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Spectroscopical characterization of CdNe van der Waals complex in the E1(3Σ+) Rydberg state
3 May 2002
Chemical Physics Letters 357 (2002) 119–125 www.elsevier.com/locate/cplett
Spectroscopical characterization of CdNe van der Waals complex in the E1ð3RþÞ Rydberg state J. Koperski a b
a,*
, M.A. Czajkowski
b
Instytut Fizyki, Uniwersytet Jagiello nski, ul. Reymonta 4, 30-059 Krak ow, Poland Department of Physics, University of Windsor, Windsor, Ont., Canada N9B 3P4 Received 31 January 2002
Abstract The lowest E1ð3 Rþ Þ Rydberg state of the CdNe van der Waals complex was investigated by an optical–optical double resonance method. The A0þ ð3 PÞ and B1ð3 Rþ Þ states were used as intermediates in the excitation from the X0þ ð1 Rþ Þ ground state. Bound–bound excitation spectra of the E1 A0þ transition were recorded. They constitute a first observation of CdNe in the E1 state. Spectroscopical parameters of the E1-state potential well were determined. In the excitation spectrum of the E1 B1 transition, a nodal structure of bound-free transitions was observed and elucidated by a projection of the B1-state vibrational wave-function onto the E1-state potential barrier according to the prediction of ab initio calculations. Ó 2002 Published by Elsevier Science B.V.
In recent articles of Czuchaj and Stoll [1] and Czuchaj et al. [2,3], the authors report on ab initio calculation on CdRG and HgRG (RG ¼ rare gas) complexes. As a result, they obtained potential energy (PE) curves and spectroscopic parameters of the molecular ground and some excited states, including the lowest Rydberg states asymptotically correlating with the n3 S1 and n1 S0 atomic asymptotes in Cd (n ¼ 6) and Hg (n ¼ 7). The nature of the binding in the van der Waals (vdW) molecule is a subject of great experimental and theoretical interest. It is very difficult to predict the balance between forces of the repulsive overlap and the multitude of attractive forces originating from
*
Corresponding author. Fax: +48-12-633-8494. E-mail address: [email protected] (J. Koperski).
dispersive, multipole–multipole and/or charge transfer interactions. Therefore, the theoretical predictions of the excited state potentials are rather rare and they are generally most welcomed by the community of experimental spectroscopists. The articles mentioned above [1–3] partially fulfil the expectations. The ab initio-calculated Rydberg state potentials of CdHe and HgHe are entirely repulsive, however, for CdNe and HgNe, the potentials display a ‘hump’ (an energy barrier) while going towards smaller internuclear separations. The interesting fact is that the barriers transform into shallow minima at yet shorter internuclear distances while the whole PE curve is still entirely above its dissociation limit. Fig. 1 shows the PE curve of the CdNe complex in the E1ð3 Rþ Þ electronic state plotted accordingly to the result of this work and theoretical predictions of [1,3]. Similar
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J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125
Fig. 1. The PE curves of the E1ð3 Rþ Þ Rydberg as well as the intermediate A0þ ð3 PÞ and B1ð3 Rþ Þ, and the ground X0þ ð1 Rþ Þ states of the CdNe molecule. The bound-well and the repulsive outer part of the E1-state potential are represented with a Morse function using parameters of this study and with ab initio points of [3], respectively. The A0þ -, B1 - and X0þ -state PE curves are drawn according to the results of [11]. The D0e and R0e denote the E1-state well depth and equilibrium internuclear separation, respectively, while the Eb0 and R0b are parameters of the E1-state potential barrier. Vertical arrows show the E1v0 ¼1 A0þ B1v00 ¼0 boundv00 ¼0 bound–bound ðm10 Þ and E1 free (b-f) transitions. vat , energies corresponding to the 53 P1 51 S0 and 63 S1 53 P1 transitions in Cd.
result was reported for HgNe complex. The lowest-lying E1 Rydberg state in HgNe correlating with the 73 S1 Hg atomic asymptote was investigated by Okunishi et al. [4] by means of an optical–optical double resonance (OODR) also known as a ‘pump-and-probe’ method [5]. The results of the experiment [4], obtained prior to the ab initio calculation [2], are in a full agreement with the theory. The E1-state potential barrier in HgNe was observed and an attempt was made to obtain a full
quantitative characterization of the whole potential energy curve. However, due to certain experimental difficulties, a partially quantitative comparison between theory and experiment was only possible. According to the ab initio results [1– 3], for heavier RG atoms (Ar, Kr, Xe) the PE curves in question become strongly attractive with decreasing internuclear distance R. The strength of the bonding is increasing rapidly while going from Ar to Xe, which is strongly supported by an earlier work performed in this laboratory [5]. The potential barrier becomes smaller when going from MeAr, through MeKr, to MeXe (Me ¼ Cd, Hg) [1,6] gradually converting into a shallow minimum and eventually vanishes, reaching the dissociation limit at yet larger values of the internuclear separation. Similar conclusion with respect to the shape of the E1-state PE curve in HgAr was drawn for the first time by Duval et al. [7]. It was based entirely on experimental observations and computer simulations of the spectra. All of the above indicate the real complexity of seemingly simple nature of the vdW bonding, especially that of the excited states, which is in fact very difficult to predict in a particular case because of the mentioned above delicate and labile balance between the repulsive overlap forces and the multitude of attractive forces [8,9]. In this Letter we report the results of systematic studies we undertook recently on CdRG complexes. We refer here to the first-time observation of the E1v0 A0þ X0þ v00 ¼0;1 ½ v¼0 bound–bound as well as E1v0 B1v00 ¼0;1 ½ X0þ v¼0 bound-free laser excitation spectrum of CdNe. The measurements were accomplished by means of the OODR approach in which the E1-state is reached by an act of absorption of two consecutive laser pulses via intermediate A0þ or B1 excited state (see Fig. 1). It is also clear that since the PE minima of the two intermediate states differ considerably ½Re ðA0þ Þ < Re ðB1Þ; the two ways of the E1-state excitation make the probing of different parts of the Rydberg state potential possible. Analysis of the spectral traces were then carried out to obtain spectroscopical characterization of the bound region of the E1-state PE curve. The arrangement of the apparatus used in the OODR experiment is shown in Fig. 2. The CdNe
J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125
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Fig. 2. Schematic diagram of the apparatus used in the OODR experiment. KDP-C: dye-laser frequency doubling crystal; BS: beam splitters; SHS: second harmonic separator; FP: Fabry–Perot interferometer; MB: molecular beam; O: oven; V: vacuum pump system; L: lens; F: filter; PMT: photomultiplier tube; C: scanning control device; PD: photodiodes.
