J. Phys. Chem. 1993,97, 4945-4950
4945
Structure and Stability of Various (C*,HS,Ge)+Ions. An ab Initio Molecular Orbital Study Paola Antoniotti,'J Paola Benzi,? Felice Grandinetti,'$tand Paolo Volpet Dipartimento di Chimica Generale ed Organica Applicata. Universitrt di Torino, C.so Massimo D'Azeglio, 48 I-10125 Torino, Italy, and the Istituto di Chimica Nucleare del CNR. Area della Ricerca di Roma, C.P. 10-00016-Monterotondo Sfazione, Rome, Italy Received: July 21, 1992
Various (C2,Hs,Ge)+ stable isomers have been identified on the corresponding SCF 3-21G* potential energy surface. Twelve distinct structures have been characterized, and their relative stability has been evaluated at the correlated MP2 and QCISD(T) post-SCF levels of theory, with double-{quality basis sets. Several analogies do exist with the previously described (C3,Hs)+ species, although significant differences can be pointed out. Distinct stable species have been found in correspondence of allyl-like, 2-propenyl-like, and 1-propenyl-like (C2,Hs,Ge)+ structures (ions 1,2,6,7-9, and 1&12), and the mechanisms of stereomutation of the allyl-like ions, via transition structures 3-5, have been examined. Whereas the allyl cation is by far the most stable among the ( C ~ , H S )isomers, + the germylene-like species 10, which contains low-coordinated germanium atoms, has been computed as the most stable among the (C2,Hs,Ge)+ investigated ions.
Introduction The gas-phase ion chemistry of cationic species containing germanium atoms is currently addressed with growing interest, as such species play a fundamental role in the formation of amorphous germanium materials by y-radiolysis of volatile hydrides.'-3 The mechanisms of formation of these ionic intermediates, as well as their reaction patterns toward several substrates, have been recently investigated by Fourier-transform mass spectrometry (FT-MS) and chemical ionization mass spectrometry (CIMS). In particular, the study of the gas-phase ion-molecule reactions of GeH4with 02 or NH3,4 CO, and C02,s and some simple saturated (CHI, C&) and unsaturated hydrocarbons (CZHZ,C2H4, C3H4, C3H6),S*6pointed out the intermediacy of various cationic species, with general formulas GeH,C,+ ( m = 0-1 1;n = M),GeH,O+ (n = 0-3), and GeH,N+ ( n = 2,3,4,6), whose structureand thermochemistryis, however, unknown to date. In fact, only a limited amount of information, based upon theoretical calculations, is presently available on a few simple cations containinggermanium atoms, such as GeH4+,7 CGeH5+,8CGeH7+,9 and H3GeCH2CHZ+.loSome of us have recently performed a ab initio MO study of (Ge,H,O)+ and (Ge,H3,0)+ions,' I whose results reinforced the expectation that the structure and the stability order of cationic speciescontaining germanium atoms cannot be rationalized by simply generalizing previous findings concerning the corresponding carbon or silicon analogues. The aim of the present investigation is to obtain detailed information on the structure and stability of various (C2,H5,Ge)+ ions. These species are obtained as one of the most abundant product in the mass spectra of GeH4/C2H4mixturesS and are also present in significant amount in the mass spectra of GeH4/ C2H2 and GeH4/C3H4 mixtures.6. The obtained results will be compared with the well-established picture concerning the structure and stability of the (C3,H5)+ ions. Computational Details Ab initio full-electron quantum-mechanical calculations have
' Universiti di Torino. * Istituto di Chimica Nucleare del CNR. 0022-3654/93/2091-4945~04.00/0
been performed by running a IBM/VM-CMS version of the GAUSSIAN 8612 and GAUSSIAN 88" set of programs. The 3-21Gand3-21G* basissets,asdeveloped byHehreandDobbs,I4 were thoroughly employed for the geometry optimizations. The latter were performed, in the framework of the assumed symmetry point group of each species, by gradient-based techniques.Is Analytical vibrational frequencies were computed, at the SCF 3-21G* level of theory, for all of the (CZ,Hs,Ge)+critical points, in order to characterize them as true minima, transition states, or higher-order saddle points on the potential energy hypersurface. In order to evaluate the correlation energy effects on the relative stability of the investigated species, single-pointcalculationswere performed, in correspondence of the SCF 3-21G* optimized geometries, at the post-SCF level of theory. The M~rller-Plesset theoryI6truncated at second order (MPZFC) and the quadratic configuration interaction theory,17 including the contributions from single, double, and triple excitations, QCISD(T), were employed. The double-{quality basis set BS was used for these single-point calculations. It was obtained as follows: for the germanium atom, starting with the Huzinaga (4333/433/4) basis,I8 the last s and p atomic orbitals, linear combinations of three Gaussians, were decontracted to the double-{level to give (43321/4321/4) or (5s,4p,ld); further, a set of d functions,I8 intended as polarization functions for the valence electrons, was added with exponent a! = 0.246. For the carbon atom, starting with the Huzinaga (43/4/1) basis,'* the last s and the p atomic orbitals, linear combinations of three and four Gaussians, respectively,weredecontracted to thedouble-{level to give (421/ 31/l)or (3s,2p,ld). Forthehydrogenatom,the6-31Gbasisset, as developed by Pople and co-worker~,~~ was employed.
