J . Phys. Chem. 1992, 96, 6269-6278 TABLE VI: J Vdws (em-')for T i 2 Q 0 R(Ti-0) RHF UHF 1.65 1.75 1.85 1.95
-23 -1 1 -6
-28 -1 1
-3
4
0
RU
CI
-131 -1 14 -108 -107
-169 -147 -135 -130
--f, - J U H F . . 0 . .J RU -6-JRHF-A-JCI
4
0
.-
-200-
I
1.65
1.70
1.75
1.80
1 1.85
1.90
1.95
R (4 Figure 3. J values for Ti2C140as a function of R(Ti-0) distance.
Magnetic Coupling Constants for TizCbO The results from the calculations for the transition metal system Ti2C140(Table VI, Figure 3) follow the trend suggested by the calculations on H-He-H and [H-F-HI-. The best agreement with Jcris again achieved by JRU. JRU covers the range from -107 to -131 cm-', while the CI results are between -130 and -169 cm-'.J R H F and JUHF are much smaller than JcI;they range from -3 to -23 cm-I and from +4 to -28 cm-', respectively. Conclusions We have calculated the energies of the singlet and triplet spin states of three model compounds using various wave functions. Coupling constants have been obtained using the appropriate energetic relationships. We have found, as derived by Noodleman and Davidson: that the J value obtained from the energy of a high spin restricted Hartree-Fock wave function and a low spin
6269
broken symmetry wave function, JRu,compares favorably to Jcr over a wide range of ion-bridge separations. If the energy for the high spin state is obtained from an unrestricted wave function, the m&itude of the resulting coupling constant, JmF,is too small; and it can be of the wrong sign. Superexchange, direct exchange, and ligand spin polarization have been shown to be included in the broken symmetry approach, if the high spin energy is obtained from a wave function which is an eigenfunction of spin. These contributions plus others are included in our CI calculations, but the computation time involved is much greater than with the S C F calculations. The broken symmetry approach offers an adequate approximation for these effects at a much lower cost.
References and Notes (1) Murray, K. S. Coord. Chem. Reu. 1974. 12. 1. (2) (a) DcLoth, P.;Cassoux, P.; Daudey, J. P:; Malrieu, J. P. J . Am. Chem. Soc. 1981,103,4007. (b) De Loth, P.; Daudey, J. P.; Astheimer, H.; Walz, L.; Haase, W. J. J . Chem. Phys. 1985, 82, 5048. (c) Charlot, M. F.; Verdaguer, M.; Journaux, Y.; De Loth, P.;Daudey, J. P.Inorg. Chem. 1984, 23, 3802. (d) De Loth, P.;Karafiloglou, P.;Daudey, J. P.; Kahn, 0. J . Am. Chem. SOC.1988, 110,5676. (e) Astheimer, H.; Haase, W. J . Chem. Phys. 1986.85, 1427. (3) (a) Noodleman, L. J . Chem. Phys. 1981, 74, 5737. (b) Norman, J. G., Jr.; Ryan, P. B.; Noodleman, L. J. Am. Chem. Soc. 1980,102,4279. (c) Aizman, A.; Case, D. A. J. Am. Chem. Soc. 1982,104,3269. (d) Noodleman, L.; Baerends, E. J. J . Am. Chem. Soc. 1984,106,2316. (e) Noodleman, L.; Norman, J. G., Jr.; Osborne, J. H.; Aizman, A.; Case, D. A. J . Am. Chem. SOC.1985, 107, 3418. (4) Noodleman, L.; Davidson, E. R. Chem. Phys. 1986, 109, 131. (5) Huzinaga, L. J . Chem. Phys. 1965, 42, 1293. (6) Dunning, T. H.; Hay, P.J. In Methods ofBlectronic Structure Theory; Schaefer, H. F., Ed.; Plenum Press: New York, 1977; Vol. 4, Chapter 1. (7) Hart, J. R.; Rap#, A. K. Unpublished results. (8) Upton, T. H.; Rap#, A. K. J. Am. Chem. Soc. 1985, 107, 1206. (9) Rap#, A. K.; Smedley,T. A.; Goddard, W. A. J . Phys. Chem. 1981, 85, 1662. (10) Kahn, 0.; Briat, B. J . Chem. SOC.,Faraday Trans. 2 1976,72,268. (11) Anderson, P. W. Solid State Phys. 1963, 14, 99. (12) Hay, P. J.; Thibeault, J. C.; Hoffmann, R. J. Am. Chem. SOC.1975, 97, 4884. (13) Bobrowicz, F. W.; Goddard, W. A. In Methods of Electronic Structure Theory; Schaefer,H. F., Ed.; Plenum Press: New York, 1977; Vol. 4, Chapter 4. (14) Yamaguchi, K.; Toyoda, Y.; Fueno, T. Chem. Lett. 1986, 625.
