Indian Journal of Chemistry Vol.39A, Jan-March 2000, pp. 1 63 - 1 72

Electronic spectrum of GeTe: An ab initio based configuration' interaction study

Antara Dutta, Biswabrata Manna & Kalyan Kumar Das* Physical Chemistry Section, Department of Chemistry, Jadavpur University,

Calcutta 700 032, India

Received 8 October 1999; accepted 26 November 1999

Low-lying electronic states of GeTe within 40 000 em-I of energy have been studied by using ab initio based configuration interac­tion calculations which include relativistic effective core potentials (RECP) of Ge and Te atoms. We have computed potential energy curves of 1 8 1\-S states which correlate with the Ge(3Pg)+ TeCPg) dissociation limit. In addition, curves of two highly excited 3 11:+ and 3 1fl states are also computed. There are 1 2 bound states of the 1\-S symmetry below 40 000 em-I. Spectroscopic constants of these 1\­S states are reported and compared with the available experimental data. The ground state of GeTe is designated as XI1:+ which is dominated by at least two equally important configurations. The calculated T, and ro, values of XI1:+ are 2.395 A and 298 cm- I , respectively. The ground-state dissociation energy of GeTe is 3.67 eV as compared with the experimental value of 4. I ±O.4 eY. The calculated transition energy of the A'fl-X'1:+ transition is found to be 26 860 cm-I which is somewhat smaller than the experimental value of 27 75 1 em- I . The 211:+ state is tentatively assigned as the E state which is observed in the Ef-X absorption. Potential energy curves of all 50 11 states arising from the spin-orbit interactions amung 1 8 1\-S states are also computed. We have reported 1 7 11 states which are bound below 30 000 cm-I of energy. The 'fl2-'flo+ splitting is estimated to be about 2200 cm-I . The compositions of the spin­orbit CI wavefunctions of all bound 11 states at rc are calculated. Transition probabilities of several dipole-allowed transitions are calculated from CI energies and wavefunctions. The AI fl-X'1:+ transition is found to be strong. In presence of the spin-orbit coupling, A'fl,-X'1:+0+ and >flo+-X'Po+ transitions are most probable. Radiative lifetimes of the upper states A'fl, and >flo+ at the lowest vibra­tional levcl are estimated.

Introduction Spectroscopic features of diatomic molecules and

clusters of group IV/VI atoms have been studied experi­mentally a few decades agol-X• The compounds formed by germanium and group VIB are known to be good semi­conductors. In material science, GeTe is significant be­cause of its superconductivity observed at very low tem­perature, though it is a semiconductor molecule ' . Bar­row and co-workers2•3 have carried out ultraviolet ab­sorption spectroscopy of these molecules. A strong band of the D-X type has been observed for each of the series of molecules such as GeO, GeS, GeSe, and GeTe. More­over, weak E-X bands for GeO, GeSe, and GeTe have also been detected. For GeTe, it has not been possible to secure any good photographs of the E-X system but a tentative vibrational analysis is given. The ground state of this series of molecules is of the Ip symmetry. The vibrational analyses of the D-X system of GeSe and GeTe have been performed from the measurements of the spectra emitted by the high-current positive-column discharges4• In this measurement, the v ' (O,O) band of the D-X system of GeTe is assigned at around 27 699.3

em-I , while for the isovalent GeSe molecule, the same band has been observed in the region of 30 776.2 em- I . Later on, the D-X system of these molecules has been reassigned as the A'n-X1:l:+ band5. No experimental or theoretical studies regarding the transition probabil ity of the A-X transition and radiative lifetime of the Nn state have been carried out s o far. The rotational con­stants and equilibrium bond lengths of GeTe have been obtained from the microwave spectra observed by Hoeft and Nolting.6 Dipole moments and hyperfine structure of the diatomic .molecules of group IV/VI have been obtained from the Stark effect measurement on the pure rotational transitions 7.X . The dissociation energy of the E state derived from the vibrational analysis of the E-X system has been found to be 0.59 e V, and the products at the dissociation limit have been predicted to be GeCP) and TeCPg) . The ground state of GeX dissociates into GeepO)+XCP2) (X=O, S , Se, and Te) , while the disso­ciation l imit of the E state could not be determined with certainty. From the extrapolation of the vibrational lev­els of the E state of the E-X band, the dissociation en­ergy of the ground state of GeTe is estimated to be

1 64 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

4. 1 0±0.4 eY. Infrared spectra of the matrix-isolated ger­manium, tin, and lead chalconides have been studied by Marino et aU. Fundamental vibrational frequencies of these molecules have been reported both in vapour, ar­gon, and N2 matrix at low temperature. The vibrational frequency of GeTe in vapour phase is found to be 32 1 .4 . cm- I , while in N2-matrix it is 3 1 7.6 cm- I . Theoretical studies on these molecules are not much attempted be­fore. Only recently, large scale ab initio based configu­ration interaction (CI) calculations on the low-lying elec­tronic states of the GeSe molecule have been performed 10.

