2926
J. Phys. Chem. 1996, 100, 2926-2933
Interstellar Silicon-Nitrogen Chemistry. 2. Spectral Signatures of the SiNH2+ Molecular Ion O. Parisel,* M. Hanus, and Y. Ellinger Equipe d’Astrochimie Quantique, Laboratoire de Radioastronomie Millime´ trique, ENS et ObserVatoire de Paris, 24 Rue Lhomond, F. 75231 Paris Cedex 05, France ReceiVed: May 17, 1995; In Final Form: October 16, 1995X
Interest for the gas phase interstellar silicon chemistry has been recently renewed by the detection of SiN in the outer envelope of the IRC+10216 carbon star. In this contribution we present a theoretical study of the SiNH2+ molecular ion which can be seen as a precursor of silicon-nitrogen products. The radio, infrared, and electronic signatures, computed by high-level ab initio treatments using at least a 6-311++G** atomic expansion are reported. The geometry and corresponding rotational constants have been determined at the Møller-Plesset (MPn, n ) 2, 3, 4), complete active space self-consistent field (CASSCF), and coupled cluster (CCSDT) levels of theory using a scaling procedure that required the evaluation of the same quantities, at the same levels of calculations, for the HNSi molecule whose rotational spectrum has been obtained experimentally. Special attention has been given to the dipole moment whose best estimated value of 0.5 ( 0.1 D has been obtained in a series of converging treatments, including up to second-order configuration interaction. The IR spectrum, calculated at the MP2, MP3, MP4, CCSDT, and CASSCF levels, shows intense bands in the 3350 and 650 cm-1 regions. Vibrational frequencies have been corrected using scaling factors derived from a previous study on the HNSi, HSiN, HSiNH2, and H2SiNH molecules. Rotational constants and vibrational frequencies are also provided in this report for a part of the isotopomers that can be formed upon deuteration or upon substitution by either 29Si or 30Si in order to facilitate future experimental interpretations or astrophysical searches. Finally, the electronic spectrum of SiNH2+ has been obtained using a coupled multiconfiguration SCF-perturbation strategy (MC/P) with an extended basis built by adding low-exponent functions to the original set: such a procedure has been shown previously to give accurate predictions for the electronic spectra of the ethylene, formaldehyde, and vinylidene molecules. In the present case, the spectrum is characterized by three intense features which should make this species observable even in low-abundance conditions.
1. Introduction The recent detection of the SiN free radical in space1,2 has given a renewed interest in the gas phase interstellar chemistry of an element3-5 which was supposed for the largest part embedded in grains, mainly in the form of silicate derivatives.1,2,6,7 Following the interstellar chemistry of the carbon-nitrogen system which led to the observation of the CN, HCN, and HNC species, a number of theoretical, experimental, and observational studies have been devoted to HNSi or HSiN and related structures (see refs 8-28 and references cited therein) in the lineage of the pioneering matrix isolation experiments by Ogilvie and Cradock who detected HNSi in 1966. Although astrophysical chemical models suppose these two species to be abundant,3,7 none of them has been detected in space to our knowledge, in spite of the support of recent gas phase laboratory experiments which provided accurate rotational constants for HNSi (the microwave spectrum of HSiN remains unknown to the present day). One of the possible difficulties in trapping HSiN might be the fact that it lies about 50 kcal/mol above HNSi. The nondetection of HNSi in the interstellar space by radioastronomy techniques could however be due to its low abundance and to the inadequacy of nowaday’s detectors for such a species whose dipole moment is only about 0.20 D.20 By analogy with the carbon chemistry29 * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-2926$12.00/0
C+ + NH3 f HCNH+ + H
(1a)
HCNH+ + e- f (HCN + H) + (HNC + H)
(2a)
HSiN and HNSi are supposed to be formed, in the interstellar medium, by a dissociative recombination reaction of a [Si, N, H, H]+ system which is produced by the action of the Si+ cation on NH3. Another possibility would be the combination of SiH3 with N+.2,3,7,12-14 However, the route via SiH3 seems to be rather unrealistic in interstellar conditions regarding the abundance of this species, although it is a possible mechanism of formation in recent laboratory experiments that involve either electric discharges in a silane/dinitrogen plasma19,20,23 or electron bombardment in a iodosilane/ammonia (or dinitrogen) mixture.24,25 The proposed scheme for the formation of HSiN and HNSi is then2,3,7,12-14
Si+ + NH3 f HSiNH+ + H
(1b)
HSiNH+ + e- f (HSiN + H) + (HNSi + H)
(2b)
Following the carbon analogy, such a reaction scheme would lead to a comparable abundance of HNSi and HSiN. The dissociative recombination process on the linear structure HCNH+ is known to produce both HCN and HNC: indeed, the observed ratio of these species is about 1.55 in dark cold clouds in favor of HNC,30 although HNC lies about 15 kcal/ mol above the HCN structure. © 1996 American Chemical Society
Spectral Signatures of SiNH2+
J. Phys. Chem., Vol. 100, No. 8, 1996 2927
TABLE 1: Optimized Structures of SiNH2+ (X1A1) method RHF/3-21G RHF/6-31G* RHF/6-311++G** MP2/6-31G* MP2/6-311++G** MP3/6-311++G** MP4/6-311++G** CCSD(T)/6-311++G** CASSCF/6-311++G** FOCI/6-311++G** a SOCI/6-311++G** a a
SiN (Å) NH (Å) SiNH (deg) energy (au) 1.678 1.646 1.639 1.665 1.659 1.651 1.662 1.661 1.668 1.668 1.668
1.015 1.009 1.008 1.026 1.022 1.022 1.023 1.022 1.028 1.028 1.028
124.99 124.73 124.91 124.64 124.84 124.88 124.86 124.85 124.55 124.55 124.55
-342.465117 -344.261258 -344.303655 -344.499879 -344.693360 -344.708404 -344.724371 -344.725598 -344.438022 -344.481517 -344.568062
CASSCF geometry.
