Anharmonic vibrational analyses for the 1-silacyclopropenylidene molecule and its three isomers

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Anharmonic vibrational analyses for the 1-silacyclopropenylidene molecule and its three isomersQunyan Wu a b , Qiang Hao b c , Jeremiah J. Wilke b , Andrew C. Simmonett b , YukioYamaguchi b , Qianshu Li a d , De-Cai Fang c & Henry F. Schaefer III ba Institute of Chemical Physics, Beijing Institute of Technology, Beijing, P. R. China 100081b Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia30602, USAc College of Chemistry, Beijing Normal University, Beijing, P. R. China 100875d Center for Computational Quantum Chemistry, South China Normal University, Guangzhou,P. R. China 510631

Accepted author version posted online: 27 Feb 2012. Version of record first published: 16Mar 2012

To cite this article: Qunyan Wu, Qiang Hao, Jeremiah J. Wilke, Andrew C. Simmonett, Yukio Yamaguchi, Qianshu Li, De-CaiFang & Henry F. Schaefer III (2012): Anharmonic vibrational analyses for the 1-silacyclopropenylidene molecule and its threeisomers, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, 110:9-10, 783-800

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Molecular PhysicsVol. 110, Nos. 9–10, 10–20 May 2012, 783–800

INVITED ARTICLE

Anharmonic vibrational analyses for the 1-silacyclopropenylidene

molecule and its three isomers

Qunyan Wuaby, Qiang Haobc, Jeremiah J. Wilkeb, Andrew C. Simmonettb, Yukio Yamaguchib, Qianshu Liad,De-Cai Fangc and Henry F. Schaefer IIIb*

aInstitute of Chemical Physics, Beijing Institute of Technology, Beijing, P. R. China 100081;bCenter for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA; cCollege of Chemistry,

Beijing Normal University, Beijing, P. R. China 100875; dCenter for Computational Quantum Chemistry,South China Normal University, Guangzhou, P. R. China 510631

(Received 16 November 2011; final version received 6 February 2012)

The global minimum among possible structures of SiC2H2 has been experimentally and theoretically determinedto be 1-silacyclopropenylidene (1S). In 1994 Maier and Reisenauer reported the generation of 1-silacyclopropenylidene and its three isomers (2S–4S) by pulsed-flash pyrolysis followed by matrix-spectroscopicidentification. Reliable quartic force fields for 1-silacyclopropenylidene and its three isomers are determinedemploying ab initio coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)] andthe correlation-consistent core-valence quadruple zeta (cc-pCVQZ) basis set. Second-order vibrationalperturbation theory (VPT2) has been utilized to determine equilibrium and zero-point vibration correctedrotational constants, centrifugal distortion constants, and harmonic and anharmonic vibrational frequencies. Thedistances between the average nuclear positions (r�) are also determined. The predicted rotational constants,centrifugal distortion constants, and anharmonic frequencies for the four lowest-lying isomers (1S-4S) of SiC2H2,as well as their 13C and deuterated isotopologues, agree well with available experiments. Excluding the CH andCD stretching modes, the mean absolute deviation between theoretical anharmonic and experimentalfundamental frequencies for isomer 1-silacyclopropenylidene (1S) is 4.1 cm�1 (5 isotopologues, 25 modes). Thecorresponding deviation for ethynylsilanediyl (2S) is 4.9 cm�1 (7 isotopologues, 38 modes) without the SiH andSiD stretching modes, while it is 8.6 cm�1 (5 isotopologues, 22 modes) for silacyclopropyne (4S) without the SiCs-stretching, SiH2 a-stretching and SiD2 wagging modes. By comparing the theoretical harmonic and anharmonicwith the experimental fundamental vibrational frequencies for the four isomers (1S-4S), it is demonstrated thatthe anharmonic effects greatly improve the harmonic results. This theoretically derived spectroscopic data shouldaid in the experimental detection of the transitions that have yet to be observed, particularly for thevinylidensilanediyl isomer.

Keywords: 1-silacyclopropenylidene; second-order vibrational perturbation theory; rotational constants; cen-trifugal distortion constants; anharmonic vibrational frequencies

1. Introduction

In 1994 Izuha, Yamamoto and Saito reported the

rotational spectra of 1-silacyclopropenylidene (1S) and

its isotopic species (29SiC2H2, SiC2D2, Si13C2H2) in the

frequency region of 220–400 GHz by using a source-

modulated microwave (MW) spectrometer combined

with a free space absorption cell [1]. Least-squares

analyses of the observed spectral lines yielded the

rotational constants and the centrifugal distortion

constants for different isotopic species. From the

observed rotational constants, the rs structure was

determined: rs(C¼C)¼ 1.3458 A, rs(Si–C)¼ 1.8200 A,

rs(C–H)¼ 1.0795 A, and �s(CCH)¼ 135.16�. In another

important experiment, the microwave rotational spec-

trum of singlet vinylidenesilanediyl (3S) and its isotopic

species (29SiCCH2, SiCCD2, SiC13CH2, Si

13CCH2) were

observed in a pulsed supersonic molecular beam by

Fourier transform microwave spectroscopy by

McCarthy and Thaddeus in 2001 [2]. The experimental

r0 structure was determined for 3S by isotopic

substitution: r0(C¼C)¼ 1.321 A, r0(Si–C)¼ 1.703 A,

r0(C–H)¼ 1.099 A, and �0(HCH)¼ 117.3�.Maier, Reisenauer, and Pacl reported generation of

SiC2H2 isomers by pulsed flash pyrolysis and their

*Corresponding author. Email: [email protected] address: Department of Chemistry, Tsinghua University, Beijing, P. R. China 100084

ISSN 0026–8976 print/ISSN 1362–3028 online

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matrix-spectroscopic identification in 1994 [3]. By thepulsed flash pyrolysis of the gaseous mixture of2-ethynyl-1, 1, 1-trimethyldisilane and argon, 1-silacy-clopropenylidene (1S) was isolated in an argon matrixat 10K. Irradiation of matrix-isolated 1S resulted in aseries of photochemical rearrangements leading toethynylsilanediyl (ethynylsilylene, 2S), vinylidenesila-nediyl (vinylidenesilylene, 3S), and silacyclopropyne(4S), as shown in Scheme 1 [3–5]. The identification ofthe SiC2H2 isomers and their 13C and D isotomers werebased on the comparison of their experimental andtheoretical infrared (IR) spectra [3–8]. The isomer 4S isthe first example of a ‘formal’ cyclopropyne, which isthe most strained cycloalkyne ever prepared.

There have been many theoretical [3–22] studies ofSiC2H2 molecular systems. In 1986 Frenking,Remington and Schaefer investigated the molecularstructures and relative energies of fifteen differentisomers of SiC2H2 on the closed-shell singlet potentialenergy surface (PES) [6]. Vacek, Colegrove, andSchaefer reported an improved theoretical study onthe 1S isomer (global minimum) at the TZþ 2P CISDand DZþP CCSD (coupled cluster with singles anddoubles) levels of theory in 1991 [8]. After Maier et al.[3–5] synthesized four isomers (1S–4S) of SiC2H2,Sherrill, Brandow, Allen, and Schaefer [15] theoreti-cally reinvestigated the singlet and triplet states of thethree SiC2H2 isomers using coupled cluster theory witha triple � quality basis set. Recently Ikuta, Saitoh, andWakamatsu [16] studied the geometric structures andisomeric stabilities of various stationary points ofSiC2H2 neutral and its cation and anion, also usingcoupled-cluster theory.

No less than seven low-lying isomers of SiC2H2

were considered in the most recent theoretical study[21]. Theoretically determined harmonic vibrationalfrequencies and associated infrared (IR) intensities forfour isomers (1S–4S) were in good agreement withavailable experimental observations at the highest levelof theory, cc-pVQZ(C,H)/cc-pV(Qþd)Z(Si) CCSD(T).One year earlier Thorwirth and Harding reported

CCSD(T) calculations on six SiC2H2 and six SiCNHstructural isomers [22]. Equilibrium geometries of atotal of 12 structures in their singlet electronic stateswere determined. In addition, anharmonic force fieldswere computed to yield anharmonic vibrational fre-quencies and rotation-vibration interaction constants.Their study mainly focused on the rotational constantsand structures of SiC2H2 and SiCNH [22].

In the present research, anharmonic vibrationalanalyses of the electronic ground states of the fourlowest-lying SiC2H2 isomers (1S–4S) shown inScheme 1 were performed employing second-ordervibrational perturbation (VPT2) theory [23–27]. Themolecular parameters are determined using the abinitio coupled cluster with single, double, and pertur-bative triple excitations [CCSD (T)] method [28,29]with the correlation-consistent polarized core-valencequadruple zeta (cc-pCVQZ) basis set [30–32]. Thepredicted IR intensities, harmonic and anharmonicvibrational frequencies will be analyzed in detail andcompared with the available experimental values.Furthermore, isotopic shifts of the r� structures (dis-tances between the average nuclear positions), rota-tional constants, centrifugal distortion constants,harmonic and anharmonic vibrational frequencies arecomputed and compared with experimental observa-tions. The results lead us to suggest reassignments forsome of the experimentally observed vibrationalmodes. The present research will hopefully stimulatefurther characterization of the SiC2H2 molecularsystems, which may be involved in organo-siliconchemistry, interstellar chemistry, chemical dynamics,and high-resolution spectroscopy.

