Bipolaron formation and desorption following Auger decay in polyacetylene

Solid State Communications, Vol. 61, No. 3, pp. 203-206, 1987. Printed in Great Britain.

0038-1098/87 $3.00 + .00 Pergamon Journals Ltd.

BIPOLARON FORMATION AND DESORPTION FOLLOWING AUGER DECAY IN POLYACETYLENE C.-M. Liegener, W. F6rner and J. Ladik Institute for Theoretical Chemistry, Friedrich-Alexander-University Erlangen-Niirnberg, Egerlandstr. 3, D-8520 Erlangen, West Germany

(Received 25 July 1986 by A. Zawadowski) The Su-Schrieffer-Heeger model has been applied to a trans-polyacetylene chain with two holes at the top of the valence band. In the kink-free chain the formation of a kink-antikink pair is observed. This is deformed to a polaron pair due to end effects and the lack of dissipation in the model. In the case of an end-kink configuration desorption may occur. The influence of a substitutional NH impurity on these phenomena has been discussed. RECENTLY THE FORMATION of a bipolaron oscillating between two stages (a kink-antikink pair and a bound-polaron pair) in doped polyacetylene has been discussed [1], where doping was assumed to result in placing two additional electrons at the bottom of the conduction band. A similar situation arises if one considers a system with two holes at the top of a valence band. Such configurations will appear as final states in Auger transitions. The transition rates for the corresponding Auger decay are large for such outer-valence double-hole states and, due to the delocalization of the corresponding orbital, almost independent of the core ionization site along the chain. The time evolution of the doubly ionized transpolyacetylene chain is studied within the Su-Schrieffer -Heeger (SSH) model [2]. The procedure developed by Su and Schrieffer [3] for the study of soliton dynamics in polyacetylene is used for the integration of the equations of motion. The motion of the CH groups is described in terms of the so-called staggered parameters ~bt defmed as ~bi = (-- 1)~ui where us is the physical displacement of the i-th CH unit. Within the Born-Oppenheimer approximation the coordinates ~i describe a classical coupled motion in a potential V({ff~}) [4] given by

v({~t}) = E ( { ~ } ) +

(~ + ~.,)2

--A(ffl + (-- 1)N~0N).

(1)

Here N is the number of CH units in the chain, K is the effective spring constant, A is a parameter which stabilizes the system against lattice shrinking [5], and E({~b~}) is the total n-electron energy. For the calculation o f E a HiJckel-type Hamiltonian is used where the resonance integrals/~t, 5÷1 are expanded linearly about the undirner203

ized C - C distance. The matrix elements of the Hamiltonian are

HiJ=

{

--/~0--(--1)i+l~ffj+~i),

/=

--/$0 + (-- 1)i+1 ot(tb] + ~i),

/ = i-- 1

Ii, 0

/=

i+ 1

i

otherwise.

(2)

The zero of energy is chosen so that I i = 0 for carbon atoms. Furthermore for polyacetylene 3o = 2.5 eV and t~ = 4.1 eVA -1 was chosen [3]. The classical equations of motion for the ~ are then solved iteratively in time steps of r = 1.25 x 10 -is s. The initial configuration is ~ki = Uo

Vi = 1 . . . N ,

where Uo is the equilibrium Peierls distortion (Uo = 0.037 A). Figure 1 shows the results for N = 40. Two electrons have been removed from the top of the valence band. The corresponding orbital is always bonding on the shorter, antibonding on the longer bonds. In consequence, removing two electrons from this orbital should destroy the bond alternation. In fact, the alternation is reversed in the middle of the chain and this region (characterized by ~t ~ -- uo) is separated from the parts of the chain with the original alternation by a kink-antikink pair separating and travelling apart from each other in time. If the end of the chain is almost reached the feature is deformed to a pair of two polarons which will dissipate to give almost the original configuration with some elongations, mainly at the end of the chain. After this, again a kink-antikink pair is generated and the motion starts from the beginning. This behaviour is similar to the motion of the bipolaron obtained by Wang et al. [1 ] for a cis-polyacetylene chain with periodic boundary conditions and

