ENDOR AIEASUHEMESTS
I N X-IRRADIATED
93
SODIUM FORMATE
Endor Measurements in X-Irradiated Sodium Formate
by R. J. Cook and D. H. Whiffen Dicision of Jfolecular Science, .Vational Physical Laboratory, Teddington, Middlesex, England (Received September 27, 1966)
Endor measurements of the sodium hyperfine coupling to the unpaired electron of the C02- radical anion trapped in irradiated sodium formate were made at 35,000 Mcps and 7 7 O K The values of the hyperfine and quadrupole coupling constants used to calculate the observed endor transitions are given. Transitions from other sodium and hydrogen nuclei were observed.
Introduction Irradiation of sodium formate gives rise to a trapped COz- radical anion which has been identified',* by its electron resonance spectrum. There was also appreciable hyperfine coupling to one sodium nucleus. A similar, but numerically different, coupling to a sodium nucleus was found3 when COz- was prepared by depositing sodium on the surface of solid carbon dioxide. It was thought interesting to observe the endor transitions in sodium formate to investigate the sodium quadrupole coupling and also to check the relative signs of the principal components of the sodium hyperfine tensor. The previous electron resonance data suggested that there was cylindrical symmetry to the sodium hyperfine coupling tensor, but the endor results showed this to be not completely correct. Results The anhydrous sodium formate was irradiated with X-rays to produce the COz- radical anion. The endor measurements were made at 77°K and at 35,000 llcps as previously de~cribed.~ giving four elecSodium-23 has a nuclear spin of tron resonance lines. In the presence of quadrupole coupling there are six distinct endor transition frequencies for a given direction of the magnetic field. The quadrupole coupling (0.3 AIcps) is much less than the hyperfine coupling, a (25 filcps), and the coupling of the sodium nucleus to the field ( U N ~= 14 3Icps). There are thus two groups of three transitions, one group given approximately by ( a / 2 ) u N a which occur between 24 and 29 AIcps and the second group given approximately by ( a / 2 ) - uxa which occur below 5 31cps. Only the higher frequency transitions were
+
systematically studied as these were the more intense. The low-frequency transitions have been observed in this material but are somewhat weaker in intensity.5 When the hyperfine coupling is of the order of the nuclear coupling to the field, then the energy levels corresponding to the low-frequency endor transitions ( M S= +'/z) become sufficiently mixed so that the normal selection rule A M I = 1 no longer holds. Under these conditions there are noJv six allowed transitions instead of the three allowed under the selection rule AM, = 1. Five of these transitions are shown in Figure 1 for a favorable crystal orientation. All the measurements reported here were made by observing only the high-frequency endor transitions, since the second-order corrections to the transition frequencies were of the order of a few kilocycles per second, which was less than the experimental errors. A given endor transition will only be observed if an electron resonance transition is saturated which connects one of the energy levels involved in the endor transition. Thus if either the high- or low-field electron lines (XI= =k3/2) are saturated, then only one endor transition will be observed on each. However, if either of the center electron lines ( J I I = =t1/2) are saturated, then two endor transitions will be observed on each line. These frequencies for the center lines will be identical apart from the small change in the (1) D. W. Ovenall and D. H. Whiffen, Mol. P h y s . , 4 , 135 (1961). ( 2 ) P. W. Atkins, N. Keen, and M. C. R. Symons, J . Chem. Soc., 2873 (1962).
(3) J. E. Bennett, B. Mile, and H. Thomas, Trans. Faraday SOC.,61, 2357 (1965). (4) R . J. Cook, J . Sci. Instr., 4 3 , 548 (1966). ( 5 ) D. H. Whiffen, Mol. Phys., 10, 595 (1966).
Volume 7 1 , N u m b e r 1
J a n u a r y 1967
R. J. COOKAND D. H. WHIFFEN
94
k&
0 = 90"
29
8.0 to 90" -Calculated 0 CkerHtd at E S R line
'N, \
II
at E S R lines U 6 O I X Observed ot E S R line III 0 Observed
4
I"
1 ! 4 '
I
1.6
I 1.8
" 2.0
'
21.2
I
2.4 Ucls
Figure 1. Five of the six possible transitions observed for the M. = + 1 / 2 energy levels when the quadrupole coupling gives considerable mixing of the energy levels; second-derivative presentation. Figure 3. Calculated and observed endor transition frequencies for 9 = 90' and e = 0-90".