2. Electronic structure considerations

The ~X1A1 state of 1-silacyclopropenylidene (1S) withC2v point group symmetry has the following electronicconfiguration

core½ �5a213b226a

217a

212b

214b

228a

21

~X1A1 ð1Þ

where [core] denotes the seven lowest-lying core (Si: 1 s,2 s, 2p-like and C:1 s-like) orbitals. In Eq. (1) the 7a1and 4b2 molecular orbitals (MOs) describe the C–Cand Si–C � bonds, while the 2b1 MO is related to SiCC� bonding. The 8a1 MO is associated with the lone-pairorbital localized on the Si atom.

The electron configurations of the other threeisomers are described as follows:

Ethynylsilanediyl (ethynylsilylene 2S, Cs pointgroup symmetry);

core½ �7a028a029a0210a0211a022a00212a02 ~X 1A0 ð2Þ

C SiCH

HSi

C CH H

C

Si

C

HH

C SiC

H

Hhν hν

hν1S 2S 3S

4S

hν

Scheme 1. Photochemical rearrangement of singlet SiC2H2

molecules.

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Vinylidenesilanediyl (vinylidenesilylene 3S, C2v

point group symmetry);

core½ �6a217a218a

212b

229a

212b

213b

22

~X 1A1 ð3Þ

Silacyclopropyne (4S, C2v point group symmetry);

core½ �5a216a213b

222b

217a

213b

218a

21

~X 1A1 ð4Þ

3. Symmetry internal coordinates

The potential energy ( �V) for the SiC2H2 species may beexpanded in terms of displacement symmetry internalcoordinates (DSi) in the vicinity of the equilibriumpoint as

�V ¼ E0 þ1

2

Xij

FijDSiDSj þ1

6

Xijk

FijkDSiDSjDSk

þ1

24

Xijkl

FijklDSiDSjDSkDSl ð5Þ

In Equation (5), Fij, Fijk, and Fijkl denote quadratic,cubic, and quartic force constants. The nine displace-ment symmetry internal coordinates and internalcoordinates for the four SiC2H2 isomers are definedin Table 1 and Figure 1.

4. Theoretical procedures

In the present research, the correlation-consistentpolarized core-valence quadruple zeta (cc-pCVQZ)basis set developed by Dunning and co-workers[30–32] was employed to optimize geometries and todetermine force constants. The zeroth-order descrip-tions of the four SiC2H2 isomers (1S–4S) were obtainedusing single configuration self-consistent-field (SCF)[restricted Hartree–Fock (RHF)] wave functions.The coupled cluster with single, double, and perturba-tive triple excitations [CCSD(T)] wave functions [28,29]were constructed by freezing only the lowest-lying core(Si: 1s-like) orbital.

The structures of SiC2H2 (1S–4S) were optimizedusing analytic derivative methods [33–35]. Dipolemoment, harmonic vibrational frequencies, and theirassociated IR intensities were determined analytically.Electronic structure computations were carried outusing the ACESII (Mainz-Austin-Budapest version)[36,37] and MOLPRO [38] suites of quantum chemis-try packages.

The Cþþ program GRENDEL [39] was used togenerate perturbed geometries and to compute forceconstants in symmetry internal coordinates. The dis-placement sizes used for force field construction are

0.01 A, 0.02�, 0.03� for bond distance, bond angle, anddihedral angle, respectively. The INTDER 2005 [40,41]code by Allen was employed to perform nonlinearcoordinate transformations of quadratic, cubic, andquartic force constants between symmetry internal andCartesian coordinates. The VPT2 analyses were thenperformed with the Cartesian force constants by theANHARM program [42]. The distances between theaverage nuclear positions (r�) [43] are determinedemploying the formulae provided in refs. 44 and 45.The corresponding bond angles (��) are evaluatedusing the r� values. In the ground vibrational state thedistance r� is denoted rz and defines the ‘zero-pointaverage’ structure of the molecule [43–45].

5. Results and discussion

The optimized geometries for the four SiC2H2 isomers(1S–4S) at the cc-pCVQZ CCSD(T) level of theory aredepicted in Figure 2. The experimental rs structure [1]for 1S and r0 structure [2] for 3S are included inFigure 2. The equilibrium structures and dipolemoments of the SiC2H2 isomers have been discussedin previous work [21]. For the effects of the basis set indetermining equilibrium structures of SiC2H2 isomers,the readers should refer to the excellent analysis byThorwirth and Harding [22].

5.1. Rotational constants and centrifugal distortionconstants

The vibrational dependence of a rotational constantBv, vi being a vibrational quantum number, has thegeneral form

Bv ¼ Be �Xr

�Br viþ1

2

� �þ higher terms ð6Þ

where Be is the equilibrium rotational constant and thesums run over all normal modes. Similar expressionshold for the vibrational dependence of Av and Cv.Formulae for the vibration-rotation coupling constants�Br for an asymmetric top from perturbation theory arepresented elsewhere [23–27]. Although the perturbativeexpression for �Br sometimes suffers from Coriolisresonances when two vibrational frequencies are veryclose, i.e. !r�!s, the B0 constant (vi¼ 0) may bedetermined without Coriolis resonances by taking thesums of �Br constants over all normal modes ratherthan their individual values, as pointed out by East,Johnson and Allen [46].

In the following discussion the equilibrium (Ae, Be,and Ce) and zero-point vibration corrected (A0, B0,and C0) rotational constants are abbreviated as Be and

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Table

1.

Thesymmetry

internalcoordinates(D

Si)usedfortheSiC

2H

2isomersinvestigated(1S–4S)a.

1S

2S

3S

4S

DSi

mode

DSi

mode

DSi

mode

DSi

mode

S1(a

1)¼

1 ffiffiffi 2p

(r4þr 5)

CH

s-str.

S1(a0 )¼r 3

CH

str.

S1(a

1)¼

1 ffiffiffi 2p

(r3þr 4)

CH

2s-str.

S1(a

1)¼

1 ffiffiffi 2p

(r4þr 5)

SiH

2s-str.

S2(a

1)¼r 1

CC

str.

S2(a0 )¼r 4

SiH

str.

S2(a

1)¼r 2

CC

str.

S2(a

1)¼r 3

CC

str.

S3(a

1)¼

1 ffiffiffi 2p

(�2þ� 3)

CCH

s-bend

S3(a0 )¼r 1

CC

str.

S3(a

1)¼

1 ffiffiffi 2p

(�1þ� 2)

CH

2scis.

S3(a

1)¼1 2(�

1þ� 2þ� 3þ� 4)

SiH

2scis.

S4(a

1)¼

1 ffiffiffi 2p

(r2þr 3)

SiC

s-str.

S4(a0 )¼� 3

CSiH

bend

S4(a

1)¼r 1

SiC

str.

S4(a

1)¼

1 ffiffiffi 2p

(r1þr 2)

SiC

s-str.

S5(a

2)¼

1 ffiffiffi 2p

(�1þ� 2)

CCH

oop

S5(a0 )¼� 2

CCH

bend

S5(b

1)¼�1

CH

2wag

S5(a

2)¼1 2(�

1þ� 2�� 3�� 4)

SiH

2tw

ist

S6(b

1)¼

1 ffiffiffi 2p

(�1–� 2)

CCH

oop

S6(a0 )¼r 2

SiC

str.

S6(b

1)¼� 3

(oop)

SiCC

bend(oop)

S6(b

1)¼

1 ffiffiffi 2p

(r4�r 5)

SiH

2a-str.

S7(b

2)¼

1 ffiffiffi 2p

(r4–r 5)

CH

a-str.

S7(a0 )¼� 1

SiCC

bend

S7(b

2)¼

1 ffiffiffi 2p

(r3�r 4)

CH

2a-str.

S7(b

1)¼1 2(�

1�� 2�� 3þ� 4)

SiH

2rock

S8(b

2)¼

1 ffiffiffi 2p

(�2–� 3)

CCH

a-bend

S8(a00)¼� 1

HCCSitor.

S8(b

2)¼

1 ffiffiffi 2p

(�1�� 2)

CH

2rock.

S8(b

2)¼1 2(�

1�� 2þ� 3�� 4)

SiH

2wag

S9(b

2)¼

1 ffiffiffi 2p

(r2–r 3)

SiC

a-str.

S9(a00)¼� 2

HSiCC

tor.

S9(b

2)¼� 4

(ip)

SiCC

bend(ip)

S9(b

2)¼

1 ffiffiffi 2p

(r1�r 2)

SiC

a-str.

