Visual EPRInteractive programs for paramagnetic resonance

The package consists of several complementary programs devoted to help researchers to

treat experimental spectra of Electron Paramagnetic Resonance, EPR, to simulate observed

spectra and their angular dependences, to obtain spectroscopic characteristics of

paramagnetic spices, and to prepare representative figures for publication.

Valentin Grachev

Visual EPR

Contents Page 1

Content

Preface 2

Definitions and notations 4

Files and their extensions 6

Spin-Hamiltonian 7

Destination of programs 8 Viewer for spectra for Windows (View_spw.exe) 8

Simulation resonance fields and EPR spectra (Fields.exe) 10

Fields-Angles-Intensities-Widths dependencies (FAIW.exe) 12

Obtaining spin-Hamiltonian parameters by fitting angular dependences

(Params.exe) 12

Interrelations of programs of the Visual EPR package 13

References 14

Make better, who can

Preface The “Visual EPR” package consists of several complementary programs devoted to help

researchers and students to treat experimental spectra of Electron Paramagnetic Resonance, EPR

or Electron Spin Resonance, ESR, to simulate observed spectra and their angular dependences, to

obtain spectroscopic characteristics, and to prepare representative figures for publication.

The programs were developed during many years in closed collaboration with experimenters in

the labs where main manpower is undergraduate and graduate students. Therefore, they have

simple and convenient interface, are flexible enough to solve most of everyday tasks, and do not

require additional programming. For instance, a change of point group symmetry, values of

electron and nuclear spins, number of equivalent centers or any parameters of spin-Hamiltonian

takes a few clicks only.

A balanced combination of exact numerical diagonalization of spin-Hamiltonian matrices and

perturbation theory allowed creating algorithms, which are fast enough to calculate spectra of the

Gd3+

or Mn2+

in a few minutes using conventional desktops and laptops. The programs have a lot

of unique useful findings inside, which help you to manage with many difficulties of spectra

treatment.

Since the first distribution of DOS versions in 1992, the programs have been successfully used in

dozen spectroscopic groups from different countries. Beginning 2005 programs for Windows

operational system (from Windows XP to Windows 7) are available.

At present, the “Visual EPR” package includes following programs designed to facilitate various

aspects of EPR spectra treatment:

Fields.exe – to calculate energy levels and resonance magnetic fields, simulate spectra,

and compare experimental and calculated angular dependencies,

Params.exe – to determine spin-Hamiltonian parameters by fitting experimental data,

View_spc.exe – to view and compare measured spectra, treat them (filtering, peak-

picking…) and collect angular dependence of resonance line positions, intensities and

widths in a file,

FAIW.exe – to represent on one plot four-dimensional table of angular dependences of

resonance magnetic field, line intensities and widths (Fields-Angles-Intensities-Widths

dependencies), to compare observed and calculated dependencies, and to prepare the

picture for publication,

Cos_Eul.exe – to find principal values and directions of principal axes of general

Cartesian and irreducible tensors of second rank.

Visual EPR

Preface Page 3

These everyday programs can accelerate experimental data treatment, enhance trustworthiness of

obtained results, improve accuracy of determined characteristics, and increase efficiency of

conducted research in laboratories, which need in characterization of magnetic properties. Due to

visual representation of calculation results, they can also be used for educational purposes.

Acknowledgement. Findings and solutions of several generations of researchers have been used

for the program development. I have a very great respect to authors of numerous publications,

which made direct or indirect influence on the program features (a short list at the end of the

tutorial cites only some of them [1,

2,

3,

4,

5,

6,

7,

8,

9,

10,

11,

12,

13,

14,

15,

16,

17,

18,

19,

20,

21,

22,

23,

24,

25,

26,

27,

28,

29,

30,

31,

32,

33,

34,

35,

36,

37,

38,

39,

40,

41,

42,

43,

44,

45,

46,

47,

48,

49,

50,

51,

52,

53,

54,

55,

56,

57,

58,

59,

60,

61,

62]).

