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getPairwiseStatistics.m
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% ========================================================================
% Calculate statistics for each bath spin pair.
% ========================================================================
%
% Input Arguments
%
% System = struct( ...
% 'Electron' struct('g', double), ...
% 'muB', double, ...
% 'muN', double, ...
% 'mu0', double, ...
% 'hbar', double, ...
% 'h', double, ...
% 'TMguess', double);
%
% Method = struct(
% 'Criteria' , cell of char vectors, ...
% 'conserveMemory', bool);
%
% Nuclei = struct(
% 'number', uint, ...
% 'Type', cell of char vectors, ...
% 'Index', array<uint>, ...
% 'Coordinates', array<double>
% 'Nuclear_g', array<double>, ...
% 'FermiContact', array<double>);
%
function pwstat = getPairwiseStatistics(System, Method, Nuclei)
ienum = 1;
STAT_SPATIAL = ienum; ienum = ienum +1;
STAT_HYPERFINE = ienum; ienum = ienum +1;
STAT_NUCLEAR_DIPOLE = ienum; ienum = ienum +1;
STAT_BAMAX = ienum; ienum = ienum +1;
STAT_ANALYTIC_HAHN = ienum; ienum = ienum +1;
STAT_PERPENDICULAR = ienum; ienum = ienum +1;
STAT_DELTAHYPERFINE = ienum; ienum = ienum +1;
STAT_NUM_ENUM = ienum-1;
if Method.conserveMemory
stat_bools = false(STAT_NUM_ENUM,1);
else
stat_bools = true(STAT_NUM_ENUM,1);
end
whichStatistics(Method);
deltaX = Nuclei.Coordinates(:,1)-Nuclei.Coordinates(:,1)';
deltaY = Nuclei.Coordinates(:,2)-Nuclei.Coordinates(:,2)';
deltaZ = Nuclei.Coordinates(:,3)-Nuclei.Coordinates(:,3)';
pwstat.DistanceMatrix = sqrt(deltaX.^2 + deltaY.^2 + deltaZ.^2);
cosTheta2 = (Nuclei.Coordinates(:,3)./vecnorm(Nuclei.Coordinates,2,2) ).^2;
gamma_e = -System.Electron.g*System.muB/System.hbar;
gamma_n = Nuclei.Nuclear_g*System.muN/System.hbar;
% spatial
if stat_bools(STAT_SPATIAL)
% Initialize separation matrix.
pwstat.Coordinates = Nuclei.Coordinates;
pwstat.Cylindrical_DistanceMatrix = sqrt(deltaX.^2 + deltaY.^2);
pwstat.ThetaMatrix = acos(deltaZ./pwstat.DistanceMatrix);
pwstat.PhiMatrix = acos(deltaX./pwstat.Cylindrical_DistanceMatrix) ...
+ pi*(deltaY<0);
pwstat.PhiMatrix(deltaY==0) = 0;
% Coordinates
pwstat.Distance = vecnorm(Nuclei.Coordinates,2,2);
pwstat.Cylindrical_Distance = vecnorm(Nuclei.Coordinates(:,1:2),2,2);
pwstat.theta = acos(Nuclei.Coordinates(:,3)./pwstat.Distance);
cos_phi= Nuclei.Coordinates(:,1)./pwstat.Cylindrical_Distance;
pwstat.phi = acos(cos_phi) + (1 - sign(Nuclei.Coordinates(:,2)))*pi/2;
pwstat.maxDistance = max(pwstat.Distance,pwstat.Distance');
end
% Hyperfine
if stat_bools(STAT_HYPERFINE)
pwstat.Hyperfine= (Nuclei.FermiContact ...
- System.hbar^2.*(System.mu0/4/pi).*gamma_n'.*gamma_e .* ...
vecnorm(Nuclei.Coordinates,2,2).^-3) ...
.*(1-3*cosTheta2); % J
pwstat.Hyperfine = pwstat.Hyperfine/(System.h); % Hz.
if stat_bools(STAT_DELTAHYPERFINE)
pwstat.DeltaHyperfine = pwstat.Hyperfine - pwstat.Hyperfine';
end
if stat_bools(STAT_PERPENDICULAR)
pwstat.Hyperfine_perpendicular = Nuclei.FermiContact ...
- System.hbar^2.*(System.mu0/4/pi).*gamma_n'.*gamma_e .* ...
vecnorm(Nuclei.Coordinates,2,2).^-3; % J
pwstat.Hyperfine_perpendicular ...
= pwstat.Hyperfine_perpendicular/(System.h); % Hz.
if stat_bools(STAT_DELTAHYPERFINE)
pwstat.DeltaHyperfine_perpendicular ...
= pwstat.Hyperfine_perpendicular - pwstat.Hyperfine_perpendicular';
end
end
end
% Nuclear Dipole-Dipole
if stat_bools(STAT_NUCLEAR_DIPOLE)
if isfield(pwstat,'ThetaMatrix')
ThetaMatrix = pwstat.ThetaMatrix;
else
ThetaMatrix = acos(deltaZ./pwstat.DistanceMatrix);
end
if isfield(pwstat,'PhiMatrix')
PhiMatrix = pwstat.PhiMatrix;
else
PhiMatrix = acos(deltaX./vecnorm(Nuclei.Coordinates(:,1:2),2,2)) ...
