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Isomerization pathways of singlet Ga2H2: quantum-mechanical predictions
Chemical Physics Letters 380 (2003) 304–312 www.elsevier.com/locate/cplett
Isomerization pathways of singlet Ga2H2: quantum-mechanical predictions Jerzy Moc *, Maria Wierzejewska Faculty of Chemistry, Wroclaw University, F. Joliot-Curie 14, Wroclaw PL-50-383, Poland Received 27 June 2003; in final form 20 August 2003 Published online: 2 October 2003
Abstract Rearrangements on the ground-state singlet Ga2 H2 surface leading from the most stable planar dibridged GaðlH)2 Ga isomer 1 to the branched GaGaH2 2 and trans HGaGaH 3 have been studied by using correlated ab initio and DFT methods. The energetically favourable rearrangements can be achieved via a two-step mechanism involving the monobridged HGaðl-H)Ga isomer 4 as intermediate. The transition states involved in the two-step pathways are predicted to lie ca. 10–15 kcal/mol above 1. A new type ÔbutterflyÕ Gaðl-H)2 Ga species 5, found in this work, would rearrange with no barrier to 1. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Hydrides formed by main group and transition metals have been actively studied for more than three decades [1]. The first experimental infrared (IR) work on subhydride Ga2 H2 isolated in argon and krypton matrices was that by Xiao et al. [2]. They reported observation of two different isomers: a dibridged form, Gaðl-H)2 Ga, and a form with two terminal hydrogens, HGaGaH. Very recently, Himmel et al. [3,4] carried out a comprehensive study of the thermally and/or photolytically activated reactions occurring in Ar matrix between Ga2 dimer and H2 . Initially, these authors
*
Corresponding author. Fax: +48-71-222348. E-mail address: [email protected] (J. Moc).
identified (by IR) the Ga2 H2 product formed thermally on deposition of the matrix to have a planar dibridged structure. The subsequent irradiation of the matrix with green light resulted in the rearrangement to a mixture of two distinct isomers, suggested to be the trans HGaGaH and branched GaGaH2 species. The two latter isomers were found to rearrange photolytically back to the dibridged species. On the theoretical side, Ga2 H2 has been studied using ab initio [5–7] and DFT [3,4] approaches. Palagyi et al. [5,6] employed SCF, single and double excitation configuration interaction (CISD) and coupled cluster (CCSD and CCSD(T)) methods to predict optimal geometries, vibrational frequencies and relative energies for the following closed-shell singlet Ga2 H2 isomers: planar dibridged Ga(l-H)2 Ga (D2h ) 1, branched GaGaH2 (C2v )
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.08.115
J. Moc, M. Wierzejewska / Chemical Physics Letters 380 (2003) 304–312
2, trans HGaGaH (C2h ) 3 and planar monobridged HGa(l-H)Ga (Cs ) 4. Treboux and Barthelat [7] investigated periodic trends in structures and stabilities of the same types of X2 H2 isomers for X ¼ B, Al, Ga, In, Tl. They performed ab initio SCF and CI calculations employing effective-core potential (ECP) on heavy atoms. To assist in the assignment of the IR spectra of Ga2 H2 , Himmel et al. [4] made DFT B3PW91 calculations. Apparently, issues of the isomerization mechanisms of Ga2 H2 and related kinetic stability of its various forms have not been addressed so far. In this Letter, the rearrangements of the planar dibridged isomer 1 to the other Ga2 H2 species detected experimentally [2–4] are studied.
2. Computational methods The 6-311++G(3df, 3pd) basis set [8,9] was used throughout. First, calculations were performed using density functional theory (DFT) with the B3LYP functional [10,11]. Optimized structures were found together with the force constant matrices (hessians) to provide harmonic vibrational frequencies and zero-point energy (ZPE) corrections. Minima were connected to each transition state (TS) by tracing the intrinsic reaction coordinate (IRC) [12,13]. The energetics were also evaluated with the ab initio coupled-cluster singles and doubles method including a perturbative estimate of triples (CCSD(T)) [14]. To examine correlation effect due to Ga 3d orbitals [15], frozen-core (FC) CCSD(T) calculations were carried out with and without these orbitals included in the correlation treatment. Next, all the structures and hessians were recalculated using ab initio secondorder Møller–Plesset perturbation theory (MP2) [16] that correlates all electrons (technically designated FULL, abbreviated FU) [17,18]. These were followed by CCSD(T)(FU) energy calculations. Additional geometry optimization and frequency analysis have been performed numerically at the CCSD(T)(FU) level for a new type of Ga2 H2 isomer 5 to verify viability of this singlet minimum [17,18]. In the next sections, our best ZPE corrected CCSD(T)(FU)//MP2(FU) relative energies will be
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used for the purpose of discussion, unless otherwise indicated.