molecules produced in a supersonic expansion beam were irradiated with two successive laser pulses. The first pulse was generated with an inhouse built dye-laser excited with the second har) of a Ndþ :YAG laser monic output (5320 A (continuum). The dye laser output was frequency ) to produce doubled (in the range of 3258–3266 A a maximum population in the A0þ v00 ¼0 or 1 - or B1v00 ¼0 or 1 -state vibrational levels by excitation from the X0þ v¼0 ground state. From there, the molecules were further excited to the E1 state by ) emitted from the second laser pulse (4740–4810 A an in-house built N2 -laser-pumped dye laser. The delay between the dye-laser pulses was set at approximately 20–50 ns to ensure an efficient excitation in the two-step process. The resulting laser induced fluorescence (LIF) signal, observed perpendicularly to the plane containing the molecular and laser beams, was detected with a Hamamatsu R2496 photomultiplier (PMT) and screened from an intense first-step-excitation radiation by an UV-
absorbing filter. The PMT signal was registered by a transient digitizer (HP 54510A scope) and stored in a computer. The molecular-beam source was operated at a temperature approximately 750 K which corresponds to the saturated Cd vapor pressure of 11 torr [10]. Further details on the supersonic-beam experiment can be found elsewhere [11]. Fig. 3a and b presents spectra obtained after þ excitation of the E1 state via the A0þ v00 ¼0 and A0v00 ¼1 levels, respectively. The whole spectrum covers a . The traces of the range of approximately 45 A spectra exhibit distinctive, blue-shaded, asymmetric bands which were assigned to the bound– bound E1v0 A0þ v00 ¼0;1 vibrational transitions with frequencies m00 ¼ 20952:1, m10 ¼ 20990:6 and m20 ¼ 21011:5 cm 1 measured with respect to the 0 A0þ v00 ¼ 0 band was asv00 ¼0 level. The v ¼ 0 signed as that having the lowest frequency. All the bands corresponding to the bound–bound transitions in Fig. 3, as well as continuum bands are
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J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125 Table 1 Spectroscopic characterization of the E1ð3 Rþ Þ Rydberg states in CdNe and HgNe (excitation spectrum from [4]) molecules based on a B–S analysis and simulation of the excitation spectra of the E1 A0þ transition Designation
E1, CdNe
E1, HgNe
x0e (cm 1 ) x0e x0e (cm 1 ) D0e (cm 1 ) ) DRe ¼ R0e R00e (A ) R0e (A
56:6 3:0a 8:8 0:4a 91:0 4:0a 0:55 0:03a 3:21 0:05a
) R0b (A Eb0 (cm 1 ) m00 (cm 1 )
4.0a 132.1a 20952.1a ; 51571.5d 2.7a
61.6a 9.6a 98.8a 0:38 0:05a 3:10 0:05a ; 2:9 0:1b 3.9b ; 3.9c 153.0b 23086.9e ; 62467b 2.71a
vD a
Fig. 3. Observed OODR excitation spectra of the (a) E1v0 A0þ X0þ A0þ X0þ v¼0 and (b) E1v0 v¼0 tranv00 ¼0 ½ v00 ¼0 ½ sitions of CdNe. The v0 v00 assignment is shown. The result of the F–CF calculation for the bound–bound transitions, assuming that the E1 and A0þ are represented by Morse functions, is shown with vertical bars.
above the dissociation limit (the 63 S1 atomic asymptote) which corresponds to mdiss ¼ 20887:0 ) if measured from A0þ00 cm 1 (kdiss ¼ 4786:3 A v ¼0 molecular state (see Fig. 1). Therefore, we can draw a conclusion that the E1-state PE curve of CdNe is very similar to that of HgNe reported in [4] (see also Fig. 1). The PE curve is essentially repulsive with a distinct potential barrier followed by a bound-well while going toward smaller values of R. Using the mv0 v00 frequencies and employing a Birge–Sponer (B–S) method, the fundamental frequency x0e , anharmonicity x0e x0e , well depth D0e , and vibrational index v0D at the bound-well dissociation limit were obtained. All the values are collected in Table 1. The E1-state well can accommodate only three bound vibrational levels. The D0e is defined from the bottom of the well to the maximum of the potential barrier. Using results of [11] for the A0þ -state parameters (including energy of the A0þ X0þ v¼0 transition), an v00 ¼0
This work. In case of the HgNe, it is also results of an analysis of this work leading to an estimations based on the spectrum of [4]. b Ref. [4]. Energy Eb is defined here as the potential barrier measured from the 73 S1 atomic level. From B–S analysis: x00 ¼ 52:0 cm 1 , x00 x00 ¼ 9:6 cm 1 and D00 ¼ 70:5 cm 1 . c Ref. [3]. d Measured from the X0þ v¼0 ground state. e Measured from the A0þ v¼0 intermediate state.
