J. Phys. Chem. 1983, 87,2509-2512
2509
Elevation of Copper Nuclear Quadrupole Coupling In Thio Complexes by Completion of the Coordination Sphere Deborah L. Llczwek, R. Linn BeHord,' Department of Chemlshy, Unlverslty of Illlnols, Urbana, Illlnols 6 180 1
John R. Pilbrow,t and James S. Hyde National Biomedical ESR Center, Medicel College of Wlsconsln, Mllwaukee, Wisconsin 53233 (Recelved: March 17, 1982; In Final Form: November 29, 1982)
Frozen solutions of %u(dtc),, bis(diethyldithiocarbamato)copper(II), show highly solvent-dependentelectron paramagnetic resonance spectra at 35,9.5, and 3.7 GHz. The general increase of line width with frequency reveals the effecta of g strain and the value of low-frequency EPR spectroscopy for frozen solutions. Simultaneous computer simulations of both the 9.5- and 3.7-GHz spectra were required for accurate spin-Hamiltonian parameters. Axial coordination by pyridine increases the copper nuclear quadrupole coupling interaction by an order of magnitude, to e2qQ/h= 86 MHz. The principal nuclear quadrupole coupling constant for all copper(I1) compounds shows consistent behavior, increasing with symmetry of the coordination sphere, and pointing to a strong contribution of ligand charges to the effective field gradients.
Experiments Introduction Isotopically pure 8 3 C ~ ( d t was ~ ) 2 prepared as before.'^^ Nuclear quadrupole coupling (NQC) of nuclei a t paraSolutions in reagent-grade pyridine were prepared in magnetic sites can be measured by careful electron paravarious concentrations sealed into fused quartz tubes for magnetic resonance (EPR) experiments on oriented dilute EPR studies. There was no appreciable concentration single ~rystalsl-~ and, in favorable cases, on powders on dependence of the EPR spectra. Therefore, spectra of the frozen solution^.^^ White and Belford2 and the group of more concentrated specimens ( 0.001 M) were selected deBoerl0have collected NQC data on a number of 'Wu(I1) for analysis. complexes having two or more sulfur ligands. These Three spectrometers were employed-the E-9 and E-15 complexes have NQC constants in the range 6 I e2qQ I Varian systems in the University of Illinois Molecular 38 MHz. In contrast, NQC data on a variety of four- to Spectroscopy Laboratory operating at -9.5 and -35 GHz, six-coordinate @Cu(II)complexes with oxygen ligands show respectively, and an S-band system, operating at 3.7 GHz, quadrupole coupling constants in the range 38 I e2qQ I built at the Medical College of Wisconsin and consisting 150 MHz?r4 Within the latter (oxygen) group, there is an of a Varian Century series EPR spectrometer fitted with excellent correlation with geometry, square-planar systems a low-frequency microwave bridge and cavity of local dehaving the smallest values of e2qQ and very symmetric systems (octahedral or tetrahedral), the l a r g e ~ t . ~ ~ ~ Jsign ~ ~and ' ~ construction. All samples were quickly frozen by immersion in liquid Within the former (sulfur) group, there is also some cornitrogen. For S-band experiments, samples were kept relation, but it is less clear because the entire range of immersed in a liquid nitrogen quartz Dewar flask passing values on record is much narrower. The largest e2qQvalue through the cavity; bubbling had little effect on the tuning. is that for the complex with the highest coordination For X-band experiments, samples were held in a similar number-copper(I1) in zinc bis(N,N-diethyldithioflask or in a cold nitrogen stream in the standard Varian carbamate) crystals, in which molecules are associated so variable-temperature apparatus. For Q-band experiments, that a chelating sulfur atom of one molecule also coordithe cavity was held just in contact with the liquid nitrogen nates in an axial position to the Cu atom of a neighbor. surface in a Dewar container. We believe that Cu(I1) NQC constants contain substantial ligand contributions, and that axial ligation (which inSimulations creases negative charge density along the z axis) augments The EPR powder simulations utilized program QPOW, the metal d-shell contribution to eq. Accordingly Belford which has been described briefly by Nilges and Beland Duan8s9demonstrated, by careful simulation analysis ford."J3J4 It employs some of the features of earlier of X-band EPR spectra of frozen solutions of copper(I1) /3-ketoenolates in coordinating solvents, that the additional (1)So,H.; Belford, R. L. J. Am. Chem. SOC. 1969, 91, 2392. strong axial ligand field greatly increases the quadrupole (2)White, L. K.; Belford, R. L. J . Am. Chem. SOC. 1976, 98, 4428. coupling constant for 63Cu. For pyridine, e2qQ is raised (3)So, H.,Ph.D. Thesis, University of Illinois, Urbana, IL, 1970. by about 70 MHz. It was our expectation that a similar (4)White, L. K., Ph.D. Thesis, University of Illinois, Urbana, IL,1975. (5)Bleaney, B. Phil. Mag. 1951,42, 441. increase would obtain in the case of the planar thio che(6)Attanasio, D. J.Magn. Reson. 