from acetylene complexes to vinylidene structures: the gec2h2 system

From Acetylene Complexes to Vinylidene Structures:The GeC2H2 System

QIANG HAO,1,2 ANDREW C. SIMMONETT,2 YUKIO YAMAGUCHI,2 DE-CAI FANG,1 HENRY F. SCHAEFER III2

1College of Chemistry, Beijing Normal University, Beijing 100875, China2Center for Computational Quantum Chemistry, University of Georgia, Athens, GA 30602

Received 5 October 2009; Revised 5 April 2010; Accepted 6 May 2010DOI 10.1002/jcc.21593

Published online 2 July 2010 in Wiley Online Library (wileyonlinelibrary.com).

Abstract: The expansion of germanium chemistry in recent years has been rapid. In anticipation of new experiments, asystematic theoretical investigation of the eight low lying electronic singlet GeC2H2 stationary points is carried out. Thisresearch used ab initio self-consistent-field (SCF), coupled cluster (CC) with single and double excitations (CCSD), andCCSD with perturbative triple excitations [CCSD(T)] levels of theory and a variety of correlation–consistent polarizedvalence cc-pVXZ and cc-pVXZ-DK (Douglas-Kroll) (where X = D, T, and Q) basis sets. At all levels of theory used in thisstudy, the global minimum of the GeC2H2 potential energy surface (PES) is confirmed to be 1-germacyclopropenylidene(Ge-1S). Among the eight singlet stationary points, seven structures are found to be local minima and one structure(Ge-6S) to be a second-order saddle point. For the seven singlet minima, the energy ordering and energy differences (inkcal mol−1, with the zero-point vibrational energy corrected values in parentheses) at the cc-pVQZ-DK (Douglas-Kroll)CCSD(T) level of theory are predicted to be 1-germacyclopropenylidene (Ge-1S) [0.0(0.0)] < vinylidenegermylene(Ge-3S) [13.9(13.5)] < ethynylgermylene (Ge-2S) [17.9(14.8)] < Ge-7S [37.4(33.9)] < syn-3-germapropenediylidene(Ge-8S) [41.2(37.9)] < germavinylidenecarbene (Ge-5S) [66.6(61.6)] < nonplanar germacyclopropyne (Ge-4S) [67.8(63.3)]. These seven isomers are all well below the dissociation limit to Ge (3P) + C2H2(X 1�+

g ). This system seemsparticularly well poised for matrix isolation infrared (IR) experiments.

© 2010 Wiley Periodicals, Inc. J Comput Chem 32: 15–22, 2011

Key words: GeC2H2; DKH2; germanium; acetylene; vinylidence; coupled cluster

Introduction

Carbenes, especially the small carbenes, are very important interme-diates in a variety of chemical reactions and have been extensivelystudied both experimentally and theoretically. In 1960, Skell andKlebe1 reported the observation of triplet propargylene (C-2T),and a series of experimental and theoretical studies were carriedout on these C3H2 isomers. In 1984, aided by theory,2 Reisenaueret al.3 presented the first laboratory generation of cyclopropenyli-dene (C-1S) and isomers thereof by flash thermolysis, throughisolation in rare-gas matrices at 10 K, as shown in Scheme 1. This(C-1S) isomer has also been detected4, 5 and deduced to be themost abundant cyclic hydrocarbon observed in interstellar space.6

A series of theoretical studies on these C3H2 isomers and otherpossible structures have been published.2, 7–14

The analogous SiC2H2 isomers have also drawn much attentionduring the past three decades and have been found to have singletground states.15, 16 In 1986, Frenking et al.17 theoretically investi-gated 15 different SiC2H2 structures at the Hartree-Fock (HF) andconfiguration interaction with single and double excitations (CISD)levels of theories and suggested 1-silacyclopropenylidene (Si-1S,

in Scheme 2) as the global minimum. In 1994 and 1995, Maieret al. reported, in a beautiful series of experiments, the generationof SiC2H2 isomers by high-vacuum flash pyrolysis,18–20 as shownin Scheme 2. The microwave spectra of Si-1S and Si-3S have alsobeen published.6, 21 Subsequent higher level theoretical studies havefollowed.6, 22–26

Much less research27–31 has been reported on the isovalent ger-manium systems. Kassaee et al. investigated the structures and

Additional Supporting Information may be found in the online version ofthis article.

Correspondence to: H. F. Schaefer; e-mail: [email protected]

Contract/grant sponsor: China Scholarship Council; contract/grant number:2008604057

Contract/grant sponsor: National Natural Science Foundation of China;contract/grant number: 20773016

Contract/grant sponsor: Doctoral Program of Higher Education of China;contract/grant number: 20080003110008

Contract/grant sponsor: U.S. National Science Foundation; contract/grantnumber: CHE-074986

© 2010 Wiley Periodicals, Inc.

16 Hao et al. • Vol. 32, No. 1 • Journal of Computational Chemistry

Scheme 1. The most significant structures for C3H2 isomers.

energetics of the GeC2H2 isomers at HF, second-order Møller-Plesset theory (MP2), and B3LYP (density functional theory, DFT)levels of theory.27–29 Recently, Teng and Xu published a matrixisolation infrared (IR) spectroscopic and theoretical study on reac-tions of group 14 atoms with acetylene. Laser-ablated group 14metal atoms were codeposited at 4 K with acetylene in excess argon.Ge-1S and Ge-2S as well as Sn(C2H2), Sn2CCH2, HSnCCH, andHPbCCH were formed and characterized using IR spectroscopy onthe basis of the isotopic shifts, stepwise annealing, and the compari-son with theoretical (DFT) predictions.31 For Ge-1S, they observedthe four vibrational modes at 1453.1 (C–C stretching), 1045.9 (CCHdeformation), 644.5 (C2H2 tilt), and 582.6 cm−1 (Ge C stretching).As to Ge-2S, a new band at 1831.3 cm−1 appeared after broadbandirradiation and was assigned to a Ge-H stretching vibration.