However, the carbon/silicon analogy breaks down as soon as in reaction 1b: the structures having the HSiNH connectivity lie about 50 kcal/mol above the C2V X1A1 SiNH2+ structure, which is found to be the absolute minimum of the [H, H, Si, N]+ potential energy surface.14,24,28 As a possible confirmation of this fact, we point out that the elusive existence of SiNH2+ has been recently demonstrated in some “collisional activation” and “neutralization-reionization” mass spectroscopy experiments; no related species having the SiH connectivity was simultaneously detected.24 By contrast, the matrix isolation experiments by Maier et al. show the existence of the HSiN and HSiNH2 compounds27 as well as their isomers HNSi and HNSiH216 when starting from silyl azide H3SiN3 as a precursor instead of the SiH4/N2, SiH3I/NH3, or SiH3I/N2 mixtures. It is moreover of interest to point out that the Si+ + NH3 reaction has already been investigated from the experimental point of view: Wlodek et al.13 produced two species having respectively (H, N, Si) and (H, H, Si, N)+ formulas that were certainly HNSi and SiNH2+; they did not however provide any spectroscopic evidence for such connectivities, and they concluded on the basis of theoretical energetics considerations only. In this report, we present the spectroscopic signatures (rotational, vibrational, and electronic) necessary to characterize the fleeting SiNH2+ species that appears to be a key intermediate in the formation of silicon-nitrogen compounds in interstellar space. In order to obtain predictive results, the calculations have been performed at increasing levels of theory and further calibrated on the parent HNSi and HSiNH2 molecules that had previously been studied at the same levels of calculation.31 The GAUSSIAN92,32 HONDO8.5,33 and ALCHEMY II 34 codes and the MC/P modules35 were used to perform the calculations. 2. Electronic Structure of SiNH2+ The structure of SiNH2+ was determined in C2V symmetry at increasing levels of theory: the results are collected in Table 1 together with the corresponding absolute energies given for further comparisons to related species. In order to allow for a large flexibility in the one-particle space, a triple-ζ basis set extended by polarization and diffuse functions36,37 on each atom was used, which is known as 6-311++G** 38 for the hydrogen and nitrogen atoms, while the expanded basis set by McLean and Chandler39 was used for the silicon atom. Smaller 3-21G 40 and 6-31G* 41 basis sets were also used for preliminary investigations. Note that, in all forthcoming MPn and CCSDT (refs 42 and 43 and references cited therein) calculations, all electrons were correlated except as specifically indicated. When not specified, the Si and N labeling refers furthermore to the 28Si and 14N isotopes, respectively. At the restricted Hartree-Fock (RHF) level of theory, the electronic ground state configuration of C2V symmetry for
Figure 1. Lewis structures of SiNH2+: (dots) in-plane σ electrons; (crosses) out-of-plane π electrons.
SiNH2+ is
(1a1)2(2a1)2(3a1)2(1b2)2(4a1)2(5a1)2(6a1)2(2b2)2(2b1)2(7a1)2 Although the RHF calculations show a strong coupling between the orbitals describing the lone pair located on the terminal silicon atom and the σSiN bond, the electronic structure of SiNH2+ in its 1A1 ground state can be described in terms of Lewis-localized orbitals as (see Figure 1a)
(1sSi)2(1sN)2(2sSi)2(2pSi)6(σ+NH)2(σ-NH)2(σSiN)2 (πSiN)2(spSi)2(3pSi)0 where (σ+NH)2 and (σ-NH)2 stand for the symmetry-adapted combinations of the NH bonds respectively of a1 and b2 symmetries. The spSi orbital is the σ-type lone pair orbital localized at the terminal silicon atom, and the 3pSi orbital represents the empty remaining in-plane silicon atomic orbital (which is usually referred to as the n orbital in the carbonyl group, for example). Such a representation that uses a π bond between Si and N should only be seen as a possible mesomeric formula: as will be discussed below, the π bond appears to be essentially located on the nitrogen atom so that a description like +Si-NH2 instead of the above SidN+H2 would be more appropriate. However, the use of the former representation has the advantage of suggesting a planar molecule. The use of such localized representations will make it possible to design specific treatments to recover part of the electronic correlation as will be emphasized in section 5: using π and π* orbitals will simplify the description of the variational spaces to be used. A bond orbital analysis shows that the highest occupied molecular orbital in all calculations is the spSi lone pair, almost entirely composed of the 3sSi atomic orbital with only small contributions from the 3pzSi orbital. Due to the strong coupling with the σSiN bond, contributions originating from the 2sN and 2pzN orbitals are also involved in the description of that lone pair for orthogonality reasons. Besides, it is worth noting that the σSiN bond is a combination of the 2pzN and 3sSi atomic orbitals with no participation of the 3pzSi orbital. The πSiN bond, mostly developed on the nitrogen atom which acts as a π donor,9,15 lies slightly below the spSi lone pair (5 kcal/mol at the RHF/6-311++G** level). As a consequence of the weakness of the πSiN bond, the positive charge appears to be essentially located at the silicon atom whatever the type of calculation performed, as anticipated previously. This bond, however, remains strong enough to ensure that the ground state does not pyramidalize and retains an sp2-type hybridization at the nitrogen atom. On a more quantitative point of view, a detailed analysis shows that, at the MP2/6-31G* level of theory for example, Mulliken charges are +0.96 (Si), -0.87 (N), and +0.45 (H);