1977,26, 81. Attanasio, D.; Desay, lates. Therefore, we have studied a representative G.; Fares, V. J. Chem. Soc., Dalton Trans 1979, I, 28. Attanasio, D.; square-planar CuS4 complex, copper(I1) biddiethyldiGardini, M. J. Magn. Reson. 1978, 32, 411. (7)Rollman, L. D.; Chan, S. I. J. Chem. Phys. 1969,50, 3416. thiocarbamate) P C u (dtc),, Figure l),in frozen solutions (8) Duan, D.; Belford, R. L. J. Magn. Reson. 1978,29, 293. and here report the results, which turned out to be in (9)Duan, D., B.S. Thesis, University of Illinois, Urbana, IL, 1976. general accord with our predictions. (10) Keijzers, C. P.; van der Meer, P. L. A. C. M.; de Boer, E. Mol.
-
'On sabbatical leave, 1979,from Physics Department, Monash University, Clayton, Victoria, Australia 3168.
Phys. 1975, 6, 1733. Keijzers, C. P.; de Boer, E. Ibid. 1975, 6,1743. (11)Belford, R. L. International ESR Symposium, Royal Dutch Chemical Society and the Chemical Society, Nijmegen, Holland, Aug, 1977.
O022-3654/83/2087-2509$0 1.5010 0 1983 American Chemical Society
2510
Liczwek et al.
The Journal of Physical Chemistry, Vol. 87, No. 14, 1983
Flgure 1. Representation of the square-planar Cu(dtc),, bis(N,Ndiethyldithiocarbamate)copper(I I).
1411
EXPERIMENTAL
0
BAND I
2.8
I
I
I
I
11.6
11.8
129
12.2
12-4
r
X BAND
I
I
I
I
2.8
29
50
31
IL
32
I
I
I
1
3,3 3.4
Figure 3. X-band spectrum of e3Cu(dtc),in pyridine. Lower scan is the experimental spectrum. Upper scan is the computer-simulated spectrum. Frequency 9.1077 GHz, gain 320, 10 mW power, 5-G field modulation. The spin-tiamittonian parametersare listed in Table I. The weaker perpendicular features between 3.14 and 3.27 kG are the most sensitive to quadrupole coupling.
12-6
rL
I
2.9 30 3.1 32 MAGNETIC FIELD ( k G )
34
33
increase accuracy, improve efficiency, and remove restrictions. The version used in this study results from further modifications by several c o n t r i b u t o r ~ . ~ J Since ~J~~~ QPOW will be described in some detail,lg we give here only a brief synopsis of its function. QPOW accepts line shape, line-width matrix, microwave frequency, nuclear g factor, and spin-Hamiltonian matrices for electronic Zeeman, nuclear quadrupole, and hyperfie coupling for each of two isotopes with specified abundances. Principal axes of g, A, and P matrices are related by specified sets of Euler angles. For each magnetic field orientation (ej,@ on a coarse angular grid, the spin-Hamiltonian (eq 1)is diag% = P,B*gS - g,P,B.I
+ h(1-ASS+ 1.P.I)
(1)
onalized; transition fields (Bkj)are calculated from the energy eigenvalues via the first-order frequency-shift perturbation formula.21 Peak transition intensities (Jkl) are calculated from the eigenvectors, proper allowances being made for (a) all possible orientations of the oscillating magnetic field vector, (b) spatial variation of the g factor in the direction of the oscillating field,22and (c) integrated intensity variation with orientation accompanying the transformation from J ( Y ) J(B).'3323 Bkj, Jk;,and line width wkj are then interpolated on other intermediate orientations to increase the sample density, each line is spread into a band, a two-dimensional Gaussian quadrature is carried out on the intensity for each field intensity, a weighted average over isotopes is computed, and the resulting spectrum is scaled and plotted. Parameters are adjusted after comparative inspection of the simulated and experimental spectra, and the process is repeated until the
-
1
$0
1.1
1.2
MAGNETIC
1.3
1
1
)4
1.5
FIELD (kG)
Figure 2. Experimental spectra for Cu(dtc), frozen in pyridine, pure %u isotope. The top scan is a @band fkst4erhrathre EPR spectrum: the bottom scan is a S-band first-derhrathre spectrum: and the center scan is an X-band spectrum.