In this research, after the fruitful experimental and theoreti-cal findings for the C3H2 and SiC2H2 analogues, eight closed-shell electronic singlet states germylene GeC2H2 structures shownin Scheme 3 are systemically investigated using high-accuracyab initio methods in concert with large Gaussian basis sets. Toencourage future experimental identification of the GeC2H2 iso-mers, reliable geometries, dipole moments, harmonic vibrationalfrequencies, and associated infrared (IR) intensities for each struc-ture are presented.

Electronic Structure Considerations

The global minimum of the GeC2H2 molecule appears27–29 to bethe 1A1 state of 1-germacyclopropenylidene (Ge-1S), which has anelectron configuration of:

(core)(9a1)2(5b2)

2(10a1)2(11a1)

2(4b1)2(12a1)

2(6b2)2 1A1

In the above (core)[= (1a1)2(2a1)

2(1b1)2(1b2)

2(3a1)2(4a1)

2(2b2)2

(5a1)2(2b1)

2(3b2)2(6a1)

2(7a1)2(1a2)

2(3b1)2(8a1)

2(4b2)2]denotes

Scheme 2. The most significant structures for singlet SiC2H2 isomers.

Scheme 3. Some possible structures of singlet GeC2H2 species.

the 16 lowest lying core (Ge: 1s, 2s, 2p, 3s, 3p, 3d-like, and C:1s-like) orbitals. The other seven GeC2H2 structures in Scheme 3,with analogous “core” notation, have the electron configurations(�1) described in Table S9.

Theoretical Methods

In this research, the correlation-consistent valence polarized basissets cc-pVXZ and cc-pVXZ-DK (where X = D, T, and Q)developed by Dunning and coworkers32, 33 were used. The cc-pVXZ-DK basis sets have been specifically recontracted for relativisticstudies based on the second-order Douglas-Kroll-Hess (DKH2)approximation.34–36 Zeroth-order descriptions of stationary pointswere obtained using restricted Hartree-Fock (RHF) self-consistentfield (SCF) theory. Dynamic correlation effects were includedusing coupled cluster (CC)37–39 with single and double excita-tions (CCSD)40, 41 and CCSD with perturbative triple excitations[CCSD(T)]42–44 methods. The correlated wavefunctions were con-structed by freezing the 11 lowest lying core (Ge: 1s, 2s, 2p,3s, 3p-like, and C: 1s-like) orbitals and scalar relativistic effectswere taken into account through the DKH2 approximation. Toanalyze the sensitivity of geometries and physical properties ofthe GeC2H2 molecules to the level of correlation effects, 14electrons in 14 molecular orbitals (14e/14MO) complete activespace SCF (CASSCF)45, 46 wavefunctions were constructed at thecc-pVQZ-DK CCSD(T) optimized geometries.

For the nonrelativistic computations, the structures of the sta-tionary points were optimized using analytic derivative methods,and dipole moments, harmonic vibrational frequencies, and asso-ciated infrared (IR) intensities were determined analytically. Forthe relativistic research, geometries were optimized using a robust4-point numerical differentiation method. Dipole moments andharmonic vibrational frequencies were evaluated numerically. Elec-tronic structure computations were carried out using the AcesII (Mainz-Austin-Budapest version),47, 48 Molpro,49 Psi2,50 andPsi351 quantum chemistry packages.

Results and Discussion

The optimized geometries and the predicted total energies and phys-ical properties for the eight structures at the cc-pVQZ-DK CCSD(T)

Journal of Computational Chemistry DOI 10.1002/jcc

From Acetylene Complexes to Vinylidene Structures 17

Figure 1. Predicted geometries for the eight GeC2H2 structures at thecc-pVQZ-DK CCSD(T) level of theory. Bond lengths are in Å.

level of theory are presented in Figure 1 and in Table 1, respectively.The geometries for the eight structures at all levels of theory are pro-vided in Figures S1–S8, and the corresponding total energies andphysical properties are given in Tables S1–S8 as SupplementaryInformation.

CASSCF Wavefunctions

The reference configuration (�1) and several configuration statefunctions (CSFs) for the eight cc-pVQZ-DK CASSCF wavefunc-tions at the cc-pVQZ-DK CCSD(T) optimized geometries whoseabsolute CI coefficients are >0.06 are presented in Table S9. Theelectron occupation numbers (Nocc) for the CASSCF active orbitalsin terms of natural orbitals (NOs) are provided in Table S10. Forall the structures, the leading CI coefficients are sufficiently largeto demonstrate the predominantly single-reference nature of theassociated wavefunctions.