Note:aSee

Figure

1fordefinitionsofinternalcoordinates.

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B0, respectively. The B0 values are reported in terms ofWatson’s determinable rotational constants, which areindependent of reduction type (A/S) [25]. In order toselect a type of reduction for each isomer, Ray’sasymmetry parameter [47], �, is employed:

� ¼2B� A� C

A� Cð7Þ

which becomes �1 for a prolate symmetric top (B¼C)and 1 for an oblate symmetric top (B¼A), varyingbetween these two values for asymmetric cases. In thispaper, we have investigated in detail both the predictedequilibrium Be and zero-point vibration corrected B0

rotational constants.

5.1.1. 1-Silacyclopropenylidene (1S)

The isomer 1S is classified as a typical asymmetric top(�¼�0.748). In Table 2 the theoretically predictedequilibrium Be and zero-point vibration corrected B0

rotational constants for the four 1S isotopologues arepresented, as well as the corresponding experimentalB0 constants [1]. For the standard SiC2H2 (1S) species,the differences between theoretical equilibrium andzero-point vibration corrected rotational constantsare D[Be(theor.) –B0(expt.)]¼ (þ146,þ41,þ48)MHzand D[B0(theor.) –B0(expt.)]¼ (�23,�24,�16)MHz,respectively. Improvement in agreement between the-oretical and experimental [1] rotational constants dueto zero-point vibration correction is significant; 0.44%deviation for the former D[Be(theor.)–B0(expt.)] and0.15% for the latter D[B0(theor.)–B0(expt.)]. For thedideutero isotopologue SiC2D2 (1S) the correspondingdifferences are: D[Be(theor.)�B0(expt.)]¼ (þ94,þ31,þ37)MHz and D[B0(theor.)�B0(expt.)]¼ (�18,�21,�13)MHz, respectively. Again, improvement inagreement between theoretical and experimental rota-tional constants is evident; 0.38% for the formerD[Be(theor.)�B0(expt.)] and 0.14% for the latterD[B0(theor.)�B0(expt.)].

Theoretically predicted quartic centrifugal distor-tion constants for the four 1S isotopologues are alsocompared with the experimentally determined values inTable 2. These centrifugal distortion constants weredetermined using Watson’s A-reduction in the Ir

representation [25]. The magnitude and absolute

Si

C C

H Hr1

r2 r3

r4 r52 3

4 5

1

θ2

θ1

θ3

τ1=τ4213

τ2=τ5312

1S

r1 r2

r3

r4

C SiC

H

H 1 2 34

5

θ2 θ3

θ1

τ1=τ4123

τ2=τ5321

2S

r3

r1r2

r4

π1=π2453

θ2

θ3θ1

C SiC

H

H

θ4

123

4

5

3S

Si1

C2 C3

H4 H5

r1 r2

r3

r4 r5

θ1 θ2

θ3=θ215

θ4=θ314

4S

Figure 1. Simple internal coordinates for four SiC2H2

isomers (1S–4S).

Si

C CH H

43.39 1.81901.8200 Expt.a

1.08041.0795

1.34481.3458

135.11135.16

H C C Si

H

1.0643

178.82 1.2194

172.941.8347

94.30 1.5122

1S 2S

C SiC

H

H

1.08631.099 Expt.b

116.24117.3

1.32721.321

1.69801.703

Si

C C

H H1.4700 108.91

1.8114

1.2632

40.81

3S 4S

Figure 2. Optimized structures for four SiC2H2 isomers (1S–4S) at the cc-pCVQZ CCSD(T) level of theory. Bond lengthsare in Angstroms and angles are in degrees.aReference 1, rs structure.bReference 2, r0 structure.


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values for the set (DJ,DJK,DK, J, K) of five quarticcentrifugal distortion constants are in good agreementwith the experimental observations.

In Table 3 theoretical and experimental isotopicshifts for the rotational constants and quartic centrif-ugal constants of the three 1S isotopologues withrespect to those of the standard SiC2H2 isotopologueare reported. Both the equilibrium and zero-pointvibration corrected rotational constants agree with theexperimental isotopic shifts quite well: the largestdeviation for the zero-point rotational constant ofeach isotopologue is only DDB0¼ 0.4MHz (29SiC2H2),DDB0¼ 5.1MHz (SiC2D2), and DDB0¼ 0.7MHz(Si13C2H2), respectively. Similarly, theoretical isotopic

shifts for the quartic centrifugal distortion constantsare in good agreement with the experimental observa-tions. Specifically, an increase of the DDk constant withthe 29Si-labelling is correctly predicted.

In Table 4 the r� structures are compared with thetheoretical re structure and experimental rs structure. Itis seen that the r� structures somewhat overestimate thetheoretical re and experimental rs structures asexpected. Dideuteration of the molecule slightly short-ens the Si–C and C–C distances and elongates the C–H(C–D) distance. For the 13C disubstituted isotopologue(Si13C2H2) the three bond distances are 0.0001–0.0002 A shorter than those for the standard SiC2H2

species.

Table 2. Rotational constants and quartic centrifugal distortion constants (MHz) for four isotopologues of C2v

1-silacyclopropenylidene (1S) at the cc-pCVQZ CCSD(T) level of theory.

SiC2H229SiC2H2 SiC2D2 Si13C2H2

Theory Expt.a Theory Expt.a Theory Expt.a Theory Expt.a

Rotational constantsAe 33651.0 33651.0 26350.6 31733.8Be 11940.1 11746.6 10672.4 11560.7Ce 8813.0 8707.2 7595.9 8473.7

A0 33481.7 33504.8 33481.5 33504.6 26238.9 26256.9 31578.5 31601.1B0 11875.6 11899.4 11683.4 11706.8 10621.0 10641.6 11499.5 11522.6C0 8749.1 8764.9 8644.3 8659.9 7546.3 7559.1 8413.4 8428.6

Quartic centrifugal distortion constants103DJ 7.863 8.015 7.640 7.786 6.001 6.122 7.355 7.496103DJK 37.112 37.544 36.314 36.705 21.554 21.838 34.648 35.058103DK 50.406 52.92 51.427 54.8 47.870 49.42 41.558 41.1103J 2.145 2.197 2.063 2.113 1.825 1.868 2.035 2.087103K 34.570 35.94 33.888 35.26 23.203 24.09 31.942 33.04

Note: aReference 1.

Table 3. Isotopic shifts for rotational constants and quartic centrifugal distortion constants (MHz), with respect to the parent1-silacyclopropenylidene (1S) isotopologue at the cc-pCVQZ CCSD(T) level of theory.

29SiC2H2 SiC2D2 Si13C2H2

Theory Expt. Theory Expt. Theory Expt.

Rotational constantsDAe 0.0 �7300.4 �1917.2DBe �193.5 �1267.7 �379.4DCe �105.8 �1217.1 �339.3

DA0 �0.2 �0.2 �7242.8 �7247.9 �1903.2 �1903.7DB0 �192.2 �192.6 �1254.6 �1257.8 �376.1 �376.8DC0 �104.8 �105.0 �1202.8 �1205.8 �335.7 �336.3

Quartic centrifugal distortion constants103DDJ �0.223 �0.229 �1.862 �1.893 �0.508 �0.519103DDJK �0.798 �0.839 �15.558 �15.706 �2.464 �2.486103DDK þ1.021 þ1.88 �2.536 �3.50 �8.848 �11.82103DJ �0.082 �0.084 �0.320 �0.329 �0.11 �0.11103DK �0.682 �0.68 �11.367 �11.85 �2.628 �2.90

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5.1.2. Ethynylsilanediyl (2S)

Ethynylsilanediyl has only been observed in matrixisolation and, hence, there is no experimental rota-tional information. The rotational constants andquartic centrifugal distortion constants for the five 2S

isotopologues are presented in Table 5. Since ethynyl-silanediyl (2S) is a highly prolate asymmetric top(�¼�0.999), these constants were determined employ-ing Watson’s S-reduction in the Ir representation [25].The 2S isomer has a singlet ground state and a planarstructure with Cs point group symmetry, whereas thecorresponding carbon analogue ethynyldiyl (HC–C�CH) has a triplet ground state with C2 pointgroup symmetry [48,49]. The theoretically predictedconstants should help future MW spectroscopic iden-tification of 2S.

The r� structures are compared with the theoreticalre structure in Table 6. The r� structures provide thelonger Si–C and Si–H bond distances than the re

structure, whereas they present the shorter C–C and C–H distances. Upon dideuteration the C–H (C–D) bonddistance is elongated, while the Si–H (Si–D) bonddistance is contracted. On the other hand, the CCH(CCD) bond angle slightly decreases, whereas the SiCCand CSiH (CSiD) bond angles increase.

