J. Phys. Chem. 1995,99, 9051-9055
9051
First-Principles Investigation of Nitrogen Nuclear Quadrupole Interactions in the RDX (C3H6N606)System Ranjit Pati, Sudha Srinivas, Tina Briere, and T. P. Das* Department of Physics, State University of New York at Albany, Albany, New York 12222
N. Sahoo Radiation Oncology Division, Albany Medical College, Albany, New York 12208
S. N. Ray Software Corporation of America, 4601 Presidents Drive, Lanham, Maryland 20706 Received: January 6, 1995; In Final Form: March 13, 1995@
Using the first-principles Hartree-Fock procedure, the nuclear quadrupole interaction parameters for I4N nuclei in the ring nitrogens of the RDX molecule are found to have the values 5.671, 5.808, and 5.839 MHz for the quadrupole coupling constants and 0.542, 0.557, and 0.562 for the asymmetry parameters, in good quantitative agreement with the corresponding experimental values 5.735,5.799, and 5.604 MHz and 0.6215, 0.6146, and 0.6024, respectively, from nuclear quadrupole resonance measurements in the single crystal. Possible reasons for the small but significant difference in trend in the theoretical and experimental nuclear quadrupole interaction parameters over the three ring nitrogen atoms are discussed. The calculated nuclear quadrupole parameters for the I4N nuclei of the three nitrogens of the three nitro groups and I7O and *H nuclei at the oxygen and hydrogen sites are also presented, with the anticipation that they will be obtained experimentally in the future for comparison with theory to obtain a more complete understanding of the electron distribution over the whole molecule than is presently possible with ring nitrogen data.
I. Introduction The material RDX, which involves the molecular system
cyclotrimethylene-trinitramine (C3H6N606) is an energetic material of substantial current interest.lS2 The explanation of its decomposition p r o ~ e d u r e ,related ~ , ~ to its explosive nature, is expected to be assisted by a thorough understanding of its electronic structure and associated properties. The properties we focus on here are on the nuclear quadrupole interactions nuclei in the nitrogen, (NQI's) of I4N, I7O, and deuteron (2H) oxygen, and hydrogen atoms in these systems. Of these, the I4N NQI's are of the greatest interest for two main reasons. First, they have been measured5 already by nuclear quadrupole resonance (NQR) for one of the two sets of three nitrogens atoms in the compound, namely, the ring nitrogens. The temperature dependence of the 14N NQI's has also been studied for these nitrogens, and these data have been used to assign5 the observed I4N nuclear quardrupole coupling constants (NQCC) to specific ring nitrogen atoms. Second, there have been extensive current eff0rts~9~ for the use of I4NNQR for the detection of explosives and controlled substances. It is, therefore, important to carry out a careful theoretical analysis to attempt to explain the observed I4N NQCC for the ring nitrogens in RDX. Additionally, it would be useful to predict the NQCC for the other three I4N nuclei as well as for the I7O and deuteron, with the hope that these could be measured in the future. Such an analysis can help us obtain an extensive check on the calculated electron distribution in this system. Section I1 will briefly present the procedure we have used, with some pertinent details that will be useful for the analysis of our results and discussion in section III. Section IV summarizes the main conclusions from our investigation and @
Abstract published in Advance ACS Absrracrs, May 1, 1995.
0022-365419512099-9051$09.0010
suggests possible additional work in the future that could enhance our current understanding of the RDX system.
