- Email: [email protected]
Ab initio MO LCAO UHF calculations of magnetic hyperfine interactions in NO3 and NO2−3. Hyperfine and quadrupole couplings from endor data for NO2−3
Volume 44, number 3
CI1EhIICAL PHYSICS LKl-WRS
15 Dcccmbcr 1976
ABlNITlOMOLCAOUHFCALCULATlONSOFMACNETICHYPERFlNELNTERACTtONSIN N03ANDNO~-.H~ERFINEANDQUADRWOLECOUPLlNCSFRO~lENDOR DATA FORNO;Anders LUND and Karl-Ake THUOMAS The Swedish Research Council’s Lahratory.
Studsvrk, S-61 I 01 Nykoping.
Swcdm
Reccwcd 12 August 1976
hb mitio methods, the unrcstrictcd IIartrcc-Fock approximation, have been used to detenninc cquihbrium geomctrics and magnetic hypcrfine couplings of NO, and NO,2-. The electric quadrupole couplmg constants of NOT are evatuated both thcorctlcolly by Uiil’ and expcrimcntally using a new method for analyzing ENIIOK data. The geometries and coupling constants for NO, and CO: have been rccalculatcd.
I. hltroductioll
Irradiation
of nitrate
and nitrite
salts produces
a
series of nitrogen-containing paramagnetic spccics, the most prominent being NO,, NO;-, NO3 and NO:-. The type of radical produced depends upon the substance, the method of irradiation and the tcmpcrature. The NO, radical has been the subject of many theorctical studies. Walsh ll], in his series of papers on the geometry of molecules, predicts that 23 valcncc clectron systems should be planar, having D3,, symmetry, and possessing a 2A; ground electronic state. Nonempirical calculations [2] of the electronic energy lcvcls have shown that the ground state of NO, is 2A> and the first excited state may be either 2E’ or 2E” since these states arc very close in energy. Extended Huckel and INDO molecular orbital methods [3] have prcdieted a Y-shaped geometry (C2v symmetry) and a ground electronic state of 2B2 symmetry. Relatively large differences in g-values and hyperfine splittings have been reported for NO, in various environments. Hyperfinc splitting has been observed only in crystals, but not in ices and glasses. Martin et al. [4] explain these different observations in terms of “hard” and “soft” lattice effects. “Hard” lattices distort or polarize the planar configuration of the NO, and cause more interaction of the unpaired electron with the 14N nucleus. “Soft” lattices, such as ices and glasses, do not distort the planar configuration, and
one observes no hyperfinc splitting. Our first aim with this paper is to perform an ab initio calculation of the planar NO, to determine the cqulhbriurn
gconwtry
and the hypcrfine
coupling
of
14N.
The NO:- radical has been predicted to exist in a slightly nonplanar 2A, state but with apparent rctention of C3 symmetry [S,G] _ However, a recent obscrvation at 4.2 K [7] has shown that fi and the hyperfine tensor A do not have axial symmetry. Our second aim is to perform a comptete geometry optimization of NOi- and to calculate its hypcrtine and quadrupole couplings. In a recent paper [S] we dcvelopcd a method for evaluating the hyperfine and quadrupoIc coupling tensors A and Q from ENDOR measurements made on single crystals. Our third aim is to apply this method to re-analyze the 14N ENDaR data for NO:- [7]. Finally we want to recalculate the geometries and coupling constants of NO2 and 6302 [91 using the UHF theory for minimizing the total eIectronic cncrgy and computing the spin density matrix and the total electron density matrix.