Results and Discussion The discussion of the results obtained during the present investigation will be divided into two parts. In the first one, the structure and stability of the various (C2,Hs,Ge)+ions will be examined, whereas a comparison between the (C2,Hs,Ge)+ and the (Cs,Hs)+ ions will be performed in the second one. Structure and Stability of the (Cz,H&)+ Ions. The detailed investigation of the general features of the (C3,H5)+ potential energy surface20led to well-accepted conclusionsconcerning the existence of the following distinct species: 0 1993 American Chemical Society
4946 The Journal of Physical Chemistry, Vol. 97, No. 19, 1993
Antoniotti et al.
H(3) I
.,
7
1
2
..
B 5
6
Figure I. SCF 3-21G* main geometrical parameters of the 1-6 ((22,Ge,H5)+ions. Bond lengths are in angstromsand bond angles in degrees.
> .e.
/
H
H
-,
I
/ci
+
H/C=C-H 1-propenyl
H,..jc-C H
e.,,
H '
cydapccpyl
On the basis of these results, the search for allyl-like, 2-propenyllike, 1-propenyl-like,and cyclopropyl-like (C2,H5,Ge)+isomers has been addressed during the present study. Following a preliminary investigation at the SCF 3-21G level of theory, 12 different critical points have been located on the SCF 3-21G* potential energy surface, and their nature (minima, transition states, or higher order saddle points) has been checked by computing the correspondingvibrationalfrequencies. Apart from the structure of ion 11 (vide infra), no appreciable differences were observed between the SCF 3-21G and the SCF 3-21G* computed geometries. As a consequence, only the SCF 3-21G* main geometrical parameters of the (Cz,Hs,Ge)+ ions are reproduced in Figures 1-3. Thecompletegeometriesare reported in Tables 1-111, together with the net total atomic charges, as derived from a Mulliken population analysis2'of the SCF 3-21G* wave functions. The relevant absolute and relative energies, at the various computational levels, are collected in Table IV. Two different allyl-like (C2,H3,Ge)+ structures can be conceived, Le., the HzGe-CH-CHz+ and the H2C-GeH-CH2+ions.
Figure 2. SCF 3-21G* main geometrical parameters of the 7-9 (C2,Ge,Hs)+ ions. Bond lengths are in angstroms and bond angles in degrees.
