Continuous Wave and Fourier Transform Pulsed Electron Magnetic

Chapter 6

Continuous Wave and Fourier Transform Pulsed Electron Magnetic Resonance Spectroscopy in Organic—Molecular Magnetism Downloaded by UNIV MASSACHUSETTS AMHERST on October 8, 2012 | http://pubs.acs.org Publication Date: October 24, 1996 | doi: 10.1021/bk-1996-0644.ch006

Theory and Applications 1

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T. Takui , K. Sato , D. Shiomi , and K. Itoh 1

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Department of Chemistry and Department of Materials Science, Faculty of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558, Japan CW electron spin resonance/electron nuclear multiple resonance (cw-Electron Magnetic Resonance: cw-EMR) has been used to examine microscopic details of high-spin molecules and molecular spin assemblies, focusing on electronic spin/molecular structural analyses and structure-magnetism relationships in solids. This pa per presents an overview of recent developments in the rapidly growing interdisciplinary area of organic/molecular magnetism in terms of cw and FT-pulsed EMR spectroscopy. The main emphasis of this work is the spectral analysis of random orientation fine -structure ESR spectroscopy to identify molecular high-spin states with high sensitivity and to determine fine structure parameters with high precision. Some important recipes and guidelines for spectral simulation procedures are given and exemplified graphical ly. This paper discusses the potential capability of high-frequency (W-band) EMR spectroscopy in comparison with the X-band spec troscopy. This paper also deals with late breaking results from FT -pulsed ESR/ESTN (Electron Spin Transient Nutation) spectroscopy applied to high spin systems.

In the last decade organic/molecular magnetism (1-10) has become a rapidly growing multi-interdisciplinary field in the pure and applied natural sciences (1117,18-23). This is not only due to the rich variety of novel physical phenomena and properties which synthetic organomagnetic materials are anticipated to exhibit both macro- and meso-scopically, but also due to their underlying potential ap plications in future molecular-device technology and molecular quantum materials science based on both their multiple supramolecular functionality and "system" property (18-23). Among the diverse topics of organic/molecular magnetism, molecular highspin chemistry continues to underlie organic/molecular magnetism, and the i m pressive progress in molecular design and synthesis of organic and inorganic molecular materials has led to various types of organic/molecular magnets (1117). Efforts to synthesize low (zero to two)-dimensional molecular magnetic sys tems which include extremely large spins (superparamagnets and super high-spin polymeric systems), are motivated not only by the device application capability 0097-6156/96/0644-0081$15.00/0 © 1996 American Chemical Society

In Molecule-Based Magnetic Materials; Turnbull, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1996.

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MOLECULE-BASED MAGNETIC MATERIALS

of novel "system" or "soft" magnetism, but also by interest in spin manipulation chemistry and in modulating spin structures of molecular orbital (crystal orbital) bands of neutral or ionic polymeric open-shell systems. More controlled attempts to generate extremely high-spin ground states of neutral or charged (polycationic or polyanionic) organic molecular systems continue, and extremely high-spin large clusters composed of transition metal ions have emerged (11-17,24).

Downloaded by UNIV MASSACHUSETTS AMHERST on October 8, 2012 | http://pubs.acs.org Publication Date: October 24, 1996 | doi: 10.1021/bk-1996-0644.ch006

Practical Importance of Non-Oriented FS (Fine-Structure) ESR Spectroscopy in High-Spin Molecular Science In order to characterize the spin structure of open-shell components or building units of molecular magnetic systems and assemblages in microscopic details, FS (Fine-Structure) ESR spectroscopy of randomly oriented or non-oriented media is a powerful spectroscopic technique and has been frequently used. Successful anal yses of FS spectra intensify the investigation a great deal. Some fine-structure from high spin origins appears as structureless, apparently single absorption peaks subject to inhomogeneous line-broadening or exchange narrowing process, while others feature complex apparently bizzare lineshapes. Thus, a facile spectro scopic method and a practical easy-to-interpret approach are required to stim ulate work in of spin manipulation science and organic/molecular magnetism. The aim of this paper is to carry readers who are not specializing in EMR spectroscopy from a qualitative understanding of high spin FS ESR spectra to the stage where they are able to extract spin Hamiltonian parameters from FS spectra with the help of spectral simulation or directly, without simulation. The spin Hamiltonian parameters include spin quantum numbers (S), g values, zerofield splitting (ZFS) parameters (D), hyperfine splitting (HFS) parameters (A), and nuclear electric quadrupole splitting parameters (P), as given below: H = EiOB-gi-Sj