evaluation of the potential energy barrier Eb0 , defined as in Fig. 1, was possible. Using potential parameters of Table 1, an attempt to simulate the Franck–Condon factors (F– CF) of the E1 A0þ bound–bound transitions of Fig. 3a and b was made. As seen in Fig. 3, the simulation provides an acceptable agreement with regards to the assumption on the shape of the E1state PE bound-well. In the simulation it was assumed that the inner bound-well is approximated by a Morse potential (similar assumption was made in [4]). We did not attempt however, to simulate the blue-shaded asymmetry of the vibrational bands, clearly originating from the rotational structure of the bands. As a direct result of the simulation, the difference DRe ¼ R0e ðE1Þ was determined. The DRe < 0 R00e ðA0þ Þ ¼ 0:55 A is expected from the observed blue-shading of the vibronic bands. Taking into account the R00e ðA0þ Þ value [11], a location of the quasi-bound part of , was deterthe E1-state potential, R0e ¼ 3:21 A mined. This should be compared with the result of The ab initio calculation [1], i.e., R0e ¼ 3:18 A agreement is remarkably good. From the same
J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125
source [1,3] we learnt about the location of the potential barrier R0b which appears to be at ap. Exactly the same value was obproximately 4 A tained graphically from the assumed Morse PE curve drawn according to the potential parameters of Table 1. All the information about the shape of the E1-state potential are important for elucidation of further features observed in the spectral traces shown in Fig. 3. The long-wavelength side of the spectra show the bound–bound vibronic bands appearing on slopes of a continuum absorption. The slope increases while going from the v0 0 to v0 1 in the E1 A0þ transition. A possible explanation of the fact is consistent with the predicted shape of the E1-state PE curve. While scanning the laser frequency from lower to higher values, we observe not only the discrete bound–bound transitions, but also the continuum absorption corresponding to the bound-free tran sitions to the repulsive potential barrier at R > 4 A (see Fig. 1). Evidently, a shape of the traces of the excitation spectra are sensitively dependent on the vibrational wave function of the A0þ v00 initial state. It is therefore quite reasonable to assume that the observed slope-differences are the results of the Condon internal diffraction (CID) in excitation. It appears as the projections of the vibrational wave function of the initial A0þ v00 state onto the repulsive part of the E1 state potential. Similar effects were observed for the HgNe [4]. The central maximum (Fig. 3a) followed by a sharp fall at k ¼ 4754:6 A off coincides with the deep minimum seen in Fig. 3b, and it indicates the maximum height (the top energy) of the potential barrier. If we proceed with the laser-frequency scan (going to the shorter wavelengths region) and an excitation above the potential barrier, we observe the CID pattern again, but originating from the projection of the vibrational wave function of the same initial A0þ v00 level onto the repulsive part of the E1-state po. If the excitatential in the region of R < 3:21 A þ tion proceeds from the A0 -state v00 ¼ 0 level, we observed a single maximum in the spectrum, so characteristic for the CID pattern reproducing the v00 ¼ 0-level wave function squared. When on the other hand, the initial state is chosen as v00 ¼ 1, then the equally characteristic single node of the CID structure appears justifying our elucidation.
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In order to collect more information, which may strengthen and further justify the explanation presented above, we explored also the possibility of the E1-state excitation using the B1 state as an intermediate in the OODR method. The excitation of the E1 state via the B1-state v00 ¼ 0 or 1 vibrational level, produces special features, which are not attainable in the former exploration of the molecule. In our recent report on the CdNe molecule [11] we presented results of a very extensive investigation of all molecular states asymptotic to the 51 S0 , 53 P1 and 51 P1 Cd atomic states. We obtained a revised set of the molecular potential parameters of all non-Rydberg CdNe electronic states. From the results of [11] we concluded that is shifted much to the region the R00e ðB1Þ ¼ 5:12 A . of higher R values than the R00e ðA0þ Þ ¼ 3:76 A According to the F-C principle, the optical transitions from the B1 to E1 state may take place to a formerly unattainable long-range region of the E1state potential. However, the oscillator strengths for the B1v00 X0þ v¼0 transitions are not large and hence, the production of CdNe complexes in the B1-state vibrational levels is not very effective. Therefore, as expected, we experienced difficulties in detection of the spectra of the B1 X0þ transitions due to the small-intensity signals. Another difficulty is the fact that the B1-state v00 ¼ 0, 1 and 2 levels lie relatively close to each other (with Dm10 and Dm21 being 4.4 and 2:2 cm 1 , respectively [11]), and therefore, even at selective v00 -level excitation an unwanted population of the neighboring levels was essentially possible. Such an effect was observed in the OODR excitation of the CdAr molecule [5] at higher density of the carrier-gas atoms. It was found that in the jet-expansion beam with not extremely high values of the X =D parameter, where X is the distance from the nozzle orifice, along the beam to the point of excitation, and D is a diameter of the orifice, the perpendicular (with respect to the direction of motion) component of velocity is not vanishingly small and hence, the collisional transfer of energy between vibrational modes (vibrational population redistribution) is highly possible [12]. Such an effect may diffuse the shapes of the observed traces in the spectra and/or introduce additional components in excitation spectra. This appears to be the case of the OODR