2. UHF calculations The calculations were performed
in a spin-unrc569
Votumc
44, number
3
CHEMICAL
strictcd MO LCAO SCF approach, using gaussian-type functions for the expansion of the molecular orbit&. ‘The basis sets used for C, N and 0 consisted of seven s-type functions and three groups of p-type func?ions. Tftese were contracted to four s-type function5 and two groups of p-type functions. The orbital exponents, and contraction coefficients were taken from the litera ture IlO, I I 3. The UIIF cakzulations were performed with the program system IJlOLECULE [ 131 using a CDC CYBER 172 computer. Spin densities at the nuclei wcrc computed using a program based on the single annih~~ti~n method [13f. Dipolar llyper~ne and electric quadrupolc couplings were determined by using a program written by Kortzcborn [ 143. A partial geometry optimization was made for NOS. The radical was assumed to be planar and the stability of the Y-shaped geometry was cxamincd by varying the do __(-,distances and the O-N-O angles. This confirmed that NO3 possessed D,, point group symmetry with a bond distance of (IN_O =I 1.24 a. Con~p~ete geometry determinations were made for NO:-, NO2 and CO?,. The cafculations prcdrcted NO:to be planar with equthbrium bond distance of d, J, = I .?7 A and bond angle of O-N-O = 120”. The cquilibriurn bond distances for NO, and CO? wcrc dcterI.22 A. The minedtobedN_O=1_19~and~~_o= bond angles O-N-O and 0- C-O were both 134”. Calculated equillb~urn ~eomctrics and energies arc summarized in table 1. lsotropio hypcrfine couphng constants have been computed for the radicals NO,, NO;-, NO2 and CO, in their cquihbriurn gcomctrres. The results of these calculations for the t4N, I70 and 13C nuclei have been Table 3 ZXpolar hyperfinc function (Ml C) __--
couplings
bcforc spin alnthilation
NUCIWS I_---_*____
NO3
14N
NO;-
r4N “0 ‘4N “0 1% 1’0
NO2
co;
s7cr
-
UHI‘.L\A(UHi~) _- _-____
-0.6
(-0.7)
-11.5(-12.2) 7.4 (7.9) 35.0 (16.3) -3 t.5(-32.5) 27.1 (28.9) -24.81-24.9)
exp. _____---______
-0.28
-9.7
T3blc I Gcometncs --_-.
13.18 -34.60 28.3 -18.7
and cnerglcs
. ___------
-_-
. -_-___ -
E((au)
NO3
LOX0 (de&!) $&J$A) __ s--P -01.24 120
NOT
1.27
120
-278.09532
NOz
1.19
134
-203.67749
CO;
1.22
I34
Radical -_-__-...
-277.88467
- L87.26984 ----___-.__
-_---
Table 2
s2
a&t -we
Nuckw
RadiGlt _-
__
NO3
f%
NO$
‘4N
NO2
‘4N
(E,
1’0
- -_-”
0.7502 (0.7565) 0.7501 (0.7605) 0.7501 (0.7661)
41.7 54.75 -20.3 166.7
0.750t (0.7593)
-32.2
(UIIFAA)
of thcS
.-____ e-v---
=
3/2 ccrnpcrrcnt of the WVC_--
By(G)
B,(G)
UIII’AA(UIII’) exp. ____ ^___-_-__
UfIPAA(UH1’)
(-0.7)
_ ---.
“.----_---.
---_a
-ll.S(-12.4) 7.4 (7.8) -7.5 (-8.4) IS.6 (16.4) -14.2(-16.3) 12.2 (11.1)
--
UWAA WI117
0.0-4.5
21.0 (45.3) 41.9 (41.8) -9.2 (-12.3) 119.5 (118.5) -25.6 i-30.91
r3c
_-._. _-.
-w..-
Utll AA exp (UHl ) ---. _ . _c__k.- .---
1’0
and after anmhktion
-0.6
1976
su~a~~ed in tabfc 2. The table also contains the expectation values of the total spin angular momentum.
__ _.__“___ ____ &(GI
Radical -_--r__-
(UtlF)
15 Deccmbcr
MIYSICS LLTTERS
-0.28 -9.7 -7.87 18.56 -16.7 10.1
1.2 (1.4) 23.0 (24.6) -14.8(-25.7) -7.5 (-7.9) 15.9 (16.1) -12.9(-12.6) 12.6 (13.8)
CXP.
0.57 19.4 -5.40 16.03 -11.7 a.7
Volume 44, number 3
CIIINICAL
PHYSICS LE-ITERS
Annihilation of the wavefunctions for NO, and CO, has little effects on the spin density at the central atoms. The other spin densities at the nuclei arc reduced by annihilation. The dipolar coupling constants have been computed under the same conditions as was described above for isotropic coupling constants. The results are given in table 3. B,, B,, and Bz are the principal values of the coupling tensor. In NO2 and CO, the principal axes are oriented as described previously [9]. In NO3 and NO;- the 14N couplings arc axially synmctric about the threefold (z) axis and the oxygen couplings have one principal axis along z, one along the bond axis (x) and one perpendicular to the bond axis (v). The couplings are only slightly affected by the spin anmhilation procedure. The clcctric quadrupole couplings of NO:-, NO, and CO, are given in table 4. The quadrupolc couplings are unaffected by annihilation in agrccmcnt with Ilarnman’s analysis [ 151 of chaTgc dcpcndent one-electron propcrtics.