2928 J. Phys. Chem., Vol. 100, No. 8, 1996 summing the hydrogen charges on nitrogen gives +0.96 (Si) and +0.04 (N). Such distributions are confirmed by a natural bond orbital analysis (NBO) (refs 44 and 45 and references cited therein) that gives natural charges as +1.46 (Si), -1.44 (N), and +0.49 (H). Such an analysis confirms the previous orbital analysis that localized the positive charge on silicon and reveals that about 88% of the electronic density of the πSiN bond resides on nitrogen; the hybridization at the nitrogen atom is roughly sp1.9, which is coherent with a planar structure. Moreover, the weight of the silicon atomic orbitals in the σSiN bond is as low as 12%, among which 85% comes from pzSi atomic orbitals. On the contrary, 91% of the electronic density of the spSi lone pair on the terminal silicon atom comes from sSi atomic orbitals. In order to investigate the role of the nondynamic correlation, and particularly that inherent to the valence double hole in the 3pSi orbital localized at the terminal Si atom, a multiconfigurational description was generated within the CASSCF framework (ref 46 and references cited therein). The wave function was expanded in the configuration space spanned by all possible distributions of the 10 valence electrons among the 10 corresponding bonding, antibonding, and nonbonding orbitals
{σ+NH σ-NH σSiN πSiN spSi 3pSi σ+*NH σ-*NH σ*SiN π*SiN}10 provided the spin and spatial symmetries of the generated configuration state functions (CSFs) were 1A1. This led to 5072 CSFs in the calculation. The analysis of the CASSCF results shows that the weight of the RHF determinant is of about 92% in the multireference wave function. The next important configurations involved in this description are represented by the following electronic distributions:
... (σ+NH)2 (σ-NH)2 (σSiN)2 (πSiN)2 (spSi)0 (3pSi)2 (π*SiN)0 ... (σ+NH)2 (σ-NH)2 (σSiN)2 (πSiN)0 (spSi)2 (3pSi)0 (π*SiN)2 The first CSF accounts for the nondynamic hole-pair correlation between the spSi and the 3pSi orbitals, while the second correlates the π system of the molecule. Such a correlation reinforces the π-donor effect of the nitrogen atom by allowing for the transfer of two electrons from the πSiN bond, which is developed on the nitrogen atom, toward the π*SiN bond, which is mostly localized on the silicon atom (about 89% of the corresponding electronic density according to the NBO analysis). The nondynamic correlation lowers the total energy by 85 kcal/mol. For the sake of comparison with forthcoming calculations on structural isomers, calculation levels were increased to a complete FOCI (first-order interaction configuration47) which involved 355 044 CSFs, and to a truncated SOCI (second-order configuration interaction47) that involved only, as references for the double excitations to the external space, the CSFs generated by single excitations from the leading determinant: 507 741 CSFs were thus considered in the final variational space. As seen from the difference between the CASSCF and SOCI energies, the magnitude of dynamic correlation effects (valencevirtuals) recovered in this process is 82 kcal/mol. 3. Radio Signature of SiNH2+ Directly linked to the geometry for rotational constants and to the dipole moment of a molecule for intensities, the rotational spectrum is an unambiguous fingerprint that has enabled radioastronomers to identify more than a hundred species. The computed geometries obtained for SiNH2+ at different levels of theory are reported in Table 1 together with their corre-
Parisel et al. TABLE 2: Unscaled Rotational Be Constants for SiNH2+ (X1A1) method
A (GHz)
B (GHz)
C (GHz)
MP2/6-31G* MP2/6-311++G** MP3/6-311++G** MP4/6-311++G** CCSD(T)/6-311++G** CASSCF/6-311++G**
351.870 356.351 359.575 355.827 356.426 349.540
16.104 16.211 16.361 16.153 16.169 16.050
15.399 15.506 15.649 15.452 15.467 15.345
TABLE 3: Scaled Rotational B0 Constants for SiNH2+ (X1A1) method
A (GHz)
B (GHz)
C (GHz)
MP2/6-31G* MP2/6-311++G** MP3/6-311++G** MP4/6-311++G** CCSD(T)/6-311++G** CASSCF/6-311++G**
359.963 363.478 357.418 366.502 363.198 355.133
16.474 16.535 16.263 16.638 16.476 16.307
15.753 15.816 15.555 15.916 15.761 15.591
sponding energy, dipole moment, and rotational constants Be. Inspection of this table shows that the computed molecular geometry in its X1A1 ground state is not very sensitive, either to the level of theory or to the basis set used. The SiN bond length remains close to 1.66 Å, the NH bond close to 1.02 Å, and the ∠SiNH bond angle close to 124.8°. As expected, bond lengths increase when going from the simplest RHF level of theory to correlated methods (all electrons are correlated) using the same basis set. At the CASSCF level, bonds lengths are slightly increased relative to the MPn or CCSDT approaches. We wish to point out that there is no significant difference between the MP4 treatment and the more time-consuming CCSDT method: even on the energetics point of view, the variation between these two methods which is about 0.001 au (less than 1 kcal/mol) is smaller than the intrinsinc error on the absolute energies provided by each of these methods. The