6882
J. Phys. Chem. A 2003, 107, 6882-6890
Classical versus Nonclassical Covalent Bonding between the Metal Hydride Radicals MH and M′Hj (MH ) HBe, HMg, HCa; M′Hj ) Li, BeH, BH2, Na, MgH, AlH2, K, CaH, GaH2) Eric Magnusson and Simon Petrie*,† School of Chemistry, UniVersity College, UniVersity of New South Wales, ADFA, Canberra, ACT 2600 Australia ReceiVed: April 29, 2003; In Final Form: June 13, 2003
We report structures, bond strengths, and relative energies for all apparent minima on the B3LYP/6-311+G** potential energy surfaces of the main group compounds [MHj+1M′] formed between the first three metal hydride radicals of group 2 (MH) and the first three metal hydride radicals of groups 1, 2, and 13 (M′Hj). Relative energies and bond strengths at the G2(MP2)thaw level of theory, using the B3-LYP/6-311+G** optimized geometries, have also been obtained: the G2(MP2)thaw values conform closely to the B3-LYP results. Significant structural trends identified include the characterization of at least one competing “nonclassical” isomer for each of the 24 classical HM-M′Hj structural formulas, an increasing preference for nonclassical rather than classical bonding as M is switched from Be to Mg to Ca, and an increased tendency toward stability of unorthodox structures as M′ progresses from group 1 to 2 to 13. An exploration of the factors underpinning bond formation between M and M′, focusing particularly on the three [CaHNa] isomers we have located, has been undertaken using the atoms-in-molecules (AIM) computational method. Although our AIM calculations confirm that the metal-metal bonds are largely covalent in character, some aspects of the bonding remain mysterious. Prospects for experimental investigation of polymorphism, via matrix isolation or other techniques, appear to be particularly promising for [MgH2Ca], for which four distinct structural isomers are separated by only approximately 30 kJ mol-1.
Introduction Electropositive atoms are generous with their valence electrons, but they do not share them gracefully. The bonds between main-group metal atoms are among the weakest examples seen across the spectrum of covalently bonded structures, and isolation of species containing a nominal intermetallic bond is beset by much difficulty. As a consequence, very little is known of the structure of main-group intermetallic compounds. We have conducted a systematic survey of the structural and energetic properties of the set of main-group binuclear hydrides HiM-M′Hj (HiM, M′Hj ∈ {H, Li, HBe, H2B, H3C, ..., H2As, HSe, Br}) in which the focus is on the factors influencing the strength of the central, nominally covalent M-M′ bond. The formulas are all capable of being represented by the classical structure of a direct single bond between the heavy atoms both of which are valence-saturated with hydrogen atoms. Pairings between the 22 different monovalent radicals {H, Li, HBe, ..., Br} yield 253 distinct structural formulas, and within this range of compounds, the subset of intermetallic molecules is notable both for the sparseness of theoretical and experimental data and for the degree of polymorphism evident in their structures. For example, in the sole study reported to date on the [AlH4Ga] potential energy surface, Leszczynski and Lammertsma1 have identified a remarkable total of eight distinct isomers for this species2 encompassing the classical covalently bonded species H2AlGaH2 and a variety of bridged and saltlike structures. Although the intermetallic compounds surveyed in the present work lack the degree of structural versatility seen for [AlH4-
Ga], they remain noteworthy for the insight they permit concerning the struggle between classical covalent and nonclassical bonding motifs in electron-deficient compounds. Of the species covered in the present work, experimental isolation has been reported only for the homonuclear dimers [MH2M] (M ) Be,3 Mg,4 and Ca5). In all three instances, these species were generated by reaction with H2 of metal atoms, followed by isolation in a rare-gas matrix. The range of theoretical studies on these species is somewhat greaters previous studies have featured [BeHLi],6-12 [BeH2Be],3,10,12-17 [BeH3B],10,12,18,19 [BeH3Al],20 [MgHLi],9 [MgH3B],19 [CaH3B],19 [MgH2Mg],4,14,21 [MgH3Al],22 and [CaH3Al].23 Some earlier surveys of energetic trends in covalent bond strength have also featured several examples of these species drawn from the first row24,25 or from the first two rows26 of the periodic table: however, those surveys appear not to have investigated any bridged or nonclassical structures for these species. The focus in the previous theoretical studies has largely been on the lightest members of the [MHj+1M′] set, and the coverage of third-rowcontaining species is particularly sparse. In the present study, therefore, we have aimed to fill a number of gaps by presenting a systematic comparison of intermetallic [MHj+1M′] compounds (M ) Be, Mg, Ca; M′Hj ) Li, BeH, BH2, Na, MgH, AlH2, K, CaH, GaH2), involving high-level ab initio and density functional theory calculations, and to explore the trends in bond strength and structural form within these compounds. We have also employed the atoms-in-molecules (AIM) approach27 for a more in-depth analysis of the intermetallic bonding seen in these species.