5.1.3. Vinylidenesilanediyl (3S)

In Table 7 the theoretical Be and B0 rotationalconstants for the five 3S isotopologues as well as thecorresponding experimental B0 constants [2] arereported. Since structure 3S is also a highly prolateasymmetric top (�¼�0.999), the MW spectrum ofH2CCSi and its isotopic species were analyzed withWatson’s S-reduced Hamiltonian [25], which repro-duces the observed spectra of each species with fourfree parameters: B0, C0, DJ, and DJK. In McCarthy andThaddeus’ experiment [2] the A0 rotational constant

Table 5. Rotational constants and quartic centrifugal distortion constants (MHz) for five isotopologues of Cs ethynylsilanediyl(2S) at the cc-pCVQZ CCSD(T) level of theory.

HSiCCH H29SiCCH DSiCCD HSi13CCH HSiC13CHTheory Theory Theory Theory Theory

Rotational constantsAe 226829.5 226412.6 119887.2 226541.3 226800.1Be 5237.0 5166.6 4715.7 5212.8 5052.6Ce 5118.8 5051.3 4537.2 5095.6 4942.4

A0 225244.0 224834.4 119280.4 224970.0 225220.2B0 5238.4 5168.0 4719.2 5213.7 5053.9C0 5114.7 5047.4 4534.3 5091.1 4938.7

Quartic centrifugal distortion constants103DJ 1.558 1.523 1.116 1.556 1.442103DJK 118.256 113.082 128.832 112.500 109.338DK 21.438 21.638 3.855 22.774 21.619106d1 �40.536 �39.306 �44.364 �40.674 �36.362106d2 �5.756 �5.461 �13.703 �5.607 �5.039

Table 4. The structures corrected for zero-point vibrational effects (r� and ��) determined from VPT2 for four isotopologues of1-silacyclopropenylidene (1S). Bond lengths are in angstroms and angles are in degrees.a

SiC2H229SiC2H2 SiC2D2 Si13C2H2 rbe rcs

r�(Si–C) 1.8266 1.8266 1.8260 1.8265 1.8190 1.8200r�(C–C) 1.3506 1.3506 1.3500 1.3504 1.3448 1.3458r�(C–H) 1.0816 1.0816 1.0820 1.0815 1.0804 1.0795��(CSiC) 43.39 43.39 43.39 43.39 43.39 –��(CCH) 135.19 135.19 135.15 135.19 135.11 135.16

Notes: aSee references 43–45 for definitions of r� and ��.bThe re values were predicted at the cc-pCVQZ CCSD(T) level of theory.cThe rs values from reference 1.


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could not be determined from the available data set;instead it was constrained to the theoretical valuederived by Cooper [7]. For the parent SiC2H2 (3S)species, the differences between theoretical Be and B0

and experimental B0 constants are: D[Be(theor.)�B0(expt.)]¼ (-,�2.4, þ1.4)MHz and D[B0(theor.)�B0(expt.)]¼ (-,�4.7,�4.5)MHz, respectively. Themean absolute deviations are 0.04% for the formerD[Be(theor.)�B0(expt.)] and 0.09% for the latterD[B0(theor.)�B0(expt.)]. For the dideutero isotopolo-gue SiC2D2 (3S) the corresponding differencesare: D[Be(theor.)–B0(expt.)]¼ (-,�3.1,þ1.8)MHz andD[B0(theor.)�B0(expt.)]¼ (-,�4.5,�4.1)MHz, for the(A, B, C) constants, respectively. The mean absolutedeviations are 0.05% for both D[Be(theor.)�B0(expt.)]and D[B0(theor.)�B0(expt.)]. For 3S isotopologues, thezero-point vibration corrections do not improve

agreement between theory and experiment, probablydue to constrained A0 constants in the experimentalanalysis. For various isotopologues of 1S and 3S

structures Thorwirth and Harding have carefullyanalysed theoretical zero-point vibrational corrections(�i �i=2) to rotational constants using three ab initioforce fields [22].

Theoretical and experimental isotopic shifts forthe rotational constants and quartic centrifugal distor-tion constants of the four 3S isotopologues withrespect to those of the standard SiC2H2 isotopologueare presented in Table 8. The theoretical isotopicshifts from both the Be and B0 rotational constantsagree quite well with the experimental values. Thelargest deviation for the zero-point rotational constantamong the four isotopologues is DDC0¼ 0.4MHz(SiCCD2).

Table 7. Rotational constants and quartic centrifugal distortion constants (MHz) for five isotopologues of C2v

vinylidenesilanediyl (3S) at the cc-pCVQZ CCSD(T) level of theory.

SiCCH229SiCCH2 SiCCD2 Si13CCH2 SiC13CH2

Theory Expt.a Theory Expt.a Theory Expt.a Theory Expt.a Theory Expt.a


A0 291766.7 300000b 291764.6 300000b 146490.2 150000b 291732.2 300000b 291773.4 300000b

B0 5327.3 5332.0 5251.2 5255.7 4760.1 4764.6 5312.4 5317.0 5146.4 5150.9C0 5229.0 5233.5 5155.6 5160.0 4606.7 4610.8 5214.6 5219.1 5054.7 5058.9

Quartic centrifugal distortion constants103DJ 1.154 1.27 1.123 1.21 0.865 1.02 1.151 1.29 1.074 1.19103DJK 176.075 143.2 171.594 139.0 122.750 110.8 176.395 143.5 164.426 133.3DK 23.465 23.469 5.796 23.464 23.477106d1 �21.639 �20.765 �31.226 �21.525 �19.362106d2 �4.147 �3.928 �9.503 �4.126 �3.590

Notes: aReference 2.bReference 7. A0 was constrained to the theoretical value.

Table 6. The structures corrected for zero-point vibrational effects (r� and ��) determined from VPT2 for five isotopologues ofethynylsilanediyl (2S). Bond lengths are in angstroms and angles are in degrees.a

HSiCCH H29SiCCH DSiCCD HSi13CCH HSiC13CH rbe

r�(C–H) 1.0541 1.0541 1.0573 1.0541 1.0541 1.0643r�(C–C) 1.2177 1.2177 1.2176 1.2177 1.2178 1.2194r�(Si–C) 1.8376 1.8376 1.8374 1.8376 1.8375 1.8347r�(Si–H) 1.5249 1.5249 1.5216 1.5249 1.5249 1.5122��(CCH) 179.03 179.03 178.94 179.03 179.03 178.82��(SiCC) 172.97 172.96 173.00 172.96 172.97 172.94��(CSiH) 94.29 94.29 94.31 94.29 94.29 94.30

Notes: aSee references 43–45 for definitions of r� and ��.bThe re values were predicted at the cc-pCVQZ CCSD(T) level of theory.

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Table 9 compares the r� structures with the theoret-ical re and experimental r0 structures. It is clearlyobserved that the r� structures show much betteragreement with the r0 structure than the re structure.Dideuteration of the molecule increases the C–C bonddistance and decreases the Si–C and C–H (C–D)distances.

5.1.4. Silacyclopropyne (4S)

Silacyclopropyne has only been observed via matrixisolation, and hence there is no experimental rotationalinformation. In Table 10 the rotational constants andquartic centrifugal distortion constants for five 4S

isotopologues are presented. The latter constants werecomputed utilizing Watson’s A (Ir) and S (Ir) reduc-tions [25], since isomer 4S has Ray’s asymmetryparameter of �¼�0.907. The theoretically predictedconstants should aid future MW spectroscopic detec-tion of the 4S species. In this regard a microwavespectroscopic investigation of the silacyclopropyne

(4S) is extremely challenging, since it is the firstexample of a ‘formal’ cyclopropyne [3,4,50]; maybethe most strained cycloalkyne ever synthesized.

In Table 11 the theoretical r� and re structures arepresented. All the r� bond distances are longer than there bond distances as anticipated. Dideuteration of themolecule slightly decreases the Si–C and C–C bonddistances, whereas it increases the Si–H (Si–D) bonddistance. For the 13C disubstituted isotopologue(H2Si

13C2) the three bond distances are shortened by0.0001–0.0002 A relative to those for the standardH2SiC2 species.

5.2. Harmonic and anharmonic vibrationalfrequencies

The rth anharmonic vibrational frequency (r) isdetermined using the following equation:

r ¼ !r þ 2�rr þ1

2

Xs 6¼r

�rs ð8Þ

Table 8. Isotopic shifts for rotational constants and quartic centrifugal distortion constants (MHz), with respect to the parentvinylidenesilanediyl (3S) isotopologue at the cc-pCVQZ CCSD(T) level of theory.

29SiCCH2 SiCCD2 Si13CCH2 SiC13CH2

Theory Expt. Theory Expt. Theory Expt. Theory Expt.

