JOURNAL DE PHYSIQIJE

Colloque C 4, supplöment au no 8-9, Tome 28, Aoüt-Septembre 1967, page C 4 -81

THE MOLECUI,AR CHARACTER OF THE O;.CENTER IN ALKALI HALIDES H. R. ZeLLsn, R. T. Snury (*) and W. KANzrc Laboratory of Solid State Physics, Swiss Federal Institute of Technology, Zidrich, Switzedand

Abstract. color centers (h isin alln'n >

THE MOLECULAR CHARACTER OF THE

r is defined by the ratio of the spin-orbit parameter to the crystal field parameter lo (See Fig. 3)

c4.83

Oz-CENTER

( tro*)

2nI1 I

111

).u

Ig2a : --! ' When contributions from excited states are included

to first order, one obtains the following g-factors

: g"cos2 c t,4 cos 2 u - B(l - sin2 a) Syy : S"coszd, *,4cos 2a * B(l - sin2a) 9,":9.*Zsin2a

:

g**

(1)

"lo* ( znot )

A

and B are sums of matrix elements between ground and excited Coulomb states divided by the corresponding excitation energies and therefore purely molecular

2rlo' "1"* {

quantities which do not depend upon the crystal field. Within the framework of a pure Coulomb crystal field theory the above expressions are completely general. However,

it

turns out that the measured

Level scheme of the Oz center Ftc. 3. - important (Only the levels for g-factor shift are shown).

Furthermore we put

quantities A and B vary with the host crystal. Thus it is impossible to describe the 0|-center with pure molecular states. A similar situation was found in transi-

A:

2.2 Gsxanar, ANALysrs oF THEg-FAcron.

-We

may

1) The wave functions

of the ground state are

distorted to some extent by the crystalline environment. (For instance by slight covalent bonding.) and B 2) The excited molecular states entering

A

are essentielly degenerate with the intrinsic alkali halide excitons and may therefore be severely modified in a manner dependent on host crystal.

To account for the first effect, one must assume only orthorhombic symmetry for the wave functions. We neglect a1l excited levels except 2rn*, since we expect that this level is most important and least modified by the crystal. The basis states are then the Coulomb

of the center (Fig. 3), and only the magnetic energy is nondiagonal. Using the notation of Koster and Statz [6] we define quantities Itand )', as follows : states

- - it, --it* : l,i, s, ' is determined by the slope. Similarly, ,4,,

plotted versus sin 2 a should give a straight line for small values of a (Fig. 8).

Figures 7 and 8 show that it is indeed possible to ft the measured ,4,, with a good accuracy with four H. F. S.-parameters using the a values derived, from the analysis of the g-factor. The results of the fit are summarized in table VI together with other hyperfine parameters of oxygen. (Note that in this table < 7l ,t >" is defined as ll2(< l/rt >ü * < llr3 >!).) The error in the parameters of 02 comes mainly from the relatively large error in

lr,

(Tab.

\).

I I

0.1261 0.038

i

4.45 3.06

3.46

3.46

3.46

3.36

3.36

3.36

3.36

I

0

I 1

is possible to qualitatively understand correlation

to Hartree-Fock hyperfine predictions by the unrestricted Hartree-Fock method, in which unpaired electrons are allowed to polarize closed correötions

shells. The spin density at the nucleus | ü(0)

l' (vani-

shing in Hartree-Fock approximation) arises from a spin polarization of the 1 s and 2 s shells, or in a diatomic molecule of the o shells. The large 6u - og splitting allows molecular configurations with ,t | fOl l' # 0 to have less excitation energy than the corresponding atomic configurations. Therefore, | *tOi l' is expected to be larger in molecules than in ätoms. Furthermore | ,lfOl 12 should be proportional to the number of unpaired ( shown in table VI could be attributed to the overlap-renormalization of atomic orbitals in an antibonding LCAO molecular orbital.

The difference between < llrt >" and the HartreeFock value for < 1lr3 > is mainly due to the follo-

2) Magnetic and elastic interactions between 02 in alkali halides. 3) Magnetic and elastic cooperative phenomenä in the alkali superoxydes 1151. centers

Work along these lines is underway in Ziric}a and supported by the Swiss National Science Foundation. In the early stages of this work the authors profited from a discussion on the hyperfine structure with

Prof. T. G.

Castner. References

wing effects : 1) Spin polarization

of the 2p

shell.

2) Spin-dependent admixture of d orbitals into the for | ,lfOi l' holds also for < llrt >" in that the large 6u - cs splitting causes alarger polarizability in the molecule than in the atom. Table IV indicates furthermore that the many-electron contribution to < Ilrt >" in O, is larger than in 02 , presumably because Or has two polarizing electrons. The difference between < llr'>i and < llrt >) comes from molecular s shell. The same reasoning applied above

binding effects.

principal conclusion of this 4. Conclusion. - The investigation is the following : The electronic structure of molecular centers in alkali halides can be analyzed by applying methods similar to those used for transition metal salts. The additional complications which arise because of the lower symmetry of the molecules can be overcome. The present investigation forms a basis for the understanding of a number of interesting phenomena due

to Of

:

1) Paraelastic alignment of 02 in alkali halides [14].