* To whom correspondence should be addressed. † Present address: Department of Chemistry, the Faculties, Australian National University, Canberra ACT 0200 Australia. E-mail: simon.petrie@ anu.edu.au.
Theoretical Methods Optimized geometries, total energies, and zero-point vibrational energies of the stationary points on the [MHj+1M′]
10.1021/jp0351526 CCC: $25.00 © 2003 American Chemical Society Published on Web 08/13/2003
Covalent Bonding between the Metal Hydride Radicals
J. Phys. Chem. A, Vol. 107, No. 35, 2003 6883
TABLE 1: Frozen Core Assignments Used for Combinations of Metallic Elementsa
TABLE 2: Stationary Points on the [MHM′] Potential Energy Surfaces, Obtained at the B3-LYP/6-311+G** Level of Theory
M′ M
Li
Be
B
Na
Mg
Al
K
Ca
Ga
Be 1s/1s 1s/1s 1s/1s 1s/2p 1s/2p 1s/2p 1s/2p 1s/2p 1s/3p Mg 2p/1s 2p/1s 2p/1s 1s/1s 1s/1s 2p/2p 1s/2p 1s/2p 1s/3p Ca 2p/1s 2p/1s 2p/1s 2p/1s 2p/1s 2p/2p 2p/2p 2p/2p 2p/3p a Orbitals shown denote the outermost extent of the frozen core on M and M′, respectively, in MP2/6-311+G(3df,2p) and QCISD(T)/6311G** calculations on the intermetallic hydrides.
potential energy surfaces were obtained at the B3-LYP/6311+G** level of theory. Further single-point total energy calculations on the stationary point geometries were undertaken at the MP2/6-311+G(3df,2p) and QCISD(T)/6-311G** levels of theory, to provide G2(MP2) relative energies. The G2(MP2) method was selected as the most appropriate “model chemistry” method for these species because of its economy, reliability, and applicability to compounds comprised of atoms from the first three rows of the periodic table.28-31 However, implementation of the standard frozen-core approximation in G2(MP2), G2, and related methods32-36 has been indentified as inappropriate for some calculations on compounds containing main-group metals; consequently, to improve the reliability of the G2(MP2) values, nonstandard or “thawed” correlation spaces32-34 were assigned in several instances as identified in Table 1. The structural preferences of various metal-metal combinations were studied by performing B3LYP calculations at the minimal basis set level and using scale factor variation to alter the effective nuclear charge parameter for the basis sets of one element at a time. Use of the STO-3G minimal basis set ensured that variation in Zeff did not engender compensating changes in other parts of the wave function. All calculations were performed using the GAUSSIAN98 suite of programs.37 Results and Discussion In the discussion throughout this paper, we distinguish between the term “orthodox”, by which we denote a compound that for each atom has a cumulative bond order formally equal to that atom’s valency, and the term “classical”, which describes a compound formally possessing only two-center, two-electron bonds. Note that some of the unorthodox stationary points investigated here (for the [MH3M′] compounds only, where M′ is a group 13 element) are nevertheless classical according to these definitions. Structural and Energetic Tendencies: An Overview. Optimized geometries (obtained at the B3-LYP/6-311+G** level), total energies, and bond dissociation energies (at B3LYP/6-311+G** and G2(MP2)thaw) for the various stationary points are shown in Tables 2-7. Perusal of these tables reveals several notable features, which we summarize below: (i) For all structural formulas considered here, there always exists at least one unorthodox isomer in competition with the orthodox HM-M′Hj structure. (ii) When the molecule contains a first-row group 2 metal atom M, orthodox structures are preferred: only [BeH3Al] and [BeH3Ga] of the eight beryllium compounds have unorthodox global minima. Conversely, when a third-row (group 2) M is featured, only three compounds of the eight possess orthodox global minima. The formulas are [CaH2Be], [CaHNa], and [CaHK] and in all three the preference for the orthodox form is comparatively slight. There is thus a clear tendency, with progression down the group, toward increasing stability of structures having an unorthodox connectivity of atoms.
