The 2ν1 overtone band of H28SiD3

Journal of Molecular Spectroscopy 282 (2012) 14–19

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The 2m1 overtone band of H28SiD3 E. Cané a, L. Fusina a,⇑, H. Bürger b, M. Litz b a b

Dipartimento di Chimica Fisica e Inorganica, Università di Bologna, Viale del Risorgimento 4, I-40136 Bologna, Italy Anorganische Chemie, FB C, Bergische Universität, D-42097 Wuppertal, Germany

a r t i c l e

i n f o

Article history: Received 26 June 2012 In revised form 2 October 2012 Available online 26 October 2012 Keywords: Trideutero silane High resolution infrared spectra Rovibration analysis Overtone band Si–H stretching

a b s t r a c t The 2m1 (A1) SiH stretching overtone band of HSiD3 has been recorded at a resolution of ca. 0.009 cm1 between 4200 and 4400 cm1. About 790 ro-vibration transitions of the H28SiD3 isotopologue have been assigned, with J0 up to 24 and K up to 21. The spectrum evidences the existence of several perturbations. The assigned transitions have been analyzed either neglecting or including in the model A1/E Coriolistype interactions between v1 = 2 and nearby dark states. The standard deviation of all the fits is, however, more than one order of magnitude larger than the estimated experimental precision and is independent of the adopted model. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Silane, SiH4, and its isotopologues, H3SiD, HSiD3, and H2SiD2, have been the subject of several spectroscopic and theoretical studies, mainly aimed at testing the applicability of the local mode theory to the pattern of the Si–H stretching excitation [1–2]. The localization of the vibration energy in an individual X–H bond in the XHn species (X = S, Se, Te, As, Sb, Si, Ge, and Sn; n = 2, 3, 4) was considered [1–2] also in comparison with the behavior of the C–H stretching vibration in CHY3 molecules, with Y = D, F, Cl, Br, I [3–5]. In case of the C–H bond, it emerged that strong Fermi resonances between the C–H stretching and bending motions led to a fast redistribution of the vibration energy among these modes. In contrast, from spectroscopic investigations of fundamentals and stretching overtones, the local mode character of the Si–H bond appeared very pronounced and was attained even at low excitation in SiH4 [6], HSiD3 [7–14], H2SiD2 [15–16], and H3SiD [17–21]. To better understand the patterns of anharmonic perturbations among vibrationally excited states and their effects on overtone spectra, the calculation of the energy of vibrationally excited levels was taken into account, including multiple excitation, for all the vibrational modes, using full dimensional high order canonical van Vleck perturbation theory [22]. These extensive CVPT calculations used the quartic ab initio force field calculated at high level of theory with the CCSD(T) method and Dunning’s cc-pVnZ basis set by Martin et al. [23].

⇑ Corresponding author. E-mail address: [email protected] (L. Fusina). 0022-2852/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jms.2012.10.007

In addition, a fourdimensional SiH stretching dipole moment surface was derived, allowing the calculation of the band intensities for HSiD3, H2SiD2, and H3SiD to be compared with the experimental values up to 9000 cm1 obtained from infrared spectra recorded at a resolution of 0.2 cm1 [12–13]. Particular emphasis was given to the intensity of the SiH stretching overtones and to the stretchingbending combination bands, whose upper levels could be connected through anharmonic resonances. The recording of the overtone spectra of the Si–H stretching mode has been extended up to 9m1 [10,11,14,24,25] in case of HSiD3, since it carries an isolated Si–H chromophore analogous to the C–H one in the CHY3 species [3–5]. With the exception of 9m1, whose band center was estimated from a low resolution photoacoustic spectrum, the nm1 overtone bands, with n = 2, 3, . . ., 8, were rotationally analyzed. Comparing the results of the analyses it was observed that the perturbations affecting the v1 = n bright states with n = 3, 4, 5, 6 decrease in effectiveness with increasing n, notwithstanding the growing density of states [14]. This unexpected evolution holds at even higher energy, v1 = 7 and 8 being as unperturbed as v1 = 6 [10,11,14]. At lower energy, both in the v1 = 1 and 2 states, the levels with J = 13 and 14 are highly perturbed by Coriolis interactions with unknown dark states [9,24]. With the aim to investigate the coupling of the stretching bright states to the dense background of dark states for increasing n, it seemed necessary to re-analyze the rotational structure of 2m1 from a high resolution FTIR spectrum, since the previous analysis used a spectrum recorded at low resolution with a grating spectrometer [24]. In that investigation about 220 transitions were assigned with J00 up to 22 and K up to 17, yielding the band origin,