By assuming the C, symmetry, both of these species, henceforth indicated as 1 and 2, were found to be absolute minima on the potential energy surface. Their optimized geometries are schematized in Figure 1,and the full list of the geometrical parameters is given in Table I. Both of these structures are fully planar, the positive charge being located on the germanium and the hydrogen atoms. The C-Ge bond length is quite similar in the two ions (1.880 A in 1 and 1.850 A in 2) and significantly shorter than the C-Ge SCF 3-21G* single bond distance of H3GeCH2CH3, 1.982 &Io and H3GeCH3,1.979 A.I3 Nevertheless, the two bond distances are longer than the double-t SCF distance, 1.756 A, between carbon and germanium in the germaethylene molecule, where evidence has been obtained for the formation of a G d double As a consequence, our calculations suggest a significantcontribution of r-interaction between the germanium and the adjacent carbon atoms in both ions 1and 2. A remarkable energy difference does exist between the two species, the former being more stable, at both the SCF and post-SCF level of theory. From Table IV, the inclusion of electroncorrelationenergy reduces the SCF energy gap from 54 kcal mol-' at the BS//3-21GS level of theory to 44 kcal mol-' at the MP2/BS//3-21G* and 35.5 kcal mol-] at the QCISD(T)/BS//3-21GS level of theory. The formationof a carbon+arbon double bond in ion 1(bond distance, 1.338 A), which cannot occur in ion 2, has to be viewed as the main structural factor that determines the computed energy difference. The problem of the stereomutation of the two allyl-like structures 1 and 2, i.e., the mechanism of the processes H
H
I
-a, H.*0
fH.*.4c\C/Hf
I
I H
H H
I
C\c/
A*
*A H
H
Structure and Stability of (C2,H5,Ge)+Ions
The Journal of Physical Chemistry, Vol. 97, No. 19, 1993 4947
TABLE I: F d List of the SCF 3-21G* Optimized Geometries and Net Atomic Charge8 of the 1-6 (Cz,HsCe)+ Investigated Species (for the Labeling of the Atoms, See Fimre 1) species
.
R,A
q, electronic
a,deg
1 (C-) ", Ge-CIl): 1.880
11
10
H(l)-Ge-H(21: 118.1 Ge-Hilj: 1.528 ~ ( ~ j - ~ e - 122.4 ~iij: Ge-H(2): 1.528 Ge-C(1)-H(3): 119.0 C(l)-H(3): 1.074 G d ( l ) - C ( 2 ) : 119.8 C(l)-C(2): 1.338 C(l)-C(2)-H(4): 120.9 C(2)-H(4): 1.074 C(l)-C(2)-H(5): 123.3 C(2)-H(5): 1.074
2 (C2") C-H(1): 1.077
H(41
C-H(2): 1.077 C-Ge: 1.850 G e H ( 3 ) : 1.514
H(l)-C-H(2): 115.8 H(2)-C-Ge: 124.4 C-Ge-H(3): 127.0 C-Ge-C: 106.1
3 (C,)
Ge-C(l): 1.920 Ge-H(1): 1.531 C(l)-H(3): 1.078 C(l)-C(2): 1.324 C(2)-H(4): 1.074 C(2)-H(5): 1.074
H(l)-Ge-H(2): 116.1 H(l)-Ge-C(l): 122.0 Ge-C(l)-H(3): 115.4 Ge-C(l)-C(Z): 123.6 C(l)-C(2)-H(4): 120.3 C(l)-C(2)-H(5): 124.2
4 (C,)
Ge-C(l): 1.792 Ge-H(1): 1.523 G e H ( 2 ) : 1.523 C(l)-H(3): 1.093 C(l)-C(2): 1.403 C(2)-H(4): 1.082
H(l)-Ge-H(2): 121.3 H(2)-Ge-C(1): 117.4 Ge-C(l)-H(3): 114.6 Ge-C(1)-C(2): 131.9 C(l)-C(2)-H(4): 122.3 H(4)-C(2)-H(5): 115.3
Ge-C(1): 2.053 Ge-H(1): 1.521 G e C ( 2 ) : 1.956 C(l)-C(2): 1.487 C(l)-H(3): 1.078 C(2)-H(4): 1.078 6 (C2") C-H(l): 1.078 C-C: 1.593 C-Ge: 1.923 G e H ( 3 ) : 1.519
H(l)-Ge-H(2): 123.5 H(l)-Ge-C(2): 118.2 C(l)-Ge-C(2): 43.4 G&(l)-H(3): 165.8 Ge-C(2)-H(4): 120.6 H(4)-C(2)-H(5): 110.0 H(l)-C-H(2): 113.6 H( 1)-C-C: 116.4 C-Ge-C: 49.0
12 Figure 3. SCF 3-21G' main geometrical parameters of the 10-12 (C2,Ge,HS)+ ions. Bond lengths are in angstroms and bond angles in degrees.