Rotational constantsDAe 0.0 �147214.6 0.0 0.0DBe �76.2 �568.1 �14.5 �181.2DCe �73.5 �622.3 �14.0 �175.0

DA0 �2.1 – �145276.5 – �34.5 – 6.7 –DB0 �76.1 �76.3 �567.4 �567.4 �14.9 �15.0 �180.9 �181.1DC0 �73.4 �73.5 �622.3 �622.7 �14.4 �14.4 �174.3 �174.6

Quartic centrifugal distortion constants103DDJ �0.031 �0.06 �0.289 �0.25 �0.003 0.02 �0.080 �0.08103DDJK �4.481 �4.2 �53.325 �32.4 0.320 0.3 �11.649 �9.9DDK 0.004 �17.669 �0.001 0.012106Dd1 0.874 �9.587 0.114 2.277106Dd2 0.219 �5.356 0.021 0.557

Table 9. The structures corrected for zero-point vibrational effects (r� and ��) determined from VPT2 for five isotopologues ofvinylidenesilanediyl (3S). Bond lengths are in angstroms and angles are in degreesa

SiCCH229SiCCH2 SiCCD2 Si13CCH2 SiC13CH2 rbe rc0

r�(Si–C) 1.7003 1.7003 1.6998 1.7004 1.7003 1.6980 1.703r�(C–C) 1.3259 1.3259 1.3265 1.3259 1.3259 1.3272 1.321r�(C–H) 1.0929 1.0929 1.0913 1.0929 1.0929 1.0863 1.099��(CCH) 121.80 121.80 121.82 121.80 121.80 121.88 –��(HCH) 116.41 116.41 116.37 116.41 116.41 116.24 117.3

Notes: aSee references 43–45 for definitions of r� and ��.bThe re values were predicted at the cc-pCVQZ CCSD(T) level of theory.cThe r0 values from reference 2.


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where !r is an rth harmonic vibrational frequencyand �rs are anharmonic vibrational constants.Expression for the anharmonic vibrational constantsfor an asymmetric top from vibrational perturbationtheory is described elsewhere [23–27]. It shouldbe realized that the normal coordinate with a lowharmonic vibrational frequency (!r) may not be asound basis to apply VPT2 theory. The anharmonicvibrational corrections (second and third terms inEquation (8)) for such a mode could be morethan 5% with respect to the correspondingharmonic vibrational frequency, which is significantlylarger than those for well behaved vibrations. In orderto partially compensate this inherent shortcoming ofVPT2 theory unphysical �rs values are excluded in

Equation (8) after careful examination for each normalmode [51,52].


In Table 12 harmonic and anharmonic vibrationalfrequencies and their associated infrared (IR) intensi-ties for the standard SiC2H2 (1S–H2) are presented.The corresponding quantities for four 1S isotopolo-gues are deposited in Tables S1–S4 as SupplementaryMaterial. In these tables the IR intensities are given as% ratios relative to the largest intensity in squarebrackets for direct comparison with Maier’s experi-ments [3,4]. For the standard 1S isotopologue [SiC2H2

(1S–H2)] seven fundamental vibrational frequencies

Table 10. Rotational constants and quartic centrifugal distortion constants (MHz) for four isotopologues of C2v

silacyclopropyne (4S) at the cc-pCVQZ CCSD(T) level of theory.

H2SiCC H292 SiCC D2SiCC H2Si

13C2 H2Si13CC

Theory Theory Theory Theory Theory


A0 40445.3 40445.4 32849.8 38008.0 39243.8B0 11054.4 10930.8 9450.9 10626.3 10829.9C0 9618.3 9524.6 8812.3 9156.0 9379.9

Quartic centrifugal distortion constantsA(Ir) reduction103DJ 6.656 6.539 4.804 6.106 6.404103DJK 170.586 167.748 96.019 159.775 164.435103DK �79.315 �76.360 �20.087 �80.173 �78.664103J 0.817 0.797 0.235 0.801 0.816103K �8.164 �7.898 �223.877 6.827 �0.313

S(Ir) reduction103DJ 6.754 6.631 6.312 6.017 6.408103DJK 170.002 167.197 86.975 160.311 164.412103DK �78.828 �75.901 �12.550 �80.620 �78.645106d1 �816.776 �796.533 �234.958 �800.807 �815.502106d2 48.685 45.954 753.666 �44.634 1.945

Table 11. The structures corrected for zero-point vibrational effects (r� and ��) determined from VPT2 for five isotopologues ofsilacyclopropyne (4S). Bond lengths are in angstroms and angles are in degrees.a

H2SiCC H292 SiCC D2SiCC H2Si

13C2 H2Si13CC rbe

r�(Si–C) 1.8217 1.8217 1.8211 1.8215 1.8220 1.8114r�(C–C) 1.2666 1.2665 1.2656 1.2665 1.2665 1.2632r�(Si–H) 1.4732 1.4731 1.4741 1.4730 1.4730 1.4700��(CSiC) 40.68 40.69 40.67 40.69 40.69 40.81��(HSiH) 108.69 108.69 108.82 108.68 108.69 108.91

Notes: aSee references 43–45 for definitions of r� and ��.bThe re values were predicted at the cc-pCVQZ CCSD(T) level of theory.

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have been observed via matrix isolation IR spectros-copy [3,4]. The strongest IR intensity is theoreticallypredicted for the !6(b1) out-of-plane CCH bendingmode, which is consistent with the experimentalobservation. The next three strong theoretical IRintensities are for the !9(b2), !8(b2), and !4(a1)modes, whose ordering is again in agreement withexperiment [3,4].

In the last column of Table 12 the anharmonicvibrational frequencies for the standard SiC2H2 (1S–H2) species are compared with the experimentallyobserved fundamental vibrational frequencies. Thelargest discrepancies (22.5 and 26.3 cm�1) are seen forthe CH symmetric (1, a1) and antisymmetric (7, b2)stretching modes, possibly due to higher anharmoni-city, or an experimental misassignment. However, it isseen that the anharmonic analysis decreases the errorsfrom 165.2 cm�1 to 22.5 and 26.3 cm�1 for these twoCH stretching modes, indicating importance of theanharmonic effects to improve the harmonic results.For the remaining five vibrational modes, there is verygood agreement between theory and experiment, themean absolute difference being 4.4 cm�1. The absolutedifferences between the seven theoretical harmonic andanharmonic and experimental fundamental vibrationalfrequencies for the standard SiC2H2 (1S–H2) isotopo-logue are D[u(theor.)�l(expt.)]¼ 433.5 cm�1 andD[l(theor.)�l(expt.)]¼ 70.9 cm�1, respectively. Here,the terms u and l indicate the sums of the sevenharmonic and anharmonic vibrational frequencies,respectively. It is evident that the anharmonic correc-tions from VPT2 theory notably improve the theoret-ical harmonic vibrational frequencies. For thedideutero isotopologue SiC2D2 (1S–D2) the agreementbetween theoretical anharmonic and experimentalfundamental vibrational frequencies is again excellent,

as shown in Table S1. The largest deviation is15.9 cm�1 for the CD symmetric stretching (1, a1)mode. The mean absolute difference for the remainingfive modes is 3.8 cm�1.

In the last columns of Tables S2–S4 the corre-sponding differences between the theoretical anharmo-nic and experimental fundamental vibrationalfrequencies for the Si13C2H2 (1S�13C2, in Table S2),SiC2HD (1S–HD, in Table S3), and Si13CCH2

(1S�13C1, in Table S4) isotopologues are presented.For each of the three isotopologues the largest devi-ations are: D1(a1)¼ 22.8 and D7(b2)¼ 26.9 cm�1 forSi13C2H2; D1(a0)¼ 26.4 and D2(a0)¼ 18.9 cm�1

for SiC2HD; D1(a0)¼ 22.3 and D2(a0)¼ 26.1 cm�1

for Si13CCH2. Excluding these CH and CD stretchingmodes, the mean absolute deviations for the remainingvibrational modes of the three isotopologues are 4.4(Si13C2H2), 4.0 (SiC2HD), and 4.3 cm�1 (Si13CCH2),respectively.

Considering possible matrix effects, the agreementbetween the theory and experiment for the vibrationalmodes of 1S appears to be superb. Our theoreticalstudy positively confirms the assignments made byMaier and Reisenauer [3,4]. For the fundamentals notobserved in the laboratory (2 and 4 for 1S–D2), thetheoretical predictions should be very reliable, butthese are the fundamentals with the weakest predictedIR intensities.


In Table 13 harmonic and anharmonic vibrationalfrequencies and their associated IR intensities for thestandard HCCSiH (2S–HH) are presented. The corre-sponding quantities for six 2S isotopologues aredeposited in Tables S5–S10 as Supplementary

Table 12. Harmonic and anharmonic vibrational frequencies (in cm�1), and infrared intensities [%ratio relative to the largestintensity] for the 1A1 state of 1-silacyclopropenylidene, SiC2H2 (1S–H2), at the cc-pCVQZ CCSD(T) level of theory. Theanharmonic vibrational frequencies were obtained by VPT2.

Mode number(assignment) Harmonic D(anh.-harm.) anharmonic Expt.a D(harm.-expt.) D(anh.-expt.)