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spectra obtained using the v00 ¼ 0 or 1 level of the B1 state as the intermediate one. The spectra are shown in Fig. 4 and spans a range of approxi. Except for one discrete narrow feamately 48 A ture (at long-wavelength part of the spectrum), bound-free continua with a characteristic undulatory (nodal) structure were observed. The narrow (m ¼ 20828:0 cm 1 ) was feature at k ¼ 4800:0 A identified as the 63 S1 53 P1 atomic transition resulted in an absorption of the excited Cdð53 P1 Þ atoms, indicating direct dissociation of the molecules in the A0þ -state potential to the free Cdð53 P1 Þ and Neð21 S0 Þ atoms. The first broad continuum (in both traces of Fig. 4) flanked at both sides by a steep falloff can be explained as a bound-free CID pattern, i.e., a projection of the vibrational wave function of the initial B1-state v00 ¼ 0 level onto the repulsive part of the E1-state . In excitation, the boundpotential at R > 4:0 A free transitions in HgRG were first reported and interpreted by Duval et al. [7] for HgAr and later by Okunishi et al. [4] for HgNe. The spectra reported here are the first-time observed bound-free
(b)
(a)
Fig. 4. Observed OODR excitation spectra of the (a) E1 B1v00 ¼0 ½ X0þ B1v00 ¼0 ½ X0þ v¼0 and (b) E1v0 v¼0 transitions of was idenCdNe. The narrow feature at approximately 4801 A tified as the 63 S1 $ 53 P1 atomic transition.
transitions in excitation observed in the CdRG molecules. Fig. 4 presents the E1 B1 ½ X0þ v¼0 spectra via the B1-state v00 ¼ 0 (trace (a)) or v00 ¼ 1 (trace (b)) level. However, the excitation of a particular v00 (e.g., v00 ¼ 0) intermediate level leads also to a certain measurable population of the neighboring v00 (e.g., v00 ¼ 1 and 2) levels, and hence, the CID patterns should reflect this occurrence. Since no bound–bound transition is observed below the dissociation limit, therefore the optically accessible region represented by the spectra in Fig. 4 is characterized by a repulsive potential energy barrier. The short-wavelength ) coincides falloff of the broad band (at 4768 A (within the accuracy of the measurement and which locates the scaling procedure) with 4754.6 A central maximum and minimum in Fig. 3a and b, respectively. In order to verify this, we had to take into account the differences in energies of the intermediate (A0þ v00 and B1v00 ) vibronic levels [11, Table 1]. Similar conclusion had been drawn by the authors of [4] with respect to the spectra of the E1 B1 transition in HgNe complex. Therefore, the energy difference related to the broad-maximum limiting values of wavelengths, i.e., 4768.0 (compare with Fig. 4), is the height and 4799.1 A of the energy barrier Eb0 , measured from the 63 S1 atomic asymptote to the top of the barrier (see Fig. 1). The obtained result, Eb0 ¼ 135 4 cm 1 , is in good agreement with our previous, more accurate B–S evaluation of the D00 . Further laser-frequency , towards shorter scan beyond the value of 4768 A wavelengths, brings the excitation into the repul, sive region of the E1-state potential at R < 3:21 A and the Condon projection of the B1-state v00 ¼ 1 level only. Evidently, the collisional population redistribution between the v00 ¼ 0 and 1 levels is quite effective and gives rise to the characteristic nodal structure of the v00 ¼ 1 projection of the vibrational wave function. All potential parameters evaluated from the analysed excitation spectra are summarized in Table 1.
Acknowledgements We would like to express our sincere gratitude to Professor Brian Atkinson of the University of
J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125
Windsor who lent us an Ndþ :YAG laser much better suitable for the requirements of the experiment. This research was supported by a grant from the Natural Science and Engineering Research Council of Canada. One of us (J.K.) acknowledges financial support from a grant 5P03B 037 20 of the Polish State Committee for Scientific Research (KBN). References [1] E. Czuchaj, H. Stoll, Chem. Phys. 248 (1999) 1. [2] E. Czuchaj, M. Krosnicki, H. Stoll, Chem. Phys. 263 (2001) 7.
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[3] E. Czuchaj, M. Krosnicki, H. Stoll, Theor. Chem. Acc. 105 (2001) 219. [4] M. Okunishi, K. Yamanouchi, K. Onda, S. Tsuchiya, J. Chem. Phys. 98 (1993) 2675. [5] M. Czajkowski, R. Bobkowski, L. Krause, Phys. Rev. A 45 (1992) 6451. [6] J. Koperski, Phys. Reports, in press. [7] M.C. Duval, O. Benoist D’Azy, W.H. Breckenridge, C. Jouvet, B. Soep, J. Chem. Phys. 85 (1986) 6324. [8] F. London, Z. Phys. Chem. B 11 (1930) 222. [9] B.L. Blancy, G.E. Ewing, Ann. Rev. Phys. Chem. 27 (1976) 553. [10] A. Nesmeyanov, Vapor Pressure of the Elements, Academic Press, New York, 1963. [11] J. Koperski, M. Czajkowski, Eur. Phys. J. D 10 (2000) 363. [12] D.M. Lubman, C.T. Rettner, R.N. Zare, J. Phys. Chem. 86 (1982) 1129.
