J . Phys. Chem. 1992, 96, 6278-6287
6278
(23)Bruna, P. J.; Wright, J. S. J . Mol. Srrucr. (THEUCHEhf)1991, 230, 213; Chem. Phys. 1991, 157, 1 1 1 ; J. Phys. Chem. 1992,96,1630. (24)Wright, J. S.; Bruna, P. J. Chem. Phys. Lett. 1989,156, 533. (25)Bruna, P. J.; Wright, J. S.J . Chem. Phys. 1990, 93,2617. (26) Moaddel, T.;Bruna, P. J.; Wright, J. S. Unpublished results on Al,*. (27) Bader, R. F. W.; Henneker, W. H.; Cade, P. E. J. Chem. Phys. 1967, 46,3341. (28) (a) Fischer, I.; Bondybey, V. E.; Rosmus, P.; Werner, H.-J. Chem. Phys. 1991, 151, 295. (b) Hogreve, H. Chem. Phys. Lerr. 1991, 187,479. (29) Bauschlicher, C. W.; Rosi, M. Chem. Phys. Lett. 1989,159, 485; 1990, 165, 501. (30) Nicolaides, C. A.; Chrysos, M.; Valtazanos, P. J . Phys. E 1990, 23, 791. Nicolaides, C. A.; Valtazanos, P. Chem. Phys. Leu. 1990, 174, 489. (31) Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1984, 80, 334. (32) Hotop, H.; Lineberger, W. C. J. Phys. Chem. Re/. Dura 1985,14, 731. (33) Clerbaux, C.; Colin, R. Mol. Phys. 1991, 72,471,and references therein. (34) Machado, F. B. C.; Ornellas, F. R. J . Chem. Phys. 199L94.7237. (35) Rackwitz, R.; Feldmann, D.; Kaiser, H. J.; Heinicke, E. Z . Narurforsch. 1977,320, 594. (36)Bruna, P. J.; Peyerimhoff, S.D. Furaduy Symp. Chem. SOC.1984, 19, 193. Gill, P. M. W.; Radom, L. Chem. Phys. Len. 1988, 147, 213. (37)Ahlrichs, R. Theor. Chim. Acru 1970,17,348. (38)Valtazanos, P.; Nicolaides, C. A. Chem. Phys. Lert. 1990, 172,254. (39)Gimarc, B. M. Moleculur Structure and Bonding Academic Press: New York, 1979. (40)Bruna, P. J.; Hirsch, G.; Buenker, R. J.; Peyerimhoff, S. D. In Molecular Ions; Berkowitz, J., Groenefeld, K. o.,Eds.; Plenum: New York, 1983;p 309. (41)Easterfield, J.; Linnett, J. W. Chem. Commun. 1970,64. (42)Siegbahn, K.; Nordling, C.; Johansson, G.; Hedman, J.; Heden, P. F.; Hamrin, K.; Gelius, U.; Bergmark, T.; Werme, L. 0.;Manne, R.; Baer, Y. ESCA Applied to Free Molecules; North-Holland: Amsterdam, 1969. (43) Curtiss, L. A.; Pople, J. A. J. Phys. Chem. 1988, 92,894;J . Chem.
Phys. 1988,89,4875;1989,90,4314;1989,91,4809;Deutsch, P. W.; Curtiss, L. A.; Pople, J. A. Chem. Phys. Lerr. 1990, 174,33. (44) Dill, J. D.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. J . Am. Chem. SOC.1977,99,6159;DeFrees, D. J.; Raghavachari, K.; Schlegel, H. B.; Pople, J. A.; Schleyer, P. v. R. J . Phys. Chem. 1987,91,1857,and references cited therein. (45)Clark, T.J . Am. Chem. SOL.1988, 110, 1672. (46)Hashimoto, K.; Osamura, Y.; Iwata, S. J. Mol. Srrucr. ( T H E 0 CHEW 1987,152, 101,and references cited therein. (47)Moore, C. Atomic Energy Levels; NBS: Washington, DC, 1971. (48)Colin, R.; DeGreef, D.; Goethals, P.; Verhaegen, G. Chem. Phys. l a r r . 1974,25, 70. (49) Meyer, W.; Rosmus, P. J . Chem. Phys. 1975,63,2356.Rosmus, P.; Meyer, W. J. Chem. Phys. 1977,66,13; 1978,69,2745. (50)Poshusta, R. D.; Klint, D. W.; Liberles, A. J . Chem. Phys. 1971,55, 252. (51)Dewar, M. J. S.; Rzepa, H. S.J . Am. Chem. SOL.1978,100, 777. (52)Herzberg, G. Molecular Spectra and Molecular Structure. Vol. 2. Spectra of Diatomic Molecules; Van Nostrand Reinhold Co.: New York, 1950. (53)Unpublished results on B2H from his laboratory. (54)Siegbahn, P. E.M.; Schaefer, H. F. J . Chem. Phys. 1975,62,3488. England, W . B.; Sabelli, N. H.; Wahl, A. C. J . Chem. Phys. 1975,63,4596. Kato, H.; Hirao, K.; Nishida, I.; Kimoto, K.; Akagi, K. J . Phys. Chem. 1981, 85, 3391. Kato, H.; Hirao, K.; Aka& K. Inorg. Chem. 1981, 20, 3659. Cardelino, B. H.; Eberhardt, W. H.; Borkman, R. F. J . Chem. Phys. 1986, 84,3230. Schleyer, P. v. R.; Pople, P. A. Chem. Phys. Lerr. 1986,129,475. ( 5 5 ) Bender, C. F.; Davidson, E. R. J . Chem. Phys. 1967,47, 4972. (56)Bauschlicher, C. W.; Liskow, D. H.; Bender, C. F.; Schaefer, H. F. J. Chem. Phys. 1975,62,4815. (57)Rao, B. K.; Khanna, S.N.; Meng, J.; Jena, P.Z . Phys. D 1991, 18, 171. (58) Frenking, G.; Koch, W. J . Chem. Phys. 1986,84,3224. (59) Pople, J. A.; Schleyer, P. v. R.; Kaneti, J.; Spitznagel, G. W. Chem. Phys. Leu. 1988, 145,359.
