- Email: [email protected]
Vibronic coupling in the 4T2g excited state of ruby
~peo~himicaAc~,l960, vol.16,pp. 493to496.Pergamon Press Ltd. Printed in X&hem Ireland
Vibronic coupling in the 4Tag excited state of ruby R. A. FORD and 0. F. HILL Mulard ResearchLaboratories, Salfords, Surrey (Received 23 December 1959) Ah&a&--The absorption spectrum of ruby in polarized light has been in~~est,iga~d at liquidnitrogen temperature, in the 5500 a region. The presence of vibrational structure in the J_C, polarization of the transition to the split 4T, excited state has been confirmed. The appearance of a, progression in an E, mode of the corundum lattice is attributed to Jahn-Teller distortion of the upper state.
1. Introduction RECENTLY,GRESCHUSHNIKOV and FEOFILOV[ l] reportedfinestructureinthelongwavelength edge of the 4T2s +- 4A,, transition of Cr3+ in corundum at 83°K. Five bands were reported, two of which had previously been observed many years ago by GIBSON [Z]. The dichroism of the band was also studied and the vibrational structure, which disappears above 170°K, was found to be polarized perpendicular to the C,-axis (~-spectrum). No analysis was attempted but it was suggested that the structure was due to ;t simple vibrational series in the 194 cm-l (E,) Raman [a] frequency [3] of the corundum Iattice. More recently, PRYCE and RUNCIMAN have observed similar structure with an average wavenumber separation of 180 cm-l in the 3T, t 3A, transition of V3+ in the same lattice. They suggested that the unexpected appearance of a simple progression in a doubly degenerate mode was due to strong Jahn-Teller distortion of the 3T, state, which will couple the electronic transition to certain antisymmetric crystal vibrations. Since the vibrational spacings reported by GRESCEUSHNIKOV and FEOFIVLOV did not indicate a simple progression of single quanta, in the 194 cm-l frequency, we decided to study this region more closely.
We have confirmed the presence of this vibrational structure in ruby using a synthetic corundum crystaf doped with O*O5o/o Cr3+ obtained from Linde Air Products Inc. However, our band positions are somewhat different from those of GRESCHUSHNIKOV and FEOFILOV and evidence of two further members has been found. Details of the spectra, shown in Fig. 1, which were recorded on a PerkinElmer spectracord 4000 are given A, in Table 1. Details of the miniature lowtemperature cell used for this work have been given elsewhere [SJ. The observed spectrum may be most simply interpreted in terms of two GRESCHUSHXIKOV and P. P.FEOFILOV, Zhur. Ekqnw. i Teoret. 2%. 29,384 (1955); JETP. 330 (1956). Translated inSo&t [email protected]. [Z]K. 8. GIBSON, Phys. Rev. 8, 38 (1916). [3] R. S. &USENAN, Proe. ~~~~~ Ad. 2%. A. 26, 450 (1947). [4] M. H. L.PRYCX andW. A. Rui-icrim.~, IXscussions~~?~~~~.~o. 26, 34 (1958). [6] E.L. HENTLEY and R. A. Fo~n,iY~ectrochim. AC@ 15, 594 (1959).
[l]B.N.
493
2,
R. A. FORD and 0. F. HILL
vibration frequencies 216 cm-r and 178 cm-l-. We 244 cm-l and 194 cm-l, i&a-red frequencies of substitution of Crs+ in this lattice will perturb the vicinity of the Cr3+ site. Simple calculation suggests
I
t
I
may associate these with the the corundum lattice. The corundum frequencies in the that these frequencies should
I
5000
6000 Wavelength,
%
Fig. I Polarized absorption spectrum of ruby at 100°K. Table 1. Polarized absorption spectrum of ruby at 100°K Band
V
(cm-l)
Av (cm-l)
v -
16,760cm-1
Assignment
_1
16,760
0
0 -
0 4.l&, +-*A,@)
216 2
16,976
216
216
438
2 x 216
649
3 x 216
828
3 x 216 _t 178
222 3
17,198 211
4
17,409 179
5
17,588 181
6
17,769
1009
3 x 216 +- 2 x 178
1183
3 x 216 f
174
_-
IIcs
( w spectrum)
7 (peak)
17,943
1 (peak)
18,272
-._-
I,
4&,
-
3 x 178 ---
4~vx,
be reduced by about 10 per cent which would bring them into good agreement with the values observed in ruby.
