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Chemical Physics

E L S E V I E R Chemical Physics 212 (1996) 331-351

Interstellar silicon-nitrogen chemistry. I. The microwave and the infrared signatures of the HSiN, HNSi, HSiNH 2, HNSiH 2 and

HSiNH ÷ species

O. Parisel *, M. Hanus, Y. Ellinger Equipe d'Astrochimie Quantique, Laboratoire de Radioastronomie Millim~trique, E.N.S. et Observatoire de Paris, 24 rue Lhomond,

F-75 231 Paris Cedex 05, France

Received 26 April 1996

Abstract

The experimental and the theoretical interests for the silicon chemistry have been renewed by the recent detection of SiN in space. In this contribution a theoretical study of the HSiN, HNSi, HSiNH 2 and HNSiH 2 molecular systems is presented that aims to help in the interpretation of available experimental results as well as in the attribution of new interstellar lines. The main goal of this report remains, however, the calibration of ab initio calculations on still-unknown silicon-nitrogen systems: the infrared and the microwave signatures of the HSiNH + cation are reported as a direct application. The signatures of the five molecules under investigation have been computed a t increasing levels of post-Hartree-Fock theories, using up to a 6-311 + -t-G * * atomic orbital expansion. Accurate geometries and B e rotational constants have been determined at the M~511er-Plesset MPn (n = 2, 3, 4), CASSCF and CCSD(T) theoretical plateaus for HNSi. The comparison with experimental data allows then to derive the scaling factors needed to obtain accurate rotational constants for related species: they are applied as such on the crude constants determined for HSiN, HSiNH 2, HNSiH 2, and finally HSiNH 2 in its floppy linear singlet ground state and in its lowest cis-bent a3p( state as well. Dipole moments are reported in order to assess the feasability for these species to be detected owing to their rotational signatures either in the laboratory or in space using millimetric radioastronomy techniques. Infrared (IR) signatures are computed at the same levels of theory and compared to the recent matrix isolation experiments devoted to HSiN, HNSi, HSiNH 2 and HNSiH 2. The calculations unambiguously confirm that all these species have been effectively produced and observed. They also lead to the determination of accurate IR scaling factors that are significantly larger than the usual ones. Such an approach allows then to quantitatively predict the IR spectra of the still-unknown HSiNH ÷ entity. The study of the IR spectra furthermore points out the failure of single-reference correlation methods to obtain predictive IR signatures in some cases, as is unambiguously illustrated in the case of the HSiN species.

1. Introduction

While silicated species were widely supposed to be embedded in grains in the interstellar medium

* Corresponding author. E-mail:[email protected].

[1-4], the recent detection of the SiN radical [1,3] has drawn the attention to the gas phase chemistry of silicon-containing molecules in space [5-7]. Further- more, the identification of SiN in the interstellar medium gives the first evidence of a link between the interstellar chemistry of silicon and that of nitro-

gen.

0301-0104/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0301-01 04(96)00216-9

332 o. Parisel et al. / Chemical Physics 212 (1996) 331-351

In order to obtain reliable spectroscopic constants that may help in the interpretation of interstellar or laboratory spectra concerning such S i / N species, we have undertaken a comprehensive study on a series of related compounds. In this report, the HNSi, HSiN, HSiNH 2 and H2SiNH species (Fig. l a - l d ) are first investigated at various levels of ab initio theory: the comparison of the computed spectral signatures with some available experimental results allows then to carefully calibrate those quantum chemistry methods that will be used to predict the spectroscopic properties of still-unknown molecules, Among such species are those necessary to charac- terize the (H ,H, Si, N) + potential energy surface: as

a direct application we present here a study of the HSiNH + cation ( H - S i - N - H connectivity) in its lowest singlet state and lowest triplet states (Fig. l e - l i ) . Other connectivities, that correspond to the SiNH~ and H2SiN + ions, are discussed elsewhere [8,9].

2. Methodo logy

2.1. Computat ional details

The calculations of absolute energies, geometries, rotational constants, IR frequencies and their corre-

0 (a)

N - - 8 i ~

(b)

H

(c)

E)

t , N Si H

Oo (e)

(h)

Si 0 ~ H

(0

(d)

N Si

(~)

Fig. 1. Lewis structures for: (a) HNSi, XtX+; (b) HSiN, XIX+; (c) H2SiNH, XlA~; (d) HSiNH 2, xlfl~; (e) HSiNH +, linear form of the singlet ground state (XtX + ); (O HSiNH +, trans-bent form of the singlet ground state (X ~A'); (g) HSiNH +, hypothetical cis-bent form of the singlet ground state (X IA'); (h) HSiNH +, cis-bent form of the a3A/ state; (i) HSiNH +, hypothetical trans-bent form of an a3K state. Dots stand for in-plane electrons and crosses for out-of-plane electrons.

O. Parisel et a l . / Chemical Physics 212 (1996) 331-351 333

sponding absorption intensities have been performed at increasing levels of theory: MP2, MP3, MP4, CCSD(T) and CASSCF ([10,11] and references therein). In order to allow for a large flexibility in the one-particle space, a triple-zeta quality basis set extended by polarization and diffuse functions [12,13] was used, which is known as 6-311 + + G* * [14] for hydrogen and nitrogen whereas the expanded basis set by McLean and Chandler [15] is used for silicon under this acronym. Smaller 3-21G [16] and 6-31G* [17] basis sets were also considered in preliminary investigations. In all forthcoming MPn and CCSD(T) calculations, all electrons are correlated.

The GAUSSIAN92 [18], HONDOS.5 [19], and ALCHEMY II [20] codes have been used.

2.2. Scaling procedures for the rotational and vibrational constants

The main goal of this contribution is to obtain accurate scaling factors to correct crude ab initio spectroscopic constants for species containing Si and N.

The scaling factors needed to increase the accuracy of the rotational constants will be discussed in the following section devoted to HNSi, the only molecule for which experimental spectra are available. For other systems investigated in this report, they will be used as such.

The large amount of data available on IR spectra has now well established the fact that crude computed frequencies should be corrected to reproduce experimental values [21]: such a way, anharmonic corrections and some missing correlation effects are taken into account. This is done here at the same time as the normal coordinate analysis: the appropri- ate B matrix [22] is evaluated and then used to transform the force constant matrix from a cartesian to an internal coordinate representation. Proceeding this way, the contaminations arising from translation and rotation motions are projected out from 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 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 proce-

dure is rigorously equivalent to the application of the usual scaling factors 0.89 (ROHF), 0.94 (MP2) and 0.945 (MP4) on the unscaled vibrational wave numbers.

These factors however depend on both the method of calculation and the basis set used so that it was found wiser in the present context to derive them by minimizing the root-mean-square deviation between the available experimental IR spectra for HNSi, HSiN, H2SiNH and HSiNH 2 and the scaled ab initio results. Such a way, confident IR spectra are expected to be obtained for species formed by atomic combinations in the (H,N, Si) set. This procedure has been applied to each ab initio methodology considered and leads to the following factors (to be applied directly on wave numbers):

RHF/6-31 G* : 0.898. RHF/6-311 + + G* ": 0.900. MP2/6-31 G" : 0.959. MP2/6-311 + + G" * : 0.959. MP3/6-311 + + G * *: 0.939. MP4/6-311 + + G" * : 0.974. CCSD(T)/6-311 + + G" * : 0.966. CASSCF/6-311 + G * ": 0.970.

These factors are slightly higher than those usually employed.

The idea behind the scaling procedure is to avoid high-level and costly computations since an adequate scaling is expected to correct the deficiencies of the methods used. However, such an approach, although frequently employed, is sometimes hazardous. As an example, scaled MPn, and even CCSD(T) approaches can lead to coherent IR spectra but the apparent convergence of the results may be biased by the fact that these methods all correspond to single-reference calculations: a correct treatment may request an accurate description of non-dynamic correlation effects [23] and thus the consideration of multireference methodologies. Such a failure of the MPn and CCSD(T) methods has been pointed out in the case of H2SiN ÷ [9] and will be unambiguously illustrated in the section devoted to HSiN.