+

Sj-Dj-Sj + J ^ - S ,

+ Zj[Tj-Aj-Sj - / 3 i j - B gl

N

k

+

Tj-Pj-ij + Z k V V i k l } . < *i»

W 3

where group-theoretically allowed quartic or higher-order terms such as BSm , Sm Sn , and Sm Sn are neglected. It should be noted that these terms effect the interpretation of FS spectra if S and the spin-orbit interaction are large. The simulation procedure is not necessarily required in order to interpret the ob served FS spectra and to extract, with high accuracy, the first four parameters mentioned above, as described later. For the ESR allowed transition (AMs = ±1 and AMi = 0), the other terms contribute to the second- and higher-order cor rections in terms of perturbation theory. Because of the above point and limited space, this paper does not deal with single-crystal EMR spectroscopy, only random orientation EMR spectroscopy. In general, random orientation spectroscopy is experimentally simple, but the spectra are not easily interpreted. This is particularly the case for FS spectra of randomly oriented non-crystalline media such as organic rigid glasses. We review mostly cw FS ESR spectroscopy from random orientation, exemplifying conven tional cw X-band (~9 GHz) FS spectra. We also present cw W-band (~95 GHz) FS spectra for comparison's sake, illustrating what makes the X-band FS spectra complex and difficult to interpret. Also, we present late breaking results from FT-pulsed ESR/ESTN (Electron Spin Transient Nutation) spectroscopy applied to high spin systems, showing what this new method arouses in high spin molecular science. A new methodological advance possibly intensifies the studies of high spin systems, organic or inorgan ic, and their quantum constrained effects in low-dimensional molecular magnetic systems, semi-macroscopically reduced dimensional magnetic systems, and charged high-spin polymeric systems created through laser excitation. 2

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6. TAKUI ETAL.

CW & FT Pulsed EMR Spectroscopy in Magnetism

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Approaches to Random Orientation X-Band FS Spectral Analyses Exchange Coupled Systems and Quantum Spin Mixing. If the definition is broadly based, there are two kinds of molecular FS spectra. One arises from non-inter acting high spin states without nearby electronic states where S is a good quan tum number and no spin mixing takes place. The other arises from the exchangecoupling of spins and the resulting ESR transition fields and probabilities are interrelated between different spin states. Readers can refer to a comprehensive treatise on this issue by Bencini and Gatteschi (25). Figure 1 exemplifies the quantum spin mixing appearing in FS ESR spectra, shows typical FS ESR spectra at K-band (~25 GHz) calculated for an exchangecoupled triplet pair with the static magnetic field Bo along a given orientation, as described by the FS spin Hamiltonian, equation 1 for i = 1,2 and D i = D2. As the spin quantum mixing grows, new transitions arise with intensity borrowing and the transition fields shift appreciably. In the case of the complete mixing, the sa lient spectroscopic features arising from a quintet state and a triplet state dis appear, and the spectra resemble a two triplet states case, where there are not two independent triplets, but where singlet-quintet complete mixing takes place due to the group-theoretical symmetry requirement for a pair of equivalent Si = 1 spins and the triplet state is isolated because of symmetry requirements. (The permutation symmetry of Bose (Si = 1) particles is symmetric, leading to no mixing between the triplet and the other spin multiplets). Thus, a drastic spectral change is anticipated from complete spin quantum mixing near vanishing Jil, as illustrated in Figure 1. In X-band FS ESR spectro scopy, the transition probabilities which gain intensity when a good high-field approximation holds, as in high-frequency ESR spectroscopy, are reduced a great deal and, as a result, the intensity distribution characteristic of the high-field approximation with high spin states is changed. This decreases the practical advantage of using X-band ESR spectroscopy for the cases of quantum spin mixing. High-frequency ESR spectroscopy is desirable for the detection of spin quantum mixing in terms of the transition probability of intermediate spin states. The molecular design and fine tuning of quantum spin mixing for potential device application are current emphases of molecular magnetic science. Salient Features of FS Spectra from Non-Interacting High Spins and Spectral Simulation. FS ESR spectral analyses for isolated molecular triplet states are well established. Assuming ZFS parameters not larger than the microwave transition energy (h\)) employed at X-band and small g-anisotropy, there appear six grouptheoretically allowed resonance peaks (singularities of absorption intensity) arising from canonical orientations where resonance fields correspond to Bo oriented along the principal axes (X, Y , and Z) of the D tensor, i.e., the number of the allowed transitions is given by 2S x 3 (X,Y,Z) for an arbitrary spin, S. For |D| Bmin

