J. Phys. Chem. 1992,96,9259-9264
9259
Theoretical Study of the Alkaline-Earth Metal Superoxides BeO, through SrO, Charles W. Bauschlicher, Jr.,* Harry Partridge, Mariona Sodupe, and Stephen R. Langhoff NASA Ames Research Center, Moffett Field, California 94035 (Received: June 3, 1992)
Three competing bonding mechanism have been identified for the alkaline-earthmetal superoxides: these result in a change in the optimal structure and ground state as the alkaline-earth metal becomes heavier. For example, BeO, has a linear 32; ground-state structure, whereas both CaO, and Sr02have C, 'Al structures. For MgO,, the theoretical calculations are less definitive, as the 3A2C, structure is computed to lie only about 3 kcal/mol above the '2; linear structure. The bond dissociation energies for the alkaline-earth metal superoxides have been computed using extensive Gaussian basis sets and treating electron correlation at the modified coupled-pair functional or coupled-cluster singles and doubles level with a perturbational estimate of the triple excitations. Our best estimates for the M-02 dissociation energies are 88 f 4, 25 f 4, 54 f 4, and 54 f 6 kcal/mol for Be02, Mg02, Ca02, and Sr02, respectively.
I. Introduction Our current knowledge of the alkaline-earth metal superoxides is based primarily on infrared spectra of these species in nitrogen and raregas While these matrix studies provide some of the vibrational frequencies of the alkaline-earth metal superoxides, the assignments are not straightforward. Often the frequencies have been interpreted based on analogies with the well-st~died~*~ alkali-metal superoxides, where the dominant bonding mechanism is M+02-; contributions from M2+022structures were thought to be small due to the large second ionization potential of the alkaline-earth metal atoms. For example, the frequency for BaO2at 1120 cm-I was attributed' to the 0-0 stretch in BaO,, because it was similar to the value' for free 0, and to the measured values4v5for the alkali-metal superoxides. In addition, similar vibrational frequencies were observed for the alkali-metal and alkaline-earth metal O3systems (see,for example, refs 4 and 8). However, the bonding in the I V ground states of the diatomic alkaline-earth metal oxides is known9 to possess covalent, ionic, and doubly ionic components. A similar diversity of the bonding is expected for the alkaline-earth metal superoxides. One of the goals of the present work is to determine the ground-state structures and vibrational frequencies for the alkaline-earth metal superoxides for comparison with experiment. In the process, we elucidate the competing bonding mechanisms in these systems. Very little is presently known about the bond energies of the alkaline-earth metal superoxides. The only experimental evidencelo is indirect, being derived from the kinetics of threebody reactions such as Mg + O2+ M and Ca + O2+ M. The fact that these reactions have been observed to p r d at temperatures between lo00 and 1120 K with no evidence of a steady state being reached, due to the unimolecular dissociation of the superoxide, provides lower bounds to the bond energies. A fit of the temperature dependence of the recombination rate coeficients to a full RRKM treatment produces bond dissociation energies that are unexpectedly large in comparison with accurate theoretical values' for the alkali-metalsuperoxides. Thus,a second goal of the present work is to determine accurate bond energies for the alkalineearth metal superoxides.