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BIPOLARON FORMATION AND DESORPTION

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Fig. 1. The normalized staggered parameter ~t = ¢dUo for a chain of 40 CH-units with two holes at the top of the valence band in time steps of 5r beginning from t = 0 (bottom picture, full line) until t = 35r (top picture, dashed line). two additional electrons at the bottom of the conduction band. Note, however, that in our case the kink-antikink pair is not bound, but is only stopped by the end effects o f the chain. (This has been checked by performing calculations also on larger chains with up to N = 80.) In the calculations of Wang et al. a bound kink.antikink pair was obtained due to the periodic boundary conditions. In Fig. 2 we give the results f o r N = 41. In this case

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Fig. 2. The normalized staggered parameter t~i = d/i/Uo for a chain of 41 CH-tmits with two holes at the top of the valence band (same time steps as in Fig. 1 .). there is an end kink with a single bond at the right end of the chain. It is interesting to note that the kink does not travel to the middle of the chain as it would do in the case of a neutral chain. Instead, there are large displacements at the right end o f the chain which can be interpreted as leading to desorption of a C2 H2 molecule at this end at t = 10~'. Due to the restrictions on the potential, however, the system is forced back to an oscillation in our model. The desorption phenomenon itself, is not surprising because double-hole states are known to play a role in electronically stimulated desorp-

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BIPOLARON FORMATION AND DESORPTION

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Fig. 3. The normalized staggered parameter ~i = ~i/Uo for a chain of 41 units with NH substitution at i = 30. (Two holes at the top of the valence band, same time steps as in Fig. 1 .)

Fig. 4. The normalized staggered parameter ~i = ~i/Uo for a chain of 41 units with NH substitution at i = 20. (Two holes at the top of the valence band, same time steps as in Fig. 1.)

tion [6, 7]. It is interesting, however, to observe that desorption may occur at the end of the chain while the double-hole state may originate from Auger decay after core ionization at the middle or even at the other end of the chain because of the delocalization of the orbital involved and the related approximate independence of the transition rates from the core ionization site, a mechanism which may for instance lead to nonlocal effects in radiation damage formation. Substitutional impurities may have dramatic

influence on soliton dynamics in polyacetylene and even act as soliton-traps [8]. We have, therefore, studied also chains with a NH substitution for CH putting the NH group in the same place where previously the CH group was situated. In consequence of this the function E({~q }) is changed but as first approximation we have recalculated K in the second term of the r.h.s, of equation (1). Since NH already has a kink-like structure, we have taken as initial configuration one where ~I'i passes over an interval of 14 units from + uo to -- Uo in the form of

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BIPOLARON FORMATION AND DESORPTION

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at i = 30, Fig. 4 the results for a NH-group in the middle of the chain (i = 20). In the first case the kink travels to the middle of the chain, back to the NH-group and then the motion is repeated. In the second case there is almost no dynamics at all. In either case it seems that the NH-group blocks the formation of a bipolaron because the highest occupied orbital is the N lone pair. Finally the last calculation (NH at i = 20) was repeated for N = 40 (Fig. 5). In this case there is an end kink and the desorption phenomenon is similar to that in the pure chain. To summarize: We have found that double-hole states such as will arise as final states in Auger processes may lead in the case of a kink-free chain to the formation of a kink-antikink pair. This is deformed to a polaron pair due to end effects and the lack of dissipation in our model. In the case of an end-kink configuration the double-hole state will lead to desorption of an acetylene molecule at the end, even if core ionization was at a different site in the chain. NH substitution will destroy the bipolaron feature, but not the desorption phenomenon.

Acknowledgement - The £mancial support by the "Fonds der Chemischen Industrie" is gratefully acknowledged. -2

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REFERENCES 1. 2. 3. -2

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Fig. 5. The normalized staggered parameter ~ = ~i/Uo for a chain of 40 units with NH substitution at i = 20. (Two holes at the top of the valence band, same time steps as in Fig. 1 .) a tank-function and N = 41 was chosen. Figure 3 shows the results if the NH-group is placed

5. 6. 7. 8.

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