Beryllium-Beryllium Bonding. 2. Stability of Polyatomic Dicatlons Be,H,
*+,for n = 1-4
Pablo J. Bruna, Gino A. Di Labio, and James S. Wright* Ottawa-Carleton Chemistry Institute, Carleton University, Ottawa, Ontario, Canada K l S 586 (Received: February 27, 1992) This ab initio study on the equilibrium geometries and stabilities of the title dications indicates that on the ground surface at least two (Be2H2+)or three (Be2H22+,Be2H?+) conformations are metastable (quasi-bound). Metastability is essentially governed by the stability of the BeBe bond since abstractions of H or H2 are endothermic reactions. Be2H2+is bent and 0.5 eV more stable than the linear isomer. For Be2H22+,bridged BeH2Be2+and T-shaped BeBeH?+ are species having comparable stabilities, whereas linear HBeBeH2+is about 4.0 eV less stable. For Be2H32+,doubly-bridged HBeH2Be2+and T-shaped HBeBeH?+ also have similar stabilities, whereas triply-bridged BeH3Be2+lies 1.7 eV higher. For Be2Hd2+,the singlet state of H2BeBeH?+ is preferred over the triplet state of bridged HBeH2BeH2+by 4.2 eV. Hydrogenation of Be2*+ stabilizes the metal-metal bond relative to 2Be+ + nH2 because of charge delocalization. Bridged BeH,Be2+ isomers also owe their stability to occupation of the strongly-bund r , MOs of Be-Be by the bridging hydrogens. Despite these stabilizing effects, higher hydrides still remain unstable, as exemplified by the reactions Be2Hd2+ BeH3++ BeH+ (AH= -2.30 eV) and Be2H82+ 2BeH3+ + H2 (AH= -3.09 eV).
-
-
1. Introduction Hez2+ and Bez2+ are the first two homonuclear diatomics having metastable ground states. An AB2+state is called metastable (or quasi-bound) when its local minimum lies energetically above A+ B+. Metastability implies the existence of a dissociation barrier (&), a feature making dications possible candidates for potential energy reservoir^.^ The weakly-bound character of neutral H e 2 and Be25reflects the zero bond order of their IZ:(27it is understandable why hydrogen attack along a line perpendicular to the metal bond is preferred over that along the Be-Be axis. Isoelectronic Li2H also has a bent ground state,2s with Li2 showing an analogous charge distribution as in Be22+.27However, both Be2H and Be2H+are more stable in the linear than in the bent conformation.16a The ground state of Be2H2+(1) is given by X2A1(2a:3al), with participation of all in-plane valence orbitals of Be. A computed R,(BeBe) of 3.92 bohr for this isomer with only one bridged H atom lies between the Re values of Be22+and Be2H22+(4), the latter with two bridged H's. A Mulliken analysis leads to a Be atomic charge of +0.994, essentially the same as in Be$+. Linear Be2H2+(2) corresponds to X2Z+ (3u4a2), the 3a and 4u MOs describing the Be-H and Be-Be bonds, respectively. Thus, the unpaired electron is mainly localized on the BeH bond. The Mulliken charges are 0.98 and 0.76 for terminal and central Be, respectively, and 0.26 for H. Lowering the molecular symmetry from linear C,, (2) to bent C, (1) allows the formation of a stable BeHBe three-center bond through mixing between H 1s and Be 2s, 2p, and the 2p, in-plane components.'6b In the linear conformation, the BeH bond invokes contribution of H 1s and Be 2s and 2p,. SCF/6-31G* computations give (scaled) bending frequencies of 160 and 1014 cm-' for the linear and bent species, respectively. These results suggest the existence of a relatively small bending barrier for 2 1 isomerization and a ring structure which is very stable. Bent BezH2+lies about 4.0 eV above Be+ BeH', but approximately 1.5 eV below Be2++ H+ or Be$+ H (section 6). These thermochemical data clearly point out that Be2H2+is metastable relative to Be-Be bond-breaking but bound relative to H abstraction. Accordingly, only fragmentation along the &-Be bond should be hindered by a potential barrier. As shown later, this observation applies to other dications of this series as well. This work focuses on portions of the hypersurfaces near equilibrium, so that we are unable to give a detailed picture of the geometric and energetic boundaries characterizing each metastable region. Exploratory MRD-CI computations at geometries relatively far away from equilibrium have been carried out mainly for the simple BezH2+isomers. Cross sections for X2Z+ of Be2H2+(2) are shown in Figure 2a. The Be-Be potential has a maximum near R, = 5.60 bohr, with a Denof 0.65 eV (about 50% the Bez2+value). For R > R,, this cross section becomes strongly repulsive since Be+ + BeH+ lies about 4.50 eV below linear BezH2+(section 6). Despite its smaller
-.
+ +
Bruna et al.