Beryllium-Beryllium Bonding. 1. Energetics of Protonation and Hydrogenation of Be, and Its Ions Pablo J. Bruna, Gin0 A. Di Labio, and James S. Wright* Ottawa-Carleton Chemistry Institute, Carleton University, Ottawa, Ontario, Canada K l S 5B6 (Received: February 27, 1992)
This paper is a theoretical study of beryllium-beryllium bonding, with emphasis on how to strengthen that bond. It deals with the structures and stabilities of several Be2H,Qspecies (with n = 1, 2 and charge q = -1, 0, +l). The ground states of Be2H, Be2H+,Be2H-, Be2H2,and Be2H2-are linear, whereas that of Be2H2+(like Be2H,) is bridged. The Be-Be bond in the linear compounds arises from sp, hybridization on Be, whereas in the bridged isomers it also has pr contribution (sp2 hybridization). Hydrogenationof the weakly bound Be2(& = 4.63 bohr, we = 276 cm-',De = 0.1 eV) strengthens the BeBe bond significantly, as shown in the hydrides by an average &(BeBe) of 4.0 bohr for linear and of 3.8 bohr for bridged isomers. The frequencies w,(BeBe) lie in the range 650 f 50 cm-'. Hydrogenation to produce BezH leads to a D,(Be-Be) of 1.24 eV, while a second hydrogenation to produce HBeBeH strengthens it further to 3.20 eV. Both Be2H+and Be2H- also exhibit a strong D,(Be-Be) of ca. 3.30 eV. The process Be2H4(bridged) 2BeH2, however, is only 1.38 eV endothermic. The stability of these diberyllium hydrides mainly results from the withdrawal of antibonding charge upon Be2effected by the attached hydrogen atoms.
-
1. Introduction He( Is2) and Be( ls22s2)are the first atoms from the periodic table with closed-shell ground states. One would therefore expect similarities in the bonding properties ofthe respective x2and X H molecules. Specifically, simple MO arguments indicate that each ground state should be repulsive. Such predictions are essentially 0022-3654/92/2096-6269$03.00/0
true for Hez(X'Z:,lu~l$,) and HeH (Xz2+,lu22u). For inStan% 0,and Re values of 0.95 meV (0.022 kcal/mol) and 5.60 bohr, respectively, have been reported for He2; studies on ground-state HeH show this species is also weakly bound.' Bez and BeH are considerably more stable than would be expected from their helium homologues. Bez(2$,2$,) has a De 0 1992 American Chemical Society
6270 The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 of 97.7 meV (2.3 kcal/mol) and R, of 4.63 bohr,2 a bond energy 2 orders of magnitude higher and a bond length 1.O bohr shorter than He2. The bond length of Be2 is even shorter than that of Liz (X1Z:,2$, with Re = 5.05 bohr and De = 1.10 eV) (ref 3), although the farger dissociation energy in Liz is consistent with its double occupation of 217, (bonding) and vacancy of 2uu (antibonding). On the other hand, a Do of 2.16 eV for BeH (X2Z+) indicates a fairly stable bond, comparable with that of LiH (De = 2.5 eV, ref 3). Obviously, a different type of interaction is operating in Be than in He. The deep potential well in BeH arises from an avoided crossing between repulsive Be(lS,,s2) + H and attractive Be(3P,,sp) H prod~cts,4*~ an effect which can be taken as an example of Be sp, hybridization. Similarly, the relatively short Re and large De in Be2 results from configuration-mixing between 2 4 3 4 [strongly bound, correlating with 3P,(sp) + 3P,(sp)J and 2 4 2 d [repulsive, IS,(s2) + 1Sg(s2)].6,7Both results underlie the relevance of excited s p atomic states in stabilizing the BeH and Be2 bond^,^-^ also important for Be3and Be4 (with atomization energies of =l and 3 eV, respectively) and higher Be,, clusters as we11.639910 The open-shell 3a MO of BeH has a Be sp, lone-pair chara c t e r ? ~ This ~ feature suggests the dimerization reaction 2BeH HBeBeH should be exothermic due to formation of metalmetal a2bonding. Prior studies have found that about 3 eV (70 kcal/mol) is required to break Be2H2into two BeH units." The relatively strongly bound character of HBe-BeH leads to the idea of stabilizing the Be-Be bond by successive hydrogenation of Be2, that is
+
-
- + -
BeBe
+H
BeBeH
+H
HBeBeH
The reaction BeBe HH HBeBeH should also be exothermic since De(H2)is approximately twice De(BeH).3 In a series of studies1*on XM-MY species (with M = Be or Mg and X, Y = H, F, or Cl), Jasien and Dykstra ascribed the high stabilities of XM-MY when compared with that of M2 to the electron-charge-withdrawingpower of the substituents X,Y acting upon M-M antibonding electrons. They also found that the reaction Be + HBeH HBeBeH is exothermic by ~ 1 . eV. 0 Little or nothing is currently known about the equilibrium geometries, bonding features, and relative stabilities of Be2H,,9 hydrides, with n = 1-2 and charge q from -1 to +1. We present here a theoretical study on these compounds, with particular emphasis on the ground state of the most stable conformations. In the spirit of Jasien and Dykstra's ideas,12our main goal is to follow how the B e B e bond strength varies on successive hydrogenation of & and its ions (&+ and Be2-). The beryllium species are compared with Li2Hn9and B2H,,9,in which the metal-metal bond is relatively strong for isolated X2. A related MRD-CI study on B%H;+ dications, hereafter called paper 2, is the following paper in this issue.13 Moreover, the importance of Be pr orbitals in describing the stability of bridged species BeH,,Be is the topic of a third comm~nication.'~