length of the SiN bond in the ground state of SiNH2+ is larger than that observed either in SiN (X2Σ, r ) 1.57 Å 48), in HNSi (X1Σ+, r ) 1.55 Å 21), in HSiN (X1Σ+, r ) 1.59 Å 31), in the quasi-linear singlet of HSiNH+ (X1A′, r ) 1.52 Å 31) or in H2SiNH (X1A′, r ) 1.62 Å 31), which indicates a weaker bond, intermediate between a single and a double bond, as discussed in the previous section. This bond length is about the same as that computed in H2SiNH (X1A′, r ) 1.62 Å 31) or in the cis-bent lowest triplet of HSiNH+ (a3A′, r ) 1.65 Å 31), but it is slightly smaller than the SiN distance encountered in HSiNH2 (X1A′, r ) 1.72 Å 31), or in H2SiN+ (X3A2, r ) 1.78 Å 49). The calculated geometries lead to the rotational constants presented in Table 2. If we consider with DeFrees et al.50 that MP3 optimized geometries provide rotational constants Be that match more closely the experimental B0 values than those obtained from MP2 or MP4 optimized structures, which was previously checked on the related isoelectronic HNSi species, we point out that the MP3 computed constants are the closest Ae, Be, and Ce values to the experimental A0, B0, and C0 values among all the theoretical methods used here. Such a conclusion leads to the following constants:
A0 ) 359.575 GHz, B0 ) 16.361 GHz, C0 ) 15.649 GHz A further improvement consists in the correction of the pure Ae, Be, and Ce constants with the scaling factors obtained, at each level of calculation, in our previous study on HNSi:31 this leads to the A0, B0, and C0 constants reported in Table 3. Even after the scaling procedure, significant differences remain between the various methods: since the scaling factor obtained
Spectral Signatures of SiNH2+
J. Phys. Chem., Vol. 100, No. 8, 1996 2929
TABLE 4: Recommended Rotational A0, B0, and C0 Constants (Scaled MP3 Ae, Be, and Ce Rotational Constants) for Some Isotopomers of SiNH2+ (X1A1) and Shifts to Those of the Most Abundant Isotopomer 28Si14NH2 isotopomer 28Si14NH
A0 (GHz)
357.418 (000.000) 28Si14NHD 246.877 (-110.541) 28 14 Si ND2 178.709 (-178.709) 29Si14NH 357.418 (000.000) 2 30Si14NH 357.418 (000.000) 2 28Si15NH 357.418 (000.000) 2 2
B0 (GHz)
C0 (GHz)
16.263 (0.000) 15.009 (-1.254) 14.020 (-2.243) 16.063 (-0.200) 15.877 (-0.386) 15.742 (-0.521)
15.555 (0.000) 13.865 (-1.690) 12.739 (-2.816) 15.066 (-0.489) 14.898 (-0.657) 14.778 (-0.777)
for HNSi at the MP3 level of calculation is the closest to unity, the scaled MP3 values are anticipated to be of the highest quality. Furthermore, the comparison of these scaled values to the other ones gives the error bar of the calculation. This error bar is thus expected not to be larger than 2% so that the following rotational constants are finally obtained:
A0 ) 357.418 GHz ( 2% B0 ) 16.263 GHz ( 2% C0 ) 15.555 GHz ( 2% Such an error bar of 2% implies variations of about 7.15 GHz on the rotational constant A0 which might result in a too large uncertainty for direct comparisons to astrophysical spectra. We think however that, despite this error bar, these constants will be of essential interest to support laboratory assignments, as it has been the case for the identification of the nonclassical monobridged structure of Si2H2,51 for example, for which the previously computed A rotational constant52 was more than 11 GHz (4.4%), far from the experimental one. These scaled MP3 rotational A0, B0, and C0 constants are reported in Table 4 for the most abundant 28Si14NH2+ isotopomer together with those expected for other isotopomers. Table 4 also contains the shifts induced by isotopic substitution of these constants and relative to the 28Si14NH2+ isotopomer’s constants: even if the absolute values of the constants suffer from a 2% uncertainty, it is expected that these shifts, that might be observed experimentally, are of a much higher accuracy. The determination of the dipole moment of charged species has always been a theoretical deathtrap since that observable depends on the choice of the origin retained for its evaluation. An accurate evaluation is however of great importance, to predict correct rotational intensities. Assuming that this moment has to be evaluated at the center of mass of the molecule in order to get a relevant value for the determination of rotational intensities,53 all of the calculations reported in this paper have been performed accordingly, using the convention that a negative value indicates that the dipole is directed along the SiN direction. In the particular case of the SiNH2+ molecule, it is essential to point out that the calculated dipole is extremely sensitive to the length of the SiN bond which determines the location of the center of mass. As seen in Figure 2, the dipole moment increases with the SiN distance, whatever the methods and the basis sets used. The small absolute value of this observable and its variation as a function of the geometry make it difficult to predict and explain why the computed values reported in Figure 2 vary from about -1.2 to -0.1 D. However, it is seen that a convergent series is obtained by increasing the quality of the basis set from 3-21G to 6-311++G** and the level of theory from RHF to MP2, CASSCF (5072 CSFs), FOCI (355 044 CSFs), and a truncated SOCI (1 128 855 CSFs) that involves, as references for the single excitations to the external space, the single, double, and triple excitations from the leading RHF-
Figure 2. Dipole moment of as a function of the SiN bond length.