Valentin Grachev (Valentyn Grachov)

Definitions and notations

Coordinate systems a, b, c Crystallographic coordinate system

a, b, c* Coordinate system for monoclinic crystals: c* is perpendicular to ab

plane

x, y, z Local coordinate system related to one paramagnetic center. High

symmetry crystals may have several electrically identical, but

magnetically non-equivalent centers with different coordinate systems.

For instance, x, y, z and -x, y, z if a crystal has mirror plane bc.

1, 2, 3 Coordinate system related to principal axes of g-tensor (“magnetic”

axes system)

X, Y, Z Laboratory coordinate system related to external magnetic field B

Vectors and Tensors Apq; p, q = x, y, z Cartesian components of second rank tensor of hyperfine interaction

Akq; k=0, 2; q=-k,…, k Irreducible components of second rank tensor of hyperfine interaction

B, Bp; p = x, y, z Cartesian vector of external magnetic field; mainly in SI units, mili

Tesla (or mT), sometimes in Gauss (or G) for a compatibility with

measured spectrum files

B1, B1p; p = x, y, z Cartesian vector of microwave magnetic field

bkq, ckq; Components of irreducible tensors described zero field splittings (ZFS)

k=2, 4, 6; q=-k,…, k

ekq, fkq; Components of irreducible tensors described Zeeman splittings of high

k=2, 4, 6; q=-k,…, k order (BS3 and BS

5)

gpq g-tensor. Sometimes, capital letter G is used in screen labels to

facilitate readability of subscripts: Geff is geff

ggpq Symmetrical g·g or g2 tensor

gn Nuclear g-factor

Visual EPR

Definitions and notations Page 5

I, Ip; p = x, y, z Vector of nuclear spin

J, Jpq; p, q = x, y, z Tensor of exchange interaction

Okq; q=0,…, k Irreducible tensor operators

Ωkq; q=1,…, k Irreducible tensor operators

Qpq; p, q = x, y, z Cartesian components of second rank tensor of quadrupole interaction

Qkq; k=0,2; q=-k,…, k Irreducible components of second rank tensor of quadrupole

interaction

S, Sp; p = x, y, z Vector of electron spin

Tkq; q=-k,…, k Irreducible tensor operators

Greek symbols

, , Alpha, Beta, Gamma - Euler angles for the description of magnetically

non-equivalent centers (English definition)

, , Xi, Eta, Zeta - Euler angles for the description of crystal misalignment

(German definition)

ν Microwave frequency (MHz)

µB Bohr magneton

µn Nuclear magneton

, Theta, Phi – polar and azimuthal angles characterized direction of

external magnetic fields.

Other terms ns1, ns2 numbers of states of the spin-Hamiltonian

Ms projection of electron spin on quantization axis ( sip quantum number)

Visual EPR

Definitions and notations Page 6

Files and their extensions Most files have the ASCII format. Their full description is placed in the Appendix.

.gem Output file for View_spw.exe program with experimental angular dependence

(road map). It contains angles defined directions of external magnetic field with

respect to crystal axes, resonance magnetic fields, intensities and line widths for

every EPR line.

.gep Input file for Fields.exe and Params.exe program. It contains all required

information about paramagnetic center symmetry, spin-Hamiltonian

characteristics, instrumentation parameters etc. The file can be created using the

spreadsheet in Fields.exe.

.gfm Output file of Fields.exe program with full angular dependencies of resonance

magnetic fields in three perpendicular planes - 180o degrees dependencies for zx,

xy and yz planes. FAIW.exe program can be used in order to view and compare

its content by special graphical representation of resonance magnetic fields,

intensities, line widths of EPR lines and angles characterized directions of

external magnetic field.

.grm Output file of Fields.exe program with angular dependencies of resonance

magnetic fields in three perpendicular planes - 90o degrees dependencies for zx,

xy and yz planes (road map). Input file for FAIW.exe.

.grt Output file of Fields.exe program with angular dependencies of resonance

magnetic fields in one selected plane defined by input angles. Similar file with

experimental data can be created by View_spw.exe. Input file for FAIW.exe.