-
2. Technical Details
The equilibrium geometries were obtained by carrying out CI computations with an A 0 basis set called basis A. The energies to be reported throughout, however, result from single point calculations with a larger basis set (basis B). The sp valence AOs on Be consists of the 1Os/5s and Sp/3p subsets from Huzinaga-Dunning15J6optimized for the 'S(s*) and 3P(sp) atomic states, respectively. The contraction 41 of the 5p primitives given by DunningI6was here slightly modified to 3 11. The 1Os5p set was expanded by semidiffuse p (ap= 0.025, ref 9) and (six-component) d functions ( a d = 0.3, ref 17). Basis A on Be thus corresponds to 10s6pld/5s4pld (23 AOs). Basis B is obtained from A by adding s (a,= 0.025), d (ad = 0.05), and a ten-component f species (af= 0.26, ref 18). The final composition of basis B is 1 Is6p2dlf/6~4p2dlf (40 AOs). Basis A on the H atom corresponds to Huzinaga's 6s primitive set, contracted to 3s,I5 plus a p function ( a p= 0.9). An extra diffuse s orbital (as= 0.02) was added to form basis B. The total
Bruna et al. TABLE I: Selected Spectroscopic Ppnmeters for Be2q Species (R,in bob, o, in cor*, and De in eV) speciesa Re wc De comments and refs Be2 X1ZB+(242$,)
4.63 4.91 4.65 4.72 Be2+ 4.22 X2Z:(242u,) 4.23 4.23 4.23 Be? 4.05 X'Z324) 4.03 4.04 4.02 Be; 4.21 X211,(242$,1r,) 4.21 4.22 A2Zi(242$,3u,) 4.58 4.57 4.62
276
0.098 0.03 185 0.10 238 0.08 502 1.97 1.95 521 2.01 521 1.99 608 -2.67 64W -2.36 -2.52 646 -2.34 [0.94] 428 [0.66] 437 0.53 620 [0.39] 350 [OS41 351 0.46
expt, ref 2 MP4, ref 57 ref 6 this work ref 28a MP4, ref 57 MRD-CI, ref 28b this work 4e- correlated, ref 30 2e- correlated, ref 29 MP4, ref 51 this work, 2e- correlatedd ref 9 ref 31 this work ref 9 ref 31 this work
"The estimated full CI energies (in hartree) are -29.2416, -28.9685, -28.4679, and -29.2561, respectively (basis B). Metastable relative to 2Bet(2S,). 'Estimated here on the basis of tabulated vibrational levels. dAn all electrons MRD-CI calculation using basis B leads to De = -2.30 eV. CDissociationenergies relative to 2Be('S,) e-. Values in brackets are estimates based on reported EAs and an experimental De(Be2) EJ 0.10 eV.*
+
compositions of A and B are 6slp/3slp (6 AOs) and 7slp/4slp (7 AOs), respectively. Results obtained with a basis set called C are also reported for BeHq.5 This Be basis is an extension of basis B by adding s (a, = 0.012), p (ap= 0.009) and replacing the most diffuse d orbital by three uncontracted functions ( a d = 0.1, 0.03 and 0.01); the contraction scheme is 12s7p4dlf/7sSp4dlf (56 components). For the H atom, basis B was expanded by two uncontracted p ( a p= 0.1 and 0.01 5) and one d species (ad = 0.8),corresponding to the contraction scheme 7s3pld/4s3pld (22 components). The MRD-CI data were generated with a multireference configuration interaction method based on configuration selection, Table CI, and extrapolation techniques.19 The total energies reported correspond to the estimated full CI (FCI),Zowhich include a Langhoff-Davidson correction for higher-excitation classes. The ground-state MRD-CI wavefunctions are well described by a single configuration, with a relative weight above 90% near equilibrium. Secondary configurations were determined by carrying out test calculations over a wide range of geometries. During the geometry optimization, neutral ground state SCF MOs were used for the CI computations of neutral and monocationic species, whereas anions and dications were studied with parent SCF MOs. The single-point calculations with basis B were carried out with parent MOs. In all cases, the CI data were obtained by using a frozen-core approximation, except for the results on BeHq from basis C, in which all electrons were correlated. At the initial optimization step, R ( b B e ) was varied from 3.0 to 8.0 bohr, while keeping R(BeH) fixed to a value close to that of BeHq. This cross section was fitted via polynomials to derive &(BeBe). The frequency w,(BeBe) was estimated by assuming a diatomic model potentia: Be-X or X-X in which BeH bonds were replaced by X species with mass mX = mBe m H . In the second step, R(BeH) was optimized by keeping R(Be-Be) frozen at its optimum value. The true minimum characters of all stationary points have been checked by calculating the vibrational frequencies at the SCF(6-31G*) level. These data were generated with GAUSSIAN90.21
+
3. Equilibrium Geometries and Electronic Structures In this section geometrical and structural properties are presented. A detailed analysis of the thermochemistry and its relation with the BeBe and BeH bonding features is given in section 5. Relevant spectroscopic data are collected in Tables I-V. The
The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 6271
