Fast dissociation of resonantly core excited H2S studied by vibrational and temporal analysis of the Auger spectra

THEO CHEM ELSEVIER

Journal of Molecular Structure (Theochem) 394 (1997) 135- 145

Fast dissociation of resonantly core excited H2S studied by vibrational and temporal analysis of the Auger spectra Amaldo Naves de Brito”,*, Alexandre Naves de Britoa, Olle Bjiirneholm”, Joaquim Soares Netoa, Andre Bueno Machadoa, Svante Svenssonb, Andrus Ausmeesb, Stuart J. Osborneb, Leif J. Szethre”, Helena Akselad, Olli-Pekka Sairanend, Antti Kivim2kid, Ergo Ndmmisted, Seppo Akselad of Physics,

“Deparrmenr bDeparrment

of Physics,

‘Department dDepartmenr

Universiry Uppsala

of Chemistry, of Physical

of Brasilia,

University,

University

Sciences,

70910-900 Brasilia

DF, Brazil

Box 530, S-752 21 Uppsala, Sweden

ofBergen,

N-5007 Bergen, Norway

Oulu University, FIN-90570

Oulu, Finland

Received 22 November 1995; accepted 13 June 1996

Abstract Excitation of a core electron to the lowest unoccupied orbital of H2S has been shown to give rise to dissociation that occurs faster than the Auger decay. Recent experimental data have allowed us to resolve vibrational structures connected with the resonant Auger decay in the core excited S*H fragment. At some photon energies, hot bands resulting from the decay of the vibrationally excited levels, v = 1 and v = 2, in the core excited fragment are observed. A new generalised potential energy surface for the 2p-‘6aI state of H2S is presented. Calculations of the vibrationally excited states at different points through the dissociation channel of the potential energy surface are presented. These allow determination of the point on the surface which has vibrational splitting consistent with the experimental values, revealing the geometry of the fragment when the core excited

state decays. A new method, based on the core hole lifetime as an internal “stop-watch”, to determine the characteristic time for dissociation of the H2S * molecule into H and S ‘H fragments from experimental data is presented. This result is compared with values obtained using the potential energy surface calculations. 0 1997 Elsevier Science B.V. Keywords:

Auger spectra; Potential energy surface

1. Introduction Recently, with the advent of high-resolution monochromators and high-intensity undulator beam lines in the soft X-ray range, it has become possible to study dynamic processes occurring in molecular core * Corresponding author. Present address: Department of Physics, Uppsala University, Box 530, S-75221 Uppsala, Sweden.

excited species. Earlier, these studies were common only at lower excitation energies for processes involving excitations of valence states. Core excited states are interesting because they exhibit strong intrinsic localisation and, therefore, very selective dissociation can be achieved for certain excitations. Also, the resonant Auger electron spectra, resulting from the decay of the core excited states, have turned out to be very valuable for the study of dynamic

0166-1280/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved SO 166- 1280(96)04828-2

PII

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processes of molecular fragmentation. Among these, the following aspects can be mentioned: (i) ultra-fast dissociation occurring before electronic decay, and (ii) the study of vibrational progression on core excited and singly ionised states of molecular fragments. The complex features observed in these experimental spectra require state-of-the-art calculations for correct interpretations of the physical phenomena observed. Indeed, the first observation of ultra-fast dissociation occurring before the Auger decay was reported in the mid-eighties [l] for the 3d-‘a* resonance of HBr. Later, 2~~‘a* core excited HCl was also found to decay predominantly after fast dissociation [2]. The first triatomic molecule, studied by a combination of spectroscopic techniques and ab initio calculations, was H2S on 2p - 6a,,3b2 resonant excitation [3,4]. Also, fast dissociation of one hydrogen atom before electronic Auger decay was found to occur. Owing to experimental limitations related to moderate intensity and resolution, it was not possible to obtain unambiguous information about either the geometry or the lifetime of the core excited states involved. Later on, weak structures connected with the above-mentioned process were also observed in electron-induced spectra [5]. For these, it was possible to observe vibrational fine structure in the Auger decay of the S*H fragment after resonant excitation, but it was not possible to obtain definite quantitative information regarding the vibrational structure. More recently, using highintensity undulator radiation from the MAX 1 synchrotron, it was possible to obtain new information on the H2S problem. The enhanced resolution made it possible to unveil the molecular-field splitting of the S 2p photoelectron lines. Consequently, it was possible to determine a much lower and hence more accurate lifetime width of 70 meV for the S 2p-’ state [6]. Analysis of the H2S fragment also showed strong propensity rules for the Auger decay of molecularfield split core excited states [7]. In this work we present an extended potential energy surface calculated for the 2p-‘6al state of H?S. Carefully chosen points on the surface are calculated using ab initio multi-configurational self-consistent field (MCSCF) wavefunction. The connected four-dimensional potential energy surface is generated using an interpolation program for all the points in the space needed for the calculation of