.jdx Spectrum file in the format recommended by the Joint Committee on Atomic and

Molecular Physical Data Exchange (JCAMP-DX) for electron magnetic

resonance. Can be viewed and treated with the help of View_spw.exe.

.fls Spectrum file often used in computerized EPR spectrometers. Can be viewed and

treated with the help of View_spw.exe.

.dsc, .dta Bruker description and spectrum data files (BEST format). Input file for

View_spw.exe.

.par, .spc Bruker parameters and spectrum data files (binary format). Input file for

View_spw.exe.

Visual EPR

Quick start Page 7

Spin Hamiltonian

The following general spin-Hamiltonian is used in the Visual EPR programs:

( ) ( ) ( ) ( )

, 2,4,6 0,..., 1,...,

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

,

( ) ( )

0,..., 1,...,

( ) ( )

( , ) ( , )

i i q q i q q i

B p p p p p

i i p q p q p

i ik k i ij j j j j j j

n n

i k i j j j

q q i q q i

B p p p p

q p q p

H f b O c

e O f

B g S S S

S J S S A I I Q I B g I

B S B S, 2,4

.i p

Here

i, k = 1,…, 9 - electron spin numbers, j = 1,…, 99 - nucleus number;

µB – Bohr magneton, µn – nuclear magneton,

f2=1/3, f4=1/60, f6=1/1260;

B – vector of external magnetic field,

S, I – vectors of electron and nuclear spins,

g, gn – electron and nuclear g-tensors,

J, A, Q – tensors of exchange, hyperfine and quadrupole interactions;

Opq, Ωp

q – irreducible tensor operators;

bpq, cp

q – parameters of zero field splitting,

epq, fp

q – parameters of high-order Zeeman splitting (BS

3).

Visual EPR

Menu items Page 8

Destination of Programs

The aim of the Visual EPR programs is to help you to pass a whole way from measurements of

spectra to publication of physical results without losses and in shortest time. The programs cover

most aspects of spectra treatment and presentation.

Viewer for spectra for Windows (View_spw.exe)

View_spw.exe is the program developed for viewing and preliminary treatment of EPR,

ENDOR and other spectra. The program allows:

1. To browse all spectra in directory (or, selectively, EPR or ENDOR only) - it helps you in

a few seconds to find the spectrum needed;

2. To convert the spectrum from one format to another - the program recognizes several

different formats: two binary formats - byte (BRUKER) and single (WIN-EPR), two ASCII

formats - one column (Y) format with signal intensities only and two column (X and Y)

format with sweeping parameter values and intensities (the last are usually used for

graphical programs, like “ORIGIN”, “GRAPHER”,...), *.sta, *.fls and *.jdx -formats;

3. To view a spectrum with “ZOOM” along X or Y or both directions;

4. To estimate line positions (g-factor, resonance magnetic field or frequency) and distance

(splitting) between any points in the spectrum;

5. To carry out filtering of the spectrum using one of 9 filters with variable width:

convolution with Gram polynoms, Gaussian and Lorentzian, as well as fast Fourier

transformation and moving average;

6. To carry out baseline correction using smoothed line, Fourier cut of high harmonics or

manual polynom.

7. To carry out peak-peaking of the spectrum - efficient auto-peaking procedure with double

filtering recognizes both absorption and derivative shapes of resonance lines;

8. To carry out resolution enhancement for spectra in derivative form using subtraction of

unknown background

9. To carry out pipeline processing of many spectra in one folder or in a 3D spectral file.

Visual EPR

Menu Page 9

Viewer for spectra for Windows (View_spw.exe)

10. To decompose complicated spectrum with overlapped lines to separate Gaussian and

Lorentzian derivatives;

11. To estimate positions, intensities and widths of constituent lines, their effective

g-factor value or in the case of ENDOR spectrum - Larmor frequency;

12. To compare several spectra on one screen, for instance experimental and calculated

spectra;

To carry out algebraic operations with discrete spectra of different resolution:

R = A + k1*B+k2*C…;

13. To view thumbnails of all spectra in a folder and to print them on a page together with

the spectrum parameters;

14. To prepare a high quality picture for publication;

15. To edit the files with parameters of your spectra adding polar and azimuthal angles of

magnetic field direction, temperature, microwave frequency and so on;

16. To create a file with four-dimensional tables of angular dependences of resonance

magnetic field, line intensities and widths (Fields-Angles-Intensities-Widths dependences),

which can be used by Fields.exe for comparison with calculated angular dependences, and

by Params.exe for fitting angular dependencies of the spectra, i.e. to collect the positions

and intensities of resonance lines (from all peak-files) and the values of polar and azimuthal

angles (from corresponding parameter files) and automatically sort them. You can view and

treat these angular dependencies with the help of FAIW.exe program;

17. To create a file with a dependence of spectra on other parameters, which were varied at

experiments, like temperature, microwave power etc. The file can also be viewed by

FAIW.exe program.

No one known program does grant you most of these possibilities

Visual EPR

Menu items Page 10

Simulation resonance fields and EPR spectra (Fields.exe)

FIELDS_w calculates angular dependencies of resonance magnetic fields and intensities of

EPR lines for the rotation of magnetic field in any plane. The program imitates a sweep of

the static magnetic field from Bmin to Bmax. Near resonance it uses a small field steps with

cubic interpolation of energy level dependencies on magnetic field; far from resonance it

increases this step.

The program has a spreadsheet for the input of all characteristics of a paramagnetic ion or

defect (we shall call it a center) required for simulation of EPR spectra and their

dependencies:

Information about crystal structure, its space group, possible electrically equivalent,

but magnetically different centers, symmetry group of the center, Euler angles for

magnetically non-equivalent centers (if present),

Spin-Hamiltonian, electron part (number of spins, spin values, parameters of Zeeman

interactions, the parameters of zero-field splitting (crystalline field),

Interactions for exact diagonalization (exchange or strong hyperfine interactions)

S-I interactions, perturbation part (weak hyperfine interactions with isotopes with

non-zero magnetic moments – natural abundances of the isotopes are used for

calculation of relative intensities of EPR lines)

Instrumental part (microwave, frequency, initial and final orientations of the static

magnetic field relative to the coordinate system which are characterized by polar and

azimuthal angles, steps on angles, range of the field sweep, threshold level separated

allowed and forbidden transitions, temperature etc.)

Spectrum attributes (initial line width, broadening mechanisms)

The above information allows to build automatically corresponding matrices of spin-

Hamiltonian.

The input parameters can be saved in <*.gep> file for further use.

The program was designed for users of different levels. Students can use templates and

change minimal sets of Spin-Hamiltonian and instrumentation parameters. Professionals

receive nearly unrestricted possibilities for analysis and simulation of EPR spectra of real

crystals.

Visual EPR

Menu Page 11

Simulation resonance fields and EPR spectra (Fields.exe)

.

The “Step by step form” allows to obtain the following dependencies:

1. Positions of energy levels on magnetic field;

2. Differences of energy levels on magnetic field;

3. Transition intensities on magnetic field;

4. Electron Paramagnetic Resonance (EPR) spectrum shape

• on line width and line shape (Gaussian, Lorentzian and their derivatives),

• on azimuthal or polar angles,

• on any parameter of Spin-Hamiltonian,

• on microwave frequency,

• on temperature.

These dependencies are drawn on screen, written into output file and can be saved as a high

resolution picture.

The calculated wave functions of the spin-Hamiltonian can be also written into file if

required.

The “Simulation form” allows to simulate interactively resonance fields for given spin-

Hamiltonian parameters and to compare and adjust simulated and experimental spectra and

their angular dependence. This helps to a great extent to decipher complicated angular

dependencies created by several equivalent and non-equivalent centers in crystals, and to

determine spectroscopic characteristics of observed paramagnetic defects including

parameters of their spin-Hamiltonians and initial line width. The form uses two panels

allowing to treat simultaneously spectra and/or angular dependencies measured at different

conditions (for instance, at different microwave frequencies, like X- and Q-bands).