3. Results and discussion 3.1. Isomers Structures of 1–4 singlet Ga2 H2 isomers are shown in Fig. 1. The planar dibridged isomer Ga(l-H)2 Ga (D2h ) 1 is found to be the most stable, in accord with the earlier calculations [3–7]. The branched GaGaH2 (C2v ) 2, trans HGaGaH (C2h ) 3 and monobridged HGaðl-H)Ga (Cs ) 4 lie 6.7, 12.1 and 7.4 kcal/mol higher than 1 (Table 1). Our relative energies are in excellent agreement with the previous best ZPE corrected CCSD(T) results [5], placing 2, 3, 4 by 6.8, 12.4 and 7.9 kcal/mol, respectively, above 1. Recall that only 1–3 are thought to have been detected experimentally so far [2–4]. Consistent with the observation made elsewhere [19], the B3LYP Ga–Ga bond lengths tend to be than the MP2 distances longer by 0.06–0.11 A (Fig. 1). All four singlet Ga2 H2 isomers have already been described in terms of structure and bonding [5–7]. Here, we have rather directed attention to their rearrangements, especially in the light of the recent matrix isolation IR experiments [2–4]. The lowest triplet (3 B3u ) planar dibridged minimum 1 is found to lie significantly above the singlet counterpart, by 27.2 kcal/mol (Table 1). This is in agreement with the previous ab initio calculations [5,7] predicting the lowest triplets of 1–4 to be higher in energy than the singlet analogues. Therefore, a systematic study of the triplet potential energy surface of Ga2 H2 has not been attempted (see Table 2). Interestingly, an additional minimum 5 has been found that corresponds to the non-planar dibridged structure Gaðl-H)2 Ga (C2v ) (Fig. 1, Table 3). This kind of isomer was reported neither in previous ab initio [5–7] nor DFT [3,4] studies. The structure 5 is peculiar because it exists at MP2(FU), but it collapses to 1 at B3LYP. The same behaviour was also observed here with the ab initio CCD and DFT B3PW91 and BLYP approaches. On the other hand, 5 has been also located using CCSD(T)(FU) and BP86 methods (Fig. 1). Apparently, the existence of C2v ÔbutterflyÕ
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, Fig. 1. Minima located on the singlet potential energy surface of Ga2 H2 using B3LYP and MP2(FU) methods (bond lengths in A bond angles in degrees); MP2(FU) geometrical parameters are shown in square brackets. Values in parentheses are from BP86 calculation, and those in curly brackets are from CCSD(T)(FU) calculation. The optimized geometrical parameters for the triplet (3 B3u ) , r(Ga– planar dibridged minimum structure obtained at the spin-unrestricted B3LYP (MP2(FU)) level are: r(Ga–Ga) ¼ 2.635 (2.584) A ,
minimum is quite sensitive to the amount of dynamic electron correlation included (explicitly, ab initio) or through the correlation functional (implicitly, DFT). 5 shows a relatively short Ga–Ga at bond length, being 2.532, 2.554 and 2.636 A MP2(FU), BP86 and CCSD(T)(FU), and HGaGaH dihedral angle of 107.6°, 106.3° and 111.4°, respectively. The two dibridged species 1 and 5 are essentially isoenergetic: 5 is found to lie only 1.2 kcal/ mol above 1 (Table 1) and this energy difference diminishes to 1.0 kcal/mol at the CCSD(T)(FU) ZPE corrected CCSD(T)(FU)//CCSD(T)(FU) level.
From the point of view of possible observation of 5, the rearrangement barrier separating it from the more stable 1 is of importance (see below). 3.2. Isomerization pathways The synchronous departure of the two hydrogens from the planar dibridged isomer Gaðl-H)2 Ga 1 via the C2v symmetry path leads to the branched GaGaH2 isomer 2. This motion results in a simultaneous breaking of both hydrogen bridges and involves a high energy TS1–2 transition state (Fig. 2), lying 47.5 kcal/mol above 1 (Figs. 3 and 4).
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Table 1 Relative energies (kcal/mol) of the Ga2 H2 isomers and isomerization transition states calculated at various levels of theorya Species
1ðD2h Þð1 Ag Þ 1ðD2h Þð3 B3u Þ 2ðC2v Þð1 A1 Þ 3ðC2h Þð1 Ag Þ 4ðCS Þð1 A0 Þ 5ðC2v Þð1 A1 Þh TSl–2ðC2v Þð1 A1 Þ SOSPðC2 Þð1 AÞ TSl–4ðC1 Þð1 AÞ TSl–5ðC2v Þð1 A1 Þh TS2–4ðCS Þð1 A0 Þ TS3–4ðC1 Þð1 AÞi 2GaH ð1 RÞ
CCSD(T)(FC)b //B3LYP
B3LYP//B3LYP d
d
CCSD(T)(FC)c //B3LYP d
CCSD(T)(FU)//MP2(FU)
DE
DE þ DZPE
DE
DE þ DZPE
DE
DE þ DZPE
DE
DE þ DZPEe
0.0 26.4 8.7 14.0 8.6
0.0 27.0 9.9 14.1 8.9
0.0 23.1 6.7 13.0 8.5
0.0 23.7 7.9 13.1 8.8
0.0 21.8 5.3 11.7 7.3
0.0 22.4 6.5 11.8 7.6
48.6 18.9 12.5
49.8 18.1 12.8
48.1 18.8 12.1
49.2 18.0 12.3
45.8 17.7 10.8
46.9 16.9 11.0
11.8 16.6 26.8
12.1 16.0 25.0
11.1 16.8 26.0
11.4 16.2 24.4
9.3 16.0 27.6
9.6 15.4 26.0
0.0 (0.0)f 22.2 6.2 12.4 7.7 0.6 (0.4)f 47.1 18.2 11.0 0.5 10.0 16.6 28.8
0.0 (0.0)g 27.2 6.7 12.1 7.4 1.2 (1.0)g 47.5 16.8 10.7 0.7 9.6 15.4 26.3
a
Symbol Ô//Õ means Ôat the geometry ofÕ. Ga 3d orbitals excluded from the correlation treatment. c Ga 3d orbitals included in the correlation treatment. d Using the unscaled B3LYP ZPEs. e Using the unscaled MP2(FU) ZPEs. f CCSD(T)(FU)//CCSD(T)(FU) result. g CCSD(T)(FU)//CCSD(T)(FU) result corrected for the unscaled CCSD(T)(FU) ZPE. h Structure does not exist at the B3LYP level (see text). i Cs structure at the MP2(FU) level (cf. Fig. 2). b
Table 2 Energy barriers for the isomerization reactions of singlet Ga2 H2 calculated at the CCSD(T)(FU) + ZPE//MP2(FU) levela Reaction
Energy barrier
Reaction
Energy barrier
l (D2h ) ! 2 (C2v ) 1 (D2h ) ! 4 (Cs ) 1 (D2h ) ! 5 (C2v ) 2 (C2v ) ! 4 (CS ) 3 (C2h ) ! 4 (Cs )
47.5 10.7 0.7 2.9 3.3
2 (C2v ) ! l (D2h ) 4 (CS ) ! l (D2h ) 5 (C2v ) ! l (D2h ) 4 (Cs ) ! 2 (C2v ) 4 (CS ) ! 3 (C2h )
40.8 3.3 –0.5 2.2 8.0
a
All values are in kcal/mol.
