- Email: [email protected]
The A∼2Σ+ state of NO–Ne
Chemical Physics Letters 441 (2007) 181–186 www.elsevier.com/locate/cplett
e 2Rþ state of NO–Ne The A Victoria L. Ayles a, Richard J. Plowright a, Mark J. Watkins a, Timothy G. Wright a,*, Jacek Kłos b, Millard H. Alexander b, Pedro Pajo´n-Sua´rez c,d, Jesu´s Rubayo-Soneira d, Ramo´n Herna´ndez-Lamoneda c a
School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742-2021, USA Centro de Investigaciones Quı´micas, Universidad Auto´noma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Morelos 62210, Mexico d Instituto Superior de Tecnologı´as y Ciencias Aplicadas, Av. Salvador Allende y Luaces, Quı´nta del Los Molinos, La Habana 10600, Cuba b
c
Received 21 March 2007; in final form 2 May 2007 Available online 10 May 2007
Abstract e 2 Rþ state of NO–Ne by high-level ab initio methods, and by (1 + 1) resonance-enhanced multiphoton ionization We investigate the A spectroscopy (REMPI). Despite being able to obtain high-quality spectra of NO–Ar, NO–Kr and NO–Xe, no spectrum of NO–Ne was e 2P observed. It is shown that this state is very weakly bound; and that the overlap between the zero-point vibrational energy level in the X e 2 Rþ state is very small: hence the Franck–Condon factors are close to zero. The location of the Ne state, and the bound levels of the A atom outside the 3s Rydberg orbital is the cause of the observations. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction The electronic spectroscopy of NO-containing van der Waals complexes has formed the basis of several studies, where the complexing partner is a closed-shell species. The simplest examples of such systems are the NO–Rg (Rg = Ne, Ar, Kr, Xe) series and a review by Kim and Meyer [1] summarizes the work up to 2001. In 2000, welle e transition in NO–Kr and resolved spectra of the A X NO–Xe (improving on earlier studies [2,3]) were reported [4] as well as for NO–Ar employing resonance-enhanced multiphoton ionization (REMPI) spectroscopy [5]. Despite considerable effort at the time, corresponding spectra of NO–Ne were not obtained, although Meyer and coworkers had recorded electronic spectra of this species employing different electronic states [6]. Similar failure to observe a structured spectrum had also been reported earlier by Miller and Cheng [7] (using REMPI) and Levy and coworkers [8] (using laser-induced fluorescence). In Ref. *
Corresponding author. E-mail address: [email protected] (T.G. Wright).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.05.019
e state spectrum for NO–Ne was attrib[4], the lack of an A uted to the repulsion between the Ne atom, and the 3s Rydberg electron. Recently, Pajo´n-Suarez et al. [9] performed RCCSD(T)/aug-cc-pVTZ calculations to obtain the intere 2 Rþ state molecular potential energy surface (IPES) of the A of NO–Ne. They found that the interaction was extremely weak, with De = 4 cm1, and some agreement with a previously-derived empirical potential [10] was found. Recently, spectra of low-lying (3p, 3d, 4s) Rydberg states of NO–Ne and NO–Ne2 were successfully recorded [11,12] and this, together with the paper of Pajo´n-Suarez et al. [9], prompted another attempt at recording (1 + 1) e e transition of NO–Ne, REMPI spectra of the A X reported herein. In addition, the present work reports the lowest rovibrational energy levels of NO–Ne, and their wavefunctions employing the IPES of Ref. [9] in the HIBRIDON program of Alexander et al. [13]. 2. Experiment The apparatus employed in the present investigation has been described in detail elsewhere [4] and only a brief
182
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
overview will be provided here. To generate NO–Ar and NO–Ne, mixtures of 5% NO (99.5%, Messer) in the rare gas are used, with pressures of 6 bar, and varying pressures up to 9 bar employed, respectively. NO–Kr and NO–Xe are generated using mixtures of 2.5% NO and 5% Rg (Kr, Xe: 99.9+%, BOC) seeded in Ar (99.9+%, BOC). The gas mixtures are expanded into vacuum using a general valve pulsed nozzle (10 Hz, 750 lm orifice, 200–250 ls opening time). The resulting unskimmed free-jet expansion travels to the extraction region of the time-of-flight mass spectrometer through a thin gate valve. Ionization is achieved in a (1 + 1) REMPI process using the frequency-doubled output of a Sirah Cobra Stretch dye laser (1800 lines/mm grating, Coumarin 450), which is pumped by the third harmonic (355 nm, 10 Hz) output of a Surelite III Nd:YAG (yttrium aluminium garnet) laser. All spectra are collected in the parent ion mass channel. (For NO–Kr and NO–Xe complexes, a number of different isotopomer channels could be sampled, and in addition, signals could be observed in the Kr+ or Xe+ mass channels, respectively, as discussed in Ref. [4].) Spectra are calibrated to the Q11(1/2), R21(1/2) and Q21(1/2) + R11(1/2) rotational lines of the A2R+ X2P1/2 transition of NO at 44198.8, 44 202.8 and 44 210.7 cm1(Ref. [14]). In order to ensure that conditions remained optimal, we recorded spectra of NO–Kr, NO–Xe and NO–Ar at regular points around the attempted recording of NO–Ne spectra. 