3. Discussion The degeneracy of the 4T2g state of Cr*+ is lifted in ruby by the trigonai component of the crystal field (Cr3+ site symmetry is 0,). The derived states are 494
Vibronic coupling in the aT,, excited stctto of ruby
then *Etl) and 4A,,,. * Frequently, these states are classified under the pseudosymmetry CsV, i.e. 4E and 4A,, but this is not preferable when polarization and vibrational interaction are considered because the intensity of transitions depends on configuration interaction. Accordingly, the 4Ec,, t 4A,,, transition will be polarized perpendicular and 4A(1j t 4Af,, parallel to the C,-axis. The value of the trigonal field parameter JZ, calculated from the splitting of these components, is -220 cm-l. This is somewhat smaller than the value quoted by SUCANO and TANABE [6) of -350 cm-‘. Under C,, transitions from the ground state to the 4Etlt and *A(,, states are allowed because of the removal of parity restrictions. Since they result from intercon~gurational excitation, (t2,)3 -+ (tz,)” (e,), expansion in the excited state is to be expected because of the anti-bonding character of the excited e, orbital. Hence the Franck-Condon principle leads us to expect the transitions to be broad with a weak O-O band extended in progressions of the totally symmetric vibrations. In considering the observed vibrational structure in the o-spectrum which is accordingly associated with the *EC,, c 4Af,, transition, we must first resolve the lattice vibrations of corundum, which have been assigned under the space group B&3], in terms of the Cr3+ site symmetry~ This is done in Table 2. Table 2.
Resolution of lattice vibrations of corundum space and site group symmetries D3d
_-_
.----Symmetry
4,
A la A 20 A 221 E!l J%
class
No. of modes
-
-~_2 3 2 2 d 4
Activity
---/ [ Raman I
/ j
Inactive Inaotiva Infra-red Raman Infra-rod
in t,erms of
Observed frequencies (cm-l)
-
c3
class
_ ----___
578, 751
Ii
,4
244, 847 375, 417, 432, 450, 642 194, 328-355, 434, 909
~
I
E
It is then necessary, in making a vibrational analysis, to decide on the position of the O-O band. With the “-Erl, t 4Aol transition we have no fluorescence to aid us here, but by working at 100°K we can be sure that the observed vibrational frequencies are only excited in the 4E,1j upper state. Hence we may safely assign the longest wavelength band at 16,760 em-l to the O-O band. The spectrum is then seen to consist of a combined progression in the 216 cm-l and 178 cm-l frequencies which belong to the representations A and E, respectively. A summary of our vibrational analysis is given in the last column of Table 1. We should not, however, expect a progression in single quanta of an antisymmetric vibration to appear in an allowed transition. This will only happen if the excited state is distorted in such a manner that the antisymmetric vibration becomes totally symmetric under * The subscript (0) refers to the ground state. Excited states of similar orbital symmetry and spin multiplicity are then denoted (I), (2) . . . . . .in sequence of increasing energy. f6J S.
SUGANO
and Y. TANABX, J. Pkys. Sot. Jquan
18,880 (1958).
495
R. A. FORD arnd0. F, HILL
the lower symmetry of the distorted struct~ [7, 81. Let us now consider whether such a distortion is possible. The orbital degeneracy of the 4E(,, state will be lifted if the symmetrical configuration of this state is unstable with respect to any of its antisymmetric normal vibrational modes. JAHN and TXLLER[9] have shown that such instability will occur if the matrix elements of Sy*E,,) FE y4E(,, G?Tare non zero. Here V, is the appropriate operator for the vibrational perturbation. This will be so for the *I#(,, state of Cr3+ in corundum because the direct product of the vibrational representation E and the electronic state rep~sentat~on [E2] contains the totally symmetric representation A. The symmetry of the distorted configuration will then become C, under which the 178 cm-l vibration will be totally symmetric. The presence of a progression in single quanta of the perturbed 194 cm-l, E,, frequency of the corundum lattice in the 4_Eo)+- 4A(o, transition is therefore clear evidence of JAHN-TELLBIR distortion of the 4Ef,, state of Cre+ in ruby. /7] W. MQFFITT and W. THORSON, Phys. Rev. 108, 1251 (1957). [S] H. C. LONGWET-HIQCXNS,U. ~PIK, M. H. L. PRYCE and R. A. SAOK, PTOC.Roy. Sot. [Q]H. A. JABCN md E. TELLER, Proc. Roy. Sot. A. 161,229(1937).