[1] Casnren (T. G.) and KÄNzrc (W.), ./. Phys.

Chem.

Solids, 1957,3, 178. lZf Zert-ex (H. R.), VnNNorrt (L.) and KÄuztc (W.), Phys. kondens, Materie, 1964,2, I33. [3] Bn r. (H.), Suren (H.) and Lncnorx (R.), Phys. Letters, 1966, ?2,241. [4] I{saszu IJroa, "I. Chem. Physics, 1964, 41,285. [5] Low (W.), Paramagnetic Resonance (Solid State Physics Suppl. 2) Academic Press, New York, 1960.

[6] Kosrsn (G. F.), Drrvrprocr (J. O.), WnBBlnn (R. G.), Surz (H.), Properties of the Thirtiy-two point groups. M. I. T. Press, Cambridge 1963, p. 39' [7] Snusv (R. T.) and ZBr,r,nn (H. R.), to be published in Helv. Phvs. Acta. [8] Zerrnn (H. R.) and KÄtqzrc (W.), to be published in Helv. Phvs. Acta.

[9] TnqrHaivr (Ni.), Proc Roy. Soc.,

1956, A 236, 549. [10] SucaNo (S.) and Snur-rrmN (R. G.), Phys. Rev., 1963, 130, 517. But see criticism by, W,q'rsoN (R. E.) and FnBBuaw (A. J.), Phys. Rev., 1964, 134 A, 1562.

[11]

Munn (S. L.), TowNns (C. H.) and Kouu

(M.),

Phys. Rev., 1953,90, 542. [12] Hanwv (J. S. M.), Proc. Roy. Soc., 1,965,4285' 581. [13] Brssa (N.), Lernnvnn-BnroN (H.) and MosBn (C. M.), Phys. Rev., 1962, 128, 213. [14] KÄr.rzrc (W.), ,r. Phys. Chem. Solids, 1962,23' 479.

(H. G.), Nrcrrow (R. M,), RauseNHetN{en -[15] Surrs (L. J.) and WrrrtNsoi.l (M.K.), J. Appl. Phys., 1966,37, L047. [16] KÄnzrc (W.) and ConrN (M. H.), Phys. 1959, 3, 509.

Rev. Letters,

Colloque C 4, supplöment au no 8-9, Tome 28, Aoüt-Septembre 1967, page C 4 -81

THE MOLECUI,AR CHARACTER OF THE O;.CENTER IN ALKALI HALIDES H. R. ZeLLsn, R. T. Snury (*) and W. KANzrc Laboratory of Solid State Physics, Swiss Federal Institute of Technology, Zidrich, Switzedand

Abstract. color centers (h isin alln'n >

THE MOLECULAR CHARACTER OF THE

r is defined by the ratio of the spin-orbit parameter to the crystal field parameter lo (See Fig. 3)

c4.83

Oz-CENTER

( tro*)

2nI1 I

111

).u

Ig2a : --! ' When contributions from excited states are included

to first order, one obtains the following g-factors

: g"cos2 c t,4 cos 2 u - B(l - sin2 a) Syy : S"coszd, *,4cos 2a * B(l - sin2a) 9,":9.*Zsin2a

:

g**

(1)

"lo* ( znot )

A

and B are sums of matrix elements between ground and excited Coulomb states divided by the corresponding excitation energies and therefore purely molecular

2rlo' "1"* {

quantities which do not depend upon the crystal field. Within the framework of a pure Coulomb crystal field theory the above expressions are completely general. However,

it

turns out that the measured

Level scheme of the Oz center Ftc. 3. - important (Only the levels for g-factor shift are shown).

Furthermore we put

quantities A and B vary with the host crystal. Thus it is impossible to describe the 0|-center with pure molecular states. A similar situation was found in transi-

A:

2.2 Gsxanar, ANALysrs oF THEg-FAcron.

-We

may

1) The wave functions

of the ground state are

distorted to some extent by the crystalline environment. (For instance by slight covalent bonding.) and B 2) The excited molecular states entering

A

are essentielly degenerate with the intrinsic alkali halide excitons and may therefore be severely modified in a manner dependent on host crystal.

To account for the first effect, one must assume only orthorhombic symmetry for the wave functions. We neglect a1l excited levels except 2rn*, since we expect that this level is most important and least modified by the crystal. The basis states are then the Coulomb

of the center (Fig. 3), and only the magnetic energy is nondiagonal. Using the notation of Koster and Statz [6] we define quantities Itand )', as follows : states

- - it, --it* : l,i, s, ' is determined by the slope. Similarly, ,4,,

plotted versus sin 2 a should give a straight line for small values of a (Fig. 8).

