Ab initio study of the electronic structure of compounds with a double-bonded silicon atom

Journal of Molecular Structure, 54 (1979) 221-229 o Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

AB INITIO STUDY OF THE ELECTRONIC STRUCTURE OF COMPOUNDS WITH A DOUBLE-BONDED SILICON ATOM Part II*. HNSi

F. F. ROELANDTt,

D. F. VAN DE VONDEL and G. P. VAN DER KELEN

Laboratory for Genenzl and Inorganic Chemistry-B, B-9000 Ghent (Belgium)

University of Ghent, Krijgslaan 271,

(Received 5 January 1979)

ABSTRACT Ab initio LCAO-MO-SCF calculations have been carried out on HNSi, with a number of different basis sets. The geometry of this molecule was optimised: R(Si-N) = 1.557 A, R(N-H) = 0.997 A and LH-N-Si = 180”. Using a harmonic force field, the force constants and vibrational frequencies are calculated and compared with the experimental values. The electron distribution is studied in terms of a Mulliken population analysis, and the electrical dipole moment is discussed. INTRODUCTION

The study of unstable molecules often reveals quite unexpected bonding situations. Recently, there has been some interest in species of the type HAB, where A and B are atoms of the first and second period, respectively, e.g. HBS and HCP. In this paper we report some computational results on the analogous molecule HNSi. This molecule was detected some years ago by Ogilvie and Craddock [ 21 during the photolysis of silylazide, SiH3N3,in a solid Ar matrix near 4 K. HNSi and the isotopic DNSi were characterized by their infrared spectra in. a solid matrix. From the force constants derived from this spectrum, Ogilvie and Newlands [3] determined a N-Si bond order of 2.7. COMPUTATIONAL

DETAILS

Ab initio LCAO-MO-SCF calculations were carried out on the lowest singlet state of HNSi with a number of different basis sets. Firstly, a set of pilot calculations were carried out using a minimal basis set (basis set I) of STO’s, each expanded into 3 GTO’s. The orbital exponents of the STO’s were taken to be those optimized for atoms, as given in the work of Clementi and Raimondi [4], though an orbital exponent of 1.25 was used for H. The expansion in GTO’s was carried out according to Stewart [ 51. *For part I of this series, see ref. 1. tAangesteld Navorser of the NFWO.

222

The second basis set (II) was built up from the following set of atomic basis sets [6-81: Si(12s9p/784p), N(985plrds2p) and H(4s/2s), where the notation should be obvious. This is of approximate double zeta quality. The basis set was then extended in two steps: firstly a set of 2p type polarization functions with orbital exponent 1.0 was added to the H atom (basis set III), and the extension was completed by adding the z2, xz and yz components of a set of Cartesian 3d GTO’s on Si (basis set IV). The orbital exponent of the 3d(Si) functions was optimized; a value of 0.5045 was obtained. All the calculations were carried out with a modified version of the POLYATOM program [9] on the Siemens 4004 computer of the Central Digital Computing Center, University of Ghent. RESULTS AND DISCUSSION

No experimental evidence for the equilibrium structure of HNSi exists. A number of calculations were therefore carried out with) basis sets I and II to determine the equilibrium geometry of this molecule. The results of these calculations are shown in Table 1, together with the geometry assumed by Ogilvie and Newlands [3]. Murrell et al. [lo] have recently published an ab initio study of HNSi, and the results of their geometry optimization are also included in Table 1. In all cases HNSi was found to be linear. This is in complete agreement with Walsh’s rules for molecules of the type HAB containing 10 valence electrons [ 111. The largest variation in the N-Si bond lengths quoted in Table 1 is 0.032 A. This bond length appears to be only a/few hundredths of an A smaller than the experimental bond length in SiN (1.571 A) [12]. On comparing the N-Si bond length in HNSi to the “mean” bond length of a single N-Si bond (1.71-1.78 A) [ 131, a considerable reduction is observed, which can be attributed to multiple bonding in HNSi. The only known experimental properties of HNSi are its vibrational frequencies. From these, Ogilvie and Newlands [3] calculated the force constants k of this molecule. They assumed a simple harmonic valence force field of the form 2V = k, Ar2 + kR AR2 + k, I2 Ae2 where V is the difference between the energy of the molecule at the geometry TABLE 1 Geometrical parametersof HNSi

