Theoretical rotational—vibrational spectrum of SiH2 (X 1A1 and a 3B1)

Chemical Physics 174 ( 1993) 45-56 North-Holland

~~eor~ti~a~ rotations-vibrational of SiH2 (X ‘Al and a 3B1)

sp~~t~rn

Wolfgang Gabriel, Pave1 Rosmus * Fachbereich Chemie der Unrversttci:. W-6000 Frankfurt. Germany

Koichi Yamashita 2, Keiji ~orok~ma

3

Instrtutefor Molecular Science, Okazaki 444, Japan

Pa010 Palmieri ~~partime~to di Chimica Fisica ed Inorganrca, Universitd di Bulogna, 1-40136 &&gnu, &a&

Received 28 January 1993

The three-dimensional potential energy and electric dipole moment functions of the X ‘A, and a 3B, states of SiHs have been calculated from highly correlated CEPA electronic wavefun~ions. The analytic rep~sentations of these functions have been used in perturbational and variational calculations of the rotationally resolved absorption spectrum of X ‘A, SiHs. In the variational calculations all anharmonicity effects and vibration-rotation couplings have been considered. The equilibrium spectroscopic constants for SiH,, SiD2, and SiHD (X ‘A, and a3Bt) isotopomers and absolute integrated band intensities are given. The calculated vibrational band origins agree to within 1O-40 cm-’ with available gas phase experimental values. It has been shown that due to strong Fermi resonances the 1vr and 22+ bands have almost equal integrated band intensities in the absorption spectrum and overlap with the 1z+ band between 1800 and 2300 cm-‘. For the most intense transitions absolute line intensities are given. in the electronic ground state of SiH2 the vibrational band intensities of the fundamental absorption transitions are found to be more intense than the pure rotational transition in the vibrational ground state.

Silylene, SiH2, plays an implant role in the thermal, electrochemical, photochemical and chemical vapor decomposition (CVD ) processes of silanes and organosilanes [ l-8 1. The latter processes are of considerable interest because of their use in the production of amorphous silicon. The first spectroscopic study of SiHz was performed by Herzberg [ 9 1, who investigated the photolysis of phenyisilane by ultra’ Visiting Fellow 1992-1993, University of Marne la Vallee, France. 2 Permanent address: Institute for Fundamental Chemistry, Kyoto, Japan. 3 Permanent address: Department of Chemistry, Emory University, Atlanta, GA, USA.

violet light. He detected many lines in the region 6500-4800 A. By comparison with the available spectrum of CH2, the lower state of the electronic spectrum has been assigned to the singlet ground state, X ‘AI, of SiHz. Dubois [ 111 photolyzed silane directly and obtained from the analysis of the spectrum rotational and centrifugal distortion constants for the electronic ground state (X ‘AI ) and for the first excited singlet state (A ’ B i ) , as well as the bending fundamental frequency of 1004 cm-‘. An extensive study of infrared and vacuum photolysis of silanes was performed by Milligan and Jacox [ 12 1. The products were trapped and identified in an argon matrix at 14 K. The fundamental vibrational frequencies of SiH:! were reported to be vr ~2032 cm-‘, v2= 1008 cm-‘, and v,=2022 cm-‘. The reaction of silicon atoms

0301-OIO4/93/$06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.