programs of Pilbrow,15J6White,**" and Northern,ls but re-formulates the problem and uses a variety of tactics to (12) White, L. K.; Belford, R. L. Chem. Phys. Lett. 1976, 37, 553. (13) Nilges, M. J. Ph.D. Thesis, University of Illinois, Urbana, IL, 1978. (14)Belford, R. L.; Nilges, M. J. "Computer Simulation of EPR Powder Spectra", Symposium on EPR Spectroscopy 21st Rocky Mountain Conference on Analytical Chemistry, Denver, CO, Aug, 1979. (15) Pilbrow, J. R.; Winfield, M. E. Mol. Phys. 1973,25, 1073. (16) Toy, A. D.; Chaston, S. H. H.; Pilbrow, J. R. Znorg. Chem. 1971, 10,2219.
(17) Albanese, N. F. A.; Chasteen, N. D. J. Phys. Chem. 1971,82,910. (18) Northern, T. M. Ph.D. Thesis, University of Illinois, Urbana, IL, 1976. (19) Altman, T. E.; Belford, R. L.; Maurice, A. M., to be published. Cf. Ph.D. Theses of Altman, T. E. (1981) and Maurice, A. M. (1982), University of Illinois, Urbana. (20) Weil, J. A.; Huang, C. Y., private communication. (21) Belford, R. L.; Davis, P. H.; Belford, G. G.; Lenhardt, T. M. ACS Symp. Ser. 1974, No. 40, 5. (22) Pilbrow, J. R. Mol. Phys. 1969, 16, 307. (23) Aaaa, R.; Vanngard, T. J . Magn. Reson. 1975,19, 308.
The Journal of Physical Chemistry, Vol. 87, No. 14, 1983
Cu(I1) NQC in Thio Complexes
2511
TABLE I: EPR Parameters for Frozen Solutions of Cu(dtc), in Pyridine at 7 7 K
4E X PE R I ME NTAL
1.0
1.1
1.2
1.3
1.4
1.5
MAGNETIC FIELD (kG)
Figure 4. S-band spectrum of '%u(dtc), in pyridine. The top scan Is experimental spectrum. The bottom scan is computer-simulated spectrum. Frequency 3.726 GHz, gain 160, M b attenuation, 5 0 fleld modulation. The spin Hamiltonian parameters are listed In Table I. The quadrupole coupling effects occur only in the shape of the spectrum between 1.23 and 1.32 kG.
operator is satisfied. That is, we employ an interative fit with human judgment in the feedback loop. For this study, we restrained all parameters of the spin Hamiltonian to be the same for all microwave frequencies.
Results Figure 2 compares experimental spectra for all three microwave frequencies, and Figures 3 and 4 compare simulated with experimental spectra for X-band or S-band frequency, respectively. The parameters of best fit, subjectively judged, are listed in Table I. Superhyperfine splitting is unresolvable. Discussion The Need for Multifrequency Spectroscopy. Even though the nuclear Zeeman mechanism causes secondary (AmI = fl) and tertiary (Am, = f 2 ) hyperfine transitions, which are sensitive to nuclear quadrupole c ~ u p l i n gto ,~ become quite strong and so makes high field and frequency (e.g., Q band) the best choice for many quadrupole coupling ~ t u d i e s , l - ~ Jthe ~ J present ~ , ~ ~ work required us to go in the opposite direction-low field (X to S band). The reason is that, as is the case for many glasses or frozen solution^,^ g-strain broadening-the spread of g factors caused by a distribution of active site environments in the sample-destroys the necessary resolution of hyperfine features at the higher fields.24 In the present case, we obtained rather poor experimental spectra characterized by broad components at Q band and could derive no information from them except for a confirmation of gll,All, g,, and A,. Both X-band and S-band spectra provided sufficient resolution to show appreciable quadrupole coupling effects in the perpendicular region. The line widths are considerably smaller at both frequencies than at Q band and are somewhat smaller at the lowest frequency. This case displays, particularly at S band, quite noticeable dependence of line width upon mI, which Froncisz and Hyde show can result from the interplay among the ~~
(24) Froncisz, W.; Hyde, J. S.J. Chem. Phys. 1980, 74, 3123. (25) Rose, M. E. 'Elementary Theory of Angular Momentum";Wiley: New York, 1957. (26) Belford, R. L. 'Abstracts of Papers", 169th National Meeting of the American Chemical Society, Philadelphia, PA, April, 1975; American Chemical Society: Washington, DC, 1975; INOR 86.
axis
g .