Figures 7 and 8 show that it is indeed possible to ft the measured ,4,, with a good accuracy with four H. F. S.-parameters using the a values derived, from the analysis of the g-factor. The results of the fit are summarized in table VI together with other hyperfine parameters of oxygen. (Note that in this table < 7l ,t >" is defined as ll2(< l/rt >ü * < llr3 >!).) The error in the parameters of 02 comes mainly from the relatively large error in

lr,

(Tab.

\).

I I

0.1261 0.038

i

4.45 3.06

3.46

3.46

3.46

3.36

3.36

3.36

3.36

I

0

I 1

is possible to qualitatively understand correlation

to Hartree-Fock hyperfine predictions by the unrestricted Hartree-Fock method, in which unpaired electrons are allowed to polarize closed correötions

shells. The spin density at the nucleus | ü(0)

l' (vani-

shing in Hartree-Fock approximation) arises from a spin polarization of the 1 s and 2 s shells, or in a diatomic molecule of the o shells. The large 6u - og splitting allows molecular configurations with ,t | fOl l' # 0 to have less excitation energy than the corresponding atomic configurations. Therefore, | *tOi l' is expected to be larger in molecules than in ätoms. Furthermore | ,lfOl 12 should be proportional to the number of unpaired ( shown in table VI could be attributed to the overlap-renormalization of atomic orbitals in an antibonding LCAO molecular orbital.

The difference between < llrt >" and the HartreeFock value for < 1lr3 > is mainly due to the follo-

2) Magnetic and elastic interactions between 02 in alkali halides. 3) Magnetic and elastic cooperative phenomenä in the alkali superoxydes 1151. centers

Work along these lines is underway in Ziric}a and supported by the Swiss National Science Foundation. In the early stages of this work the authors profited from a discussion on the hyperfine structure with

Prof. T. G.

Castner. References

wing effects : 1) Spin polarization

of the 2p

shell.

2) Spin-dependent admixture of d orbitals into the for | ,lfOi l' holds also for < llrt >" in that the large 6u - cs splitting causes alarger polarizability in the molecule than in the atom. Table IV indicates furthermore that the many-electron contribution to < Ilrt >" in O, is larger than in 02 , presumably because Or has two polarizing electrons. The difference between < llr'>i and < llrt >) comes from molecular s shell. The same reasoning applied above

binding effects.

principal conclusion of this 4. Conclusion. - The investigation is the following : The electronic structure of molecular centers in alkali halides can be analyzed by applying methods similar to those used for transition metal salts. The additional complications which arise because of the lower symmetry of the molecules can be overcome. The present investigation forms a basis for the understanding of a number of interesting phenomena due

to Of

:

1) Paraelastic alignment of 02 in alkali halides [14].

[1] Casnren (T. G.) and KÄNzrc (W.), ./. Phys.

Chem.

Solids, 1957,3, 178. lZf Zert-ex (H. R.), VnNNorrt (L.) and KÄuztc (W.), Phys. kondens, Materie, 1964,2, I33. [3] Bn r. (H.), Suren (H.) and Lncnorx (R.), Phys. Letters, 1966, ?2,241. [4] I{saszu IJroa, "I. Chem. Physics, 1964, 41,285. [5] Low (W.), Paramagnetic Resonance (Solid State Physics Suppl. 2) Academic Press, New York, 1960.

[6] Kosrsn (G. F.), Drrvrprocr (J. O.), WnBBlnn (R. G.), Surz (H.), Properties of the Thirtiy-two point groups. M. I. T. Press, Cambridge 1963, p. 39' [7] Snusv (R. T.) and ZBr,r,nn (H. R.), to be published in Helv. Phvs. Acta. [8] Zerrnn (H. R.) and KÄtqzrc (W.), to be published in Helv. Phvs. Acta.

[9] TnqrHaivr (Ni.), Proc Roy. Soc.,

1956, A 236, 549. [10] SucaNo (S.) and Snur-rrmN (R. G.), Phys. Rev., 1963, 130, 517. But see criticism by, W,q'rsoN (R. E.) and FnBBuaw (A. J.), Phys. Rev., 1964, 134 A, 1562.

[11]

Munn (S. L.), TowNns (C. H.) and Kouu

(M.),

Phys. Rev., 1953,90, 542. [12] Hanwv (J. S. M.), Proc. Roy. Soc., 1,965,4285' 581. [13] Brssa (N.), Lernnvnn-BnroN (H.) and MosBn (C. M.), Phys. Rev., 1962, 128, 213. [14] KÄr.rzrc (W.), ,r. Phys. Chem. Solids, 1962,23' 479.

(H. G.), Nrcrrow (R. M,), RauseNHetN{en -[15] Surrs (L. J.) and WrrrtNsoi.l (M.K.), J. Appl. Phys., 1966,37, L047. [16] KÄnzrc (W.) and ConrN (M. H.), Phys. 1959, 3, 509.

Rev. Letters,