R(N-Si) R(N-H) L(H-N-Si)

Basis set I

Basis set II

Ref. 3

Ref. 10

1.636 A 1.021 A 180’

1.557 A 0.997 A 180’

1.54 A 1.00 A 180’

1.526 A 0.986 A 180”

223

considered and that at the equilibrium geometry, r, R and 6 refer to the N-H and N-Si bond lengths and the H-N-Si bond angle, respectively. The factor l(= 1 A) is introduced to express S in the same units as k, and k,. Using basis set II we have fitted a few points of the energy surface around the calculated equilibrium structure to the equation of the harmonic valence force field. The increments Ar, AR and A0 were 0.03 bohr, 0.05 bohr and 3” respectively. The calculated force constants, and the vibrational frequencies derived from them, are displayed in Table 2, together with the results of Ogilvie and Newlands [3]. Although the sequence of the force constants is correctly reproduced, the stretching force constants k, and kR exceed the experimental values by 16% and 17% respectively. Such a deviation should be considered normal for the kind of calculations carried out here, as pointed out by Schaefer [14] and others. The main reason for the error is that the correlation energy is neglected in our calculations. The bending force constant k, , on the other hand, differs from the value obtained by Ogilvie and Newlands [3] by as much as 61%. The different equilibrium geometry assumed by these authors is not likely to affect this error by more than a few percent. Apart from the reason mentioned above, the bent form of HNSi may be stabilized by the contributions of configurations originating from one of the n-type configurations of the linear form to the ground state A’ species of the non-linear form [ 151. This type of correlation has been termed non-dynamical, and was also invoked by Preuss et al. [16] in an ab initio study of HCP. Due to the approximate square-root dependence of the vibrational frequencies on the force constants [12], the deviations of the frequencies from the experimental values are lower than those of the force constants; the deviations amount to 13%, 29% and 8% for vl, v2 and v3, respectively. The total energy and orbital energies obtained with the different basis sets are listed in Table 3. With respect to the atomic energies calculated from the atomic basis sets of basis set II, the atomization energy calculated with this TABLE 2 Force constants k (10’ Nm-‘) and vibrational frequenciesa Y (wavenumbers, cm-‘) of HNSi Calculated (basis set II)

4 kR ke “I Vl V3

8.978 9.765 0.2188 4037 676 1298

%,; (N-H)-stretching;

Ref. 3

7.732 8.305 0.1358 3583 523 1198

v2: bending; vl: (N-Si)-stretching.

224 TABLE 3 Total energy (hartree), virialand orbital energies(eV) of HNSi calculated with different basis sets I Total energy Viriai energy, -V/T Orbital energies 1U 20 30 40 In 50 60 70 2n

II

-339.918605 2.007 -1845.3 -418.2 -161.7 -108.7 -108.6 -29.35 -18.88 -10.32 -10.31

-343.909230 1.9998 -1E 2.4 -422.7 -167.7 -116.0 -116.0 -29.63 -19.56 -11.54 -10.96

IIP

lva

-343.915198

-343.951615

1.99996 -1872.5 -422.4 -167.7 -116.1 -116.0 -29.54 -19.42 -11.56 -10.87

2.0002 -1871.9 -422.6 -167.1 -115.5 -115.4 -29.36 -19.20 -11.51 -10.35

aAt equilibrium geometry calculated with basis set II.