dynamical properties. For this process, care was taken to avoid the introduction of strong spurious wiggling in the generated surface by the interpolation procedure. Vibrational energies along one of the dissociative channels were calculated. Comparison with the experimentally determined hot-band splitting allowed the derivation of a H-S *H distance, at which the dissociation can be considered to have produced the fragments H and S*H. In the resonant Auger spectra, contributions from both H-S*H and S*H decay are identified. By comparing the relative intensities of these two contributions and using the known lifetime of the 2p-‘6at core excited state as an internal “stopwatch” [9], we get an independent value of the time required for the dissociation of the core excited HS *H molecule. Using a semi-classical model, we calculate the H-S*H distance corresponding to the derived dissociation time, which allows a comparison with the value obtained from the vibrational analysis.

2. Potential energy surface calculation interpolation Fig. 1 shows indicate the H$ Rl, R2, D, and The process surfaces for a

Rl

and

a description of the notation we use to interatomic distances and angles, i.e. 19. of calculation of potential energy triatomic molecule such as H$ is

H

‘\

s\H Fig. 1. H >S molecule with angle and distances indicated. R I and R2 are the S-H distances, 0 is the H-S-H interatomic angle, and D is the interhydrogen distance, H-H. The distance D is a function of Rl, R2, and 0.

Arnaldo

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time consuming owing to its multi-dimensional nature and the large scale ab initio calculation involved. Therefore, an optimisation procedure to obtain the four-dimensional surface must be employed. In the present case, an accurate description of the dissociative channels is critical for obtaining information on the dissociation process we are aiming to describe. Three possible dissociative channels are present for the H2S molecule [3,4]: (i) dissociation of only one hydrogen, H + S*H; (ii) dissociation of both hydrogens as independent atoms, H + H + S *; and (iii) dissociation of both hydrogens forming a hydrogen molecule, H2 + S*. The channels H + S*H and H + H + S* are described using the coordinates R 1, R2, and 8. These coordinates were found to be adequate since by fixing 0, three-dimensional curves with varying Rl and R2 can be plotted, allowing the two dissociative channels to be followed easily. For the third dissociative channel, Hz + S *, a better set of coordinates is R 1, R2, and D, where D is the distance between the hydrogens. In this case, a possible threedimensional curve would be R 1 = R2 plotted versus D and the total energy. By choosing values of D approaching the Hz equilibrium distance, it is possible to foliow this third dissociative channel easily, thus checking the quality of the calculations (see Ref. [3] for figures and details on these calculations). In order to obtain the four-dimensional potential energy surface, we employed a spline procedure using the calculated points as well as an approximation explained below. This allowed us to obtain energy values for arbitrary H$S geometry. We explain below in more detail how the interpolation was done. Three potential energy surfaces for the 2pm’6a, state at the fixed bonding angles 8 of 91.96”, 135”, and 180” were taken from Ref. [3]. These curves describe the dissociative channels H + S*H and H + H + S *. Calculation of the surface at eequ = 9 1.96” was chosen because this is the ground state equilibrium bond angle obtained from a theoretical geometry optimization [3]. This agrees very well with the experimental equilibrium angle of 92.12”, the ground state angle [8]. According to the calculations, the molecule in the 2p-‘6a, state has its energy minimum at 180”, and consequently we made more extensive calculations at geometries with 19> Bequ. The surface energy was found to be only very weakly dependent on the opening angle 0, and only one extra point