It is easily seen from Fig. 4 that TS1–2 represents the highest energy point on the calculated singlet potential energy surface of Ga2 H2 . In fact, among the rearrangements considered, the 1!2 reaction taking place via the concerted mechanism is the most energy demanding. For comparison, the disP sociation energy of 1 into 2GaHð þ Þ fragments is calculated to be 26.3 kcal/mol. The interconversion of 1 into 2 can occur through a competetive step-wise mechanism. The first step is the 1!4 rearrangement during which
one of the hydrogen bridges is broken and the monobridged HGaðl-H)Ga isomer formed. At the TS1–4 transition state involved, the moving hydrogen makes a dihedral angle with the Ga–H–Ga plane of about 90° (Fig. 2). The 1!4 step requires overcoming the barrier of 10.7 kcal/mol (Fig. 4). The second step is the 4!2 rearrangement proceeding via the Cs symmetry TS2–4 transition state. The corresponding reaction coordinate is mostly the in-plane GaH2 rotation that results in breaking the second hydrogen bridge and forming the GaGaH2 branched structure 2 (note that the reaction coordinate vector at TS2–4 is appropriate for the reverse 2!4 process). TS2–4 is found to lie only 2.2 kcal/mol above 4. Consequently, the monobridged isomer 4 resides in a shallow minimum with the barriers of 3.3 and 2.2 kcal/mol, respectively, separating it from the planar dibridged isomer 1 and branched isomer 2 (cf. Fig. 4). The energy of TS2–4 with respect to the global minimum 1 is 9.6 kcal/mol. We conclude here that, for the interconversion of 1 into 2, the
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Table 3 Comparison between IR spectra calculated and observed for Ga2 H2 isomersa Isomer
Ar matrixb
Calculations c;d
c
c
Assignment
b
B3LYP
MP2(FU)
CCSD(T)(FU)
B3PW91
2200, 1176
m1 þ m4 ; m2 þ m4
1220 (0) 1016 (1973) 852 (209) 879 (0) 188 (23) 187 (0)
1367 (0) 1194 (2364) 999 (181) 1067 (0) 194 (72) 203 (0)
1331 1174 968 1026 196 199
1232 (0) 1032 (1946) 866 (213) 920 (0) 201 (18) 190 (0)
1220e 1002 906.5 880
m1 (ag ) m4 (b1u ) m5 (b2u ) m3 (b3g ) m6 (b3u ) m2 (ag )
1841 (391) 1829 (537) 767 (381) 349 (76) 221 (29) 175 (12)
1888 (356) 1885 (464) 778 (404) 394 (94) 210 (32) 193 (14)
1848 (370) 1836 (509) 770 (367) 359 (73) 224 (23) 179 (13)
1765.1 1752.1 752
m5 (b2 ) m1 (a1 ) m2 (a1 ) m4 (b1 ) m6 (b2 ) m3 (a1 )
1707 (1108) 1688 (0) 493 (0) 206 (28) 175 (42) 152 (0)
1835 (985) 1821 (0) 520 (0) 244 (27) 233 (70) 186 (0)
1728 (1046) 1709 (0) 503 (0) 224 (24) 186 (53) 163 (0)
1686.1
m5 (bu ) m1 (ag ) m2 (ag ) m4 (au ) m6 (bu ) m3 (ag )
1753 (758) 1159 (332) 847 (454) 158 (9) 158 (9) 205 (14)
1847 (733) 1260 (321) 888 (513) 189 (13) 189 (13) 207 (18)
1753 (731) 1165 (347) 822 (436) 401 (11) 169 (9) 197 (13)
1266 (80) 1149 (317) 898 (746) 812 (0) 758 (149) 110 (1)
1397 (82) 1259 (365) 1006 (953) 900 (0) 791 (176) 112 (1)
1351 1170 1044 911 711 75
175e
0
m1 (a ) 0 m2 (a ) 0 m3 (a ) 0 m4 (a ) 0 m5 (a ) 0 m6 (a )
m1 (a1 ) m5 (b1 ) m4 (b2 ) m3 (a2 ) m6 (a1 ) m2 (a1 )
a
Frequencies are in cm1 , intensities (in parentheses) are in km mol1 . Ref. [4]. c This work. d ln case of the isomer 5, BP86 results (see text). e Value estimated from a combination band [4]. b
two-step mechanism is energetically preferred over the concerted mechanism. In the former case, the higher barrier of 10.7 kcal/mol is for the 1!4 step.