Beryllium-Beryllium Bonding TABLE Ik selected Specboseopic Parameters for BeHq Species ( R e in bobr, we i.cm-', a d De in eV)
species" BeH X22+(2$3a) BeHt X'2+(2$) BeH2+c X22+(2a) BeH-d X'Et(2$3u2)
R, we De 2.54 2072 2.16 2.54 2081 2.12 2065 2.15 2.54 2079 2.15 2.54 2222 3.28 2.48 2222 3.14 2.48 2.48 2227 3.18 2.48 2224 3.20 3.41 =IO00 -2.86 3.40 1085 -2.85 3.41 1091 -2.87 2.79 1520 2.04 2.68 1742 1620 1.90 2.69 1626 1.97 2.67
comments and refs expt, refs 3 and 33 3e- correlated, ref 4 CEPA, ref 49 MRD-CI, ref 5* expt, ref 3 ref 34 CEPA, ref 49 MRD-CI, ref 5b all e- correlated, ref 30 MRD-CI, ref 5b SCF data, this work MP2, ref 58 SCF, ref 59 CEPA, ref 49 MRD-CI, ref 5b
"In the same order as above, the FCI energies (in hartree) with basis B are -15.194, -14.890, -14.172, and -15.213. bData from basis C correlating all electrons. The FCI energies (in hartree) are -15.226, -14.912, -14.189, and -15.245. CMetastablewith respect to Bet(%,) + H+('S,). dAn experimental EA(BeH) = 0.70 eV (ref 35) leads to Do(BeH-) = 1.94 eV. TABLE III: Selected Equilibrium Data for Be&* Species (R,in bohr, Angle LHBeH in den, .ad 0. in eV) species' RJBeH) LHBeH 0. BeHq + H 0.6 Beq + Hz
BeHzC 2.540 180.0 4.10 1.61 X'z;(2424) BeH2+c 3.543 23.4 1.91 0.42 X2Al(2a:3al) [0.25] BeHZzt 3.069 28.7 5.30 2.39 X1Al(2a:) (2.211 'The FCI energies (in hartree) with basis B are -15.8450, -15.4602, and -14.8665, respectively. *Valuesin brackets from ref 38. For BeHZt,ref 43 gives De = 0.52 eV. 'Equilibrium geometries from refs 37 and 38. dBeH+ + H+ and Bet + Hzt lie 0.64 and 0.19 eV below BeH?+, respectively. TABLE I V Canonical Orbital Energies,-e (in bartree), for Ground-State Species (Data from Bnsia Bad)
Be
BeH'
BeHz
Bez
0.313 3u 0.447 lu, 0.243 20, 0.309 2s 0.471 2a 0.488 2ug 0.396 2a8 4.733 IS 4.708 l a 4.679 lug 4.732 la, 4.732 lug
BezHc 0.280 5a 0.374 4u 0.468 30 4.672 20 4.699 l u
BezHz 0.352 3ag 0.459 20, 0.472 2ag 4.667 la,, 4.667 lug
"H(%), E = -0.500 hartree. *BeH orbitals have e values from -0.488 to -0,447 hartree. 'The HOMO is an open shell species. diatomic potential curves are shown in Figures 1 and 2. Unless otherwise specified, variations in spectroscopic parameters are relative to the neutral species. 3.1. Be2q, BeH9, and BeH29Species. To facilitate future discussions on dications Be2H?+ (paper 2, ref 13), results on the
Be; I
I
I
I
4
5
6
7
R (bohr) Figure 1. Ground-state potential curves of neutral and charged B e
species. The potential curves of the positive ions have been shifted by -0.247 (Be2') and -0.721 hartree (Be?'). FCI data, basis B.
systems Be22+,BeH", and BeH22+are also reported here. Be#. Be2 X1Z;(242$,)shows a shallow potential curve,2,6 although the bonding is stronger than for typical van der Waals compounds.'.' Such a relatively high bond strength arises from the contribution of the doubly-excited configuration 2$, 34 to the wavefunction (see Introduction). This excitation also generates the second most important configuration for ground B2= and C2.23The importance of s p atomic states in describing low-lying molecular is revealed by the profusion among particular diatomics of strongl bound $, M e states, with MO standing for 34,3ug1?r,or 1 ~ " .Examples are provided by neutral and/or positively-charged Be2,8B2,22,25 C2,23,24 and A12.2a In Be2 the charge-density maxima of the antibonding 2uu
-
r
-
(2s-2s)HOMOandbonding3ug(2p2p)LUMOlieoutsideand within the &Be bond, respectively? According to Bader et al.,t7 the ground state SCF wavefunction of Be2 indicates that the amount of charge accumulated in the binding region (between the nuclei) is less pronounced than in Liz and B2. In a complementary way, in Be2 there is a large increase in the charge transferred to the antibonding region (outside the internuclear region) when compared with that of both neighbor diatomics. Thus the excitation 262 36: strengthens the Be-Be bond by
-
TABLE V: Equilibrium Bond Distances, R,(BeBe) and R,(BeH) (in bohr), Vibratioaal Frequencies, @,(&Be) (in liartree) for Selected States of Be2H*and Be2H2g Species (Bridged Be2H4 Also Included)
species" Be-BeHC
-
(in cm-l),and Absolute Energies
state Re(BeBe) we( BeBe) RJBeH) energqb 22+(3024$5u) 4.02 624 2.52 -29.858 I -29.8230 2rI(3$4$1 r ) 3.75 692 2.51 Be-BeH+ '2+(3$4$) 4.11 548 2.47 -29.5972 Be-BeH311(3$4$5a1s) 3.89 644 2.60 -29.8739 '2+(3$4$5$) 4.28 423 2.63 -29.8664 HBe-BeH' l2:(242434) 3.97 648 2.52 -30.5064 BeHzBe+ zBiu(2a:lbLbiJ 3.79 (709Y 2.82 -30.1746 HBe-BeH+ 'Z:(242$,3a8) 4.68 374 2.49 -30.1633 HBe-BeHzrIu(2$82$u341s,) 3.84 675 2.59 -30.5117 HBeHzBeHg 'A,( lb:,,Zb:,3a:) 3.81 (652)' 2.52 -31.7317 "MRD-CI geometries (basis A). *FCI energies from basis B, except for BezH4(basis A). cThe dipole moments (in Debye) are 0.17 for z2+ [(-)BeBeH(')] and -2.8 for 'II [(')BeBeH(-)] MRD-CI data, basis B. d l Z + might be bent at equilibrium (see text). %CF(6-31G*) optimization gives &(Be&) = 4.10 and R,(BeH) = 2.54 bohr. 'Scaled SCF frequency (by 0.9). Data for B%H4from ref 44. 'Geometry from ref 37. The BtHbridgc distance is 2.76 bohr.