29L
ILL-.
25 I
25 3
25 5
257
25 9
// 251
I
'
U
' 22 3
'
22 5
257
L 2 5 9 Mc/S
W
25
-Calculated o Cberved at E.S.R. line
Figure 2. Sodium-23 endor transitions observed while saturating electron resonance transitions I-IT in turn; first-derivative presentation.
II
E SR
lines II L X Observed at E S R. line IU
,@
Observed at
m
Angle @-+
nuclear coupling to the field (0.01 Mcps) as the field is changed from one electron line to the next. Figure 2 shows the endor transitions observed while saturating each of the electron lines in turn. The lines are numbered I-IV, where I is the highest frequency or low-field electron line. The relative sign of the hyperfine and quadrupole coupling can be obtained4 from a knowledge of whether the highest or lowest frequency endor trarisitlon is observed while saturating the lowfield electron line. The J o u T of ~ Physical ~ ~ Chemistry
Figure 4. Calculated and observed endor transition frequencies for e = 8.5' and 9 = 0-90'.
The endor transitions were observed by saturating each of the center electron resonance lines ( M I = + '/2) in turn for a range of crystal directions. All of the endor transitions were corrected to the same value of the nuclear coupling to the field, as if they occurred at the same magnetic field. The observed frequencies are plotted as a function of crystal orientation in
ENDOR MEASUREMENTS IN X-IRRADIATED SODIUM FORMATE
95
cylindrically symmetric to within 300 kcps. The principal directions of all three tensors are given in Table 11. The new values of the A and g tensors are within the experimental errors of the earlier determination at room temperature. .-8 .-+nl
25
t-' $
x
0
6
Table I1 : Principal Values and Direction Cosines of the g, A, and P Tensors Given in the a(y), 6(z), and c*(z) Axis System
-Calculated 0 Observed a t E.S.R line
C
Observed a t E.S.R line
Linewidth 24
Principal valuea (77OK) -A, MCPB-
a
Direction coaines b
28.12f0.02 22.69 22.39
0 0.798 -0.602
1 0 0
0 0.602 0,798
0 0.156 0.988
1 0 0
0 0.988 -0.156
0 0,968 -0.250
1 0 0
0 0.250 0.968
C*
I
H,at
x
6'to
Angle o(
CC*)
-
Figure 5. Calculated and observed endor transition frequencies for a = 0-180' where the values of 8 and are obtained from tan + = tan 6O/cos 8 cos (Y and tan 8 = sin altan 6'.
+
Figures 3-5. The full lines give the calculated transition frequencies calculated from the Hamiltonian X = PHgX
+ hSAI + hIPI - (h7/27r)HI
A computer program was written to calculate the endor transition frequencies. The program was written for a crystal-fixed coordinate system with the magnetic field described by the cylindrical coordinates 8 and 4. No assumptions were made about the symmetry of the g, A , and P tensors or the directions of these. The program assembled the 8 X 8 matrix from trial values of the elements of the g, A , and P tensors. This was then solved to give the energy levels, endor transition frequencies, and g factors. For directions where the 8 X 8 matrix became imaginary, the complete 16 X 16 matrix was solved. The input parameters were then varied to obtain the best fit for all of the observed data. The values of the elements of the tensors used to calculate the transitions of Figures 3-5 are given in Table I. The b crystal axis, which is also the twofold z axis of the COz- ion, was a principal axis of all tensors. The sodium hyperfine coupling tensor was found to be Table I: Values (Mcps) of Input Parameters Used in the Calculation of the Endor Transition Frequencies ve = 35,000 a=== 22.50 a,, = 22.58 a,, = 28.12 ary = 0.14 a,, = a,, = 0
14.044
VN-
=
p,, p,, p,, p,,
= 0.065 = 0.250
P,,
=
-0.340
= -0.030 = PZ, = 0
-P,
Mcp-
-0.33rtO.01 0.07 0.26 2.0019 f 0.0001 1.9980 2.0034
From the diagram (Figure 6) of the undamaged formate lattice it can be seen that there are many protons surrounding a particular formate molecule. I t is these protons that give rise to unresolved hyperfine interactions in the electron resonance causing the lines to be about 10 Mcps wide. The endor transitions for these weakly coupled protons are shown in Figure 7, where it can be seen that there are at least eight weakly coupled protons in the upper part of the figure. The high degree of resolution obtainable in endor measurements is illustrated in the lower part of Figure 7 where the magnetic field is rotated by only lo. Four of the endor transitions have been split into two since the field is no longer perpendicular to the twofold symmetry axis of the monoclinic crystal. From the endor transitions that do not split, one can see which ones lie on the symmetry plane of the COz- radical anion. Similar endor transitions were observed in the region of 14 Mcps where the unresolved hyperfine interactions of the other sodium nuclei were observed. Sodium-23 endor transitions have also been observed at room temperature as shown in Figure 8, although the signal-to-noise ratio is not good.