46

W. Gabriel et al. /Chemical Physics 174 (1993) 45-56

with molecular hydrogen was studied by Fredin et al. [ 13 1, who found v,= 1964.4 cm-‘, v,=994.8 cm-l, 2~,=1992.8 cm-‘, and v3=1973.3 cm-‘. Besides these studies in low-temperature matrices a number of investigations using absorption and emission spectroscopy and laser-induced fluorescence (LIF) were performed [ 14-181. Yamada et al. [ 191 used infrared diode laser spectroscopy and the ArF laser photolysis of phenylsilane to study SiH2. They analyzed the v2 band of X ‘A, SiH2 and the band origin for the bending frequency was found to be vZ= 998.6 cm-‘. Recently, based on the LIF excitation spectra of the A ‘B, (0, 6, 0)+X IA, (0, v2, 0) transitions, Ishikawa and Kajimoto [ 20 ] investigated the Fermi resonances in the singlet ground state and reported band origins for several low lying vibrational states. Fukushima et al. [ 2 1 ] generated silylene and SiD2 by ArF laser photolysis of phenylsilane and measured the fluorescence spectra for the u2 vibronic bands of the A ‘B,-X ‘A, transition. To date, no experiments h&b resolution data exist for the a 3B, state of silylene. The singlet-triplet separation was reported by Kashdan et al. [ 22 ] to be 14 kcal/mol from a photoelectron detachment of the silylene anion SiH, . In an extensive study Berkowitz et al. [ 231 examined the decomposition of silanes and reported a singlet-triplet seperation of 2 1.Okcal/mol. Silylene was the subject of many theoretical investigations [ 24-48 1. A review of these studies was published recently by Allen and Schaefer [ 431. Very recently, Duxbury et al. [ 491 investigated the RennerTeller and spin-orbit interactions in SiH2. In the present work we have calculated for the first time spectroscopic data based on three-dimensional theoretical near equilibrium potential energy functions (PEFs) and electric dipole moment functions for the X ‘Al and a 3B, state of SiH, using highly correlated CEPA. electronic wavefunctions. The variationally calculated rotation-vibration spectra consider all anharmonicity and vibration-rotation coupling effects. In section 2 the electronic structure and nuclear motion calculations are described. In section 3 the properties related to the near equilibrium PEFs of the X ‘A, and a 3B, state are reported. In section 4 the electric dipole moment functions and integrated band intensities are discussed. The last section 5 deals with

the theoretical rotationally resolved spectra of X ‘A, SiH2.

2. Electronic structure and nuclear motion calculations In the calculation of the potential energy and electric dipole moment functions highly correlated electronic wavefunctions obtained by coupled electron pair approach (CEPA) [ 50-521 were used. The version 1 of CEPA was employed. The Gaussian basis set comprised 143 primitive basis functions contracted to 105 groups. For silicon the s and p basis consisted of the ( 17s 12p ) set of Partridge [ 53 ] contracted to [ 11s8p], for hydrogen the (8s) set of van Duijneveldt [ 541 was contracted to [ 4~1. These basis sets were augmented by four d and two f functions on Si and three p and one d set on H. The p function exponents were chosen to be 1.8, 0.6, 0.2 for H and the d function exponents to be 2.1, 0.9,0.4,0.15 for Si, and 0.7 for H. The exponents of the f functions for Si were chosen to be 1.6 and 0.55. All valence electrons were correlated. The dipole moments were calculated as expectation values of the CEPA wavefunctions. For the solutions of the nuclear motion problem perturbational [ 551 and variational approaches [ 561 were employed. The variational calculations of the ~bration-rotation energy levels were ~~o~ed with the nuclear motion Hamiltonian in internal coordinates [ 571. The vibration-rotation wavefunctions consisted of products of Morse oscillator functions for the symmetric stretch coordinate, harmonic oscillator functions for the asymmetric stretch coordinate, and associated Legendre functions for the bending coordinate. For details of the method we refer to refs. [ 56,581.

3. Near equilibrium potential energy functions of SiH, (X ‘Al and a 3B,)

The calculated CEPA energies for 48 geometries in the vicinity of the equilibrium were fitted to a polynomial expansion in bond stretching and angle bending coordinates:

W. Gabrwl et ai. / Chemxal Physrcs I?4 (19930 45-56

J’CQ,,

Qz,

Q3)

=

C

CdQ, )‘(Qd’fQdk.

The Simons-Pan-FinIan (SPF) coordinates Q= RSPF== 1-RJR have been used for the stretches (Qi and Q,), the bending coordinate Q3 was expressed in terms of a cubic expansion in @=LY-_(y, as Q3=A,,8+A,@+A@. This coordinate 1591 was chosen to satisfy the condition Q3( 8= 180” ) = 1 and dQ,/dB= 0 (for @= 180” ) . The A0 parameter was set to be 1.2 for the singlet and 1.7 for the triplet state. The analytic expansions are given explicitly in tables 1 and 2. For the dipote moment functions of both states displacement coordinates Q= R - R,have been used (cf. section 4). The singlet-triplet separation has been calculated to be 19.9 kcal/mol (cf. the difference between the Cm0 coefficients in tables 1 and 2) which is in good agreement with the value of 2 1.O kcalfmol reported by Berkowitz et al. 1231 derived from a photoelectron spectrum. The crossing seam between the X *Ai and the a 3B, states has been calculated to lie about 1600 cm-’ above the minimum energy of the a 3B, potential energy functions (cf. fig. 1). Already low

