Orientation of Molecular Frame and choosing unique axis in Monoclinic

[seradır]

Hi.
I want to simulate paramagnetic center (S=5/2) in monoclinic crystal structure (C2h) to extract crystal field parameters (B22,B20,B21,...). I anticipate that the structure exhibits orthorhombic symmetry. According to the literature, the total ZFS (Zero field splitting) Hamiltonian can be written as; H=Hortho+Hi. Hortho is orthorhombic part of Hamiltonian (related articles: https://doi.org/10.1002/pssb.2221470226, https://doi.org/10.1002/pssb.2221980229, https://doi.org/10.1080/05704928.2018.1494601). Hi is monoclinic part of Hamiltonian which depends on the diection of magnetic axes (X,Y,Z) relative to te unique axis (C2) as follows:

Image1.jpg (226.37 KiB) Viewed 3592 times

I consider the magnetic axes (X,Y,Z) in the literature (see image1) as the axes of molecular frame (xM,yM,zM) in the EasySpin documentation. yC is also chosen along unique axis (that is C2‖yC) for monoclinic point group in the EasySpin documentation. At the beginning (no orientation of the paramagnetic center within the crystal, default), molecular frame (xM,yM,zM) is assumed to be collinear with crystal frame (xC,yC,zC(means zC*, perpendicular to xC-yC plane)), as shown in Image2(c). In that case;
Q1: Should I choose Eq(1)+Eq(4) for C2‖yC‖yM (for d-orbital (S=5/2);cancel B6 coefficients), to constitute total Hamiltonian in the EasySpin code?

Image2.jpg (57.99 KiB) Viewed 3592 times

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In the literature article, the unique axis is chosen along magnetic Z-axis (C2‖Z) and Eq(3) are used to define monoclininic part of Hamiltonian. In order to obtain Eq(4) from Eq(3), (XYZ-->ZXY) transformation should be performed, as shown in Image2(a,b). On the contrary, the unique axis is chosen along crystal yC-axis at EasySpin and this axis is parallel to molecular yM-axis (and magnetic Y-axis) for Exp.MolFrame=[0 0 0].
Q2: Can we use Eq(3) instead of Eq(4) in the EasySpin code with transformation (XYZ-->YZX) (that is Exp.MolFrame=[-90 -90 0]*pi/180))? as shown in image2(c,d)

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In the EasySpin documentation; for full Hermann-Mauguin symbols, the space group symbol defines the unique axis (P211:xC, P121:yC, P112:zC). So,
Q3: Since the unique axis changes with choosing P121 to P112, can we expect the hamiltonian to change from Eq(4) to Eq(3)? ( (4): Sys.B2=[0 value 0 0 0];Sys.B4=[0 value 0 value 0 0 0 0 0] ----> (3): Sys.B2=[0 0 0 0 value];Sys.B4=[0 0 0 0 0 0 value 0 value] )

THANKS!.

[Stefan Stoll]

The choice of molecular frame is totally up to you. Pick the choice where the Hamiltonian is easiest to specify. If you rotate the definition of your molecular frame relative to the crystal, then you have to adjust MolFrame, as you are showing. You can use the currently undocumented tool rotview to visually examine rotations.

It is always advisable to use a simple spin system (e.g. a S=1/2 with rhombic g tensor) where you can more easily check the line positions to test whether your frame orientations are as intended.

[seradır]

Thank you very much for your valuable advices.

From EasySpin Documents (https://easyspin.org/easyspin/documentation/frames.html, see Monoclinic point group at "Crystal Frame" section), the direction of unique axis depend on choosing point group (P211, P121, P112). So, Can we expect for EPR line to change when P112 (C2‖zC) changes into P121(C2‖yC)

It doesn't happen in the following ES codes:

Code: Select all

clear all; clc;

g= [2 2.02 2.52]; 
lw=10;
S=5/2;   

FieldRange=[0 700];        

Freq=9.18;               % in GHz
talfa=15; tbeta=25; tgama=0;      

Center1=[talfa tbeta tgama]*pi/180;        % tilt angles in Euler System for paramagnetic center 1
Center2=[talfa+90 tbeta tgama]*pi/180; % tilt angles in Euler System for paramagnetic center 2

Center=[Center1;Center2]; 
%======================= Define all System ==============================%
Sys=struct('S',S,'g',g,'lw',lw);
Sys.B2=[4000 0 7000 0 0];                % in MHz
Sys.B4=[0 0 0 0 0 0 0 0 0];

Exp=struct('Range',FieldRange,'mwFreq',Freq, 'Harmonic',1); % magnetic field units of mT
Exp.Mode='perpendicular';
Exp.CrystalSymmetry='P112';  % 'C2h', '16', Hermann-Mauguin:'P21/m','2/m'

Opt.Output = 'separate';  % make sure spectra are not added up
Opt.nKnots = 10;
Opt.Threshold=0.0003; % max=0.99, min=1e-4 
Opt.Transitions=[1 2;3 4]; % for out of plane  all sites --> [1 2;3 4;5 6]
Opt.Sites = [1 2];                   % for Site
%=========================================================================%
                                %---rotation crystal---%
I1=[];I2=[];
                        

CrystalOri=[];
Fangle=180;                      % final angle
step=2;
ang = 0:step:Fangle;             % rotation until final angle

                             %--- out of plane ---%
rotL = [0 1 0];                             % rotation axis of "out of plane" in lab frame
CrystalOriStart = [0 90 0]*pi/180;    % initial crystal orientation for "out of plane" with EULER angles in lab frame
CrystalOri = rotatecrystal(CrystalOriStart,rotL,ang*pi/180);   % rotate crystal for "out of plane"
Exp.CrystalOrientation = CrystalOri;
Exp.MolFrame=Center(1,:);
Bres1_op = resfields(Sys,Exp,Opt);
Exp.MolFrame=Center(2,:);
Bres2_op = resfields(Sys,Exp,Opt);

%----------------------- Angular Dependence ---------------------------%
              

figure(1)
clf
%set(gcf, 'Color', 'w');
set(gca,'LooseInset',get(gca,'TightInset'));

                  %--- out of plane ---%
hold on
plot(ang,Bres1_op/100,'r','Linewidth',2)   % dividing 100, to convert mT to kOe 
plot(ang,Bres2_op/100,'b','Linewidth',2)   % dividing 100, to convert mT to kOe 
xlabel('Angle(°)');
ylabel('Resonance Field (kOe)');
set(gca,'XTick',0:30:180)
xlim([0 Fangle])
ylim([0 FieldRange(2)/100])
title('out of plane')

Please, try to change P112 to P121 and run.

[Stefan Stoll]

Changing from P112 to P121 to P211 should change the plot - this is a bug. Thanks for reporting!

This should be fixed now in v6.0.0-dev.37 and v5.2.35.

[seradır]

I run my codes with v5.2.35. Well! Thanks.

I realized now that monoclinic unique axis choice for old version (v5.2.33):
C2h: (C2‖Z), not Y
P211: (C2‖Y)
P121: (C2‖Y)
P112: (C2‖Y)

[Stefan Stoll]

Glad it works now. Thanks for reporting the bug.