Graphical representations of IR spectra are presented throughout this contribution: they have been obtained by fitting each vibrational transition with a Lorentzian having a 4 cm-~ FWHM.

334 O. Parisel et a l . / Chemical Physics 212 (1996) 331-351

3. HNSi

Among the compounds having multiple bonds to silicon [24] one of the most attractive is HNSi, the silicated counterpart of HNC, which is suspected to be present in dense interstellar clouds [1-7]. Numer- ous studies, experimental and theoretical, have been devoted to this species for many decades [25-42].

Using Lewis-localized orbitals, the electronic structure of HNSi in its X 1"~ + ground state can be written

(ISs i )2 (lsN)2 (2Ssi)2 (2Psi)6 (CrN H )2 (O.SiN)2

X ('rr si N )2 (SPs i )2 (2PN)2 (3Ps i )0.

Such a representation (Fig. 1 a) strongly suggests a double bond between the silicon and the nitrogen atoms. However, an NBO (Natural Bond Orbital) analysis [43] performed at the MP2/6-31G* level of calculation gives charges as +0.83 (Si), - 1 .26 (N) and + 0.43 (H). Such a distribution indicates a strong formal charge separation between Si and N: a single-bonded Lewis structure such as HN-Si + would thus appear as a better description according to the sole Mulliken analysis. Refined conclusions can however be derived from the quantitative analysis of the natural orbitals: the electronic density of the so-called "rr-system on the nitrogen atom is 80%, which indicates a very weak rr bond as a consequence of the ~r-donor capability of the nitrogen atom [28,44]. Even the trsi N density resides on nitrogen for 85%, among which 60% come from the s N orbitals and 40% from the PN orbitals; the silicon counterpart (15%) comes from the Ssj orbitals for

16% and from the Psi orbitals for 84%. The hybridization at the nitrogen atom is found to b e sp 15.

Although the Lewis structure written above does not account for the subtleties pointed out by the NBO analysis, it suggests that the CASSCF space arising from the distribution of the 10 valence electrons in 9 active orbitals:

2 2 2 )6 ( 1 S s i ) ( I S N ) ( 2 S s i ) ( 2 P s i

× [CrN H CrSiN "rrsiN SPsi 2p N 3Psi error1 Crs, iN,rr SiN ] ,0

should offer a good representation. Proceeding this way, 5292 (in CI symmetry, which reduces to 1436 for the A I representation of the C2v symmetry) spin and spatial symmetry-adapted CSFs (Configuration State Function) span the variational space.

The analysis of the CASSCF wave function shows a weight of 92% for the reference configuration depicted above and a weight of 2% for the two CSFs that involve a double excitation from the so-called 'rrsi N (respectively 2PN) orbital to the Tl'si N (respectively 3Ps i) orbital. Such excitations tend to reinforce the n-donor capability of nitrogen towards silicon and therefore slightly reinforce the multiple bond character of the SiN bond.

The geometries obtained for HNSi at different levels of theory are reported in Table 1 together with their corresponding energies, dipole moments and rotational constants B e. Inspection of this Table shows that the computed structure of HNSi in its X IE+ ground state is not very sensitive to the level of theory (correlation or basis set). The SiN bond

Table 1 Optimized structures, dipole moments p., unscaled rotational constants Be, absolute energies E and scaling factors ot (see text for details)

for HNSi ( X I E +)

Method SiN (,~) NH (,~) /z (D) B e (MHz) ot E (au)

R H F / 3 - 2 1 G 1.562 0.990 0.24 18 838 1.0096 R H F / 6 - 3 1 G * 1.523 0.988 0.15 19 638 0.9684

RHF/6-311 + + G * * 1.529 0.988 0.70 19609 0.9699 M P 2 / 6 - 3 1 G * 1.570 1.008 0.61 18 599 1.0225 MP2/6-311 + + G * * 1.569 1.006 0.13 18644 1.0201

MP3/6-311 + + G * * 1.548 0.999 19 139 0.9937

MP4/6-311 + + G * * 1.577 1.007 18 458 1.0303 CCSD(T)/6-311 + + G * * 1.567 1.006 18 672 1.0185 CASSCF/6 -311 + + G * " 1.565 1.001 0.04 18712 1.0164

- 342.109698 - 343.918300

- 3 4 3 . 9 6 0 2 5 8 -344 .180311

- 344.367988

-344 .370231 - 344.396640

- 344.393359 - 344.094843

O. Parisel et al . / Chemical Physics 212 (1996) 331-351 335

o

length remains close to 1.57 A, i.e. very close to the experimental values observed either in HNSi or in SiN (SiN X 2E: r = 1.572 ,~ [45], HNSi X1E+: r = 1.551 ,~ [37]). The NH bond length is close to 1.00 ,~ in agreement with experimental and other theoretical values [25,37].

As pointed out by DeFrees et al. [46], MP3 optimized geometries should provide rotational constants B e that match more closely the experimental B 0 values than those obtained from MP2 or MP4 optimized structures. The best estimate of the rotational constant of HNSi (Dooh-X l E+ ) is thus

Be(MP3 ) = 19 139.166 MHz.

The rotational constant of HNSi is however known from several experimental works [36,37,42]: 19018.800 MHz. We point out that the MP3 B e value is the closest to the experimental B 0 constant among all theoretical methods used here: it is only 0.65% far from the experimental determination. However, the accurate knowledge of B 0 derived from experiment allows to obtain accurate scaling factors a , for each theoretical method considered, as

O~theo r -~ B~*P(HNSi)/Bth¢°~(HNSi).

Such factors are reported in the last column of Table 1 and will be applied as such to forthcoming species.

Turning now to the dipole moment, there are strong dependencies on the choice of the basis set and the methodology: the computed values vary from 0.04 D up to 0.70 D according to the level of

calculation. Such variations have been observed previously in other works [29,30,32]. There is no doubt however that electron densities based on multireference approaches are of better quality than those obtained using simpler single-reference correlation methodologies: at the present day, the CASSCF value of 0.04 D should thus be recommended as the most reliable theoretical estimate to the exact dipole moment. The astrophysical consequences of such a small value are dramatic: it must be unfortunately concluded that HNSi, if it exists in space, will have its rotational signature impossible to record using present-day spatial detectors. Even a value of about 0.5 D would make the rotational identification of a species a feasible, but a difficult task for millimetric radiotelescopes.

Table 2 reports the scaled vibrational wave numbers and intensities obtained at each level of theory. There are no dramatic differences between the different ab initio methods used. Experimental values [34] are also reported. The agreement with experiment is very good and even excellent for wave numbers and relative intensities at the CASSCF level of calculation: the bending mode falls at 530 cm-1, to be compared to the experimental 522 c m - t value (523 cm- l in Ref. [25]). The two stretching modes appear at 1183 cm -~ and 3600 cm -J whereas experiment reports 1201 cm - l (1198 cm - t in Ref. [25]) and 3585 cm- I (3588 cm -1 in Ref. [35,39] and 3583 cm-1 in Ref. [25]). The scaled CASSCF/6-311 + + G * * IR spectrum is given in Fig. 2.

Table 2 Scaled vibrational wavenumbers (cm "1) with normalized intensities, absolute total intensities (KM/Mole) for HNSi (Xl2 + ). (w) and (s) stand for weak and strong

Method 8HNSi rsi N rNH Total intensity

RHF/6-31 G* 585 (70.8%) 1246 (12.4%) 3612 (16.7%) 689 RHF/6-311 + + G ° ' 535 (64.9%) 1223 (15.8%) 3600 (19.4%) 811 MP2/6-31G * 567 (80.0%) 1135 (1.2%) 3592 (18.8%) 510 MP2/6-311 + + G * * 471 (78.1%) 1136 (4.2%) 3796 (13.1%) 567 MP3/6-311 + + G* * 464 1213 3617 MP4/6-311 + + G ' * 431 1101 3636 CCSD(T)/6-311 + + G * * 442 1156 3622 CASSCF/6-311 + + G * * 530 (74.5%) 1183 (7.9%) 3600 (17.6%) 603

Experiment 522 (s) 1201 (w) 3585 (w)


1C0-

80-

~ .

c

20-

O- 4000 3500 3000 2500 2000 1500 1000 500

Wavenumbers (cm-1)

Fig. 2. Simulated (scaled CASSCF/6-311 + + G* * ) infrared spectrum of HNSi.