Structure

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131

between 180” and eequ was found to be needed to describe adequately the changes in potential energy. We used 135” as the mid-point. For smaller angles, only one dissociation channel is to be described, namely the S* + Hz dissociation. For the description of this channel, some values were taken from Ref. [3], and new points were added to improve the spline interpolation. For these calculations, the basis set and the active space were kept identical to the previous calculations. A detailed description of these parameters is given in Ref. [3]. For calculation of the four-dimensional surface, we had to provide the energy of additional points at bonding angles smaller than 9 1.96”. In order to describe the dissociation for decreasing angles without wasting time calculating points of no physical interest, we first calculated more points describing the symmetric dissociation of H2 + S* using the MCSCF program. This curve had already been partially calculated for H-S distances Rl = R2 equal to 2.53, 2.75, and 3.00 a.u., and for various H-H distances D varying from 0.4 to 4.2 a.u. [3]. We then used a surface spline procedure to interpolate these points, for which the order was kept low to minimise interpolation-induced wiggling. This surface is referred to as H-H. Based on this surface, we have used the following method to generate surfaces for angles i9ranging from 4.5” to 45” in steps of 4.5”. As a first approximation, the potential energy E(Rl,R2,8), taken at the bonding angle 8 and S-H distances R 1 and R2, is different from the potential energy E(Rl,R2,91.96”) owing to the H-H interaction, since the S-H distances are kept constant. If we represent this correction factor due to change in the H-H interaction by “Corr(R l,R2,91.96”,0)“, where Corr(R 1, R2,91.96”, 19) = E(R 1, R2, B)/E(R 1, R2,9 1.96”)

(1)

we can then write E(Rl,R2,Q=E(Rl,R2, 91.96”)Corr(R 1, R2,9 1.96”, 0). However, calculating these corrections would require the same computational effort as calculating the whole E(Rl,R2,q). An approximation can be used instead. First, the distance between the hydrogens in the H2S molecule having the coordinates Rl, R2, and 0 is called D(Rl,R2,8). Instead of using the parameters Rl and R2 in the calculation of the corrections, we

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of Molecular Structure (Theochem) 394 (I 997) 13% 145

substitute them with a single parameter RI = R2 = Rm, where Rm is the average internuclear distance: Rm = (R I + R2)/2

-392.3

(2)

Now we define a new 0m that is the H2S internuclear angle for the following geometry: HS distances Rm and H-H distance equal to D(Rl,R2,8). Using these parameters we can define energies E(Rm,Rm,Bm). These energies were obtained directly from the potential energy surface H-H, which describes the dissociative channel S* + HZ. So, for a given angle 0, distances R 1, R2, and energy E(Rl,R2,8,,,), we can calculate new energies for 0 < eequ, E(R 1,R2,0), using the following formulae: Corr= E(Rm, Rm, Bm)/E(Rm, Rm, Omequ)

(3)

E(R 1, R2,O) = CorrE(R 1, R2, Oequ)

(4)

Note that here Omequis the angle for HS distances equal to Rm and H-H distance equal to D(R 1, R2, qequ). E(Rl,R2,q) is the value of the energy calculated at S-H distances Rl, R2 and angle @ according to Fig. 1. For values out of the H-H surface we use the corresponding boundary value. The reason we expect this approximation to be valid is that it is used only for angles t9 smaller than eequ, and in these cases of geometry the only physically important dissociative channel is S + Hz. In this channel, the interaction between the two hydrogens is the most important in describing correctly the dissociation. This interaction is well described in our approximation, since only the H-S distance is taken as the average, while the H-H distance is not approximated because we calculate the new 0m and emequ for the corrected H-H distances. Further, since the exact correction given by Eq. (1) contains Rl and R2 in both the denominator and nominator, the replacement of these by Rm in the approximated correction (Eq. (3)) should not give rise to any large errors. A value of the correction other than unity is expected to be largely related to the different @m and #mequ occurring in the nominator and denominator. These angles correspond to the correct distance between the hydrogens, thus giving fairly accurate approximated correction factors “Corr” (Eq. (3)). Finally, it must be pointed out that for the dissociation phenomena we are dealing with in this paper, the dissociation channel H2 + S plays a negligible role

-392.4

5‘ d

-392.5

i B

-392.6 -392.7 2 2

4

Ci

6

s

8 10 R2

(a.u.)