11. Procedure Descriptions of the variational Hartree-Fock-Roothaan procedure8 used in the present work for the determination of electronic energy levels and wave functions are available9 extensively in the literature, including our own work on a number of condensed matter systemsI0 and large biologically important molecules" and will not be repeated here. Only a few points important for the present investigation will be described. Thus, since the present system involves an even number of electrons with zero total spin, it is sufficient to use the restricted Hartree-Fock approximationI2 with identical spatial characters for paired orbitals of opposite spin. As is customary at the present time for economy of computational effort, we have used Gaussian basis functionsl3 centered about the various atoms, either single ones or a number of them combined to represent a single basis function referred to as contracted orbitals.I4 The Gaussian set of programsI5 referred to as Gaussian 92 has been used for the present investigations. The arrangement of the atoms in the RDX (C3H6N606) molecule is shown in Figure 1, the structure being chair shaped as indicated, with three nitrogens in the ring, each one having a NO2 group attached to it. Also, the molecule has approximate, but not exact, reflection symmetry about a plane passing through atoms 2 and 4 and perpendicular to the average plane of the chair formed by atoms 1, 3, 5 , and 6. For the all-electron procedure used in the present work, we haved to deal with 21 atoms and 114 electrons. We have used as extensive basis sets as possible within the limits of practicability and studied convergence with respect to the size of the latter. One of the basis sets we have employed is the D95 basis set,I6 which 0 1995 American Chemical Society
Pati et al.
9052 J. Phys. Chem., Vol. 99, No. 22, 1995
TABLE 1: 14N Nuclear Quadrupole Coupling Constants e2a0 (MHz) in the RDX Molecule
19
t
16
t
20
I
?
b
10
Figure 1. Atomic arrangements in the RDX molecule. Numberings from 1 to 3 refer to carbon, 4 to 9 refer to nitrogen, 10 to 1.5 refer to oxygen, and 16 to 21 refer to hydrogen. involved a total of 162 basis functions with 384 Gaussian primitives. To test the convergence of our results with respect to the size of the basis set, we have uncontracted the outermost p orbitals on the carbon, nitrogen, and oxygen atoms, which led to an increase in the net size of the basis set used to 207. We have also used another extensive basis set referred to as 6-31 l g in the literature," involving a total of 213 basis functions and 420 Gaussian primitives. The result for this larger basis set, which indicate very good convergence for the field gradient tensors, will be presented in section 111. The geometry used for the atomic positions in the RDX molecule was taken from the structure'* determined by a careful analysis of neutron diffraction data in the single crystal. The field gradient tensor at a nucleus is calculated using the following expression for the component^:'^*^^
In eq 1, j and k ranging from 1 to 3 refer to the X , Y, and Z Cartesian coordinates. The coordinates R ~ and N distance RN for various nuclear charges in the molecule are referred to the nucleus under study; r, and r refer to the instantaneous coordinates and distances for the electrons with respect to the nucleus. The first term in eq 1 represents the contributions to yk from the nuclear charges, the summation refemng to the charges on all the nuclei except the one under study. The second term refers to the contributions from the electrons in the molecule, with q,urepresenting the wave functions for the occupied states in the molecules, the summation over p being carried out over all the occupied states. The tensor &k obtained in the chosen coordinate system is d i a g o n a l i ~ e d 'to ~ .give ~ ~ the the parameter q in the coupling principal components q,,, constant e2qQ being the largest component Vz,z,,with lVr,.r,l < IV,,,,l < IVr,2,1, and 7 = (Vri;, - V,,,,)/Vr,z,, the asymmetry parameter, when there is lack of axial symmetry at the nuclear site, as is the case here for all the I4N in Figure 1. A similar procedure has been used to obtain e2qQ and 7 for the oxygen and deuterium nuclei, I7O and *H, with the I6O and protons in the molecule replaced by ''0 and deuterons to obtain the e2qQ and 7 corresponding to these sites for nuclei having finite quadrupole moments. As mentioned earlier, experimental data are currently available for e2qQ and 7 only in I4N, and it is
nucleus"
D95
D95ulb
D95u2'
6-311g
exptd
4 5 6 7 8 9
5.639 5.806 5.838 1.287 1.217 1.216
5.679 5.819 5.849 1.407 1.338 1.337
5.671 5.808 5.838 1.422 1.359 1.3.59
5.686 5.852 5.883 1.406 1.343 1.343
5.735 5.799 5.604
a The numbering for the different 14N nuclei refer to the numbering in Figure 1. u l refers to uncontracted basis set for carbon and nitrogen derived from D95. u2 refers to uncontracted basis set for carbon, nitrogen, and oxygen derived from D95. d T h e assignment of the experimental result for nucleus 4 is from ref 5. No assignment has been made for nuclei 5 and 6, so the order of the entries for these two nuclei could be interchanged.