A. 244,1 (19.58).
Vibronic coupling in the 4Tag excited state of ruby R. A. FORD and 0. F. HILL Mulard ResearchLaboratories, Salfords, Surrey (Received 23 December 1959) Ah&a&--The absorption spectrum of ruby in polarized light has been in~~est,iga~d at liquidnitrogen temperature, in the 5500 a region. The presence of vibrational structure in the J_C, polarization of the transition to the split 4T, excited state has been confirmed. The appearance of a, progression in an E, mode of the corundum lattice is attributed to Jahn-Teller distortion of the upper state.
1. Introduction RECENTLY,GRESCHUSHNIKOV and FEOFILOV[ l] reportedfinestructureinthelongwavelength edge of the 4T2s +- 4A,, transition of Cr3+ in corundum at 83°K. Five bands were reported, two of which had previously been observed many years ago by GIBSON [Z]. The dichroism of the band was also studied and the vibrational structure, which disappears above 170°K, was found to be polarized perpendicular to the C,-axis (~-spectrum). No analysis was attempted but it was suggested that the structure was due to ;t simple vibrational series in the 194 cm-l (E,) Raman [a] frequency [3] of the corundum Iattice. More recently, PRYCE and RUNCIMAN have observed similar structure with an average wavenumber separation of 180 cm-l in the 3T, t 3A, transition of V3+ in the same lattice. They suggested that the unexpected appearance of a simple progression in a doubly degenerate mode was due to strong Jahn-Teller distortion of the 3T, state, which will couple the electronic transition to certain antisymmetric crystal vibrations. Since the vibrational spacings reported by GRESCEUSHNIKOV and FEOFIVLOV did not indicate a simple progression of single quanta, in the 194 cm-l frequency, we decided to study this region more closely.
We have confirmed the presence of this vibrational structure in ruby using a synthetic corundum crystaf doped with O*O5o/o Cr3+ obtained from Linde Air Products Inc. However, our band positions are somewhat different from those of GRESCHUSHNIKOV and FEOFILOV and evidence of two further members has been found. Details of the spectra, shown in Fig. 1, which were recorded on a PerkinElmer spectracord 4000 are given A, in Table 1. Details of the miniature lowtemperature cell used for this work have been given elsewhere [SJ. The observed spectrum may be most simply interpreted in terms of two GRESCHUSHXIKOV and P. P.FEOFILOV, Zhur. Ekqnw. i Teoret. 2%. 29,384 (1955); JETP. 330 (1956). Translated inSo&t [email protected]. [Z]K. 8. GIBSON, Phys. Rev. 8, 38 (1916). [3] R. S. &USENAN, Proe. ~~~~~ Ad. 2%. A. 26, 450 (1947). [4] M. H. L.PRYCX andW. A. Rui-icrim.~, IXscussions~~?~~~~.~o. 26, 34 (1958). [6] E.L. HENTLEY and R. A. Fo~n,iY~ectrochim. AC@ 15, 594 (1959).
[l]B.N.
493
2,
R. A. FORD and 0. F. HILL
vibration frequencies 216 cm-r and 178 cm-l-. We 244 cm-l and 194 cm-l, i&a-red frequencies of substitution of Crs+ in this lattice will perturb the vicinity of the Cr3+ site. Simple calculation suggests
I
t
I
may associate these with the the corundum lattice. The corundum frequencies in the that these frequencies should
I
5000
6000 Wavelength,
%
Fig. I Polarized absorption spectrum of ruby at 100°K. Table 1. Polarized absorption spectrum of ruby at 100°K Band
V
(cm-l)
Av (cm-l)
v -
16,760cm-1
Assignment
_1
16,760
0
0 -
0 4.l&, +-*A,@)
216 2
16,976
216
216
438
2 x 216
649
3 x 216
828
3 x 216 _t 178
222 3
17,198 211
4
17,409 179
5
17,588 181
6
17,769
1009
3 x 216 +- 2 x 178
1183
3 x 216 f
174
_-
IIcs
( w spectrum)
7 (peak)
17,943
1 (peak)
18,272
-._-
I,
4&,
-
3 x 178 ---
4~vx,
be reduced by about 10 per cent which would bring them into good agreement with the values observed in ruby.
