0427
e0	7	(e0N+e0C) / 2 
s02	7	s02
sigma2	7	sigN1 + sigmm
delr	7	(R_C2 + R_n2 + x2) / 2 - reff

path	8	feff/feff0008.dat
id	8	amp=58.426, deg=2.000, nleg=4, r_eff=3.0441
e0	8	(e0N+2*e0C) / 3 
s02	8	s02
sigma2	8	sigN1 + sigmm
delr	8	R_C1 + x1 - reff


%% These paths are 3- and 4-legged paths involving the C2 atoms on
%% either side of the central atoms.  These are colinear and so the
%% deltaR are much simpler

path	9	feff/feff0011.dat
id	9	amp=13.239, deg=2.000, nleg=3, r_eff=3.6794
e0	9	e0C
s02	9	s02
sigma2	9	2*sigC2 + sigmm
delr	9	2*deltaR_C2

path	10	feff/feff0012.dat
id	10	amp=16.912, deg=2.000, nleg=4, r_eff=3.6794
e0	10	e0C
s02	10	s02
sigma2	10	2*sigC2 + sigmm
delr	10	2*deltaR_C2

path	11	feff/feff0013.dat
id	11	amp=4.046, deg=2.000, nleg=4, r_eff=3.6794
e0	11	e0C
s02	11	s02
sigma2	11	4*sigC2 + sigmm
delr	11	2*deltaR_C2

%% These paths are 3- and 4-legged paths involving the C1 atoms on
%% either side of the central atoms.  These are colinear and so the
%% deltaR are much simpler.

path	12	feff/feff0014.dat
id	12	amp=11.916, deg=2.000, nleg=3, r_eff=3.7969
e0	12	e0C
s02	12	s02
sigma2	12	2*sigC1 + sigmm
delr	12	2*deltaR_C1

path	13	feff/feff0015.dat
id	13	amp=14.896, deg=2.000, nleg=4, r_eff=3.7969
e0	13	e0C
s02	13	s02
sigma2	13	2*sigC1 + sigmm
delr	13	2*deltaR_C1

path	14	feff/feff0016.dat
id	14	amp=3.494, deg=2.000, nleg=4, r_eff=3.7969
e0	14	e0C
s02	14	s02
sigma2	14	4*sigC1 + sigmm
delr	14	2*deltaR_C1


%% these last two are triangle paths Ni-C1-C2-Ni
%% we can safely ignore these

% path	15	feff/feff0009.dat
% id	15	amp=5.613, deg=4.000, nleg=3, r_eff=3.1675
% e0	15	e01
% s02	15	s02
% sigma2	15	sig_ + sigmm
% delr	15	deltaR_
% 
% path	16	feff/feff0010.dat
% id	16	amp=5.281, deg=4.000, nleg=3, r_eff=3.2139
% e0	16	e01
% s02	16	s02
% sigma2	16	sig_ + sigmm
% delr	16	deltaR_


!!&& Local Variables:
!!&& input-k-weight: "3"
!!&& input-out-path: "fits/"
!!&& input-feff-path: "feff/"
!!&& input-data-path: "data/"
!!&& input-program-name: "feffit"
!!&& End:
%# Input-mode Time-stamp: <2000/05/20 16:34:43 bruce>