6
Ei Z t
wo
2
8 2.0
3.0
4.0
5.0
6.0
7.0
R(BeBe) (bohr)
BeBeH 2+
8
I
2.0
3.0
4.0
5.0
I
6.0
I
7.0
R(BeH) (bohr)
F
i 2. MRD-CIpotential energy curves for bond stretchingin linear
BeBeH2+('E:, ground state): (a) variation of BeBe, for fixed R(BeH) = 3.40 bohr; (b) variation of BeH, for fured R(BeBe) = 4.02 bohr. The first eight (a) and five (b) vibrational levels are shown. Den,about 10 vibrational levels w,(BeBe) of isomer 2 are expected to be metastable. For bent Be2H2+(l),by keeping the distance from H to the center of the BeBe bond frozen at its equilibrium value, the BeBe stretching potential does not show any barrier up to R(BeBe) = 6.0 bohr (the largest distance considered). At this geometry, the system destabilizes by about 1.70 eV. This feature suggests that for isomer 1 the barrier Deffis, at least, as high as for Be22+. For both the linear and bent species, the potential curve along the BeH bond looh quite regular up to 6.00 bohr (Figure 2b, Linear Be2H2+). These results confirm expectations based on the thermochemistry for H+ or H abstraction: both reactions are endothermic and without a barrier. However, breaking of the BeH bond may require more internal energy than that required to overcome the Be-Be barrier. The fact that the cross section for H+ (or H) abstraction from dicationic hydrides usually behaves regularly has been pointed in their ~ ~ study of the process N2H:+ out by Gill and R a d ~ m NzH5+ H+. In the first step (short elongations), abstraction involves a hydrogen atom rather than a proton, whereas in the second step (large XH distances) the actual switch in the wavefunctions from H to H+ takes place. This tYpe of "late transition structure" has little or no potential barrier. Our results on BezH2+
+
-.
The Journal of Physical Chemistry, Vol. 96, No. 15. 1992 6281
Beryllium-Beryllium Bonding and Be2Hz2+corroborate Gill and Radom's observations. The chance to detect a metastable dication experimentally depends on its tunneling lifetime, which in turn is mainly determined by the deepness of the potential minimum. For instance, a barrier Dcrrof 1.10 eV in Be22+allows formation of a dozen vibrational levels. According to literature data?' the dissociation lifetimes are extremely long for the lowest levels (practically, 7 = = for u' I7). Thus, the diatomic barrier is deep enough to prevent spontaneous fragmentation: despite its thermal instability, isolated Be22+behaves like a bound, long-lived species (low 09. Since the potential depth D,dBeBe) and frequency w,(BeBe) in &H2+ compare with that of h2+, it can be assumed that the tunneling lifetimes for the triatomic are roughly as long as for the diatomic (low u'). 3.2. Be2HzZ+Isomers. Three types of conformations were studied: T-shaped BeBeH$+ (3, Cb),bridged BeH2Be2+(4, D2&, and linear HBe-BeH2+ (5, D..,,). As shown below, the first two species have similar stabilities, whereas the latter is very unstable. Particular ways of generating isomer 3 are through lateral attachment of H2 upon as well as through the reactions Be+ BeH2+or Be + BeH22+,the Be species attacking BeH2q from the metal side. Bridged BeH2Be2+4 can be generated by similar reactions between Be4 and BeH2q,the metal now attacking BeH2q from the H H side. On the other hand, species 4 and 5 can be seen as resulting from two different dimerization mechanisms of BeH+: cyclic for 4 versus linear for 5. FCI results from basis A indicate T-shaped 3 lies only 0.05 eV below bridged 4. Basis B gives essentially the same answer, namely 0.03 eV. On the other hand, extensive calculations at the MP4(SDTQ)/6-31 l++G(Zdf,p) level found a reversed order of stabilities, with an isomerization energy, Mi,of -0.04 eV. Inclusion of zero point corrections does not change the overall picture since the zero point energies are 0.38 eV for 3 and 0.46 eV for 4. Therefore, within *3 kcal/mol, species 3 and 4 of Be2H$+ are predicted to be quasi-degenerate. Despite their comparable stabilities, the bonding features of these two conformations are quite different. The ground electronic structure of the T-isomer 3 corresponds to 'A1(3a:4a:). The 3al MO is an H2 (a) species, whereas 4al essentially retains the sp, sp, character of 2ug of Be$+. A Mulliken population analysis gives Be atomic charges of 0.94 (terminal) and 0.77 (central), whereas H is slightly positive (0.14). The overall charge distribution here compares with that of linear Be2H2+. In a simple picture, the stability of 3 essentially originates in the lateral polarization of H2 by Be$+, which reduces the net charge on the central Be. A scaled w,(H-H) of 3775 cm-' in species 4 lies in the same range as reported for BeH$+l4 and &H,Z+ (n = 4,8).' The ground state of bridged Be2H22+(4) arises from the configuration lAg(2a:1 b:,,). Both valence MOs show hydrogen contribution, namely s + s for 2a, and s - s for 1b2". From the side of Be atom, 2a, involves sp, hybrids whereas 1b2,, uses pr in-plane AOs. Active participation of Be pr-type orbitals in the BeHBe bonds explains the shorter R,(BeBe) in isomer 3 when compared with that of species 4.16b The SCF atomic charge on Be lies close to 1.0, as similarly observed for bent Be2H2+. As discussed in section 3.1, bent BeHBe2+(1) is more stable than linear BeBeH2+(2) by about 0.53 eV. It can be easily seen that addition of another bridged H atom upon 1 generates isomer 4 of Be2H22+.Similarly, attachment of a second H to the same Be center of 2 forming the BeH bond leads to (3). Since 3 and 4 are quasi-degenerate, it follows that formation of a terminal H2 bond in 3 is about 0.50 eV more exothermic than that leading to bridged Hzin 4. Linear HBeBeH2+ (5) lies roughly 4.0 eV above isomers 3 and 4. Since the latter are unstable with respect to BeH+ BeH+ by 3.60 eV (section 6), the instability of 5 is quite substantial. This feature stands in sharp contrast with the high stability of linear HBe-BeH, the most stable conformation of neutral Be2Hz.16923*30 However, the quick destabilization of the linear conformation upon ionization is already shown by the monocation: bridged BeH2Be+(4) lies ca. 0.31 eV below linear HBeBeH' (5) [paper 1, ref 16al.