Fig. 2. Calculated potential energy surface for the 2pm’6al state of H2S at 0 = 45”. The H + S*H dissociative channel is Indicated by a horizontal arrow. The H-S interatomic distance where the vertical excitation from the ground state takes place is indicated by a vertical arrow.

and therefore the importance of the energy points with 0 < 19~~”is small. An example of these generated surfaces is given in Fig. 2. Here the bonding angle was fixed at 45”. Similarly to the surface generated at tiequ, it can be seen that there is no barrier in the direction of the strongly dissociative H + S*H channel, indicated by an arrow. However, there is a barrier towards the dissociative H + H + S* channel, represented by RI = R2. The molecular symmetry was not restricted beforehand in the spline procedure, but it can be observed that the surface in Fig. 2 is symmetric, as would be expected for a molecule belonging to the Czv symmetry group, thus confirming that the above calculation did not introduce spurious values. In Fig. 3 we also show the potential energy corresponding to Rl = R2 and 0 varying from 4.5 to 180”. A horizontal arrow indicates the dissociative S* + H2 channel. However, taking into account that the excitation geometry is at 0 = 91.96” and R 1 = R2 = 2.53 a.u. (indicated by the vertical arrow), a small barrier is present in the direction of this channel. Going from the excitation geometry in the direction of increasing 0, there is a deep valley leading to a minimum around 180”, corresponding to the equilibrium H-S *-H angle

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variable representation. This method was introduced by Light and co-workers [lo- 121 and has been used in many multi-dimensional calculations. The simplicity and accuracy of the method explain its success in theoretical calculations. Recently, Echave and Clary [ 131 and Soares Neto and Costa [ 141 introduced numerically optimised DVRs which have the grid adapted to the potential energy surface being used. In this method, the matrix representing the potential is diagonal and the kinetic energy matrix elements can be calculated analytically. We consider an interval (a,b) and divide it into Nequally spaced sub-intervals. The grid for such an equally spaced DVR is defined as x,=a+ I

10

Fig. 3. Calculated potential energy surface for the 2pm’6a 1state of H:S with RI = R2 and 0 varying from 4.5 to 180”. The ground state equilibrium geometry is indicated by a vertical arrow. The horizontal arrow indicates the dissociative channel S’ + HZ.

of the core excited state. The two potential energy surfaces in Figs. 2 and 3 show two different aspects of the post-excitational dynamics. In reality, a combination of the two processes occurs: a simultaneous increase in bond angle 8 and HS*-H distance Rl (or R2), i.e. a dissociation of the molecule. Note that the potential energy is largely constant from 90 to 180”, thus strengthening the argument that the calculated curves at 91.96”, 135”, and 180” are sufficient as starting curves for the spline procedure used to generate the intermediate points between 91.96 and 180”. As an example of the use of the generated four-dimensional potential energy surface, we briefly describe vibrational energy calculations in Section 2. The present analysis does not make full use of all the information contained in the four-dimensional potential energy surface, but as will be discussed below, more advanced calculations completely based on quantum mechanical principles are presently under way.

3. Vibrational

energy calculation

3.1. The discrete variable representation

(DVR)

The vibrational spectrum of the H*S molecule has been calculated using an equally spaced discrete

(b--ah N

i=l,...,N-1

and the associated function

for each grid point as

,,)=(&)‘sin(F)

i=l,...,

N-l

(6) The kinetic energy matrix elements in this representation, in atomic units, are given by

X sin

n7r(x;, -a) 1 1 b-a

The potential

I

1

matrix elements

Vii’ = 6;;’V(Xj)

171 \

1

are (8)

300 grid points were used to calculate the vibrational spectrum of S*H in the present calculation.