4. HSiN

Contrary to the HCN/HNC system whose absolute minimum has the HCN connectivity, HSiN lies higher in energy than the HNSi isomer [30]. HSiN had been proposed to be the carrier of some interstellar bands many years ago [47]: such an attribution was ruled out, however, by a number of theoretical calculations. To our knowledge and from the molecular spectroscopy viewpoint, the only unambiguous identification of HSiN in laboratory experiments, as the first compound having a formal SiN triple bond (except the SiN radical), is that by Maier et al. [48].

The electronic structure of HSiN in its X~Y', + ground state can be seen in terms of Lewis-localized orbitals as:

( l S s i )2 ( I S N ) 2 ( 2Ss i )2 (2Ps i )6 ((rsi.)2 (O.siN)2

X ( 'B'Si N )2 ( 31" SiN )2 (SPN)2 .

Such a representation strongly suggests a triple

bond between the silicon and the nitrogen atoms (Fig. lb). However, an NBO analysis performed at the MP2/6-31G* level of calculation reveals that the charges are: +0.87 (Si), -0 .71 (N) and -0 .16 (H). As seen previously for HNSi, such a strong charge separation makes H-Si + = N - a better Lewis structure than H-S i=N. However, the electronic density of the so-called double ~r-system on the nitrogen atom is 67%, which is very different from that observed in HNSi: this indicates a stronger ~r bond and points out that the multiple bond in HSiN is in fact an intermediate between a double and a triple bond; in accordance, the hybridization for the Si-H bond is found to be sp 14. Moreover, the trs~ N density resides on nitrogen for 67%, among which only 23% come from the s N orbitals and 75% from the PN orbitals. The silicon counterpart (33%) comes from the Ss~ orbitals for 58% and from the Ps~ orbitals for 42%. Both these repartitions are again very different from those computed in HNSi.

In order to account for non-dynamic correlation effects, a CASSCF calculation was performed in the space generated by distributing the 10 valence electrons in 9 active orbitals:

( lssi) 2 (lSN) 2 (2Ssi) 2 (2psi) 6

. , . , 1 1 0

X [Orsi H O'si N '/'/'SIN Ti'SiN SpN O'SiH O'SiN 'r/'SiN qrSiN J "

The analysis of the CASSCF wave function shows a 86% contribution of the reference configuration described above and a weight of 3% for the two CSFs that involve a double excitation from a ~rsi N orbital to the corresponding Ws~y, mostly developed on the silicon atom. Such excitations tend to rein-

Table 3 Optimized structures, dipole moments /z, rotational constants B o (scaled Be), absolute energies E and relative energies AE to HNSi for HSiN (Xl~ + )

Method SiN (.~) Sill (,g,) /.t (D) B 0 (MHz) E (au) A E (kcal/mol)

RHF/3-21G 1.575 1.459 4.61 18845 -341.963316 91.9 RHF/6-31G * 1.526 1.425 5.42 19 158 - 343.780611 86.4 RHF/6-311 + + G * * 1.524 1.417 5.92 19233 -343.818526 88.9 MP2/6-3 ! G * 1.631 1.492 3.40 17 866 - 344.088396 57.7 MP2/6-311 + + G * * 1.622 1.478 3.77 18049 -344.272807 59.7 MP3/6-311 + + G * * 1.547 1.461 19179 -344.268409 63.9 MP4/6-311 + + G * * 1.667 1.496 17280 -344.309159 54.9 CCSD(T)/6-311 + + G* * 1.590 1.479 18 676 - 344.287107 66.7 CASSCF/6-311 + + G * * 1.586 1.473 4.46 18 734 - 343.988541 66.7


force the w-donor capability of the nitrogen atom and reinforce the multiple bond system as found for HNSi.

The geometries obtained for HSiN at different levels of theory are gathered in Table 3 together with the corresponding energies and dipole moments. The rotational constants B 0 are also included: they have been obtained as scaled B e constants using the scaling factor determined for HNSi. Inspection of this table shows that the computed geometry of HSiN is much more sensitive to the level of correlation and the basis set used than it is for HNSi. For example, the SiN bond length varies from 1.547 ,~ (MP3/6- 311 + + G * * ) t o 1 .667 ,~ (MP4/6 -311+ + G * * ) ; the Sill bond length also presents significant variations. Due to the smaller weight of the leading configuration in the CASSCF wave function describing HSiN relative to that in HNSi, it can be antici- pated that single-reference theories might lead to biased results. The CASSCF geometry and the corresponding rotational constant B 0 are thus to be considered as the most reliable quantities, which gives

B0(HSiN ) = 18734 MHz.

The SiN bond length obtained at the CASSCF level of calculation (1.586 #,) increases by 0.02 .~ relative to that in HNSi, and is longer than that observed in SiN (SiN X 2E: r = 1.572 A [45], HNSi XIE+: r = 1.551 ,~ [37]), in accordance with the previous assumption that this bond is intermediate between a double and a triple bond.

The CASSCF dipole moment is '4.46 D which makes HSiN an attractive candidate for a spatial detection using radioastronomy techniques.

The last column of Table 3 contains the energy of HSiN relative to that of the lowest-lying HNSi (h E). Relative to the RHF value, this difference is reduced by more than 25 kcal /mol when electronic correlation is included in the calculation. Defining the non-dynamic correlation energy as the difference between the RHF and CASSCF energies, one finds, using the same 6-311 + + G * * basis set, 106.7 kcal /mol for HSiN but only 84.5 kcal /mol for HNSi. The variation of the non-dynamic correlation energy is thus about 22 kcal /mol which explains most of the variation of A E when going from the simplest RHF approach to correlated levels of wave functions. Why non-dynamic correlation effects are more important in HSiN than in HNSi is due to a lower weight of the SCF closed-shell determinant in the CASSCF wave function as a consequence of a more multiply-bonded system: the HSiN isomer has to be seen as more "resonant" in terms of Lewis terminology. The correlated values of A E are about 60 kcal /mol, in agreement with previous calculations [30]. Such an energy difference is four times larger than the experimental separation between HCN and HNC (15 kcal /mol as quoted in Ref. [30]), which might be important if comparing the interstellar HSiN/HNSi and H N C / H C N ratios.

Table 4 collects the scaled vibrational wave numbers obtained at each level of theory for HSiN

Table 4 Scaled vibrational wavenumbers (cm -t) with normalized intensities, absolute total intensities (KM/Mole) for HSiN (X ~v+). (s) and (m)

stand for strong and medium

Method 6HSiN rsi N rsi H Total intensity

RHF/6-3 IG * 208 (61.2%) 1258 (0.7%) 2230

RHF/6-31 IG + + ' * 229 (83.3%) 1263 (6.3%) 2194 MP2/6-31G * 423 (4.9%) 952 (54.0%) 2157

MP2/6-311 + + G * * 391 (1.95%) 975 (65.6%) 2187

MP3/6-311 + + G * * 173i 1274 2236

MP4/6-311 + + G * * 543 745 2080

CCSD(T)/6-311 + + G * * 58 1110 2169 CASSCF/6-311 + + G * * 196 (25.5%) 1122 (50.2%) 2251

Experiment 1162 (s) 2150

(36.7%) 25 (10%) ~4 (40.9%) 144 (32.3%) 117

(24.2%)

(m)

103

338 O. Parisel et al. / Chemical Physics 212 (1996) 331-351

60-

40~ _c

20-

o - ~ 4000 35430 3000 2600 20GO 1500 1000 800

Wavenumbers (cm-1)

Fig. 3. Simulated (scaled RHF/6-311 + + G * * ) infrared spectrum of HSiN.