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= (2g0)-i [(hv) + 4(XY + YZ + Z X ) ] ^ 2

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= (2gP)-« [(hV) - (4/3)(D + 3E )] / . 2

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Xsin 9cos + Ysin 8sin 1) (26,27). In order to understand straightforwardly the anomalous behavior of the forbidden transition |Ms>«— ->|Ms+2>, the general expression for the resonance field, Bo and transition prob ability, IMSMS+2 at an arbitrary coordinate-axis system are given explicitly ( Iwasaki, M ; Toriyama, K . , unpublished. Takui, T.; Itoh, K. Spectroscopy M, Maruzen Publishers, Tokyo, 1993; pp 452). Additional peaks due to angular anomalies corresponding to off-principal-axis orientations (Bo \ X , Y, or Z) are called, in general, off-axis extra lines (or simply extra lines). The first HFS extra line observed was in the copper HFS spectrum of copper(II)phthalocyanine in H 2 S O 4 glass (28). Physical origins of HFS extra lines have been explained by several authors (29,30) . FS extra lines have been studied extensively in terms of a higher-order per turbation treatment (27). Angular anomalies do not show up for the allowed tran sitions of the triplet state within the framework of a second-order perturbation treatment (27). Appearance of the extra lines features in FS ESR spectra arising from high spins larger than Si = 1, inevitably from half-integer spins. In terms of perturbation theory, the angular anomaly originates in second- and higher-order corrections for resonance fields. For half-integer spins, first-order terms of the the resonance field corresponding to an Ms = -1/2 «—>|Ms+l, Mi> transition. Thus, first-order treatment is not enough to generate simulated FS spectra nor to interpret observed FS spectra from spins larger than unity. Recipes for the analyses of FS extra lines and their appearance conditions have been given in detail (27). For the smaller ZFS parameters, first-order perturbation treatment has been used, for the sake of simplicity, in order to extract the ZFS parameters and g values. It turned out that most of the documented analyses based on first-order treatment of molecular high spins where 7T-7T spin-spin interactions dominate the contribution to the ZFS parameters do not lead to the appearance of FS extra lines. During the simulation procedure, readers are strongly recommended to check the appearance condition by substituting the trial ZFS parameters and the


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microwave frequency employed into the equation given in the literature (27). Whether or not extra lines appear also depends on the linewidth of a single tran sition used for the simulation. If the difference in resonance fields between extra lines and principal-axis lines is comparable to or smaller than the linewidth, the extra line will not be resolved, but asymmetry in the lineshape or intensity ano maly will be appreciable. Higher-Order Perturbation Approach. In order to reproduce overall FS spectra including low-field absorption peaks from forbidden transitions, second-order, at least, or higher-order perturbation treatments are recommended with calculation of the angular dependence of all the resonance fields and corresponding transition probabilities. Taking the Boltzmann distribution into account for the peak intensi ties of the FS spectra observed at low temperature is trivial, but sometimes nec essary even for X-band spectroscopy. When the perturbation approach is applied in order to simulate the low-field X-band FS spectra, including forbidden transitions, attention must be paid to the appearance of somewhat peculiar-looking lineshapes (e.g., out-of-phase lineshape) of the simulated spectra, which strongly indicates the possible breakdown of the perturbation approach. All the mathematical expressions required for the spectral simulation are available in analytical forms with respect to an arbitrary coordinate-axis system (27,31,32) and complete FORTRAN program software packages based on the second-order perturbation approach including HFS terms have been made avai lable by several authors for some times (33,34). The perturbation approach has been developed to third-order only in terms of FS terms (27). A program package based on the second-order perturbation approach to the spectral simu lation for an arbitrary electron spin, S and arbitrary nuclear spins, I is commer cially available, but its utility is hampered by the failure to simulate forbidden transition peaks (35). The perturbation-approach programs are efficient in terms of computation time, but their weakness is still the failure to reproduce low-field peaks in X-band FS spectra. Programs to enable the simulation of complete FS spectra should, however, still be useful for the cases of | D | transition for a half-integer high spin even in the high field approximation. The strongest cen tral peak on the high field side is attributable to the angular anomaly. The transi tion intensities for the forbidden transitions are diminished whereas the allowed transitions have gained intensity and dominate as expected, as seen in Figure 4 (bottom). In the W-band FS spectrum, the assignments for the canonical orien tations are straightforward, facilitating the determination of the spin Hamiltonian parameters with good accuracy. 3+