3. Theory The potential energy surface employed in the present work is that reported in Ref. [9]. The partially spinrestricted coupled cluster, RCCSD(T) method [15,16], as programmed into MOLPRO [17] was employed, with an augmented, correlation-consistent triple zeta (aug-cc-pVTZ) basis set of Dunning et al.; this basis set had been further augmented with both diffuse s, p and d functions on the N and O atoms to describe the 3s Rydberg orbital, and bond functions to aid in the description of the van der Waals interaction as described in Ref. [9]. The IPES was found to be extremely weakly bound, with a De value of ˚ . No rovibrational 4 cm1, and an Re value of 6.5 A energy calculations were performed as part of that work, and so it is not possible to conclude whether the complex is bound or not, and hence whether one may expect to see an electronic spectrum or not. In order to investigate this surface further, rovibrational energies were calculated for the complex in the present work using the close-coupling formalism [18,19] and the HIBRIDON program [13], employing the IPES from Ref. [9]. 4. Results 4.1. Experiment e e A number of attempts were made to record the A X spectrum of NO–Ne, each time alternating with recording
spectra of the other heavier NO–Rg species. The fact that we were able to record strong, cold spectra of NO–Ar, NO–Kr and NO–Xe, coupled with recent experience with previous recording of spectra of NO–Ne via the higher electronic states [11,12], gave some confidence that large numbers of NO–Ne complexes were being formed throughout the study (vide infra). No signals were observed which were due to NO–Ne, however, whilst scanning around the A X transition energy for NO (in line with observations e made previously by Miller and Cheng [7]). Given that the A state is so weakly bound [9], and knowing that the e 2 P state is <35 cm1 (Ref. dissociation energy of the X [20]), one could reasonably expect that the spectrum of NO–Ne would appear 30 cm1 to the blue of the origin of the A X transition of uncomplexed NO, although much wider energetic regions were investigated. In addition, a range of backing pressures were used from 1 atm up to 9 atm, and various portions of the free-jet expansion were probed; in all cases without success. The NO–Rg e state spectra are shown in Fig. 1, (Rg = Ar, Kr, Xe) A along with a scan of the same spectral region obtained whilst gating over the expected time-of-flight of the NO– Ne complex, and a corresponding spectrum of the A X transition in uncomplexed NO. We conclude that the experimental results are consistent with there being either e e transitions for NO–Ne, or if there are no bound A X any, the corresponding Franck–Condon factors are extremely small. We have noted in the above that in our recent work on e 0 ; Fe Þ transitions [11], we were able to see the 3d 2pp ð H both NO–Ne and NO–Ar, obtaining strong spectra for each. Noting that NO–Ne has a weaker binding energy than NO–Ar might suggest that the expected number density for NO–Ne would be less than that for NO–Ar (although there will be effects owing to the dynamics of the complex-formation/cooling processes); further, taking account of the relative intensities of the corresponding 3d 2pp* spectra for each species, it is plausible that some e e estimate of the expectation for the intensity of the A X NO–Ne spectrum could be made (since we are starting from the corresponding ground state in that work, and this). Note that absolute values are not straightforwardly possible, as these would involve a detailed calibration of the apparatus. However, relative values of the FCFs are also not meaningful, as the relative FCFs for the 3d 2pp* transitions are not expected necessarily to be e e transitions for the two species; the same for the A X in time these could be calculated and compared to those e e transition, but such calculations for for the A X highly-excited states are much more demanding. It suffices to say that our previous work makes it certain that we were producing easily enough NO–Ne complexes to be seen, with intensities for the 3d 2pp* transitions for NO–Ne and NO–Ar being comparable. The fact that we could observe an extremely strong NO–Ar signal in the present work, yet none for NO–Ne means that the non-observation e e transition lies in the Franck–Condon factor for the A X
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
183
Table 1 e 2 Rþ Þ–Ne – see text for details Lowest rovibrational energy levels of NOð A
e e transition for the NO–Rg Fig. 1. (1 + 1) REMPI spectra of the A X van der Waals complexes where Rg = Ar, Kr and Xe. We were unable to observe the NO–Ne complex in the 3s Rydberg state. The corresponding spectrum of uncomplexed NO is also shown. Note that although a spectrum of a particular isotopomer is shown, spectra are essentially indistinguishable whichever isotopomer is monitored, or even if a number of isotopomers is monitored – see Ref. [4].
(the electronic transition strength being expected to be similar, since NO is the chromophore). These conclusions are completely in line with those we reached earlier in Ref. [4] and are confirmed by the results of the calculations, described below. 4.2. Theory The lowest energy levels are presented in Table 1, where J is the total angular momentum of the system, the +/ is the parity and v is a vibrational quantum number. As may be seen, for each (J, parity) pair, there are two values.