II. Qualitative Consideratious The ground states of the alkaline-earth metal superoxides are determined by several competing bonding mechanisms. For C, geometries, the lowest triplet state is 3A2,which, by analogy with the *A2ground states of the alkali-metal superoxides,'I is derived by transferring a metal valence s electron into the in-plane a* orbital of 02,keeping the out-of-plane a* and the remaining metal s electrons high-spincoupled. The metal s electron polarizes away from the O2to reduce the repulsionsee Figure 1. The 0-0 bond length' is similar to that in 0,and the alkali-metal superoxides,ll and the bonding is principally electrostatic. The second bonding mechanism axresponds to transferring both metal s electrons to the O2r* orbitals, resulting in a IAl state with
M2+02-character. This state also has a triangular structure, but the O2bond length is significantly longer than in the triplet state. The Mulliken populations indicate that there is some back-donation of charge into the metal p and d orbitals. This state can also be viewed as bonding between 0, and either the ,P or ,D state of M+. Thus, this state has both an electrostatic and a covalent component to the bonding. The third bonding mechanism produces a linear molecule, which in the ionic limit corresponds to M2+bonding with two 0-ions. In the covalent limit, the metal sp orbital hybridizes and forms two covalent bonds to the oxygen atoms. The true bonding lies between these extremes but, on the basis of the Mulliken populations, is closer to the ionic limit. For the linear system where the metal has inserted into the 0-0 bond, each oxygen atom has one unpaired p a electron, which gives rise to a manifold of six low-lying states. It is difficult to predict which of these bonding mechanisms will be preferred. A low second ionization potential favors the 'Al state, because this enhances the M2+02,-contribution to the bonding. Low-lying p and d orbitals also favor the 'Al state, because this enhances the covalent contribution to the bonding. These two factors are the most favorable for Ca and Sr. The 0-0 bond is broken in the symmetric linear structure; this cost must be recovered by the electrostatic and covalent bonding. The electrostatic component of the bonding increases as the size of the metal atom decreases. In addition, Be is known to form the strongest covalent bonds. Thus, the linear structure is favored by the light metals.
III. Methods The [Al and 3A2states with C, geometry are well described by a single configuration and are studied using the SCF-based modified coupled-pair functional (MCPF) method', or the coupled-cluster singles and doubles approach including a perturbational estimate of the triple excitations [CCSD(T)]." In the correlation treatment 16 electrons are correlated for Be0, and 22 electrons for the heavier alkaline-earth metal superoxides. That is, only the 0 1s and the inner-core electrons of the alkaline-earth metal atoms, except Be, are left uncorrelated. For the linear geometry, none of the six nearly degenerate states is well described by a single configuration using real orbitals. Therefore, these states are treated using a state-averaged complete active space selfconsistent-field (SA-CASSCF) approach. Specifically, calculations are performed for the triplet 32;,3A,,,and '2: states) and singlet ('4,lZ;, and '2; states) manifolds separately. The oxygen p?r orbitals are included in the active space, corresponding to six electrons in the four orbitals. This is followed by multireference configuration-interaction (MRCI) calculations in which the four valence u electrons are correlated in addition to the six a electrons. The effect of higher excitations is estimated using the multireference analogue of the Davidson correction (denoted +Q). In order to put these linear states on an equal footing with the triangular structures, we make use of the fact that the 3& and '2: states are nearly degenerate plus and minus combinations of
This article not subject to US.Copyright. Published 1992 by the American Chemical Society
Bauschlicher et al.
9260 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 1
TABLE I: MRCI+Q R e ~ u l t afor ~ the Low-Lying Lhmr States of the Alluliae-Earth Metal Superoxidea state r.. A T.. cm-' state r.. A T.. cm-' ~
~~
1.456 1.470 1.471
0 1443 1603
1.856 1.856 1.857
0 83 129
'2:
2.170 2.172 2.173
0 87 117
'2, 'Au '2:
2.330 2.333 2.334
0 112 138
'22,
'4 '2:
NO2
'2: '2,
Mg02
'2i
'4 '2:
'A
1.463 1.467 1.468
880 1343 1225
:$ ::E '2; 1.856
88 144 55
CaO, '2;
'4
'2;
SrO*
:$ '2;
E: 2.172
;:z
2.332
81 125 87 95 142 112
OThe MRCI+Q energies (EH)for the 32-gstate at the computed point closest to the minimum are BeO, -164.71 1 929(2.78a0), MgO, -349.628 286(3.50u0), CaO, -826.807 098(4.100,), and Sr0, -3281.591 821(4.40~,).