6272 The Journal of Physical Chemistry, Vol. 96, No. 15, 1992
Bruna et al.
+
equilibrium, the BeH bond is described by 2u (s p, of Be plus s of H), whereas 3u is a hybridized sp, lone-pair on Be, with some antibonding BeH character. These features justify the changes in Re and w, in going from BeH' ( 2 d ) to BeH- (2$3u2), all species with Re 2.60 f 0.1 bohr and o, 1900 f 300 cm-'. The largest R, (3.4 bohr) and smallest o, (1050 cm-') in BeHz+(2u) is in line with single occupation of the bonding MO. At R = 2.5 bohr, the dipole moment p for BeH X22+(2u23u) is 0.17 D, to be compared with a value of 2.28 D for A211 (3u lr), both states with Be6+Hbpolarity.43 The latter p reveals the truly polar character of the BeH bond after a lone-pair 3u electron (localized on the rear side of Be) has been promoted to 1 r (mainly localized at Be). Rather striking is the stabilizing effect in BeH2+caused by just one valence electron. At R = 3.40 bohr the Coulomb repulsion Be+-H+ is as high as 8.0 eV; however, BeHz+lies 2.85 eV above its dissociation products, so that one u electron alone stabilizes the system by 5.15 eV (120 kcal/mol). BeH2q. Singlepoint calculations have been carried out at the equilibrium geometries reported in prior ab initio We are unaware of any study on BeHy, a species which may be unbound. BeH237has a linear ground state X'Z+ ( 2 4 1 4 ) [or XIAI (2a:b:) in Cb symmetry], with an Re(BeH) close to that of diatomic BeH (Tables I1 and 111). Both BeH2+(X2Al,2a:3al) and metastable BeH?+ (X'A1,2a:) are strongly bent?8*39As dimmed in refs 39 and 40, this is a general feature expected for singleand doubleexcitationsor ionizations from l b (H-H antibonding). This is caused by a reversed order of stabilities near 90' between this MO and the 3al (H-H bonding) species (which represents an avoided crossing in the lowest C, symmetry). The bonding in both cations, with an H-H distance =0.1 bohr larger than in H2, is better represented as complexes of type Beq-H2,41 Table IV contains the canonical orbital energies q for neutral Be,H,. BeH bonds are described by those MO's species having ei from -0.488 to -0.447 hartree. A given core orbital (here, a localized 1s Be species) destabilizes as the corresponding atomic center becomes positively charged.42 As seen in Table IV, c( 1s) Be destabilizes steadily from Be to BeH to BeH2, a feature revealing that the polarization Be*+H" is stronger in BeHz than in BeH. The ESCA (core ionization) chemical shifts42with respect to atomic Be are approximately 0.7 eV (BeH) and 1.5 eV (BeH2). Summarizing, in BeH and BeHz the hydrogen atoms act as effective agents to withdraw electronic charge from Be. This feature is relevant to explain why the weak Bez bond stabilizes through hydrogenation, as shown below. 3.2. Be2H Species. The equilibrium geometries, frequencies w , ( b B e ) and total energies are collected in Table V. All isomers discussed in this subsection exhibit a linear conformation at equilibrium. In general, the R,(BeH) values for Be2Hqcompare with those of the corresponding BeHq (Table 11). Be.@. The ground state of this radical is XZ2+(3$4$5u). The B e H and %Be bonds are described by 3u and 4u, respectively, whereas 5u represents an sp, lone-pair orbital on terminal Be (hereafter labeled Be, to differentiate it from central Be, called Be,). According to Table IV, in Be2H the eigenvalues ci of la(&) and 2u(Be,) destabilize with respect to eI,,l,, = -4.732 au of Be,!. This feature indicates both Be centers become 6q+ charged, in particular Be, forming the Be-H bond (e2, = -4.672 au for Be, versus el, = -4.699 au for Be,). On the basis of Koopmans' approximation, the ESCA spectrum of BezH should contain two peaks separated by -0.75 eV, the energetically lowest lying of these core ionization potentials due to Be, (near 128 eV). On the basis of the charge distribution arising from the core orbital shifts, in ground state Be2H the two bond dipole moments essentially cancel each other
-
-
-
BeH
15.245 I
I
2
3
A
5
I
4
7
R (bohr) Figure 2. Ground-state potential curves of neutral and charged BeH species. The potential curves of the positive ions have been shifted by -0.180 (BeH+)and -0.900 hartree (BeHZ+). FCI data, basis C.