+
HBeBeH"
w2+
+
+
3.0
4.0
5.0
6.0
7.0
8.0
R(BeBe) (bohr)
Figure 3. SCF potential curves for BeBe stretching of linear H B t BcH2+,with R(BeH) fixed at 3.40 bohr. The configurations SI,S2, and S3are respectively 2 4 2 4 , 2 4 3 4 , and 2 4 2 0 ~ 3 ~ ~ .
Formally, species 5 is isoelectronic with Be2 and B22+,both diatomic ground states being weakly bound and strongly repulsive, r e s p e c t i ~ e l y . ~ JDespite ~ . ~ ~ . ~the ~ instability of the linear dication, it is of general interest to understand the reasons for such a behavior in some detail, particularly because of the possibility for 5 of being generated through double ionization of linear Be2H2. Cross sections of interest are shown in Figures 3 and 4. Two symmetries of 5 were investigated via the MRD-CI approach, namely '2: and 32:. Because of a strong configuration mixing, the metastable character of the singlet surface can only be detected by using multireferencial methods. Perturbational treatments restricted to one reference configuration probably predict 132: to be the metastable ground state. At the SCF level and along the Be-Be coordinate, the singlet configurations 2 4 2 4 (SI)and 2 4 3 4 ( s 2 ) are repulsive and bound, respectively (Figure 3). The SCF potential curve for 13Z:, with a configuration 2u,,3ug (S3),shows a local minimum near R(Be-Be) = 4.00 bohr. At this level of treatment, the triplet appears to be the ground state of isomer 5. The MRD-CI computations reveal that 1'2: and 13Z: are almost isoenergetic, the singlet lying about 0.09 eV lower (Table I). The ground-state 1'Z: owes its metastability to a heavy admixture between 2 4 2 4 (SI, repulsive) and 2 4 3 4 (S2,quasi-bound). The Be-Be cross section (at the CI level) has a maximum of about 0.16 eV near R(Be-Be) = 5.2 bohr (Figure 4). Since this potential well is able to accommodate only a few quanta, o,(BeBe) = 515 cm-', the ground state of linear BeH22+ has little or no chance of being detected experimentally. The 2l2: state also appears to be metastable (Figure 4). After CI, the Be-Be barrier for l32:(2uU3ug) occurs near 6.0 bohr, with a D,ff = 0.80 eV (6500 cm-I). Since this potential contains about eight metastable vibrational levels, 132: should have a longer tunneling lifetime than X'Z: and therefore a higher probability for its experimental observation. This triplet state is well described by its leading configuration. The Mulliken charges are 0.75 (Be) and 0.25 (H). The B t H cross section of X128+ shows a regular behavior up to R = 7.0 bohr, similar to that observed for linear h H 2 +(Figure 2). Despite the fact BQH+ H+ lies 1.64 eV below Be2Hi+(S), the energy profile for H abstraction looks as if it were convergmg to Be2H2++ H (a channel placed 1.0 eV above linear Be2H?+).
+
6282 The Journal of Physical Chemistry, Vol. 96, No. 15, 1992
HBeBeH2+
Bruna et al. of f 3 kcal/mol). Since the parent isomers 3 and 4 of Be2H*+ are quasi-degenerate, it follows that the stabilization caused by formation of a Be-H bond along the reaction Be2HzZ+(3 or 4) + H Be2H32+(6 or 7) is comparable for both Be2H22+conformations. Species 6 has a 2A1(3a:4a:3al) ground state. The open-shell 5al MO corresponds to terminal BeH, whereas the lower-lying valence MOs have the same structure as in 3 of Be2Hz2+(namely H H and BeBe character, section 3.2). Delocalization in 6 (HBe,Be,H$+) of the positive charge along the BeBe bond is reflected by the computed net charges, with essentially a common value of 0.73 for both Be atoms. This has to be compared with q+ of 0.94 (Bq) and 0.77 (Be,) in the related species 3 (BqBe,H$+) of BezH2+. Obviously, H attack on Be, of 3 to form terminal Be-H of 6 (one-electron bond) lowers the charge on that Be, center. At this point, it is clear that the stability of T-Be2H?+ 6 is governed by two kinds of bonding: one of classical type (the &Be and BqH bonds) and another of nonclassical nature (lateral polarization of the H2 group by Be,). The latter type of bonding already operates in BeH2+and BeH22+.13J6a The ground state structure of 7 is represented by 2Al (3aflb:4al). The singly-occupied BeH bond corresponds to 4al, while the two BeHBe "banana" bonds are described by 3al and 1b2 (the C , MO counterparts of 2a, and 1b2, of the DZhisomer 4 of & H P ) . Active participation of all in-plane Be sp AOs (sp2 hybrids) to form the BeBe bond as well as both bridged and terminal BeH bonds is responsible for the stability of HBeH2Bez+.16b In isomer 7, (HBe,H2BeJ, with one terminal and two bridging hydrogens, the charge distribution is nonsymmetrical: Be, and Be, have charges of 0.98 and 0.77, respectively. The former compares with that assigned to the Be, atoms in BezH?+ (4); on the other hand, a smaller charge of 0.77 for Be, of 7 is understandable since this center is connected to all three hydrogens. The stabilizationeffected by charge delocalization after formation of terminal BeH is thus the same in isomers 6 and 7. This has already been noticed above by an almost common value of the bonding energy BezHz2++ H Be2H32+. The less stable isomer 8 (BeH3Bez+)can be obtained from species 4 (BeHzBe2+) by adding a third bridging hydrogen. According to MRD-CI (basis A) calculations, triply-bridged Be2H32+8 lies 1.70 eV above isomer 6. MP4(SDTQ)/631 l++G(Zdf,p) data essentially reproduce the CI results, with conformation 8 lying at 1.62 and 1.71 eV above 6 and 7, respectively. Species 8 has a 2E'(2a'121e'3) ground state. The 2atl MO is a u-type orbital described by linear combinations involving s AOs from all atoms, whereas 1e' is formed by pXAOs of Be and linear combinations of hydrogenic 1s AOs. Here, Be uses sp' hybridization; a computed net charge of 0.83 for that atom is slightly higher than in species 6 or 7 but smaller than in Be?