has been successively addressed. The Occurrence of the same process in the allyl cation has been carefully examined,*O and it seems to be interesting to compare the results obtained for the two systems. The relevant transition structures for the rotation of the methylene and germylene groups in ions 1and 2 have been located, in the framework of the C, symmetry, on the (C2,H$,Ge)+ potential energy surface. Four different critical points, indicated as 3, 4, 5, and 6, have been characterized, whose optimized geometriesareshownin Figure 1 andTable I. Structure 3 is the transition state for the rotation of the H2Ge group around the carbon-germanium bond in ion 1. A lengthening of the C-Ge distance (1.920 A vs 1.880 A) and a shortening of the C-C one (1.324~s1.338A) isobservedfroml to3,consistentwithalower germanium-rbon ?F interactionin the latter species. FromTable IV, the activation energy of the rotation process, i.e., the energy difference between 1 and 3, is computed as 9.6 kcal mol-' at the SCF 3-21G* level of theory and 12.6 kcal mol-' at the MP2/ BS//3-21G* computational level. Structure 4 is the transition state for the rotation of the methylene group around the carboncarbon bond in 1. In this case, it is interesting to point out the lengthening of the C-C distance (1.403 vs 1.338 A) and the shortening of the G e C one (1.792 vs 1.880 A), which is accompanied by a significant decrease of the positive charge on the germanium atom (+0.202 in 1 and +0.015 in 4), thus suggesting an increase of the germanium4arbon u interaction by rotation of the methylene group in 1. Furthermore, the GeCC bond angle is sharply increased (from 119.8O to 131.9') from 1 to 4. In contrast with the rotation of the germylene group in 1, the rotation of the methylene group is found to be a high-energy process, the energy barrier being 57.9 kcal mol-' at the SCF 3-21G* computational level. As in the previous case, the inclusion of electron correlation energy does not appreciably affect the computed energy gap, which becomes 54.7 kcal mol-' at the MP2/BS//3-21G* and 51.1 kcal mol-' at the QCISD(T)/BS//3-21G* level of theory (see Table IV). The transition structure 5 (C, symmetry) refers to the symmetry-allowed disrotatory twisting of both methylene and germylenegroups in ion 1. Irrespectiveof the employedtheoretical level, also this process is computed as a high-energy one, with a barrier of 59.9 kcal mol-' at the post-SCF (MP2) level of theory (see Table IV). As to the structure of the cyclopropyl-like ion 5, a single bond is formed between the germylene and the
5 (C,)
units Ge: +0.202 C( 1): -0.703 C(2): -0.606 H(1): +0.362 H(2): +0.383 H(3): +0.457 H(4): +0.438 H(5): +0.467 Ge: +0.261 C: -0.784 H(1): +0.473 H(2): +0.484 H(3): +0.393 Ge: +0.274 C(1): -0.679 C(2): -0,643 H( 1): +0.365 H(3): +0.449 H(4): +0.455 H(5): +0.414 Ge: +0.015 C(1): -0.831 C(2): -0.401 H(1): +0.336 H(2): +0.352 H(3): +0.489 H(4): +0.520 Ge: +0.03 1 C(1): -0.317 C(2): -0.899 H(1): +0.368 H(3): +0.525 H(4): +0.462 Ge: +0.470 C( 1): -0.852 H(1): +0.441 H(2): +0.470
TABLE 11: Full List of the SCF 3-21G* 0 timized Geometries and Net Atomic Charges of the !-9 (Cz,H&e)+ Investigated Species (for the Labeling of the Atoms, See F i m e 2) species
R,A
7 (C,)
C(1)-H(1): 1.080 C(l)-H(2): 1.086 C( l)-Ge: 1.959 C(2)-Ge: 1.828 C(2)-H(4): 1.081
a,deg
q, electronic units
H(l)-C(l)-Ge: 110.2 H(2)-C(l)-Ge: 107.9 H(2)-C(l)-H(3): 109.2 C( l)-Ge-C(2): 131.9 H ( 4 ) - C ( 2 ) 4 e : 119.0 H(4)-C( 2)-H(5): 123.3 H(l)-Ge-C(1): 102.8 Ge-H(1): 1.527 Ge-H(3): 1.532 H( l)-Ge-H(2): 117.0 H(3)-Ge-C(1): 97.3 Ge-C(l): 2.051 C(l)-C(2): 1.270 Ge-C(l)-C(2): 180.0 C(2)-H(4): 1.082 H(4)-C(2)-C( 1): 121.O C(2)-H(5): 1.082 H(4)-C(2)-H( 5): 118.1