Discussion The details of Figures 3-5 make it certain that all of the principal elements of the sodium hyperfine coupling tensor have the same sign, presumably positive because the unpaired electron occupied, in part, the 3s Volume 71, Number 1 January 1967
R. J. COOKAND D. H. WHIFFEN
96
0 “rwh
eC
D
~
~
9-
e %diu”
Figure 8. Sodium-23 endor transitions observed a t 300%; aemndderivative presentation; dillerent orientation from that of Figure 2.
Figure 6. Part of a plane of the formate lattiee.
hb*L&.a’d&aLdo
w
2+&i%%dd*
Figure 7. Proton endor tramitions near the proton nuclear magnetic m n a n c e frequency of 52.96 Mcps; secondderivative presentation.
sodium and +1.7, -0.85, and -0.85 Mcps for the next nearest sodium. The values calculated for the sodium adjacent to the oxygen atoms agree best with the observed values of +3.72, -1.71, and -2.01 Mcps, indicating that this is probably the one giving rise to the hypefine interaction of 25 Mcps. The quadrupole tensor is very anisotropic and its principal directions are not the same as those of the sodium coupling tensor, showing that one must include all electrons and not solely the unpaired electron in any computations. The negative coupling for the z direction is that which is to be expected for excess negative charge on this axis and a positive quadrupole moment for Na”. This work shows that the endor technique, especially that described in ref 4, is able to obtain accurate hyperfine and quadrupole tensors of such a system without excessive difficulty. Aclcnowledgmenls. The authors wish to thank Miss
S. King for assistance with the computer program and orbit.al of the Na+ ion. The departure fmm cylindrical symmetry is very small, only 300 kcps. The crystal structure6 and Figure 6 show one sodium atom adjacent to the oxygens of the Cot- and one adjacent to the carbon atom fmm which the proton was removed. The sodium atom adjacent to the oxygen atoms is the nearest one to the carbon atom of the COI-, the distances from the carbon in the undamaged molecule being 2.83 and 3.89 A, respectively. It is interesting to try to decide which of these sodium atoms give rise to this large hypefine coupling of 25 Mcps. If one uses these distances and the spin populations obtainable from ref 1 and performs a McConnell and Strathdee’ type of calculation for the complete u system of the Cotradical, one can calculate the anisotropic coupling arising fmm each of these two sodium atoms. The calculated values for the components of the anisotropic tensor are +4.0, -1.9, and -2.1 Mcps for the nearest
MissR. Colton for identifying the crystal axes.
Discussion H. SILLESCW (University of California, Los Angela). (1) Did you find a t the Larmor frequency of Na” the “distant” endor linea which are reported by John Lambe for other substanm? (2) The quadrupole splitting of the nmr of Nays would give the quadrupole tensor at the distant Na+ in HCOtNa. A eomparison with your endor width would perhaps give informstion about the position of the Naf ion which makes the hyperfine coupling. D. H. WHIPFEN. Figure 7 of the paper shows the “semidistant” proton transitions hut the spectrum is featureless at the exact pmton m n a n c e frequency probably hecailse the truly distant pmtons have too slow a relaxation to m p o n d to the 87-cps modulation. A many-line spectrum of this type WVLLS also Observed near 14 Mcps, the sodium raonance frequency, hut it
(6) W.H.Zsehariassn. J . Am. C h m . .%.. 62. 1011 (1940). (7) H. M. McCannell and J. Strathdes. Mol. Phyd.. 2. 129 (1959).