47

lying levels in the triplet state will be perturbed by the singlet state. The potential energy functions in tables 1 and 2 are expected to be valid in the geometry range rsi_H= LO4.0 a0 and (Yu_s,_n=60e-i 50”. The functions in tables 1 and 2 were reexpanded in the form of quartic force fields in internal coordinates (cf. table 3 ). The internal force fields were then transformed using Itensor algebra 1601 to the quartic force fields in dimensionless normal coordinates. Based on perturbation theory these data were employed in calculations of the spectroscopic constants [ 5 5 1. In tables 4 and 5 we give full sets of these constants for SiH2, SiD,, and SiHD ( X ‘A, and a 3BI ) . The data are compared also with the available theoretical results of Allen and Schaefer [ 43 1. Their harmonic frequencies based on CI calculations are somewhat larger for all three modes of X ‘A1 SiH2. Besides the w2 frequency this is also the case for the triplet state. As found by Allen and Schaefer [ 43 1, the harmonic frequencies for the Si-H and Si-D stretches of SiHD are nearly exactly the average of the symmetric and asymmetric stretches of SiHz and SiDz. (cf. table 4). The sets of our 11!values for both states are in good agreement

Table

1 Expansion coefficients of the three-dimensional near equilibrium PEF and dipole moment surfaces of X ‘A, SiH2 (in au) Potential energy surface (C,=

C,sk) a)

Dipole moment surfaces x component ( C,,k= C,,,)

2 component ( C,, = - C,rk)

a) Reference geometry: R, =Rz=

C,, -290.1757118 C 101 0.0180646 Go 0.0329582 C *CL? -0.0293966 G20 0.0546296 Gz, -0.2800989 c 103 0.0069205

c 2oo 0.6505253 C wz 0.0525320 c 201 0.0000841 Cm3 0.0110257 c,,, -0.1518485 C,,, - 0.0529250 C,, 0.0236468

cIto 0.0117717 C,, -0.1738588 C,, , -0.0744888 C,, -0.2186821 c,, -0.0930353 C 112-0.0949413

Cow Gxl Go2 C 201 CC%3 G,@ C ‘IZ GM

0.09161 -0.05160 0.19045 -0.06316 -0.06799 0.31 I40 0.15163 -0.19566

C,, -0.30724 c,,, 0.03194 c,, 0.04495 C, at -0.24998 c 400 0.05281 C,,, - 0.10244 C 022 0.05384

0.51768 C,, c ,,,, -0.02314 0.08331 C,,, c 0,2 0.06177 C,,, -0.07892 c,,, -0.15313 C ,0, 0.05732

C*00 - 0.34972 C 300 0.04378 C LO2 0.04817 Go, -0.05655 C4W 0.02018

C,, -0.06584 C,,, -0.04132 c ,#J3 0.01835 C 21, 0.19595

c ,*s 0.04393 C,,, -0.03721 0.00806 c,,, c,, -0.07159

1.5168 A, ~~=92.040”.

48

W. Gabrielet al. I Ckemic5i P#zpfcsI14 (1993) 45-56

Table 2 Expansion coefftcients of the three-dimensional near equilibrium PEF and dipole moment surfaces of a 3BI SiHs (in au) Potential energy surface ( C,,= C,&*)

Dipole moment surfaces x component ( CUk=C,,,)

c 200 0.7310662 c Q@s 0.02 13667 C,,, 0.0113266 C,, 0.0065000 C,,, 0.3624345 c,,, -0.0454507 C,, 0.0013942

C,,, -0.0152636 C,, -0.1981094 C ,,r -0.0085868 C,, -0.8756074 Cro2 0.2397708 C ,,a 0.0011666

-0.01749 0.02180 0.~990 -0.O4011 -0.10156 0.21828 -0.26479 0.10217

c 100 -0.06775 C l,D 0.01504 &NJ 0.00313 C,,, -0.11336 Cda, - 0.0660 1 c 30, 0.02528 co,, 0.009 14

c,, 0.46579 C,,, -0.07426 c 210 0.00794 Co,, -0.12496 CszO-0.18576 C,,, -0.05260 C ,03 -0.25977