transferring electron density from the antibinding (quasi-lonepair 2u,) into the binding region (3ug MO).24 Moreover, such a HOMO charge distribution appears rather suitable to build up terminal BeH bonds by hydrogenation or protonation of Be,! (see below). We are unaware of any experimental study on Be2q ions. The ionization process u, 00 (Be2 Be2+) strengthens the bond due to an increase in the formal bond order. An equivalent view is that there is an increase of the bmding/antibinding ratio of the as shown by aR, -0.40 bohr and Awe 230 charge cm-' (80%) upon ionization. A &(Bez+) of about 2.0 eV is relatively high when compared with that of the neutral; similar results have been reported in prior calculations on this cation (ref 28). Double-ionization 2 4 00 (Be2 Be?') generates a metastable dication having the shortest R, and highest w, among all Be+ ground states (Table I). Depending on the type of theoretical treatment, the Bez2+minimum lies from 2.34 to 2.67 eV above Be+ Be'. The potential barrier (Deff)measured with respect to that minimum is about 1.1 eV, large enough to accommodate a dozen vibrational levels. The tunneling lifetime for low vibrational levels is extremely long,29J"so that isolated b2+ practidy behaves like a bound species. Our calculations on Be2- corroborate earlier predictions9J' indicating that this anion has two bound states. Because of the bonding character of lr,, the ground state X211,(242d1r,) of Bez- exhibits shorter Re and higher we than the neutral. The excited state AzZ:( l r u 3u.J lies nearby at T, = 0.1 eV. Since Be- is the dissociation energies of Bez- given in Table I correspond to 2Be e- products. Summarizing, the bond strength in diatomic Bez increases by taking out antibinding (as in the cations) or by adding binding charge density through occupation of the bonding 3u and lu,, MOs (as in the anionic states). BeHq. BeH and BeH+ are well studied, experiment all^^.^^ and t h e ~ r e t i c a l l y . ~The * ~ * photodetachment ~~ spectrum of BeH- is available.35 Doubly-charged BeH2+ has been predicted to be m e t a ~ t a b l e ,a~feature ~ confirmed by our results; it is the only first-row XH2+ hydride having a quasi-bound ground state.36 The bond length Re increases and the frequency o,decreases BeH BeHBeHz+. Near along the sequence BeH+
- -
-
- -
+
-
+
- - -
-
-++
it-
'Bet -Be,-H
This picture is corroborated by a computed pq = 0.17 D (MRD-CI, basis B), with (-)BeBeH(+)polarity. Certainly, this
The Journal of Physical Chemistry, Vol. 96,NO.15, 1992 6273
Beryllium-Beryllium Bonding charge distribution will favor either hydrogenation (- HBe-BeH) or protonation (aHBe-BeH+) on the Be, site over that of Be,. The excited state l2II (5u lr), also with a linear equilibrium conformation, lies at low energy (T,= 0.96 eV). The bonding character of the 1 r MO is reflected in the variations occurring for the Be-Be bond upon excitation, namely a shortening AR, = -0.27 bohr and an increase A@, = 70 cm-I. A relatively broad Franckxondon envelope thus should appear in the corresponding electronic spectrum. A noticeable rearrangement of the electron density takes place between XzZ+ and l 2 n , as pointed out by ~,(~ll)= -2.80 D (MRD-CI, basis B) and with (+)BeBeH(-)polarity. Since the 1 r MO has about 80% contribution from 2p, on terminal Be,, a change in dipole moment IApall of about 3.0 D upon excitation is caused by the promotion of a lone-pair 5u electron (rear side of Be,) into 1 r (also localized around Be, but lying closer to the center of gravity of the positive charge). Similarly to the situation observed for BeH radical (section 3.1), the odd electron in ground-state BezH masks the actually high polarity of the BeH bond. &H+. The most stable isomer corresponds to linear BeBeH'. The ground state XIZ+ (3u24$) can be generated through 5a ionization from ground-state W H (XzZ+). In BezH+,the positive charge is mainly localized on Be,. A predicted R,(BeBe) of 4.1 1 bohr in BezH+ is about 0.1 1 or 0.52 bohr shorter than the equilibrium bond length of Bez+or Bez, respectively. Clearly, the reaction Bez + H+ BezH+ strengthens the Be-Be bond by withdrawing antibonding (u,) electrons. Such a stabilization due to charge reorganization is reflected in w,(Be-Be), which in the triatomic amounts to roughly twice the Bez value. Moreover, breaking of the BeBe bond as in the reaction BeBeH' Be+ BeH requires about 1.5 eV more energy than in Bez+ (section 5 ) . BezH-. This anion, with a X 3 n (3u24$5u1r) ground state, lies 0.43 eV below BezH. Since ab initio electron affinities commonly underestimate experiments by roughly 0.3 eV, the true separation between Be2H- and BezH might lie near 0.70 eV. The excited state l l Z + (3uz4$5u2) is also bound. Restricted to linear geometries, this singlet lies ca. 0.20 eV above X3n, or equivalently, about 0.23 eV below the neutral (Table V). The llZ+ (1IA') bending potential is rather flat, so that this state might be bent at equilibrium. This topic was not further investigated. The partially optimized geometry for linear 1'2' indicates a &(EkBe) longer than in X311by 0.40 bohr. Accordingly, w,('Z+) is smaller than w,(~II) by about 220 cm-' (Table V). The existence in BezH- of two bound states is in line with the quasi-degeneracy of the products Be, (XzII,,AZZ:) + H and Bez H- (sections 3.1 and 5 ) . Isoelectronic BzH+ similarly has a X 3 n ground- and a close-lying A'Z+ state.43 A recording of the photodetachment spectrum of BezH-(X311) will be appropriate to measure the splitting between the lZn(5u a) and XzZ+ ( 1 r -=) states in neutral BezH. Since the anionic and neutral states have comparable equilibrium geometries (Table V), little vibrational structure is expected for these spectra. 