basis set is 4.7 eV. This value is expected to be seriously in error because of the lack of any correlation contribution in our calculations. If we assume that the correlation energy for HNSi is of about the same order of magnitude as that in the isoelectronic molecule SiO, we can take the estimation of Yoshimine and McLean [24] i.e. 3.0 eV, for the correlation energy of SiO. This would then lead us to an estimated value of 7.7 eV for the atomization energy of HNSi. Comparing this value with the corresponding atomization energies of HBS and HCP [ 171, it is seen that HNSi is the least stable of the three molecules, a fact which could have been anticipated from the relative ease with which these compounds are handled experimentally. It is remarkable to note that basis set I predicts orbital energies corresponding to a near degeneracy between the 7a and 2n levels. This near degeneracy is removed completely for the more extended basis sets II-IV, The sequence of the orbital energies parallels the sequence in the isoelectronic compounds HCP and HBS, but is different from that in SiN [ 121, for which the order of the highest two levels is reversed. The nature of the MO’s of HNSi, which are very similar to those of HCP and HBS [ 17-201, can be studied by a Mulliken population analysis [ 211 of the electron distribution. The valence orbital populations and atomic charges calculated with each of the basis sets used are presented in Table 4. It is seen that, although the trends are much the same for all basis sets, the absolute values of the populations may differ significantly. Only the results of basis sets II and III are quantitatively similar for practically all populations. In Table 4, the largest differences occur on comparing the results of basis set I with those of sets II--IV. This is especially true for the PJ27r) populations, and (conse-

Q

P&27rx t 2ny)

PJJ(2%+2ny)

pd(7U)

pd(6c)

pdh’)

Ps(5u) P&W P&70) P,(54) PP(6c) P,(7c)

0.337

1.306

0.153 0.360 1.201 0.076 0.020 0.550

0.103 0.342 1.339 0.038 0.036 0.473

0.122 0.348 1.275 0.098 0.048 0.568 0.066 0.055 -0.041 0.798 0.816 0.780 0.078 0.856 0.848 0.596

0.117 0.323 1.350 0.047 0.034 0.470

IV

-0.580

2.694

1.574 0.003 0.051 0.006 1.109 0.141

I

III

I

II

N

Si

-1.245

3.202

1.642 0.004 0.034 0.007 1.249 0.113

II

-1.110

3.173

1.589 0.003 0.033 0.014 1.184 0.120

III

-0.859

3.129

1.506 0.001 0.034 0.001 1.078 0.118

IV

Muihken grossorbitai populations(P)forthevaience she&and atomiccharges(q)ofHNSi

TABLE4

II

III

0.244

0.194 0.459 0.046 0.014 0.010 0.000

IV

0.389 0.262 0.264

0.012 0.013

0.191 0.187 0.241 0.508 0.390 0.425 0.057 0.033 0.035 0.015 0.010 0.000

I

H

226

quently) the total charges. The discussion will therefore be limited mainly to trends that can be observed in the populations. In all cases the 50 MO appears to be an almost pure nitrogen 2s atomic orbital (AO). The 60 MO shows a considerable contribution from the 2p, orbitals of N, which overlap with the s(H) and s(Si) orbit& The extent of overlap can be judged from the Mulliken overlap populations given in Table 5. The N-H overlap population for the 60 MO is much larger than the N-Si overlap population, which on the whole resembles the overlap population of the 5a MO. We therefore conclude that the 60 MO is primarily o(N-H) bonding, and to a lesser extent, u(N-Si) bonding. The nature of the 70 MO can be unambiguously inferred from the gross A0 populations, as well as from the negative N-Si overlap populations: it is a very pronounced lone pair orbital on the Si atom. The electron distribution in the 2n MO is shown to be strongly polarized toward the N atom by the ratio of the Si and N P(2n) values given in Table 4. The minimal basis set is probably not flexible enough to locate a higher n electron density on the N atom. Going to basis set II, a large transfer of electron density to N is observed and this is also shown clearly in Fig. 1. The increase of the electron density in the outer regions of N is to be especially noted. The greater overlap populations for the 2n orbit& (Table 5) may indicate that the N-Si bonding is mainly a result of these 2a MO’s. From the values of the d orbital populations, we see that adding 3d orbitals has about equal effects on the u and a parts of the molecule, even though two 3d orbitals with n symmetry and only one with u symmetry were used. The overall effect of the 3d orbit& on the charge distribution is quite complex, as may be seen from Fig. 2. Note, in particular, the increase of electron density in the middle of the N-Si bond, which is consistent with the large total N-Si overlap population for basis set IV, given in Table 5. Consider the charge redistribution on molecule formation for basis set II, as shown in Fig. 3. It is apparent that the electron density is increased in the Si lone pair region and in the N-H bonding region, whereas it is decreased in the extra-molecular H region. A shift of electron density towards the N atom in the N-Si region, also takes place. Although we could formally describe HNSi with a triple bond between N TABLE