-0.16661 0.02132 0.01727 -0.08536 -0.04947

c,

c 10% 0.11135 c 201-0.03435 c 3t0 0.03583 c so2 0.07641

C, - 290.1440123 C 101 0.0041913 Cz*o - 0.0326903 C LO2 -0.0028465 GO -0.9070946 Cl21 0.0967887 c 103 0.0082041

Fig. 1. Contour plots of the CEPA potentials for the X ‘A, (ru,=92O ) and a ‘Br (cyc= 118” ) electronic states of SiHs. The contours are plotted in steps of loo0 cm-’ relattve to the minimum energy of the X ‘At state, the crossing seam is indicated by a full line.

with their results as well (cf. table 4B). Table 6 contains the experimental determined spectroscopic constants for silylene, reported by Dubois et al. [ 111

c210 C, c,,,

-0.02997 0.00668 0.02023 -0.03900

and Yamada et al. [ 19 ] . Our rotationa constants A and B agree well with both experimental values, the C constant is larger by about 0.05 cm-“‘. Yamada et al. f 191 reported the Si-H bond distance larger by 0.002 A, the error in calculated bond angle is only 0.04”. The centrifugal distortion constants r of Yamada et al. [ 19 ] agree within 2-8Oh with our results, whereas the deviations from the values from Dubois [ 10 ] are larger. Table 8 contains the vibrational band origins and integrated band intensities (cf. next section) for X ‘A, SiH2. The calculated vibrational frequencies agree to within 2-40 cm-’ with the recent expe~mental values of Ishikawa and Kajimoto [ 201. The vibrationai band origins for the a 3B1state are given in table 9, they are expected to be of similar accuracy as those for the electronic ground state. The largest integrated band intensity of the fundamental transitions is calculated for the antisymmetric stretching mode (857.8 atm-’ cmm2), followed by the symmetric stretching mode (397.6 atm-’ cmB2). Due to the strong Fermi resonance between the 1Y, and 2 v2 modes (cf. table 7) the first overtone of the bending mode exhibits a large intensity in absorption as well. In fig. 2 the vi-

W. Gabriel et al. /Chemical Physics I74 (19930 45-56

49

Tabie 3 Internal quartic force field of X ‘A, and a 3B1SiH2 (in aJ/ftnj X ‘Al Si& this work

a ‘B, SiH2 this work

ref. [43j

ref [43]

0.538 2.913

0.523 2.949

s0.058 0.015 - 11.477

-0.030 0.021 -13.416

-0.021 0.037 - 13.502

-0.341 0.053

-0.391 0.001

-0.047 -0.267

--0.297 0.073

-0.169 - 0.082

-0.167 -0.033

-0.029 0.048

-0.091 -0.039

-44.57 0.270

-0.224 43.66

- 41.776 0.063

-0.155 so.94

- 3.330 1.018

0.57

-2.412 2.254

0.660 2.465

0.708 2.517

0.062 0.023

-11.056

-0.676 0.0016 -0.222 -0.617 -0.446 0.495

brational eigenfunction (for J= 0) of the 1p1 stretching mode in symmetry adapted coordinates Q, =2-r’ ’ (R,+&) (bohr) and&=cu (degree) isdisplayed, The strong Fermi resonance between the 1Y, and 2 u2 levels can be clearly recognized. Table 7 contains the composition for the lowest lying Fermi polyads in terms of our “pure” basis functions for the stretching and bending modes [61]. For 2v,+ v2=2, 3 and 4 there are strong Fermi coupling effects in agreement with the findings of Ishikawa [ 201. A weak DarlingDennison type resonance exists between the ( I, 2,O ) level and (0, 0,2). The dominant anharmonic couplings occur within such poIyad blocks in low lying vibrational states of SiH2. Yamada et al. [ 191 have reported v,=998.6 cm-’ and the previous result from Dubois [ 111 was v2= 1004 cm-‘, measured in gas phase, whereas Ishikawa and Kajimoto (201 obtained v,=997.1 cm-‘. Two values are known in the argon matrix at low tem~rature. ~illig~ and Jacox [ 121 obtained v2= 1008 cm-i, whereas Fredin et al. [ 13 ] reported ~~~994.8 cm-‘. There seems to be a more significant matrix shift for the stretches. Our results for v1 and v3 deviate by 23 and 50 cm-’ from the frequen-