like determinant and, as references for the double excitations to the external space, single and double excitations from the leading determinant. At the largest level of basis set, namely, 6-311++G**, and with use of the fully optimized MP2 geometry with the corresponding MP2 electronic density, the computed dipole moment is -0.44 D; with use of the same basis set but the fully optimized CASSCF geometry, this value is slightly decreased to about -0.50 D at the CASSCF, FOCI, and SOCI levels. We thus propose, as a recommanded quantity for further uses, -0.50 ( 0.1 D for the dipole moment evaluated at the center of mass. 4. IR Signature of SiNH2+ The large amount of data available on IR spectra has now well-established the fact that calculated frequencies should be scaled to reproduce experimental values.54 This is done here at the same time as the normal coordinates analysis. The appropriate B matrix55 is evaluated and then used to transform the force constant matrix from a Cartesian to an internal coordinate representation which leads to the annihilation of the contaminations arising from translation and rotation motions to the molecular vibrations. In order to correct the general overestimation of the diagonal force constants, it is an usual procedure to scale these terms by factors of 0.792 (ROHF), 0.884 (MP2), and 0.893 (MP4). In those cases where couplings between normal modes are negligible, the force constant matrix is diagonal in the internal representation, so that the scaling procedure is rigorously equivalent to the application on the initial frequencies of the usual scaling factors 0.89 (ROHF), 0.94 (MP2), and 0.945 (MP4). These scaling factors however depend on both the method of calculation and the basis set. It was found more attractive here to use scaling factors obtained by preliminary studies on species related to SiNH2+ and for which experimental infrared spectra are available: as a consequence, we use here scaling factors deduced from comparisons with experiments devoted to the parent HNSi, HSiN species and to the close HSiNH2 and HNSiH2 molecules.31 This leads to use
2930 J. Phys. Chem., Vol. 100, No. 8, 1996
Parisel et al.
TABLE 5: Scaled Frequencies (Wave Numbers in cm-1) and Relative Intensities Normalized to the Total Intensity I (km/mol) for SiNH2+ (X1A1)
vibration b2 NH2 wagging b1 NH2 out of plane a1 SiN stretchb a1 NH2 bending a1 NH2 stretch (symmetric) b2 NH2 stretchc (asymmetric)
MP2 RHF CASSCF 6-31G* 6-31G* 6-311++G** 6-311++G** (I ) 1003 km/mol) (I ) 948 km/mol) (I ) 856 km/mol) (I ) 782 km/mol) MP3 MP4 CCSD(T) wave wave wave 6-311++G** 6-311++G** 6-311++G** wave number intensity number intensity number intensity wave number wave number wave number number intensity 605 667 933 1538 3301 3376
0.9 36.8 11.0 14.9 21.7 15.8
578 676 941 1534 3333 3423
1.2 35.1 5.8 13.0 27.3 17.7
553 631 942 1478 3347 3429
0.9 33.1 7.8 12.5 27.6 18.0
567 649 948 1481 3287 3356
564 636 944 1504 3388 3468
568 633 940 1500 3366 3443
632 686 942 1545 3299 3380
1.1 34.6 8.8 12.3 26.6 16.7
a Scaling factors (see text for details): RHF, 0.806; MP2, 0.920; MP3, 0.882; MP4, 0.949; CCSD(T), 0.933; CASSCF, 0.941. b Coupled with the NH2 bending mode (95%/5%). c Coupled with the NH2 wagging mode (99%/1%).
of the following values (that refer to scales applied on frequencies): RHF/6-31G*, 0.898; MP2/6-31G* or MP2/6311++G**, 0.959; MP3/6-311++G**, 0.939; MP4/6311++G**, 0.974; CCSDT/6-311++G**, 0.966; and CASSCF/ 6-311+G**, 0.970. These values have been discussed elsewhere: the MP4 and CASSCF approaches both seem to be of better quality than the CCSDT method since their corresponding scaling factor is slightly larger. According to our experience for other compounds of this kind, we expect the deviation of our scaled predicted infrared frequencies from the experimental values to be smaller than 5% on the whole spectrum. The scaled vibrational frequencies and normalized intensities evaluated at increasing levels of theory are presented in Table 5. Since the intensities of vibrational transitions are the derivatives of the dipole moment with respect to the normal coordinates, the spurious problems pointed out in the determination of an accurate value of the dipole moment are no longer crucial: with use of normal coordinates, the constant term due to the presence of a charge that appears in the expression of the dipole moment vanishes with the derivation. Furthermore, as Figure 2 reveals that the variations of the dipole moment as a function of geometry are practically parallel whatever the method used for its evaluation, the intensities are expected to be insensitive to the level of theory. As seen in Table 5, this is effectively true: the RHF, MP2, and CASSCF methods give comparable normalized intensities. The vibrational spectrum thus presents three strong bands easily identified: two bands at about 3300 and 3400 cm-1 that correspond to the antisymmetric and symmetric stretchings of the NH bonds which are close to those observed in the aminosilylene HSiNH2 molecule (3494-3395 cm-1 region16). The third one appears at about 650 cm-1 and is the out-ofplane deformation that represents the pyramidalization of the molecule. Two bands of medium intensity have to be expected: one at about 950 cm-1 for the SiN stretching mode (to be compared with 1151 cm-1 for SiN,17 1198 cm-1 for HNSi,8 and 866 cm-1 in HSiNH2), and the other at about 1500 cm-1 corresponding to the NH2 symmetric in-plane bending (1562 cm-1 in HSiNH2). The remaining mode is weak and appears at 560 cm-1 for the NH2 wagging (570 cm-1 in HSiNH2). The analysis of the normal coordinates shows that four out of the six vibration modes are pure. Weak couplings however mix the SiN stretching and NH2 symmetric bending modes, as well as the NH2 antisymmetric stretching and NH2 wagging. This spectrum is presented in Figure 3 (using the scaled MP2/6311++G** level of calculation): it has been obtained by fitting each vibrational transition with a Lorentzian having a 4 cm-1 full width at half-maximum (FWHM). Scaled frequencies for selected isotopomers of SiNH2+ are gathered in Table 6 together with the relative transition intensities and force constants.