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4307.09(11) cm1, and a rough estimate of DB and DC. Transitions with K 6 5 were not resolved and the overlapping of lines at high J values was so severe that it prevented unambiguous assignments. The effect of perturbations was evidenced only in excited levels with J = 13 and 14 [24]. In the present paper we report on the analysis of the 2m1 band of H28SiD3 recorded at 0.0088 cm1 optical resolution in the region between 4200 and 4400 cm1. 2. Experimental details HSiD3 was prepared as described earlier [13]. The spectrum was recorded between 3850 and 5200 cm1 with the Bruker 120 HR interferometer at Wuppertal. A 1.6 m long glass cell, outfitted with KBr windows, was employed. The pressure used was ca. 1000 Pa. The instrument was equipped with a Halogen source, a CaF2 beam splitter and an InSb detector. The resolution (1/maximum optical path difference) was adjusted to 0.0088 cm1. This combines with the Doppler width, ca. 0.009 cm1, to an effective line width (FWHM) of ca. 0.013 cm1. Altogether 120 scans were co-added. Calibration was done by comparison with H2O lines [26] applying the corrections according to Ref. [27]. Wavenumber precision is ca. 3  104 cm1, wavenumber accuracy ca. 1  103 cm1.

unexpected line intensities, resulting from the strong energy perturbations affecting the indicated levels of v1 = 2. The lines evidenced in Figs. 3 and 4 by an asterisk are extra lines due to perturbation. Their assignments are based on GSCD. Differently from what had been observed in m1, the sub-branches with J0 larger than 14 still show anomalous line spacing and intensity, localized on lines assigned to different K values in each sub-branch. This behavior highlights that ro-vibration interactions of Coriolis type with dark states of E symmetry are effective in excited levels of v1 = 2 with J P 13. Splitting of the K = 3 lines, corresponding to A1, A2 doublet transitions as characterized in the ground vibrational state [28], was never observed, even for the highest values of J. In total, 788 transitions were assigned with J0 and K up to 24 and 21, respectively, mostly by means of accurate GSCD. However, at low J, these values are so close for K = 0, 1, and 2, that it is difficult to discriminate merely on the basis of GSCD between alternative assignments. The Q-branch region appears very congested and several observed lines result from overlapped transitions. Most of the observed features in the spectrum have been identified. Several lines that could be attributed to the 29Si or 30Si isotopologues were observed, too. They are extremely weak owing to the low natural abundance of the 29Si or 30Si isotopes (4.7% and 3.1%, respectively) and were not analyzed.

3. Description of the spectrum and assignments 4. Analysis The 2m1 parallel band is located between 4200 and 4400 cm1. It is of medium-strong intensity at the chosen recording conditions. Its overall shape shows the typical features of a parallel band of a C3v molecule, without macroscopic alterations in the branch intensity (see Fig. 1). The qP and qR branches, that extend to low and high wavenumbers from the band center, respectively, are constituted by groups of transitions, qPK(J) and qRK(J), with the same J00 value and K values ranging from 0 to J00  1 or J00 , respectively. Adjacent qP and qR sub-branches are separated by about 4 cm1. The prominent qQ branch extends for about 6 cm1 from 4307 cm1 towards low wavenumbers. Many qQ transitions are overlapped so their identification was based on the corresponding q P and qR transition wavenumbers and the ground state combination differences (GSCD), calculated from the precise ground state spectroscopic parameters [8]. Details of the spectrum illustrating the unperturbed qPK(12) and q RK(10) sub-branches are reproduced in Fig. 2. The K structure of each sub-branch degrades regularly towards higher wavenumbers and the 11, 8, 8 intensity alternation of subsequent lines for k = 3p and 3p ± 1 (p = 0, 1, 2, . . .) is apparent. Figs. 3 and 4 show the changes induced in the pattern of the K structure for the qP and q R sub-branches with J0 = 13 and 14. Anomalous separations between consecutive K transitions are evident, together with