J
Parity
v
Energy/cm1
1/2 1/2 1/2 1/2 3/2 3/2 3/2 3/2 5/2 5/2 5/2 5/2
+ + + + + +
0 1 0 1 0 1 0 1 0 1 0 1
2.043 0.316 1.988 0.285 1.988 0.285 1.878 0.223 1.878 0.233 1.714 0.133
These are two vibrational energy levels. It may also be noted that there are degeneracies between pairs of levels corresponding to (J,) and (J + 1,+); these are simply spin-rotation pairs (we set the spin-rotation term to be zero here.) Calculations involving the collocation approach [21– 25] (in which NO is assumed to be closed-shell) gave almost identical energies to the (J = 1/2,+) pair of energy levels. The wavefunctions shown in Fig. 2 show these vibrations to be the v = 0 and v = 1 levels of the intermolecular stretch. Both of these energy levels are very weakly bound and spatially very extended, with almost no angular dependence. It thus appears that there are no bound bending leve state of NO–Ne. One way of rationalizing this els for the A is to note that the dipole of NO will be oriented along the intermolecular axis, and so this is where the dipole/ induced-dipole is likely to be dominant. The 3s Rydberg density is close to being isotropic, and so any movement of the Ne off the intermolecular axis will lead to a diminution of the attractive interaction, but the same repulsive term. This combination of effects could lead to there being no bound bending modes. These observations are confirmed in cuts through the potential energy surface, presented in Fig. 3 of Ref. [9], where it can be seen that the collinear approach of Ne and NO is by far the lowest energy direction. From Table 1, we can see that D0 = 2.04 cm1, with e state of D1 = 0.32 cm1. The dissociation energy of the X NO with Ne has been calculated to be 35 cm1 using HIBRIe 2 PÞ–Ne RCCSD(T) diabatic DON program with new NOð X potential energy surfaces of Kłos et al. [26], and so it is anticipated that there will be large geometry changes dure e transition; alternatively, it is expected that ing the A X e state will access the disthe vertical transition from the X e state — confirming the sociation continuum of the A results of Ref. [8]. Thus, any observed spectrum will correspond to off-diagonal Franck–Condon factors, and will therefore be expected to be weak (see below). For example, e state of NO–Ar has been successfully observed by a the A number of workers [1,5]; however, in this case the differe (44 cm1) and X e ence in binding energies of the A 1 (88 cm ) is only a factor of two. In Fig. 3 we compare
184
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
e state (lower, Fig. 3. Contour map (cm1) of the v = 0 levels of the X e state (upper, red, trace) showing that there is very black, trace) and the A little overlap of these wavefunctions. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
e 2 Rþ Þ–Ne. Fig. 2. The calculated vibrational wavefunctions for NOð A These are the v = 0 and v = 1 levels of an intermolecular stretch.
e (v = 0). As may be e ðv ¼ 0Þ, with A the wavefunctions for X seen, the overlap is minimal, and confirms that the Franck– Condon factors will be extremely small (and similarly for the v = 1 level). 5. Discussion e state of the NO–Ar One of the main features of the A complex is that the observed binding is much lower than in the higher Rydberg states due to the orbital radius of the Rydberg electron. In higher states, the rare gas atom is more exposed to the NO+ core as the Rydberg electron occupies a spatial region that is far removed from that of the rare gas atom (with penetrative effects playing an important role) [11]. Conversely, the reduced orbital radius e state brings the rare gas atom and Rydberg elecof the A tron into direct spatial conflict; the overall nature of the e state binding, then, is a result of the attractive dipole/ A
induced-dipole and a repulsive Pauli interaction [4]. For e state binding energy is found to be lower NO–Ar, the A e 2 P ground state, manifested in a blue shift of than the X e e transition compared to that of uncomplexed the A X e state is less NO. It is, at first, surprising to find that the A e e state, since the dipole of the A strongly bound than the X e state is 1.1 D [27], versus a value of 0.2 D [28] for the X state, this suggests that the attractive dipole/induced-dipole e state; of course, there term should be much greater in the A are also changes in the induced-dipole/induced dipole interactions, which are expected to be larger in the Rydberg state. The implication therefore is that the repulsion between the electrons on the Ar atom and the 3s Rydberg electron cancels out the majority of the increased attractive terms. For NO–Kr, owing to the greater polarizability of the Kr atom, the changes in the attractive and repulsive terms almost equal each other, leading to the origin of e e transition being almost coincident with that the A X of uncomplexed NO [4]; for Xe, the even greater polarizability leads to the changes in the attractive terms being greater, and so this spectrum is actually red shifted [4]. The trends, therefore, are strongly suggestive for the changes in the NO–Ne complex being dominated by the repulsive term, owing to the much smaller polarizability of Ne. In Fig. 4 we show that the 3s Rydberg state is highly extended. It can be seen that the Ne atom is expected to lie outside the main 3s Rydberg electron density and thus have little interaction with the NO+ core, confirming the picture presented. For comparison we show, in Fig. 4b, the electron density for the X2P ground state of NO which is much less radially extended thus allowing a closer approach of the neon atom.