4. Experimental In this work we analyse the resonant Auger decay spectra of H:S recorded at the undulator beam line 5 1 (the Finnish beam line) [ 1.51 at MAX-Lab in Lund, Sweden. The kinetic energies of the Auger electrons were analysed by a hemispherical electron spectrometer of 144 mm mean radius [ 161. For this type of analyser with the retardation lens, the resolution does not depend significantly upon the initial electron kinetic energy. The experiments were performed

140

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using 20 eV pass energy, resulting in a spectrometer resolution of about 60 meV. In this paper we focus only on two aspects of the resonant Auger spectra, namely the hot bands connected with the vibrational spacing in the core excited state and relative intensity parts of the spectrum representing the resonant Auger decay in the S*H fragment and in the H+ molecule. The extended vibrational progressions and fine details of the decay have been treated elsewhere [7].

5. Vibrational

energy analysis

In this section the vibrational energies for the S*H fragment through the dissociation channel S*H + H are presented. We follow the notation of Refs. [3,4] and denote this dissociation path as channel 2. Fig. 4 shows a “cut” along the dissociative channel 2, where the bonding angle 0 and one of the interatomic distances R2 are kept fixed and equal to the ground state equilibrium values (0 = 91.96” and R2 = 2.53 a.u.). The calculated energy of the S 2p - 6al core excitation is plotted for different values of R 1. An arrow indicates the Rl distance equal to 2.53 a.u., which corresponds to the geometry of the molecule after a vertical transition from the ground state. After the excitation, resonant Auger decay starts simultaneously with the hydrogens’ movement away from the core excited sulphur atom. In Fig. 4 this would correspond to increasing the R2 distance. If the core excited and singly ionised final state potential energy curves involved in the decay are not parallel, the ejected electron has different energies as the geometry of the dissociating H-S*H molecule is changing. Thus, broad features can be expected in the decay spectrum. As the two curves become parallel with changing H-S*H geometry, sharp lines can be expected in the decay spectrum, provided, of course, that other factors such as lifetime and instrumental broadening are negligible. We consider the latter type of decay as occurring in the S*H fragment while the former type of decay is referred to as H-S *H molecular decay. A part of the Auger decay spectrum following resonant excitation to the 2p$3bi core excited state is shown in Fig. 5. According to the discussion in Ref. [3], the excitation from S 2p core levels to both 6a, and 3b2 levels leads to the same core excited

from the ground state -392.80

I Interatomic

distance Rl (au.)

Fig. 4. The dissociative H + S’H channel. An arrow indicates the geometry at which a vertical transition from the ground state reaches the core excited state S 2p-‘6a 1. A small distortion around this excitation point is due to interaction with the S 2pm’3bi state.

fragment through the dissociative channel 2. This is due to a crossing of the two potential energy surfaces close to the point of vertical excitation. Therefore, the same potential energy surface can be used for both excitations. It can be seen that, upon excitation to the 3b2 level, the vibrational state v = 1 is also populated in the core excited fragment, while practically only v = 0 is populated upon excitation to the 6a, level since in this spectrum the hot bands are negligible according to the discussion in Ref. [7]. The spectrum is dominated by two peaks at about 148.3 eV and 149.5 eV. Following Ref. [7], these two peaks can be identified as belonging to the O-O vibrational components of the ‘A and “ES- final states of SH+, respectively. The smaller peaks on the higher kinetic energy side of each O-O peak are the hot bands, corresponding to the decay from the vibrational state v = 1 in the core excited S 2p$3b: state to the v = 0 in the final state. The difference between the O-O and 1-O peaks, the vibrational energy, is 0.365 + 0.015 eV for the ‘Cm state and 0.347 i 0.005 eV for the ‘A state. To determine the point in the dissociation path where the Auger decay would give sharp vibrationally resolved peaks, we have performed both a careful curve fitting as well as a series of calculations of the vibrational splitting for the calculated potential energy surface. The results of these calculations are