-3.121 3.040 -1.014 0.483 0.033 0.803

ties of Fredin et al. [ 13 1. This is also the case for the dc.uteride species SiD2 and SiHD. 4. Electric dipole moment function of SiHz (X ‘A, and a 3B1)and vibrational band intensities The analytic expansions of the two Cartesian cornponents of the CEPA electric dipole moment functions are given in tables 1 and 2. The coordinates were such that the molecule lies in the xz plane, the origin coincides with the silicon atom and the positive x axis bisects the angle which include the Si-H bonds; the z axis is perpendicular to the x axis and the H(‘) atom lies in the positive xz quadrant. The dipole moment functions were also transformed into Eckart frame internal coordinates and dimensionless normal coordinates. In table 10 the linear and quadratic terms of these expansions are given for X ‘At SiH2. The electric dipole moment in the vibrational ground state was calculated to be 0.075 D (X ‘A, ) and 0.043 D (a 3B1). Allen and Schaefer [43] obtained 0.087 D for the singlet ground state. The expansion coefficients show that the electric dipole moment functions of the singlet ground state of silylene can be well approximated by its linear form,

W. Gabrielet al. /Chemical PhystcsI 74 (I 993) 45-56

50

Table 4 (A) Rotational and (B) vibrational constants for the X IAl state of Si&, SiD,, and SiHD SiH2

(A)

R$?’ RFH

(A) (A) agSH (deg) cxfLH (deg) A. (cm-‘) A0 (cm-‘) B, (cm-‘) B0 (cm-‘) C, (cm-‘) C, (cm-‘) *M_+,fMHz1 %BBB

(MHz)

kccc(MHz) TMBB(MHz) *BBcC

(MHz)

%xz.uWH~) ?mmWHz) (BJ

(cm-‘) oz (cm-‘) u, (cm-‘) xi1 (cm-‘) x, (cm-‘) 0,

x33fcm-'1 +(=+I ~13 (cm-') ~23 (cm-')

(cm-“) G(~) (cm-‘)

y')

Cl2b,

at

(cm-*) cuf (cm-‘) ff$ (cm-‘) ffjj (cm-‘) ff? (cm-‘) at: (cm-‘) fx? (cm-‘) a$ (cm-‘) cu$ (cm-‘)

SiD2

SiHD

1.5168 1.5180 92.04 92.15 8.0823 8.0860 7.0208 7.0103 3.7571 3.7221 -162.7 -98.2 -5.9 79.0 -11.1 -12.5 - 24.0

92.08 4.3158 4.3174 3.5133 3.5094 1.9367 1.9237 -46.4 -24.6 -1.6 21.1 -3.2 -2.9 -6.4

7.6092 7.6041 3.8569 3.8540 2.5595 2.5402 -57.7 -13.0 -3.0 2.5 -5.4 -5.4 -45.3

2080.9 998.5 2066.0 -17.0 5.6 -15.5 -13.9 -66.5 -11.8 - 35.3 2543.0 0.0022 - 1.0 0.0 0.099 -0,272 0.160 0.098 -0.12 0.061 0.049 0.055 0.035

f495.2 718.4 1487.5 - 8.6 2.9 -8.2 -7.3 - 34.2 -6.1 - 18.4 1835.2 0.0443 -0.999 0.0 0.034 -0.102 0.064 0.038 - 0.043 0.020 0.015 a.021 0.017

2073.4 869.9 1491.4 -33.5 4.6 -17.3 - 14.1 1.8 - 7.4 0.034 2200.9 0.0189 -0.5917 -0.806 0.212 -0.194 0.003 -0.002 -0.060 0.074 0.019 0.031 0.027

Ref. 1431 1.5141 1.5243 92.0 92.05

1.5171

2099 1036 2091 (2069) cf

0.110

-0.266 0.160 0.100 -0.109 0.063 0.052 0.056 0.035

‘) Darling-Den&son resonance parameter. b, Coriolis constants. =) Scaled vaiue.