+. Using a simple homonuclear model, the ground configuration of BeH3Be2+corresponds with the uiri configuration of a prototype X2 diatomic, in which all electrons are occupying bonding orbitals. Hence, it is understandable why the BeBe bond in isomer 8 of &H32+ has the shortest R, and highest we values (3.65 bohr and 741 cm-I) among all dications listed in Table I. Moreover, &(&-Be) decreases steadily from 6 -.7 -.8, a behavior easily correlated with the number of bridging hydrogens.16bAs expected, w,(BeBe) shows the opposite trend. On the other hand, a bond distance R(HH) of about 4 bohr is much longer than in H3+ (-2 bohr). In the latter, the e' MO is antibonding. This shows that in BeH3Be2+the correct picture is not an H3 ring with weak Be bonding. Summarizing, gradual population of the Be-Be bonding A, species along the series BeBe2+-. BeHBez+ BeHzBe2+-. BeH3Be2+increases the BeBe bond strength (short R,, high oe). In an equivalent picture, Be hybridization varies from sp to sp2 to sp3.16b This effect represents a chemical replica of the strongly-bound, doubly-excited spectroscopic states (DES) studied in this laboratory3'for several diatomics and resulting from double +
&0 1 9"
-7
7 3.0
5.0
4.0
6.0
7.0
8.0
R(BeBe) (bohr)
Figure 4. MRD-CIpotential energy curves for BeBe stretching of linear HBtBeH2+. In the region from 4.0 to 6.0 bohr, the singlet states arise from a heavy mixing between the configurations SI and S2.
As discussed in section 3.1, similar cases of *late transition structures" for H abstraction are known in the l i t e r a t ~ r e . ~ ~ The structure of isomer 5 can be represented as H.Be:Be.H, corresponding to a doubly-occupied &Be and two singly-occupied Be-H bonds. This bonding situation points out that doubleionization HBeBeH HBeBeH2+(both linear) proceeds through ejection of an electron from each Be-H bond (section 4). The high instability of linear HBeBeH2+can also be understood by looking at the dimerization of BeH', both Be atoms approaching frontally. Since in BeH+ the positive charge is localized on Be, formation of linear HBe-BeH2+ requires the transfer of one electron from each terminal BeH into the central Be-Be bond, a process energetically unfavorable because of the significant charge reorganization. The following arguments make this point clear. Isomer 5 (singlet) lies at -6.60 eV aboue BeH+ BeH+ according to our calculations (section 6). On the other hand, the Coulomb repulsion between two positive charge separated by a distance R = 4.0 bohr (similar to Re of singlet 5) is 6.80 eV. Certainly, the instability of linear HBe-BeH2+ is dictated by the Coulomb repulsion between the two BeH+ groups. 3.3. Be2Hs2+Isomers. As shown in Figure 1, three structures were investigated: T-shaped HBeBeH?' (6, Cb),doubly-bridged HBeH2Be2+(7, C ,), and triply-bridged BeH3Be2+(8, D3*). The latter isomer is less stable than the other two (cf. Table I), so that we discuss first the most stable conformations. Isomers 6 and 7 can be formally generated through hydrogenation upon terminal Be of the T-shaped 3 and bridged 4 species of BezHZ2+,respectively. In line with this formation mechanism, the geometry of the corresponding BezHzmoiety remains practically unchanged upon hydrogenation (Table I). In these pentaatomic radicals, the odd electron is localized on the terminal, newly formed Be-H bond. Other formation mechanisms are given by the reactions HBe+ BeH2+ and HBe BeHz2+. More precisely, frontal attack between both Be atoms leads to isomer 6, whereas that between HBeq and the Hz side of BeHzq generates isomer 7. Isomers 6 and 7 exhibit comparable stabilities. The MRD-CI (basis A) treatment indicates 6 lies below 7 by only 0.03 eV. computations lead to However, MP4(SDTQ)/6-311++G(2df,p) a reversed order of stabilities of 4 . 1 0 eV. The SCF zero point energies are 0.47 eV for 6 and 0.55 eV for 7, so that in practical terms, both Be2H32+species are equally stable (within a margin
-
+
+
+
-
-
The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 6283
Beryllium-Beryllium Bonding
TABLE lk Computed Single ( I P ) d Double (IPz+) Adhbatic IOaiution Potentials (in ionization Be, Be2H (2) Be2H2 (5) A At (IP') 7.45 7.10 (2, 2) 9.03 (5, 4) 9.34 (5, 5)
-
At
AZt (IP')
13.60
A
AZt (1P2')
21.05
-
15.65 16.18 22.75 23.28
-
(2, (2, (2, (2,
1) 2) 1) 2)
12.95 (5, 4) 13.29 (4, 4) 22.32 (5, 4) 26.49 (5, 5)
Be,H., (101'
Be2I-h (7) 7.75 (7, 7)
11.62 (10, 10)
(7, 6) (7, 7) (7, 6) (7, 7)
22.63 (10, 9 ) 26.79 (10, 10)
15.86 15.88 23.61 23.63
-
'Zero-point corrections are not included. Numbers in parentheses indicate the conformations of the initial and final states. *The adiabatic I F for BeH?+ BeHqZtlies at 18.50 eV. 'The I F (Be2H4 Be2H4+)corresponds to the vertical value. The transition A (10) A2+(10) involves the 3BBI,stateof BkzH42t. -+
excitations from the antibonding u, into bonding MOs, ?rU in p a r t i c ~ l a r . Since ~ ~ ~ ~Be22+ ~ ~ ~does ~ not have antibonding u, electrons, and on the other hand, bridging hydrogens formally occupy BeBe A, MOs, it can be seen that BeH,Be2+ species (n = 1,2,3) show an increase in BeBe bond strength in analogy with that expected for high-bond-order 44 states of an isovalent homonuclear molecule. 