Ge: +0.812 C(l):-l.l39 C(2): -0.871 H( 1): +0.420 H(2): +0.417 H(4): +0.472 Ge: -0.337 8 (C,) C( 1): -0,052 C(2): -0,668 H(1): +0.329 H(3): +0.323 H(4): +0.538 H(5): +OS38 9 (C,) C(1)-H(1): 1.085 H(l)-C(l)-C(2): 113.7 Ge: +O. 1 15 C(l)-H(3): 1.106 H(l)-C(l)-H(2): 112.5 C(1): -0.987 C(l)-C(2): 1.434 H(3)-C( l)-C(2): 103.5 C(2): -0,240 H( 1): +0.434 C(l)-C(2)-Ge: 180.0 C(2)-Ge: 1.788 H(3): +0.450 H(4)-Ge-C(2): 116.1 G e H ( 4 ) : 1.518 H(4): +0.395 H(4)-Ge-H(5): 127.8 Ge-H(5): 1.518 H(5): +0.399
methylene moieties (bond distance, 1.956 A), whereas the other germanium-rbonbond, 2.053 A, is slightly longer than a typical single-bond distance. From the above results, the stereomutation of ion 1could occur by a concerted route, via transition structure 5, and/or by a stepwise route. In the latter case, the ratedetermining step is the rotation of the methylene group, via transition structure 4, whereas the rotation of the germylenegroup
4948 The Journal of Physical Chemistry, Vol. 97, No. 19, 1993
TABLE III: F d List of the SCF 3-216* Optimized Geometries and Net Atomic Charges of the 10-12 (C2,H&e)+ Investigated Species (for the Labeling of the Atoms, See Figure 3) species
R,A
q, electronic
a,deg
units
10 ( C , ) C(1)-H(1): 1.082 C(I)-H(2): 1.081 C(l)-H(3): 1.082 C(I)-C(2): 1.563 C(2)-H(4): 1.088 C(2)-H(5): 1.173 C(2)-Ge: 1.910 Ge-H(5): 2.010
H(l)-C(l)-C(2): 111.8 Ge: +0.921 H(2)-C(l)-C(2): 109.0 C(1): -0.958 H(3)-C(l)-C(2): 110.0 C(2): -0.849 H(l)-C(l)-H(2): 108.8 H(1): +0.381 H(I)-C(l)-H(3): 108.7 H(2): +0.344 C(l)-C(2)-H(4): 114.9 H(3): +0.385 H(4): +0.423 H(4)-C(2)-Ge: 120.2 H(5)-Ge-C(2): 34.7 H(5): +0.352 Dihedral angle H(5)-Ge-C(2)-H(4): 88.6O 11 (C,) Ge-H(1): 1.526 H(l)-Ge-C(l): 94.0 Ge: -0.321 C(1): -0.478 G e H ( 3 ) : 1.527 H(l)-Ge-H(2): 118.8 Ge-C(1): 2.337 H ( 3 ) - G e C ( l ) : 109.0 C(2): -0.361 H(1): +0.348 Ge-C(2): 2.556 H(4)-C(l)-Ge: 110.3 H(3): +0.336 C(l)-C(2): 1.206 C(2)-C(I)-Ge: 86.1 C(l)-H(4): 1.061 H(5)-C(2)-C(1): 179.4 H(4): +0.561 C(2)-H(5): 1.059 H(5): +0.567 12 (C,) C(1)-H(1): 1.084 H(1)-C(l)-Ge: 108.6 Ge: +0.519 C(l)-H(3): 1.082 H(3)-C(l)-Ge: 110.5 C(1):-1.153 Ge-C(1): 1.945 H(l)-C(l)-H(2): 109.1 C(2): -0.523 Ge-C(2): 1.804 C(l)-Ge-H(4): 128.5 H(1): +0.415 Ge-H(4): 1.524 C(2)-Ge-H(4): 110.8 H(3): +0.414 C(2)-H(5): 1.070 GeC(2)-H(5): 179.4 H(4): +0.387 H(5): +0.527
takes place in the fast step, via transition structure 3. It is interesting to point out that also in the case of the allyl cation, C3H5+,the stereomutation could occur both via two subsequent rotations of the methylene groups (stepwise route) or by the cyclopropyl transition structure (concerted route). In fact, at the post-SCF level of theory, the activation barriers of the two competitive processes are computed to be almost the same (35 vs 36 kcal mol-').20 The search of the relevant transition structures for the stereomutation of ion 2 gave rather unexpected results. In fact, only the C2, symmetry cyclopropyl-like ion 6 was located, whose vibrational frequencies revealed it to bea minimum (stablespecies) on the SCF 3-21G* (C2,H5,Ge)+potential energy surface. From Figure 1 and Table I, the relevant geometrical features of this species clearly indicate the formation of two germanium*arbon single bonds (bond distance 1.923A), whereas the carbonGarbon bond is slightly longer (1.593 A) than a typical single one. As to the stability order of ion 6, at the SCF 3-21G* level of theory it is less stable than ion 1 by 33.8 kcal mol-' (see Table IV). This energy gap is not significantly reduced by extending the