Table 4 The clcctric quadrupole couplings bcforc spm annllulatlon (UIli:) and after annlhd&ion of the S = 3/2 component of the wavcfunctlon (in MIl7) ---___---__--
--
Clectric quadrupolc couphg Radical
--
NO;-
Nucleus
.-_-_
UI1FAA = UIII’
-_-_-_--____
‘4N pzz = 1’0
1.7
PXX = -1.6 = -1.5 = 3.1
cxp. - _-_ -0.8 -1.4 2.1
l.5
Table 5 Principal values and direction for the A-matris in NOT (in hI1I.z) ------------ -_ - ______ Principal values ----_.-
Dcccmbcr 1976
and the Q-matrix __ ___-_ _ _
Principal dlrcctions with respect to a*-3x1s b-axis c-axis - -- __-___
A, = 114.0 AYY’ 112.1 AZ.2 = 191.9
0.123 50.864 0.487
50.957 -0.234 L-o.173
-0.263 TO.445 0.856
@xx = -1.5
0.663 so.612 0.431
c-o.599 0.779 co.184
-0.449 c-O.136 (I.883
Q yy== -K Qzz ----
3. Evaluation of A and Q from ENDOR data Recently [8] WCsolved the spin hamiltonian by second-order perturbation treatment for the high-field case with the additional assumption that the quadrupoIe term is much smaller than the effective hypertine term. The second order hypcrfine energy contribution and the cross product of fine and hypcrfinc energy contribution both canceIIcdwhen suitabIe combinations of ENDOR frequencies were added. This method was successfully applied to m-analyze the 14N ENDOR data for NO,. The hypertine couplings of NOi- arc a LIO-195 MHz and the components of the qucrdrupolc tensor are of the order of 2 MHr. while the second order corrcction from the effective hyperfine term is =0.4 MHz. Second order quadrupole corrections can bc neglected. Evaluation of the _hyperfine and quadrupolc tensors of NO:- were dctcrmincd in agreement with appendix B of ref. [8]. Principal values and direction for the Amatrix and the Q-matrix in NO:- arc summarized in table 5. Our ENDOR-analysis shows an axial asymmetry of the hyperfine tensor A and the quadrupole tensor 0. This result is contrary to our UHF-analysis but in agreement with the predictions of ref. [7].
4. Discussion Expcrimentalists arc in agreement as to a planar structure for NO,. Some workers [t6] have proposed a trigonally symmetric geometry (D3h point group), while others [I 7,l S] are more in favour ofa Y-shaped 571
Volume 44, number 3
CHtiMICAL PHYSICS LETTEHS
C,, structure. It stems that the difference between various observations is due to the high sensitivity of the radical to the nature of the matrix. The three lowest energy levels of NO3 are veryclosc in energy and permit energy level inversion, explaining the large variation in ERR spectral parameters for NO, in different matrices. A scmi-cmpirical UHF calculation using the INDO method [3] has confirmed Walsh’s conclusion that the planar D3h configuration should be more stable than the pyramidal C3, configurations for 23 valence electron systems. On the other hand, their calculations suggest that D 3h species arc unstable with respect to an in-plane bendmg distortion and that the radicals belong to the Czv point group. Deviations from the trigonal arrangement are related to the Jahn-Teller theorem. Our UHF calculations of NO3 predicts a Dgh pomt group for the radical. A comparison of the spin densities at the t4N nucleus before and after anmhilation, indicates that the free-space ground state of NO3 has a large n-electron contribution of the unpaired electron on oxygen. The isotropic and anisotropic couplings of 14N fall in the range of experimentally predicted values. Changing the angie O-N-O of NO:- increases the isotropic coupling of 14N in agrcemcnt with the larger s character of the unpaired electron. This has been observed before for Cl-radicals in ref. [ 19 1. Of the hyperfine coupling the anisotropic part is in good agreement with experimental
