Ga2H2: planar dibridged, vinylidene-like, monobridged, and trans equilibrium geometries

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CHEMICAL PHYSICS LETTERS

19 February 1993

Ga2H2: planar dibridged, vinylidene-like, monobridged, and trans equilibrium geometries ZoltPn PalCigyi‘, Henry F. Schaefer III Centerfor Computational Quantum Chemistry, UniversityofGeorgia, Athens, GA 30602, USA

and Ede Kapuy Departmentof Theoretical Physics,JbzsefAttiia University,6720, Szeged, Hungary Received 13 November 1992

The singlet potential energy surface of Ga2H1has been studied using the self-consistent-field (SCF), single and double excitation configuration interaction (CISD ), and single and double excitation coupled cluster (CCSD) methods. Optimized geometries and harmonic vibrational frequencies were obtained for four geometrical isomers with a double-zeta plus polarization basis set (DZP) . Relative energies of the above structures were also predicted using a triple-zeta plus polarization basis set augmented with a set off functions on the gallium atoms (TZP+f ). For final energetic predictions with this basis set we included the effects of triple excitations perturbatively using the CCSD(T) method. The planar dibridged structure is the global minimum - two additional low-lying minima were found, corresponding to tram-bent and vinylidene-like structures. Our analysis also predicts the existence of a remarkable low-lying monobridged minimum, which has recently been observed experimentally for S&HZ,and predicted by ab initio methods for the valence-isoelectronic AlzHz.

1. Introduction The hydrides of gallium have received increasing attention in recent years, especially since the synthesis and characterization of digallane Ga2H6 by Downs et al. [ 11. Several theoretical studies have appeared for Ga,H, systems [ 2-61 as well as related systems including boron [ 7-101, aluminum [ 11,121, aluminum-boron [ 131, silicon [ 14- 171, and germanium [ 16-181 hydrides. A common feature of these systems is the presence of electron-deficient hydrogen bridges, which have been studied extensively by Trinquier [ 16,17,19]. The remarkable recent experimental discovery [20] of the nonclassical monobridged structure of S&Hz has focused increasing interest on these unconventional structures, which have been found to

be low-lying stable minima in theoretical studies of BJ% [7l,AMG [211,.4M%[12l,andGaA PI, as well as in the heavier group 14 compounds Sn,H, and Pb2H4 [ 171. In the present Letter, ab initio methods explicitly including electron correlation effects are applied to study various isomers ofGazH2 - including the monobridged structure - a system on which no theoretical or experimental data have been available until now. By comparing the results for Ga2H, with the previously studied A&Hz [ 2 1] system, we see a remarkable similarity in the behavior of gallium and aluminum in their hydrides. Thus the absence of a successful synthesis of dialane A12H6becomes more puzzling.

2. Theoreticalmethods 1 Permanent address: Quantum Theory Group, Physical Institute, Technical University, 1521, Budapest, Hungary.

Several stationary points on the Ga2Hz potential

0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.

195

energy surface were initially located by using SCF gradient techniques [22,23] in conjunction with a basis set designated double-zeta plus polarization (DZP) The DZP basis for gallium consists of Dunning’s [24] 14~1lp5d primitive set of Gaussian

functions contracted to 7s5p2d #’augmented by a set of six Cartesian d-like functions (ad (Ga ) = 0.207 ) For hydrogen we used the standard Huzinaga-Dunning-Hay [ 26-281 double-zeta basis set augmented by a set ofp-like functions (o,(H) ~0.75). The contraction scheme for this DZP basis is Ga[6112211/61211/411],

H[31/1].

For the evaluation of the relative energies of various structures we employed a basis set designated triple-zeta plus polarization plus f functions (TZP+f ). For gallium, it consists of the above primitive set more loosely contracted to lOs8p2d [4] augmented with a set of d- and f-like polarization functions, [cr,(Ga)=0.16], [o+(Ga)=0.33] [5]. For hydrogen it is the standard Huzinaga-Dunning triple-zeta basis set augmented by a set of p-like functions (a,(H) ~0.75). Thus the contraction scheme for this basis set is Ga[5111111111/41111111/411/1],

H[311/1].