Arnaldo Naves de Briro et al./Journal of Molecular Strucrure (Theochem) 394 (1997) 135 145

141

(0-O)

HS hv=I 66.95 eV 2prj;‘3b,

Auger decay

149

Kinetic energy (eV) Fig. 5. Part of the Auger spectrum of HIS after resonant excitation at hr = 166.95 eV to the S 2p$3b: state, showing the hot bands, The solid lines correspond to the fitted curves as well as the added envelope, while the dotted line is the experimental original spectrum. The different vibrational transitions and the symmetry of the final electronic states are indicated.

separations larger than 5 a.u. between H and S*H, the Auger decay spectrum is representative of the S’H fragment species, without any noticeable influence of the outgoing H atom.

shown in Fig. 6. The vibrational spacing, as a function of Rl, can be divided into two regions. From Rl = 5.2 up to 10 au. only a small variation is observed in the vibrational spacing. This variation appears to be spurious, and can be attributed to the somewhat imperfect spline interpolation routine. At lower RI, between 3.2 and 5.2 a.u., however, a strong variation is observed. Decay in this part of the curve cannot give rise to the sharp peaks observed in the spectrum in Fig. 5. The calculations thus indicate that at 3.0

4.0

5.0

i

, I I I

. .

. Region I

-0.41

I I II

analysis of the dissociation

Fig. 7 shows the Auger decay spectrum of H2S after resonant excitation to the S 2p$6ai state. The photon 6.0

I

.

6. Temporal

7.0

8.0

9.0

10.0

“Dissociation distance” H+S*H

Region II

Rl internucleardistanceSH (a.~.)

Fig. 6. Calculated vibrational energies as a function of S-H distance, using the generated potential energy surface. The vibrational splitting in Region II corresponds to the experimental energy difference between the “hot band” (I-O) and the (O-O) band in the HS* fragment.

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I

KS G

.z

g

hv=164.35 2p,,,“6a,

eV Auger decay

d

2 x

.z g

2

135

140

145

150

Kinetic energy (eV) Fig. 7. The Auger spectrum of HIS following resonant excitation to the S 2p&6a i state at hv = 164.35 eV. The solid lines correspond to the fitted curves as well as the added envelope, while the dotted line is the experimental original spectrum. The different symmetry of the final electronic states is indicated.

energy was set to 164.35 eV and the monochromator exit slit to 600 pm, resulting in a photon band width of about 1 eV. For the Auger decay in the fragment the band width of the photon beam does not determine the width of the lines [7,17]. Apart from the resonant structures, the direct valence photoelectron lines are also present in this energy region, but for the sake of clarity these have been subtracted from the spectrum using a non-resonant valence spectrum excited just below the resonance energies. The virtually complete removal of the direct single ionisation peaks shows that the resonant enhancement of these peaks due to the participator decay is practically negligible. Following Ref. [7], the structures can be identified as follows: five peaks between 140 and 147 eV can be assigned, in order of decreasing kinetic energy, to the “C-, ‘A, ‘Cf, “II and ‘II singly ionised final states of the SH+ fragment, respectively. According to the calculations of Ref. [3], there is a sixth final state (5s027r4) ‘C’ at approximately 137.8 eV, which can be attributed to the broad peak at 138 eV (see Fig. 7). In the same figure the two peaks at around 134 and 132.8 eV are assigned to the decay in the molecule; these, however, could also possibly be due to highly excited states of the fragment. No calculation exists for this energy region at the moment. Over the whole

spectral range, we note a background which is assigned to the decay of the H-S’H molecule. The Auger spectra resulting from resonant excitation of the H2S molecule can thus be described as consisting of two components: one due to the Auger decay of neutral S*H fragments, and another one due to the decay taking place in H-S*H molecules in an intermediate, i.e. partially dissociated, geometry. The S*H contribution consists of sharp, well-defined transitions, indicating well-defined initial and final states. The H-S*H contribution, however, is observed as broad and structureless features. This can be seen as the result of Auger decays occurring during the dissociation process, thus consisting of a superposition of different H-S *H geometries, ranging from the ground state molecular geometry all the way to configurations where the outgoing H atom has only the weakest influence on the S*H fragment. This is consistent with an interplay between the two different processes, Auger decay and dissociation, occurring on the same time scale. In Ref. [ 181 a molecular dynamics approach was used to study the analogous phenomena in HCl and DCl. We use an even more simplified approach in this paper. Here we apply the so-called “core hole clock” method [9] to the dissociation of H2S. The lifetime