These calculations are now possible to carry out due to the availability of the RECPs of the constituent atoms.

The present paper deals with the computations of the potential energy curves and spectroscopic constants of several low-lying electronic states of GeTe by using ab initio based multireference singles and doubles configu­ration interaction (MRDCI) method which takes care of the relativistic effects through the effective core poten­tials. The spin-orbit coupling has also been included in the calculation to study its effects on the low-lying elec­tronic states. The calculations of transition probabilities of some dipole allowed transitions and lifetimes of up­per states are also topic of interest in the present study.

Details of the computation In the present study, CI calculations of the GeTe mol­

ecule have been carried out by using semi-core RECPs of Ge and Te. The outer 3d I04s24p2 electrons of Ge and 4dlO5s25p4 electrons of Te are being kept in the valence space, while the remaining inner electrons are replaced by the RECPs which are reported by LaJ ohn et al. I I . The primitive Gaussian basis sets which are compatible with the semi-core RECPs are also taken from the same ref­erence. Because of the use of RECPs, the total number of active electrons in GeTe is reduced to 30. In order to generate optimized molecular orbitals (MO) which are used as one-electron basis functions for the CI calcula­tions, we have performed self-consistent-field (SCF) cal­culations for the .. n2n2 5L+ state of GeTe at different in­ternuclear distances of the potential energy curve. The molecule is placed along the Z-axis. The entire calcula­tions have been carried out in the C2v subgroup of C�v in which the molecule belongs. Analyzing the compositions of the symmetry-adapted SCF-MOs at different bond distances, it has been found that 3d 10 electrons of Ge and 4dlo electrons of Te remain localized on the d-orbit­als of the corresponding atoms. Hence, 20 electrons oc­cupying 3d and 4d shells of Ge and Te, respectively are

not involved actively in the formation of the Ge-Te bond in the low-lying electronic states of the molecule. There­fore, these 20 d-electrons are not allowed to excite, and only 1 0 valence electrons remain active in the CI steps. The MRDCI method of Buenker and co-workers 12-15 have / been used for the CI calculations. The codes use the Table-CI algorithml6-18 to tackle open-shell configura­tions efficiently. For the lowest eight roots of each irre­ducible representation of C2v in a given spin multiplic­ity, a set of main reference configurations is chosen to describe the low-lying A-S states of the molecule. All possible single and double excitations have been carried out from these reference configurations. These excita­tions generate a large number of configurations. The larg­est dimension of the generated CI space is of the order of 2 00 000. However, a configuration selection tech­nique is used to reduce the size of the secular equation. In addition, the energy-extrapolation method along with the Davidson's correction 19.20 has been employed to esti­mate the full CI energies in the same AO basis. A thresh­old of 1 Jlhartree has been chosen for the configuration selection throughout the calculations. The dimension of the corresponding largest selected CI space is reduced to 33 000. The CI wavefunctions obtained from these calculations are used to compute one-electron property matrix elements.

Spin-orbit calculations have been performed in the C2} group. The integrals for the spin-orbit interactio.n are derived from RECPs of the corresponding atoms of GeTe by LaJohn et al. l l • The wavefunctions obtained from the spin-independent CI are multiplied with appro­priate spin functions which transform as Czv irreducible representation . Full CI energies estimated in the A-S CI calculations are kept as diagonal Hamiltonian matrix el­ements, while the off-diagonal elements are computed by using the RECP based spin-orbit operators and A-S CI wavefunctions. Many-electron spin-orbit matrix ele­ments for pairs of Ms values are calculated. To compute the final results, the Wigner-Eckert theorem is used. Spin­orbit components of each A-S eigenfunction obtained from the spin-independent calculations are included in the spin-orbit treatment. A I ' A2, and B I representations of C2} consist of all spin-orbit states in the calculation. Transition properties are extracted from the spin-orbit CI wavefunctions.

Potential energy curves of A-S and n states are fitted into polynomials, and vibrational Schrodinger equations are solved numerically2 ! . The electric dipole transition moments are averaged over pairs of vibrational func-

DUITA et al. : ELECTRONIC SPECTRUM OF Ge Te 165

'i E v

50000

40000

30000

-lJJ

20000

10000

O�---L���--�-----L----�--�--��----L---� 3 0 4-0 �O 6·0 7-0 8·0 9 0 10·0 no r / 00

Fig. I - Computed potential energy curves of the low-lying A-S states of GeTe.

tions involved in a given transition. Einstein spontane­ous emission coefficients are calculated from the result­ing vibrational matrix elements. Radiative lifetimes of vibrational levels of excited states are computed by sum­ming over their respective transition probabilities to all lower states and then inverting the total probabi l i ties. Transitions involving A In and 3n excited states of GeTe are given a special attention.