At the beginning of the analysis assignments were based on the predicted spectrum, calculated using the reported band origin, 4307.09(11) cm1 [24], and as initial values of B, C, DJ, DJK, and DK, those derived from the corresponding spectroscopic parameters of v1 = 1 [9], accounting for their vibrational dependences. The term values of the excited ro-vibration levels were obtained as 2

2

Ev ðJ; kÞ ¼ E0v þ Bv ½JðJ þ 1Þ  k  þ C v k  Dv;J ½JðJ þ 1Þ2 2

4

 Dv;JK JðJ þ 1Þk  Dv;K k þ Hv;J ½JðJ þ 1Þ3 þ Hv;JK ½JðJ 2

4

6

þ 1Þ2 k þ Hv;KJ ½JðJ þ 1Þk þ Hv;K k

ð1Þ

where v = v1 = 2 and the signed quantum number k = ±K. The ground state (GS) term values used to calculate the transition wavenumbers were derived from the corresponding parameters [8] using Eq. (1) with v ¼ 0 and E0v ¼ 0. The predicted spectrum reproduced quite well the observed spectral features for low J values, and transitions of the qP and qR sub-branches were easily assigned up to J0 = 12, using as a guide also the regular increase of the separation between adjacent lines with increasing K and the 11, 8, 8 intensity alternation (see Fig. 2). The obtained, still incomplete data set, comprising about

Fig. 1. Overview of the 2m1 infrared band of H28SiD3.

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E. Cané et al. / Journal of Molecular Spectroscopy 282 (2012) 14–19

Fig. 2. Portions of the H28SiD3 infrared spectrum illustrating the K structures of qPK(12) and of the corresponding qRK(10) sub-branch. The K assignments are indicated.

two hundred transitions, was fitted by a least-squares procedure to improve the starting values of the upper state parameters. The assignment of transitions with higher J and K values was more difficult because of the effects of perturbations, particularly strong on levels with J0 = 13 and 14, but also active on levels with higher J values. With the help of the predicted spectrum and of the method of GSCD, the number of controversial assignments to the experimental lines was greatly reduced. After the completion of the assignment procedure, the data set containing many strongly perturbed transitions was analyzed according to two models. In the first one, the interactions of v1 = 2 with nearby states were neglected and the energies of the rotational levels in the excited state were calculated using Eq. (1). A weighted leastsquares fit was performed, assigning unitary weights to isolated lines, while for lines with multiple assignments the weight was reduced by a factor equal to the number of overlapped transitions. Moreover, in the final cycle of the refinement 248 out of 788 transitions, about 31%, that differed from their calculated values by more than 0.02 cm1, were excluded from the data set. About fifty of the discarded experimental transition wavenumbers differed from the calculated ones by more than 0.1 cm1 and less than 0.3 cm1. The value of the rejection limit was chosen equal to that used in the v1 = 1 analysis to favor the comparison be-

tween the qualities of the fits. The standard deviation of the fit, 0.0078 cm1, is about 20 times larger than the experimental precision, but smaller than the effective line width. The parameters obtained from the fit according to the first model are listed in Table 1, together with those of the ground state [8] and of v1 = 1 [9] for comparison. The second model included the Coriolis type interaction between v1 = 2 and one perturbing dark state of E symmetry. The anharmonic interactions were not taken into account since only a few anharmonicity constants involving v1 have significant values [22], i.e. K1,23 = 4.922 cm1, K1,45 = 10.274 cm1, and K1,46 = 0.251 cm1. They couple v1 = 2 with the A1 states v1 = v2 = v3 = 1, v1 = v4 = v5 = 1, and v1 = v4 = v6 = 1, whose term values are calculated [22] at 4429, 4622, and 4465 cm1, respectively, more than 100 cm1 higher than that of v1 = 2. The anharmonic force field of Martin [23] was used to calculate by means of the SPECTRO program [29] the Coriolis coupling constants to favor the identification of the perturbing levels. The calcu1 lated Coriolis f constants related to v1 = 1 are fxy 15 ¼ 0:88 cm , xy 1 1 fxy ¼ 0:080 cm , and f ¼ 0:034 cm . The reliability of the re16 14 1 sults was tested comparing the ab initio fxy with 24 ¼ 0:035 cm ð1Þ 1 the value 0.034 cm derived from the experimental C 11 listed in Table 2 of [9]. Actually, the energies of the eight E levels of the