Generation of the minimum energy path connecting the planar dibridged isomer 1 and trans isomer 3 within C2 symmetry, followed by the
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Fig. 2. Transition states connecting various minima shown in Fig. 1 and located using B3LYP and MP2(FU) methods (bond lengths in , bond angles in degrees); MP2(FU) geometrical parameters and symbols are shown in square brackets. Values in parentheses are A from BP86 calculation. The reaction coordinate vector and the corresponding imaginary frequency are included for each transition state. For SOSP structure, both imaginary modes of A and B symmetry are shown; the associated imaginary frequencies are given in the order, A (first) and B (second).
optimization of the highest energy structure on this path, yielded a second order saddle point (two imaginary frequencies) denoted SOSP in Fig. 2. The fully symmetric imaginary mode with the larger (in absolute value) imaginary frequency is the C2 -constrained 1!3 isomerization reaction coordinate. The constrained barrier height for the 1!3 rearrangement is found to be 16.8 kcal/mol (Fig. 4).
When the C2 symmetry constraint in SOSP was relaxed, the structure optimized to the transition state between the minima 3 and 4, TS3–4. The trans isomer 3 is thus reachable from the monobridged isomer 4 through the latter transition structure. Unlike the B3LYP structure of C1 symmetry for TS3–4, the MP2(FU) calculation afforded the Cs structure (Fig. 2). The predicted interconversion
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Fig. 3. Overview of the isomerization pathways for the singlet Ga2 H2 . The CCSD(T)(FU) + ZPE//MP2(FU) energies (kcal/mol) are relative to the planar dibridged isomer 1.
Fig. 4. CCSD(T)(FU) + ZPE//MP2(FU) potential energy diagram for the singlet Ga2 H2 . All energies are in kcal/mol.
barrier of 4 into 3 via TS3–4 is 8.0 kcal/mol relative to 4, with TS3–4 placed 15.4 kcal/mol above the global minimum 1. On passing, 1 can rearrange to 3
via a two-step mechanism, where the first 1!4 step is common for the isomerizations leading to 3 and 2 (Fig. 4).
J. Moc, M. Wierzejewska / Chemical Physics Letters 380 (2003) 304–312
Although we have not been able to locate a transition state linking the branched 2 and trans 3 species, their two-step isomerization pathway involving intermediate 4 is easily seen from Fig. 4. Isomer 3 is formed through this mechanism with the larger barrier characterizing the 4!3 step already discussed. The TS1–5 transition state connects the two dibridged minima 1 and 5 (Fig. 2). As with 5, we have located this TS using BP86 and MP2(FU) methods (TS1–5 has not been pursued at CCSD(T)(FU)). The calculated barrier separating 5 from 1 is only 0.38 and 0.35 kcal/mol at MP2(FU)//MP2(FU) and BP86//BP86, respectively, and becomes negative ()0.10 kcal/mol) at CCSD(T)(FU)//MP2(FU). After the inclusion of respective ZPE values, TS1–5 falls below 5 at all three levels and this barrier vanishes being )0.01, )0.16 and )0.49 kcal/mol, respectively. Therefore, the ÔbutterflyÕ isomer 5 rearranges with no barrier to 1. 3.3. Vibrational frequencies As can be seen from Table 3, our B3LYP results for 1–4 are very close to those predicted using B3PW91 functional, and the two sets of frequencies compare well with the available experimental values [3,4]. Somewhat worse agreement with experiment is obtained at the MP2(FU) and CCSD(T)(FU) levels. Perusing the contents of Table 3 also reveals that both 1 and 2 are experimentally well described. By contrast, isomer 3 is characterized in argon matrix by only one band at 1686 cm1 .
4. Conclusions In summary, Ga2 H2 isomerization pathways leading from the most stable planar dibridged 1 to the branched 2 and trans 3 species have been calculated. The energetically favourable rearrangement of 1 into 2 or 3 can be achieved via a two-step mechanism involving the monobridged isomer 4 as intermediate, and is accompanied by breaking one hydrogen bridge in each step. The transition states involved in the two-step pathways are found to lie
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ca. 10–15 kcal/mol above 1. The highest calculated barrier (47.5 kcal/mol), for a one step rearrangement of 1 into 2 via TS1–2, corresponds to the parallel cleavage of two hydrogen bridges and conforms to the wavelength of the irradiation (k 546 nm or ca. 52 kcal/mol) suggested to induce this process [3,4]. However, because the TS1–2 barrier is so large, competitive processes, such as the dissociation of 1 into 2 GaH fragments appear likely to take place. A new type ÔbutterflyÕ species 5 would not exist kinetically. Finally, a good overall agreement between the CCSD(T) (FU)//MP2(FU) relative stabilities and those predicted at the B3LYP//B3LYP and CCSD(T) (FC)//B3LYP levels is seen from Table 1. Acknowledgements The authors acknowledge a generous support of computing time at the Wroclaw Center for Networking and Supercomputing. We thank Prof. A.J. Downs for providing us a copy of [1] and Dr. Mike Schmidt for a copy of [19].
References [1] S. Aldridge, A.J. Downs, Chem. Rev. 101 (2001) 3305. [2] Z.L. Xiao, R.H. Hauge, J.L. Margrave, Inorg. Chem. 32 (1993) 642. [3] H.-J. Himmel, L. Manceron, A.J. Downs, P. Pullumbi, Angew. Chem. Int. Ed. 41 (2002) 796. [4] H.-J. Himmel, L. Manceron, A.J. Downs, P. Pullumbi, J. Am. Chem. Soc. 124 (2002) 4448. [5] Z. Palagyi, H.F. Schaefer III, E. Kapuy, Chem. Phys. Lett. 203 (1993) 195. [6] Y. Yamaguchi, B.J. Deleeuw, C.A. Richards, H.F. Schaefer III, G. Frenking, J. Am. Chem. Soc. 116 (1994) 11922. [7] G. Treboux, J.-C. Barthelat, J. Am. Chem. Soc. 115 (1993) 4870. [8] M.J. Frisch, J.A. Pople, J.S. Binkley, J. Chem. Phys. 80 (1984) 3265. [9] L.A. Curtiss, M.P. McGrath, J.-P. Blaudeau, N.E. Davis, R.C. Binning Jr., L. Radom, J. Chem. Phys. 103 (1995) 6104. [10] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [11] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [12] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [13] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523.