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
185
ficulty, since there could be experimental reasons as to why a signal is not seen. To try and assuage doubts over such an interpretation, we alternated our search for the NO–Ne spectrum, with recording spectra of the other NO–Rg species, confirming that our conditions were optimal throughout. Additional support for the conclusions comes from the results of the theoretical studies, which show that: first there are only two bound intermolecular (stretch) vibrations; secondly that the vibrational wavefunctions of these are very extended; and thirdly that the overlap of these e ðv ¼ 0Þ level is very poor. wavefunctions with the starting X Overall, then, the theory is in line with the experimental observations. Further, the extended nature of the 3s Rydberg state, and the position of the Ne atom in relation to the Rydberg orbital electron density, supports the interpree state has a repulsive term that is large tation that the A compared to the changes in the attractive terms that occur e states. e and A during the transition between the X Fig. 4a. Contour plot of the total electron density of NO in its A2R+ state. e 2 Rþ state of The neon atom is shown at the equilibrium distance of the A the NO–Ne complex for comparison.
Acknowledgements The Nottingham group thanks the EPSRC for funding, particularly for studentships to VLA and RJP. PPS, JRS and RHL thank Citma-Conacyt for financial support through the bilateral Grant J200.645. JK and MHA thank the NSF for funding under Grant CHE-0413743. References
Fig. 4b. Contour plot of the total electron density of NO in its X2P ground state. The neon atom is shown at the equilibrium distance of the e 2 P state of the NO–Ne complex for comparison. X
6. Conclusions e state NO–Ne spectrum The non-observation of the A e state is either could alone be taken as evidence that the A unbound, or only extremely weakly bound. Note that this e state in fact has no bearing on the ease of forming the X the free-jet expansion: we [11,12] (and others [1,6]) have shown that this is straightforward. However, the interpretation of a non-observation of a signal is fraught with dif-
[1] Y. Kim, H. Meyer, Int. Rev. Phys. Chem. 20 (2001) 219. [2] A.M. Bush, J.M. Dyke, P. Mack, D.M. Smith, T.G. Wright, J. Chem. Phys. 105 (1996) 9804. [3] P. Mack, J.M. Dyke, T.G. Wright, J. Chem. Soc., Faraday Trans. 94 (1998) 629. [4] S.D. Gamblin, S.E. Daire, J. Lozeille, T.G. Wright, Chem. Phys. Lett. 325 (2000) 232. [5] J. Lozeille, S.D. Gamblin, S.E. Daire, T.G. Wright, D.M. Smith, J. Chem. Phys. 113 (2000) 7224. [6] J. Fleniken, Y. Kim, H. Meyer, J. Chem. Phys. 109 (1998) 8940. [7] J.C. Miller, W.-C. Cheng, J. Phys. Chem. 89 (1985) 1647. [8] M.E. Carrasquillo, P.R.R. Langridge-Smith, D.H. Levy, in: A.R.W. McKellar, T. Oka, B.P. Stoicheff (Eds.), Laser Spectroscopy V, Springer, Berlin, 1981, p. 333. [9] P. Pajo´n-Suarez, G. Rojas-Lorenzo, J. Rubayo-Soneira, R. Herna´ndez-Lamoneda, Chem. Phys. Lett. 421 (2006) 389. [10] G. Rojas-Lorenzo, J. Rubayo-Soneira, F. Vigliotti, M. Chergui, Phys. Rev. B 67 (2003) 115119. [11] D.E. Bergeron et al., J. Chem. Phys. 124 (2006) 214302. [12] D.E. Bergeron, A. Musgrave, V.L. Ayles, R.T. Gammon, J.A.E. Silber, T.G. Wright, J. Chem. Phys. 125 (2006) 144319. [13] HIBRIDON is a package of programs for the time-independent quantum treatment of inelesatic collisions and photodissociation spectra written by M.H. Alexander, D.E. Manopoulos, H.-J. Werner, and B. Follmeg, with contributions by W. Kearney, A. Berning, A. Degli-Esposti, C. Rist, and P. Dagdigian. More information on the code can be obtained from the website. [14] J. Danielak, U. Domin, R. Kepa, M. Rytel, M. Zachwieja, J. Mol. Spect. 181 (1977) 394. [15] J.D. Watts, J. Gauss, R.J. Bartlett, J. Chem. Phys. 98 (1993) 8718. [16] C. Hampel, K. Peterson, H.-J. Werner, Chem. Phys. Lett. 190 (1992) 1.
186
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
[17] MOLPRO is a package of ab initio programs written by H.-J. Werner, et al. [18] A. Arthurs, A. Dalgarno, Proc. Roy. Soc. (London Ser.) A 256 (1960) 540. [19] D. Secrest, in: R.B. Bernstein (Ed.), Atom–Molecule Collision Theory: A Guide for the Experimentalist, Plenum, New York, 1979, p. 265. [20] M.H. Alexander, P. Solda´n, T.G. Wright, Y. Kim, H. Meyer, P.J. Dagdigian, E.P.F. Lee, J. Chem. Phys. 114 (2001) 5588. [21] I.P. Hamilton, J.C. Light, J. Chem. Phys. 84 (1986) 306.