Results and Discussion

Low-lying A-S states and their potential energy curves The ground state (4s24p2; 3p g) of Ge interacts with the

ground state (5s25p4; 3Pg) ofTe to generate 1 8 A-S states of singlet, triplet, and quintet mUltiplicities. The type and number of s tates in each symmetry are given in Table I . However, interactions between low-lying states of Ge and Te produce many other molecular states of different

symmetries. The dissociation relationships between the atomic states (Ge+ Te) and the corresponding molecular states (A-S) of GeTe in the absence of any spin-orbit coupling are also shown in Table 1 . The experimental relative energies which are averaged over j at different dissociation l imits of the molecule are tabulated in Table I . We have compared the MRDCI estimated rela­tive energies of lowest three dissociation limits with the experimental values. The calculated energy of the IDg(Ge)+3Pg(Te) asymptote is about 1 000 cm-I larger, while for the third limit 3Pg(Ge)+ID g(Te), it is 1 000 cm-I smaller than the observed values as reported in the atomic energy data table22. In the present study, we are mainly concerned with electronic states which converge with the ground dissociation l imit 3Pg(Ge)+ 3PgCTe). In Fig . I , we have shown the potential energy curves of all 1 8 A-S states correlating with 3Pg(Ge)+3P/Te). In addi­tion, curves of two high-lying bound states such as 3 1P

1 66 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

Table I - Correlation between the A-S states of GeTe and atomic states at the dissociation limits.

Molecular States (A-S) Atomic states Relative energies in the dissociation (in cm-I) limits (Ge + Te) Expt.' Calculation

I L+(2), IL-, I IT (2), Ill, 3L+(2), 3L-, 3IT(2), 311, SL+(2),

sL-, SIT(2), 511 3p + 3 p 0 0 g g 3L+' 3L-(2), 3IT(3), 311(2), 3<1> 10 + 3p 7 1 25 8274 g g 3L+, 3L-(2), 3IT(3), 311(2), 3<1> 3p + 1 0 1 0559 9503 g g 3L-, 3IT I S + 3p 1 6367 -

g g IL+(3), IL-(2), I IT(4), 111(3),

1<1>(2), I i 10 + 10 1 7684 -g g

3L-, 3IT 3p + IS 23 1 99 -g g

'Averaged over j( Ref. 22)

Table 2 - Spectroscopic constants of the low-lying A-S states of GeTe!

State T / cm-I r / A ro/ cm-I . c

XIL+ 0 2.395 (2.340) 298 (32 1 )

3L+ 1 4 440 2.664 204

311 1 7 741 2.697 193

3L- 1 9 258 2.725 1 8 \ . III 1 9 400 2.767 1 69

I� 1 9 5 14 2.763 1 67

3IT 2 1 292 2.486 228

AlIT 26 860 (27 75 1 ) 2.6 1 3 1 69 (22 1 )

5L+ 27 280 3.33 1 8 1

21L+ 28 8 1 2 3 . 1 60 54

31L+ 38 436 3 . 1 82 1 3 8

3 1 IT 39 322 3.21 0 1 38

'Numbers in parantheses refer to the experimental values (Ref. 4)

and 3 1IT which correlate with higher asymptotes are also computed. There are several bound states of GeTe within 40 000 cm-1 of energy. Table 2 displays spectroscopic constants (T , r , and ro ) of the lowest l 2 A-S bound e e e states of GeTe. The remaining states are repUlsive in nature. The ground state is of the Xrp symmetry. The calculated re is 0.055 A longer than the experimental value of 2.34 A, while the vibrational frequency at the mini­mum of the potential well is 298 cm-1 as compared with the infrared spectroscopic value of 32 1 cm-1 • Earlier cal­culations23-25 suggest that the discrepancy is within the

accuracy of the MRDCI method. It is interesting to note that the ground state is not characterized by any single configuration, and it is a multiconfiguration state. As seen from Table 3, both crI2cr220}1t14 and crI2cr/cr/1t131t2 configurations participate strongly, while cr/cr22cr3cr41t14 contributes weakly in the formation of the X I 1:+ state of GeTe at reo The compositions of all bound A-S states are displayed in Table 3 .