values while the isotropic
coupling
shows worse agreement. However, the effect of mo!ecular vibrations has not been considered. The principal values of the 14N hypcrfine and quadrupole couplings of table 5 arc almost the same as those given by Rustgi and Box [7]. Our analysis conErms that the principal axes which correspond to the maximum principal components of A and 0 for 14N are parallel, the deviation of 3.6” bzing within the experimental error for the NO:- radical [7]. A dnd Q were assumed to have parallel axes in the analysis of ref. [7]. This is not confirmed for the x and y components. It is possible that the NOi- radical has a lower symmetry than D3B in the glycylclycine HNO, matrix. The recalcuIated equilibrium geometries of NO2 and COT are shown in tab!o 1. Our changed equilibrium parameters of CO, are in good agreement with a recent ab initio calculation using large basis sets [20]. The anisotropic couplings of C, N and 0, table 3, are in good agreement with given experimentai values [9 1. Contrary to the previous calculation [9] we see that 572
15 December 1976
spin annihilation is not essential to obtain agreement with cxpcrimcnt for the CO, and NO2 n~olccules. The principal values of the quadrupole couplings are in good agreement with experimental data [9,21].
5. Conclusions Ab initio MO LCAO UIlF calculations have dcmonstratecl that anisotropic hypertine couplmgs and electric quadrupole couplings can be computed reliably from the spur-annihilated wavcfunctron of small inorganic radicals. Spin annihilation has a small effect on the anisotropic coupiings and no effect on the quadrupole couplings. Equivalent results have previously [19,22] been found for small rr-radicals.
Acknowledgement The ENDOR data were kmdly supplied by Dr. H.C. Box. Fmancial support was obtained from the Atomic Research Council of Sweden.
References [ 11 A.D. Walsh, J. Ckm. SIX. (1953) 2301. [2] T.E.H. Walker and J.A. Horsley, Mol. Phyn 21 (1971) 939. [3] J.F. OIscn and L. Burnell. J. Am. Chem. Sot. 92 (1970) 3639. [4] T.W. Martin, L.L. Swift and J.11. Vcnablc, J. Chcm. Phys. 52 (1970) 2138. [S] M.C.R. Symons. D.X. Wcrt and J.G. Wdkinson, J. Chcm. Sot. Dalton Trans. (1974) 2247. (61 P.W. Atkms and M.C R. Symons. The structure of inorganic radrcds (Elsevier, Amsterdam, 1967). [7] S.N. Rustgi and H.C. Box, J. Chem. Phys 59 (1973) 4763. [8] K.A. Thuomas and A. Lund, J. Magn. Reson. 18 (1975) 12. [9] J. Almlbf, A. Lund and K.A. Thuomas, Chem. Phys. Letters 28 (1974) 179. and references thcrcin. [ 10 J B. ROOS and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 209. Ill] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [12] J. AImIGf, USIP Rept. 72-09 (Sept. 1972). [ 131 T. Amos and L.C. Snyder, J. Chem. Phys. 41 (1964) 1773. [14] R.N. Kortzeborn, IBM report RJ 577 (1969). [15] J.E. Harriman, J. Chem. Phys. 40 (1964) 2827.
Volume
44, number
3
CHEMICAL
[ 161 D.E. Wood and G.P. Lozos, J. Chcm. Phys. 64 (1976) 546, and rcfercnccs thcrcin. [ 17) G.H. Chantry, A. Horsficld, J.R. Morton and D.H. Whiffen, Mol. Phys. 5 (1962) 589. 118) T.K. Gundu Rao, K.V. Lingam and B.N. Bhattacharya, J. hlagr.. Reson. 16 (1974) 369. [ 191, K.A. Thuomas and A. Lund, J. Mngn. &son. 22 (1976) 315.
PHYSICS LETTERS
15 December
1976
[20] J. Padansky, U. Wahlgren and P.S. Bagus, 5. Chrm. Phys. 62 (1975) 2740. [2L] P.D. Foster, LA. Hodgesonand R.P. Curt Jr.. I. ChemPhys. 45 (1966) 3760. [22] J. Almlof, A. Lund and K.A. Thuomas. Chcm. Phys. 7 (1975) 465.