5

Valence orbital overlap populations p in HNSi N-H

N-Si I PSU P60 P70 Pwr(?l~+ Total ny)

0.296 0.246 -0.254 0.689 0.977

II 0.201 0.294 -0.678 0.706 0.523

III

IV

0.170 0.299 -0.672 0.711 0.508

0.348 0.332 -0.288 0.792 1.184

II

III

0.247 0.460 -0.001

0.242 0.411 0.015

0.706

0.668

0.315 0.434 0.015 0.022 0.786

I

IV 0.266 0.422 -0.011 0.023 0.700

227

-

Ap-33

-Ap>o

A.U.

,

’

Angstrom

-Ap=o

’

’

’

’

’

Fig. 1. Difference density Ap plot of the 2n MO density of HNSi for basis sets II and I: Ap(r) = IJ/$(r)l’ - I& @)I’. The absolute values of the difference densitiesplotted are 0.0, 0.0002; 0.001, 0.004, 0.02, 0.1 and 0.4 e- bohrl.

-

Apco Ap>o

Angstrom

-Ap=o

A.U.’

-I ’

’

I

’

Fig. 2. Difference density Ap plot of the total molecular charge density of HNSi on adding *I1 (r). For difference density values, 3d(Si) orbitals to the basis set: Ap(r) = p&si(r) - pHNSi see Fig. 1.

and Si (6a, 27r,, 27r,), the relatively small N-Si interaction in the 6a MO and the great polarity of the 2n MO’s lead us to consider a bond order lower than 3, and possibly even approaching 2, as also suggested by Murrell et al. [lo] from the double occupation of the 3s(Si) orbital. It is difficult to assess the N-Si bond order by comparison of the’ N-Si stretching force constant k, (derived from the experimental vibration frequencies) with the corresponding force constant of molecules with a single N-Si bond, since the values for this

228

-

-

Apco Ap>o

-Ap=o

’

Angstrom

I

A.U. -’

Fig. 3. Difference density Ap plot of the total molecular density of HNSi and the sum of atomic densities for basis set II: Ap(r) = p zNSi(r) - c p ‘,‘,(r). For difference density values, see Fig. 1.

latter force constant are spread over a wide range, 2.5-4.45. lo2 Nm-‘, as shown by Burger [13]. Finally, we shall discuss the dipole moments calculated using each of the basis sets I-IV: Basis set: Dipole moment (Debye):

I -1.98

II +0.65

III +0.60

IV +0.20

A positive sign indicates a direction (-)HNSi(+). The large variation of the dipole moment with the choice of basis set was also found for the isoelectronic molecules HCP and HBS. For HCP, calculated values of 0.353 D and 0.998 D are reported by Thomson [ 171 and values of 1.28 D, 1.08 D, 0 .ll D and 1.2 D by Van Wazer et al. [ 191; the experimental value is 0.39 D [22] . For HBS, values of 2.01 D (Gropen and Wisl$ff-Nilssen [ 201) and 0.79 D (Thomson [ 181) were obtained, while the experimental value is 1.30 D [ 231. For HNSi, there is a change in the sign of the dipole moment in going from the minimal basis set (I) to the basis sets of about double zeta quality (II-IV). The origin of this drastic change lies in the large transfer of n electrons from Si to N that occurs in the 2n MO, as discussed previously. It should also be noted that the value of the dipole moment appears to be very sensitive to changes in the value of the orbital exponent of the 3d orbitals on Si. If this is changed to 0.6, the dipole moment increases to 0.37 D. ACKNOWLEDGEMENTS

We wish to express our gratitude to Prof. Dr. Z. Eeckhaut for stimulating discussion. One of us (F. F. R.) acknowledges the Belgian National Foundation for Scientific Research (NFWO) for financial support.

229

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