[22] [23] [24] [25]
W. Yang, A.C. Peet, Chem. Phys. Lett. 153 (1988) 98. A.C. Peet, W. Yang, J. Chem. Phys. 90 (1989) 1746. W. Yang, A.C. Peet, J. Chem. Phys. 92 (1990) 522. S. Cybulski, J. Couvillion, J. Kłos, G. Chałasin´ski, J. Chem. Phys. 110 (1999) 1416. [26] J. Kłos et al., unpublished results. [27] E.D. Glendening, D. Feller, K.A. Peterson, E.A. McCullough Jr., R.J. Miller, J. Chem. Phys. 103 (1995) 3517. [28] R.M. Neumann, Astrophys. J. 161 (1970) 779.
e 2Rþ state of NO–Ne The A Victoria L. Ayles a, Richard J. Plowright a, Mark J. Watkins a, Timothy G. Wright a,*, Jacek Kłos b, Millard H. Alexander b, Pedro Pajo´n-Sua´rez c,d, Jesu´s Rubayo-Soneira d, Ramo´n Herna´ndez-Lamoneda c a
School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742-2021, USA Centro de Investigaciones Quı´micas, Universidad Auto´noma del Estado de Morelos, Av. Universidad 1001, Cuernavaca, Morelos 62210, Mexico d Instituto Superior de Tecnologı´as y Ciencias Aplicadas, Av. Salvador Allende y Luaces, Quı´nta del Los Molinos, La Habana 10600, Cuba b
c
Received 21 March 2007; in final form 2 May 2007 Available online 10 May 2007
Abstract e 2 Rþ state of NO–Ne by high-level ab initio methods, and by (1 + 1) resonance-enhanced multiphoton ionization We investigate the A spectroscopy (REMPI). Despite being able to obtain high-quality spectra of NO–Ar, NO–Kr and NO–Xe, no spectrum of NO–Ne was e 2P observed. It is shown that this state is very weakly bound; and that the overlap between the zero-point vibrational energy level in the X e 2 Rþ state is very small: hence the Franck–Condon factors are close to zero. The location of the Ne state, and the bound levels of the A atom outside the 3s Rydberg orbital is the cause of the observations. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction The electronic spectroscopy of NO-containing van der Waals complexes has formed the basis of several studies, where the complexing partner is a closed-shell species. The simplest examples of such systems are the NO–Rg (Rg = Ne, Ar, Kr, Xe) series and a review by Kim and Meyer [1] summarizes the work up to 2001. In 2000, welle e transition in NO–Kr and resolved spectra of the A X NO–Xe (improving on earlier studies [2,3]) were reported [4] as well as for NO–Ar employing resonance-enhanced multiphoton ionization (REMPI) spectroscopy [5]. Despite considerable effort at the time, corresponding spectra of NO–Ne were not obtained, although Meyer and coworkers had recorded electronic spectra of this species employing different electronic states [6]. Similar failure to observe a structured spectrum had also been reported earlier by Miller and Cheng [7] (using REMPI) and Levy and coworkers [8] (using laser-induced fluorescence). In Ref. *
Corresponding author. E-mail address: [email protected] (T.G. Wright).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.05.019
e state spectrum for NO–Ne was attrib[4], the lack of an A uted to the repulsion between the Ne atom, and the 3s Rydberg electron. Recently, Pajo´n-Suarez et al. [9] performed RCCSD(T)/aug-cc-pVTZ calculations to obtain the intere 2 Rþ state molecular potential energy surface (IPES) of the A of NO–Ne. They found that the interaction was extremely weak, with De = 4 cm1, and some agreement with a previously-derived empirical potential [10] was found. Recently, spectra of low-lying (3p, 3d, 4s) Rydberg states of NO–Ne and NO–Ne2 were successfully recorded [11,12] and this, together with the paper of Pajo´n-Suarez et al. [9], prompted another attempt at recording (1 + 1) e e transition of NO–Ne, REMPI spectra of the A X reported herein. In addition, the present work reports the lowest rovibrational energy levels of NO–Ne, and their wavefunctions employing the IPES of Ref. [9] in the HIBRIDON program of Alexander et al. [13]. 2. Experiment The apparatus employed in the present investigation has been described in detail elsewhere [4] and only a brief
182
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
overview will be provided here. To generate NO–Ar and NO–Ne, mixtures of 5% NO (99.5%, Messer) in the rare gas are used, with pressures of 6 bar, and varying pressures up to 9 bar employed, respectively. NO–Kr and NO–Xe are generated using mixtures of 2.5% NO and 5% Rg (Kr, Xe: 99.9+%, BOC) seeded in Ar (99.9+%, BOC). The gas mixtures are expanded into vacuum using a general valve pulsed nozzle (10 Hz, 750 lm orifice, 200–250 ls opening time). The resulting unskimmed free-jet expansion travels to the extraction region of the time-of-flight mass spectrometer through a thin gate valve. Ionization is achieved in a (1 + 1) REMPI process using the frequency-doubled output of a Sirah Cobra Stretch dye laser (1800 lines/mm grating, Coumarin 450), which is pumped by the third harmonic (355 nm, 10 Hz) output of a Surelite III Nd:YAG (yttrium aluminium garnet) laser. All spectra are collected in the parent ion mass channel. (For NO–Kr and NO–Xe complexes, a number of different isotopomer channels could be sampled, and in addition, signals could be observed in the Kr+ or Xe+ mass channels, respectively, as discussed in Ref. [4].) Spectra are calibrated to the Q11(1/2), R21(1/2) and Q21(1/2) + R11(1/2) rotational lines of the A2R+ X2P1/2 transition of NO at 44198.8, 44 202.8 and 44 210.7 cm1(Ref. [14]). In order to ensure that conditions remained optimal, we recorded spectra of NO–Kr, NO–Xe and NO–Ar at regular points around the attempted recording of NO–Ne spectra. 