Figure 3. Simulated infrared spectrum of SiNH2+ (X1A1) from scaled MP2/6-311++G** calculations.
5. Electronic Signature of SiNH2+ 5.1. Methodology and Computational Details. In order to provide a quantitative description of the vertical electronic absorption spectrum of the SiNH2+ ion, we used the MC/P strategy recently developed in our laboratory. It consists of a coupled variation-perturbation treatment that aims to treat the nondynamic correlation effects involved in the zero-order description of a particular state at a MCSCF level, followed by the recovering of the dynamic correlation through a large scaled second-order perturbation treatment on this variational wave function. This methodology, whose details can be found in ref 35, has been successfully applied to the description of the vertical spectra of the ethylene, formaldehyde, vinylidene, and cyclopropene molecules taken as benchmarks.56,57 As shown in these calculations, the use of a Møller-Plesset partition of the electronic Hamiltonian combined with a well-designed variational zero-order space described by averaged MCSCF orbitals provides quantitative results. On a whole vertical spectrum, we expect the root-mean-square deviation from relevant experimental data not to be larger than a few tenths of an electronvolt. All calculations were done at the fully optimized MP4/6311++G** geometry of the ground state. Variational zeroorder spaces were defined as follows: the orbitals were obtained by averaging the MCSCF calculations, for each spin and spatial symmetry, on those states lying up to 9 eV above the ground state. The perturbation step of the MC/P method was done with all valence electrons active and with no virtual orbitals frozen. Singlet, triplet, and quintet states were investigated. The atomic expansion consists of the 6-311++G** basis extended by a set of diffuse s, p, and d functions on both heavy atoms. The exponents for these Rydberg-type orbitals have been taken as 0.017, 0.014, and 0.015 for the 4s, 4p, and 3d functions of the silicon atom; the values of 0.028, 0.025, and 0.015 have been used for the corresponding 3s, 3p, and 3d orbitals of the nitrogen atom.
Spectral Signatures of SiNH2+
J. Phys. Chem., Vol. 100, No. 8, 1996 2931
TABLE 6: Scaled MP2/6-31G* Computed Vibrational Frequencies (Wave Numbers in cm-1), Normalized Intensities (%) Relative to the Absolute Total Intensities (km/mol), and Scaled Force Constants (mDyn/Å) for Some Isotopomers of SiNH2+ (X1A1) for given isotopomer (total intensity) 28
14
+
28
Si NH2 (948)
b2 b1 a1 a1 a1 b2
+
14
Si14ND2+ (563)
28
Si NDH (755)
28
Si15NH2+ (942)
Si14NH2+ (946)
29
30
Si14NH2+ (898)
freq
intens
force const
freq
intens
force const
freq
intens
force const
freq
intens
force const
freq
intens
force const
freq
intens
force const
578 676 941 1534 3333 3423
1.2 35.1 5.8 13.0 27.3 17.7
0.23 0.34 3.19 1.56 6.88 7.55
466 566 923 1314 2477 3384
0.8 34.0 5.9 14.3 17.1 27.8
0.27 0.35 2.56 1.54 8.04 7.25
420 491 873 1127 2425 2526
0.8 32.1 4.0 18.5 29.8 14.9
0.29 0.47 2.05 2.36 7.56 8.73
550 627 925 1472 3343 3419
1.2 35.3 5.9 12.7 27.0 17.8
0.23 0.33 3.39 1.54 6.84 7.48
553 631 937 1478 3349 3428
1.1 35.2 5.6 13.0 27.4 17.8
0.23 0.34 2.90 1.56 6.88 7.55
553 631 931 1478 3348 3428
1.2 37.0 5.7 13.7 28.8 18.7
0.23 0.34 3.10 1.56 6.88 7.55
TABLE 7: Configuration Space for MCSCF1 Calculations of SiNH2+ symmetry
set 1 (frozen)
set 2
set 3
a1 b1 b2 a2
1sSi 1sN 2sSi 2pSi 2pSi 2pSi
σNH+ σSiN spSi
σNH+* σSiN*
σNH- 3pSi
σNH-*
12 12 12 12 12 12 12 12
set 4 π π*
Electronic Distributions 10 9 8 8 7 7 6 5
0 0 2 0 2 0 2 2
0 1 0 2 1 3 2 3
TABLE 8: Configuration Spaces for MCSCF2a and -2b Calculations of SiNH2+ symmetry
set 1 (frozen)
set 2
set 3
a1
1sSi 1sN 2sSi 2pSi σNH+ 2pSi 2pSi σNH-
σSiN σSiN*
spSi spSi*
b1 b2 a2 A A A B B B C C C
Electronic Distributions 16 2 2 16 1 3 16 2 0 16 2 1 16 2 0 16 2 2 16 2 1 16 1 2 16 1 2
set 4
set 5 8R
π π* 3pSi
4R 4R 2R
2 0 4 2 3 1 3 3 2
0 0 0 1 1 1 0 0 1
According to the principle of the MC/P method, the first step consists of a series of MCSCF calculations aimed at obtaining the best orbitals and zero-order space to be used in the subsequent perturbation treatment. The first zero-order expansion considered is focused on the valence spectrum. It is developed in the MCSCF space constructed on all the spin and spatial symmetry-adapted CSFs arising from the electronic distributions presented in Table 7. All valence electrons are correlated. These calculations will be hereafter referred to as MCSCF1. The second series of expansions had for its only objective to check for the possible existence of diffuse states. It is built on the CSFs arising from the electronic distributions presented in Table 8. In a first step, only classes of configurations A and B are included (MCSCF2a). The diffuse orbitals (denoted “R”) are explicitly taken into account in the variational treatment by allowing monoexcitations from the valence electrons to the R set.56,57 In addition, a spSi correlating function (spSi*) has been explicitely included in the zero-order configuration space56,58 to allow for the spatial relaxation of this important orbital which