A/MHz
W O / Cll CZI P/MHzC MHz MHz MHz
ea
6 -7.17 9.6 0 0 f 6 -7.67 10.6 0 0 z * 10 +14.33 12.3 4.7 0.84 0.9 Euler Angle,b deg LY 0 0 P 1 . 5 f 0.5 6 f 2 7 0 0 a Bands are Lorentzian with line width W = half-width at half-height. W z W x z l X z+ WyzZYzt WzzZzz,l's being direction cosines between B and principal axes of g matrix. Wlz (WZo))'+ Cl~Z(mz)z + CzIzuzt eC,Cz(mI)u, where ( m z ) is the average nuclear spin orientational quantum number for the transition; see ref 24. Euler angles follow the convention of Rose (ref25); i.e., to find principai axes for new frame, rotate about k b j pf,angle p , sending 1 int2 lower half of sphere, to get ( 1 ' J , ). The rotatetbguik', as the first rotation was done, by angle 7 to get ( i " J ' , k ' ) , QD = 3Pz/2 = e2qQ/4. x y
2.030 -43 2.033 -76 2.120 -423
f
intrinsic line width and the contributions from g strain and A strain.24 In favorable cases, one can use the frequency dependence to obtain information about the correlation between A and g variations. Unfortunately in this case the analysis developed for this purpose by Froncisz and Hyde cannot be applied because the experimental line shapes are not Gaussian, as required for the analysis, but are rather close to Lorentzian. Although the X band spectra displayed quadrupolar effects, and we were able to obtain approximate parameters by attempting to simulate them alone, we found the resolution insufficient to allow us to do a good job of refining the many parameters involved (18, not including C1 and C2). In this respect, the S-band data were crucial. First, test simulations show that the S-band spectra are influenced by the quadrupolar terms. Second, there is overlap between parallel and perpendicular features in both bands, but since it occurs in different manners (see Figures 3 and 4), any confusion resulting from the overlap is minimized. Third, the comparison of spectra at the two or more fields makes it much easier for one to detect and measure angles of noncoincidence between the axis frames for the g, A, and P matrices. In this case, we had to allow noncoincidence to fit the two bands simultaneously. There is no )~ reason to expect the pyridine-solvated C ~ ( d t cmolecule to be highly symmetrical, and it is not surprising that principal axes of the various matrices are somewhat misaligned. Quadrupole Coupling and Solvate Structure. The Cu(dtc), molecule in frozen pyridine has a spectrum quite unlike that in frozen noncoordinating aromatic solvents2' and also very different from the powdered dilute crystals in N i ( d t ~ or ) ~Z n ( d t ~hosts. )~ There is no indication of multiple sets of lines corresponding to different chemical species in solution. The discernible parallel features are reasonably sharp (-4 G). All these observations strongly imply that we are seeing a single kind of specific solvate molecule. The chelate molecule is coordinated axially by either one or two molecules of pyridine. Clearly, the prediction that axial solvation would elevate quadrupole coupling of planar copper thio complexes is strongly confirmed. In this case, pyridine coordination has raised e2qQ tenfold-from ca. 8.4 MHz2v4to ca. 84 MHz, similar to values we have found for copper bidketoeno(27) Liczwek, D. L., Ph.D. Thesis, University of Illinois, Urbana, IL, 1981.