We determined DZP SCF quadratic force constants and harmonic vibrational frequencies using analytic energy second derivative methods [ 291. Starting with the DZP SCF geometries and force constants, we then reoptimized the structures using the configuration interaction (CI) method [ 301, and then the coupled cluster (CC) method [ 311 in conjunction with the DZP basis set. Only the valence electrons have been correlated explicitly; the core-like SCF molecular orbitals (Ga Is, 2s, 2p, 3s, 3p, 3d) and the virtual orbital counterparts (Ga Is, 2s) were not included in the CI and CC procedures. Otherwise, all single and double excitations from the SCF reference wavefunction have been included (CISD, CCSD). For final energy predictions the effects of triple excitations were also included perturbatively using CCSD( T) wavefunctions. The CISD energies have been corrected to approximately include the effects of unlinked quadruple excitations using Dav$’ The contraction ( 14~1lpSd/7sSp2d) is due to R.S.Grewand H.F. SchaeferIII [25 1.

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idson’s formula [32]. These corrected energies are denoted CISD t Q. We obtained CISD and CCSD harmonic vibrational frequencies by taking finite differences of analytic energy gradients [ 33,341.

3, Results and discussion In this section results are presented for the stationary point geometries depicted in figs. l-4. Three levels of theory (SCF, CISD, CCSD) have been used to obtain these structures, each with the basis sets designated DZP. The relative energies as well as the total energies for the global minimum dibridged structure are given in table 1. Table 2 summarizes the predicted harmonic vibrational frequencies and H 1.628 1.628 1.631

2.168 2.661 .Ga

a

2.656

Ga

DZP DZP DZP

SCF CISD CCSD

/

4.30 / H

120.40 120.4”

Fig. 1. Theoreticalgeometriesfor the tram closed-shellsingletof Ga2H2.Bond distancesare in A.

Fig. 2. Theoreticalgeometriesfor the vinylidene-likeclosed-shell singletstate of Ga*H,.Bond distancesare in A.

72.3O DP 72.4- DZP

CISD CCSD

Fig. 3. Theoretical equilibrium geometriesfor the closed-shell singlet,planar dibridgedelectronicground state of Ga2H2.Bond distancesare in A.

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CHEMICAL PHYSICS LETTERS

2.697 2.619 2.686

and dibridged structures we found the triplet states to be higher lying than the corresponding singlet states already at the DZP SCF level. The triplet state of the monobridged structure - which has the lowest lying LUMO among the closed shell isomers - lies lower than the singlet state at the DZP SCF level. However, this order is reversed by introducing correlation effects; therefore we investigated only the singlet closed shell electronic states for all structures with higher levels of theory. The harmonic vibrational frequency analyses show that all structures considered are local minima on the lowest singlet potential surface, the global minimum being the planar dibridged isomer. The trans isomer (fig. 1) is the most weakly bound - it lies 12.4 kcal mol-* above the planar dibridged minimum. The Ga-Ga bond distance (2.656 A) exhibits a great sensitivity to correlation effects; it decreases by 0.107 8, while going from the DZP SCF to the DZP CISD level of theory. A similar tendency was observed in the A12Hzmolecule [ 2 1 ] and ascribed to the presence of SCF unoccupied bonding molecular orbitals. The localized bond analysis [ 351 shows a pair of banana-type bonds between the gallium atoms. Effectively, this structure can be ex-

32.9' DZP SCF 32.7' DZP CISD 33.5' DZP CCSD

Fig. 4. Theoretical geometries for the monobridged closed-shell singlet state of GazHz. Bond distances are in A.

infrared (IR) intensities, Table 3 contains a list of the largest CI coefftcients for each wavefunction and the corresponding electron configurations. Unless otherwise indicated, data reported explicitly in this discussion were obtained with the DZP CCSD method, except relative energies, which are TZP +f CCSD (T ) results including DZP CCSD harmonic zero-point vibrational energy corrections (see the final column of table 1). Standard Cotton coordinate systems have been used, and whenever there is a choice of coordinate systems the Ga atoms have been chosen to lie along the x axis. A common feature of the various geometrical isomers is a low-lying LUMO, and a small HOMOLUMO gap. We have therefore examined the lowest triplet states for all isomers. For the tram, branched,