employed basis set, but it is decreased by ca. 9 kcal mol-I by inclusion of correlation energy effects, at both the MP2 and the QCISD(T) level of theory. This result is consistent with the usual performance of the post-SCF methods concerning the cyclic and the nonclassical ionic species, whose stability is expected to be underestimated at the S C F level of theory.23 The search of the 2-propenyl-like species has been successively addressed. Three different structures, indicated as 7,8, and 9, have been located, by assuming C,symmetry, on the (Cz,H5,Ge)+ potential energy surface. Their S C F 3-21G* main geometrical parameters are shown in Figure 2, and the complete geometries, together with the net atomic charges, are collected in Table 11. All of these species correspond to absolute minima (stable isomers) on the surface, as deduced from the calculation of the relevant vibrational frequencies. From Table IV, irrespective of the employed theoretical level, ion 7 is the most stable among the 2-propenyl-like structures. Nevertheless, the extension of the employed basis set and, mostly, the inclusion of the electron correlation energy have a influence on the computed energy gaps. In fact, at the S C F 3-21G' level of theory, ion 7 is more stable than ion 8 by only 4.8 kcal mol-', and the latter is in turn more stable than ion 9 by 26.7 kcal mol-'. By upgrading the
Antoniotti et al. computational level to the BS//3-21G*, the energy difference between ions 7 and 8 is increased to 14 kcal mol-', whereas the energy difference between ion 8 and 9 is not significantly affected. At the post-SCF level of theory, irrespective of the approach employed for the inclusion of electron correlation, ion 7 is more stable than ion 8 by more than 30 kcal mol-', and the energy gap between 8 and 9 is decreased by almost 8 kcal mol-'. From Table IV, the quadratic configuration interaction approach reduces by some kilocalories per mole the MP2 computed energy differences of these species with the more stable ion 1. The results concerning the stability order of the 2-propenyllike structures are consistent with their geometrical features. In fact, divalent germanium species, which are formal analogues of carbenes, are currently believed to be particularly stable, whereas the presence of a germyl group, H3Ge, in a given structure, is not appreciably stabilizing. For instance, germaethylene, H2GedbdCH2, is more stable than the carbene H3GeCH by 57 kcal mol-' but is less stable than the germylene CH3GeH by 23 kcal mol-'.* A nonlinear skeleton is associated to ion 7, and the value of the germylenic angle, 131.9O, is quite larger than the typical values found for small neutral systems (HG,H, 92.9'; H G ~ C H ~ , 94.9O; CH3~,CH3, 97.8O). The methyl-germanium bond, 1.959 A, has to be viewed as a single one, whereas a significant contribution of 7~ character is associated to the germaniummethylene interaction (bond distance, 1.828 A). The high positive charge on the germanium atom (+0.812, see Table 11) has also been noted. As to the structure of ion 8, the H3Ge-C bond distance, 2.051 A, is longer than a typical single germaniumcarbon bond, due to the strong interaction between the two adjacent carbon atoms (C-C bond distance, 1.270 A). Consistently, the HzGe-C distance in ion 9, 1.788 A, is the shortest among the computed ones and suggestive of the formation of a real double bond between germanium and carbon. The search of the 1-propenyl-like structures has been finally addressed. Also in this case, three different critical points have been located on the (C2,H5,Ge)+ potential energy surface. From the