2512
J. Php. Chem. 1983, 87, 2512-2525
lates) which are solvated to become 5 - ~ o o r d i n a t e . ~ ~ ~pansion, ~~*~~ or weakening of the planar complex, that any such The conference abstract literature gives a preview of one disturbance should reduce the (negative) contribution of other studyB with similar results-Cu(I1) doped into zinc the equatorial ligand system to e2qQ, and that any such bis(xanthine)pyridine single crystals. Here, a preliminary reduction ought to be greater for thio ligands, which contribute much more heavily to e2qQ. The observation that perturbation analysis of AmI # 0 transitions suggested e2qQ = 89 f 6 M H Z . ~ ~ axial ligation elevates e2qQabout 20% more for a thio than for an oxo chelate is therefore not at all surprising and does For the present data, a very simple model suffices for their interpretation. Let us regard the principal electric not necessarily indicate the thio solvate either to be field gradient at the copper nucleus to be a sum of constronger or to have more axial ligands. tributions from the ligands and the metal valence shell and Conclusions write e2qQ(solvate) = e2?Q(complex) + ne2qQ(axial ligands), where n (= 1or 2) IS the axial coordination number. Enough exact information content is provided by augOne may estimate e2qQsolvate from White and Belford’s menting X-band with S-band EPR spectra to permit good measurement2i4in the N i ( d t ~host, ) ~ where there is no axial determination of Zeeman, hyperfine, and nuclear quadcoordination; e2q(complex) = 8.4 MHz. So, Belford, and rupole coupling matrices by computer simulation of spectra and Dums measured e2qQfor N ~ r t h e r n , l * ~and J &Belford ~ of frozen solutions of C ~ ( d t c in ) ~pyridine. A specific solvate molecule, probably Cu(dtc),.Py, is indicated, with C ~ ( a c a cin ) ~Pd(acad2and in frozen pyridine, respectively, getting a difference of ca. 62 MHz. That is, nq(axia1 py) a quadrupole coupling constant that is more than twice for Cu(dtc),, = 1.2nq(axial py) for Cu(acac)2 We have no as large as the largest value that is recorded in the regular reliable information on which to assess the axial coordiliterature for any copper-sulfur complex. The result is in nation numbers for the two molecules. Supposing them line with predictions carried over from planar CuOI centers to be the same, one would conclude pyridine to be a with and without axial adducts and points to substantial somewhat more effective axial ligand for Cu(dtc)* (and, ligand contributions to electric field gradients at Cu(I1) presumably, other planar Cu(I1) thio chelates) than for centers. C u ( a ~ a c(and, ) ~ presumably, other planar Cu(I1) oxo cheAcknowiedgment. This work was supported by grants lates). One must remember, however, that axial ligation from the National Science Foundation Quantum Chemis almost certainly accompanied by some distortion, existry Program (University of Illinois) and National Institutes of Health Grant No. 5-P41-RR01008 (National (28) Northern, T. M.; Belford, R. L.; Duan, D. C., EPR Lecture No. Biomedical ESR Center at the Medical College of Wis4,6th International Symposium on Magnetic Resonance, Banff, Alberta, Canada, May, 1977. consin). (29) Attanasio, D.; Tomlinson, A. A. G. Abstracts of the 6th InternaRegistry No. Bis(diethyldithiocarbamato)copper(II), 13681tional SvmDosium on Magnetic Resonance ISMAR, Banff, Alberta, 87-3; pyridine, 110-86-1; copper-63, 14191-84-5. Canada,-May, 1977, p 233.-
Elementary Methods for the Evaluation of Electrostatic Potentials in Ionic Crystals Howard Coker Department of Chemistry, Universtfy of S o h Dakota, Vermiiiion, South Dakota 57069 (Received: October 1, 1982; I n Final Form: November 1. 1982)
A new and elementary method for the calculation of electrostatic potentials in ionic crystals is presented. The method is applicable to crystals of any symmetry and complexity. It is denoted the method of dipolar addition since it involves an arbitrary pairing of the charges of the unit cell into dipoles. The rate of convergence is rapid with an accuracy suitable for most purposes achieved on the addition of three shells around a central unit cell. The traditional direct-summation methods of Evjen and Frank have been modified and extended.
Because of the success of the Born model, the determination of the Madelung energies of ionic crystals continues to be an important problem in crystal physics. The starting point for these calculations is the presumption that the charge distributions within ionic crystals may be adequately represented by nonoverlapping, spherical, charge distributions. The spherical charge distributions are replaced by point charges in most methods for the evaluation of the potentials and self-potentials. This may be done since a point charge and a spherical charge distribution both impress the same potential at points lying outside the spherical charge distribution. Since the potential at a point within an array of point charges is simply a sum of reciprocal distances, properly 0022-3654/83/2087-25 12$07.50/0
signed and scaled for charge, one might think that the electrostatic potentials appropriate to equilibrium macroscopic crystals could always be obtained in a direct and elementary fashion. However, this did not seem to be the case, and a general direct-summation method was not believed to exist.l The direct-summation methods of Evjen2 and Frank3 and the newer method of Calara and Miller4 can only be used for special cases. The problem is not the slow rate of convergence that obtains for the (1) M. P. Tosi, Solid State Phys., 16, 14 (1964). (2) H. M. Evjen, Phys. Reu., 39, 675 (1932). (3) F. C. Frank, Philos. Mag., 41, 1287 (1950). (4) J. V. Calara and J. D. Miller, J. Chem. Phys., 65, 843 (1976).
0 1983 American Chemical Society