The first excited state of GeTe is 31:+ lying 1 4 440 cm-1 above the ground state. The re and roe values of the 3p state are 2.664 A and 204 cm-1 , respectively. This state is reasonably strongly bound. The CI wavefunctions of the 31:+ state is found to be dominated by the open­shell configuration cr 12cr2 2cr/1t131t2 ' However, contribu­tions of two other configurations, namely, cr 12cr/cr/1t/1t/ and crI2cr/cr3cr41t131t2 are significant. A single excitation of the type . . . 1t14� . . . 1t131t2 not only generates 31:+ but also five other states of which, two are triplet multiplicities such as 31:- and 3�, and the remaining three singlets are of 11:+, 11:-, and l� symmetries. The ground state XI1:+ itself consists of about 35% contribution of the . . . 1t131t2 configuration . There exists no other lp state which is purely described by the . . . 1t 131t2 configuration . Tables 2 and 3 show that '�, ';-, l�, and 11:- states originate mainly from the same configuration . . . 1t1 31t2, and lie in the increasing order of energy. It may be noted from Table 3 that there is a 1 0- 1 5% contribution of a doubly excited configuration crI2cr/cr,cr41t131t2 (cr,1tl �cr41t2) in the char­acterization of these A-S states. The third excited state of the�� symmetry has a transition energy of 1 7 74 1 cm-1 , while 31:-, l�, and 11:- are nearly degenerate around 1 9 500 cm-1 • The equilibrium bond lengths of these states are much longer compared with the ground-state re, while the vibrational frequencies are smaller than the ground­state roc' None of these A-S states is suitable for allowed transitions to the ground state in the absence of the spin­orbit coupling. However, the situation changes once the spin-orbit interaction is taken into consideration.

There is a strongly bound 'IT state having a transition energy of 2 1 292 cm-1 at equilibrium. It has a shorter bond length with re=2.486 A as obtained from the MRDCI calculations . The equilibrium vibrational frequency in this state is considerably large. At around re, the CI wavefunction of 3n is dominated by a singly excited cr/cr/cr,1t141t2 configuration with c2=0.6 1 where c is the C I coeffic ient . A doub l y e x ci te d configuration crI2cr/cr31t1 31t/ (c2=0.22) is present strongly in this ex­cited state. Two more higher excited configurations: crI 2crz<J321t141t2 (c2=0.04) and crI2cr/cr41t141t2 (c2=0.04) also

DUTrA et at. : ELECTRONIC SPECTRUM OF Ge Te 1 67

Table 3 - Composition of 1\-S states at their equilibrium distances.

State Composition'

X1L+ 0120/0/ 1t14(48), 0/0/0/1t13 1t2(3S), 0/0/op41t

t(6)

3L+ 0120/0/ 1t13 1t2(74), 0 120/ 0/1tI2x/( l I ) , °120/0P41t13 1t2(7)

3fl. 0/0/0321t/ 1t

2(78), 0120/0P

41t13 1tPO), 0/0/0/ 1t121t/(4)

3L- 0/0/0/ 1t13 1t2(79), OI20/0P41t13 1t2( l 1 )

IL- 0120/03 2x/ 1t2

(77), 0120/OP4 1t13 1tP 3)

Ifl. 0/0/032x/ 1t

2(76), OI20/0

30

4 1t13 1tP S)

30 0120/031t14 1t/61 ) , 0120/031t1371:/(22), 0/0/041t14 1t2(4), 01202

032x14 1tzC4)

NO 0120/031t141t2(S8), 0120/031t131t/(2 1 ), 0120P32x14 1tzC7), 0120/0

41t14 1t2(3), 01 20/03

21t13 1t2(2), 012020/1t131t/( l )

5L+ °120/032 1t/1t/(93)

21L+ 0120/032 1t/1t/(69), 012022aP4 1t14( l 3), 0120/0P4 1t131t/4), 012a2

20/ 1t14(4), 0120/0/ ':14( 1 )

3 1L+ 0/0/OP4 1t14(3 1 ) , 0/0/0/1t/1t/( l7), 0120/0/ 1t131t/ I S), 0/0/0/ 1t14(9), 0120220P4 1t131t2(7),

0120220/1t14(6), 0/Op)204 1t14( l ) , OI20/0P61t14( l )

3 10 0120/031t1'1t/(39), 0120/0) 1t141t2(3S), 0/0/0

41t141t2( 1 4), 0/op/ 1t141t/l )

'Numbers i n parantheses are percentage contributions.

contribute in the formation of the 3n state. Analyzing the SCF-MOs, it is found that cr3 is a strongly bonding MO comprising of s and Pz atomic orbitals, while the 1t2 MO is strongly antibonding involving PxJy atomic orbit­als of Ge and Te. Therefore, the cr3�1t2' excitation makes the Ge-Te bond in the 3n state slightly longer than that in the ground state. The same cr3�1t2' excitation also generates In which is designated as the A state. As noted in Table 3, compositions of the CI wavefunctions of 3n

and Aln states are very similar. The Aln state is the same D state as denoted by Barrow and co-workers .2.3 It is an important state because of its involvement in the symmetry allowed transition AlnHX1I.+ which is ob­served experimentally. The MRDCI calculated transi­tion energy of the A 'n state is about 26 860 cm-' as compared with the observed value of 27 75 1 em-I . The computed re and we values of the A state are 2.6 1 3 A and 1 69 cm-' , respectively. The experimental re of this state is not yet known, while the observed we value is some­what larger than the calculated value (see Table 2) .