Chemical Physics Letters 357 (2002) 119–125 www.elsevier.com/locate/cplett
Spectroscopical characterization of CdNe van der Waals complex in the E1ð3RþÞ Rydberg state J. Koperski a b
a,*
, M.A. Czajkowski
b
Instytut Fizyki, Uniwersytet Jagiello nski, ul. Reymonta 4, 30-059 Krak ow, Poland Department of Physics, University of Windsor, Windsor, Ont., Canada N9B 3P4 Received 31 January 2002
Abstract The lowest E1ð3 Rþ Þ Rydberg state of the CdNe van der Waals complex was investigated by an optical–optical double resonance method. The A0þ ð3 PÞ and B1ð3 Rþ Þ states were used as intermediates in the excitation from the X0þ ð1 Rþ Þ ground state. Bound–bound excitation spectra of the E1 A0þ transition were recorded. They constitute a first observation of CdNe in the E1 state. Spectroscopical parameters of the E1-state potential well were determined. In the excitation spectrum of the E1 B1 transition, a nodal structure of bound-free transitions was observed and elucidated by a projection of the B1-state vibrational wave-function onto the E1-state potential barrier according to the prediction of ab initio calculations. Ó 2002 Published by Elsevier Science B.V.
In recent articles of Czuchaj and Stoll [1] and Czuchaj et al. [2,3], the authors report on ab initio calculation on CdRG and HgRG (RG ¼ rare gas) complexes. As a result, they obtained potential energy (PE) curves and spectroscopic parameters of the molecular ground and some excited states, including the lowest Rydberg states asymptotically correlating with the n3 S1 and n1 S0 atomic asymptotes in Cd (n ¼ 6) and Hg (n ¼ 7). The nature of the binding in the van der Waals (vdW) molecule is a subject of great experimental and theoretical interest. It is very difficult to predict the balance between forces of the repulsive overlap and the multitude of attractive forces originating from
*
Corresponding author. Fax: +48-12-633-8494. E-mail address: [email protected] (J. Koperski).
dispersive, multipole–multipole and/or charge transfer interactions. Therefore, the theoretical predictions of the excited state potentials are rather rare and they are generally most welcomed by the community of experimental spectroscopists. The articles mentioned above [1–3] partially fulfil the expectations. The ab initio-calculated Rydberg state potentials of CdHe and HgHe are entirely repulsive, however, for CdNe and HgNe, the potentials display a ‘hump’ (an energy barrier) while going towards smaller internuclear separations. The interesting fact is that the barriers transform into shallow minima at yet shorter internuclear distances while the whole PE curve is still entirely above its dissociation limit. Fig. 1 shows the PE curve of the CdNe complex in the E1ð3 Rþ Þ electronic state plotted accordingly to the result of this work and theoretical predictions of [1,3]. Similar
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 4 6 4 - 5
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Fig. 1. The PE curves of the E1ð3 Rþ Þ Rydberg as well as the intermediate A0þ ð3 PÞ and B1ð3 Rþ Þ, and the ground X0þ ð1 Rþ Þ states of the CdNe molecule. The bound-well and the repulsive outer part of the E1-state potential are represented with a Morse function using parameters of this study and with ab initio points of [3], respectively. The A0þ -, B1 - and X0þ -state PE curves are drawn according to the results of [11]. The D0e and R0e denote the E1-state well depth and equilibrium internuclear separation, respectively, while the Eb0 and R0b are parameters of the E1-state potential barrier. Vertical arrows show the E1v0 ¼1 A0þ B1v00 ¼0 boundv00 ¼0 bound–bound ðm10 Þ and E1 free (b-f) transitions. vat , energies corresponding to the 53 P1 51 S0 and 63 S1 53 P1 transitions in Cd.
result was reported for HgNe complex. The lowest-lying E1 Rydberg state in HgNe correlating with the 73 S1 Hg atomic asymptote was investigated by Okunishi et al. [4] by means of an optical–optical double resonance (OODR) also known as a ‘pump-and-probe’ method [5]. The results of the experiment [4], obtained prior to the ab initio calculation [2], are in a full agreement with the theory. The E1-state potential barrier in HgNe was observed and an attempt was made to obtain a full
quantitative characterization of the whole potential energy curve. However, due to certain experimental difficulties, a partially quantitative comparison between theory and experiment was only possible. According to the ab initio results [1– 3], for heavier RG atoms (Ar, Kr, Xe) the PE curves in question become strongly attractive with decreasing internuclear distance R. The strength of the bonding is increasing rapidly while going from Ar to Xe, which is strongly supported by an earlier work performed in this laboratory [5]. The potential barrier becomes smaller when going from MeAr, through MeKr, to MeXe (Me ¼ Cd, Hg) [1,6] gradually converting into a shallow minimum and eventually vanishes, reaching the dissociation limit at yet larger values of the internuclear separation. Similar conclusion with respect to the shape of the E1-state PE curve in HgAr was drawn for the first time by Duval et al. [7]. It was based entirely on experimental observations and computer simulations of the spectra. All of the above indicate the real complexity of seemingly simple nature of the vdW bonding, especially that of the excited states, which is in fact very difficult to predict in a particular case because of the mentioned above delicate and labile balance between the repulsive overlap forces and the multitude of attractive forces [8,9]. In this Letter we report the results of systematic studies we undertook recently on CdRG complexes. We refer here to the first-time observation of the E1v0 A0þ X0þ v00 ¼0;1 ½ v¼0 bound–bound as well as E1v0 B1v00 ¼0;1 ½ X0þ v¼0 bound-free laser excitation spectrum of CdNe. The measurements were accomplished by means of the OODR approach in which the E1-state is reached by an act of absorption of two consecutive laser pulses via intermediate A0þ or B1 excited state (see Fig. 1). It is also clear that since the PE minima of the two intermediate states differ considerably ½Re ðA0þ Þ < Re ðB1Þ; the two ways of the E1-state excitation make the probing of different parts of the Rydberg state potential possible. Analysis of the spectral traces were then carried out to obtain spectroscopical characterization of the bound region of the E1-state PE curve. The arrangement of the apparatus used in the OODR experiment is shown in Fig. 2. The CdNe
J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125
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Fig. 2. Schematic diagram of the apparatus used in the OODR experiment. KDP-C: dye-laser frequency doubling crystal; BS: beam splitters; SHS: second harmonic separator; FP: Fabry–Perot interferometer; MB: molecular beam; O: oven; V: vacuum pump system; L: lens; F: filter; PMT: photomultiplier tube; C: scanning control device; PD: photodiodes.