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[14] K. Raghavachari, G.W. Trucks, J.A. Pople, M. HeadGordon, Chem. Phys. Lett. 157 (1989) 479. [15] L.A. Curtiss, P.C. Redfern, V. Rassolov, G. Kedziora, J.A. Pople, J. Chem. Phys. 114 (2001) 9287. [16] J.A. Pople, J.S. Binkley, R. Seeger, Int. J. Quantum Chem. Symp. 10 (1976) 1.
[17] M.J. Frisch et al., GAUSSIAN 94, Revision E.2, Gaussian, Inc., Pittsburgh, PA, 1995. [18] M.J. Frisch et al., GAUSSIAN 98, Revision A.lx, Gaussian, Inc., Pittsburgh, PA, 2001. [19] N. Takagi, M.W. Schmidt, S. Nagase, Organometallics 20 (2001) 1646.
Isomerization pathways of singlet Ga2H2: quantum-mechanical predictions Jerzy Moc *, Maria Wierzejewska Faculty of Chemistry, Wroclaw University, F. Joliot-Curie 14, Wroclaw PL-50-383, Poland Received 27 June 2003; in final form 20 August 2003 Published online: 2 October 2003
Abstract Rearrangements on the ground-state singlet Ga2 H2 surface leading from the most stable planar dibridged GaðlH)2 Ga isomer 1 to the branched GaGaH2 2 and trans HGaGaH 3 have been studied by using correlated ab initio and DFT methods. The energetically favourable rearrangements can be achieved via a two-step mechanism involving the monobridged HGaðl-H)Ga isomer 4 as intermediate. The transition states involved in the two-step pathways are predicted to lie ca. 10–15 kcal/mol above 1. A new type ÔbutterflyÕ Gaðl-H)2 Ga species 5, found in this work, would rearrange with no barrier to 1. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Hydrides formed by main group and transition metals have been actively studied for more than three decades [1]. The first experimental infrared (IR) work on subhydride Ga2 H2 isolated in argon and krypton matrices was that by Xiao et al. [2]. They reported observation of two different isomers: a dibridged form, Gaðl-H)2 Ga, and a form with two terminal hydrogens, HGaGaH. Very recently, Himmel et al. [3,4] carried out a comprehensive study of the thermally and/or photolytically activated reactions occurring in Ar matrix between Ga2 dimer and H2 . Initially, these authors
*
Corresponding author. Fax: +48-71-222348. E-mail address: [email protected] (J. Moc).
identified (by IR) the Ga2 H2 product formed thermally on deposition of the matrix to have a planar dibridged structure. The subsequent irradiation of the matrix with green light resulted in the rearrangement to a mixture of two distinct isomers, suggested to be the trans HGaGaH and branched GaGaH2 species. The two latter isomers were found to rearrange photolytically back to the dibridged species. On the theoretical side, Ga2 H2 has been studied using ab initio [5–7] and DFT [3,4] approaches. Palagyi et al. [5,6] employed SCF, single and double excitation configuration interaction (CISD) and coupled cluster (CCSD and CCSD(T)) methods to predict optimal geometries, vibrational frequencies and relative energies for the following closed-shell singlet Ga2 H2 isomers: planar dibridged Ga(l-H)2 Ga (D2h ) 1, branched GaGaH2 (C2v )
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.08.115
J. Moc, M. Wierzejewska / Chemical Physics Letters 380 (2003) 304–312
2, trans HGaGaH (C2h ) 3 and planar monobridged HGa(l-H)Ga (Cs ) 4. Treboux and Barthelat [7] investigated periodic trends in structures and stabilities of the same types of X2 H2 isomers for X ¼ B, Al, Ga, In, Tl. They performed ab initio SCF and CI calculations employing effective-core potential (ECP) on heavy atoms. To assist in the assignment of the IR spectra of Ga2 H2 , Himmel et al. [4] made DFT B3PW91 calculations. Apparently, issues of the isomerization mechanisms of Ga2 H2 and related kinetic stability of its various forms have not been addressed so far. In this Letter, the rearrangements of the planar dibridged isomer 1 to the other Ga2 H2 species detected experimentally [2–4] are studied.
2. Computational methods The 6-311++G(3df, 3pd) basis set [8,9] was used throughout. First, calculations were performed using density functional theory (DFT) with the B3LYP functional [10,11]. Optimized structures were found together with the force constant matrices (hessians) to provide harmonic vibrational frequencies and zero-point energy (ZPE) corrections. Minima were connected to each transition state (TS) by tracing the intrinsic reaction coordinate (IRC) [12,13]. The energetics were also evaluated with the ab initio coupled-cluster singles and doubles method including a perturbative estimate of triples (CCSD(T)) [14]. To examine correlation effect due to Ga 3d orbitals [15], frozen-core (FC) CCSD(T) calculations were carried out with and without these orbitals included in the correlation treatment. Next, all the structures and hessians were recalculated using ab initio secondorder Møller–Plesset perturbation theory (MP2) [16] that correlates all electrons (technically designated FULL, abbreviated FU) [17,18]. These were followed by CCSD(T)(FU) energy calculations. Additional geometry optimization and frequency analysis have been performed numerically at the CCSD(T)(FU) level for a new type of Ga2 H2 isomer 5 to verify viability of this singlet minimum [17,18]. In the next sections, our best ZPE corrected CCSD(T)(FU)//MP2(FU) relative energies will be
305
used for the purpose of discussion, unless otherwise indicated.