hoped that they will be available for the other nuclei in the future to compare with our predictions. It should be remarked that because we are working with the all-electron approach, the effects of the distortion of the core states on ezqQ and 7 are explicitly included. This allows Stemheimer shielding or antishielding effects to be directly included in the field gradient tensor components, obviating the need to use any Sternheimer shielding or antishielding parameters.z1
111. Results and Discussion By using the procedure outlined for the determination of the electronic wave functions and electric field gradient tensors at the nuclei, we have obtained the quadrupole coupling constants e2qQand 7 for the three ring I4N nuclei and the three peripheral I4N nuclei which are parts of the three NO2 groups. For the quadrupole moment (Q) of the I4N nucleus, we have used a cmz. This value was obtained in value22-z4of 0.015 x the literaturezzby combining the experimentally observed I4N quadrupole coupling constant in a number of small molecules with the electric field gradient at the nitrogen nuclear sites using the Hartree-Fock procedure. This value of Q(14N) has been verified23by a relativistic calculation of the coupling constant in the ground state of the nitrogen atom. The latter is spherical in the nonrelativistic approximation, but the spherical symmetry is destroyed in relativistic theory through the influence of a number of mechanisms including C a ~ i m i r , *spin-orbit, ~s~~ and Breit interactionz7effects. Our results for ezqQ and 7 for the three basis sets discussed in section I1 are presented along with the experimental results in Table 1. The notations for the various I4N nuclei correspond to the numbering in Figure 1 for the chair-shaped RDX molecule. The available experimental results5 for ring nitrogens 4,5, and 6 are also included. No results are currently available for the peripheral nitrogens. For ring nitrogen 4, the experimental assignment has been made in the literature through a consideration of the observed temperature dependences of the three ring I4N nuclei as discussed later in this section. No definitive assignment has been made for the other two ring I4N nuclei. The two other observed sets of ezqQ and 7 could therefore be applicable to either I4N nucleus 5 or 6. The results for both e2qQ and 7 for the basis sets show very good convergence with respect to the increase in flexibility of the basis sets used. The uncontracted basis sets are based on the same number of primitives as for the D95 basisI6 but with the number of p basis functions enhanced by the process of uncontracting. The reason for focusing on the p basis functions is that they make the main contributions to the electric field gradient. Considering, for instance, I4N nucleus number 4, there is an increase of only about 0.5% in ezqQ in going from the D95 basis set to D95u1, involving uncontracting the carbon and
J. Phys. Chem., Vol. 99, No. 22, 1995 9053
NQI's in the RDX (C3H6N606) System
TABLE 2: Asymmetry Parameters (11) for I4N Nuclei in the RDX Molecule nucleus" D95 D95ulb D95u2' 6-311g exptd 4 0.574 0.544 0.542 0.546 0.6215 5 0.579 0.560 0.556 0.558 0.6146 6 0.582 0.566 0.562 0.564 0.6024 7 0.976 0.702 0.693 0.718 8 0.643 0.560 0.554 0.560 9 0.623 0.560 0.554 0.560 a The numbering for the different I4N nuclei refer to the numbering in Figure 1. u l refers to uncontracted basis set for carbon and nitrogen derived from D95. 'u2 refers to uncontracted basis set for carbon, nitrogen, and oxygen derived from D95. "The assignment of the experimental result for nucleus 4 is from ref 5. No assignment has been made for nuclei 5 and 6, so the order of the entries for these two nuclei could be interchanged.
TABLE 3: Nuclear Quadrupole Coupling Constants and Asymmetry Parameter for 1 7 0 Nuclei in RDX nuclei
e2a0."MHz
na
10 11 12 13 14 15
16.154 16.277 16.102 16.037 16.142 15.993
0.851 0.975 0.807 0.835 0.784 0.831
Based on electric field gradient tensors obtained using the D95u2 basis set.