molecules produced in a supersonic expansion beam were irradiated with two successive laser pulses. The first pulse was generated with an inhouse built dye-laser excited with the second har) of a Ndþ :YAG laser monic output (5320 A (continuum). The dye laser output was frequency ) to produce doubled (in the range of 3258–3266 A a maximum population in the A0þ v00 ¼0 or 1 - or B1v00 ¼0 or 1 -state vibrational levels by excitation from the X0þ v¼0 ground state. From there, the molecules were further excited to the E1 state by ) emitted from the second laser pulse (4740–4810 A an in-house built N2 -laser-pumped dye laser. The delay between the dye-laser pulses was set at approximately 20–50 ns to ensure an efficient excitation in the two-step process. The resulting laser induced fluorescence (LIF) signal, observed perpendicularly to the plane containing the molecular and laser beams, was detected with a Hamamatsu R2496 photomultiplier (PMT) and screened from an intense first-step-excitation radiation by an UV-
absorbing filter. The PMT signal was registered by a transient digitizer (HP 54510A scope) and stored in a computer. The molecular-beam source was operated at a temperature approximately 750 K which corresponds to the saturated Cd vapor pressure of 11 torr [10]. Further details on the supersonic-beam experiment can be found elsewhere [11]. Fig. 3a and b presents spectra obtained after þ excitation of the E1 state via the A0þ v00 ¼0 and A0v00 ¼1 levels, respectively. The whole spectrum covers a . The traces of the range of approximately 45 A spectra exhibit distinctive, blue-shaded, asymmetric bands which were assigned to the bound– bound E1v0 A0þ v00 ¼0;1 vibrational transitions with frequencies m00 ¼ 20952:1, m10 ¼ 20990:6 and m20 ¼ 21011:5 cm 1 measured with respect to the 0 A0þ v00 ¼ 0 band was asv00 ¼0 level. The v ¼ 0 signed as that having the lowest frequency. All the bands corresponding to the bound–bound transitions in Fig. 3, as well as continuum bands are
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J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125 Table 1 Spectroscopic characterization of the E1ð3 Rþ Þ Rydberg states in CdNe and HgNe (excitation spectrum from [4]) molecules based on a B–S analysis and simulation of the excitation spectra of the E1 A0þ transition Designation
E1, CdNe
E1, HgNe
x0e (cm 1 ) x0e x0e (cm 1 ) D0e (cm 1 ) ) DRe ¼ R0e R00e (A ) R0e (A
56:6 3:0a 8:8 0:4a 91:0 4:0a 0:55 0:03a 3:21 0:05a
) R0b (A Eb0 (cm 1 ) m00 (cm 1 )
4.0a 132.1a 20952.1a ; 51571.5d 2.7a
61.6a 9.6a 98.8a 0:38 0:05a 3:10 0:05a ; 2:9 0:1b 3.9b ; 3.9c 153.0b 23086.9e ; 62467b 2.71a
vD a
Fig. 3. Observed OODR excitation spectra of the (a) E1v0 A0þ X0þ A0þ X0þ v¼0 and (b) E1v0 v¼0 tranv00 ¼0 ½ v00 ¼0 ½ sitions of CdNe. The v0 v00 assignment is shown. The result of the F–CF calculation for the bound–bound transitions, assuming that the E1 and A0þ are represented by Morse functions, is shown with vertical bars.
above the dissociation limit (the 63 S1 atomic asymptote) which corresponds to mdiss ¼ 20887:0 ) if measured from A0þ00 cm 1 (kdiss ¼ 4786:3 A v ¼0 molecular state (see Fig. 1). Therefore, we can draw a conclusion that the E1-state PE curve of CdNe is very similar to that of HgNe reported in [4] (see also Fig. 1). The PE curve is essentially repulsive with a distinct potential barrier followed by a bound-well while going toward smaller values of R. Using the mv0 v00 frequencies and employing a Birge–Sponer (B–S) method, the fundamental frequency x0e , anharmonicity x0e x0e , well depth D0e , and vibrational index v0D at the bound-well dissociation limit were obtained. All the values are collected in Table 1. The E1-state well can accommodate only three bound vibrational levels. The D0e is defined from the bottom of the well to the maximum of the potential barrier. Using results of [11] for the A0þ -state parameters (including energy of the A0þ X0þ v¼0 transition), an v00 ¼0
This work. In case of the HgNe, it is also results of an analysis of this work leading to an estimations based on the spectrum of [4]. b Ref. [4]. Energy Eb is defined here as the potential barrier measured from the 73 S1 atomic level. From B–S analysis: x00 ¼ 52:0 cm 1 , x00 x00 ¼ 9:6 cm 1 and D00 ¼ 70:5 cm 1 . c Ref. [3]. d Measured from the X0þ v¼0 ground state. e Measured from the A0þ v¼0 intermediate state.