3. Theory The potential energy surface employed in the present work is that reported in Ref. [9]. The partially spinrestricted coupled cluster, RCCSD(T) method [15,16], as programmed into MOLPRO [17] was employed, with an augmented, correlation-consistent triple zeta (aug-cc-pVTZ) basis set of Dunning et al.; this basis set had been further augmented with both diffuse s, p and d functions on the N and O atoms to describe the 3s Rydberg orbital, and bond functions to aid in the description of the van der Waals interaction as described in Ref. [9]. The IPES was found to be extremely weakly bound, with a De value of ˚ . No rovibrational 4 cm1, and an Re value of 6.5 A energy calculations were performed as part of that work, and so it is not possible to conclude whether the complex is bound or not, and hence whether one may expect to see an electronic spectrum or not. In order to investigate this surface further, rovibrational energies were calculated for the complex in the present work using the close-coupling formalism [18,19] and the HIBRIDON program [13], employing the IPES from Ref. [9]. 4. Results 4.1. Experiment e e A number of attempts were made to record the A X spectrum of NO–Ne, each time alternating with recording
spectra of the other heavier NO–Rg species. The fact that we were able to record strong, cold spectra of NO–Ar, NO–Kr and NO–Xe, coupled with recent experience with previous recording of spectra of NO–Ne via the higher electronic states [11,12], gave some confidence that large numbers of NO–Ne complexes were being formed throughout the study (vide infra). No signals were observed which were due to NO–Ne, however, whilst scanning around the A X transition energy for NO (in line with observations e made previously by Miller and Cheng [7]). Given that the A state is so weakly bound [9], and knowing that the e 2 P state is <35 cm1 (Ref. dissociation energy of the X [20]), one could reasonably expect that the spectrum of NO–Ne would appear 30 cm1 to the blue of the origin of the A X transition of uncomplexed NO, although much wider energetic regions were investigated. In addition, a range of backing pressures were used from 1 atm up to 9 atm, and various portions of the free-jet expansion were probed; in all cases without success. The NO–Rg e state spectra are shown in Fig. 1, (Rg = Ar, Kr, Xe) A along with a scan of the same spectral region obtained whilst gating over the expected time-of-flight of the NO– Ne complex, and a corresponding spectrum of the A X transition in uncomplexed NO. We conclude that the experimental results are consistent with there being either e e transitions for NO–Ne, or if there are no bound A X any, the corresponding Franck–Condon factors are extremely small. We have noted in the above that in our recent work on e 0 ; Fe Þ transitions [11], we were able to see the 3d 2pp ð H both NO–Ne and NO–Ar, obtaining strong spectra for each. Noting that NO–Ne has a weaker binding energy than NO–Ar might suggest that the expected number density for NO–Ne would be less than that for NO–Ar (although there will be effects owing to the dynamics of the complex-formation/cooling processes); further, taking account of the relative intensities of the corresponding 3d 2pp* spectra for each species, it is plausible that some e e estimate of the expectation for the intensity of the A X NO–Ne spectrum could be made (since we are starting from the corresponding ground state in that work, and this). Note that absolute values are not straightforwardly possible, as these would involve a detailed calibration of the apparatus. However, relative values of the FCFs are also not meaningful, as the relative FCFs for the 3d 2pp* transitions are not expected necessarily to be e e transitions for the two species; the same for the A X in time these could be calculated and compared to those e e transition, but such calculations for for the A X highly-excited states are much more demanding. It suffices to say that our previous work makes it certain that we were producing easily enough NO–Ne complexes to be seen, with intensities for the 3d 2pp* transitions for NO–Ne and NO–Ar being comparable. The fact that we could observe an extremely strong NO–Ar signal in the present work, yet none for NO–Ne means that the non-observation e e transition lies in the Franck–Condon factor for the A X
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
183
Table 1 e 2 Rþ Þ–Ne – see text for details Lowest rovibrational energy levels of NOð A
e e transition for the NO–Rg Fig. 1. (1 + 1) REMPI spectra of the A X van der Waals complexes where Rg = Ar, Kr and Xe. We were unable to observe the NO–Ne complex in the 3s Rydberg state. The corresponding spectrum of uncomplexed NO is also shown. Note that although a spectrum of a particular isotopomer is shown, spectra are essentially indistinguishable whichever isotopomer is monitored, or even if a number of isotopomers is monitored – see Ref. [4].
(the electronic transition strength being expected to be similar, since NO is the chromophore). These conclusions are completely in line with those we reached earlier in Ref. [4] and are confirmed by the results of the calculations, described below. 4.2. Theory The lowest energy levels are presented in Table 1, where J is the total angular momentum of the system, the +/ is the parity and v is a vibrational quantum number. As may be seen, for each (J, parity) pair, there are two values.