3. Results and discussion 3.1. Isomers Structures of 1–4 singlet Ga2 H2 isomers are shown in Fig. 1. The planar dibridged isomer Ga(l-H)2 Ga (D2h ) 1 is found to be the most stable, in accord with the earlier calculations [3–7]. The branched GaGaH2 (C2v ) 2, trans HGaGaH (C2h ) 3 and monobridged HGaðl-H)Ga (Cs ) 4 lie 6.7, 12.1 and 7.4 kcal/mol higher than 1 (Table 1). Our relative energies are in excellent agreement with the previous best ZPE corrected CCSD(T) results [5], placing 2, 3, 4 by 6.8, 12.4 and 7.9 kcal/mol, respectively, above 1. Recall that only 1–3 are thought to have been detected experimentally so far [2–4]. Consistent with the observation made elsewhere [19], the B3LYP Ga–Ga bond lengths tend to be than the MP2 distances longer by 0.06–0.11 A (Fig. 1). All four singlet Ga2 H2 isomers have already been described in terms of structure and bonding [5–7]. Here, we have rather directed attention to their rearrangements, especially in the light of the recent matrix isolation IR experiments [2–4]. The lowest triplet (3 B3u ) planar dibridged minimum 1 is found to lie significantly above the singlet counterpart, by 27.2 kcal/mol (Table 1). This is in agreement with the previous ab initio calculations [5,7] predicting the lowest triplets of 1–4 to be higher in energy than the singlet analogues. Therefore, a systematic study of the triplet potential energy surface of Ga2 H2 has not been attempted (see Table 2). Interestingly, an additional minimum 5 has been found that corresponds to the non-planar dibridged structure Gaðl-H)2 Ga (C2v ) (Fig. 1, Table 3). This kind of isomer was reported neither in previous ab initio [5–7] nor DFT [3,4] studies. The structure 5 is peculiar because it exists at MP2(FU), but it collapses to 1 at B3LYP. The same behaviour was also observed here with the ab initio CCD and DFT B3PW91 and BLYP approaches. On the other hand, 5 has been also located using CCSD(T)(FU) and BP86 methods (Fig. 1). Apparently, the existence of C2v ÔbutterflyÕ
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, Fig. 1. Minima located on the singlet potential energy surface of Ga2 H2 using B3LYP and MP2(FU) methods (bond lengths in A bond angles in degrees); MP2(FU) geometrical parameters are shown in square brackets. Values in parentheses are from BP86 calculation, and those in curly brackets are from CCSD(T)(FU) calculation. The optimized geometrical parameters for the triplet (3 B3u ) , r(Ga– planar dibridged minimum structure obtained at the spin-unrestricted B3LYP (MP2(FU)) level are: r(Ga–Ga) ¼ 2.635 (2.584) A ,
minimum is quite sensitive to the amount of dynamic electron correlation included (explicitly, ab initio) or through the correlation functional (implicitly, DFT). 5 shows a relatively short Ga–Ga at bond length, being 2.532, 2.554 and 2.636 A MP2(FU), BP86 and CCSD(T)(FU), and HGaGaH dihedral angle of 107.6°, 106.3° and 111.4°, respectively. The two dibridged species 1 and 5 are essentially isoenergetic: 5 is found to lie only 1.2 kcal/ mol above 1 (Table 1) and this energy difference diminishes to 1.0 kcal/mol at the CCSD(T)(FU) ZPE corrected CCSD(T)(FU)//CCSD(T)(FU) level.
From the point of view of possible observation of 5, the rearrangement barrier separating it from the more stable 1 is of importance (see below). 3.2. Isomerization pathways The synchronous departure of the two hydrogens from the planar dibridged isomer Gaðl-H)2 Ga 1 via the C2v symmetry path leads to the branched GaGaH2 isomer 2. This motion results in a simultaneous breaking of both hydrogen bridges and involves a high energy TS1–2 transition state (Fig. 2), lying 47.5 kcal/mol above 1 (Figs. 3 and 4).