1 (a1) CH s-str. 3213.9[7] �142.6 3071.2 3048.7[10] 165.2 22.52 (a1) CC str. 1474.9[2] �30.3 1444.6 – –3 (a1) CCH s-bend 897.0[7] �17.7 879.3 875.3[26] 21.7 4.04 (a1) SiC s-str. 780.4[64] �14.9 765.6 761.9[56] 18.5 3.75 (a2) CCH oop 999.1[0] �17.4 981.7 – –6 (b1) CCH oop 689.9[100]b �7.9 682.0 677.2[100] 12.7 4.87 (b2) CH a-str. 3191.7[9] �138.8 3052.8 3026.5[9] 165.2 26.38 (b2) CCH a-bend 1120.0[72] �27.9 1092.1 1085.8[87] 34.2 6.39 (b2) SiC a-str. 688.1[79] �12.7 675.4 672.1[90] 16.0 3.3

Notes: aReference 4.bThe absolute intensity is 59.5 km mol�1.


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Material. Seven fundamental vibrational frequencieshave been observed for the standard 2S HCCSiH (2S–HH) from matrix isolation IR spectroscopy [4]. Thestrongest IR intensity is theoretically predicted forthe !2(a

0) SiH stretching mode followed by that for the!4(a

0) CSiH bending mode. The ordering of IRintensities for the two modes is consistent with theexperimental findings. The two fundamentals (7 and9) not observed by Maier and co-workers have thesmallest predicted IR intensities (3% of that for 2) andthe lowest frequency, making their detection verychallenging. Our predictions await experiments withhigher resolution.

Since the SiCC bending !7(a0) and HSiCC torsional

!9(a00) modes have very low harmonic vibrational

frequencies, it was found that the anharmonic vibra-tional constant �79, the coupling constant between twomodes, is unphysically too large. In order to evaluatethe anharmonic vibrational frequencies, the relevantanharmonic vibrational coupling constants in Eq. (8)are adjusted to be zero: �77¼�99¼�79¼ 0.0.The largest deviation (21.6 cm�1) between the theoret-ical anharmonic and experimental fundamentalfrequencies is found for the SiH stretching 2(a

0)mode. Excluding this mode, the mean absolute differ-ence for remaining six modes is 4.9 cm�1. For thestandard HCCSiH (2S–HH) species the absolute devi-ations between the seven theoretical harmonic andanharmonic and experimental fundamental vibrationalfrequencies are D[u(theor.)� l(expt.)]¼ 331.6 cm�1

and D[l(theor.)� l(expt.)]¼ 51.2 cm�1, respectively. Itis clearly observed that the anharmonic effects greatlyimprove the theoretical harmonic vibrationalfrequencies.

For the dideutero isotopologue DCCSiD (2S–DD)the agreement between theoretical anharmonic and

experimental fundamental vibrational frequencies isagain excellent, as shown in Table S5. The largestdeviation is 13.6 cm�1 for the SiD stretching 3(a

0)mode. The fundamental frequency at 479.9 cm�1 forthe 8(a

00) DSiCC torsional mode in Maier’s paper [4]should be assigned to the 6(a

0) CCD bending mode.With this new assignment the mean absolute deviationfor the five fundamental vibrational modes becomes3.4 cm�1. In the last columns of Tables S6–S10 thecorresponding differences for the DCCSiH (2S-DH, inTable S6), HCCSiD (2S–HD, in Table S7),H13C13CSiH (2S�13C13C, in Table S8), HC13CSiH(2S–C13C, in Table S9), and H13CCSiH (2S�13CC, inTable S10) are presented. For each of five isotopolo-gues, the largest deviations between theory and exper-iment are: D2(a0)¼ 20.4 cm�1 for DCCSiH (2S-DH),D3(a0)¼ 13.8 cm�1 for HCCSiD (2S–HD),D2(a0)¼ 21.0 cm�1 for H13C13CSiH (2S�13C13C),D2(a0)¼21.0 cm

�1 for HC13CSiH (2S–C13C), andD2(a0)¼ 21.2 cm�1 for H13CCSiH (2S�13CC).Excluding these SiH and SiD stretching modes, themean absolute deviations of the remaining vibrationalmodes for the five isotopologues are 4.8 (DCCSiH), 6.8(HCCSiD), 4.6 (H13C13CSiH), 4.4 (HC13CSiH), and5.5 cm�1 (H13CCSiH), respectively.

5.2.3. Vinylidensilanediyl (3S)

In Table 14 harmonic and anharmonic vibrationalfrequencies and their associated IR intensities for thestandard isotopologue H2C¼C¼Si (3S–H2) are pre-sented. The corresponding quantities for five 3S

isotopologues are deposited in Tables S11–S15 asSupplementary Material. For isomer 3S only twofundamental frequencies, 2(a1) and 5(b1), have beenexperimentally observed [4]. For the parent

Table 13. Harmonic and anharmonic vibrational frequencies (in cm�1), and infrared intensities [%ratio relative to the largestintensity] for the 1A0 state of ethynylsilanediyl, HCCSiH (2S–HH), at the cc-pCVQZ CCSD(T) level of theory. The anharmonicvibrational frequencies were obtained by VPT2.

Mode number(assignment) harmonic D(anh.-harm.) anharmonic Expt.a D(harm.-expt.) D(anh.-expt.)

1 (a0) CH str. 3439.8[18] �131.3 3308.5 3304.2[31] 135.6 4.32 (a0) SiH str. 2071.2[100]b �79.7 1991.5 1969.9[100] 101.3 21.63 (a0) CC str. 2036.7[32] �35.0 2001.7 1995.7[27] 41.0 6.04 (a0) CSiH bend 830.1[48] �16.4 813.7 814.8[49] 15.3 �1.15 (a0) CCH bend 622.1[23] �2.5 619.6 613.9[32] 8.2 5.76 (a0) SiC str. 611.1[33] �2.6 608.6 605.0[41] 6.1 3.67 (a0) SiCC bend 241.2[3] �0.6 240.7 � –8 (a00) HCCSi tor. 746.9[12] �15.2 731.7 722.8[14] 24.1 8.99 (a00) HSiCC tor. 189.2[3] �10.8 178.5 – –

Notes: aReference 4.bThe absolute intensity is 212.8 kmmol�1.

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isotopologue [SiC2H2 (3S–H2)], the percentage devia-tions for the two anharmonic fundamental frequenciesrelative to the theoretical harmonic frequencies areD2(a1)¼ 2.3% and D5(b1)¼ 2.7%, respectively. The IRintensity is strongest for the !2(a1) CC stretchingmode, whereas those for the !1(a1), !4(a1), !5(b1), and!9(b2) modes are reasonably strong. However, theabsolute IR intensities for isomer 3S are as a wholesignificantly weaker than those for isomer 1S. In thislight the CD2 wagging mode for the dideutero struc-ture D2C¼C¼Si (3S–D2 in Table S11) has not beenexperimentally detected due to a significantly weakerIR intensity compared to that of the standardisopologue (3S–H2).

Since the SiCC out-of-plane !6(b1) and in-planebending !9(b2) modes have very low harmonic fre-quencies, the related unphysical anharmonic vibra-tional coupling constants in Equation (8) are adjustedto be zero in order to compute anharmonic vibrational

frequencies: �46¼�49¼�69¼ 0.0. The deviationsbetween the two theoretical anharmonic and experi-mental fundamental vibrational frequencies for thestandard isotopologue are 6.6 and 23.3 cm�1, respec-tively. Similar deviations have been observed for thefive other isotopologues shown in Tables S11–S15. Theexcellent agreement with experiment for the twoobserved fundamentals attaches a strong measure ofreliability to our vibrational predictions for the sevenvibrational frequencies yet unobserved.


In Table 15 harmonic and anharmonic vibrationalfrequencies and their associated IR intensities for thestandard H2SiC2 (4S–H2) are presented. The corre-sponding quantities for four 4S isotopologues aredeposited in Tables S16–S19 as SupplementaryMaterial. For the 4S isotopologues strong Fermi

Table 15. Harmonic and anharmonic vibrational frequencies (in cm�1), and infrared intensities [%ratio relative to the largestintensity] for the 1A1 state of silacyclopropyne, H2SiC2 (4 S–H2), at the cc-pCVQZ CCSD(T) level of theory. The anharmonicvibrational frequencies were obtained by VPT2.

Mode number (assignment) harmonic D(anh.-harm.) anharmonic Expt.a D(harm.-expt.) D(anh.-expt.)