Table 1 Relative energies (kcal/mol) of stationary point structures for the GazH, system. Only the final column includes zero-point vibrational energies Isomer

tram monobridged branched planar c) dibridged

CISD *’

SCF

CCSD

CCSD(T)

DZP

TZP+fb’

DZP

TZP+f b’

DZP

TZP+f bl

TZP+f”

+ZPVE *’

II.3

11.5

13.6 13.2

13.1 12.6

13.5

13.0

12.6

12.4

7.9

9.0 9.1

8.3 8.3

9.3

8.5

8.2

7.9

0.1

5.6 6.8

4.7 5.7

6.4

5.4

6.1

6.8

0.0

0.0 0.0

0.0 0.0

0.0

0.0

0.0

0.0

8.0 -0.1 0.0

a) The lower number in the CISD boxes is the Davidson corrected energy difference. b, At the DZP optimized geometry obtained with the corresponding level of theory. ‘) At the DZP CCSD optimized geometry. d, TZP+f CCSD(T) including DZP CCSD harmonic zero point vibrational energy correction (see footnote c)). e, Total energies (au) for the dibridged structure arc as follows: DZP SCF: - 3847.389799;TZPtf SCF: -3847.557723 (see footnote b)); DZP CISD: -3847.531444; DZP CISDtQ: -3847.546776; TZPtfCISD: -3847.707945 (see footnote b)); TZPSf CISD+Q: -3847.724453 (see footnoteb)); DZPCCSD: -3847.543005;TZP+fCCSD: -3847.720441 (see footnoteb)); TZPCfCCSD(T): -3847.725701 (see footnote c)); tZPVE: -3847.714713 (see footnoted)).

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Table 2 Harmonic vibrational frequencies in cm-’ (infrared intensities in parentheses in km/mol) for Ga,H, structures Isomer

Description

DZP SCF

DZP CISD

DZP CCSD

a, a, b, a, a,

Ga-H antisym stre Ga-H sym stre sym bend antisym bend Ga-Ga stre oop

1822 (1234) I809 (0) 500 (0) 181 (135) 105 (0) 222 (10)

1806 (959) 1793 (0) 507 (0) 218 (68) 146 (0) 218 (15)

1787 (890) 1774 (0) 505 (0) 226 (54) 147 (0) 212 (14)

monobridged

a’ a’ a’ a’ a’ a”

terminal H-Ga stre bridging H sym stre bridging H antisym stre H-Ga-H bend Ga-Ga stre terminal H oop bend

1869 (801) 1182 (460) 793 (758) 398 (67) 123 (7) 273 (17)

1825 (662) 1183 (343) 848 (573) 412 (24) 158 (9) 218 (15)

1797 (617) 1172 (322) 850 (542) 413 (19) 156 (9) 199 (13)

branched

bz aI al bl aI bz

Ga-H antisym stre Ga-H sym stre H-Ga-Ga sym bend oop bend Ga-Ga stre H-Ga-H in-plane wag

1915 (338) 1923 (509) 826 (506) 424 (118) 184 (14) 249 (32)

1884 (291) 1884 (436) 784 (425) 382 (89) 183 (11) 226 (25)

1865 (277) 1863 (413) 773 (406) 370 (82) 182 (11) 221 (23)

2” b BP b2u a, b l”

sym Ga-H stre H’s -+ same Ga H’s --t opposite Ga’s antisym Ga-H stre Ga-Ga stre oop bend

1357 (0) 1108 (3317) 778 (0) 948 (221) 199 (0) 325 (48)

1346 (0) 1143 (2595) 916 (0) 964 (183) 203 (0) 278 (47)

1337 (0) 1139 (2492) 918 (0) 959 (176) 202 (0) 268 (45)

trans

b,

planar dibridged

Table 3 Coefkients greater than 0.05 in the TZP+f CISD wavefunctions for the different Ga,H, structures Isomer