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Table 1 Relative energies (kcal/mol) of the Ga2 H2 isomers and isomerization transition states calculated at various levels of theorya Species
1ðD2h Þð1 Ag Þ 1ðD2h Þð3 B3u Þ 2ðC2v Þð1 A1 Þ 3ðC2h Þð1 Ag Þ 4ðCS Þð1 A0 Þ 5ðC2v Þð1 A1 Þh TSl–2ðC2v Þð1 A1 Þ SOSPðC2 Þð1 AÞ TSl–4ðC1 Þð1 AÞ TSl–5ðC2v Þð1 A1 Þh TS2–4ðCS Þð1 A0 Þ TS3–4ðC1 Þð1 AÞi 2GaH ð1 RÞ
CCSD(T)(FC)b //B3LYP
B3LYP//B3LYP d
d
CCSD(T)(FC)c //B3LYP d
CCSD(T)(FU)//MP2(FU)
DE
DE þ DZPE
DE
DE þ DZPE
DE
DE þ DZPE
DE
DE þ DZPEe
0.0 26.4 8.7 14.0 8.6
0.0 27.0 9.9 14.1 8.9
0.0 23.1 6.7 13.0 8.5
0.0 23.7 7.9 13.1 8.8
0.0 21.8 5.3 11.7 7.3
0.0 22.4 6.5 11.8 7.6
48.6 18.9 12.5
49.8 18.1 12.8
48.1 18.8 12.1
49.2 18.0 12.3
45.8 17.7 10.8
46.9 16.9 11.0
11.8 16.6 26.8
12.1 16.0 25.0
11.1 16.8 26.0
11.4 16.2 24.4
9.3 16.0 27.6
9.6 15.4 26.0
0.0 (0.0)f 22.2 6.2 12.4 7.7 0.6 (0.4)f 47.1 18.2 11.0 0.5 10.0 16.6 28.8
0.0 (0.0)g 27.2 6.7 12.1 7.4 1.2 (1.0)g 47.5 16.8 10.7 0.7 9.6 15.4 26.3
a
Symbol Ô//Õ means Ôat the geometry ofÕ. Ga 3d orbitals excluded from the correlation treatment. c Ga 3d orbitals included in the correlation treatment. d Using the unscaled B3LYP ZPEs. e Using the unscaled MP2(FU) ZPEs. f CCSD(T)(FU)//CCSD(T)(FU) result. g CCSD(T)(FU)//CCSD(T)(FU) result corrected for the unscaled CCSD(T)(FU) ZPE. h Structure does not exist at the B3LYP level (see text). i Cs structure at the MP2(FU) level (cf. Fig. 2). b
Table 2 Energy barriers for the isomerization reactions of singlet Ga2 H2 calculated at the CCSD(T)(FU) + ZPE//MP2(FU) levela Reaction
Energy barrier
Reaction
Energy barrier
l (D2h ) ! 2 (C2v ) 1 (D2h ) ! 4 (Cs ) 1 (D2h ) ! 5 (C2v ) 2 (C2v ) ! 4 (CS ) 3 (C2h ) ! 4 (Cs )
47.5 10.7 0.7 2.9 3.3
2 (C2v ) ! l (D2h ) 4 (CS ) ! l (D2h ) 5 (C2v ) ! l (D2h ) 4 (Cs ) ! 2 (C2v ) 4 (CS ) ! 3 (C2h )
40.8 3.3 –0.5 2.2 8.0
a
All values are in kcal/mol.
It is easily seen from Fig. 4 that TS1–2 represents the highest energy point on the calculated singlet potential energy surface of Ga2 H2 . In fact, among the rearrangements considered, the 1!2 reaction taking place via the concerted mechanism is the most energy demanding. For comparison, the disP sociation energy of 1 into 2GaHð þ Þ fragments is calculated to be 26.3 kcal/mol. The interconversion of 1 into 2 can occur through a competetive step-wise mechanism. The first step is the 1!4 rearrangement during which
one of the hydrogen bridges is broken and the monobridged HGaðl-H)Ga isomer formed. At the TS1–4 transition state involved, the moving hydrogen makes a dihedral angle with the Ga–H–Ga plane of about 90° (Fig. 2). The 1!4 step requires overcoming the barrier of 10.7 kcal/mol (Fig. 4). The second step is the 4!2 rearrangement proceeding via the Cs symmetry TS2–4 transition state. The corresponding reaction coordinate is mostly the in-plane GaH2 rotation that results in breaking the second hydrogen bridge and forming the GaGaH2 branched structure 2 (note that the reaction coordinate vector at TS2–4 is appropriate for the reverse 2!4 process). TS2–4 is found to lie only 2.2 kcal/mol above 4. Consequently, the monobridged isomer 4 resides in a shallow minimum with the barriers of 3.3 and 2.2 kcal/mol, respectively, separating it from the planar dibridged isomer 1 and branched isomer 2 (cf. Fig. 4). The energy of TS2–4 with respect to the global minimum 1 is 9.6 kcal/mol. We conclude here that, for the interconversion of 1 into 2, the
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Table 3 Comparison between IR spectra calculated and observed for Ga2 H2 isomersa Isomer
Ar matrixb
Calculations c;d
c
c
Assignment
b
B3LYP
MP2(FU)
CCSD(T)(FU)
B3PW91
2200, 1176
m1 þ m4 ; m2 þ m4
1220 (0) 1016 (1973) 852 (209) 879 (0) 188 (23) 187 (0)
1367 (0) 1194 (2364) 999 (181) 1067 (0) 194 (72) 203 (0)
1331 1174 968 1026 196 199
1232 (0) 1032 (1946) 866 (213) 920 (0) 201 (18) 190 (0)
1220e 1002 906.5 880
m1 (ag ) m4 (b1u ) m5 (b2u ) m3 (b3g ) m6 (b3u ) m2 (ag )
1841 (391) 1829 (537) 767 (381) 349 (76) 221 (29) 175 (12)
1888 (356) 1885 (464) 778 (404) 394 (94) 210 (32) 193 (14)
1848 (370) 1836 (509) 770 (367) 359 (73) 224 (23) 179 (13)
1765.1 1752.1 752
m5 (b2 ) m1 (a1 ) m2 (a1 ) m4 (b1 ) m6 (b2 ) m3 (a1 )
1707 (1108) 1688 (0) 493 (0) 206 (28) 175 (42) 152 (0)
1835 (985) 1821 (0) 520 (0) 244 (27) 233 (70) 186 (0)
1728 (1046) 1709 (0) 503 (0) 224 (24) 186 (53) 163 (0)
1686.1
m5 (bu ) m1 (ag ) m2 (ag ) m4 (au ) m6 (bu ) m3 (ag )
1753 (758) 1159 (332) 847 (454) 158 (9) 158 (9) 205 (14)
1847 (733) 1260 (321) 888 (513) 189 (13) 189 (13) 207 (18)
1753 (731) 1165 (347) 822 (436) 401 (11) 169 (9) 197 (13)
1266 (80) 1149 (317) 898 (746) 812 (0) 758 (149) 110 (1)
1397 (82) 1259 (365) 1006 (953) 900 (0) 791 (176) 112 (1)
1351 1170 1044 911 711 75
175e
0
m1 (a ) 0 m2 (a ) 0 m3 (a ) 0 m4 (a ) 0 m5 (a ) 0 m6 (a )
m1 (a1 ) m5 (b1 ) m4 (b2 ) m3 (a2 ) m6 (a1 ) m2 (a1 )
a
Frequencies are in cm1 , intensities (in parentheses) are in km mol1 . Ref. [4]. c This work. d ln case of the isomer 5, BP86 results (see text). e Value estimated from a combination band [4]. b
two-step mechanism is energetically preferred over the concerted mechanism. In the former case, the higher barrier of 10.7 kcal/mol is for the 1!4 step.