TABLE 4: Nuclear Quadrupole Coupling Constants and Asymmetry Parameter for 2Hin RDX nuclei
e2qQ,0 MHz
?la
16 17 18 19 20 21
0.255 0.199 0.208 0.216 0.220 0.217
0.039 0.058 0.062 0.028 0.039 0.055
Based on electric field gradient tensors obtained using the D95u2 basis set.
nitrogen basis orbitals. In going from D95ul to D95u2, the latter involving an uncontracted basis set for oxygen as well as for both carbon and nitrogen, there is an even smaller change of only about 0.1%. A similar convergence behavior is observed for 7 of I4N4 and indeed for e2qQ and 7 for all of six nitrogen nuclei. These convergence tests suggest that in future investigations involving I4N nuclear quadrupole interactions in large molecules, it may be sufficient to use the D95ul basis set. It also can be seen from Table 1 and Table 2 that a different basis set, 6-31 lg, gives results quite close to those from the D95ul and D95u2 basis sets, providing additional confidence regarding the accuracy of the theoretical results. Before comparing our theoretical values for e2qQ and 7 with experiment,it is important to remark on the basis for the assignment of the experimental results to N4, N5, and N6 in Tables 1 and 2. The temperature dependence5of the resonance leading to the values of e2qQ and 7 assigned to N4 in Tables 1 and 2 is significantly weaker than that for the other two resonances. Using the considerations that the temperature dependence arises from librational motionsZS in the solid and that on the basis of neutron diffraction data the principal axis corresponding to the strongest librational motion makes an angle of 34" with the N4-N8 bond axis and the disposition of the principal axes at N4, N5, and N6, it has been proposed5 that the stronger temperature dependences were associated with the latter two nitrogen nuclei. The weaker temperature dependence would thus, by these arguments, be associated with nucleus N4 and that is the basis of the assignment of e2qQ and 17 in Tables 1 and 2. However, it is
TABLE 5: Effective Charges on Different Nuclei in RDX ~~~
index
nuclei
1 2 3 4 5 6 7 8 9 10 11
C C
atomic charge
-0.196 -0.25 1 -0.206 -0.259 -0.205 -0.198 0.430 0.453 0.45 1 -0.304 -0.327
index
nuclei
12 13 14 15 16 17 18 19 20 21
0 0
0 0 H H H H H H
atomic charge
-0.291 -0.307 -0.290 -0.304 0.274 0.327 0.316 0.293 0.264 0.331
not possible with this argument to make the appropriate assignments for N5 and N6, both because, experimentally: the temperature dependences of their nuclear quadrupole resonance frequencies are nearly the same and, t h e o r e t i ~ a l l y one , ~ ~ also ~~ expects very similar temperature dependences from the orientations of the principal axes and the nature of the librational motions of the RDX molecule. From Tables 1 and 2, on comparing the calculated results with experiment, it can be seen that there is good overall agreement between the two for both e2qQ and 7. The maximum difference between theory and experiment for e2qQ is only 5%, namely in the case of N6. For 7, the maximum difference between experiment and theory is about 12%, in this case for N4. Additionally, the maximum range of variations in eZqQ from theory over the three nitrogens N4, N5, and N6 is about 3.4%, almost exactly the same as from e~periment.~The corresponding figures for 7 are also close, being 3.4% from theory and 3.1% from experiment. Thus, theory is able to explain quite well both the absolute magnitudes of e2qQ and 17 as well as their closeness for all three nitrogens for which they have been observed. A closer examination of the results in Table 1 and Table 2 reveals that even though the differences between nitrogens N4, N5, and N6 are small, there are differences in the trends in the variations of e2qQ and from theory and experiments5 In particular, for ezqQ, the lowest magnitude is seen from Table 1 to belong to N6 and the highest to N5, the corresponding ones from theory being N4 and N6, respectively. Also for 7,the lowest and highest values from experiment are for N6 and N4, respectively, the corresponding ones from theory being N4 and N6. In looking for possible reasons for these differences in trend for theory and experiment, one might consider various sources. One possibility could be uncertainties in the atomic coordinates used in our calculations. However, since the error ranges assignedl8 to the bond distances and the bond angles in the experimentally determined structure are quite small, this does not seem to be the likely source for the differences in the trends