-1 2
-3
1
Figure 1. Orbital density plot of the in-plane valence orbital from the 'A2 state of CaO,, depicting the polarization of the predominantly 4s orbital of calcium away from the 0,molecule.
two c o n f i i t i o n s (&rLrLr& i rtr' rkrty).Thus, we perform a symmetry-broken calculation for axnear combmtion of these two states that is well represented by a single configuration (rLr&rty). In order to compute the binding energy of the lowest linear state, the 3Z, state, we then correct this symmetry-broken MCPF binding energy using the average of the '4 - 32-and '2: - 32;MRCI+Q separations. CXSSCF-based internally ~ o n t r a c t e d ' averaged ~ CPFI5 (ICACPF) calculations are performed for Be02and Mg02. Like the CCSD(T) calculations, these are used to calibrate the MCPF results. These calculations are discussed in more detail below. Large flexibly contracted basis sets are used. They are described in detail in the Appendix and can be denoted as Be (14s8p6d4f)/ [8s8p6d4fl, Mg (21s16p7d6f)/ [9s9p7d4fl, Ca (20815p8d6f)/ [8s7p5d3fl,Sr (26s16p14d4f)/ [ 1OslOp7d3fl,and 0 ( 14s9p6d4f)/[6s5p2dlfl1. The metal basis sets contain sufficiently tight functions to allow correlation of the semicore electrons. Only the pure spherical harmonic components of the basis functions are used. The vibrational frequencies of Ca02 and MgO, are computed at the CASSCF level using smaller basis sets. For oxygen, we use the (lOs6p)/[Ss3p] set of Dunning16 supplemented with a diffuse p (0.059) and d (0.85) polarization function. The Mg basis set is the (12s9p)/[6s4p] set of McLean and Chandler" sup plemented with a d polarization function with an exponent of 0.28. The Ca basis set is the [8s4p] contraction given by Pettersson et a1.I8 of the (12s6p) primitive set of Roos et al.I9 supplemented with two diffuse p functions (0,099 13 and 0.03464). The five d functions optimized18 for the 2D state of Ca+ are contracted to three functions as (31 1). The active spaces employed in these CASSCF calculations are described later. As noted in our previous study" of the alkali-metal superoxides, for ionic systems it is preferable to compute the M-02 dissoCiation energy (0,)with respect to the ionic limits as D,(MOJ
E(M+) + E(O2-) - E(M02)
- IP(M) + EA(02) (1)
The ionization potentials of the metals are well-known,2° and the
electron affinity of O2has been accurately measured.' Note that the EA without zero-point energy is required; thus, we correct the measured EA value of 0.440eV to 0.41 eV using the experimental vibrational frequencies73' of O2and OF,This approach avoids having to accurately calculate the differential correlation contribution to 0,that occurs when dissociating directly to neutral fragments. This approach is clearly most accurate for the 'A2 state, which is beat described as M+Oy. Because of the doubly ionic character of the 'Al state, even eq 1 is expected to underestimate the disociation energy. However, it should do so by less than dissociating to the neutral fragments. The SCF/MCPF and CASSCF/MRCI calculations were performed using the MOLECULE-SWEDENU program system. The CCSD(T) calculations were preformed using TITANZ3for the closed-shell cases and the program developed by Scuseriaz4 for the open-shell cases. The CASSCF calculations for the vibrational frequencies were performed using SIRIUS/ABACUS.ZS The CASSCF/ICACPF calculations were performed using MOLPR0.14*26All calculation were performed on the NASA Ames Central Computer Facility CRAY Y-MP or the Computational Chemistry CONVEX C210 and IBM RISC/6000 computers.
IV. ReePlts and Discussion For the linear symmetric 0-M-O systems, there are six lowlying states arising from coupling in different ways the open-shell electrons in the predominantly oxygen 2pr orbitals. The MRCI4-Q separations between these states are summarized in Table I; the MRCI results are similar, with the T,valucs being about 10% smaller. The 32;,'4, and '2: states are linear combinations of the r4r2and rtr4occupations, while the other three states have a rur8 Y B principal occupation. The ruorbital enhance the metal-oxygen bonding character by mixing in the metal p orbitals, while the rs orbital enhances the bonding by mixing in the metal d orbitals. In all cases, the ground state is Q;. For Be02, thip state is substantially stabilized, because the Be 2p orbital contribution mdts in a r,,orbital with good malent bonding. At the MRCI level, the occupation of the ruorbital is signifiarntly larger than the reorbital, 3.26 vs 2.66 electrons. The difference in the ru and rs populations is smaller (3.1 1 vs 2.81) for the I$ state, while for the remaining states the occupation of the rUand r8orbitals is essentially 3.0 electrons. For Mg02, Ca02, and Sr02,the interaction between the metal and oxygen is smaller than for Be02, and all states have valence ruand rB populations near three. The small separations between these six states for Mg02, CaOz, and SrOz are due to the weak coupling of the oxygen p~ orbitals through the metal orbitals.