. • 60,

Q) 40" c:

0 - ~ 4000 3800 3000 2800 2000 1500 I0~0 500

Wavenumbers (cm-1)

Fig. 5. Simulated (scaled CASSCF/6-311+ + G * * ) infrared spectrum of HSiN.

together with their corresponding intensities; experimental values [48] are reported as well. Dramatic variations occur when going from a method of calculation to another. As an example, the bending mode appears at 208 cm-1 with a relative intensity of 61.2% at the RHF/6-31G* level of calculation but at 423 c m - l with a 4.9% relative intensity using the MP2/6-31G * methodology. The same mode is furthermore found at 58 cm-1 by the CCSD(T) approach, and even becomes imaginary (173i cm - l ) if the MP3/6-311 + + G** is considered! Such variations are depicted in Figs. 3 and 4. On the contrary, the CASSCF wave function leads to a more balanced spectrum (Fig. 5) and gives features that correctly match experimental observations. At this level of theory, the SiN stretching mode is located at 1122 cm- ~, close to the experimental value of 1162 cm- 1, which is slightly smaller than that observed in HNSi, in agreement with a longer SiN bond length and with a weaker bond as well. The Sill stretching mode

O) 4O.

4000 3500 3000 2 ~ 2000 I ~ 1000 500

Wavenumbers (cm-1)

Fig. 4. Simulated (scaled MP2/6-311 + + G * * ) infrared spectrum of HSiN.

appears at 2251 cm-~, only 5% far from experiment. Moreover, relative intensities also are in accordance with the matrix isolation IR spectrum. The bending mode has not been observed in the quoted experiment: it is predicted here at 196 cm- 1 and absorbs as strongly as the SiN stretching mode. The limit of the experimental observation window at small energies (down to 220 c m - l ) can be invoked as the simplest explanation for the non-detection of this mode in the experiment performed by Maier et al.

The variations in the computed IR spectra (wave number and intensities) illustrated above point out that, in some cases, the well-established single-reference approaches are not reliable if aiming at predictive results. In those cases, it seems that the role of non-dynamic correlation effects are crucial even if no strong configuration mixing dominates the CASSCF wave function. This is of special impor- tance when intensities (the derivatives of the dipole moment relative to the normal modes) are concerned: even if the CASSCF wave function remains dominated by a leading configuration, the one-particle Hartree-Fock determinant in the present case, the electron density is modified as seen when dis- cussing the dipole moment of HSiN. It seems however difficult to trace the failure of single-reference approaches as the lack of some specific valence excitations: the a priori anticipation of which molecular structure would request a multireference calculation in order to get a reliable IR spectrum is thus delicate. Moreover, CASSCF frequencies are rare in the literature at the present day so that no general trend can be derived. It has however been recently pointed out that, when dealing with the C 9, C~t and


C 1 3 , entities the ordering of the harmonic frequencies and their intensities as well are crucially depen- dent on the size of the CASSCF space [23]. Within the present series of molecules, it can furthermore be noticed that single-reference approaches failed for HSiN and H2SiN + [9] that both contain Sill bonds, while succeeding in the description of both HNSi and SiNH~- [8] that do not. The spectacular changes observed in HSiN and H2SiN + when rising the calculation level up to CASSCF are however less pronounced for the HSiNH 2, H2SiNH and HSiNH + species that are considered in the next sections.

5. H S i N H z

HSiNH 2 has been observed recently using matrix isolation IR spectroscopy and its electronic absorption spectrum has also been reported [34]. Previous theoretical studies [30,49,50] have concluded to a planar C S structure as the absolute minimum of the (H, H, H, Si, N) potential energy surface.

The electronic structure of this species (XW ground state) can be seen to be

2 2 2 ) 6 2 2 ( lss i ) (ISN) (2Ssi) (2psi (O'siH) (O'siN)

+ _ 2 2 2 X(O-NH)2(O-NH) ( ' r r s i N ) ( S p S i ) •

The + and - labels refer to the symmetric and antisymmetric combinations of the NH bonds in a local C2v symmetry at the nitrogen atom.

At the MP2/6-31G * level of calculation, a Mul- liken charge analysis gives: +0.33 for Si, - 0 .88 for N, + 0.36 for each of the hydrogen atom bonded to N, and - 0 . 1 7 for the remaining hydrogen atom linked to silicon. The NBO analysis leads to a no-

ticeably different charge distribution:' + 0.78 for Si, - 1 . 2 9 for N, +0.41 for each N-bonded hydrogen and -0 .31 for the Si-bonded hydrogen. As in the previous cases, 88% of the electronic density involved in the so-called 7rs~ N bond resides on the nitrogen atom. The weak "rrs~ N bond can in fact be seen as the result of the bonding overlap between the nitrogen 2p lone-pair orbital with the silicon empty 3p orbital which are both orthogonal to the molecular plane (Fig. ld): the out-of-plane rotation of the NH 2 group around the SiN axis would have this bonding overlap decreased and thus non-planar structures destabilized, at least in the ground state. Simi- larly, an unbalanced electronic distribution is found in the %~N bond that has 85% of the corresponding electron density localized on nitrogen. Among these 85%, 42% come from the s N atomic orbitals and 58% from the ps orbitals. On the contrary, the remaining 15% of the electronic density localized on silicon come for 84% from Ps~ orbitals but only for 14% from the Ss~ orbitals. The hybridization scheme is found to b e sp 24 for the NH bonds: this is coherent with a SiN bond intermediate between a single and a double bond. Finally, a s p 0"34 hybridization is found for the terminal lone-pair localized on the silicon atom.

In order to properly account for non-dynamic correlation effects, MCSCF calculations were performed in the space built on the CSFs generated by distributing the 12 valence electrons in 11 active orbitals:

+ -- , * * + O'SiH O'SiN O"NH O'NH "n'SiN SPsi O'SiH O'SiN O-NIt

, _ . ] 1 2 . XO 'NH qTsi N

Table 5

Optimized structures, dipole moments /x and absolute energies for HSiNH 2 (X ~K)

Method SiN (,~) NH~ (,~) NH 2 (A) Z.SiNH, ZS iNH 2 Z_NSiH 3 Sill 3 (A) /x (D) E (au)

R H F / 3 - 2 1 G 1.730 1.002 1.002 121.6 126.0 95.4 1.534 2.22

R H F / 6 - 3 1 G * 1.706 0.998 0.998 121.8 126.1 95.5 1.514 2.16

RHF/6-311 + + G * * 1.704 0.997 0.997 122.0 126.0 95.8 1.516 1.89

M P 2 / 6 - 3 1 G * 1.719 1.014 1.014 121.6 126.1 94.1 1.524 2.39

MP2/6-311 + + G * * 1.719 1.011 1.011 121.9 126.2 94.0 1.515 1.84

MP3/6-311 + + G * * 1.713 1.007 1.007 122.1 126.2 94.0 1.5t6

MP4/6-311 + + G * * 1.724 1.012 1.012 121.9 126.3 93.7 1.519

CCSD(T) /6 -311 + + G * * 1.723 1.012 1.012 122.1 126.3 93.8 1.521

MCSCF a/6-311 + + G * * 1.732 1.018 1.018 122.2 125.7 94.7 1.546 1.96

- 343.281592

- 345.087683

- 345.134528

- 345.340815

- 345.552188

- 345.571095

- 345.577757

- 345.589366

- 345.264304

a See text for details.


For the geometry optimization and the corresponding IR calculation, the excitation level has been limited to 4 electrons with respect to the closed-shell RHF determinant. Such a truncation leads to retain 7028 CSFs (C~ symmetry) in the variational space. The final MCSCF energy reported in Table 5 corre- sponds however to the exact CASSCF energy where no restriction has been given to the excitation levels: this calculation includes 31 248 CSFs. The weight of the leading reference CSF in the CASSCF wave function is 94%.

Optimized geometries are collected in Table 5. Compared to HSiN and HNSi, an important increase is observed for the SiN bond length which averages around 1.72 .&, about 0.15 .& longer than that found for HSiN, HNSi and SiN. The NH bonds remain

o close to 1.00 A, and the Sill terminal bond is as long

o as 1.54 A, which is larger than in HSiN. The/_SiNH angles are about 120 °, having only a slight dissym- metry relative to the SiN axis. The remaining/__NSiH angle is about 95 ° , in agreement with the calculations quoted above: this surprising value might be seen as another example of the strange bonding capabilities of the silicon atom [51-54].