for e2qQ and 9 between theory and experiment. The main sources for the differences in trends and also the small but finite differences in magnitudes from theory and experiment seem to us could be the influence of intermolecular interactions. There is support for this expectation from the earlier investigation^^^ on the spectroscopy and energetics of RDX,where it was shown that on including the influence of neighboring molecules on the electrons in one of the molecules, through the dipole and quadrupole moments of the surrounding molecules, changes are obtained for the total energy of the central molecule of 0.8706 atomic unit, amounting to 23.69 eV. In Table 5, we have presented the results we have obtained for the charges on different atoms using the Mulliken app r o ~ i m a t i o n . The ~ ~ results are presented only for the D95u2 basis set, one of the most extensive basis sets that we have used. These charges are very similar to those from the other two basis
9054 J. Phys. Chem., Vol. 99, No. 22, 1995
sets D95ul and 6-311g. The results in Table 5 show great similarity between the charges on the nitrogens within the groups N4, N5, and N6, on the one hand, and N7, N8, and N9, on the other, although the charges for the two groups are quite different. This difference mirrors the strong difference from Tables 1 and 2 in our calculated parameters e2qQ and 7 for the two sets of I4N nuclei. This by itself would not assure one that the field gradient parameters will be about the same within each group and quite different between the groups, because e2qQ and 7 involve the anisotropies of the electron distributions over the atoms, especially around the nuclei, whereas the charges on the atoms reflect the average or isotropic component of the electron distributions. Nevertheless, the fact that the charges are very similar within each group and very different between the two groups could at least be considered as qualitatively, reflecting the nature of the similarities and differences between the overall charge distributions on the atoms, including their anisotropy. This weaker expectation is seen to be valid from the results for e2qQ and 11 in Tables 1 and 2. It is interesting to attempt a physical understanding of the signs of the charges on the various atoms in Table 5. Considering the nitrogen atoms first, the charges on the group of ring nitrogens 4, 5, and 6 are negative, while those on nitrogens 7, 8, and 9 belonging to the NO2 groups are positive. The negative charges on the first group of nitrogens could be understood from the considerations that each of these nitrogens is singly bonded to one nitrogen and two carbons and the nitrogen atom is more electronegative than carbon. Each of the nitrogens on the NO2 groups is, on the other hand, bonded to one nitrogen and two oxygens. In addition to the fact that oxygen is more electronegative than nitrogen, which would lead to electron transfer from nitrogen to oxygen, making the latter positively charged, there is another effect to consider, namely, the double-bond character of the NO bonds in the NO2 groups, which leads to a transfer of n electrons away from the nitrogen atom and would also increase the tendency for the nitrogens to be positively charged. For the oxygen atoms, on the other hand, the electronegativity difference with respect to nitrogen would lead to negative charge on oxygen, which would be opposed by double-bond formation with nitrogen. This consideration could perhaps explain the smaller magnitude of the positive charges on the oxygens as compared to the negative charges on the nitrogen in the NO2 groups. Carbon atoms 1, 2 , and 3 are each bonded to two nitrogen atoms with higher electronegativity and two hydrogen atoms with lower electronegativity. It is interesting that the carbon and nitrogen atoms on the ring, namely, (1, 2 , 3) and (4,5,6), respectively, carry negative charges of nearly equal magnitude, although carbon has lower electronegativity than nitrogen and would be expected to donate electrons to the nitrogen. This feature could be understood as a result of the carbon atoms being attached to hydrogen atoms with higher electronegativity, which in turn donate electrons to the carbon atoms, nearly balancing out the electrons donated by the carbons to nitrogens. The positive charges on hydrogen atoms 19, 20, and 21 in Table 5 can, of course, be understood from the electron donation to the more electronegative carbon atoms to which they are bonded. Thus, the trends in the distribution of charges over the atoms in the RDX, molecule appear to be in qualitative agreement with the expectations from physical and chemical considerations. The fact that the nuclear quadrupole parameters for the ring I4N are in good quantitative argument with the experimental results gives further confidence in the charge distribution obtained for the molecule. It would be helpful in this connection to have experimental data for the NQI parameters for the isotopes of oxygen and hydrogen, namely,”O and *H (deuteron),