Geometries

1-Germacyclopropenylidene (Ge-1S in Figure 1 and Figure S1)

This structure is the global minimum on the singlet potential energysurface (PES) of GeC2H2. All three unique bond lengths [re(GeC),re(CC), and re(CH)] decrease with increase of the basis set sizeand increase with an advanced treatment of correlation effects. Thelatter feature may be attributed to the doubly excited CSFs (�2

and �3) shown in Table S9, where the electrons shift from the C–C π bonding (4b1) and Ge C σ bonding (6b2) MOs to the C–Cπ antibonding (2a2) and Ge C σ antibonding (7b2) MOs. TheC–C bond length 1.342 Å at the cc-pVQZ-DK CCSD(T) level oftheory is similar to that of the corresponding SiC2H2 [Si-1S, 1.348 Åat the cc-pVQZ CCSD(T) level of theory], but is longer than thatfor cyclopropenylidene (C-1S, 1.326 Å). The Ge C and C–C bondlengths are predicted to be slightly shorter when scalar relativisticeffects are taken into account.

Ethynylgermylene (Ge-2S in Figure 1 and Figure S2)

Because the two dominating CSFs (�2 and �4 in Table S9) involveexcitations from orbitals with C–C π bonding character (17a′ and5a′′) to C–C π nonbonding orbitals (19a′ and 6a′′), the C–C bondlength significantly increases with more complete correlation treat-ments. On the other hand, the �3 CSF represents a double excitationfrom the 18a′ MO (in-plane C–C π bonding and Ge C antibonding)to the 6a′′ MO (Ge 3p like nonbonding), which shortens the Ge–Cbond length. The relativistic computations provide again a slightlyshorter Ge–C bond length than the standard CC calculations. TheC–C bond length 1.221 Å is similar to the corresponding value forethynylsilanediyl (Si-2S, 1.222 Å) but longer than that of acetylene(1.207 Å). Because the two C atoms have sp hybridized electronicstructure, the C–C bond has near triple bond character.

Vinylidenegermylene (Ge-3S in Figure 1 and Figure S3)

The C–C and Ge C connections in this isomer may be assigned tobe double bonds, because the 4b1 and 5b2 MOs are the C–C andGe C π bonding orbitals, respectively. These two bond lengthsincrease with correlation effects, because of the double excitationsfrom the two π bonding orbitals (4b1 and 5b2) to the nonbondingorbitals 5b1 (�3) and 6b2 (�2), as shown in Table S9. The C–C andC–H bond lengths are nearly the same as those of the correspondingvinylidenesilanediyl (Si-3S, within 0.002 Å).

Nonplanar Germacyclopropyne (Ge-4S in Figure 1 and Figure S4)

The C–C bond length for this twisted structure increases markedlywith the consideration of correlation effects. This phenomenon ismainly attributed to four dominant CSFs (�2–�5) in Table S9,which arise from excitations from the C–C σ and π bonding orbitals(12a1 and 5b1) to the σ nonbonding and π antibonding orbitals (6b2

and 2a2). The Ge–C bond length (1.911 Å) is slightly shorter thanthose of Ge-1S and Ge-2S, and the Ge-H bond distance (1.511 Å)is also shorter than that for Ge-2S.



Table 1. Theoretical Predictions of the Total Energy (in hartree), Dipole Moment (in debye), HarmonicVibrational Frequencies (in cm−1), and Zero-Point Vibrational Energy (ZPVE in kcal mol−1) for the EightStructures of the GeC2H2 System at the cc-pVQZ-DK CCSD(T) Level of Theory.

Structures Energy µe ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8 ω9 ZPVE

Ge-1S −2174.531426 0.653 3200(a1) 1475(a1) 888(a1) 607(a1) 974(a2) 671(b1) 3175(b2) 1088(b2) 597(b2) 18.11Ge-2S −2174.502851 0.354 3435(a′) 2030(a′) 1978(a′) 773(a′) 629(a′) 487(a′) 234(a′) 742(a′′) 196(a′′) 15.02Ge-3S −2174.509221 0.679 3083(a1) 1682(a1) 1433(a1) 589(a1) 979(b1) 191(b1) 3157(b2) 1011(b2) 244(b2) 17.68Ge-4S −2174.423397 4.005 2235(a1) 1787(a1) 929(a1) 661(a1) 216(a2) 2234(b1) 593(b1) 699(b2) 159(b2) 13.59Ge-5S −2174.425317 6.504 2267(a1) 1910(a1) 899(a1) 659(a1) 580(b1) 99(b1) 2272(b2) 604(b2) 138(b2) 13.13Ge-6S −2174.418602 4.041 2227(a1) 1659(a1) 934(a1) 621(a1) 96i(a2) 612(b1) 2225(b2) 667(b2) 122i(b2) 12.78Ge-7S −2174.471874 2.403 3367(a′) 1848(a′) 1737(a′) 747(a′) 738(a′) 494(a′) 260(a′) 778(a′′) 275(a′′) 14.64Ge-8S −2174.465833 2.729 3323(a′) 2057(a′) 1646(a′) 909(a′) 619(a′) 372(a′) 336(a′) 744(a′′) 101(a′′) 14.88

Germavinylidenecarbene (Ge-5S in Figure 1 and Figure S5)

The 4b1 and 5b2 MOs in Table S9 are out-of-plane Ge–C–C π

bonding and in-plane C–C π bonding orbitals, respectively. Theelectron excitations from these MOs to the nonbonding (5b1 and6b2) and C–C π antibonding (6b1) MOs naturally lengthen the Ge–C and C–C bond lengths, as shown in Figure S5. The Ge–C andC–C bond distances are shorter than those of Ge-3S, and the Ge-Hbond length is also shorter than that of Ge-4S.

Planar Germacyclopropyne (Ge-6S in Figure 1 and Figure S6)

The C–C bond length increases with the level of sophisticationbecause of the electron excitations from the C–C bonding MOs(4b1 and 12a1) to the nonbonding (5b1) and antibonding (7b2 and2a2) MOs. The Ge–C and C–C bond distances are much longerthan those for Ge-2S and Ge-4S, which demonstrates the weakerGe–C and C–C bonds in the strained three-membered ring. The Ge-H bond length is nearly the same as that of Ge-4S (within 0.001 Åat correlated levels of theory).