573
CI1EhIICAL PHYSICS LKl-WRS
15 Dcccmbcr 1976
ABlNITlOMOLCAOUHFCALCULATlONSOFMACNETICHYPERFlNELNTERACTtONSIN N03ANDNO~-.H~ERFINEANDQUADRWOLECOUPLlNCSFRO~lENDOR DATA FORNO;Anders LUND and Karl-Ake THUOMAS The Swedish Research Council’s Lahratory.
Studsvrk, S-61 I 01 Nykoping.
Swcdm
Reccwcd 12 August 1976
hb mitio methods, the unrcstrictcd IIartrcc-Fock approximation, have been used to detenninc cquihbrium geomctrics and magnetic hypcrfine couplings of NO, and NO,2-. The electric quadrupole couplmg constants of NOT are evatuated both thcorctlcolly by Uiil’ and expcrimcntally using a new method for analyzing ENIIOK data. The geometries and coupling constants for NO, and CO: have been rccalculatcd.
I. hltroductioll
Irradiation
of nitrate
and nitrite
salts produces
a
series of nitrogen-containing paramagnetic spccics, the most prominent being NO,, NO;-, NO3 and NO:-. The type of radical produced depends upon the substance, the method of irradiation and the tcmpcrature. The NO, radical has been the subject of many theorctical studies. Walsh ll], in his series of papers on the geometry of molecules, predicts that 23 valcncc clectron systems should be planar, having D3,, symmetry, and possessing a 2A; ground electronic state. Nonempirical calculations [2] of the electronic energy lcvcls have shown that the ground state of NO, is 2A> and the first excited state may be either 2E’ or 2E” since these states arc very close in energy. Extended Huckel and INDO molecular orbital methods [3] have prcdieted a Y-shaped geometry (C2v symmetry) and a ground electronic state of 2B2 symmetry. Relatively large differences in g-values and hyperfine splittings have been reported for NO, in various environments. Hyperfinc splitting has been observed only in crystals, but not in ices and glasses. Martin et al. [4] explain these different observations in terms of “hard” and “soft” lattice effects. “Hard” lattices distort or polarize the planar configuration of the NO, and cause more interaction of the unpaired electron with the 14N nucleus. “Soft” lattices, such as ices and glasses, do not distort the planar configuration, and
one observes no hyperfinc splitting. Our first aim with this paper is to perform an ab initio calculation of the planar NO, to determine the cqulhbriurn
gconwtry
and the hypcrfine
coupling
of
14N.
The NO:- radical has been predicted to exist in a slightly nonplanar 2A, state but with apparent rctention of C3 symmetry [S,G] _ However, a recent obscrvation at 4.2 K [7] has shown that fi and the hyperfine tensor A do not have axial symmetry. Our second aim is to perform a comptete geometry optimization of NOi- and to calculate its hypcrtine and quadrupole couplings. In a recent paper [S] we dcvelopcd a method for evaluating the hyperfine and quadrupoIc coupling tensors A and Q from ENDOR measurements made on single crystals. Our third aim is to apply this method to re-analyze the 14N ENDaR data for NO:- [7]. Finally we want to recalculate the geometries and coupling constants of NO2 and 6302 [91 using the UHF theory for minimizing the total eIectronic cncrgy and computing the spin density matrix and the total electron density matrix.