Pati et al. which have nuclear spin s/2 and 1 and, therefore, finite quadrupole moments (whereas the abundant isotopes I6O and proton have nuclear spins 0 and l/2 and no quadrupole moments) to allow comparison with theoretical predictions of the electric field gradient tensors at these nuclei. We have presented in Tables 3 and 4 our predictions for e2qQ and 7 for these two nuclei using our calculated electronic wave functions with the extensive D95u2 basis set and the quadrupole moments -0.025 78 x and 0.002 860 x cm2 for ‘’0 and 2H, respecti~ely.~].~~ It is important to remark further about the comparison between experiment and theory for the observed e2qQ and 7 for the ring I4N nuclei before finishing this section. As remarked earlier in this section, while there is overall good quantitative agreement with experimental datas (within 5% for eZqQand 12% for v), there is a difference in the trends observed from theory and experiment (Tables 1 and 2 ) among the three ring nitrogens. It was pointed out earliers that the main source of this difference is most likely the influence of the intermolecular interactions in the solid-state system. In view of the relatively large size of the RDX molecule, it is impracticable to carry out first-principle all-electron calculations including a molecule and its relatively close neighbors. However, one could carry out a treatment similar to the one adopted for cluster calculation^^^ of NQI’s in ionic crystals. Thus, one could simulate the environment of the central RDX molecule by including the Coulomb potential due to the charges on the different atoms of each of the surrounding molecules in the Hartree-Fock calculation of the electronic structure of the central molecule. The nature of the potential produced by the point charges over the neighboring molecules would be sensitive to the latter charges and the atoms of the neighboring molecules. This nature of the intermolecular potential can thus be different at the sites of the different ring nitrogens and influence the electron distributions and therefore the field gradient tensors differently, indicating that this could explain the different trends in the nuclear qudrupole interaction parameters between the theoretical and experimental results in Tables 1 and 2 . The discussions earlier in this section about the charges in Table 5 suggest there is good reason to expect the correctness of the calculated charged for an isolated RDX molecule and that one could use them to simulate the effect of neighboring molecules on a central molecule. For accuracy, one would, however, have to carry out the calculation self-consistently, determining the charge distributions on the atoms in the central molecule iteratively, including the influence of Coulomb potential due to the surrounding molecules by making use of the calculated charges on the central molecule from the preceding cycle. This would make the calculation rather time consuming, but it would be interesting to carry out in the future to see if this allows one to explain the trends in e2qQ and 7 from N4 to N6 in Tables 1 and 2 based on the experimental assignment of the observed NQI parameters. In principle, a calculation of the intermolecular interaction could also be utilized to obtain the potential associated with the librational motion of an RDX molecule, needed to determine the corresponding librational wave functions. A knowledge of the latter would allow an analysis28of the observed temperature dependence of the NQI parameters for the ring I4N nuclei. A somewhat similar approach has been used in the literature for the vibrational averaging34 of the hyperfine interactions for the muonium atom (the light counterpart of the hydrogen atom, with the muon at the center being about one-ninth of the protons mass). The corresponding calculation envisaged for the effects of the librational motion for the RDX molecule on e2qQ and 7 would be much more time consuming but is not beyond the realm of possibility in the future.