5. Ro~tioa~ly resolved vibrational absorption spectrum of SiHz The r~vibrationa~ energy levels for the electronic ground state have been calculated up to 5000 cm-’

and up to 2” = 9 and the dipole transition matrix elements for all transitions between these levels [62] have been evaluated as well. Using the dipole transition matrix elements, the line intensities have been evaluated from the usual formula,

W. Gabriel ef al. /Chemical Physics 174 (19930 45-56 Table 5 (A) Rotational

and (B) vibrational

constants

for the ‘B, state of SiHZ, SiD2, and SiHD SiH2

(A)

118.426

&‘s”

125.862

1.4788

(deg)

15.6393 15.8638 5.1788 5.1581 3.8905 3.8565 - ‘1634.9

r(MHz) %BBBB (MHz) (MHz

)

TMBB

(MHz)

+mzc

(MHz

)

~CAA

(MHz

)

TABAB (MHz) 0, (cm-‘) w2 (cm-‘) q (cm-‘)

(B)

xl1 (cm-‘) x22 (cm-’ ) x33 (cm-’ ) x12 (cm-‘) x13 (cm-‘) xz3 (cm-’ y’) (cm-‘) G(OOO) (cm-‘) (Y? (cm-‘) c$ (cm-‘) cue (cm-‘) cxy (cm-‘) a! (cm-‘) CUT(cm-‘) cuy (cm-‘) (YE (cm-‘) (YF (cm-‘) a) Darling-Dennison

S,=3054.6

resonance

g,,v,R’exp(

Ref. [43]

1.4793

(cm-‘) (cm-‘) (cm-‘) (cm-‘) (cm-‘) (cm-‘)

7cccc

SiHD

SiDl

RFH (A) RFH (A) cxFSIH(deg) A. A0 B. B0 C, C,

51

-30.5 -5.7 146.7 -8.1 -18.4 -28.9 2223.6 933.8 2284.9 -24.2 -11.8 -30.6 -11.8 - 86.2 -15.0 -41.7 2676.2 0.220 - 1.430 0.312 0.07 1 -0.050 0.061 0.055 0.039 0.043

1.4768 1.4789 118.30 118.759 8.3511 8.4377 2.5915 2.5839 1.9778 1.9653 -466.2 -7.6 -1.5 39.2 -2.3 -3.3 -i.5

12.5398 12.6820 3.3404 3.3308 2.6378 2.6190 -916.0 - 10.4 -2.9 53.6 -4.1 -7.1 -28.1

1587.3 676.2 1656.6 - 12.5 -6.3 - 16.3 -5.6 -44.4 -7.9 -21.8 1936.8 0.1333 -0.546 0.133 0.027 -0.019

1620.4 815.2 2255.8 -23.5 -3.0 -45.9 -31.0 -9.9 -13.8 -2.5 2313.9 0.08 -0.952 0.300 0.049 -0.031

0.02 1 0.020 0.014 0.016

2241.0 921.0 2295.0

0.191

.1.471 0.328 0.074 -0.045

0.020 0.03 1 0.021

0.058 0.053 0.041 0.043

parameter.

-EJkT)

x[l-exp(-v,lkT)l!(Te,), where S, (in cm-’ atm- r) denotes the line intensity at temperature T, gNs is the nuclear spin statistical weight, v, is the transition frequency in cm-‘, R2 is the squared transition dipole matrix element in D2, E, (in cm-’ ) is the energy of the rotational level in the vibrational ground state, k is the Boltzmann con-

stant and T is the absolute tion function

temperature.

The parti-

Qr= ~~og,,(2J+l)exp(-E,IkT) has been calculated to be 7 19 (at T= 300 K). Independently, the partition sum was calculated with the equation [ 63 ] Q,=2[n(kT)3/A,BeCe]“2,

Table 6 Comparison of experimental and theoretical spectroscopic constants for the X ‘A, state of SiH2 This work

Ref. [I93

1.5168 1.5180 92.04 92.15 8.0823 8.0860 7.0208 7.0103 3.7571 3.7221 - 162.7 -98.2 -5.9 79.0 -11.1 - 12.5 - 24.0

1.5140 1.5256 92.08 91.8 8.0987 8.1001 7.0240 7.0221 3.7027 3.703 1 - 165.3 - 104.5 -6.4 81.0 - 12.1 - 12.0 - 26.0

RsiH(A) RFH (A)

CU,HS”~ (deg) (Y!jrSIH( deg ) A. (cm-‘) A0 (cm-‘) 8, (cm-‘) B0 (cm-‘) C, (cm-‘) Co (cm-‘) r,, (MHz) 7BBBB (ha&

)

rem: (MHz f 7AABB (MHz)

rancc (MHz 1 7-

(MHz)

~ABAB

(MHz)

Table 7 Composition of the vibrational ~vefunctions Fermi polyads ‘)

for the first three

2n,+ 4=2

A

B

(0, 2, 0) (LO,O) energy (cm-‘)