2. UHF calculations The calculations were performed
in a spin-unrc569
Votumc
44, number
3
CHEMICAL
strictcd MO LCAO SCF approach, using gaussian-type functions for the expansion of the molecular orbit&. ‘The basis sets used for C, N and 0 consisted of seven s-type functions and three groups of p-type func?ions. Tftese were contracted to four s-type function5 and two groups of p-type functions. The orbital exponents, and contraction coefficients were taken from the litera ture IlO, I I 3. The UIIF cakzulations were performed with the program system IJlOLECULE [ 131 using a CDC CYBER 172 computer. Spin densities at the nuclei wcrc computed using a program based on the single annih~~ti~n method [13f. Dipolar llyper~ne and electric quadrupolc couplings were determined by using a program written by Kortzcborn [ 143. A partial geometry optimization was made for NOS. The radical was assumed to be planar and the stability of the Y-shaped geometry was cxamincd by varying the do __(-,distances and the O-N-O angles. This confirmed that NO3 possessed D,, point group symmetry with a bond distance of (IN_O =I 1.24 a. Con~p~ete geometry determinations were made for NO:-, NO2 and CO?,. The cafculations prcdrcted NO:to be planar with equthbrium bond distance of d, J, = I .?7 A and bond angle of O-N-O = 120”. The cquilibriurn bond distances for NO, and CO? wcrc dcterI.22 A. The minedtobedN_O=1_19~and~~_o= bond angles O-N-O and 0- C-O were both 134”. Calculated equillb~urn ~eomctrics and energies arc summarized in table 1. lsotropio hypcrfine couphng constants have been computed for the radicals NO,, NO;-, NO2 and CO, in their cquihbriurn gcomctrres. The results of these calculations for the t4N, I70 and 13C nuclei have been Table 3 ZXpolar hyperfinc function (Ml C) __--
couplings
bcforc spin alnthilation
NUCIWS I_---_*____
NO3
14N
NO;-
r4N “0 ‘4N “0 1% 1’0
NO2
co;
s7cr
-
UHI‘.L\A(UHi~) _- _-____
-0.6
(-0.7)
-11.5(-12.2) 7.4 (7.9) 35.0 (16.3) -3 t.5(-32.5) 27.1 (28.9) -24.81-24.9)
exp. _____---______
-0.28
-9.7
T3blc I Gcometncs --_-.
13.18 -34.60 28.3 -18.7
and cnerglcs
. ___------
-_-
. -_-___ -
E((au)
NO3
LOX0 (de&!) $&J$A) __ s--P -01.24 120
NOT
1.27
120
-278.09532
NOz
1.19
134
-203.67749
CO;
1.22
I34
Radical -_-__-...
-277.88467
- L87.26984 ----___-.__
-_---
Table 2
s2
a&t -we
Nuckw
RadiGlt _-
__
NO3
f%
NO$
‘4N
NO2
‘4N
(E,
1’0
- -_-”
0.7502 (0.7565) 0.7501 (0.7605) 0.7501 (0.7661)
41.7 54.75 -20.3 166.7
0.750t (0.7593)
-32.2
(UIIFAA)
of thcS
.-____ e-v---
=
3/2 ccrnpcrrcnt of the WVC_--
By(G)
B,(G)
UIII’AA(UIII’) exp. ____ ^___-_-__
UfIPAA(UH1’)
(-0.7)
_ ---.
“.----_---.
---_a
-ll.S(-12.4) 7.4 (7.8) -7.5 (-8.4) IS.6 (16.4) -14.2(-16.3) 12.2 (11.1)
--
UWAA WI117
0.0-4.5
21.0 (45.3) 41.9 (41.8) -9.2 (-12.3) 119.5 (118.5) -25.6 i-30.91
r3c
_-._. _-.
-w..-
Utll AA exp (UHl ) ---. _ . _c__k.- .---
1’0
and after anmhktion
-0.6
1976
su~a~~ed in tabfc 2. The table also contains the expectation values of the total spin angular momentum.
__ _.__“___ ____ &(GI
Radical -_--r__-
(UtlF)
15 Deccmbcr
MIYSICS LLTTERS
-0.28 -9.7 -7.87 18.56 -16.7 10.1
1.2 (1.4) 23.0 (24.6) -14.8(-25.7) -7.5 (-7.9) 15.9 (16.1) -12.9(-12.6) 12.6 (13.8)
CXP.
0.57 19.4 -5.40 16.03 -11.7 a.7
Volume 44, number 3
CIIINICAL
PHYSICS LE-ITERS
Annihilation of the wavefunctions for NO, and CO, has little effects on the spin density at the central atoms. The other spin densities at the nuclei arc reduced by annihilation. The dipolar coupling constants have been computed under the same conditions as was described above for isotropic coupling constants. The results are given in table 3. B,, B,, and Bz are the principal values of the coupling tensor. In NO2 and CO, the principal axes are oriented as described previously [9]. In NO3 and NO;- the 14N couplings arc axially synmctric about the threefold (z) axis and the oxygen couplings have one principal axis along z, one along the bond axis (x) and one perpendicular to the bond axis (v). The couplings are only slightly affected by the spin anmhilation procedure. The clcctric quadrupole couplings of NO:-, NO, and CO, are given in table 4. The quadrupolc couplings are unaffected by annihilation in agrccmcnt with Ilarnman’s analysis [ 151 of chaTgc dcpcndent one-electron propcrtics.