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of the core excited state is used as an internal femtosecond stop-watch to monitor processes occurring on the same time scale as the Auger decay, such as electron transfer or nuclear motion. The Auger decay is reasonably well described by an exponential function, i.e. the fraction of remaining core holes ncorc hotesat time r after the core excitation event at t = 0 is given by ncoreholes

-t/7

(9)

=e

where 7 is the lifetime of the core hole. The negative of the time derivative of Eq. (9) gives the rate of core hole decays, ndccays: d

1 -t/r

fldecPys = - $kare

(101

holes = F

However, the H-S*H separation process follows a different time development. In the present case, we can spectroscopically distinguish between Auger decay processes taking place in the dissociating H-S*H species and the dissociated S*H species, but not between different H-S *H geometries. We assume that the actual electronic separation between H and S*H takes place in a very short time compared to the time scales of the dissociation and the core hole lifetime. We will, therefore, as a first approximation, use a model in which the molecule is described as H-S’H from the core excitation event at t = 0 up to t = tD, the dissociation time, and as S*H after to. The fraction of core hole decay events occurring in the H-S*H species relative to the total number of core hole decay events, n&.ays(u _ s’u), is then given by the time integral of the decay rate (Eq. (10)) from t = 0 to t = tD: ‘d 1 ndecays(H -S’H) =

The dissociation rD = - 7 ln(l

-e

-‘/‘dt=(l

-e- fd/T)

(11)

s0 7

time tD is then obtained

-ndecays(H-S*H))

as

Structure (Theochem) 394 (1997) 135-145

decay fraction obtained:

for the 2p&6a,

&cays(u~s’u) =0.43 2 0.1

143

core excited state is

(13)

Note that this value and the error estimate are derived using the spectrum shown. As seen, there may well be additional intensity connected with molecular decay at even lower kinetic energies. Possible implications of this will be discussed below. An estimate for the core hole lifetime can be obtained from the high-resolution S 2p-’ photoelectron spectrum [6].’ The widths of the individual spectral lines are given by the lifetime broadening F, which is found to be 70(S) meV for the S 2p&,2 core ionised states. The lifetime 7 of the core hole is then directly obtained as r = h/2pF. This yields a value of 9.4 fs. Inserting the values of ?&aYs(u_s*u) and 7 into Eq. (12), we obtain a dissociation time of 5.3 + I .5 fs for the S 2p$6a, core excited state. The H-S*H contribution corresponds to a decay at a geometry where the H atom is still sufficiently close to the S*H fragment to influence significantly the S *H valence orbitals. In contrast, the S*H contribution corresponds to geometry situations where the H atom is so far from S*H as to have negligible influence. It is also important to bear in mind that the dissociation process is influenced by the vibrational state of the molecule upon core excitation. Depending on the direction of the H-S*H motion at t = 0, the individual dissociation times may be shorter or longer than tD. However, in Ref. [ 181 it was concluded that for the dissociation of core excited HCl, the relative motion of the atoms in the ground state could be neglected in comparison with the dynamics after core excitation. It is reasonable to assume that the same is valid in the case of H2S. The derived dissociation times should be understood as characteristic times necessary for a core excited

(12)

As discussed above, the experimental spectra consist of two contributions: sharp lines corresponding to Auger decay in the dissociated S*H species, and a broad background due to Auger decays occurring in the dissociating H-S*H species. By fitting the experimental spectra, using narrow Voigt profiles for the S’H contribution and broad gaussians for the H-S*H background (see Fig. 7), the following H-S*H

’ The lifetime of the core excited 2p&6aI state need not be exactly identical to that of the 2~;)~ state. Apart from possibly causing a somewhat different lifetime, the influence of the 6al electron on the decay would manifest itself in a resonant enhancement of the spectral features corresponding to single-hole valence final states, produced by parttcipator-type decays. The absence of any such significant resonant enhancements strongly indicates that the influence of the 6at electron on the decay is very small, and consequently that the lifetimes of the 2p$ and 2p$6aI states are practically tdentical ai this level of accuracy.