Ge-7S (in Figure 1 and Figure S7)

This isomer may be viewed as a bent version of Ge-2S, being stabi-lized by the Ge–C–C out-of plane π bond (specifically the 5a′′ MO).The Ge–C and C–C bond lengths are longer than those of Ge-2S andappear to release more ring strain, stabilizing the three-memberedring structure. The C–C bond length increases with the inclusionof correlation effects, because of the double excitations from theπ bonding MOs (5a′′ and 17a′) and nonbonding MO (18a′) to thenonbonding MOs (6a′′ and 19a′) and C–C π antibonding MO (7a′′).However, it should be noted that the two Ge–C bond distances (aswell as the Ge· · · X distance) are shortened upon including cor-relation effects. With the two π bonding orbitals and the almost170◦ C–C-H angle (169.4◦), the C–C bond has an sp-hybridizedelectronic structure and near triple-bond character, like Ge-2S.

syn-3-Germapropenediylidene (Ge-8S, in Figure 1 and Figure S8)

The geometrical parameters and their variations with basis sets andcorrelation effects of structure Ge-8S are similar to those of struc-ture Ge-7S. The absence of an in-plane C–C π bond and a longerbond distance suggest that the C–C bond has nearly double-bond

character. The distance between Ge and the center of the C–C bond(Ge· · · X distance) (2.060 Å) is noticeably longer than that of Ge-7S(2.034 Å), which may be attributed to the extra lone-pair electrons(nonbonding) on the C atom. Although the Ge-H bond length isshorter than that of Ge-7S, the C-H bond distance is slightly longer.

Dipole Moments

The polarization of a molecule delicately reflects, among otherthings, the configurations of the constituent atoms and their elec-tronegativities. The standard electronegativity values52, 53 for H, C,Si, and Ge are 2.20, 2.55, 1.90, and 2.01 on the “Pauling scale”,while they are 7.26, 6.73, 4.96, and 4.71 on the “Mulliken scale”.

The dipole moments (in debye) of the eight structures are in theorder of Ge-2S (0.35) < Ge-1S (0.65) < Ge-3S (0.68) < Ge-7S(2.40) < Ge-8S (2.73) < Ge-4S (4.01) < Ge-6S (4.04) < Ge-5S (6.50). The dipole moment of isomer Ge-2S, whose direction ismainly along the Ge–C bond with a sign +HCCGe−H, is the small-est in magnitude among the eight structures considered here. Thisfeature may due to the counteracting effects of the two electroposi-tive ends. The dipole moment of structure Ge-5S, whose directionis along the C2 axis with a sign −CCGeH+

2 , is the largest among theeight structures, reflecting the terminal electropositive GeH2 groupand electronegative lone-pair carbene atom. The decrease of thedipole moment with the level of sophistication may be attributed tothe excited CSF (�2), which represents a degree of electron transferfrom the C–C π bonding MO (4b1, Nocc = 1.903, negative end)to the nonbonding MO (5b1, Nocc = 0.081, positive end), partiallyneutralizing the charge separation in the molecule.

Harmonic Vibrational Frequencies and Infrared (IR) Intensities

Among the eight low lying singlet GeC2H2 structures, seven struc-tures (Ge-1S, Ge-2S, Ge-3S, Ge-4S, Ge-5S, Ge-7S, and Ge-8S)have been characterized to be minima, whereas one structure(Ge-6S) is a second-order saddle point.

1-Germacyclopropenylidene (Ge-1S in Table 1 and Table S1)

All the harmonic vibrational frequencies decrease with an improvedtreatment of correlation effects, whereas there are no significantdifferences between the nonrelativistic and relativistic predictions.The two C-H stretching frequencies [ω1(a1) = 3200 cm−1and



ω7(b2) = 3175 cm−1] are lower than the corresponding frequen-cies of acetylene (3502 cm−1 and 3410 cm−1). The C–C stretchingfrequency [ω2(a1) = 1475 cm−1] lies in between the correspond-ing frequencies of 1-silacyclopropenylidene (Si-1S, 1467 cm−1) andcyclopropenylidene (C-1S, 1622 cm−1). Our theoretically predictedharmonic vibrational frequencies for ω2, ω6, ω8, and ω9 modes(1475, 671, 1088, and 597 cm−1, respectively) are reasonably con-sistent with the experimental fundamental frequencies31 (1453.1,644.5, 1045.9, and 582.6 cm−1). These four modes have relativelystrong IR intensities, as shown in Table S1, and another mode(ω4) with a considerably large theoretical IR intensity, may alsobe detected.