Table 4 The clcctric quadrupole couplings bcforc spm annllulatlon (UIli:) and after annlhd&ion of the S = 3/2 component of the wavcfunctlon (in MIl7) ---___---__--
--
Clectric quadrupolc couphg Radical
--
NO;-
Nucleus
.-_-_
UI1FAA = UIII’
-_-_-_--____
‘4N pzz = 1’0
1.7
PXX = -1.6 = -1.5 = 3.1
cxp. - _-_ -0.8 -1.4 2.1
l.5
Table 5 Principal values and direction for the A-matris in NOT (in hI1I.z) ------------ -_ - ______ Principal values ----_.-
Dcccmbcr 1976
and the Q-matrix __ ___-_ _ _
Principal dlrcctions with respect to a*-3x1s b-axis c-axis - -- __-___
A, = 114.0 AYY’ 112.1 AZ.2 = 191.9
0.123 50.864 0.487
50.957 -0.234 L-o.173
-0.263 TO.445 0.856
@xx = -1.5
0.663 so.612 0.431
c-o.599 0.779 co.184
-0.449 c-O.136 (I.883
Q yy== -K Qzz ----
3. Evaluation of A and Q from ENDOR data Recently [8] WCsolved the spin hamiltonian by second-order perturbation treatment for the high-field case with the additional assumption that the quadrupoIe term is much smaller than the effective hypertine term. The second order hypcrfine energy contribution and the cross product of fine and hypcrfinc energy contribution both canceIIcdwhen suitabIe combinations of ENDOR frequencies were added. This method was successfully applied to m-analyze the 14N ENDOR data for NO,. The hypertine couplings of NOi- arc a LIO-195 MHz and the components of the qucrdrupolc tensor are of the order of 2 MHr. while the second order corrcction from the effective hyperfine term is =0.4 MHz. Second order quadrupole corrections can bc neglected. Evaluation of the _hyperfine and quadrupolc tensors of NO:- were dctcrmincd in agreement with appendix B of ref. [8]. Principal values and direction for the Amatrix and the Q-matrix in NO:- arc summarized in table 5. Our ENDOR-analysis shows an axial asymmetry of the hyperfine tensor A and the quadrupole tensor 0. This result is contrary to our UHF-analysis but in agreement with the predictions of ref. [7].
4. Discussion Expcrimentalists arc in agreement as to a planar structure for NO,. Some workers [t6] have proposed a trigonally symmetric geometry (D3h point group), while others [I 7,l S] are more in favour ofa Y-shaped 571
Volume 44, number 3
CHtiMICAL PHYSICS LETTEHS
C,, structure. It stems that the difference between various observations is due to the high sensitivity of the radical to the nature of the matrix. The three lowest energy levels of NO3 are veryclosc in energy and permit energy level inversion, explaining the large variation in ERR spectral parameters for NO, in different matrices. A scmi-cmpirical UHF calculation using the INDO method [3] has confirmed Walsh’s conclusion that the planar D3h configuration should be more stable than the pyramidal C3, configurations for 23 valence electron systems. On the other hand, their calculations suggest that D 3h species arc unstable with respect to an in-plane bendmg distortion and that the radicals belong to the Czv point group. Deviations from the trigonal arrangement are related to the Jahn-Teller theorem. Our UHF calculations of NO3 predicts a Dgh pomt group for the radical. A comparison of the spin densities at the t4N nucleus before and after anmhilation, indicates that the free-space ground state of NO3 has a large n-electron contribution of the unpaired electron on oxygen. The isotropic and anisotropic couplings of 14N fall in the range of experimentally predicted values. Changing the angie O-N-O of NO:- increases the isotropic coupling of 14N in agrcemcnt with the larger s character of the unpaired electron. This has been observed before for Cl-radicals in ref. [ 19 1. Of the hyperfine coupling the anisotropic part is in good agreement with experimental
values while the isotropic
coupling
shows worse agreement. However, the effect of mo!ecular vibrations has not been considered. The principal values of the 14N hypcrfine and quadrupole couplings of table 5 arc almost the same as those given by Rustgi and Box [7]. Our analysis conErms that the principal axes which correspond to the maximum principal components of A and 0 for 14N are parallel, the deviation of 3.6” bzing within the experimental error for the NO:- radical [7]. A dnd Q were assumed to have parallel axes in the analysis of ref. [7]. This is not confirmed for the x and y components. It is possible that the NOi- radical has a lower symmetry than D3B in the glycylclycine HNO, matrix. The recalcuIated equilibrium geometries of NO2 and COT are shown in tab!o 1. Our changed equilibrium parameters of CO, are in good agreement with a recent ab initio calculation using large basis sets [20]. The anisotropic couplings of C, N and 0, table 3, are in good agreement with given experimentai values [9 1. Contrary to the previous calculation [9] we see that 572
15 December 1976
spin annihilation is not essential to obtain agreement with cxpcrimcnt for the CO, and NO2 n~olccules. The principal values of the quadrupole couplings are in good agreement with experimental data [9,21].