corresponding SCF 3-21G* vibrational frequencies, all of these species, indicated as 10,11, and 12, are true minima (stable species) on the surface. Their optimized geometries are shown in Figure 3 and Table 111. As to ion 11, a remarkably long distance (2.337 A) has been computed, a t the SCF 3-21G* level of theory, between the H3Ge and C2H2moieties. Further, the carboncarbon distance, 1.206 A, is only slightly longer than the S C F 3-21G* value for the acetylene molecule, 1.188 A.z4 As a whole, these results suggest ion 11 to be a tightly-bound ion-molecule complex between the germyl cation and the C2H2 molecule. It has to be pointed out that the value of the GecC bond angle of ion 11 was found to be sensitive to the employed level of theory. In fact, it changed from 106.3' at the SCF 3-21G to 86.1O at the SCF 3-21G* computational level, thus revealing the crucial importance of the inclusion of polarization functions on the germanium atom for the description of the structureof this species. A tight interaction between the CH3 and HGeCH building blocks also exists in ion 12, as can be deduced from the S C F 3-21G* computed value of the germanium-carbon distance, 1.945 A (see Figure 3). A significantly short HGe-CH distance, 1.804 A, has also been found. As to the relative stability of ions 11 and 12, irrespective of the employed theoretical level, the former was found to be more stable. The SCF 3-21G* energy gap, 30.3 kcal mol-I, is not substantially reduced by extending the employed basis set and including the contribution from the electron correlation energy effects. From Table IV, both of these species are less stable than ion 1. The structure and the stability of the germylene-like ion 10 deserve careful discussion. In fact, as previously pointed out, the (C2,H5,Ge)+species, like the abovediscussed ions 3 and 7, which contain a low-coordinated germanium atom, are expected to be particularly stable. From the energy data of ion 10 (see Table IV) this seems to be the case.
Structure and Stability of (Cz,Hs,Ge)+ Ions
The Journal of Physical Chemistry, Vol. 97, No. 19, 1993 4949
TABLE I V Total Energies (Atomic Units), Relative Energies' (kcal mol-', in Parentheses), and Zero-PointEneriges (kcal mol-') of the 1-12 (C*,H5,Ce)+Investigated Species species 1 (OIL 2 (0) 3 (1) 4 (1) 5 (1) 6 (0) 7 (0) 8 (0) 9 (0) 10 (0) 11 (0) 12 (0)
3-21G* -2143.432 -2143.344 -2143.415 -2143.335 -2143.341 -2143.380 -2143.395 -2143.378 -2143.340 -2143.430 -2143.384 -2143.341
00 (0.0) 37 (+54.2) 76 (+9.6) 26 (+57.9) 36 (+53.8) 18 (+33.8) 61 (+24.2) 43 (+29.0) 13 (+55.7) 83 (+4.0) 54 (+25.9) 08 (+56.2)
BS//3-21G* -2151.650 -2151.562 -2151.630 -2151.561 -2151.558 -2151.603 -2151.620 -2151.589 -2151.553 -2151.668 -2151.600 -2151.551
34 (0.0) 65 (+54.2) 37 (+11.9) 16 (+53.2) 23 (+54.7) 51 (+30.7) 80 (+19.9) 18 (+33.8) 67 (+58.8) 88 (-8.3) 10 (+27.6) 36 (+61.3)
MP2/BS//3-21GS -2151.976 -2151.905 -2151.955 -2151.885 -2151.876 -2151.945 -2151.962 -2151.900 -2151.875 -2152.000 -2151.931 -2151.866
94 (0.0) 74 (+43.9) 89 (+12.6) 25 (+54.7) 50 (+59.9) 52 (+21.0) 08 (+10.7) 03 (+43.7) 89 (+61.5) 50 (-11.5) 99 (+24.3) 32 (68.6)
QCISD(T)/BS//3-21GS -2152.025 -2151.967 -2152.005 -2151.939 -2151.932 -2151.993 -2152.018 -2151.959 -2151.935 -2152.049 -2151.980 -2151.926
18 (0.0) 30 (+35.5) 15 (+12.0) 29 (+51.1) 32 (+55.2) 26 (+21.3) 15 (+5.8) 47 (+36.6) 26 (+54.5) 24 (-11.8) 51 (+23.9) 23 (+61.3)
ZPE 38.5 37.7 37.9 35.7 35.4 39.8 39.9 33.9 36.6 41.8 34.6 37.7
The zero-point contributions have been included. For the specification of the basis set, BS, see the Computational Details. Number of imaginary frequencies.