E. Cané et al. / Journal of Molecular Spectroscopy 282 (2012) 14–19

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Fig. 3. Portions of the H28SiD3 infrared spectrum illustrating the K structures of qPK(14) and of the corresponding qRK(12) sub-branch. The K assignments are indicated. The lines marked by an asterisk are extra lines due to perturbation, assigned to K00 = 8.

Fig. 4. Portions of the H28SiD3 infrared spectrum illustrating the K structures of qPK(15) and of the corresponding qRK(13) sub-branch. The K assignments are indicated. The lines marked by an asterisk are extra lines, due to perturbation, assigned to K00 = 0 or 1.

m4 + 4m6 manifold, calculated from the parameters of Table VI of [22], are in the range 4297–4307 cm1, very close to that of v1 = 2, 4307 cm1. We tried to fit the experimental data taking into account, one at a time, the possible A1/E ro-vibration interactions, assuming that the perturbation is local and can be modeled by a simple two level interaction or, alternatively, that the interaction

with the grid of the manifold levels is too weak to be of significant strength beyond the local perturbation. The perturbed rotational energies were obtained as eigenvalues of effective Hamiltonian matrices. The diagonal matrix elements were calculated for the non degenerate and the degenerate states, according to Eq. (1) and to the following expression, respectively,

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E. Cané et al. / Journal of Molecular Spectroscopy 282 (2012) 14–19

Table 1 Spectroscopic parameters (cm1) for H28SiD3.a

v1 = 2, v1 = 1 v1 = 1b

v1 = 2 0

Ev B C DJ  105 DJK  105 DK  105 HJ  1010 HJK  1010 HKJ  1010 HK  1010 No. of data r(fit)  103 a b c d

and for the ground state of Ground statec

4307.010796 (946)

2187.193703 (875)

1.7611169 (102) 1.429950 (257) 1.59025 (174) 0.9649 (144) 0.3442 (152) 4.5488d 24.92 (238) 81.68 (287) 1.728d 540 7.8

1.76924346 (798) 1.43159012 (949) 1.74927 (171) 1.34420 (433) 0.34280 (347) 4.5488d 8.373d 6.463 d 1.728d 614 6.6

1.77748032 1.4334268 1.63283 1.17427 0.28516 4.5488 8.373 6.463 1.728

Standard uncertainties (1r) in parentheses refer to the least significant digits. Ref. [9]. Ref. [8]. Constrained to the ground state value.

Table 2 Variation of the spectroscopic parameters (cm1) with

v1 = 1–8 for H28SiD3.a

v1

DB

v 1  10

DC

v 1  10

Gv 1 ðobs:Þ

Gv 1 ðobs:Þ  Gv 1 ðcalc:Þb

1c 2 3d 4d 5d 6d 7e 8e

8.24(1) 8.18(1) 8.2(2) 10.15(2) 8.60(1) 8.72(1) 8.83(3) 9.00(4)

1.84(1) 1.7(1) – 2.0(1) 1.78(4) 1.83(1) 1.89(2) 1.96(4)

2187.1937(9) 4307.0108(9) 6359.3(1) 8344.641(7) 10262.239(2) 12113.366(6) 13897.506(8) 15614.66(1)