Scaled rotational constants are reported in Table 6. The high dipole moment, about 2 D, makes detection in the interstellar medium possible: if HSiN exists in space, a discussion which is beyond the scope of this report but that has been sketched in Ref. [55], it is then possible that the dihydrogen adduct HSiNH 2 might also be detected.

The IR spectrum is given in Table 7 and Fig. 6. The agreement with the experimental results obtained by Maier et al. [34] is very good. Two more absorptions at 824 cm - t and 1012 cm -1 should have been detected in the experimental spectrum since their calculated intensity is higher than those of

Table 6

Scaled rotat ional constants for HSiNH 2 (X tA~)

Method A 0 (GHz) B o (GHz) C o (GHz)

M P 2 / 6 - 3 1 G * 141.050 15.281 13.787

M P 2 / 6 - 3 1 1 + + G * * 142.341 15.239 13.765

M P 3 / 6 - 3 1 1 + + G * * 139.009 14.945 13.494

M P 4 / 6 - 3 1 1 + + G * * 143.102 15.323 13.840

C C S D ( T ) / 6 - 3 1 1 + + G * * 141.423 15.155 13.689

M C S C F / 6 - 3 1 1 + + G * " 137.686 14.952 13.488

other modes that have been observed. A careful inspection of the experimental spectrum reveals, however, that these features might effectively be present either as small signals or as shoulders. The remaining mode at 760 cm-~ is too weak to unambiguously conclude for its experimental assignment.

6. H2SiNH

H2SiNH has been trapped recently in matrix isolation experiments: its IR and electronic signatures have been obtained [48]. Previous studies have predicted a planar C~ structure [30,50]: it was checked by preliminary investigations that the C2v structure reported in Ref. [30] becomes a transition state when a large enough basis set and correlated levels of theory such as MP2/6-31G* and MP2/6-311 + + G* * are considered.

The electronic structure of this species (X~A~ ground state, Fig. 1 c) can be written

( I S s i ) 2 ( I S N ) 2 ( 2 S s i ) 2 ( 2 p s i ) 6 ( O . N H ) 2 ( O . s i N ) 2

x

As seen previously, the "rr bond is very weak and the corresponding electrons are again essentially located on the nitrogen atom. At the MP2/6-31G* level of calculation, a Mulliken charge analysis gives +0.51 for Si, - 0 . 67 for N, +0.33 for the nitrogen- linked hydrogen and an almost zero charge for the two hydrogens linked to silicon. The NBO charges are rather different: - 1 .18 on N, +1.22 on Si, + 0.40 on the nitrogen-bonded hydrogen, and about - 0 . 2 0 on the remaining hydrogen atoms bonded to silicon. Contrary to what has been observed in the case of HSiNH a, only 74% of electronic density involved in the so-called rrs~ N bond resides on nitrogen: the WS~N bond is thus more pronounced than in the HSiNH 2 isomer, as confirmed by the higher contributions of p character in the Sill hybrid, namely sp TM. An analogous electronic distribution is found for the Crs~ N bond where 76% of the electron density is localized on nitrogen. Among these, 36% come from the s N atomic orbitals and 64% from the PN orbitals. On the contrary, the remaining 24% of the

O. P arisel et al. / Chemical Physics 212 (1996) 331-351 341

-_<

7" o~ . v

-6

o

_=

=_

o e -

-<

b bbb÷÷

!

342 O. Parisel et a l . / Cheraical Physics 212 (1996) 331-351

6 0 -

( D 40- _= L

0 . . . . i . . . . i . . . . i . . . . i . . . . I . . . . i . . . . i , , ,

4000 :21500 3000 2500 2000 1500 1000 500

Wavenumbers (cm-1)

Fig. 6. Simulated (scaled MCSCF/6 -311 + + G * * ) infrared spec-

trum of HSiNH 2.

electronic density localized on silicon come for 61% from Psi orbitals and for 37% from the Ssi orbitals. The hybridization scheme for the NH bond is sp z6 whereas that of the silicon lone-pair is sp L8+.

Non-dynamic correlation effects have been evaluated following the procedure described for HSiNH 2 (MCSCF calculations for the geometry optimization and vibrational calculations, but CASSCF calculation for the energetics) and using the spin and spatial symmetry-adapted CSFs generated from the repartition of the 12 valence electrons in 11 orbitals:

+ - - , * + *

O'NH O'Si N O'si H O'si H '/Tsi N s p N O'NH O'Si N O'si H

, - , 112 X O'SiH "if'SiN] •

The weight of the leading reference CSF in the optimized CASSCF wave function is 92% with a very small contribution from rr ~ ~r * double excitations.

Table 9

Scaled rotational constants for H 2 SiN H (X IK)

Method A o (GHz) B o (GHz) C o (GHz)

M P 2 / 6 - 3 1 G * 138.502 16.764 14.954

MP2/6 -311 + + G * * 139.702 16.869 15.052

MP3/6-311 + + G * * 137.097 16.711 14.896

MP4/6-311 + + G * * 139.959 16.907 15.085

CCSD(T)/6-311 + + G * * 138.346 16.812 14.990

MCSCF/6-311 + + G * * 139.608 16.755 14.959

The geometries optimized ensuring a planar C s symmetry are collected in Table 8. Compared to HSiNH 2, the SiN bond is dramatically reduced by about 0.1 ,~ as a consequence of a stronger 7r bond: it averages around 1.60 ,~ which is also slightly longer than in HNSi or HSiN. The NH bond remains close to 1.01 ,~ while the Sill bonds are about 1.47

o

A, slightly shorter than in HSiNH 2, but almost iden- tical to that observed in HSiN. The /_NSiH angles are about 120 °, and again have only a slight dissym- metry relative to the SiN axis. The remaining/_SiNH angle is also in the vicinity of 120 ° . The energy gap from the lowest HSiNH 2 species is 16 kcal /mol, in accordance with previous calculations [50].

Scaled rotational constants are reported in Table 9. The high dipole moment, about 2.7 D, makes radio detection possible: if HNSi exists in space, which has been shown to be possible [55], then the dihydrogen adduct H 2 SiNH might also be present in the interstellar medium.

The vibrational spectrum is given in Table 10. The MPn and CCSD(T) approaches give very close

Table 8 Optimized structures, dipole moment /z and absolute energies for H2SiNH (Xl ,~)

Method SiN (A) Si l l I (,g,) S i l l 2 (,g,) Z_NSiH~ Z.NSiH 2 Z_SiNH 3 NH 3 (,~) ~ (D) E (au)

R H F / 3 - 2 1 G 1.611 1.469 1.482 118.2 127.8 118.2 1.002 2.28

R H F / 6 - 3 1 G * 1.573 1.463 1.475 119.6 128.7 126.7 0.997 2.67 RHF/6-311 + + G * * 1.569 1.464 1.475 119.9 128.5 128.9 0.995 2.98

M P 2 / 6 - 3 1 G * 1.617 1.473 1.489 117.0 130.6 120.7 1.020 2.24 MP2/6-311 + + G * * 1.614 1.463 1.477 118.0 129.9 119.3 1.017 2.65

MP3/6-311 + + G * * 1.597 1.463 1.475 118.8 129.9 120.9 1.001

MP4/6-311 + + G * * 1.622 1.465 1.478 117.6 130.2 118.2 1.019 CCSD(T)/6-311 + + G * * 1.616 1.467 1.480 118.1 129.6 118.9 1.018 MCSCF a/6-311 + + G * * 1.608 1.479 1.490 118.8 129.2 124.0 1.019 2.67

- 343.211214

- 345.051173 - 345.097431 - 345.317043

- 345.527652

- 345.538338 - 345.561932 - 3 4 5 . 5 6 0 9 0 9

- 345.239776

a See text for details.


y.

X , v

z

~v

0

v -<

.=_

o

e .

.=_

e .