Ethynylgermylene (Ge-2S in Table 1 and Table S2)

The C–C stretching frequency [ω2(a′) = 2030 cm−1] of Ge-2Sis slightly higher than that of the isolated acetylene molecule[2006 cm−1 at the cc-pVQZ level]. Similarly, the C-H stretchingfrequency (3435 cm−1) is close to the corresponding frequencies(3502 cm−1 and 3410 cm−1) of C2H2, showing the triple-bondcharacter of the C–C bond in the germanium structure. All vibra-tional modes, except ω7(a′) and ω9(a′′) modes, present significantIR intensities. Specifically, the Ge-H stretching [ω3(a′)] modepossesses an extraordinarily strong intensity of 287 km mol−1.Therefore, the experimentally detected fundamental frequency(1831.3 cm−1) can be assigned to the Ge-H stretching mode [ω3(a′),1978 cm−1], as Teng and Xu’s suggestion.31

Vinylidenegermylene (Ge-3S in Table 1 and Table S3)

The harmonic vibrational frequency for the C–C stretching mode(ω2 = 1682 cm−1) of Ge-3S is markedly higher than the corre-sponding mode of the global minimum Ge-1S (ω2 = 1475 cm−1),which indicates the higher multi-bond character of isomer Ge-3Sthan Ge-1S. Our theoretical computations predict relatively strongIR intensities for the five vibrational modes [ω1(a1), ω2(a1), ω4(a1),ω5(b1), and ω9(b2)].

Nonplanar Germacyclopropyne (Ge-4S in Table 1 and Table S4)

There are two imaginary vibrational frequencies [ω5(a2) andω9(b2)] at the RHF level, and one imaginary vibrational frequency(ω9) at the cc-pVDZ CCSD, cc-pVDZ-DK CCSD, and cc-pVDZ-DK CCSD(T) levels of theory. However, they become real with thelarger basis sets. The harmonic vibrational frequency for the C–Cstretching mode [ω2 = 1787 cm−1] is much higher than the corre-sponding mode of isomer Ge-1S (ω2 = 1475 cm−1), reflecting theshorter C–C bond length of Ge-4S. For isomer Ge-4S, all vibrationalmodes, except ω2(a1) and ω5(a2) modes, have markedly large IRintensities.

Germavinylidenecarbene (Ge-5S in Table 1 and Table S5)

The vibrational frequency for the C–C stretching mode [ω2(a1) =1910 cm−1] is much higher than the corresponding mode of iso-mer Ge-1S (1475 cm−1) and lower than that of isomer Ge-2S(2030 cm−1). All vibrational modes, excluding ω6(b1) and ω9(b2)

modes, have significant associated IR intensities. Among them, the

C–C stretching [ω2(a1)] mode has a particularly strong intensity of513 km mol−1.

Planar Germacyclopropyne (Ge-6S in Table 1 and Table S6)

Structure Ge-6S has two imaginary vibrational frequencies for theGeH2 twisting (ω5) and Ge–C asymmetric stretching (ω9) motions,indicating a second-order saddle point. The twisting mode [ω5(a2)]leads Ge-6S to Ge-4S, whereas the Ge–C antisymmetric stretchingmode [ω9(b2)] takes Ge-6S to Ge-5S. Because of the longer C–Cbond length, the vibrational frequency of the C–C stretching mode[ω2(a1) = 1659 cm−1] is lower than the corresponding mode forisomer Ge-4S [ω2(a1) = 1787 cm−1].

Ge-7S (in Table 1 and Table S7)

The harmonic vibrational frequencies of the C-H (ω1 = 3367 cm−1)and Ge-H (ω2 = 1848 cm−1) stretching modes are slightly lowerthan the corresponding modes for isomer Ge-2S (ω1 = 3435 cm−1

and ω3 = 1978 cm−1, respectively), indicating weaker (and longer)C-H and Ge-H bonds of this isomer. For this structure, all vibrationalmodes, except ω3(a′), ω7(a′), and ω9(b′′), have considerable IRintensities.

syn-3-Germapropenediylidene (Ge-8S in Table 1 and Table S8)

The harmonic vibrational frequency of the Ge-H stretching mode ofstructure Ge-8S (ω2 = 2057 cm−1) is significantly higher than thecorresponding frequencies of structures Ge-2S (ω3 = 1978 cm−1)and Ge-7S (ω2 = 1848 cm−1) and shows the strongest (and shortest)Ge-H bond among the three Cs isomers. On the other hand, isomerGe-8S presents the lowest C–C stretching (ω3 = 1646 cm−1) andC-H stretching (ω1 = 3323 cm−1) frequencies among the threeCs isomers. Noticeable IR intensities are predicted for the fivevibrational modes, ω1(a′)-ω4(a′) and ω8(a′′), of structure Ge-8S.

Energetics

The total energies for the eight GeC2H2 structures are presentedin Tables S1–S8 in the Supporting Information, and the relativeenergies for the seven structures with respect to the global minimum(Ge-1S) are presented in Table 2.

Isomer Ge-1S, 1-germacyclopropenylidene, is unambiguouslyseen to be the global minimum on the singlet PES of GeC2H2.Isomer Ge-3S that lies 13.9 (13.5) kcal mol−1 [where the ZPVE cor-rected value is shown in parentheses, at the cc-pVQZ-DK CCSD(T)level of theory] above Ge-1S is the second lowest lying isomer. Asindicated by the largest total electron occupation number in the vir-tual space of Ge-3S (0.32), the energy difference between thesetwo structures becomes smaller with the level of correlation treat-ment. The third lowest lying structure is predicted to be Ge-2S,which lies 17.9 (14.8) kcal mol−1 above the global minimum. Struc-tures Ge-7S and Ge-8S, which are 37.4 (33.9) kcal mol−1 and 41.2(37.9) kcal mol−1 higher in energy than structure Ge-1S, are pre-dicted to be the fourth and fifth lowest lying isomers. These firstthree structures (Ge-1S, Ge-2S, and Ge-3S) are relatively low lyingand may be identified with appropriate laboratory conditions.31 Forthese three isomers Kassaee et al. presented the relative energiesto be 0.0 (Ge-1S), 11.9 (Ge-3S), and 16.9 kcal mol−1 (Ge-2S) at



Table 2. Relative Energies (in kcal mol−1, Where the ZPVE Corrected Values are Shown in Parentheses) of theGeC2H2 Structures with Respect to the 1-Germacyclopropenylidene (Ge-1S).