The program has a tutorial designed to illustrate capabilities of Fields.exe program for users

of different levels, which helps to build up understanding of its features.

Visual EPR

Menu items Page 12

Obtaining spin-Hamiltonian parameters by fitting angular dependences

(Params.exe)

Params.exe uses experimental angular dependencies edited with the help of FAIW.exe for

refinement of obtained spin-Hamiltonian parameters by fitting.

Fields-Angles-Intensities-Widths dependencies (FAIW.exe)

FAIW.exe is powerful tool for viewing, comparing and transformation of 2-3-4 dimensional

arrays of EPR, ENDOR or other data. It is developed mainly to represent four-dimensional

tables of angular dependences of resonance magnetic field, line intensities and widths

(Fields-Angles-Intensities-Widths dependencies) on one graph. It visualizes experimental or

calculated angular dependencies of resonance magnetic fields (EPR) or resonance

frequencies (ENDOR) and converts into special symbols the information about other

resonance line characteristics - intensity and width.

The program has large sets of symbols for the representation of experimental data and sets of

color lines for the representation of calculated angular dependencies. This allows convenient

comparison of observed and calculated dependencies (including multi-frequency EPR data),

and preparation of the graph for publication.

FAIW.exe is designed also to prepare a data file for adjustment angular dependencies with

the help of Fieds.exe and for fitting angular dependence by Params.exe using extraction and

erasing corresponding visual data on the graph instead of strings in the text file.

It allows editing angular dependence, extracting the points, what you need, from array of

experimental data measured for real crystal containing several paramagnetic dopants and

trace impurities. It can shift all points on definite angle and save the result. It helps to

exclude from experimental data those points, which are close to calculated angular

dependencies. It has many other useful visual procedures, which transform the data in the

table of the treated file. For instance, a possibility to change wrong angles in *.grt-file, to

insert or delete data for one angle, to change line intensities for one plane, to create of road

map file from three files with angular dependencies for separate planes.

It works with special ASCII files. These files are output files of View_spw.exe

(experimental angular dependencies, <*.grt> or <*.gem> ) or Fields_w.exe (calculated

angular dependencies, <*.grt> or <*.grm> ).

Visual EPR

Menu Page 13

Interrelations of programs of the Visual EPR package

View_spw.exe is the basic program, which you can use immediately after measurements for

the spectrum treatment. It prepares spectra and files with four-dimensional tables for other

programs.

View_spw.exe can be used for preparation of spectral files for Fields.exe (filtering, baseline

correction, and algebraic procedures).

View_spw.exe must be used to prepare angular dependencies of experimental spectra for

comparison with calculated dependencies with the help of Fields.exe and for refinement of

obtained spin-Hamiltonian parameters by fitting with Params.exe.

FAIW.exe can be used for editing experimental angular dependencies obtained with the help

of View_spc.exe.

View_spw.exe must be used to prepare angular dependencies of experimental spectra for

comparison with calculated dependencies.

Fields.exe must be used to prepare calculated angular dependencies for comparison with

experimental ones.

Params.exe can be used for refinement of obtained spin-Hamiltonian parameters by fitting

experimental angular dependencies. It uses angular dependencies edited with the help of

FAIW.exe.

CosEul.exe can be used for a conversion of spin-Hamiltonian parameters from Cartesian to

irreducible tensor components, as well as for evaluation of principal values and principal axes

of second rank tensors.

Visual EPR

Page 14

References 1 A. Abraham, B. Bleaney. Electron Paramagnetic Resonance of Transition Ions (Clarendon Press,

Oxford, 1970). 2 S. A. Altshuler, B. M. Kozirev. Electron Paramagnetic Resonance in Compounds of Transition Elements

(Science, Moscow, 1972; Wiley, New York, 1974). 3 V.G.Grachev. Correct expression for generalized spin-Hamiltonian for non-cubic paramagnetic centers.

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Visual EPR

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