There is a weakly bound sI.+ state having a shallow potential well at the longer bond distance (re=3 .33 1 A). The potential well consists of only eight vibrational lev­els. The vibrational frequency at re is 8 1 em- I . The CI wavefunction of this state is dominated by cr/cr22cr321t/1t/ (c2=0.93). Other quintet states, namely, 2sr.+, 5I.-, 5n, 25n,

and 5� which converge with the lowest asymptote 3PgCGe)+3Pg(Te), are repulsive in nature. The 2 'I.+ state which has the same dominant configuration as in sP, is also very weakly bound. The re and we values of 2'P are 3 . 1 6 A and 54 em-I , respectively. The potential well can accommodate only seven vibrational levels. The remain­ing low-lying states such as 2 'n, 23P, and 23n which correlate with the lowest limit, are repulsive. There are no bound states in the 29 000-38 000 cm-' energy re­gion. The present calculations reveal two highly excited 3 'P and 3 'n states with transition energies 38 436 and 39 322 cm-' , respectively. Both these states dissociate into higher limits. The potential energy curves of these two states in the Franck-Condon region are shown in Fig. I . These states have similar re and we. The composi­tions of these states show their multiconfiguration char­acter. There is a strong mixing among various configu­rations as shown in Table 3. As for example, the domi­nant configuration (cr/cr/cr3cr41t,4) of the 3 1P state has only 3 1 % contribution at around re, while five other con­figurations contribute significantly. The 3 'n state is a mixture of three important configurations (Table 3).

The ground-state dissociation energy (Dc) of GeTe estimated from the present MRDCI calculations has been found to be 3 .67 e V which is somewhat smaller than the experimental value of 4 . 1 ±0 .4 eV as reported by

1 68 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

Table 4 - Dissociation correlation between the atomic and molecular states of GeTe in the presence of the spin-orbit

coupling.

Molecular Atomic states in Relative energies States (n) the dissociation (in cm-I )

l imits (Ge + Te) Expt.' Calculation

O+, 1 , 2 Jpo + ' P2 0 0

O+, 0-(2), 1 (3), 2(2), 3 'PI + 'P2 557 441

0+(3), 0-(2), 1 (4), 2(3), 3 (2), 4 'P2 + 'P2 1 4 1 0 1 330

0+ 'Po + 'Po 4707 60 1 1

0-, I 'Po + 'PI 475 1 40 1 6

0-, I 'PI + 'Po 5264 6470

0+(2), 0-, 1 (2), 2 'PI + 'PI

5308 4450

O+, 1 , 2 'Pz + 'Po 6 1 1 7 7346

0+, 0-(2), 1 (3), 2(2), 3 'Pz + 'PI 6 1 6 1 534 1

' Moore's table [ref. 22]

Drummond and Barrow4 from the UV absorption spec­tra. Earlier studies26 of group III/V semiconductor mol­ecules have shown that an improvement of Dc by 0. 1 -

0.2 e V is expected due to the d-correlation. The basis sets used in the present calculations are sufficiently large so that any further extension would unlikely improve the dissociation energy. The computed Dc of the excited A In state is about 0.34 e V.

Spin-orbit coupling and low-lying .Q states The above discussion has so far been restricted with

A-S states only. In this section we shall discuss about the effects of the spin-orbit interaction on these A-S states (Table 4). After the inclusion of the spin-orbit op­erators which are derived from RECPs, the A-S states of different symmetries interact through the same Q com­ponents. In the spin-orbit calculations, we have included all ] 8 A-S states which dissociate into 3Pg +3pg • Disso­ciation correlations between the atomic and molecular (Q) states of GeTe in presence of the spin-orbit coupling are given in Table 5. The 3Pg +3Pg l imit splits into nine limits which correlate with 50 spin-orbit states of O+,

0-, ] , 2, 3 , and 4 symmetries. The calculated relative energies of these nine asymptotes are compared with the experimental data22. The agreement is good for the low­est three limits. However, the energetic order of the re­maining six dissociation limits differs from the experi­mental one. It may be noted that the energy separations of three components of the ground state ePg) of Ge are in excellent agreement with the observed values. How­ever, the disagreement occurs in the spliuings of the cor­responding spin-orbit components of the 3Pg state of Te. The 3pl_3po energy separation of Te obtained from the MRDCI calculation is about 2000 cm- I, while the val­ues reported in the Moore's table22 suggest that 3PI and 3po components of Te are nearly degenerate.

Table 5 - Spectroscopic constants of the low-lying n-states of GeTe.