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Program Software Package. The exact analytical expressions are tedious to write explicitly. They are available on diskette (46) The program package gene rates the transition fields and probabilities, and eigenenergies in the principal-axis orientations of Bo for a given set of spin Hamiltonian parameters, viz., a spin quantum number S (< 4), g values, and ZFS parameters. The transition proba bilities in the principal-axis orientations are calculated by means of the "hybrid" approach mentioned above (42). Statistical Molecular Structural Fluctuation and Linewidth Variation as a Function of the Orientation of Bo. Statistical fluctuations of molecular structure show up prominently in organic rigid glasses and spectral simulations assuming random orientation do not repro-




Figure 3. Transition assignments (top) of the quartet FS spectrum of C r in a cage complex and the angular dependence (bottom) of the transition fields and intensities. 3 +


CW & FT Pulsed EMR Spectroscopy in Magnetism


TAKUI ETAL.

INTENSITY 3

Figure 4. Simulated W-band FS spectrum (top) of Cr * in the cage complex and the angular dependence (bottom) of the transition fields and intensities.



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duce observed FS spectra for this reason. The existence of geometrical isomers, conformers of high spin molecules, or various degrees of molecular clustering are the most common sources of such fluctuations. Particular absorption peaks arising from canonical orientations are subject to linebroadening in some cases. Thermally stimulated relaxation processes aroused by thermal annealing can change the ratio of the conformers or favor particular conformations if they persist during annealing of organic rigid glass states. In order to interpret the occurrence of the statistical molecular fluctuation due to the continuous distribution of conformers, structurally reinforced molecu lar design has been invoked such as bridging to suppress the angular fluctuation of dihedral angles. Large or small, rigid planar or round molecules that do not experience intermolecular clustering show fewer statistical fluctuation effects in FS ESR spectra. On the other hand, linear high spin systems or hyperbranched 7T-aryl systems are made subject to various kinds of fluctuations. Simulation Programs. In the case of linewidth variations originating in hyperfine interactions, spectral simulation procedures should incorporate the aniso tropic contribution to overall FS lineshapes. Simulation programs executing the anisotropic linewidth variation are available. They are based on both the numerical direct diagonalization (eigenenergy approach) and the higher-order perturbation treatment. Phenomenological treatments of linewidth variations are also available. A program package based on a second-order approximation for fine structure terms and first-order in hyperfine interaction terms is commercially available with some restrictions (35). Pilbrow et al. have recently developed more general theoretical treatments of linewidth variations (47). New EMR Spectroscopic Approach to Molecular High-Spin Systems: FT-Pulsed Electron Spin Transient Nutation (ESTN) Spectroscopy; Motivation With increasing spin quantum number, S, of molecular high-spin systems, the spectral density of the central regions increases rapidly (« ~S ) even if the spinspin or spin-orbit interaction is kept constant. FS ESR absorption peaks spread out in the both outlying directions of the magnetic field. The peaks appearing at outermost field lose their intensity so rapidly. This arises from the |Ms>«— -*|Ms+l> allowed transition probability, as given to zeroth-order transition pro bability for the |Ms>«—*|Ms+l> transition in the following; 2

IMSMS.I

2

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« (20Bi) | G | (l/4) [S(S+l)-Ms(Ms+l)] | or |S, Ms=0>«—*|S, Ms'=-1> transition. Therefore, even if the ESR transitions involving the | S, Ms=0> level overlap due to the small ZFS para meters, the spin quantum number S can be discriminated in the nutation spectrum by time-domain ESTN spectroscopy. Practically, the effect of the offset frequency on the nutation must be carefully considered in some cases in carrying out Boswept 2D nutation spectroscopy. For half-integer spins, S = 3/2, 5/2, • • •, the fine structure term U)D(2MS-1) to first order for allowed Ms «—• M s - l transitions vanishes for the | S , Ms=l/2>

Continuous Wave and Fourier Transform Pulsed Electron Magnetic

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