Theory Ge-1S Ge-2S Ge-3S Ge-4S Ge-5S Ge-6S Ge-7S Ge-8S

cc-pVDZ RHF 0.0 (0.0) 14.7 (11.5) 16.1 (15.7) 69.8 (64.1) 64.5 (59.4) 68.3 (-) 37.4 (33.6) 37.9 (34.1)cc-pVTZ RHF 0.0 (0.0) 13.7 (10.6) 16.7 (16.3) 68.2 (62.4) 64.5 (59.3) 68.0 (-) 36.8 (33.0) 38.4 (34.6)cc-pVQZ RHF 0.0 (0.0) 13.5 (10.4) 16.7 (16.3) 67.3 (61.6) 64.0 (58.7) 67.4 (-) 36.7 (32.9) 38.4 (34.6)cc-pVDZ CCSD 0.0 (0.0) 17.0 (13.7) 12.4 (12.0) 69.1 (64.1) 78.0 (73.0) 70.5 (-) 37.6 (34.0) 40.9 (37.5)cc-pVTZ CCSD 0.0 (0.0) 16.8 (13.7) 14.9 (14.4) 66.6 (61.9) 80.1 (75.2) 69.5 (-) 38.1 (34.6) 41.9 (38.4)cc-pVQZ CCSD 0.0 (0.0) 16.9 (14.3) 15.1 (14.6) 65.6 (61.0) 79.8 (75.1) 69.1 (-) 38.3 (34.7) 42.0 (23.6)cc-pVDZ CCSD (T) 0.0 (0.0) 17.5 (14.2) 11.6 (11.1) 67.8 (63.0) 65.4 (60.4) 69.1 (-) 36.7 (33.1) 40.2 (36.8)cc-pVTZ CCSD (T) 0.0 (0.0) 17.6 (14.4) 14.1 (13.6) 65.7 (61.1) 65.4 (60.5) 68.5 (-) 37.3 (33.8) 41.2 (37.8)cc-pVQZ CCSD (T) 0.0 (0.0) 17.7 (14.6) 14.2 (13.7) 64.7 (60.3) 64.4 (59.7) 68.1 (-) 37.5 (34.0) 41.3 (38.0)cc-pVDZ-DK RHF 0.0 (0.0) 14.7 (11.6) 15.7 (15.3) 72.9 (67.2) 67.0 (61.6) 71.1 (-) 37.0 (33.2) 37.6 (33.9)cc-pVTZ-DK RHF 0.0 (0.0) 13.8 (10.7) 16.3 (15.9) 71.2 (65.5) 66.9 (61.4) 70.7 (-) 36.5 (32.7) 38.2 (34.4)cc-pVQZ-DK RHF 0.0 (0.0) 13.6 (10.5) 16.3 (15.8) 70.4 (64.7) 66.3 (60.9) 70.1 (-) 36.4 (32.6) 38.1 (34.4)cc-pVDZ-DK CCSD 0.0 (0.0) 17.1 (13.9) 12.1 (11.7) 72.1 (67.0) 69.5 (64.3) 73.2 (-) 37.4 (33.8) 40.8 (37.4)cc-pVTZ-DK CCSD 0.0 (0.0) 17.0 (13.9) 14.7 (14.2) 69.5 (64.6) 68.8 (63.7) 72.1 (-) 38.0 (34.4) 41.7 (38.3)cc-pVQZ-DK CCSD 0.0 (0.0) 17.1 (14.0) 14.8 (14.4) 68.7 (63.9) 67.9 (62.9) 71.8 (-) 38.2 (34.6) 41.9 (23.5)cc-pVDZ-DK CCSD (T) 0.0 (0.0) 17.7 (14.4) 11.3 (10.9) 70.7 (65.8) 67.6 (62.4) 71.7 (-) 36.6 (33.3) 40.0 (36.5)cc-pVTZ-DK CCSD (T) 0.0 (0.0) 17.8 (14.6) 13.8 (13.3) 68.5 (64.0) 67.4 (62.3) 71.1 (-) 37.3 (34.0) 41.0 (37.6)cc-pVQZ-DK CCSD (T) 0.0 (0.0) 17.9 (14.8) 13.9 (13.5) 67.8 (63.3) 66.6 (61.6) 70.8 (-) 37.4 (33.9) 41.2 (37.9)

the CCSD(T)/6-311++G**//MP2/6-311++G** level of theory.27

Their values are 1.6 (Ge-3S) lower and 2.1 kcal mol−1 (Ge-2S)higher than our predictions.

Isomer Ge-5S is determined to be the sixth lowest lying struc-tures, which lying 66.6 (61.6) kcal mol−1 above the global minimumand 52.7 (48.1) kcal mol−1 above structure Ge-3S. In this light, it iswell known that the second- and third-row atoms readily form ter-minal carbenes.54–56 The seventh lowest lying structure is predictedto be Ge-4S, which lies 67.8 (63.3) kcal mol−1 above the globalminimum. The relative energy is seen to slightly diminish with theincrease of basis set size and correlation effects. Structure Ge-4Shas a relative energy [67.8 (63.3) kcal mol−1] similar to Ge-5S. Thesecond-order saddle point Ge-6S is the highest energy structureamong the eight GeC2H2 stationary points, lying 70.8 kcal mol−1

above the global minimum Ge-1S. The eigenvectors of the two imag-inary frequencies for Ge-6S lead to the energetically lower lyingGe-4S and Ge-5S isomers, respectively.