formula
structure
M-M′ a
H-Ma
HBeLi (C∞V) BeHLi (C∞V) Be(H)Li (Cs) HMgLi (C∞V) MgHLi (C∞V) Mg(H)Li (Cs) HCaLi (C∞V) CaHLi (C∞V) Ca(H)Li (Cs) HBeNa (C∞V) BeHNa (C∞V) HMgNa (C∞V) MgHNa (C∞V) HCaNa (C∞V) CaHNa (C∞V) Ca(H)Na (Cs) HBeK (C∞V) BeHK (C∞V) HMgK (C∞V) MgHK (C∞V) Mg(H)K (Cs) HCaK (C∞V) CaHK (C∞V) Ca(H)K (Cs)
I In(1) In(2) I In(1) In(2) I In(1) In(2) I In(1) I In(1) I In(1) In(2) I In(1) I In(1) In(2) I In(1) In(2)
2.400
1.354 1.576 1.523 1.748 2.308 2.282 2.029 2.292 2.234 1.354 1.504 1.748 2.059 2.022 2.236 2.164 1.362 1.488 1.764 2.046 2.090 2.028 2.217 2.147
2.196 2.765 2.746 3.237 2.946 2.663 2.989 3.428 3.164 3.124 3.465 3.363 3.911 3.582
H-M′ a
∠HMM′ b 180
1.697 1.712 1.623 1.620 1.646 1.653
51.0 180 36.1 180 33.8 180
2.034 180 1.962 180 1.981 2.069
40.6 180
2.399 180 2.325 2.323 2.344 2.404
43.0 180 40.7
a
Optimized bond length in ångstroms. b Optimized bond angle in degrees.
(iii) When the “heteroatom” M′ is group 1, only one of the nine formulas, namely [CaHLi], has an unorthodox global minimum. When M′ is group 2, two formulas out of 6, [MgH2Ca] and [CaH2Ca], have unorthodox global minima; when M′ is group 13, the corresponding value is 8 of 9 compounds. Therefore, progression of M′ from group 1 through 2 to 13 clearly leads to an increased preference for unorthodox structures. Three broad categories of unorthodox structures can be discerned. First, the structure may feature one or more bridging hydrogens that augment the M-M′ bond. Second, the direct M-M′ bond may be supplanted by two-electron, three-center M(H)M′ bonds. (These first two structural motifs are both therefore nonclassical by virtue of possessing three-center bonds.) Third, a direct M-M′ bond may exist in a structure in which all the hydrogens are formally bonded to M′. Schematic examples of such bonding patterns, shown in Figure 1, are respectively In(2), IIn(3), and XIIIht, where the Roman numeral signifies the group number of the “heteroatom” M′, the n notation indicates a nonclassical structure, and ht denotes a “hydride transfer” structure that is unorthodox but nevertheless classical because it lacks bridging hydrogens. The labels shown in Figure 1 are used throughout this discussion, and in Tables 2-7, so as to distinguish between the various isomers. Note, however, that description of a structure as, for example, IIn(2) does not necessarily indicate the presence, nor absence, of a direct M-M′ bond. A more rigorous assessment of bonding requires an analysis such as has been undertaken, for some of these compounds, using the AIM (atoms-in-molecules) approach, which is detailed in a subsequent subsection. In the following subsections, we discuss in greater detail the specific features of the [MHM′] (M′ from group 1), [MH2M′] (M′ from group 2), and [MH3M′] (M′ from group 13) potential energy surfaces. [MHM′] Structures. These group-1-containing species, detailed in Tables 2 and 5, all feature two distinct linear structures M′MH (I) and M′HM (In(1)), both of which are