3.3. BezH2qSpecies. Structural information is given in Table V. The cation Be2Hz+constitutes the only species of this family having a nonlinear equilibrium geometry. Be2Hz. This BeH dimer shows a linear X'Z: ( 2 4 2 4 3 ~ ' ) ground state. A search for a bridged BeHzBe isomer wit\ GAUSSIAN90 (SCF level) indicates the h e a r structure is more stable by about 1.7 eV.I4 Three prior ab initio works also studied linear HBeBeH.11Jz,44BezHzis formally isoelectronic with B2, although the latter has an X 3 Z ; ( 2 ~ 2 4 1 d )ground state. &(&Be) of &H2 is shorter than &(&) by 0.70 bohr. This leads to an w,(BeBe) value in the former about 21/2times larger than in the diatomic. Relative to &H, however, the Be-Be bond of BezHzis 0.07 bohr shorter; accordingly, the frequencies of the tri- and tetraatomic differ by less than 5%. These data clearly point out that the most significant electronic rearrangement within the Be-Be group takes place in the step Bez H. The core orbitals 1us and 1a, of BezHzdestabilize relative to Bez as well as Be2H. Thus, the BeH bonds are slightly more
-
-
-
+
+
-
-
+
polarized in BezHzthan in BezH, a behavior confirming Jasien and Dykstra's assumptions of BeBe bond stabilization through partial formation of a Bez+-likemoiety through hydrogenation. The BeH bonds are described by 2ug and 2uu,whereas that of Be-Be corresponds to doubly-occupied 3u,. The latter MO arises by pairing odd electrons from two BeH radicals through the reaction HBet + tBeH HBe(t4)Ek.H. Since sp, hybridization is essential to generate ground BeH, it follows that Be hybridization similarly contributes to the Be-Be bond of BezHz. Analogous effects operate during dimerization of isovalent MX radicals, with M = Be, Mg, and X = F, C1, *--.I* The formation mechanism abovejustifies why b H has a ( 2 4 3 4 ) ground state structure rather than ,)3Z; , ' .lZ lk( as in isoelectronic BZ. To generate this triplet, dimerization would proceed through the BzII ( 2 d l r ) state of BeH (both monomers being excited), a process less favorable energetically. The 3Z- state also arises from 3 6 1 1 relative to ground BezHz, a double excitation d e s t a b i h g the linear conformation by destroying the Be-Be u-bond. To regain stability along that bond, the molecular symmetry has to be lowered to allow for mixing between the s, p,, and p, (in-plane) AOs of Be (spz hybridization). The arguments above have been tested by carrying out SCF computations on the lowest triplet of Be2H2. Since the LUMO corresponds to lr,, the excitation 3u, IT, ('.'I,) should be the lowest-lying for linear HBeBeH. Formally, that multiplet can also be generated by collinear reaction between BeH(XZZ+,2$3a) and BeH(AzII,2$lr). At the SCF(6-31G*) level and restricted to linear conformations, the 311ustate exhibits R,(BeBe) = 3.92 bohr and &(BeH) = 2.51 bohr. An MRD-CI calculation (basis A) at this geometry leads to an excitation energy T,= 2.93 eV. However, the SCF gradient indicates the linear conformation is not a true minimum for this triplet, as speculated earlier. The In, state probably behaves similarly. Summarizing, excited states of B%HZresulting from depletion of 3ug and population of lr, should be nonlinear (cis, trans, bridged), with active participation of Be 2pTUin-plane components in forming the BeH bonds (besides 2s and 2p,). Hence, the electronic spectrum of BqHz should exhibit a complex vibrational structure. BezH2+. During an ab initio study on several one-electron u-bonded radical cations, ClarP5 investigated linear HBe-BeH+. He found all frequencies to be positive, so that this isomer r e p resents a true minimum on the BezHz+surface. Using the same methodology as Clark (Gaussian package and SCF/6-3 lG* optimization), we have detected another true minimum for the BezHz+radical. Most importantly, this new structure is more stable than that reported earlier. The lowest species has DZhsymmetry, corresponding to a bridged BeHzBe+ conformation with %(BeBe) = 3.76 bohr, about 0.2 and 0.9 bohr shorter than in linear HBeBeH and HBeBeH+, respectively. Other geometrical parameters are R,(HH) = 4.20 bohr and R,(BeH) = 2.820 bohr. At the MP2/6-31GS level, the bridged species lies 0.22 eV below the linear conformation. MRD-CI computations on &Hz+ corroborate the MP2 results, with a AE- of 0.31 eV (FCI, basis B). These data were obtained at R,(BeBe) = 3.79 bohr, R,(HH) = 4.18 bohr, and R,(BeH) = 2.821 bohr, a geometry optimized at the MRD-CI level (basis A). In general, inclusion of correlation effects does not change the SCF optimized geometries significantly because of the high weight (above 90%) of the leading SCF configuration in the CI expansion. The structure of bridged (or cyclic) BezHz+corresponds to X2Bl, (2a:2b:,lbl,), with 2a, arising from 2s and 2p, of Be and s(Hl) + s(HZ), and with 2bz, having contribution of 2p, Be (in-plane) and s(Hl) - s(HZ). The open-shell lbl, MO correlates with the antibonding 2uu of Bez. Therefore, the short RJBeBe) and stability of bridged BezHz+results from two effects: an enhanced participation of Be 2p orbitals (BeBe binding) in forming two threecentered BeH-Be bonds and loss of antibonding density along the BeBe axis. Linear HBe-BeH+ has a 2Z:(2$,2$,3u8) structure. It is characterized by an anomalously large R,(BeBe) of 4.68 bohr