evaluation of the potential energy barrier Eb0 , defined as in Fig. 1, was possible. Using potential parameters of Table 1, an attempt to simulate the Franck–Condon factors (F– CF) of the E1 A0þ bound–bound transitions of Fig. 3a and b was made. As seen in Fig. 3, the simulation provides an acceptable agreement with regards to the assumption on the shape of the E1state PE bound-well. In the simulation it was assumed that the inner bound-well is approximated by a Morse potential (similar assumption was made in [4]). We did not attempt however, to simulate the blue-shaded asymmetry of the vibrational bands, clearly originating from the rotational structure of the bands. As a direct result of the simulation, the difference DRe ¼ R0e ðE1Þ was determined. The DRe < 0 R00e ðA0þ Þ ¼ 0:55 A is expected from the observed blue-shading of the vibronic bands. Taking into account the R00e ðA0þ Þ value [11], a location of the quasi-bound part of , was deterthe E1-state potential, R0e ¼ 3:21 A mined. This should be compared with the result of The ab initio calculation [1], i.e., R0e ¼ 3:18 A agreement is remarkably good. From the same
J. Koperski, M.A. Czajkowski / Chemical Physics Letters 357 (2002) 119–125
source [1,3] we learnt about the location of the potential barrier R0b which appears to be at ap. Exactly the same value was obproximately 4 A tained graphically from the assumed Morse PE curve drawn according to the potential parameters of Table 1. All the information about the shape of the E1-state potential are important for elucidation of further features observed in the spectral traces shown in Fig. 3. The long-wavelength side of the spectra show the bound–bound vibronic bands appearing on slopes of a continuum absorption. The slope increases while going from the v0 0 to v0 1 in the E1 A0þ transition. A possible explanation of the fact is consistent with the predicted shape of the E1-state PE curve. While scanning the laser frequency from lower to higher values, we observe not only the discrete bound–bound transitions, but also the continuum absorption corresponding to the bound-free tran sitions to the repulsive potential barrier at R > 4 A (see Fig. 1). Evidently, a shape of the traces of the excitation spectra are sensitively dependent on the vibrational wave function of the A0þ v00 initial state. It is therefore quite reasonable to assume that the observed slope-differences are the results of the Condon internal diffraction (CID) in excitation. It appears as the projections of the vibrational wave function of the initial A0þ v00 state onto the repulsive part of the E1 state potential. Similar effects were observed for the HgNe [4]. The central maximum (Fig. 3a) followed by a sharp fall at k ¼ 4754:6 A off coincides with the deep minimum seen in Fig. 3b, and it indicates the maximum height (the top energy) of the potential barrier. If we proceed with the laser-frequency scan (going to the shorter wavelengths region) and an excitation above the potential barrier, we observe the CID pattern again, but originating from the projection of the vibrational wave function of the same initial A0þ v00 level onto the repulsive part of the E1-state po. If the excitatential in the region of R < 3:21 A þ tion proceeds from the A0 -state v00 ¼ 0 level, we observed a single maximum in the spectrum, so characteristic for the CID pattern reproducing the v00 ¼ 0-level wave function squared. When on the other hand, the initial state is chosen as v00 ¼ 1, then the equally characteristic single node of the CID structure appears justifying our elucidation.
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In order to collect more information, which may strengthen and further justify the explanation presented above, we explored also the possibility of the E1-state excitation using the B1 state as an intermediate in the OODR method. The excitation of the E1 state via the B1-state v00 ¼ 0 or 1 vibrational level, produces special features, which are not attainable in the former exploration of the molecule. In our recent report on the CdNe molecule [11] we presented results of a very extensive investigation of all molecular states asymptotic to the 51 S0 , 53 P1 and 51 P1 Cd atomic states. We obtained a revised set of the molecular potential parameters of all non-Rydberg CdNe electronic states. From the results of [11] we concluded that is shifted much to the region the R00e ðB1Þ ¼ 5:12 A . of higher R values than the R00e ðA0þ Þ ¼ 3:76 A According to the F-C principle, the optical transitions from the B1 to E1 state may take place to a formerly unattainable long-range region of the E1state potential. However, the oscillator strengths for the B1v00 X0þ v¼0 transitions are not large and hence, the production of CdNe complexes in the B1-state vibrational levels is not very effective. Therefore, as expected, we experienced difficulties in detection of the spectra of the B1 X0þ transitions due to the small-intensity signals. Another difficulty is the fact that the B1-state v00 ¼ 0, 1 and 2 levels lie relatively close to each other (with Dm10 and Dm21 being 4.4 and 2:2 cm 1 , respectively [11]), and therefore, even at selective v00 -level excitation an unwanted population of the neighboring levels was essentially possible. Such an effect was observed in the OODR excitation of the CdAr molecule [5] at higher density of the carrier-gas atoms. It was found that in the jet-expansion beam with not extremely high values of the X =D parameter, where X is the distance from the nozzle orifice, along the beam to the point of excitation, and D is a diameter of the orifice, the perpendicular (with respect to the direction of motion) component of velocity is not vanishingly small and hence, the collisional transfer of energy between vibrational modes (vibrational population redistribution) is highly possible [12]. Such an effect may diffuse the shapes of the observed traces in the spectra and/or introduce additional components in excitation spectra. This appears to be the case of the OODR