Infact,at theSCF3-21G*leveloftheory, thisspeciesispractically degenerate with ion 1, but it becomes largely favored, by 11.5 kcal mol-', at the MP2/BS//3-21G* and QCISD(T)/BS//321G* level of theory. However, for this species, the crucial importance of extending the employed basis set clearly emerges, whereas the inclusion of correlation energy effects only plays a minor role. In fact, the energy gap with ion 1 is significantly increased up to 8 kcal mol-I, at the BS//3-21GS level of theory and only slightly modified at the post-SCF one. From Figure 3 and Table 111, ion 10 has to be viewed as a hydrogen-bridged species, H(5) being almost 90° out of the H(4)-C(2)-Ge plane. The C(2)-H(5) bond distance, 1.173 A, is quite shorter than the Ge-H(5) distance (2.01 A). The structure of this ion is quite unusual, and it does not find any correspondencein the (C3,H5)+ family of ions. Nevertheless, it is actually the most stable among the (C2,H5,Ge)+investigatedspecies, thus confirmingthe crucial role of those structures, which contain a low-coordinated and sharply positively-charged germanium atom. In fact, from Table 111, the net atomic charge computed for the germanium atom is +0.921 electronic units. Comparison between the (C2,H&e)+ and the (C3,H5)+Ions. After discussing the results concerning the structure and the stability of the (C2,H5,Ge)+ions, it seems appropriate to compare the relevant emerging picture with the available data concerning the (C3,Hs)+ions.20 Several analogies between the two families of ions exist, but significant differences can be also pointed out. As in the case of the (C3,H5)+structures, distinct stable species have been found in correspondenceof the allyl-like, 2-propenyllike, and 1-propenyl-like(CZ,Hs,Ge)+ structures, i.e., ions 1, 2, 7-9, and 10-12. Moreover, the transition methylene and germylene groups in ion 1 find their counterpart in the C2, cyclopropyl cation, which has been so far described as a possible transition structure for the concerted stereomutation of the allyl cation. However, at variance with the (C3,H5)+ case, a energy minimum was located in correspondence to the Cz,-symmetry cyclopropyl-like structure 6. As in the case of the allyl cation, the perpendicular allyl-like (C2,H5,Ge)+structures 3 and 4 were found to be the conformational transition states for the rotation of the germylene and methylene groups, respectively, in ion 1. The bridged corner-protonated cyclopropene, which has been proposed to play a role on the (C3,H5)+potential energy surface, finds a partial correspondence in ion 11, whereas ion 12 has to be viewed as the counterpart of the previous reported I-propenyl cation. The main structural aspect, which is peculiar of the (C2,H5,Ge)+family and does not find any correspondence with the (C3,H5)+ species, has to be traced in the existence of the germylene-like structures 7 and 10. As to the relative stability of the various (C3,H5)+and (Cz,H5,Ge)+ ions, significant differences can be pointed out. In fact, in the case of the (C3,Hs)+ species, irrespective of the employed theoretical level, the planar allyl cation is by far the most stable
isomer, the 2-propenyl ion being less stable by about 15 kcal mol-I. The perpendicular allyl, the 1-propenyl, the cyclopropyl, and the corner-protonated cyclopropene ions are practically degenerate and less stable than the allyl cation by about 35 kcal mol-]. A more complex picture does emerge on passing to the (CzIH5,Ge)+ions. First of all, from Table IV, the computed order of stability of the various species is sometimes affected by upgrading from the SCF to the post-SCF level of theory. Moreover, significant differences have been found with the stability order of the (C3,H5)+ions. In fact, whereas the allyllike structure 1 is the most stable at the SCF 3-21G* level, and practically degenerate with the germylene-likeion 10, the latter becomes the most stable species at the MP2/BS//3-21G* computational level. The inclusion of electron correlation energy by quadratic configurationinteraction does not modify this result. The other germylene-like structure 7 is also markedly stable, although less stable than ion 10 by 17.6 kcal mol-' at the QCISD(T)/BS//3-21G* level of theory; on the contrary, the two other conceivable 2-propenyl-like structures 8 and 9 are significantly less stable than ion 1. In conclusion, although the two l-propenyllike structures 11 and 12 are computed to be less stable than the allyl-like structure 1, their energy difference is as large as 37.4 kcal mol-I at the QCISD(T)/BS//3-21G* level of theory, the former species being energetically favored.
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