-
-
-
6274 The Journal of Physical Chemistry, Vol. 96, No. 15, 19'92 when compared with that of BeH2Be+ (3.79 bohr), HBe-BeH (3.95 bohr), Be2H (4.02 bohr), or Be2H+ (4.11 bohr). These differences are easy to understand since in the last four compounds the B e B e bond arises (at least) from a doubly-occupied a-type species, whereas that MO is singly-occupied in HBe-BeH+.4s M o r a ~ e rsince , each metal atom in HBe-BeH shows a net positive charge, ejection of a 3ag electron (BeBe localized) allows for additional repulsion between them, finally leading to a rather shallow b B e stretching potential. As an illustration, o,(BeBe) is lowered by about 45% after ionization HBeBeH HBeBeH+ (both linear). A third cationic conformation was also investigated, namely T-shaped BeBeH2+ (C, with terminally attached H2 being perpendicular to the metal bond). The lowest doublet of this conformation corresponds to 2A1(4a:5al), with SCF optimized distances (in bohr) of 4.16 (BeBe), 3.39 (BeH), and 1.40 (HH). Since the latter is equal to the equilibrium distance of the H2 molecule? this conformation actually represents an ion complex, Bez+-Hz (with Sa localized on BeBe). Moreover, the SCF frequencies indicate this C, structure is not a true minimum on the Be2H2+surface. MP2(6-31G*) data puts this saddlepoint about 1.0 eV above the bridged isomer. As discussed in paper 2,13 however, both cyclic and T-shaped Be2HZ2+are energetically quasi-degenerate but substantially more stable than linear HBeBeH2+. HBe-BeH-. Electron attachment to HBeBeH(X'Z+) generates the ground state X211,(242$,341r,) of HBeBefI-, also with a linear equilibrium conformation. The anion lies 0.15 eV below the neutral (by about 0.45 eV assuming an error of 0.30 eV for the computed electron affiities). The isoelectronic boron cation HB-BH+ also exhibits a linear X2n, ground state.43 Simultaneousoccupation in &H2- of 3ug and lr,, (both Be-Be bonding) leads to the shortest R, (3.835 bohr) and highest o,(675 cm-l) for the B e B e coordinate among all linear HBe-BeHq species (Table V). When compared with the equilibrium data for &H- in the X311(..Salr) ground state (3.885 bohr and 644 cm-I), it follows that the reaction
-
+
Be2H-(X311) H
-
HBe-BeH-(X211,)
has little effect on the Be-Be bonding. Similar to that for the neutral species, the most relevant change in charge distribution along the B e B e bond already takes place on the first hydrogenation process Be2q H Be2Hq. 3.4. Be2% Species. It is intructive to consider additional hydrogenation of &H2 to form B%H3and &H4. Due to space limitations, the structures and stabilities of Be2H3qradicals are discussed elsewhere. 3 ~ 1 Earlier s t ~ d i e have s ~ ~proven ~ ~ that bridged HBeHzBeHis the most stable conformation of Be2H4. Certainly, the most appropriate hydrogenation site of linear HBeBeH corresponds to l r , (Be-Be bonding) since this LUMO stabilizes through mixing with 1s AOs from the bridging hydrogens. According to literature data,37the BeBe distance in Be2H4lies near 3.81 bohr. Thus, formal occupation of lr,,through formation of threecenter BeHBe 'banana" bonds along the series BezH2 BezH3 BezH4 gradually shortens RJBeBe), as e ~ p e c t e d . ~ ~ . ' ~ An analogous mechanism involving occupation of the virtual ru MO of linear XMMX explains the tendency of related M2 moieties (Bq,Mg2, B2, ...) to build up bridged compounds of type XMY2MX.46 A well-known example corresponds to diborane, B2&.39*43-M Solid (BeH2), also appears to be formed by polymeric chains containing bridging hydrogen^.^'
+
-
- -
4. Adiabatic Ionization Potentials a d Electron Affinities
Ionization potentials (IP+)and electron affiities (EA) are given in Table VI (without zero-point corrections). These IP+s serve as a guide to estimate the location of molecular Rydberg states on the basis of the term values of 4.1. Ioniutim PdeatirLs. Our results reproduce the experimental atomic reasonably well, with underestimation errors less than 0.15 eV." The molecular data given in Table VI are expected to have a similar accuracy.
Bruna et al.
ionization A-A+
A+ A
-.
-
Az+
A2+
A-- A'
Be'
BeHd
BeH2
Bez
BezH
B%H2
9.28 [9.32] 18.12 [18.21] 27.40 [27.53] -0.50
8.28 [8.21] 19.54
10.47
7.45
7.10
9.34
16.16
13.60
16.18
17.01
27.83
26.63
21.05
23.28
26.35
0.39 [0.32)/
0.43 [0.23]8
[CO]
?
0.54 [0.70]
0.15
-
Without zero-point corrections. Unless otherwise stated, all transitions between ground states. bThe vertical IP+ (BezH4 Be2H:) is 11.62 eV (basis A). CExperimental data from refs 32 and 47 in brackets. dExperimental data from refs 35 and 48 in brackets. 'Corresponds to electron affinity (EA). f2Z:(Be