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spectra obtained using the v00 ¼ 0 or 1 level of the B1 state as the intermediate one. The spectra are shown in Fig. 4 and spans a range of approxi. Except for one discrete narrow feamately 48 A ture (at long-wavelength part of the spectrum), bound-free continua with a characteristic undulatory (nodal) structure were observed. The narrow (m ¼ 20828:0 cm 1 ) was feature at k ¼ 4800:0 A identified as the 63 S1 53 P1 atomic transition resulted in an absorption of the excited Cdð53 P1 Þ atoms, indicating direct dissociation of the molecules in the A0þ -state potential to the free Cdð53 P1 Þ and Neð21 S0 Þ atoms. The first broad continuum (in both traces of Fig. 4) flanked at both sides by a steep falloff can be explained as a bound-free CID pattern, i.e., a projection of the vibrational wave function of the initial B1-state v00 ¼ 0 level onto the repulsive part of the E1-state . In excitation, the boundpotential at R > 4:0 A free transitions in HgRG were first reported and interpreted by Duval et al. [7] for HgAr and later by Okunishi et al. [4] for HgNe. The spectra reported here are the first-time observed bound-free
(b)
(a)
Fig. 4. Observed OODR excitation spectra of the (a) E1 B1v00 ¼0 ½ X0þ B1v00 ¼0 ½ X0þ v¼0 and (b) E1v0 v¼0 transitions of was idenCdNe. The narrow feature at approximately 4801 A tified as the 63 S1 $ 53 P1 atomic transition.
transitions in excitation observed in the CdRG molecules. Fig. 4 presents the E1 B1 ½ X0þ v¼0 spectra via the B1-state v00 ¼ 0 (trace (a)) or v00 ¼ 1 (trace (b)) level. However, the excitation of a particular v00 (e.g., v00 ¼ 0) intermediate level leads also to a certain measurable population of the neighboring v00 (e.g., v00 ¼ 1 and 2) levels, and hence, the CID patterns should reflect this occurrence. Since no bound–bound transition is observed below the dissociation limit, therefore the optically accessible region represented by the spectra in Fig. 4 is characterized by a repulsive potential energy barrier. The short-wavelength ) coincides falloff of the broad band (at 4768 A (within the accuracy of the measurement and which locates the scaling procedure) with 4754.6 A central maximum and minimum in Fig. 3a and b, respectively. In order to verify this, we had to take into account the differences in energies of the intermediate (A0þ v00 and B1v00 ) vibronic levels [11, Table 1]. Similar conclusion had been drawn by the authors of [4] with respect to the spectra of the E1 B1 transition in HgNe complex. Therefore, the energy difference related to the broad-maximum limiting values of wavelengths, i.e., 4768.0 (compare with Fig. 4), is the height and 4799.1 A of the energy barrier Eb0 , measured from the 63 S1 atomic asymptote to the top of the barrier (see Fig. 1). The obtained result, Eb0 ¼ 135 4 cm 1 , is in good agreement with our previous, more accurate B–S evaluation of the D00 . Further laser-frequency , towards shorter scan beyond the value of 4768 A wavelengths, brings the excitation into the repul, sive region of the E1-state potential at R < 3:21 A and the Condon projection of the B1-state v00 ¼ 1 level only. Evidently, the collisional population redistribution between the v00 ¼ 0 and 1 levels is quite effective and gives rise to the characteristic nodal structure of the v00 ¼ 1 projection of the vibrational wave function. All potential parameters evaluated from the analysed excitation spectra are summarized in Table 1.
Acknowledgements We would like to express our sincere gratitude to Professor Brian Atkinson of the University of
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Windsor who lent us an Ndþ :YAG laser much better suitable for the requirements of the experiment. This research was supported by a grant from the Natural Science and Engineering Research Council of Canada. One of us (J.K.) acknowledges financial support from a grant 5P03B 037 20 of the Polish State Committee for Scientific Research (KBN). References [1] E. Czuchaj, H. Stoll, Chem. Phys. 248 (1999) 1. [2] E. Czuchaj, M. Krosnicki, H. Stoll, Chem. Phys. 263 (2001) 7.
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[3] E. Czuchaj, M. Krosnicki, H. Stoll, Theor. Chem. Acc. 105 (2001) 219. [4] M. Okunishi, K. Yamanouchi, K. Onda, S. Tsuchiya, J. Chem. Phys. 98 (1993) 2675. [5] M. Czajkowski, R. Bobkowski, L. Krause, Phys. Rev. A 45 (1992) 6451. [6] J. Koperski, Phys. Reports, in press. [7] M.C. Duval, O. Benoist D’Azy, W.H. Breckenridge, C. Jouvet, B. Soep, J. Chem. Phys. 85 (1986) 6324. [8] F. London, Z. Phys. Chem. B 11 (1930) 222. [9] B.L. Blancy, G.E. Ewing, Ann. Rev. Phys. Chem. 27 (1976) 553. [10] A. Nesmeyanov, Vapor Pressure of the Elements, Academic Press, New York, 1963. [11] J. Koperski, M. Czajkowski, Eur. Phys. J. D 10 (2000) 363. [12] D.M. Lubman, C.T. Rettner, R.N. Zare, J. Phys. Chem. 86 (1982) 1129.