Generation of the minimum energy path connecting the planar dibridged isomer 1 and trans isomer 3 within C2 symmetry, followed by the
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Fig. 2. Transition states connecting various minima shown in Fig. 1 and located using B3LYP and MP2(FU) methods (bond lengths in , bond angles in degrees); MP2(FU) geometrical parameters and symbols are shown in square brackets. Values in parentheses are A from BP86 calculation. The reaction coordinate vector and the corresponding imaginary frequency are included for each transition state. For SOSP structure, both imaginary modes of A and B symmetry are shown; the associated imaginary frequencies are given in the order, A (first) and B (second).
optimization of the highest energy structure on this path, yielded a second order saddle point (two imaginary frequencies) denoted SOSP in Fig. 2. The fully symmetric imaginary mode with the larger (in absolute value) imaginary frequency is the C2 -constrained 1!3 isomerization reaction coordinate. The constrained barrier height for the 1!3 rearrangement is found to be 16.8 kcal/mol (Fig. 4).
When the C2 symmetry constraint in SOSP was relaxed, the structure optimized to the transition state between the minima 3 and 4, TS3–4. The trans isomer 3 is thus reachable from the monobridged isomer 4 through the latter transition structure. Unlike the B3LYP structure of C1 symmetry for TS3–4, the MP2(FU) calculation afforded the Cs structure (Fig. 2). The predicted interconversion
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Fig. 3. Overview of the isomerization pathways for the singlet Ga2 H2 . The CCSD(T)(FU) + ZPE//MP2(FU) energies (kcal/mol) are relative to the planar dibridged isomer 1.
Fig. 4. CCSD(T)(FU) + ZPE//MP2(FU) potential energy diagram for the singlet Ga2 H2 . All energies are in kcal/mol.
barrier of 4 into 3 via TS3–4 is 8.0 kcal/mol relative to 4, with TS3–4 placed 15.4 kcal/mol above the global minimum 1. On passing, 1 can rearrange to 3
via a two-step mechanism, where the first 1!4 step is common for the isomerizations leading to 3 and 2 (Fig. 4).
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Although we have not been able to locate a transition state linking the branched 2 and trans 3 species, their two-step isomerization pathway involving intermediate 4 is easily seen from Fig. 4. Isomer 3 is formed through this mechanism with the larger barrier characterizing the 4!3 step already discussed. The TS1–5 transition state connects the two dibridged minima 1 and 5 (Fig. 2). As with 5, we have located this TS using BP86 and MP2(FU) methods (TS1–5 has not been pursued at CCSD(T)(FU)). The calculated barrier separating 5 from 1 is only 0.38 and 0.35 kcal/mol at MP2(FU)//MP2(FU) and BP86//BP86, respectively, and becomes negative ()0.10 kcal/mol) at CCSD(T)(FU)//MP2(FU). After the inclusion of respective ZPE values, TS1–5 falls below 5 at all three levels and this barrier vanishes being )0.01, )0.16 and )0.49 kcal/mol, respectively. Therefore, the ÔbutterflyÕ isomer 5 rearranges with no barrier to 1. 3.3. Vibrational frequencies As can be seen from Table 3, our B3LYP results for 1–4 are very close to those predicted using B3PW91 functional, and the two sets of frequencies compare well with the available experimental values [3,4]. Somewhat worse agreement with experiment is obtained at the MP2(FU) and CCSD(T)(FU) levels. Perusing the contents of Table 3 also reveals that both 1 and 2 are experimentally well described. By contrast, isomer 3 is characterized in argon matrix by only one band at 1686 cm1 .
4. Conclusions In summary, Ga2 H2 isomerization pathways leading from the most stable planar dibridged 1 to the branched 2 and trans 3 species have been calculated. The energetically favourable rearrangement of 1 into 2 or 3 can be achieved via a two-step mechanism involving the monobridged isomer 4 as intermediate, and is accompanied by breaking one hydrogen bridge in each step. The transition states involved in the two-step pathways are found to lie
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ca. 10–15 kcal/mol above 1. The highest calculated barrier (47.5 kcal/mol), for a one step rearrangement of 1 into 2 via TS1–2, corresponds to the parallel cleavage of two hydrogen bridges and conforms to the wavelength of the irradiation (k 546 nm or ca. 52 kcal/mol) suggested to induce this process [3,4]. However, because the TS1–2 barrier is so large, competitive processes, such as the dissociation of 1 into 2 GaH fragments appear likely to take place. A new type ÔbutterflyÕ species 5 would not exist kinetically. Finally, a good overall agreement between the CCSD(T) (FU)//MP2(FU) relative stabilities and those predicted at the B3LYP//B3LYP and CCSD(T) (FC)//B3LYP levels is seen from Table 1. Acknowledgements The authors acknowledge a generous support of computing time at the Wroclaw Center for Networking and Supercomputing. We thank Prof. A.J. Downs for providing us a copy of [1] and Dr. Mike Schmidt for a copy of [19].
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