The most plausible dissociation reaction for each of the elec-tronic singlet states of the GeC2H2(S) isomers is

GeC2H2(S) → Ge(1D) + C2H2(X 1�+

g

)(1)

The lowest singlet state (1D) of Ge is experimentally determinedto be 7125.26 cm−1 (20.4 kcal mol−1) above the 3P ground state.57

The total energy for Ge (3P) + C2H2 (X 1�+g ) is computed to be

−2174.42135 hartree at the cc-pVQZ-DK CCSD(T) level of theory.The energy difference between the global minimum Ge-1S and Ge(3P) + C2H2 (X 1�+

g ) is 0.11008 hartree (69.1 kcal mol−1) at thesame level. The classical dissociation energy for the global mini-mum Ge-1S in eq. 1, therefore, is predicted to be 89.5 kcal mol−1.With the ZPVE corrections, the quantum mechanical dissociationenergy for Ge-1S becomes 88.3 kcal mol−1.

Similarly, the dissociation energies for the fifth (Ge-8S) and sev-enth (Ge-4S) lowest lying isomers are determined to be 48.3 (50.4)

and 21.7 (25.0) kcal mol−1, respectively. As a whole, the seven equi-librium structures located in this research are confirmed to be wellbelow the dissociation limit to Ge (1D) + C2H2 (X 1�+

g ).

Comparison with the C3H2 and SiC2H2 Analogues

In Table 3, relative energies and selected physical properties of var-ious C3H2 [C-analogues at the cc-pVQZ CCSD(T) level], SiC2H2

[Si-analogues at the cc-pV(Q+d)Z CCSD(T) level], and GeC2H2

[Ge-analogues at the cc-pVQZ-DK CCSD(T) level] structures arecompared. For the C-analogues, three isomers (C-1S, C-2T, andC-3S) have been both experimentally3, 5, 11 and astronomically4

observed, whereas the four Si-analogues (Si-1S, Si-2S, Si-3S, andSi-4S) have been experimentally identified.6, 19, 20 Quite recently,Teng and Xu have reported detection of the two Ge-analogues(Ge-1S and Ge-2S) by a matrix isolation IR spectroscopic study.31

For each family of the three XC2H2 (where X = C, Si, and Ge)analogues, cyclopropenylidene (C-1S, Si-1S, and Ge-1S) has beenconfirmed to be the global minimum. The next lowest lying singletequilibrium structures are predicted to be C-3S, Si-3S, and Ge-3S,followed by the C-2S, Si-2S, and Ge-2S isomers. It should be notedthat the C-2T isomer is lower in energy than the C-2S structure by10.8 (12.2) kcal mol−1.

Although isomer Si-7S has not been experimentally identified,Si-7S and Ge-7S are the fourth lowest lying equilibrium structures.The fifth-lowest lying isomer Si-4S (silacyclopropyne) has beenobserved by matrix isolation IR spectroscopy,19 whereas the cor-responding C-analogue C-4S is known to be a saddle point. TheGe-7S and Ge-8S, first located in this study, are lower in energythan isomer Ge-4S and isomer Ge-5S.

For the X-1S analogues (C-1S, Si-1S, and Ge-1S), the C–C bond distances are (1.326, 1.348, and 1.342 Å), whereas thecorresponding C–C stretching frequencies are (1622, 1467, and1475 cm−1). The shorter C–C bond distance and its associatedhigher C–C stretching frequency for the carbon analogue (C-1S)



Table 3. Selected Physical Properties and Relative Energies (in kcal mol−1) (with Respect to Their RespectiveGlobal Minima) of C3H2, SiC2H2, and GeC2H2 Structures.

Structures X-1S X-2T X-2S X-3S X-4S X-5S X-6S X-7S X-8S

X = C Energy 0.0 (0.0) 15.5 (11.3) 26.3 (23.5) 14.2 (13.3) 60.1 (-) – 51.9 (-) – –re(C–C)/Å 1.326 1.275 1.235 1.331 1.250 1.291 1.333 – –re(X-C)/Å 1.423 1.275 1.365 1.291 1.530 1.331 1.547 – –re(C-H)/Å 1.077 1.065 1.064 1.085 – – – – –re(X-H)/Å – – 1.098 – 1.088 1.085 1.088 – –θe(CXC)/◦ 55.5 – – – 48.2 – 51.0 – –

ωe(C–C)/cm−1 1622 1629,1266 1954 1117 1882 1996 1566 – –ωe(X-C)/cm−1 1305,1087 – 1099 1996 1099,614i 1117 979,426i – –

µe/debye 3.41 0.42 2.40 4.16 2.02 4.16 2.94 – –X = Si Energy 0.0 (0.0) – 21.9 (18.6) 18.2 (17.6) 49.9 (46.1) 56.7 (52.1) 57.7 (-) 42.1 (38.7) –

re(C–C)/Å 1.348 – 1.222 1.330 1.263 1.278 1.291 1.270 –re(X-C)/Å 1.826 – 1.841 1.704 1.819 1.691 1.856 1.933 –re(C-H)/Å 1.082 – 1.066 1.088 – – – 1.071 –re(X-H)/Å – – 1.516 – 1.474 1.471 1.476 1.540 –θe(CXC)/◦ 43.4 – – – 40.8 – 40.7 – –