State T fcm-' r fA 00, fcm - ' Dominant A-S states at r,' , ,

XIL+o+ 0 2.40 1 295 X'L+(99)

'L+I

1 3 586 2.675 200 'L+(86), 'L-( 1 3)

'L+u- 1 4 2 1 3 2.672 1 97 'L+(94), '0(4), IL-(2)

l,1z 1 6 203 2.723 1 8 1 'd(7 ! ), Id(28)

'd , 1 6 833 2 .7 1 1 1 89 'd(99)

'dl 1 8 362 2.669 1 83 'd(84), '0( 1 2), A 1 0(2), 'L-( l )

'L-o+ 1 8 938 2.670 1 66 'L-(8! ) , '0( 1 8)

IL-o_ 1 9 279 2.673 1 62 IL-(72), 30(27)

'L-I

1 9 842 2.705 1 80 'L-(76), 'L+( 1 0), 30(7), 'd(4), A' 0(3)

Idz 20 6 1 3 2.653 1 73 'd(52), '0(32), 'd( l5)

'00+ 2 1 9 1 9 2.583 247 '0(64), 'L-(3 1 ), IL+(2)

'00_ 22 325 2.603 237 '0(67), IL-(26), 'L+(6)

'0 1 22 8 \ 0 2.577 238 '0(67), 'd( 1 4), 'L-( I 2), 'P(4), NO(2)

302 24 \ 30 2 . 6 \ 0 225 30(65), I d(20), 3d( l 3)

5L+o' 26 367 3. 396 78 5L+(76), 50(24)

A'O, 27 769 2.632 1 74 A 10(92), 3L-(3), 'L+(2), '0(2)

2IL'0' 29 350 2.969 1 29 2 IL'(89), '0( 1 0)

a Numbers in parantheses refer to the percentage contributions.

JM OF G( Te

7.() 8-0 r/Oo

100 n·o

Computed potential energy curves of the low-lying ltes of GeTe with 0=1 and 3.

5-0 '1-0 a.o r/oo so 100 11-0

1 69

- Computed potential energy curves of the low-lying states of GeTe with 0=2 and 4.

1 70 INDIAN J CHEM, SEC. A, JAN - M ARCH 2000

In Figs 2-5, we have plotted potential energy curves of all 50 Q states generated from the spin-orbit interac­tion of 1 8 A-S states. The spectroscopic constants of the bound Q states as obtained by fitting mostly the adia­batic curves are given in Table 5 . In some cases diabatic curves are fitted. The compositions of the spin-orbit CI wavefunctions at around rc are also given in the same table. There is a bunch of six A-S states whose energies are very closed to each other. The potential energy curves of these states in the Franck-Condon region also over­lap. The spin-orbit coupling will therefore affect these curves as well as their spectroscopic constants. The ground state XIL+o+ is almost pure XIL+, and hence re and we values are not much affected by the spin-orbit cou­pling. Two Q components of the 3L+ state are separated by about 627 em-I . The lower component 3L+1 correlates with 3PO+3P2 limit, while the upper one of the 3Po_ sym­metry dissociates into the next higher limit 3pl+3P2. The component with Q= 1 is composed of 3p (c2=0.86) and 3r,-(c2=0. 1 3) , while the 0- component at re is relatively pure with 94% contribution from 3P. As seen from Fig. 1 , the potential energy curves of 3L+ and 3n cross at r=4.3 an' But in presence of the spin-orbit interaction, avoided crossings of the curves of 3L+o_ and 3L+ 1 states with those of the corresponding components of 3n take place at around the bond length of 4.3 an' Of three com­ponents of 3L1, the component I is shifted upward by a large amount, and the remaining two components with Q=2 and 3 are shifted downward. The 3� state is found to be lower in energy than 3L1

3 by about 630 em- I . As

seen from Table 5, the 3L13

state is not interacted by any nearby component of the same Q. On the other hand, the 3L12 state is strongly influenced by I L12, and the 3L11 com­ponent is composed of 3L1(c2=0.84), 3n(c2=0. 1 2) , Nn (c2=0.02), and 3L-( c2=0.0 l ) . As a result of the mixing with 3nl ' the re of the 3L11 component is shortened by 0.028 A. The we values of all three components of 3L1 remain almost unchanged. Some avoided crossings at the shorter and longer bond distances are also noted for 3L11 and 3L12 components .

The second 0+ component of GeTe is dominated by 3L- with 1 8% contribution from the 3TI state. Such a mix­ing lowers the bond length of 3L-o+ by 0.055 A. The spin-orbit splitting between the two components of the 31:- state is about 900 em-I as obtained in the present study. The potential energy curve of 3L- crosses with the 3n curve at r=4.7 an (see Fig. O. Such a crossing is not allowed between the 0+ components of these two

states. A strong avoided crossing between the curves of 3L-o+ and 3TIo+ may be noted in Fig. 2. After analyzing the spin-orbit CI wavefunctions of 0+ components, it is found that in the bond distances below 4.8 an' second and third 0+ components are dominated by 3n and 3L-, respectively, while at the longer bond length regions, the dominant states are interchanged. As a result of such crossing, the nature of the potential energy curves of 3L-o+ and 3no+ is changed considerably. We have fitted the adiabatic curves for the spectroscopic constants re­ported in Table 5 . The 3L-1 component also undergoes similar avoided crossing with 3TII . The IL-o_ compo­nent lies in between 3L-o+ and 3L-

I. The bond length of

the IL-o_ component is also shortened considerably due to strong mixing with 3TIo_ (c2=0.27) as evident from Table 5 . The CI wavefunction of the 1L1, component near re shows that there i s a strong mixing of 1L1(52%), 3TI(32%), and 3L1( 1 5%) . The spin-orbit coupling, there­fore, increases Te of 1L12 by 1 200 em- I and decreases the bond length by about 0. 1 1 A.