61.8 37.2 1991.5

37.6 62.2 2014.8

2~,++=3

A

B

(I, 1,O)

(0,3,0) energy (cm-‘)

78.4 20.5 2913.7

20.5 77.6 3023.0

2v,+q=4

A b,

B

c

(L2,Of

69.6 2.5 15.0 3960.3

4.4 92.8 1.7 4008.1

11.8 4.2 79.9 4043.0

(2,0,0) (0,4,0) energy (cm-t)

*) In percent of the pure state in the total wavefunctions. b, This state interacts also with the (0, 0,2 ) state (weight 12%) (see text).

where A,, Be, and C, are the rotational constants (cf. table 6). The partition function amounts to 731, which deviates by about 2Ohfrom the sum. Using the value Q,= 7 i 9 the absoiute line intensities were eval-

Ref. [ if ]

1.5163 92.5 8.0964 7.0209 3.7003 - 159.8 -100.4 110.0

-43.2

uated. The results are given in table 11 for the most intense transition within the P, Q, and R branches in the vibrational ground state and for the r~r, I vz, 2 y2, and p3 rovibrational transitions of X ‘Al of SiHz. In fig. 3 we have plotted the deviations of the calculated transition energies in the 2~~band relative to those determined experimentally [ 191. Providing the vibrational band origin is shifted by about 3.2 cm-‘, most of the transition energies agree with experiment to within about 0.02-0.76 cm-‘. The absorption spectrum is displayed in fig. 4. The question arises if such theoretical data can help in the assignment of the ex~~rnen~l spectra. The energy differences alone are probably not accurate enough. However, the region of the absorption spectrum of SiHz between 1800 and 2200 cm-’ show that such ab initio data might prove quite useful, if combined with the line strengths. The theory predicts three bands (1 vl, 2~5 and 1v3) of appreciably large intensities in the region of 18002200 cm-“. The spectra of the 1ZQ,1u2and 2~~bands in figs. 4-7 have been shifted to match the positions of the experimental band origins (cf. table 8 for the deviations between the calculated and experimental values). Such spectra can be useful in the analysis of the complex absorption spectrum in this spectral region. It is remarkable that the absolute line intensities of

Table 8 Vibrational band origins and integrated vibrational band intensities (at 300 K) for the X ‘At state of SiH,

0 0 0

1 2 0 0 1 1 3 0 0 2 2 0 4

1 1 0 0 0 1

1 0 2 0

0 0

1 0 0

1 0 2 1 0 1 0 0

Pert. a) (cm-‘)

Var. b, (cm-‘)

Ref. [20]

3”) (atm-’ cme2)

996.8 2004.8 1995.6 2006.9 2989.8 2980.9 3024.0 3960.8 3936.3 3984.0 3977.2 3960.8 4054.3

995.3 1991.5 1996.8 2014.8 2973.7 2980.4 3023.0 3933.9 3936.7 3960.3 3976.5 4008.1 4043.0

997.1 2002.7

230.3 230.8 857.8 397.6 3.1 0.2 0.8 10.2 7.5 0.8 0.5 2.4 0.1

1975.2 2952.7 2998.6 3907.4 3923.3

3976.8 3997.5

a) Calculated from the spectroscopic constants of table 4. bt Calculated variationally for J= 0. c) S= 2 S, (sum over all rotational levels up to P = 9 ). 5.0

Table 9 Vibrational band origins for the a ‘I.%,state of Si&

0

0 0 1 0 0 1 0 0

1

1 2 0 0 3 1 I 4 2 2

0 0 1 0 0 1 0 0 I 0

4.8

Pert. 8) (cm-‘)

Var. b, (cm-‘)

896.7 1769.9 2173.0 2126.2 2619.4 3054.7 3011.1 3445.3 3912.8 3872.4

899.4 1771.6 2165.6 2178.0 2615.0 3052.7 3069.9 3426.6 3912.7 3933.3

60

80

70

‘) Calculated from the spectroscopic constants oftable 5. b, Calculated variationally for J= 0.

80

so

100

110

lse

190

140

Q2 Fig. 2, Contour plot of the vibrational wavefunction of the ( 1,0, 0) state in the electronic ground state of SiHr showing a strong Fermi resonance with the (0,2,0) state.