3.4. Ee2Hd2+Isomers. The isomeric form of Be2Hd2+with terminal H2 groups (S,species 9, Figure 1) has been studied by Nicolaides and Va1tazan0s.l~They found that this isomer lies 0.25 eV above 2Be+ 2H2. Since Bezz+also lies above 2Be+, but by about 2.40 eV, the relative stabilization of the BeBe bond due to charge delocalization after H2 attachment is quite substantial. The stabilization trend is continued in Be2HsZ+(with two H2 on each Be side), which is found at 0.57 eV below 2Be+ 4H2.I4 Although this dication is bound with respect to those products, it still remains metastable (section 6). For isomer 9, the ground state corresponds to 'Ag(2ai3a:2a:). MO charge density contours are shown in ref 14. The Be atom has a net charge of 0.73, close to that of the T-isomer 6 of &H$+. This finding is understandable since 9 (HZBeBeHz2+)and 6 (HBeBeHzZ+)are related by addition of a second hydrogen to terminal Be(H) of 6. We investigated also the bridged isomer HBeH2BeH2+(10). Optimization at the SCF level does not detect any stable minimum on the singlet ground surface. No extra effort has been made to see whether inclusion of correlation is mandatory to obtain a metastable minimum having a singlet multiplicity and a bridged conformation (as is the case for the singlet surface of linear HBeBeH2+,with a heavy mixing of configurations, section 3.2). The SCF gradient detects a metastable conformation 10 but with triplet multiplicity. The existence of a metastable biradical can be understood by considering hydrogenation upon Be, of 7 (Be2H32+) HBeCH2Bet2+ + H HBeH,BeH
+
+
7
-
10
The parent radical 7 contains an open-shell BecH bond, so that formation of a similar Be,H group on the opposite side of 10 justifies formation of a metastable 3Blustate for HBeH2BeHZt. The biradical (IO) can also be generated through double hydrogenation (bridged position) upon the '2: biradical state of linear HBe-BeH2+ (5). Isomer 10 (triplet) is notably less stable than 9 (singlet), as shown by a relative M iof 4.16 eV (MRD-CI) or 3.99 eV (MP4/SDTQ). It should be pointed out that in the case of the neutral species, bridged HBeH2BeH is the most stable isomer.16a The BeBe bond length of 10 (two bridging Hs) is shorter by 0.28 bohr than that of 9 (no bridging Hs), as expected by xu MOs contributing only to the bridged BeH,Be2+ isomers. The atomic charges in 10 are 0.76 for Be, 0.26 for terminal, and -4.02 for bridging hydrogens. Similar small net charges, q = 0, are found for bridging hydrogens in the isomers 1, 4, and 7. 4. Adiabatic Ionization Potentials
Table I1 contains the adiabatic single and double ionization potentials (IP+ and IP2+)derived in this work. To facilitate the discussion, the identities of the initial and final isomeric species involved are specified in parentheses. The computed IPS are expected to be accurate within 0.30 eV.
-
The experimental values for Be8 are 9.32 (IP') and 27.53 eV (IP2+),corresponding to an IP+ of 18.21 eV for Be+ Be2+. On the other hand, the computed ionization potentials for the BezH, hydrides are generally smaller. This is particularly true for IP2+, with values lying below 24 eV for transitions between ground states. Photoelectron spectroscopy (PES) is a standard technique to study ionization processes. However, the possibility of measuring an adiabatic IP is partially govemed by the Franck-Condon factor (FCF) between zeroth vibrational levels: the smaller the change in geometries between the initial and final states the higher the FCF for the 0transition. As seen in Table 11, several of the energetically lowest IPS involve quite different isomeric structures. Therefore, the present IP values are more relevant because of their thermochemical information (as appearance potentials, for instance) than for actual PES studies. A few transitions, however, could be fully monitored by photoionization experiments. The main premise is that along the process A A+ A2+all species have a common topological structure. Ionization from the radicals W H and Be2H3are good examples (with the IP+ values explicitely given)
- - - --
Be2H Be2H3
7.10
7.15
Be2H+
Be2H3+
16.18
15.88
Be2H2+(all linear, structure 2)
BezH32+(all bridged, structure 7)
In both cases, the IP+ (A A+) corresponds to the ejection of a lonepair electron from terminal Be. In line with their open-shell ground states, ionization requires from 1.5 to 2.0 eV less energy than for Be. Since molecular ionization occurs with almost no change in geometries, these spectra should have little or no vibrational structure. It also implies the vertical IP+ lies close to the adiabatic value. With respect to the ionization of cations, the quantity I F (A+ A2+)represents ejection of an electron from the terminal BeH bond of B%H+or &H3+. Since this process lengthens that bond, both PES spectra should exhibit short progressions in w,(BeH, terminal). Summing up, the ionization spectra of Be2H and Be2H3are expected to show common features, not only because of the similar changes in electronic structure but also from an energetic point of view. The corresponding IP2+s(A A2+),for example, lie in the 23.50 f 0.2 eV region (Table 11). The whole process Be2H2 Be2H2+ BezHz2+is more difficult (if not impossible) to follow experimentally if the geometry constraint (in this case, a linear conformation) has to be maintained. In detail, linear HBeBeH' has a weak BeBe bonding since ionization takes one electron out from this u bond. Accordingly, this ionization process shows a rather broad Frank-Condon envelope because of the large R,(BeBe) in the upper ionic state.16a Moreover, the transition HBeBeH' HBeBeH2+is accompanied by an enormous rearrangement in electronic structure since the bonding in the dication corresponds to a doubly-occupied BeBe and two open-shell BeH bonds. Hence, it appears more plausible that the vertical ionization from linear &H2+ proceeds via ejection of the unpaired electron from the BeBe bond. This may lead to the direct break of the system into two BeH+ ions. Linear HBeBeH2+ (32:) can be generated from neutral (Le., siHBeBeH (~#$9) through double-ionization uuug multaneous ejection of one electron from each BeH bond). This process requires about 26.5 eV to proceed (Table 11). Since the
-
-
-
+
-
--
6284 The Journal of Physical Chemistry, Vol. 96, No. 15, 1992
Bruna et al.