Four components of the 3n state are heavily mixed up with the similar components of the nearby states. The largest splitting between 3TIo+ and 3n2 has been found to be 2200 em- I . The energetic order of these components is 0+, 0-, I , and 2. All four components of 3n suffer elongation of the Ge-Te bond due to the strong cou­pling with other states. As is discussed before, the po­tential energy curves of 3TIo+ and 3TI I undergo strong avoided crossings with that of 3L-o+ and 3L-1 ' respectively. There are sharp avoided crossings of the curves of 0+ and I components of 3n with 5L\+ and 5L+I , respec­tively at around 6 .0 an as noted in Fig. 2. The 3TIo_ curve also undergoes an avoided crossing with the IL-o_ curve at around 4.7 an' Spectroscopic constants and potential energy curve of the 3TI2 component are also strongly af­fected by its interaction with 1L12 and 3L12• At around 5 .8 an' the sharp avoided crossing between 3n2 and 5L+2 is seen in Fig. 5 . As we have already seen that the 5p state is very weakly bound, we have reported spectroscopic parameters of the 0+ component only. The 5L+()+ state is the fourth 0+ state of GeTe, and this state is composed of 76% 5p and 24% 5n at re ' The transition energy as well as the vibrational frequency of the N n state are im-

. proved after the inclusion of the spin-orbit coupling. The computed transition energy of NTII is 27 769 em-I which matches almost exactly with the observed A-X transi­tion energy of 27 751 em-I . The N nl state is dominated by NTI with small contributions from 3L-, 3L+, and 3n.

DUTIA el al. : ELECTRONIC SPECTRUM OF Ge Te 1 7 1

Table 6 - Radiative lifetimes(v'=O)of some excited A-S states of GeTe

Transition Partial l ifetime of Total l ifetime of the the upper state (�s) upper state (�s)

A'n-X IL+ 1 .70 A'n-IL- 8 1 .9 t(A'n)= 1 .67 3n-3L+ 7 1 .2 3n-3d 1 .74X \02 3n-3L- 6.37x J 02 tCn)=68.3

Transition properties and Lifetimes of the excited states In the absence of the spin-orbit coupling, the A'n,

state of GeTe is the only excited state which undergoes two dipole-allowed transitions: A 'n-X'l:+ and A'n­'!;-. The transition probabilities calculated from the MRDCI wavefunctions suggest that the A-X transition is much more probable than the A 'n-'!;- transition. Al­though transition dipole moments of these two transi­tions are comparable (see Fig. 6), the larger energy dif­ference in the former transition makes it more probable. Table 6 shows the radiative l ifetimes of the upper states at v'=O. For the observed A'n state the lifetime is calcu­lated to be 1 .67 �s. There are no experimental data for comparison. Besides A'n, transitions involving the 3n state are also considered. Transition moments of all three transitions: 3n_3!;+, 3n_3�, and 3n_3!;- are considerably large, but small !:lE values make these transitions weak. The 3n state is found to be long-lived. In Fig. 6, we have plotted transition moments of all five transitions as a function of the Ge-Te bond length .

After the inclusion of the spin-orbit coupling, many other transitions become allowed with �n=o, ± 1 . Table 7 shows all possible transitions involving A 'nl ' 3no+. O-" ,2 and 3!;+, components. The estimated partial life­times of the upper states of most of these transitions are somewhat large. Only two transitions, namely, A'n,­X'!;+o' and 3no+-X'!;+o' are found to be more probable. Other transitions are fairly weak. The total radiative life­time of A'n, as obtained by summing up 1 3 transitions shown in Table 7, is estimated to be 1 .55 �s, while that of 3no+ is 4 . 1 2 �s . The remaining components of the 3n state are longer-lived. The lifetime of the 3!;+, compo­nent is about 1 62 �s.