Table 10 First and second derivatives of the E&art frame *) dipole moment for the X ‘At state of SiHr with respect to dimensionless normal coordinates (in debye) n component

6 component

p; pi Jo;

0.0 0.0 0.1152

p; -0.0991 J& 0.0841 jLu; 0.0

r;, j&

0.0 0.0

.u;a J&

p’j,

0.0

&3

/I;, - 0.0047 & -0.0015 jl;a -0.0044

*) The Eckart system is defined with respect to the molecular fixed axes a, b, and c.

0.0 0.0073 -0.0021

& -0.0071 jl;s 0.0 & 0.0

54

W. GaMeI et al. /~he~i~a~ Phyms f 74 (1993) 45-56

Table 11 Absolute absorption line ~tensities a) for tire most intense lines (at 300 K) of the fu~damen~l transitions in the X *At electronic ground state of SiHs J’

R8

J”

IC” II

4 6

7 5

3 5

41.3 93.8

21 3

3 7 5

23 4

2005.8 1928.8 2247.7

3.15 5.63 9.03

I1 1

5 3 5

02 0

986.8 954.5 1042.4

2.30 1.91 1.25

band 020-000 35 03

3 6

21

2024.6 1941.9

2.06 5.66

1

5

0

2060.8

3.82

vibrational band OOl-~ : 3

31

3 4

31

1993.8 1963.0

12.97 7.92

R

0

5

0

2043.3

16.54

I&E (cm-‘)

s (atm-’ cmmZ)

vibrational band 000-000 : R

7 6

<0.001(upt0J”=9) 0.001 0.01

vibrational band 100-000 E R

63 6

vibrational band 01~~0 G R vibrations E R

43 6

6

6

a) See text for definition.

Fig. 3. Absolute energy differences between calculated and experimental absorption lines of the 1v2 mode of X ‘A, SiHr (cf. text ).

purely rotational transitions in the vibrational ground state are less intense than the line intensities of fundamental vibrational transitions in SiH2 (cf. table

Fig.4.Rotationally

resolved absorption spectrum of I EJ~ of X ‘A, SiH~(at3~~~hm=0.1~m-1,~e~do~~~has~nshift~ by - 39.6 cm-’ (cf. text)).

11)” This is due to the very small permanent dipole moment of 0.075 D in the vibrational ground state of SiH2.

W. Gabriel et al. /Chemical Physm I74 (19930 45-56

55

6. Conclusions

0 850

900

950

1000

1050

1100

1150

1200

[CIll-l]

Fig. 5. Rotationally resolved absorption spectrum of 1~~of X ‘A, SiHz (at 300 K, fwhm=O. 1cm-‘, the band origin has been shifted by + 1.8 cm-’ (cf. text)).

7

Acknowledgement

1 0 1850

In this work so far the most accurate and compact theoretical characterization of the near equilibrium properties of the singlet and triplet state of silylene SiHz have been obtained. Full set of quartic spectroscopic constants of SiHa, SiHD, and SiDz is reported. A variational procedure has been used to calculate the rovibrational energy levels and absorption line intensities. Very good agreement for the 1 v2 band of X ‘A, SiH, has been achieved. Most of the calculated rovibrational transitions with a shifted band origin agree with experiment to within 1 cm-‘. Due to the lack of experimental information about the triplet state it is hoped that our results for this state can serve as a reliable prediction.

1900

1950

2000

2050

2100

2150

-4 2200

[cd]

Fig. 6. Rotationally resolved absorption spectrum of 2v, of X ‘A, SiH2 (at 300 K, fwhm = 0.1 cm-‘, the band origin has been shifted by + 11.2 cm-’ (cf. text)).

This work has been supported by the Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie. The electronic structure calculations were performed at HITAC S820/80 supercomputer of the computer center at the Institute of Molecular Science in Okazaki. We thank this institution for providing us with the necessary computer time. PP wishes to acknowledge the kind hospitality at the Fachbereich Chemie der Universitat Frankfurt in 1990 and to CNR (Progetto Finalizzato Sistemi Informatici e Calcolo Parallel0 e Progetto Strategic0 di Chimica Computazionale) for a grant.

1

35 7

References

30 N ii o 25': a 3 20 -

1950

2ml

2050

2100

2150

[cm']

Fig. 7. Rotationally resolved absorption spectrum of v, of X ‘A, SiHa (at 300 K, fwhm=O.l cm-‘).

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