0.10 0.08 0.21 0.20 0.68 0.37 0.20 1.0

3

3

a

Standard uncertainties (1r) in parentheses refer to the least significant digits. Energy calculated from Gv 1 ¼ 2220:71ð1Þv 1  33:626ð1Þv 21 obtained from the fit of the vibrational term values of the v1 = 1–8 levels. c Ref. [9]. d Ref. [14]. e Ref. [10]. b

2

2

Ev ðJ; kÞ ¼ E0v þ Bv ½JðJ þ 1Þ  k  þ C v k  Dv;J ½JðJ þ 1Þ2 2

4

 Dv;JK JðJ þ 1Þk  Dv;K k þ Hv;J ½JðJ þ 1Þ3 þ Hv;JK ½JðJ 2

4

comparison with those involving v1 = 2. The lack of experimental data for these dark states prevented the extension of the model to a cluster of interacting levels. Next, the states of E symmetry obtained by the addition of a vibration quantum of v1 to those already considered as possible perturbers of v1 = 1 [9] were taken into account. They 1 1 are m1 þ 2m3 þ m1 m1 þ m3 þ m1 5 ðEÞ; ð4367:07 cm Þ, 5 þ m6 ðEÞ; 0 1 1 ð4380:5 cm1 Þ, m1 þ m1 þ 2 m ðEÞ; ð4387:3 cm Þ, m þ m þ 2m2 1 5 6 5 6 1 ðEÞ; ð4390:4 cm Þ. A two state Coriolis interaction involving the first of these states, which is the closest to v1 = 2 and can interact through the large fxy 15 constant, was tested. The rotational parameters for the degenerate state were calculated using those of the corresponding fundamental bands reported in the literature [7–9], while the D and H constants were fixed to their corresponding ground state values. Cf was set equal to that of v5 = 1, 1.21552 cm1. We first refined, in addition to the v1 = 2 parameters, only the Coriolis interaction coefficient Rs,t, (see Eq. (3)), keeping the spectroscopic parameters and the term value of the E state fixed to their initial values. However, the adopted least-squares procedure was unable to reduce the number of rejected transitions, to improve the standard deviation of the fit, and to determine a meaningful value of Rs,t. Slightly better results were achieved by refining the term value of the E state together with the interaction coefficient. The number of rejected lines decreased from 248 to 239, and the standard deviation of the fit was 0.0077 cm1. The spectroscopic constants of v1 = 2 differed from the values listed in Table 1 by less than 2r, while their uncertainties were practically unchanged. The values of the energy of the v1 = 1, v3 = 2, v5 = 1±1 state and of Rs,t were 4352.5(7) and 0.0136(7) cm1, respectively. The term value of v1 = 1, v3 = 2, v5 = 1±1 obtained from the fit differs by about 14.6 cm1 from the initial one calculated from the force field. This difference could be due to the uncertainties affecting the values of the harmonic frequencies and of the anharmonicity constants [22] used in the calculation. However, the fxy 15 constant obtained from the experimental Rs,t coefficient is 0.0054 cm1, more than two orders of magnitude smaller than the ab initio one, 0.88 cm1. This large discrepancy indicates that these parameters should be considered as effective ones without a definite physical meaning.

6

þ 1Þ2 k þ Hv;KJ ½JðJ þ 1Þk þ Hv;K k  ½2Cfv  gv;J JðJ 2

2

þ 1Þ  gv;K k  sv;J J 2 ðJ þ 1Þ2  sv;JK JðJ þ 1Þk 4

 sv;K k kl

5. Discussion of results and conclusions

ð2Þ

The spectroscopic parameters for the degenerate states were calculated using those of the corresponding fundamental levels [7–9]. The off-diagonal matrix elements were expressed by:

< v s JkjðH41 =hcÞjv t lt Jk  1 >¼ Rs;t ½JðJ þ 1Þ  kðk  1Þ1=2

ð3Þ

with vs = v1 = 2, vt = one of the E states mentioned above. However, the results of each fit, adopting the same rejection limit of 0.02 cm1, were close to that obtained neglecting any interaction: the number and the assignments of the discarded lines and the standard deviation of the fit did not change. The extra lines, identified by an asterisk in Figs. 3 and 4, should belong to the interacting state, but were not predicted in the calculated spectrum. Thus, they could be assigned either to 2m1 or to one of the bands of the m4 + 4m6 manifold. The values of the parameters for v1 = 2 were practically unchanged and the interaction constants were mostly undetermined. We then concluded that the numerous perturbations observed in the spectrum could arise from interactions involving v1 = 2 and two or more levels of the above mentioned manifold, which, in turn, could interact with each other. The interactions within the manifold could be even stronger in