is not really accounted for in a limited variational space. In order to check for the importance of couplings that were not included in the MCSCF2a calculations, configurations of classes C were added in MCSCF2b. These restricted MCSCF calculations freeze the NH electrons in the variational part of the MC/P treatment: the correlation effects in which they are involved are recovered at the perturbation step together with the dynamic correlation. 5.2. Results and Discussion. The analysis of the MCSCF zero-order wave functions shows that the σSiN bonding orbital remains doubly occupied in all states. At least one electron remains in the (π,π*) and (spSi, spSi*) systems, as seen by inspection of Table 9. This result holds whatever the zeroorder space used. In addition, the MCSCF1 treatment does not generate excited states involving the NH bonds, a point which was worth checking in view of the experience on the H2SiN+ isomer59 before investigating the possibility of diffuse states. Using MCSCF2 spaces, no diffuse state is found below 9 eV, which is consistent with the electronic spectrum of a positively charged molecule whose core may undergo a Coulombian explosion upon such a Rydbergization. MCSCF2a and MCSCF2b lead to the same ordering for the excited states which are the same as MCSCF1, although some inversions appear in that case. Since the nature of the excited states is well accounted for by MCSCF2a that involves less CSFs than the extended MCSCF2b, only MC/P2a calculations were performed. The ordering thus obtained is, at least for the lowest lying states, the same as that obtained using the MCSCF1 zero-order space. All these preliminary studies pointed to MCSCF1 as a reliable base for the perturbation step. From a cursory examination of the results it is seen that the MC/P1 treatment does not generate any excited state which was not already present in the MCSCF1 calculation, which justifies the present strategy. The quadratic deviation of the MC/P1 from the MCSCF1 values is about 0.66 eV, which is comparable to the deviation observed in preceding studies on ethylene.57 The oscillator strengths, which are generally little affected by dynamic correlation,60 have been determined using the MCSCF1 transition moments (calculated at the center of mass) and MC/ P1 transition energies. These energies and oscillator strengths were used to produce the pictorial representation of the vertical electronic spectrum presented in Figure 4, where the electronic transition has been fitted with a Gaussian having a 900 cm-1 fwhm. A more detailed analysis of the electronic signature shows that the lowest excited state is obtained by the promotion of a nonbonding spSi electron to the hole located at the silicon atom and described by the 3pSi orbital (Figure 1b). This 3B2 state lies about 3 eV above the ground state. It is more than 1 eV higher than the corresponding transition in the isovalent vinylidene H2C2 that is observed and calculated at 2.0 eV.57,61,62 The next excited states are located about 4 eV above the X1A1
2932 J. Phys. Chem., Vol. 100, No. 8, 1996
Parisel et al.
TABLE 9: Vertical Electronic Absorption Spectrum of SiNH2+ states
MCSCF1
MC/P1
X1A1 sp2 π2 21A1 sp2 π1 π*1 11A2 sp2 π1 3pSi1 11B1 sp1 π2 π*1 21B1 sp1 π1 3pSi2 11B2 sp1 π2 3pSi1 13A1 sp2 π1 π*1 13A2 sp2 π1 3pSi1 13B1 sp1 π2 π*1 23B1 sp1 π1 3pSi2 13B2 sp1 π2 3pSi1 15B2 sp1 π1 π*1 3pSi1
0.00 6.67 3.50 7.36 9.23 6.00 4.22 3.59 4.56 9.18 3.19 5.75
0.00 5.87 4.21 6.27 8.90 5.43 4.58 4.14 4.23 8.54 2.99 6.80
f1
MCSCF2a
MCSCF2b
MC/P2a
0.336 (z) 0.0 0.196 (x) 0.004 (x) 0.120 (y) 0.0 0.0 0.0 0.0 0.0 0.0
0.00 6.53 3.98 7.90 8.68 6.33 4.40 3.90 5.44 8.20 3.47 6.63
0.00 6.53 3.99 7.35 8.71 5.57 4.56 3.91 4.92 7.84 3.22 6.53
0.00 6.04 4.71 6.92 8.51 5.93 4.82 4.61 4.55 8.00 3.68 6.90
(c) The electronic spectrum, obtained by our MC/P treatment presents three intense features that should be observed in the 5.4, 5.9, and 6.3 eV regions. We hope that the present results will stimulate experimental or observational work to get more information on a molecular ion which may be a key intermediate in silicon-nitrogen space chemistry.