TABLE 111: Ground-StateBinding Energies, D,(BeH) (in eV), of BeH,' and BeH:t products
species BeH'
D,c
Bet + H Be H' BeH' H BeH + H' Be' + H2 Be H2' BeH2' H BeH, H t H2 BeH' BeH H2' Be H3' H H2 Be' BeH3' H' BeHg2' H H2' BeH2' BeH22' H 2
+
BeH2' (11)
+
BeH3' (12)
3.02 7.35 1.92 7.26 0.38 6.66 3.74 6.95 1.10 8.39 3.79 4.12 0.38 5.28 1.51 2.10
+
+ + +
+ + + + + +
+
BeH?'
(13)
+
Spi es (Zen, Point Corrections Not Included)'~~
products
species BeH2+
0,' -2.89 1.62 -0.63 5.29 -0.21 2.35 -1.16 1.39 -1.85 2.11 -5.43 3.73 -3.17 1.89 4.45 8.16
+ +
Be' H' Be2' H BeH' H' BeH2' + H H2+ Bet H2 Be2' BeH2' H' BeH22t H BeHt + H2' BeH2' + H 2 H3' Be' Be2+ H H 2 BeH' + H3t H2 Be' + H2' Be2' + 2H2 Be + 2H2'
+
BeH22t (11)
+
+
BeH32t (12)
+ +
+ + +
BeH?' (13)
+
"The equilibrium geometries are ( R in bohr, a in degrees) as follows: BeHt (R= 2.48); BeHZt (R = 3.41); BeH2' (R = 3.34, a(HBeH) = 23.4, ref 13); BeH22t (R = 3.07, a(HBeH) = 28.7, ref 13); BeHgt ( R = 2.46, R(BeH(H) = 3.09, a(BeH2) = 26.7); BeH32t (R = 3.27, R(BeH(H)) = 3.00, a(BeH2) = 28.7); BeH42t ( R = 3.02, a(BeH2) = 28.8, ref 14). *In the same order as in a, the MRD-CItotal energies (in hartree) are -14.8880, -14.1706, -15.4586, -14.8650, -16.0961, -15.4161, and -16.1101. ' D e from refs 13 and 14: 0.25 (BeH2'; Be' H2);-0.53 (BeHZzt;Bet + Hz'); 2.21 (BeH22t; Be2' + H2); 3.54 (BeH32t; Be2' + H H2); 1.53 (BeH?'; Bet H2' + H2); 4.27 (BeH22t; Be2+ 2Hz).
11
12
13
Figure 5. Equilibrium geometries of the dications BeH;',
BeH,2t, and
BeH42t.
linear dication 5 is markedly less stable (4.0eV) than the bridged structure BeH2Be2+(3),it is difficult to speculate what happens after vertical ionization. The biradical HBeH2BeH2+can be generated through double ionization from HBeH2BeH, both initial and final states with equilibrium structures of type 10. This process, which involves the simultaneous (single) ionization of both terminal BeH bonds, is predicted at IP2+ = 26.8 eV. This value compares with that assigned above to the transition HBeBeH HBeBeH2+,also arising from ionization of terminal BeH.
-
Stability of BeH,' and B e H F Ions Fragmentation of Be2H,Z+may involve BeH,q products with total charge q = 0, 1, or 2. Most of these species have been studied theoreticall~,7,~~-'~,~~ though at different levels of treatment. We are unaware of any study on BeH4+. Table I11 summarizes dissociation energies from MRD-CI calculations (basis A). For each ion, the data have been ordered by considering first dissociation into (BeHW1+ H)q, followed by (BeHW2+ H2)4,etc. Since we are mainly interested in the &H,2+ thermochemistry, no extra effort has been spent in geometry reoptimizations of the monoberyllium hydrides. These species are labeled as 11, 12,and 13 in Figure 5; the equilibrium parameters are specified in Table 111. BeHt and BeH2+respectively show the strongest (3.02 eV) and weakest (0.38 eV) bonding among the monocations. In the former species, the strong bond (2u MO) results from the combination of Be sp, with H 1 ~ On. the~other ~ hand, ~ the weak bond for Be+-H2 (11) reflects the electrostatic nature of the bonding effected through lateral polarization of H2by Be+ 2s.I3-l5 In fact, BeH2+ constitutes the first member of the "cluster" family Be+(Hz)".l5 Dimerization of BeH2+ to form H2BeBeH?' (9) represents the polyatomic analogue of the reaction 2Be+ B$+. T-shaped BeH3+(12)has been detected in mass spectrometry ~tudies.'~This ion, which can be generated by hydrogen attack upon the Be side of BeH2' (ll),is bound by 1.10 eV with respect to BeH+ + HI. An increase in stability for BeH3+of about 3 times relative to that of BeH2+correlates with the directional character in HBe'-H2 of the second Be sp, hybrid (the empty 3u MO of BeH+) versus the nondirectional charge distribution of the Be 2s orbital in the Be+--H2 complex.14J5 5.