ωe(C–C)/cm−1 1467 – 2029 1700 1798 1925 1700 1722 –ωe(X-C)/cm−1 777,684 – 608 735 822,387 789 776,134i 594 –

µe/debye 1.04 – 0.87 0.94 3.15 6.01 3.29 2.40 –X = Ge Energy 0.0 (0.0) – 17.9 (14.8) 13.9 (13.5) 67.8 (63.3) 66.6 (61.6) 70.8 (-) 37.4 (33.9) 41.2 (37.9)

re(C–C)/Å 1.342 – 1.221 1.328 1.269 1.277 1.301 1.267 1.296re(X-C)/Å 1.918 – 1.916 1.777 1.911 1.752 1.943 2.032 1.964re(C-H)/Å 1.082 – 1.065 1.088 – – – 1.071 1.073re(X-H)/Å – – 1.566 – 1.511 1.503 1.511 1.593 1.553θe(CXC)/◦ 41.0 – – – 38.8 – 39.1 – –

ωe(C–C)/cm−1 1475 – 2030 1682 1787 1910 1659 1737 1646ωe(X-C)/cm−1 607,597 – 487 589 661,159 659 621,122i 494 372

µe/debye 0.65 – 0.35 0.68 4.01 6.50 4.04 2.40 2.73

indicate efficient hybridization and the more distinctly aromaticnature of the all-carbon three-membered ring compared with thetwo heavier analogues.

The C–C bond distances for the X-2S analogues are 1.235,1.222, and 1.221 Å, whereas the related C–C stretching frequen-cies are 1954, 2029, and 2030 cm−1. The C–C bond length for eachX-2S analogue is the shortest, and the C–C stretching frequencyis the highest among the five/seven/eight singlet stationary points,indicating the strongest multiple bond character of the C–C bond.

The C-3S analogue presents a significantly lower C–C stretchingfrequency (1117 cm−1) than other two heavier analogues (1700 and1682 cm−1), although the C–C bond distances of the three X-3Sanalogues (1.331, 1.330 and 1.328 Å) are similar. This feature maybe attributed to a strong coupling between the two C–C stretchingvibrations with the same a1 symmetry.58

As mentioned above, the C-4S analogue is a saddle point,whereas the other two structures, Si-4S and Ge-4S, are minimaon the singlet PES. The C–C bond lengths for the X-4S analogue(1.250, 1.263 and 1.269 Å) are shorter than those of X-1S but longerthan those for X-2S. Consequently, the C–C stretching frequencies(1882, 1798 and 1787 cm−1) are in-between the C–C stretchingfrequencies of the X-1S and X-2S analogues.

The C–C bond distances for the X-5S analogues are 1.291, 1.278,and 1.277 Å, whereas the associated C–C stretching frequencies are1996, 1925, and 1910 cm−1. Because of the strong coupling betweenthe two C–C stretching modes mentioned above, the C-5S analoguehas the highest C–C stretching frequency (1996 cm−1).

For the X-1S and X-3S analogues, the positive ends (HCCH andCH2) and the negative ends (C:, Si:, and Ge:) reside at oppositesides of the molecules. The dipole moments of these two analogues,therefore, decrease with the positiveness of the carbene atom as X-1S (3.41, 1.04, and 0.65 debye) and X-3S (4.16, 0.94, and 0.68 D).On the other hand, for the X-4S, X-5S, and X-6S analogues, thepositive ends exist as the XH2 (CH2, SiH2, and GeH2) group. Con-sequently, the dipole moments of these three analogues increase withthe decrease of electronegativity of the X atom in the XH2 group asX-4S (2.02, 3.15, and 4.01 D), X-5S (4.16, 6.01 and 6.50 D), and X-6S (2.94, 3.29 and 4.04 D). The remaining physical properties maybe characterized in a manner similar to the chosen several examplesdescribed above.

Concluding Remarks

Ab initio molecular electronic structure theory has been employedto systematically investigate eight stationary points on the elec-tronic singlet state GeC2H2 potential energy hypersurface. Myriadphysical properties have been computed using state-of-the-artwavefunction based techniques. Seven of these molecules werefound to be equilibrium structures, whereas one structure Ge-6S is a second-order saddle point. The energetic ordering andenergy differences (in kcal mol−1, with the zero-point vibrationalenergy corrected values in parentheses) of the seven equilib-rium structures at the cc-pVQZ-DK CCSD(T) level of theory



with the second-order Douglas-Kroll-Hess approximation, are pre-dicted to be 1-germacyclopropenylidene (Ge-1S)[0.0(0.0)] <

vinylidenegermylene (Ge-3S)[13.9(13.5)] < ethynylgermylene(Ge-2S)[17.9(14.8)] < Ge-7S [37.4(33.9)] < syn-3-germapropenediylidene (Ge-8S)[41.2(37.9)] < germavinylide-necarbene (Ge-5S)[66.6(61.6)] < nonplanar germacyclopropyne(Ge-4S)[67.8 (63.3)]. These isomers are energetically well belowthe dissociation limit to Ge(1D) + C2H2(X 1�+

g ). We hope thespectroscopic fingerprints determined for the seven equilibriumstructures presented in this research will assist in the furtherexperimental characterization of the GeC2H2 isomers.

Acknowledgments

Q. H. thanks the support by the University of Georgia Center forComputational Quantum Chemistry for hospitality during his one-year visit. We thank Mr. Tongxiang Lu, Ms. Qunyan Wu, and Dr.Justin M. Turney for many helpful discussions.

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from acetylene complexes to vinylidene structures: the gec2h2 system

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