J. Phys. Chem., Vol. 99, No. 22, 1995 9055 Lastly, we would like to remark on the possible effects on e2qQ and 7 of going beyond the Hartree-Fock approximation, that is, including many-body effects. A full-fledged calculation involving either many-body perturbation theory35 or configuration i n t e r a ~ t i o nemploying ,~~ the empty excited states of the RDX molecule, would be much too time consuming, because of the large number of electrons involved. Perhaps one can carry out a more practicable but approximate procedure of selective excitations to empty molecular orbitals involving significant amounts of characters of ring nitrogen orbitals. The results of many-body perturbation investigations in atomic systems37and of NQI’s of the excited nuclear state I9F* of the fluorine nucleus in fourth group tetrafluoride^^^ suggest that many-body effects may not be too important.
IV. Conclusion First-principle Hartree-Fock self-consistent-field investigations of the electronic structure and nuclear quadrupole interactions of the ring I4N nuclei in the RDX molecule have led to quadrupole coupling constants and asymmetry parameters in good quantitative agreement with the results of nuclear quadrupole resonance measurements. There is, however, a difference in the trends of the calculated coupling constants and asymmetry parameters over the three ring nitrogens with those obtained by the assignments made5 of the observed I4N quadrupole frequencies to the three ring nitrogens using experimental temperature-dependent data. This difference in trend between theory and experiment may be associated with intermolecular interactions that could influence the electron distributions at different I4N nuclei differently. A possible procedure for carrying out an investigation of the influence of intermolecular interactions, similar to that used for inter-ionic interactions in ionic crystals, is suggested. Nuclear qudrupole coupling constants and asymmetry parameters are presented for the I4N nuclei of the NO;! groups and for the I7O and deuteron nuclei in the molecule to compare with corresponding experimental results that may become available from future resonance measurements.
Acknowledgment. We are grateful to Dr. A. N. Garroway and Dr. J. P. Yesinowski of the Naval Research Laboratory for very helpful discussions. This research was conducted using the resources of the Comell Theory Center, which receives major funding from the National Science Foundation (NSF) and IBM Corp. and additional support from New York State and members of the Corporate Research Institute. References and Notes (1) Liebenberg, D. H.; Armstrong, R. W.; Gilman, J. J., Mater. Res. Soc. Symp. Proc. 1992, 296. (2) Shaw, Julian, NQI News Letter 1994, 1, 26. (3) Russell, T. P.; Miller, P. J.; Piermarini, G. J.; Block, S. Mater. Res. Soc. Symp. Proc. 1992, 296, 199. (4) Beard, B. C.; Sharma, J. Mater. Res. Soc. Symp. Proc. 1992,296, 189. ( 5 ) Karpowicz, R. J.; Brill, T. B. J . Phys. Chem. 1983, 87, 2109. (6) Buess, M. L.; Garroway, A. N.; Miller, J. B.; Yesinowski, J. P. Adv. Anal. Detect. Explos. Proc. Int. Symp. 1992, 4, 361. (7) Buess, M. L.; Garroway, A. N.; Miller, J. B. J . Magn. Reson. 1991, 92, 3480362. (8) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (9) Seel, M.; Bagus, P. S. Phys. Rev. B 1983, 28, 2023. Sahoo, N.; Mishra, S. K.; Mishra, K. C.; Coker, A.; Mitra, C. K.; Snyder, L. C.; Glodeanu, A.; Das, T. P. Phys. Rev. Lett. 1983, 60, 913. (10) Sahoo, N.; Sulaiman, S.; Mishra, K. C.; Das, T. P. Phys. Rev. B 1989,39, 13389. Dev, B. N.; Mohapatra, S. M.; Sahoo, N.; Mishra, K. C.; Gibson, W. M.; Das, T. P. Phys. Rev. E 1988, 38, 13335. Kelires, P. C.; Das, T. P. Hyperfine Interact. 1987, 34, 285. (11) Sahoo, N.; Ramani Lata, K.; Das, T. P. Theor. Chim. Acta 1992, 82,285. Ramani Lata, K.; Sahoo, N.; Das, T. P. Bull. Am. Phys. Soc. 1995, 39, 735.
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