2~ E

e~


results when wave numbers are considered, and they are not so far from the MCSCF values as long as only high-energy vibrations are concerned. Scaled CCSD(T) vibrational wave numbers are in remark- able agreement with the experimental values [34]. A theoretical prediction of an IR signature should not however be limited to the determination of wave numbers: the intensities of the transitions are equally important. Contrary to HSiNH 2, some significant differences in the relative intensities have to be pointed out when going from a level of theory to another. As an example, the relative intensity of the NH stretching mode reduces from 30.9% at the RHF/6-31G* level of calculation to 3.7% at the MP2 level. Significant differences also appear going from MP2 calculations to the MCSCF calculation: especially noticeable is the energy redistribution between the two Sill stretching modes. Only 3 features have been observed in laboratory experiments, that have been assigned to the symmetric and antisymmetric Sill stretching and to the SiN stretching modes. As seen from Table 10, the agreement of the scaled MCSCF values for these 3 modes is excellent. Unfortunately, Ref. [48] does not specify if only 3 features have been observed in the 220-3500 cm-J experimental window: the calculation predicts 3 other transitions at 583 cm-~ 792 cm-~ and 800 c m - l whose relative intensity are all strong enough to allow detection as shown in Fig. 7.

7. The floppy singlet ground state of HSiNH +

To our knowledge, there is no report of the spectroscopic identification of the HSiNH + cation while the carbon analogue HCNH + has been produced in laboratory experiments [56], identified in space [57], and proved to be a key intermediate in the H C N / H N C interstellar chemistry [58]. Some evidences for the existence of SiNH~- in mass spec- trometers have been reported [40], but it seems that HSiNH + has not been simultaneously produced in these experiments. On the contrary, HSiNH-, although not isolated from the spectroscopy viewpoint, has been shown to undergo in situ reactions with a large number of reactants such as CO 2, COS, CS 2, SO2, 02, C6F 6, CH3COOH or alcohols [59]. Some theoretical studies have been devoted to HSiNH +

I I 40"

2O'

0 . . . . . . . . i . . . . i . . . . t . . . . i . . . . i . . . . i , , , 4000 3500 ~ 2,500 ~ 1500 1000

Wavenumbers (cmq)

Fig. 7. Simulated (scaled MCSCF/6-311 + + G * * ) infrared spectrum of H~SiNH.

[31,33,40] that point to a singlet as the ground state but differ in the geometry: linear or bent?

A possible Lewis representation of the singlet ground state of HSiNH + is

( 1 S s i ) 2 ( I S N ) 2 ( 2 S s i ) 2 ( 2 p s i ) 6 ( O . N H ) 2 ( O . s i H ) 2

x

This suggests a triple bond and thus the positive charge located on the nitrogen atom. However, and according to the previous sections, a strong electronic transfer towards nitrogen is to be expected so that a better representation probably is

( l ssi )2 ( l s N )2 ( 2Ssi )2 (2ps i )6 ( O'NH )2 ( O'SiH )2 2 2 0

X(O'siN)2('rrsiN (spN) (SPsi)-

In accordance with atomic electronegativities, the formal Lewis positive charge has been shifted to silicon.

CASSCF calculations were performed using the space generated by the distribution of the 10 valence electrons into 10 active orbitals:

[ . . . . ],0 CrNH Crs~H CrsiN ~siN SpN SPs~ CrN, CrSiH O%~N "trS~N •

A first series of calculations was performed as- suming a linear structure for HSiNH + (Fig. le), in the A l representation of the C2v group to which states correlate. Proceeding this way, 5180 CSFs span the variational CASSCF space and the weight of the leading CSFs is 88% in the optimized wave function. The double promotion from the rrs~ N orbital to the rrs~ N orbital has a weight of 2%. The corresponding optimized geometries and energies

O. Parisel et al. / Chemical Physics 212 (1996) 331-351 345

Table 11 Optimized structures and absolute energies for linear HSiNH + (IX). A E (kcal /mol) is the relative energy to SiNH~- (C 2v-X IA I) which is the absolute minimum of the (H, H, Si, N) + potential energy surface. £ stands for transition state structures

Method SiN (fk) Sill (,~) NH (,~) Energy (au) A E

RHF/3-21G 1.517 1.450 0.996 - 342.341983 77.7 RHF/6-31G * 1.480 1.449 0.994 - 344.159086 64.5 RHF/6-311 + + G" * 1.479 1.452 0.995 - 344.200260 65.2

MP2/6-31G ' 1.524 1.464 1.014 - 344.418653 51.2 £MP2/6-311 + + G * " 1.521 1.455 1.0l 1 -344,610021 52.6 zMP3/6-311 + + G" * 1.500 1.454 1.004 -344.611012 61.5

~MP4/6-311 + + G * * 1.530 1.457 1.012 - 344.639354 53.6 "CASSCF/6-311 + + G * " 1.516 1.477 1.017 - 344.358345 50.3

have been collected in Table 11 and the corresponding vibrational wave numbers in Table 12.

The SiN bond length increases to about 1.52 /k when correlation is taken into account; this bond is however significantly shorter than those observed in the SiN radical or in HNSi (SiN X 2E: r = 1.572 [45], HNSi X~E+: r = 1.551 ,~ [37]) which indicates a stronger multiple bond. The NH bond remains close to 1.01 A and the Sill bond close to 1.46 ,~. The Mulliken analysis leads to atomic charges of +0.81 for Si, - 0 . 4 2 for N, +0.45 for the hydrogen atom bonded to nitrogen and + 0.17 to the remaining hydrogen. Adding hydrogen contributions to those of the bonding heavy atom gives: + 1.26 on Si and - 0 . 2 6 on nitrogen, which localizes the positive charge entirely on the silicon atom and shows a 0.26 electron transfer from silicon towards nitrogen. At the NBO level of analysis (MP2/6-31G*) , the charge repartition becomes + 1.60 on Si, - 1.07 on N, +0.50 for the hydrogen atom bonded to N and -0 .03 to the remaining hydrogen, which shows a larger electronic transfer from Si to N relative to the

Mulliken results. Inspection of the natural orbital leads to a sp Ll° hybridization on N for the NH bond, and to a n s p 0"99 hybridization on Si for the Sill bond. An sp t°3 hybridization is furthermore found for the SiN bond. Moreover, 80% of the electronic density of the crs~ N bond reside on nitrogen, among which 52% come from s N atomic orbital and 47% from the PN orbitais. On the contrary, the 20% silicon remaining counterpart originates by 50% from Ss~ and by 50% from Ps~ atomic orbitals: it is significantly different from what has been seen previously for HSiN, HNSi, HSiNH 2 and H2SiN in which the contribution of the Ps~ atomic orbitals was by far larger. The ~rsi N bond also presents the same electronic transfer towards nitrogen: 76% of the electronic density is located on this atom. Such a distribution is however smaller than discussed for the compounds studied previously and agrees with a stronger multiple bond.

As pointed out in Table 12, linear structures obtained at correlated levels of wave function all are transition states: the imaginary frequency corre-

Table 12 Scaled vibrational HSiNH + ( rE )

wave numbers (cm -j ) with normalized intensities, absolute total intensities 1 (KM/Mole ) for the singlet conformer of

MP2/6 -31G* , MP2/6-311 + + G " ", CASSCF/6-311 + + G * *, / = 758 l = 764 I = 675

MP4/6-311 + + G* *

Vibration Wave number Intensity Wave number Intensity Wave number Intensity Wave number

Antisymm. bending 128i 4.8 221 i 7.1 55i 9.9 313i

Symm. bending 587 10.0 548 7.7 560 9.8 533 SiN stretching 1188 0.3 1194 0.1 1276 0.4 1160 SiH stretching 2188 14.3 2181 18,4 2110 13.5 2198 NH stretching 3334 70.6 3333 66.7 3398 66.4 3391


Table 13 Optimized structures and absolute energies for the trans-bent singlet conformer of HSiNH ÷ ('A~). AE (kcal /mol) is the relative energy to SiNH~ (C2v-X IA I ) which is the absolute minimum of the (H, H, Si, N) ÷ potential energy surface

Method SiN (~,) Sill (,~) NH (,~) SiNH (o) HSiN (o) Energy (au) AE

MP2/6-31G * 1.534 1.466 1.017 159.61 158.70 -344.418904 51.1 MP2/6-311 + + G * * 1.536 1.457 1.014 157.49 158.97 -344.610561 52.2 MP3/6-311 + + G* * 1.502 1.454 1.005 168.77 170.10 -344.611056 61.4 MP4/6-311 + + G * * 1.562 1.463 1.018 149.18 148.79 - 344.641536 52.3 CCSDT/6-311 + + G * * 1.543 1.463 1.014 152.84 151.60 - 344.6374887 55.3 CASSCF/6-311 + + G * * 1.519 1.478 1.017 170.65 171.17 -344.358342 50.3

sponds to the antisymmetric bending mode that tends to deform the molecule towards a trans-bent structure.