1 (a1) SiH2 s-str. 2285.3[55] �83.4 2201.9 2214.4[(49] 70.9 �12.52 (a1) CC str. 1808.5[3] �31.0 1777.5 1769.8[7] 38.7 7.73 (a1) SiH2 scis. 1047.0[100]b �15.4 1031.6 1023.1[100] 23.9 8.54 (a1) SiC s-str. 827.2[68] �15.7 811.5 836.5[50] �9.3 �25.05 (a2) SiH2 twist 322.5[0] �12.3 310.2 – –6 (b1) SiH2 a-str. 2293.4[54] �84.6 2208.8 2228.9[49] 64.5 �20.17 (b1) SiH2 rock 670.0[29] �9.6 660.4 676.4[25] �6.4 �16.08 (b2) SiH2 wag 774.4[33] �11.5 762.9 757.4[42] 17.0 5.59 (b2) SiC a-str. 395.7[65] �17.9 377.8 – –

Notes: aReference 4.bThe absolute intensity is 167.2 km mol�1.

Table 14. Harmonic and anharmonic vibrational frequencies (in cm�1), and infrared intensities [%ratio relative to the largestintensity] for the 1A1 state of vinylidensilanediyl, H2C¼C¼Si (3S–H2), at the cc-pCVQZ CCSD(T) level of theory. Theanharmonic vibrational frequencies were obtained by VPT2.

Mode number (assignment) harmonic D(anh.-harm.) anharmonic Expt.a D(harm.-expt.) D(anh.-expt.)

1 (a1) CH2 s-str. 3091.8[63] �150.9 2940.9 – –2 (a1) CC str. 1707.7[100]b �33.3 1674.5 1667.9[100] 39.8 6.63 (a1) CH2 scis. 1442.8[7] �38.6 1404.2 – –4 (a1) SiC str. 739.2[56] �7.9 731.3 – –5 (b1) CH2 wag 984.5[60] �3.6 981.0 957.7[100] 26.8 23.36 (b1) SiCC oop-bend 185.3[14] �2.2 183.1 – –7 (b2) CH2 a-str. 3166.5[8] �153.1 3013.4 – –8 (b2) CH2 rock 1023.5[21] �18.7 1004.8 – –9 (b2) SiCC ip-bend 256.3[61] �1.3 255.0 – –

Notes: aReference 4.bThe absolute intensity is 37.7 kmmol�1.


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resonances were observed between 4 (a1) and 9 (b2)modes, 29� 4. For the standard 4S isotopologue[H2SiC2 (4S–H2)] seven fundamental vibrational fre-quencies have been experimentally observed. Thestrongest IR intensity is theoretically predicted forthe SiH2 scissoring !3(a1) mode followed by the Si–Cs-stretching, SiH2 s- and a-stretching modes. Theordering of these IR intensities is consistent with theexperimental observations. In the last column of Table15 the theoretical anharmonic vibrational frequenciesfor the standard H2SiC2 (4S–H2) are compared withthe experimental fundamental frequencies. The largestdeviations (25.0 and 20.1 cm�1) between the predictedanharmonic and experimental fundamental frequenciesare found for the SiC symmetric stretching 4(a1) andSiH2 anti symmetric stretching 6(b2) modes. Excludingthese modes the mean absolute deviation for theremaining five modes is 10.0 cm�1. For the standardH2SiC2 (4S–H2) molecule the absolute differencesbetween the seven theoretical harmonic and anharmo-nic and experimental fundamental vibrational frequen-cies are D[u(theor.)�l(expt.)]¼ 230.7 cm�1 andD[l(theor.)�l(expt.)]¼ 95.3 cm�1, respectively. It isobvious that the anharmonic effects significantlyimprove the theoretical harmonic results. For thedideutero isotopologue D2SiC2 (4S-D2) in Table S16the largest deviation is 21.5 cm�1 for the SiD2 wagging8(b2) mode. The mean absolute deviation for theremaining six modes is 8.3 cm�1, which is in reasonableagreement. In the last columns of Tables S17-S19 the

corresponding differences between the theoreticalanharmonic and experimental fundamental vibrationalfrequencies for the H2Si

13C2 (4S�13C2, in Table S17),H2Si

13CC (4S�13CC, in Table S18), and HDSiC2 (4S–HD, in Table S19) isotopologues are provided. Foreach of the three isotopologues the largest deviationsare: D6(b1)¼ 20.0 cm�1 for H2Si

13C2;D7(a00)¼ 20.0 cm�1 for H2Si

13CC; D5(a0)¼ 24.2 cm�1

for HDSiC2. Excluding these largest deviations, themean absolute deviations for the remaining vibrationalmodes of the three isotopologues are 9.3 (H2Si

13C2),9.4 (H2Si

13CC), and 8.0 cm�1 (HDSiC2), respectively.The anharmonic fundamentals 5(a2) and 9(b2) for

silacyclopropyne have not yet been observed. For 5this is readily understood, since this frequency is IRforbidden. However, 9 has the third highest IRintensity (108 kmmol�1) of the nine fundamentals.Our predictions associated with 9 should be highlyreliable, and we hope that observation will be shortlyforthcoming.

5.3. Isotopic shifts for vibrational frequencies


In Table 16 isotopic shifts for harmonic and anhar-monic vibrational frequencies (in cm�1) of SiC2D2 (1S-D2), Si13C2H2 (1S�13C2), and Si13CCH2 (1S�13C)with respect to the standard 1-silacyclopropenylidene(1S–H2) isotopologue are compared with the

Table 16. Theoretical and experimental isotopic shifts of vibrational frequencies (cm�1) for three 1S isotopologues, withrespect to the parent isotopologue, at the cc�pCVQZ CCSD(T) level of theory. The anharmonic vibrational frequencies wereobtained by VPT2.

Mode (symmetry)SiC2D2

theory SiC2D2 expt.Si13C2H2

Theory Si13C2H2 expt.Si13CCH2

theory Si13CCH2 expt.

D!1(a1)(a0) �805.5 �12.7 �5.0

D!2(a1)(a0) �56.8 �53.9 �26.6

D!3(a1)(a0) �268.4 �2.8 �1.5

D!4(a1)(a0) 7.3 �13.6 �6.7

D!5(a2)(a00) �200.4 �10.7 �5.3

D!6(b1)(a00) �164.2 �4.0 �2.0

D!7(b2)(a0) �841.3 �9.9 �6.3

D!8(b2)(a00) �157.2 �18.8 �9.2

D!9(b2)(a0) �91.4 �15.2 �7.9

D1(a1)(a0) �741.7 �735.1 �12.6 �12.9 �4.8 �4.6D2(a1)(a0) �53.7 – �51.0 – �25.2 –D3(a1)(a0) �260.2 – �2.3 �2.6 �1.3 �1.4D4(a1)(a0) 7.0 7.2 �13.3 �13.1 �6.6 �6.4D5(a2)(a00) �194.6 – -10.3 – �5.1 –D6(b1)(a00) �161.4 �158.8 �3.8 �3.7 �2.0 �1.9D7(b2)(a0) �798.3 �777.8 �9.3 �9.9 �6.1 �5.9D8(b2)(a0) �148.3 �147.2 �18.1 �17.9 �8.9 �8.7D9(b2)(a0) �89.1 �88.2 �14.6 �14.5 �7.6 �7.6

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experimental observations [4]. Due to deuteration

(SiC2D2) the isotopic shifts of the vibrational modes

involving the H atoms [such as CH(D) stretchings andCCH(D) bendings] are significantly large, as expected.

Both theoretical harmonic and anharmonic vibrationalfrequencies reproduce the experimental isotopic shifts

quite well, positively confirming the experimentalassignments of vibrational modes. For the 13C labelled

isotopologues (Si13C2H2 and Si13CCH2) the C–C

stretching 2(a1) modes show the largest isotopicshifts. Specifically the 13C isotopic shifts from theoret-

ical anharmonic vibrational frequencies are in excellentagreement with the experiment, differences being less

than 0.6 cm�1.


The theoretical and experimental isotopic shifts

(in cm�1) for the four isotopologues with respect to

the standard HCCSiH (2S–HH) are provided inTable 17. For the deuterated isotopologues

(DCCSiD, DCCSiH, HCCSiD) the isotopic shifts ofthe vibrational modes involving the H atoms [such as

CH(D) and SiH(D) stretchings, CCH(D) and CSiH(D)bendings] are markedly large as anticipated. For the13C labelled isotopologue (H13C13CSiH) the C–Cstretching 3(a

0) mode presents the largest isotopic

shift. Probably due to strong couplings among various

vibrational modes, the agreement between theoretical

and experimental isotopic shifts is less satisfactorycompared to the 1S isotopologues.

5.3.3. Vinylidensilanediyl (3S)

In Table 18 theoretical and experimental isotopic shiftsof vibrational frequencies for the four isotopologueswith respect to the standard H2C¼C¼Si (3S–H2) arereported. Experimentally only two vibrational modes,the C–C stretching 2(a1) and CH2 wagging 5(b1)frequencies, have been observed. For the 13C labelledisotopologues the isotopic shifts from theoreticalharmonic and anharmonic vibrational frequencies arein good agreement with the experimental values. Thelargest differences are 1.3 cm�1 for harmonic vibra-tional frequencies and 0.3 cm�1 for anharmonic vibra-tional frequencies, respectively.