J
Parity
v
Energy/cm1
1/2 1/2 1/2 1/2 3/2 3/2 3/2 3/2 5/2 5/2 5/2 5/2
+ + + + + +
0 1 0 1 0 1 0 1 0 1 0 1
2.043 0.316 1.988 0.285 1.988 0.285 1.878 0.223 1.878 0.233 1.714 0.133
These are two vibrational energy levels. It may also be noted that there are degeneracies between pairs of levels corresponding to (J,) and (J + 1,+); these are simply spin-rotation pairs (we set the spin-rotation term to be zero here.) Calculations involving the collocation approach [21– 25] (in which NO is assumed to be closed-shell) gave almost identical energies to the (J = 1/2,+) pair of energy levels. The wavefunctions shown in Fig. 2 show these vibrations to be the v = 0 and v = 1 levels of the intermolecular stretch. Both of these energy levels are very weakly bound and spatially very extended, with almost no angular dependence. It thus appears that there are no bound bending leve state of NO–Ne. One way of rationalizing this els for the A is to note that the dipole of NO will be oriented along the intermolecular axis, and so this is where the dipole/ induced-dipole is likely to be dominant. The 3s Rydberg density is close to being isotropic, and so any movement of the Ne off the intermolecular axis will lead to a diminution of the attractive interaction, but the same repulsive term. This combination of effects could lead to there being no bound bending modes. These observations are confirmed in cuts through the potential energy surface, presented in Fig. 3 of Ref. [9], where it can be seen that the collinear approach of Ne and NO is by far the lowest energy direction. From Table 1, we can see that D0 = 2.04 cm1, with e state of D1 = 0.32 cm1. The dissociation energy of the X NO with Ne has been calculated to be 35 cm1 using HIBRIe 2 PÞ–Ne RCCSD(T) diabatic DON program with new NOð X potential energy surfaces of Kłos et al. [26], and so it is anticipated that there will be large geometry changes dure e transition; alternatively, it is expected that ing the A X e state will access the disthe vertical transition from the X e state — confirming the sociation continuum of the A results of Ref. [8]. Thus, any observed spectrum will correspond to off-diagonal Franck–Condon factors, and will therefore be expected to be weak (see below). For example, e state of NO–Ar has been successfully observed by a the A number of workers [1,5]; however, in this case the differe (44 cm1) and X e ence in binding energies of the A 1 (88 cm ) is only a factor of two. In Fig. 3 we compare
184
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
e state (lower, Fig. 3. Contour map (cm1) of the v = 0 levels of the X e state (upper, red, trace) showing that there is very black, trace) and the A little overlap of these wavefunctions. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
e 2 Rþ Þ–Ne. Fig. 2. The calculated vibrational wavefunctions for NOð A These are the v = 0 and v = 1 levels of an intermolecular stretch.
e (v = 0). As may be e ðv ¼ 0Þ, with A the wavefunctions for X seen, the overlap is minimal, and confirms that the Franck– Condon factors will be extremely small (and similarly for the v = 1 level). 5. Discussion e state of the NO–Ar One of the main features of the A complex is that the observed binding is much lower than in the higher Rydberg states due to the orbital radius of the Rydberg electron. In higher states, the rare gas atom is more exposed to the NO+ core as the Rydberg electron occupies a spatial region that is far removed from that of the rare gas atom (with penetrative effects playing an important role) [11]. Conversely, the reduced orbital radius e state brings the rare gas atom and Rydberg elecof the A tron into direct spatial conflict; the overall nature of the e state binding, then, is a result of the attractive dipole/ A
induced-dipole and a repulsive Pauli interaction [4]. For e state binding energy is found to be lower NO–Ar, the A e 2 P ground state, manifested in a blue shift of than the X e e transition compared to that of uncomplexed the A X e state is less NO. It is, at first, surprising to find that the A e e state, since the dipole of the A strongly bound than the X e state is 1.1 D [27], versus a value of 0.2 D [28] for the X state, this suggests that the attractive dipole/induced-dipole e state; of course, there term should be much greater in the A are also changes in the induced-dipole/induced dipole interactions, which are expected to be larger in the Rydberg state. The implication therefore is that the repulsion between the electrons on the Ar atom and the 3s Rydberg electron cancels out the majority of the increased attractive terms. For NO–Kr, owing to the greater polarizability of the Kr atom, the changes in the attractive and repulsive terms almost equal each other, leading to the origin of e e transition being almost coincident with that the A X of uncomplexed NO [4]; for Xe, the even greater polarizability leads to the changes in the attractive terms being greater, and so this spectrum is actually red shifted [4]. The trends, therefore, are strongly suggestive for the changes in the NO–Ne complex being dominated by the repulsive term, owing to the much smaller polarizability of Ne. In Fig. 4 we show that the 3s Rydberg state is highly extended. It can be seen that the Ne atom is expected to lie outside the main 3s Rydberg electron density and thus have little interaction with the NO+ core, confirming the picture presented. For comparison we show, in Fig. 4b, the electron density for the X2P ground state of NO which is much less radially extended thus allowing a closer approach of the neon atom.