Comparison with the isovaLent GeSe moLecuLe Recently, spectroscopic features of the low-lying states

of GeSe have been reported from the MRDCI study. '0 It may be interesting to compare the present results of GeTe with those of the isovalent GeSe molecule. Potential energy curves of 1 8 low-lying states of these two mol-

0040 -,---------------, ;:1 III :: 0 .30 c: III 8 o 8 0 .20 I=l o ..... ..., .... til I=l 0 . 1 0 III s... Eo-<

0 . 0 0 4 . 0

a : Alrr-xl2;+ b: 3rr _32;+ c : Alrr_ l2;-d: 3rr _ 3 tl e : 3rr _32:-

4 .5 5.0 5.5 6 .0 r{ Ge-Te ) in Bohr

6.5 Fig. 6 - Transition dipole moment functions of five transitions

involving A'n and 3n states.

ecules dissociating into 3Pg + 3Pg look similar. Three states such as '!;-, 3L-, and '� of both molecules are nearly degenerate. In general transition energies of the low-ly­ing excited states of GeTe are lower by about 3000 cm-' as compared with those of the corresponding states of GeSe. The 2'!;+ state of GeSe is found to be more strongly bound than that of GeTe. As expected the Ge­Se bonds in the ground and low-lying bound states are shorter than Ge-Te bonds due to the smaller size of the Se atom. The configuration mixings in the A-S states are found to be stronger in GeTe than GeSe. The ener­getic order of the spin-orbit components of 3!;+, 3�, 3L-, and 3n states of both molecules are same. However, due to the presence of the heavier atom, the spin-orbit splittings in GeTe are larger than those in GeSe. The transition probability of the most probable A'n-X'p transition in GeSe is higher than that of the similar tran­sition in GeTe. As a result, the A'n state of GeSe is shorter lived than that of GeTe. The radiative lifetime of A 'n in GeSe is 0.42 �s, while for GeTe, the value is 1 .67 �s.

Concluding Remarks The present MRDCI calculations based on semi-core

RECPs confirm the ground state of GeTe as X'P. The calculated spectroscopic properties of the observed X'L+ and A'n states agree well with the experimental values. Three states: 3L-, '�, and '!;- are nearly degenerate with transition energies around 1 9 500 cm-' . The Ge-Te bond length in the 3n state is comparatively short. The calculations reveal that the ground state is a mixture of two equally important configurations : cr /o}o} 1t,4( 48%)

1 72 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

Table 7 - Radiative l ifetimes at v'=O of some excited a-states of GeTe.

Transition Partial l ifetime Total l ifetime of of upper state the upper state ( Ils) ( Ils)

N n ,-X'L+o+ 2.43 A'nl-IL-o- 45.9 N n ,-'dz 1 .06x \ O

z

N n ,-3dz I .39x l Oz A lnl-3L+o_ 1 .55x \ Oz A

lnl-3L+1 2.79x 1 02

A 'nl-3 no_ 9.68x \ Oz A'n ,-3 no+ 1 . 1 3x I 0) N n,-3d, 4.02x 1 03 A ' n l-3 nz 5.36x 1 03 A ' nl-3L-1 6.4 l x 1 03 N n ,-3L-o+ 1 .45><1 Q4 N n,-3 n , l .72x l O.l t(A'n, )= 1 .55

3 no+ _XIL+o+ 4. 1 2 tC no+)=4. 1 2

3 n l-'L+o_ 45.0 3 n l-3L\ 90.8 3 nl-X IL+o+ I . l Ox I Oz 'tcn 1 )=23.63

1 no-- _lL+o_ 68.3 3 no-- _lL\ 1 .94x l Oz tcno_)=50.52

3 nz -JL+I 39.0 tC nz)=39.0

3 L+ I-XIL+o+ 1 .62x l OJ tC L+,)=1 .62x l Oz

and crI20,/cr/7t137t2(35%). The present calculations sug­

gest that the 2 1L+ state having a shallow minimum at r=3. 1 6 A, is the possible candidate for the E state which has been reported by Drummond and Barrow4 in the E� X absorption at around 3 1 470 cm-I . The calculated 2IL+-X'-P transition energy is 28 8 1 2 cm-I which is about 2600 cm-I smaller than the observed transition energy of the E state. There is no other nearby state which can be assigned for the E state. The calculations also reveal the existence of two highly excited singlets 3 1L+ and 3 1n which are relatively strongly bound.

The spin-orbit coupling is found to be important in the description of the electronic spectrum of GeTe. The 3n2-3no+ splitting has been found to be the largest. Sev­eral avoided crossings change the shapes of the poten­tial energy curves. The interactions among the compo­nents of 3n, 3L-, IL-, 3L+, 3�, and I� states are notice­able. The spectroscopic constants of the spin-orbit com­ponents of these states change considerably due to such interactions. The A'n-xIL+ transition is the most prob­able one. The radiative lifetime of the A'n state is esti­mated to be 1 .67 Ils, while that of 3n is considerably large. The A Inl state, however, undergoes several weak

transitions of which A Inl-XIL.+o+ is the strongest. The total l ifetime of A Inl at v ' =0 is estimated to be 1 .55 Ils. Another reasonably strong transition 3nO+_XIL+o+ is yet to be observed. The radiative lifetime of the 3no+ com­ponent at the lowest vibrational level is of the order of 4. 1 2 Ils.

Acknowledgement The authors are grateful to Prof. Robert J Buenker,

Wuppertal, Germany, for his permission to use his MRDCI codes.

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