The spectroscopic constants of v1 = 2 have been determined for the first time using spectra recorded at high resolution. All the parameters are statistically well determined. The uncertainty of the band origin of 2m1 is comparable to that of m1 in spite of the stronger effects of perturbations. The values of B, C, DJ, DJK, and DK, are close to those of v1 = 1 [9]. On the contrary, the values of HJK and HKJ are effective, the perturbations being particularly active on levels with high J and K values. The standard deviation of the fit, 7.8  103 cm1, is slightly worse than that of m1, 6.6  103 cm1. Perturbations in v1 = 2 are effective in levels with J0 P 13, while in v1 = 1 they are localized on levels with J0 = 13 and 14. This difference is responsible for the larger number of discarded lines, 31% in 2m1 as compared with 14% in m1, while the total number and the J and K maximum values of assigned transitions are almost the same in the fundamental and in the first overtone. The inclusion in the model Hamiltonian of a two states Coriolis interaction between v1 = 2 and one state of E symmetry close in energy, was insufficient to provide an adequate description of v1 = 2. The failure testifies that the perturbation is not localized, but is due to a grid of strong self perturbing dark levels whose effects concentrate on levels of v1 = 2 with different K as J varies. The adopted approach was the only accessible due to the lack of experimental information on

E. Cané et al. / Journal of Molecular Spectroscopy 282 (2012) 14–19

the dark states, and to the values of the anharmonicity and interaction constants, which ab initio calculations cannot provide with sufficient accuracy. From these results it can be stated that 2m1 is more perturbed than m1. On the other hand, the very weak 3m1 band was found to be even more perturbed. In fact, no transition belonging to the P branch had been detected, and only the band origin and the B constant could be determined [14]. The results of the present investigation complete the characterization of the Si–H stretching mode of HSiD3, from the fundamental up to v1 = 8 , based on spectra recorded at high resolution. The term values of all the vibrational states and the ratio of the corresponding DB and DC rotational parameters with respect to the v quantum numbers are gathered in Table 2 with the quoted uncertainties. The local mode character of the Si–H stretching vibration is confirmed by the regular trend of the vibrational energy with the quantum number v. In fact, the simple Morse oscillator expression Gv 1 ¼ 2220:71ð1Þv 1  33:626ð1Þv 21 reproduces the term values of the v1 = 1–8 states with an rms value equal to 0.44 cm1. This result is similar to that obtained in [14] notwithstanding that the energies of v1 = 1 and 2 have smaller uncertainties. The uniformity of DB and DC divided by v1 with increasing excitation represents a further proof of the local mode character. The missing value of DC of v1 = 3 and the too large values of DB and DC of v1 = 4 reflect the effect of strong perturbations of v1 = 3 and 4 with dark states. Therefore, it can be assessed that the effects of perturbations increase up to the second overtone and then decrease with increasing n in the nm1 overtones [14]. This behavior, unexpected if considered in relation to the increasing density of states with increasing Si–H stretching excitation, is peculiar of HSiD3 and cannot be generalized. Acknowledgments E.C and L.F. acknowledge the financial support from the Università di Bologna and from the Ministero della Ricerca e dell’Università, PRIN 2009 ‘‘Spettroscopia molecolare per la Ricerca Atmosferica e Astrochimica: Esperimento, Teoria ed Applicazioni’’; E.C and L.F. thank Prof. Riccardo Tarroni for the calculation of the Coriolis Zeta matrix. Appendix A. Supplementary material Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State Univer-

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sity Molecular Spectroscopy Archives (http://library.osu.edu/sites/ msa/jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/ 10.1016/j.jms.2012.10.007. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

[28] [29]

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