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HzS* molecule of average vibrational excitation to separate electronically the H and S*H fragments. To shed some more light on this process, it is interesting to compare the above-derived electronic dissociation times with the time development of the H-S*H separation. As a first and very simplified approximation, we have used a semi-classical model of the dissociation process. In this representation, the H atom is modelled as a ball following the path of steepest descent on the H-S*H potential energy surface, i.e. the path shown in Fig. 4 with the restriction of fixed bond angle and starting point t = 0 as indicated by the arrow. The resulting H-S*H separation as a function of time is shown in Fig. 8. The above-derived dissociation time of 5.3 ? 1.5 fs is seen to correspond to a H-S*H separation of 4.3 % 0.5 a.u. This value is lower than that of 5.2 a.u. This obtained from the vibrational analysis. discrepancy can be attributed to different reasons, discussed here in order of decreasing importance. First, the experimental Auger spectrum unfortunately covers only a limited energy range. As mentioned intensity above, there may well be additional connected with molecular decay at lower kinetic energies. Inclusion of this would increase the mOleCUlx fraction &ecaYs(n_s*n), and consequently the derived dissociation time to as well as the internuclear distance at which dissociation occurs, making this more consistent with the values from the vibrational analysis. Second, the semi-classical model used to describe the dissociation of the H-S*H molecule is restricted to a fixed bond angle. Consequently, it does not yield the globally steepest 5.00

T ; 4.50 a

z

t

2.50 0.00

.

2.00

4.00

.

.

:

.

6.00

.

I

path of descent. A less restricted calculation would yield a faster separation of the H and S*H fragments, resulting in better agreement between the two different methods. Such a calculation using wavepackets is now in progress. Third, the vibrational analysis and the “core hole clock” method have been used on two different excitations. The dissociation in the case of these two core excited states initially follows slightly different paths, and the internuclear separations at the moment of dissociation of the two processes do not necessarily have to be identical.

7. Conclusions In this paper we have presented a combined theoretical and experimental study of the fast dissociation of core excited H$i* into H and S*H. A new four-dimensional potential energy surface was generated for the 2pm’6ai core hole state. Comparing the experimentally determined vibrational splittings in the Auger decay spectra with those calculated from the potential energy surfaces, it is found that the H-S*H species can be considered as fully separated into non-interacting H and S*H fragments when an internuclear separation of 5 au. is reached. The generated potential energy surface also allows more accurate time-dependent quantum mechanical calculations, making more extended use of the generated surface. Work in this direction is in progress. A useful approximation to study the dissociation processes was presented. From the observed spectral contributions from Auger decay in H-S*H and S*H, and the known lifetime of the core hole, the dissociation time was determined to be 5.3 i 1.5 fs. Using a semi-classical model of the dissociation process, this was found to correspond to an internuclear separation of 4.3 2 0.5 a.u. The discrepancy between this and the above value is probably due to the limited energy range of the experimental Auger spectrum, and not necessarily to the simple theoretical model itself.

8.00

Time (fs) Fig. 8. Dissociation time versus H-S *H internuclear distance. For a derived dissociation time of 5.3 2 1.5 fs the H-S*H separation is 4.3 + 0.5 u.

Acknowledgements This work was supported by the Brazilian Science Research Council (CNPq); in particular O.B. would

Arnaldo

Naves de Brito et al./Joumal

ofMolecular

like to acknowledge a foreign visiting scientist grant from CNPq. We would also like to thank the Swedish Natural Science Research Council (NFR), the Royal Swedish Academy of Sciences (KVA), the Nordic Academy for Advanced Study (NorFA), and the Finnish Academy of Science for economical support.

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