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
185
ficulty, since there could be experimental reasons as to why a signal is not seen. To try and assuage doubts over such an interpretation, we alternated our search for the NO–Ne spectrum, with recording spectra of the other NO–Rg species, confirming that our conditions were optimal throughout. Additional support for the conclusions comes from the results of the theoretical studies, which show that: first there are only two bound intermolecular (stretch) vibrations; secondly that the vibrational wavefunctions of these are very extended; and thirdly that the overlap of these e ðv ¼ 0Þ level is very poor. wavefunctions with the starting X Overall, then, the theory is in line with the experimental observations. Further, the extended nature of the 3s Rydberg state, and the position of the Ne atom in relation to the Rydberg orbital electron density, supports the interpree state has a repulsive term that is large tation that the A compared to the changes in the attractive terms that occur e states. e and A during the transition between the X Fig. 4a. Contour plot of the total electron density of NO in its A2R+ state. e 2 Rþ state of The neon atom is shown at the equilibrium distance of the A the NO–Ne complex for comparison.
Acknowledgements The Nottingham group thanks the EPSRC for funding, particularly for studentships to VLA and RJP. PPS, JRS and RHL thank Citma-Conacyt for financial support through the bilateral Grant J200.645. JK and MHA thank the NSF for funding under Grant CHE-0413743. References
Fig. 4b. Contour plot of the total electron density of NO in its X2P ground state. The neon atom is shown at the equilibrium distance of the e 2 P state of the NO–Ne complex for comparison. X
6. Conclusions e state NO–Ne spectrum The non-observation of the A e state is either could alone be taken as evidence that the A unbound, or only extremely weakly bound. Note that this e state in fact has no bearing on the ease of forming the X the free-jet expansion: we [11,12] (and others [1,6]) have shown that this is straightforward. However, the interpretation of a non-observation of a signal is fraught with dif-
[1] Y. Kim, H. Meyer, Int. Rev. Phys. Chem. 20 (2001) 219. [2] A.M. Bush, J.M. Dyke, P. Mack, D.M. Smith, T.G. Wright, J. Chem. Phys. 105 (1996) 9804. [3] P. Mack, J.M. Dyke, T.G. Wright, J. Chem. Soc., Faraday Trans. 94 (1998) 629. [4] S.D. Gamblin, S.E. Daire, J. Lozeille, T.G. Wright, Chem. Phys. Lett. 325 (2000) 232. [5] J. Lozeille, S.D. Gamblin, S.E. Daire, T.G. Wright, D.M. Smith, J. Chem. Phys. 113 (2000) 7224. [6] J. Fleniken, Y. Kim, H. Meyer, J. Chem. Phys. 109 (1998) 8940. [7] J.C. Miller, W.-C. Cheng, J. Phys. Chem. 89 (1985) 1647. [8] M.E. Carrasquillo, P.R.R. Langridge-Smith, D.H. Levy, in: A.R.W. McKellar, T. Oka, B.P. Stoicheff (Eds.), Laser Spectroscopy V, Springer, Berlin, 1981, p. 333. [9] P. Pajo´n-Suarez, G. Rojas-Lorenzo, J. Rubayo-Soneira, R. Herna´ndez-Lamoneda, Chem. Phys. Lett. 421 (2006) 389. [10] G. Rojas-Lorenzo, J. Rubayo-Soneira, F. Vigliotti, M. Chergui, Phys. Rev. B 67 (2003) 115119. [11] D.E. Bergeron et al., J. Chem. Phys. 124 (2006) 214302. [12] D.E. Bergeron, A. Musgrave, V.L. Ayles, R.T. Gammon, J.A.E. Silber, T.G. Wright, J. Chem. Phys. 125 (2006) 144319. [13] HIBRIDON is a package of programs for the time-independent quantum treatment of inelesatic collisions and photodissociation spectra written by M.H. Alexander, D.E. Manopoulos, H.-J. Werner, and B. Follmeg, with contributions by W. Kearney, A. Berning, A. Degli-Esposti, C. Rist, and P. Dagdigian. More information on the code can be obtained from the website
186
V.L. Ayles et al. / Chemical Physics Letters 441 (2007) 181–186
[17] MOLPRO is a package of ab initio programs written by H.-J. Werner, et al. [18] A. Arthurs, A. Dalgarno, Proc. Roy. Soc. (London Ser.) A 256 (1960) 540. [19] D. Secrest, in: R.B. Bernstein (Ed.), Atom–Molecule Collision Theory: A Guide for the Experimentalist, Plenum, New York, 1979, p. 265. [20] M.H. Alexander, P. Solda´n, T.G. Wright, Y. Kim, H. Meyer, P.J. Dagdigian, E.P.F. Lee, J. Chem. Phys. 114 (2001) 5588. [21] I.P. Hamilton, J.C. Light, J. Chem. Phys. 84 (1986) 306.
[22] [23] [24] [25]
W. Yang, A.C. Peet, Chem. Phys. Lett. 153 (1988) 98. A.C. Peet, W. Yang, J. Chem. Phys. 90 (1989) 1746. W. Yang, A.C. Peet, J. Chem. Phys. 92 (1990) 522. S. Cybulski, J. Couvillion, J. Kłos, G. Chałasin´ski, J. Chem. Phys. 110 (1999) 1416. [26] J. Kłos et al., unpublished results. [27] E.D. Glendening, D. Feller, K.A. Peterson, E.A. McCullough Jr., R.J. Miller, J. Chem. Phys. 103 (1995) 3517. [28] R.M. Neumann, Astrophys. J. 161 (1970) 779.