+ pi*(deltaY<0);
PhiMatrix(deltaY==0) = 0;
end
b_fliflopPerp = -(0.25*(System.mu0/4/pi).* ...
(Nuclei.Nuclear_g'.*Nuclei.Nuclear_g).*System.muN^2) ...
./pwstat.DistanceMatrix.^3; % J.
b_fliflopPerp = b_fliflopPerp/(System.h); % Hz.
b = b_fliflopPerp.*(1-3*cos(ThetaMatrix).^2);
if stat_bools(STAT_PERPENDICULAR)
pwstat.Nuclear_Dipole_perpendicular = 4*b_fliflopPerp; % Hz.
pwstat.Nuclear_Dipole_perpendicular ...
= inf2nan(pwstat.Nuclear_Dipole_perpendicular);
end
pwstat.Nuclear_Dipole = 4*b; % Hz.
J = -2/3*Nuclei.methylTunnelingSplitting;
pwstat.Nuclear_Dipole_methyl = pwstat.Nuclear_Dipole - 2*J;
pwstat.Nuclear_Dipole_x_iy_Z = zeroDiag(...
4*b_fliflopPerp.* ...
exp(1i*PhiMatrix) .* ...
sin(ThetaMatrix) .* cos(ThetaMatrix)...
);
if any(isnan(pwstat.Nuclear_Dipole_x_iy_Z(:)))
error(['Error in getPairwiseStatistics(): ', ...
'Nuclear_Dipole_x_iy_Z contains NANs.']);
end
pwstat.Nuclear_Dipole = inf2nan(pwstat.Nuclear_Dipole);
end
% |bA_{mav}|^{1/2}.
if stat_bools(STAT_BAMAX)
pwstat.Amax = max( ...
abs(pwstat.Hyperfine_perpendicular), ...
abs(pwstat.Hyperfine_perpendicular'));
pwstat.bAmax = sqrt(pwstat.Amax.*abs(pwstat.Nuclear_Dipole));
pwstat.Amax = inf2nan(pwstat.Amax);
pwstat.bAmax = inf2nan(pwstat.bAmax);
end
% modulation depth
if stat_bools(STAT_ANALYTIC_HAHN)
% Hyperfine to nucler dipole-dipole ratio
cp = pwstat.DeltaHyperfine_perpendicular./...
pwstat.Nuclear_Dipole_perpendicular;
c = pwstat.DeltaHyperfine./pwstat.Nuclear_Dipole;
pwstat.DeltaHyperfine_over_Nuclear_Dipole_p = cp;
pwstat.DeltaHyperfine_over_Nuclear_Dipole = c;
modDepth_p = 4*cp.^2./(1+cp.^2).^2;
modDepth = 4*c.^2./(1+c.^2).^2;
pwstat.Modulation_Depth_p = modDepth_p;
pwstat.Modulation_Depth = modDepth;
bCH3 = pwstat.Nuclear_Dipole_methyl;
dACH3 = pwstat.DeltaHyperfine;
pwstat.Modulation_Depth_methyl = (2.*bCH3.*dACH3./(bCH3.^2 + dACH3.^2)).^2;
% modulation frequency
pwstat.Frequency_Pair_p = b_fliflopPerp.*sqrt(1+cp.^2); % Hz
pwstat.Frequency_Pair = b.*sqrt(1+c.^2); % Hz
pwstat.Frequency_Pair_methyl = 1/8*sqrt(bCH3.^2 + dACH3.^2);
TM = System.TMguess;
pwstat.GaussianRMSD_p = getGaussianRMSD(...
modDepth_p,pwstat.Frequency_Pair_p,TM);
pwstat.GaussianRMSD = getGaussianRMSD(...
modDepth,pwstat.Frequency_Pair,TM);
pwstat.Frequency_Pair_p = inf2nan(pwstat.Frequency_Pair_p);
pwstat.Frequency_Pair = inf2nan(pwstat.Frequency_Pair);
pwstat.Modulation_Depth_p = inf2nan(pwstat.Modulation_Depth_p);
pwstat.Modulation_Depth = inf2nan(pwstat.Modulation_Depth);
pwstat.GaussianRMSD_p = inf2nan(pwstat.GaussianRMSD_p);
pwstat.GaussianRMSD = inf2nan(pwstat.GaussianRMSD);
end
% delta_gm_gn
pwstat.Same_g = Nuclei.Nuclear_g == Nuclei.Nuclear_g';
%<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
function whichStatistics(Method)
stat_bools(STAT_HYPERFINE) = true;
stat_bools(STAT_NUCLEAR_DIPOLE) = true;
if ~Method.Ori_cutoffs
stat_bools(STAT_PERPENDICULAR) = true;
end
if strcmp(Method.method,'rCCE') || strcmp(Method.method,'rCE')
stat_bools(STAT_ANALYTIC_HAHN) = true;
end
for ii = 1:numel(Method.Criteria)
switch Method.Criteria{ii}
case {'minimum-frequency','Gaussian RMSD','modulation'}
stat_bools(STAT_ANALYTIC_HAHN) = true;
case {'bAmax','minAmax','maxAmax'}
stat_bools(STAT_BAMAX) = true;
stat_bools(STAT_DELTAHYPERFINE) = true;
case {'delta hyperfine'}
stat_bools(STAT_DELTAHYPERFINE) = true;
end
end
end
%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
end