-
+
+
+
+
Considering the dissociation energies of BeH2+,BeH22+,and BeHj2+,the data from Table I11 show that the number of stable products (channels) is equal to the number of hydrogens contained in each dication. This feature is simply related to the possibility of the ions H+, H2+, and H3+being formed. Measured by their destabilization with respect to the energetically lowest-lying products, the intermediatespecies BeH?+ (-0.63 eV) and BeH:+ (-5.43 eV), are less and more metastable in character, respectively. BeHZt and BeH42+are unstable by about -3.0 eV (Table 111). An exothermicity of 5.30 eV for BeH2++ H BeH?+ compares with that for the reaction BeH32++ H BeH4*+.In each case, a strongly bound H2 species attached to Be2+is formed. The bonding similarities in dications 12 and 13 are also reflected in the thermochemistry for H2 abstraction: the process BeH32+ BeH2++ H2 requires the same energy as does BeH,2+ BeH?+ + H2 (about 2.10 eV). The data from Table I11 can be combined internally to derive other heats of reaction. The largest exothermicity (about 11-33 eV or 260 kcal/mol) is assigned to the reaction Be 2H2+ BeH+ H3'.
--
+
- + -
6. Bond Energies of Be2H? Species The computed dissociation energies are summarized in Tables IV-VI. Corrections due to zero point energies are not taken into account. Unless otherwise specified, the bond energies are for the most stable isomers. A detailed analysis of the result leads to the following general observations: (a) Dissociation products of type Be2HWI+ + H+ or B%HFl2+ + H invariably lie above the corresponding Be2H,2' ground state (with n = 1, ..., 4). (b) Dissociation into Be2HW2++ H2+or Be2H,?+ H2 is also an endothermic reaction for those Be2H,2+ions with n = 2-4. (c) The only way for Be2H,2+species (with n = 3,4) to form energetically lower-lying channels by the breaking of BeH bonds alone is through formation of H3+products, as in &H32t Be2+ + H3+or Be2H42+ Be2H+ + H3+. These reactions are exothermic by 2.45 and 0.90 eV, respectively. (d) Breaking of the BeBe bond through formation of two monopositivelycharged fragments invariably leads to more stable products. Bez2+and Be2H2+have one channel of this type each, whereas for Be2H?+ (n = 2-4) two combinations are possible. Stable products lie from 3.0-4.3 eV lower, with the exception of Be?+ and Be2H42+showing smaller destabilizations of -2.40 eV. On the basis of the features given above, it is clear that the metastability of Be2H,Z+essentially depends on the stability of only the k B e bond. As shown earlier for Be2H2+and Be2HZ2+, cross sections along the B e B e bond exhibit dissociation barriers. In the discussion to follow, the relation between metastability and the energetics at dissociation will be analyzed. In a simple
+
-
-
The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 6285
Beryllium-Beryllium Bonding
TABLE IV: Ground-State Binding Energies, D,(BeH), of BerH?+ Species (Zero Point Corrections Not Included, AU
species Be2H2' (1)
4
products Be2' + Ht Be22++ H Be2H2' + H+ Be2H22++ H Be?' + H2 Be2++ H2+
Be2H32t(6) Be2H2+(3)
Be2H++ H2+ Be2H2' + H2 Be2++ H3' Be22t + H + H2
Be2Hj2+(6)
-.
1.40 1.44 1.26 0.89 1.35 3.28
species Be2H22+ (3)
Data in eV)O
products Be2H++ H+ Be2H2++ H Be2H3++ H+ Be2H32++ H Be2H2++ H2+ Be2H22+ + H2 Be2Ht + H3t Be2H2++ H + H2 Be2++ H2++ H2 Be2+ 2H2+ Be22++ 2H2
Be2H12+(9) Be2Hd2+ (9)
0.12 0.80 -2.45 2.24
DC 2.44 4.48 2.17 5.02 3.67 1.34 -0.86 6.35 4.61 12.83 2.69
"Reference 14 gives 2.45 eV for D,(Be2Hd2+ Be22++ 2H2). TABLE V Ground-State Biding Energies, D,(BeBe) (in eV) (Zero Point Corrections Not Included)
species
products Bet + Be+ Be2++ Be Be+ + BeHt Be2++ BeH Be + BeH2+ BeH+ + BeH' BeH + BeH2+ Be+ + BeH2+ Be + BeH?+ Be2++ BeH2
Be2H2+(1) Be2H2' (3)
De -2.40 6.49 -3.99 5.89 6.25 -2.54 8.12 -1.43 5.44 6.29
TABLE VI: Comparison of the Relative Stabilities of Be2H,ft Species with Respect to 2Bet aH2 ( A E ) and the Most Stable Products ( A E * ) (AU Data in eV).
+
species Be? Be2HZt Be2H:' Be2H32+ Be2HIZt Be2HS2+
2Bet + nH2 products n=O n n n n n
= 'I2 =1 = 3/2 =2 =4
AE -2.40 -0.96 -1.05 -0.16 -0).29b [+0.57]