6884 J. Phys. Chem. A, Vol. 107, No. 35, 2003
Magnusson and Petrie
TABLE 3: Stationary Points on the [MH2M′] Potential Energy Surfaces, Obtained at the B3-LYP/6-311+G** Level of Theory formula
structure
M-M′ a
H-Ma
∠HMM′ b
M′-Ha
∠MM′Hb
HBeBeH (D∞h) BeH2Be (D2h) HBeMgH (C∞V) BeHMgH (C∞V) HBeCaH (C∞V) Be(H)CaH (Cs) HMgMgH (D∞h) MgHMgH (C∞V) Mg(H)2Mg (D2h) HMgCaH (Cs) HMgHCa (C∞V) Mg(H)CaH (Cs) Mg(H)2Ca (C2V) HCaCaH (D∞h) Ca(H)CaH (Cs) Ca(H)2Ca (D2h)
II IIn(3) II IIn(2) II IIn(2) II IIn(1) IIn(3) II IIn(1) IIn(2) IIn(3) II IIn(1) IIn(3)
2.082 2.071 2.484 5.148 2.944 2.630 2.861 5.772 2.857 3.328 4.736 3.182 3.175 3.797 3.420 3.501
1.336 1.513 1.340 3.441 1.350 1.498 1.725 4.066 1.924 1.740 1.701 2.227 1.951 2.016 2.201 2.179
180 46.8 180 0 180 57.3 180 0 42.1 179.4 180 40.5 41.6 180 36.7 36.5
1.336 1.513 1.719 1.706 2.036 2.010 1.725 1.706 1.924 2.022 3.012 2.019 2.149 2.016 2.017 2.179
180 46.8 180 180 180 173.3 180 180 42.1 174.5 0 177.7 37.0 180 172.2 36.5
a
∠HMM′Hc 180
0
180 180 180 180 0 180
Optimized bond length in ångstroms. b Optimized bond angle in degrees. c Optimized dihedral angle in degrees.
TABLE 4: Stationary Points on the [MH3M′] Potential Energy Surfaces, Obtained at the B3-LYP/6-311+G** Level of Theory ∠HMM′ b
formula
structure
M-M′ a
H-Ma
HBeBH2 (C2V) HBe(H)2B (C2V) BeBH3 (C3V) HBeAlH2 (C2V) HBe(H)2Al (C2V) BeAlH3 (C3V) HBeGaH2 (C2V) HBe(H)2Ga (C2V) BeGaH3 (C3V) HMgBH2 (C2V) HMg(H)2B (C2V) MgBH3 (C3V) HMgAlH2 (C2V) HMg(H)2Al (C2V) MgAlH3 (C3V) HMgGaH2 (C2V) HMg(H)2Ga (C2V) MgGaH3 (C3V) HCaBH2 (Cs) HCaBH2 (Cs) HCa(H)2B (Cs) CaBH3 (C3V) HCaAlH2 (C2V) HCa(H)2Al (C2V) CaAlH3 (C3V) HCaGaH2 (C2V) HCa(H)2Ga (C2V) CaGaH3 (C3V)
XIII XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2) XIII XIIIr XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2) XIII XIIIn(1) XIIIn(2)
1.868 2.045 1.956 2.338 2.485 2.653 2.266 2.527 2.555 2.288 2.540 2.438 2.738 2.899 3.072 2.659 2.916 2.960 2.664 2.670 2.259 2.698 3.184 3.252 3.390 3.080 3.263 3.235
1.331 1.324
180 180
1.334 1.335
180 180
1.331 1.338
180 180
1.714 1.707
180 180
1.714 1.703
180 180
1.712 1.705
180 180
2.027 2.031 1.996
139.2 141.2 177.2
2.023 2.029
180 180
2.023 2.031
180 180
a
M′-Ha
∠MM′Hb
1.198 1.328 1.200 1.596 1.864 1.592 1.582 1.929 1.572 1.200 1.268 1.196 1.601 1.831 1.590 1.589 1.886 1.571 1.207 1.207 (1.206) 1.248 1.198 1.613 1.829 1.592 1.605 1.879 1.573
123.4 48.5 95.0 122.7 35.5 93.9 123.8 35.0 93.8 123.4 54.6 93.1 123.5 39.5 93.4 124.4 39.4 93.1 125.0 122.1 (127.8) 80.1 92.9 125.5 40.0 94.2 126.5 40.2 93.9
∠HMM′Hc
(89.0 0 (180) (128.6
Optimized bond length in ångstroms. b Optimized bond angle in degrees. c Optimized dihedral angle in degrees.
consistently found to be true minima (i.e., lacking any imaginary vibrational frequencies) according to our B3-LYP/6-311+G** calculations. In all instances, I is seen to be lower-energy than In(1), with the energy difference between isomers being ∼90120 kJ mol-1 when M is Be, but with a markedly smaller relative energy gap (