In Table 19 theoretical isotopic shifts of vibrationalfrequencies for the three isotopologues with respect tothe standard H2SiC2 (4S–H2) are compared with thecorresponding experimental observations. For the 13Clabelled isotopologues theoretical harmonic and anhar-monic isotopic shifts are in good agreement withexperimentally available four vibrational modes, withdiscrepancies less than 2.7 cm�1 (harmonic) and0.3 cm�1 (anharmonic), respectively.

Table 17. Theoretical and experimental isotopic shifts of vibrational frequencies (cm�1) for four 2S isotopologues, with respectto the parent isotopologue, at the cc-pCVQZ CCSD(T) level of theory. The anharmonic vibrational frequencies were obtainedby VPT2.

Mode(symmetry)

DCCSiDtheory

DCCSiDexpt.

DCCSiHtheory

DCCSiHexpt.

HCCSiDtheory

HCCSiDexpt.

H13C13CSiHtheory

H13C13CSiHexpt.

D!1(a0) �792.2 �792.2 0.0 �17.3

D!2(a0) �581.2 �0.1 �581.2 �0.1

D!3(a0) �121.2 �121.3 0.1 �73.5

D!4(a0) �176.9 �0.9 �174.1 �2.8

D!5(a0) �135.4 �134.5 �1.2 �6.5

D!6(a0) �31.1 �6.0 �25.5 �11.3

D!7(a0) �22.5 �12.7 �10.6 �7.1

D!8(a00) �154.9 �154.9 0.0 �7.3

D!9(a00) �12.9 �11.1 �1.7 �5.9

D1(a0) �734.1 �734.1 �734.3 �734.6 �0.1 0.0 �16.2 �15.3D2(a0) �542.6 �534.6 �0.9 0.3 �542.5 �534.7 �0.6 0.0D3(a0) �115.5 �116.0 �115.8 �116.1 0.9 �0.3 �70.8 �71.8D4(a0) �168.8 �173.2 �0.5 �0.9 �165.7 �170.2 �2.6 �2.3D5(a0) �137.2 �134.0 �133.0 � �5.6 �13.8 �6.7 �5.5D6(a0) �32.7 �29.5 �6.0 5.0 �26.9 � �11.0 �10.0D7(a0) �23.2 – �12.7 – �11.6 – �7.3 –D8(a00) �154.8 – �151.1 – �4.0 �0.2 �6.1 �5.7D9(a00) �10.3 – �8.9 – �1.2 – �5.6 –


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6. Concluding remarks

Anharmonic rotational-vibrational analyses have been

carried out for the electronic singlet states of 1-

silacyclopropenylidene (1S) and its three isomers (2S–

4S) employing second-order vibrational perturbation

theory (VPT2). The equilibrium geometries and quartic

force fields of four SiC2H2 isomers have been deter-

mined using ab initio cc-pCVQZ CCSD(T) level oftheory. The predicted rotational constants, centrifugaldistortion constants, harmonic and anharmonic quan-tities for SiC2H2 molecules are in good agreement withavailable experimental values. Specifically, excluding

Table 18. Theoretical and experimental isotopic shifts of vibrational frequencies (cm�1) for four 3S isotopologues, with respectto the parent isotopologue, at the cc-pCVQZ CCSD(T) level of theory. The anharmonic vibrational frequencies were obtained byVPT2.

Mode(symmetry)

D2CCSitheory

D2CCSiexpt.

H132 C13CSitheory

H132 C13CSiexpt.

H132 CCSitheory

H132 CCSiexpt.

H2C13CSi

theoryH2C

13CSiexpt.

D!1(a1) �836.1 �5.8 �5.8 �0.1D!2(a1) �35.5 �61.6 �23.4 �36.9D!3(a1) �365.0 �7.3 �0.9 �6.9D!4(a1) �33.3 �13.5 �10.8 �3.1D!5(b1) �199.1 �10.3 �9.4 �0.8D!6(b1) �8.3 �6.1 �0.8 �5.3D!7(b2) �809.7 �12.8 �12.8 0.0D!8(b2) �201.3 �12.0 �7.6 �4.4D!9(b2) �23.6 �7.1 �0.6 �6.4

D1(a1) �757.2 – 3.9 – �8.9 – 8.8 –D2(a1) �22.2 �19.6 �60.1 �60.3 �22.5 �22.7 �36.4 �36.1D3(a1) �345.4 – �3.9 – 1.6 – �6.4 –D4(a1) �34.1 – �13.3 – �10.6 – �3.1 –D5(b1) �197.7 – �10.4 �10.1 �9.4 �9.1 �1.0 �1.1D6(b1) �9.1 – �5.7 – �0.9 – �4.8 –D7(b2) �751.1 – �11.9 – �11.7 – �0.2 –D8(b2) �194.7 – �12.1 – �7.5 – �4.6 –D9(b2) �24.5 – �7.0 – �0.8 – �6.2 –

Table 19. Theoretical and experimental isotopic shifts of vibrational frequencies (cm�1) for three 4S isotopologues, withrespect to the parent isotopologue, at the cc-pCVQZ CCSD(T) level of theory. The anharmonic vibrational frequencies wereobtained by VPT2.

Mode(symmetry)

D2SiC2

theoryD2SiC2

expt.SiH13

2 C2

theorySiH13

2 C2

expt.H2Si

13CCtheory

H2Si13CC

expt.

D!1(a1)(a0) �648.4 0.0 0.0

D!2(a1)(a0) 0.6 �71.1 �35.2

D!3(a1)(a0) �320.5 �0.2 �0.1

D!4(a1)(a0) 20.8 �17.8 �8.5

D!5(a2)(a00) �69.4 �2.9 �1.5

D!6(b1)(a00) �634.0 0.0 0.0

D!7(b1)(a00) �159.5 �1.3 �0.6

D!8(b2)(a0) �182.7 �2.6 �1.6

D!9(b2)(a0) �5.7 �13.2 �6.7

D1(a1)(a0) �609.2 �612.5 0.0 0.0 0.0 0.0D2(a1)(a0) 1.5 1.3 �68.7 �68.4 �34.0 �33.8D3(a1)(a0) �314.5 �300.9 �0.5 0.0 �0.3 0.0D4(a1)(a0) 15.7 5.8 �16.7 – �8.1 –D5(a2)(a00) �66.5 – �2.4 – �1.2 –D6(b1)(a00) �593.5 �602.6 0.1 0.0 0.1 0.0D7(b1)(a00) �158.2 �175.9 �1.3 – �0.7 –D8(b2)(a0) �180.2 �153.2 �2.2 – �1.3 –D9(b2)(a0) �4.8 – �12.5 – �6.3 –

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highly anharmonic CH (CD) and SiH (SiD) stretchingvibrational modes the mean deviations between theo-retical anharmonic and experimental fundamentalfrequencies are 4.1 cm�1 (5 isotopologues, 25 modes)for isomer 1S and 4.9 cm�1 (7 isotopologues, 38modes) for isomer 2S, respectively. The correspondingdeviation for isomer 4S is 8.6 cm�1 (5 isotopologues, 22modes) without the SiC symmetric stretching, SiH2

anti-symmetric stretching, and SiD2 wagging modes.From the anharmonic analyses for the four isomers(1S–4S), it is demonstrated that the anharmonic effectsgreatly improve the harmonic results. Reliable theo-retical predictions have been made for the as yetundetected modes of vinylidensilanediyl and the 9mode of silacyclopropyne. We hope that the presentresearch will aid further characterization of the SiC2H2

molecules and encourage theoretical and experimentalstudies in the areas of organo-silicon chemistry, inter-stellar chemistry, chemical dynamics, and high-resolu-tion spectroscopy.

Supplementary material available

Harmonic and anharmonic vibrational frequencies andtheir associated IR intensities for four 1S isotopolo-gues are given in Tables S1–S4. The correspondingquantities for six 2S isotopologues are given in TablesS5–S10, for five 3S isotopologues in Tables S11–S15,and for four 4S isotopologues in Tables S16–S19.

Acknowledgements

This research was supported by the Department of Energy,Office of Basic Energy Sciences, Division of Chemistry,Fundamental Interactions Branch (Grant No. DE-FG02-00ER14748) and used resources of the National EnergyResearch Scientific Computing Center (NERSC), which issupported by the Office of Science of the US Department ofEnergy under Contract No. DE-AC02-05CH11231. Q.W.and Q.H. gratefully acknowledge the support provided bythe China Scholarship Council (CSC) [2008] 3019, and theUniversity of Georgia Center for Computational QuantumChemistry for hospitality during their one-year visit. Wethank Dr Justin M. Turney for many helpful discussions.Q.W. is indebted to China Postdoctoral Science Foundation.We are also indebted to the National Natural ScienceFoundation of China (Grant No. 21103097) and the 111Project (B07012) by Ministry of Education in China.

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Anharmonic vibrational analyses for the 1-silacyclopropenylidene molecule and its three isomers