A second series of calculations was then performed in C s symmetry: the results are gathered in Tables 13 and 14. Such calculations involve 19404 CSFs in the CASSCF space (Af representation). As seen in Table 13, the departure from linearity is very weak at this level of theory. The SiNH and HSiN bond deviations from the SiN axis are only about 10°; such values are also observed at the MP3 level of calculation. Deviations are more pronounced at the MP2 and MP4 levels of theory: they reach up to 30 ° so that further conclusions from single-reference approaches may be hazardous. The CASSCF SiN bond length is increased by 0.003 ,~ in the trans-bent form relative to the linear one, as is the Sill bond length by 0.001 A. The NH bond remains un- changed. As a consequence, the NBO analysis does not reveal any significant modification relative to the linear form.

As seen in Table 14, all vibrational wave numbers are positive in the planar conformation which con-

firms the stability of the trans-bent structure. The comparison of absolute energies at a given level of calculation for the linear (Table 11) and the planar (Table 13) structures shows however a very low energetic separation (at the CASSCF/6-311 + + G * * level of calculation, there is no difference within the accuracy of the numerical procedure). Since the trans-bent structure has no imaginary frequency, contrary to the linear one, there is no doubt that its absolute energy has to lie below that of the linear form, which is observed at the MPn levels of calculation: a separation of about 1.4 kcal /mol is found at the MP4/6-311 + + G * * level of theory. At this stage, zero-point vibrational energies (ZPE) must be taken into account. Using scaled MP4 frequencies, the ZPE-corrected energies becomes -344.621547 au for the trans-bent structure and -344.623184 au for the linear form. The trans-bent structure is then higher in energy than the linear one by a significative amount (360 cm- l ) : there is thus no activation barrier for the trans-bent inversion of HSiNH ÷ through the linear form. It follows that the discussion whether the structure is linear or not

Table 14 Scaled wavenumbers (cm ~) with normalized intensities, absolute total intensities 1 (KM/Mole) for the trans-bent singlet conformer of HSiNH + (IA~)

MP2/6-31G*, MP2/6-311+ +G**, CASSCF/6 -311+ +G**, MP4/6-311 + +G** I = 710 1= 717 1= 633


a ' -S iH-NH antisymm. bending 207 5.4 248 6.0 164 6.6 369

a ' -S iH-NH symm. bending 560 12.0 557 12.1 563 9.6 547 a"-SiH-NH out of plane 580 10.2 560 9.0 573 10.8 564 a '-SiN stretching 1147 1.6 1153 1.3 1252 0.6 1088 a '-SiH stretching 2174 10.8 2167 14.3 2118 12.1 2163 a ' -NH stretching 3303 60.0 3300 57.3 3379 60.3 3324


_=

4000 3500 3000 2500 ~ 1500 1000 500

Wavenumbers (cm-1)

Fig. 8. Simulated (scaled CASSCF/6-311 + +G * * ) infrared spectrum of HSiNH ÷ (floppy singlet ground state).

according to the various possible levels of calculation or basis sets used is a purely academic problem. However, it must be pointed out that such a discussion assumes a gas phase hypothesis: an activation barrier might exist if the molecule is trapped in a matrix, which will have the molecular propensity to floppiness reduced. Moreover, the barrier could also appear upon the substitution of at least one hydrogen by heavier groups.

If one now turns to the CASSCF IR calculation (Fig. 8), no significant differences in the wave numbers and in their relative intensities are observed between the linear and the trans-bent conformation. The CASSCF values for the trans-bent structure will thereafter be used to predict the IR spectrum of HSiNH ÷. The lowest mode that figures the linear- bent inversion motion appears at 164 cm -~ and might be difficult to observe using usual infrared spectroscopy techniques. The SiN stretching mode appears at 1252 cm -~ slightly higher than in HNSi and HSiN (1183 cm -~ and 1122 cm -~) but it has almost no intensity. The NH stretch at 3379 cm- (3600 cm -~ in HNSi) and the Sill stretch at 2118

cm -I (2251 cm -1 in HSiN) are slightly shifted towards lower energies as a consequence of the change in the hybridizations with respect to the linear triatomics.

Table 15 reports the scaled rotational constants B0(lin) for the linear structure, and B0(trans) and C0(trans) for the trans-bent geometry. An exact calculation of the rotational constants would require to average these values over the vibrational wave functions: such an approach is however beyond the scope of this paper. As seen in Table 15, B0(trans) and C0(trans), that would be equal in the case of a linear molecule, do not dramatically differ (0.2% at the most reliable CASSCF level of calculation). More- over, both are very close to the B0(lin) constant so that they can be reasonably taken as reliable theoretical predictions for supporting experimental interpre- tations. We finally recommend B 0 = 17.500 + 2% GHz for the rotational constant of HSiNH + in its singlet ground state. The dipole moment, evaluated at the center of mass of the molecule, is 2.58 D for both the trans-bent and the linear forms at the CASSCF level. Such a value should stimulate experimental and astrophysical searches.

Finally, it must be pointed out that all attempts to optimize a stable cis-bent structure for the singlet ground state of HSiNH + failed and led either to a linear or to a trans-bent geometry. Why the linear structure is stable contrary to a cis-bent one may be explained by the bonding overlap interaction between the nitrogen lone pair and the empty orbital localized on silicon. Going to a cis-bent structure has both the parallelism and the overlap of these orbitals reduced and thus has the bonding interaction less efficient (Fig. le and Fig. lg). At variance, the trans-bent structure still ensures the parallelism of both orbitals, but their overlap is again greatly reduced (Fig. l f). It has been known however for a

Table 15

Scaled rotational constants for the singlet ground state of HSiNH ÷

Method Bo(lin) (GHz) Bo(trans) (GHz) Co(trans) (GHz)

M P 2 / 6 - 3 IG" 17.372 17.396 17.216 MP2/6-311 + + G * * 17.416 17.454 17.266

MP3/6-311 + + G " * 17.381 17.420 17.374

MP4/6-311 + + G * * 17.411 17.459 17.081 CASSCF/6-311 + + G ° * 17.382 18.192 18.157


long time that electrons residing in lone-pair orbitals are more mobile than those residing in bonding orbitals. Such a mobility is enhanced when a lone pair is oriented trans to an empty orbital (Fig. l f) [60]: as a consequence, the floppy trans-bent structure is stabilized relative to the cis-bent structure. It is however highly possible that some excited states of HSiNH + (singlet or triplet) might have a linear or a cis-bent conformation.

8. The lowest triplet state of HSiNH +

A possible Lewis representation of the electronic distribution describing the 3,a/state of planar HSiNH + is

( l S s i ) 2 ( l S N ) 2 ( 2 S s i ) 2 ( 2 P s i ) 6 ( t rNH) 2 (OrSiH) 2

X(OrSiN)2(q1.SiN)2 ( S P N ) l ( S P s i ) l ,

which derives from the singlet state orbital occupancy by promoting an electron from the SPN orbital to the SPs i empty orbital.

As for the singlet state, CASSCF calculations were performed using the space generated by the distribution of the 10 valence electrons into 10 active orbitals:

[O,N H O'SiH O'SiN TI'SiN sPN SPsi O'NH O'sin O'SiN ,r/.SiN ] 10

Within this definition, 14 784 CSFs span the variational space in C s symmetry. The weight of the leading configuration in the optimized CASSCF wave function is 96% with a weight of 1% for the ~r 2 ('rr * )2 double excitation. Using the same electronic

distribution, the lowest 3A~' state has also been studied, but the optimized structure was found to lie higher in energy than the 3A~ state which is thus the lowest triplet state of HSiNH +. The 3M state will not be considered further in this report.