5. Conclusions Ab initio MO LCAO UIlF calculations have dcmonstratecl that anisotropic hypertine couplmgs and electric quadrupole couplings can be computed reliably from the spur-annihilated wavcfunctron of small inorganic radicals. Spin annihilation has a small effect on the anisotropic coupiings and no effect on the quadrupole couplings. Equivalent results have previously [19,22] been found for small rr-radicals.
Acknowledgement The ENDOR data were kmdly supplied by Dr. H.C. Box. Fmancial support was obtained from the Atomic Research Council of Sweden.
References [ 11 A.D. Walsh, J. Ckm. SIX. (1953) 2301. [2] T.E.H. Walker and J.A. Horsley, Mol. Phyn 21 (1971) 939. [3] J.F. OIscn and L. Burnell. J. Am. Chem. Sot. 92 (1970) 3639. [4] T.W. Martin, L.L. Swift and J.11. Vcnablc, J. Chcm. Phys. 52 (1970) 2138. [S] M.C.R. Symons. D.X. Wcrt and J.G. Wdkinson, J. Chcm. Sot. Dalton Trans. (1974) 2247. (61 P.W. Atkms and M.C R. Symons. The structure of inorganic radrcds (Elsevier, Amsterdam, 1967). [7] S.N. Rustgi and H.C. Box, J. Chem. Phys 59 (1973) 4763. [8] K.A. Thuomas and A. Lund, J. Magn. Reson. 18 (1975) 12. [9] J. Almlbf, A. Lund and K.A. Thuomas, Chem. Phys. Letters 28 (1974) 179. and references thcrcin. [ 10 J B. ROOS and P. Siegbahn, Theoret. Chim. Acta 17 (1970) 209. Ill] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [12] J. AImIGf, USIP Rept. 72-09 (Sept. 1972). [ 131 T. Amos and L.C. Snyder, J. Chem. Phys. 41 (1964) 1773. [14] R.N. Kortzeborn, IBM report RJ 577 (1969). [15] J.E. Harriman, J. Chem. Phys. 40 (1964) 2827.
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44, number
3
CHEMICAL
[ 161 D.E. Wood and G.P. Lozos, J. Chcm. Phys. 64 (1976) 546, and rcfercnccs thcrcin. [ 17) G.H. Chantry, A. Horsficld, J.R. Morton and D.H. Whiffen, Mol. Phys. 5 (1962) 589. 118) T.K. Gundu Rao, K.V. Lingam and B.N. Bhattacharya, J. hlagr.. Reson. 16 (1974) 369. [ 191, K.A. Thuomas and A. Lund, J. Mngn. &son. 22 (1976) 315.
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1976
[20] J. Padansky, U. Wahlgren and P.S. Bagus, 5. Chrm. Phys. 62 (1975) 2740. [2L] P.D. Foster, LA. Hodgesonand R.P. Curt Jr.. I. ChemPhys. 45 (1966) 3760. [22] J. Almlof, A. Lund and K.A. Thuomas. Chcm. Phys. 7 (1975) 465.
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