3. Discussion The degeneracy of the 4T2g state of Cr*+ is lifted in ruby by the trigonai component of the crystal field (Cr3+ site symmetry is 0,). The derived states are 494
Vibronic coupling in the aT,, excited stctto of ruby
then *Etl) and 4A,,,. * Frequently, these states are classified under the pseudosymmetry CsV, i.e. 4E and 4A,, but this is not preferable when polarization and vibrational interaction are considered because the intensity of transitions depends on configuration interaction. Accordingly, the 4Ec,, t 4A,,, transition will be polarized perpendicular and 4A(1j t 4Af,, parallel to the C,-axis. The value of the trigonal field parameter JZ, calculated from the splitting of these components, is -220 cm-l. This is somewhat smaller than the value quoted by SUCANO and TANABE [6) of -350 cm-‘. Under C,, transitions from the ground state to the 4Etlt and *A(,, states are allowed because of the removal of parity restrictions. Since they result from intercon~gurational excitation, (t2,)3 -+ (tz,)” (e,), expansion in the excited state is to be expected because of the anti-bonding character of the excited e, orbital. Hence the Franck-Condon principle leads us to expect the transitions to be broad with a weak O-O band extended in progressions of the totally symmetric vibrations. In considering the observed vibrational structure in the o-spectrum which is accordingly associated with the *EC,, c 4Af,, transition, we must first resolve the lattice vibrations of corundum, which have been assigned under the space group B&3], in terms of the Cr3+ site symmetry~ This is done in Table 2. Table 2.
Resolution of lattice vibrations of corundum space and site group symmetries D3d
_-_
.----Symmetry
4,
A la A 20 A 221 E!l J%
class
No. of modes
-
-~_2 3 2 2 d 4
Activity
---/ [ Raman I
/ j
Inactive Inaotiva Infra-red Raman Infra-rod
in t,erms of
Observed frequencies (cm-l)
-
c3
class
_ ----___
578, 751
Ii
,4
244, 847 375, 417, 432, 450, 642 194, 328-355, 434, 909
~
I
E
It is then necessary, in making a vibrational analysis, to decide on the position of the O-O band. With the “-Erl, t 4Aol transition we have no fluorescence to aid us here, but by working at 100°K we can be sure that the observed vibrational frequencies are only excited in the 4E,1j upper state. Hence we may safely assign the longest wavelength band at 16,760 em-l to the O-O band. The spectrum is then seen to consist of a combined progression in the 216 cm-l and 178 cm-l frequencies which belong to the representations A and E, respectively. A summary of our vibrational analysis is given in the last column of Table 1. We should not, however, expect a progression in single quanta of an antisymmetric vibration to appear in an allowed transition. This will only happen if the excited state is distorted in such a manner that the antisymmetric vibration becomes totally symmetric under * The subscript (0) refers to the ground state. Excited states of similar orbital symmetry and spin multiplicity are then denoted (I), (2) . . . . . .in sequence of increasing energy. f6J S.
SUGANO
and Y. TANABX, J. Pkys. Sot. Jquan
18,880 (1958).
495
R. A. FORD arnd0. F, HILL
the lower symmetry of the distorted struct~ [7, 81. Let us now consider whether such a distortion is possible. The orbital degeneracy of the 4E(,, state will be lifted if the symmetrical configuration of this state is unstable with respect to any of its antisymmetric normal vibrational modes. JAHN and TXLLER[9] have shown that such instability will occur if the matrix elements of Sy*E,,) FE y4E(,, G?Tare non zero. Here V, is the appropriate operator for the vibrational perturbation. This will be so for the *I#(,, state of Cr3+ in corundum because the direct product of the vibrational representation E and the electronic state rep~sentat~on [E2] contains the totally symmetric representation A. The symmetry of the distorted configuration will then become C, under which the 178 cm-l vibration will be totally symmetric. The presence of a progression in single quanta of the perturbed 194 cm-l, E,, frequency of the corundum lattice in the 4_Eo)+- 4A(o, transition is therefore clear evidence of JAHN-TELLBIR distortion of the 4Ef,, state of Cre+ in ruby. /7] W. MQFFITT and W. THORSON, Phys. Rev. 108, 1251 (1957). [S] H. C. LONGWET-HIQCXNS,U. ~PIK, M. H. L. PRYCE and R. A. SAOK, PTOC.Roy. Sot. [Q]H. A. JABCN md E. TELLER, Proc. Roy. Sot. A. 161,229(1937).
A. 244,1 (19.58).