Figure 4. Simulated electronic absorption spectrum of SiNH2+ (X1A1).
state and are obtained by promoting one π electron to the 3pSi hole, either in a triplet coupling (3A2, 4.14 eV) or in a singlet coupling (1A2, 4.21 eV). By comparison, these A2 states (Figure 1c) are located at 2.85 eV (triplet) and 3.66 eV (singlet) above the ground state in vinylidene. Following these states, all those arising from excitations between the (sp, π) orbitals and the empty (π*, 3pSi) orbitals are reached below 9 eV, except the 1A excited state corresponding to the closed-shell π2 3p 2 Si 1 occupancy (Figure 1d). The π f π* states are found at 6.5 eV (21A1) and at 4.5 eV (13A1) while positioned at 7.9 and 5.02 eV in H2C2, at 8.0 and 4.30 eV in ethylene, and at 10.5 and 5.86 eV in formaldehyde.56,57 The electronic spectra of these neutral species are, however, dominated by Rydberg transitions, which is not the case for SiNH2+. The oscillator strength for the (X1A1 f 21A1) transition is high (f ) 0.336). Two other symmetry allowed transitions (X1A1 f 11B2) at 5.43 eV and (X1A1 f 1B1) at 6.27 eV exhibit medium intensities with f ) 0.120 and 0.196, respectively. The transition to the 21B1 state at 8.90 eV presents a very weak oscillator strength and may be difficult to identify using absorption techniques. We point to the first quintet at 6.81 eV in the same series of calculations. 6. Concluding Remarks In this paper, we have reported a theoretical investigation of the spectroscopic signatures of the ground state of SiNH2+ (C2V), which is the absolute minimum on the (Si, N, H, H)+ potential energy surface. (a) The rotational constants and dipole moment have been determined in order to help radio identification. Although the value of 0.5 ( 0.1 D may be a little small for a direct search on the telescope, it should be large enough for detection in the laboratory. (b) The infrared spectrum is characterized by three strong (3300, 3400, and 650 cm-1), two medium (1500 and 950 cm-1), and one weak (560 cm-1) bands whose relative intensities do not depend significantly on the amount of correlation included in the wave function and should be quite reliable.
Acknowledgment. Part of the calculations presented in this contribution were supported by the CNRS “Institut du De´veloppement et des Ressources en Informatique Scientifique” (IDRIS) supercomputing center. We wish to thank N. Talbi for developing graphic interfaces to our codes. References and Notes (1) Turner, B. E. BAAS 1991, 23, 933. (2) Turner, B. E. Astrophys. J. 1992, 388, L35. (3) Herbst, E.; Millar, T. J.; Wlodek, S.; Bohme, D. K. Astron. Astrophys. 1989, 222, 205. (4) Langer, W. D.; G.A. E. Astrophys. J. 1990, 352, 123. (5) Glassgold, A. E. Molecules in Stellar Winds. In Astrochemistry of Cosmic Phenomena; Singh, P. D., Ed.; International Astronomical Union: Dordrecht, The Netherlands, 1992, p 379. (6) Turner, B. E. Astrophys. J. 1991, 376, 573. (7) Turner, B. E. What species remain to be seen? In Astrochemistry of Cosmic Phenomena: Singh, P. D., Ed.; IAU, 1992; p 181. (8) Ogilvie, J. F.; Cradock, S. Chem. Commun. 1966, 364. (9) Preuss, R.; Buenker, R. J.; Peyerimhoff, S. D. J. Mol. Struct. (THEOCHEM) 1978, 49, 171. (10) Luke, B. T.; Pople, J. A.; Krogh-Jespersen, M. B.; Apeloig, Y.; Karni, M.; Chandrasekhar, J.; Schleyer, P. v. R. J. Am. Chem. Soc. 1986, 108, 270. (11) Flores, J. R.; Largo-Cabrerizo, J. Chem. Phys. Lett. 1987, 142, 159. (12) Flores, J. R.; Gomez Crespo, F.; Largo-Cabrerizo, J. Chem. Phys. Lett. 1988, 147, 84. (13) Wlodek, S.; Rodriquez, C. F.; Lien, M. H.; Hopkinson, A. C.; Bohme, D. K. Chem. Phys. Lett. 1988, 143, 385. (14) Flores, J. R.; Largo-Cabrezio, J. J. Mol. Struct. (THEOCHEM) 1989, 183, 17. (15) Hopkinson, A. C.; Lien, M. H. Can. J. Chem. 1989, 67, 991. (16) Maier, G.; Glatthaar, J.; Reisenauer, H. P. Chem. Ber. 1989, 122, 2403. (17) Foster, S. C. J. Mol. Spectrosc. 1989, 137, 430. (18) Ye, S.; Dai, S. J. Mol. Struct. (THEOCHEM) 1991, 236, 259. (19) Elhanine, M.; Farrenq, R.; Guelachvili, G. J. Chem. Phys. 1991, 94, 2529. (20) Bogey, M.; Demuynck, C.; Destombes, J. L.; Walters, A. Astron. Astrophys. 1991, 244, L47. (21) Botschwina, P.; Tommek, M.; Sebald, P.; Bogey, M.; Demuynck, C.; Destombes, J. L.; Walters, A. J. Chem. Phys. 1991, 95, 7769. (22) Chong, D. P.; Papousek, D.; Chen, Y. T.; Jensen, P. J. Chem. Phys. 1993, 98, 1352. (23) Elhanine, M.; Hanoune, B.; Guelachvili, G. J. Chem. Phys. 1993, 99, 4970. (24) Goldberg, N.; Hrusak, J.; Iraqi, M.; Schwarz, H. J. Phys. Chem. 1993, 97, 10687. (25) Goldberg, N.; Iraqi, M.; Hrusak, J.; Schwarz, H. Int. J. Mass Spectrom. Ion Process. 1993, 125, 267. (26) Damrauer, R.; Krempp, M.; O’Hair, R. A. J. J. Am. Chem. Soc. 1993, 115, 1998. (27) Maier, G.; Glatthaar, J. Angew. Chem., Int. Ed. Engl. 1994, 33, 473.
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