Contrary to Ref. [40] that concluded a trans-bent structure for the lowest triplet state, all attempts to find out a trans-bent or a linear structure for the lowest triplet state of HSiNH + failed, leading either to the departure of the hydrogen atom linked to silicon or to a cis-bent geometry. An explanation for the existence of a more favorable cis-bent structure might be that a strong overlap exchange interaction can occur between the singly-occupied in-plane orbital remaining on silicon, namely SPs~, and the singly-occupied in-plane lone pair located on nitrogen, Sps: such a stabilizing interaction is less efficient in a trans-bent structure (Fig. lh and Fig. li). Moreover, relative to a linear triplet conformation that would have the same orbital occupancy and thus the two singly-occupied orbital parallel, the cis-bent form has the Coulomb repulsion between the two electrons reduced.

The optimized structures for the a3A~ state of HSiNH ÷ are gathered in Table 16. Due to the triplet coupling of the two unpaired in-plane electrons, the SiN bond length is increased relative to the singlet

o

state and averages about 1.65 A. The Sill bond also slightly increases as the consequence of the lack of interaction between an empty neighbouring orbital, as is the case in the singlet state. The same situation prevails for the NH bond. Departure from linearity is by far larger than that observed in the floppy singlet state: relative to the SiN axis, the deviation is about

Table 16 Optimized structures and absolute energies for the cis-bent a3A ' state of HSiNH +. AE (kcal/mol) is the relative energy (C2v-X tA1) which is the absolute minimum of the (H, H, Si, N) + potential energy surface

to SiNH~

Method SiN (,~) Sill (,~) NH (,~) SiNH (°) HSiN (°) Energy (au) A E

ROHF/3-21G 1.679 1.479 1.008 159.21 116.03 -342.335672 81.7 ROHF/6-31G ° 1.632 1.467 1.002 159.82 116.60 - 344.148480 71.2 ROHF/6-311 + + G * * 1.628 1.471 1.002 159.82 116.80 - 344.188756 72.5 MP2/6-31G * 1.651 1.493 1.020 159.03 115.30 - 344.347865 95.9 MP2/6-311 + + G ° * 1.646 1.484 1.017 158.39 115.31 -344.538889 97.5 MP3/6-311 + + G * * 1.643 1.485 1.015 158.57 115.34 - 344.558703 94.5 MP4/6-311 + + G * * 1.651 1.490 1.020 158.10 114.98 -344.571134 96.7 CASSCF/6-311 + + G * * 1.654 1.478 1.026 157.96 115.38 - 344.289237 93.9


Table 17 Scaled rotational constants for the cis-bent a3.~/ state of HSiNH ÷

Method A o (GHz) B o (GHz) C O (GHz)

MP2/6-31G * 275.582 1 6 . 6 0 5 15.662 MP2/6-311 + + G * * 276.982 16.681 15.733 MP3/6-311 + +G* * 269.887 1 6 . 3 0 8 15.379 MP4/6-311 + +G* * 275.644 16.761 15.801 CASSCF/6-311 + +G* * 277.078 16.457 15.534

20 ° for the SiNH bond, but raises up to 65 ° for the HSiN bond. At the Mulliken charge level of analysis (MP2/6-31G*) , +0.92 is found on Si, -0.44 on N, + 0.40 on the hydrogen linked to the nitrogen, and +0.05 on the remaining silicon bonded hydrogen; on the other hand the NBO analysis reports 1.48 on Si, - 0 . 8 0 on N, +0.47 on the hydrogen linked to N, and - 0 . 1 5 on the remaining Si-bonded hydrogen. Although presenting noticeable differences, both population analysis agree with the a priori electronic distribution given above. As in other molecules studied in this report, the arsi N and the trsi N bonds are highly polarized: for each bond, about 85% of the electronic density resides on the nitrogen atom. The Grsi N bond is built on almost equal contributions from s N and PN atomic orbitals but the silicon counterpart has a 17% Ssi atomic orbital character and more than a 80% Psi atomic orbital contribution. The singly-occupied orbital on the silicon atom can be seen as an sp °'48 hybrid whereas the one located at the nitrogen atom is an almost pure in-plane 2PN atomic orbital (88% for the PN contributions). Both the Sill and the NH bonds closely correspond to an sp 2 hybridization.

~ -

2 0

Wavenumbers (cm-1)

Fig. 9. Simulated (scaled CASSCF/6-311+ + G * * ) infrared spectrum of HSiNH + (cis-bent a3g state)

From the energetic point of view, the a3A~ state lies 45 kcal /mol above the singlet ground state.

The scaled rotational constants A 0, B 0 and C O are collected in Table 17. Compared to the large value obtained for the singlet ground state (2.58 D), the dipole moment, computed at the center of mass, is reduced to 0.50 D for the lowest triplet state.

The vibrational wave numbers and intensities are reported in Table 18. Significant differences occur when comparing MP2 or MP4 calculations to the CASSCF treatment, which still points at the need for a multireference approach to deal with such a species. Relative to the singlet state, the SiN stretching mode is lowered in energy as a consequence of a longer bond length. On the other hand, the NH and Sill stretches are slightly shifted to higher energies. Turn- ing now to the CASSCF intensities, the Sill stretching mode is almost completely extinguished while the SiN stretching mode now gets a weak intensity: the situation is reversed compared to the singlet

Table 18 Scaled wavenumbers (cm t ) with normalized intensities, absolute total intensities / (KM/Mole) for the cis-bent 3g state of HSiNH ÷

MP2/6-31G *, MP2/6-311 + + G * *, CASSCF/6-311 + + G* * MP4/6-311 + + G* * I = 805 I = 798 / = 762


a"-SiH-NH out of plane 317 26.5 264 26.5 292 27.2 23 I a ' -SiH-NH symm.

bending 527 9.5 507 8.1 348 8.9 516 a ' -SiH-NH antisymm.

bending 715 11.5 725 12.1 544 12.3 725 a'-SiN stretching 1013 8.0 1013 9.7 917 8.0 1009 a'-SiH stretching 2130 0.4 2018 0.3 2193 0.3 2002 a'-NH stretching 3472 44.1 3544 43.3 3484 43.3 3569

350 O. Parisel et al. / Chemical Physics 212 (1996) 331-351

ground state. The CASSCF simulated infrared spectrum is given in Fig. 9.

9. Conclusion

In this contribution, the microwave and the in-

frared signatures of 5 different species related to the chemistry of the H - S i - N system have been reported. A series of comparisons with the available

rotational and vibrational experimental spectra has led to the determination of accurate scaling factors used to correct crude ab initio results.

The need for multireference approaches, such as MCSCF calculations, to properly predict the IR spectra ( w a v e numbers and intensities) of some of the species investigated here has been clearly illustrated: non-dynamic correlation effects have been pointed out to be especially important in the case of HSiN. More generally, M C S C F calculations appear necessary as soon as the electronic structure involves interactions between holes and lone pairs or very unbalanced charge distributions so that accurate electron densities, and accurate derivatives as well, can be obtained. In some cases however, the usual MPn approaches have been found to be of enough quality, but this should certainly not be considered as the rule: owing to the large flexibility in the bonding character of the silicon atom, results always should be considered with an extremely critical mind.

Using proper theoretical methodologies, agreement with experiments for the HNSi, HSiN, HSiNH 2 and H2SiNH signatures has been found to be excellent. Based on that experience, the signatures of the HSiNH ÷ cation, either in its f loppy singlet ground state or in its cis-bent lowest triplet state, have been determined with a reduced error bar. We hope that these calculations will stimulate experimental works on this still-unknown cation and will help in the discussion of laboratory results and in the interpretation of possible astrophysical observations.

Acknowledgements

Part of the calculations presented in this contribution were supported by the CNRS "Inst i tu t du D6veloppement et des Ressources en Informatique Scient if ique" (IDRIS) supercomputing center. This

research was also partly conducted with supercom- puter resources at the Jet Propulsion Laboratory, California Institute of Technology, under contract to

the National Aeronautics and Space Administration. We wish to thank N. Talbi for developing graphic

interfaces to our codes.

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