Coefficient Configuration

tram

0.940 -0.125

(core)ll$l2~1lb:12b: 12b:+ 134

monobridged

0.943 -0.070

(core)2 1a’z22a’223a’224a’2 24a’z+25a’2

branched

0.947 - 0.052 -0.052

(core) 15a: 16a: 17a:7b: 17a:+18a: 16a: -+8b:

planar dibridged

0.943 -0.072 0.054 0.051

(core)84944b$,8b:, 9a,8bJ,-14b2,4b,, 9a,8b,,-r4b,6bl, 9%8b,,+4b,,5bz,

plained as two weakly interacting GaH fragments. The branched or vinylidene-like structure (fig. 2 ) is the only one involving exclusively two-center, twoelectron bonds. Upon localization of the DZP SCF 198

orbitals we find a pair of Ga-H 0 bonds, a Ga-Ga o bond, and a lone pair of electrons on the terminal gallium atom. The Ga-Ga bond distance is 2.747 A, 0.091 A longer than that in the tram structure, which has a double bond. The relative energies of the branched isomer show a great sensitivity to correlation effects. At the DZP SCF level the branched isomer lies 0.1 kcal mol-’ below the dibridged isomer, while at the correlated level it is 6.8 kcal mol- ’ above it. Once correlation effects are included via DZP CISD, changes of basis set or levels of theory have little effect on this relative energy value. Since the relative energies of the other three structures do not change much as we go from SCF to correlated levels of theory, we observe that SCF theory favors the branched isomer, which may be due to the classical nature of bonding in this structure. A similar effect was observed for the A&H2molecule [ 2 11. The planar dibridged isomer (fig. 3) is the global minimum for Ga2H2. It features two non-classical three-center (Ga-H-Ga) bridging bonds, with a lone

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pair of electrons on each gallium atom. Trinquier has

tive or three-center two-electron bonds derived from

extensively analyzed such bridged bonded structures in the group 14 compounds CZH4, Si2H4, GeZH4, Sn2H4, Pb2H4, as well as in XzH6 (X=B, Ga) [ 1617,191. The Ga-Ga cage distance is 3.027 A, the longest gallium-gallium separation of all the isomers. Finally we arrive at the monobridged structure, which is the most interesting. It is predicted to lie 7.9 kcal mol-’ above the dibridged minimum. The Ga-Ga bond distance (2.686A) lies between the values for a single and double bond. This result is explained by the localized bond analysis: the gallium atoms are connected by a banana-type bond of the sort found in the trans isomer, and a three-center bridging bond similar to that found in the dibridged isomer. Furthermore, the terminal hydrogen is connected to one of the gallium atoms by a conventional o bond, and there is a lone pair of electrons on the other gallium atom. The low vibrational frequencies for the Ga-Ga stretch ( 156 cm-‘) and the terminal hydrogen out-of-plane bend ( 199 cm-’ ) suggest a possible transition state from the monobridged isomer to the planar dibridged global minimum. This suggestion does not follow trivially from the mechanistic study of ref. [ 15 1, since the planar dibridged structure lies 11 kcal mol-’ above the butterfly structure for the S&H2system examined there. Among the structures considered in this paper, the branched isomer has the largest dipole moment (1.72 D), and thus may be the best target for microwave detection. The monobridged isomer has a smaller dipole moment (0.56 D) .

the three possible ways that the two electron-rich regions in the AIH monomer can donate electron density to the electron deficient aluminum centers. The presence of the unsymmetrical monobridged structure of GazH2 as a genuine minimum proves that this structural type is not limited to Si,H, [ 14,151, for which solid experimental structural confirmation now exists [ 201, This work surely suggests that related potential energy hypersurfaces - BzH2, BAlH2, BGaH,, AlGaH,, SiCH1, Ge,H,, GeCH2, GeSiHa should be carefully searched for new unsymmetrical monobridged structures.

4. Concludingremarks The singlet potential energy surface of Ga2H2 has been analyzed at the SCF, CISD, CCSD, and CCSD(T) levels of theory. Our results show the necessity of including correlation effects to accurately describe the relative energies. The planar dibridged global minimum and the low-lying monobridged minimum demonstrate the importance of bridging hydrogen atoms in creating Ga-Ga bonds. The only classically bonded structure that emerges is the vinylidene-like structure, if one excludes the trans structure due to its two banana bonds. The other stable isomers are best viewed as AlH dimers with da-

Acknowledgement We thank Dr. Mingzuo Shen for many helpful discussions. This research was supported by the Air Force Office of Scientific Research, Grant AFOSR92-J-0047.

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