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9261
AlkalineEarth Metal Superoxides Be02 through S r 0 2
TABLE Ik B o d Lemgtbs (A)a d M-02 llimacirtion Energies (kd/mol) for the AlkrliaeEartb Metal sllperoxldes (MCPF Level of Theory Used unieaa otbcnrisc Noted) 0,"
40-0)
r(M-0) %('A2) Be(3Z;y
Bc(~ZE;)CCCSD(T)d
W3Az)
Mg(lAi) Mg(3Z-)e Ca('AA3 Ca(lAd Ca(IA,) CCSD(T)d Ca('z-)c
W'A3
Sr('A1) Sr('Z;)C
1.562 1.47 1 1.471 1.967 1.799 1.854 2.203 1.984 1.984 2.150 2.349 (2.350) 2.114 (2.109) 2.306
neutral
1.360
44.5 87.9 85.4 19.6 3.4 25.4 43.6 49.9 51.9 39.7 46.0 54.8 37.7
1.356 1.703 1.342 1.542 1.542 1.340 (1.341) 1.531 (1.538)
ion
recommendedb
47.8 88 22.8 6.6
*4
25 i 4 (42.8) (47.8)
44.9 (44.5) 51.3 (49.9) 52.8
(42.4) (48.1)
46.1 (44.4) 54.9 (50.1)
54
*4
54
6
aYNeutraI"denotes that dissociation is directly to neutral fragments, whereas "ion" denotes that eq 1 has been employed. The values under *ion" arc superior--see the text. The values in parentheses include a perturbation theory estimate of the mass-velocity and Darwin relativistic corrections. bTherecommended bond dissociation energies-ee text. CComputedusing the symmetry-broken'2: + '4result and then corrected to the '2; state using the average T,value from the MRCI+Q calculation-ee text. dThe CCSD(T) calculations are performed at the MCPF minimum. TABLE IIk CASSCF ~
8
d Frequencies c (cm-') a d Intensities (Lm/mol)
stretch I
W.
M-O asym
M-O sym
0-0 1519 1580 1069 1090 1050 1096 1101 679 720
1 109 121
1078
0
0
w.
I
412 391 419 57 1 592
68
540 68 1
104
348 333 368 538 512 498 406 421
94 75 88
stretch We
I
w.
MgO2 ('ZJ 533 0 796 a Reference 21, Reference 7. Referenccs 5 and 6. Reference 1. Reference 3. In Table I1 we summarize the geometries and dissociation energies for the different structures considered for the alkalineearth metal superoxidesat the MCPF and CCSD(T) levels. The 3A2states have 0-0 bond lengths in the range 1.340-1.360 A; this is similar to the alkali-metal superoxides, where our calculations" yielded 1.347 f 0.006 A, and to the value of 1.341 f 0.010 A given for gas-phase 02-based on a Franck-Condon analysis of the photodetachment spectrum.' This is consistent with our view that this state is analogous to the ground state of the alkali-metal superoxides and is best described as M+02-. The bonding in the IAl state is clearly very different from that in the 3A2state, as evidenced by the much shorter M-O distance and much larger 0-0 distance for the 'Al state. At the MCPF level, the net metal charge for the IAl state is about 1.2 electrons compared with 0.7 electron for the state. While the populations are only qualitative in nature, they suggest that the 'Al state is more ionic than the 3A2state, which implies significant M2+022+ character. The much larger 00 bond length for the IAl state is also consistent with doubly ionic contributions to the wave function. For Mg02, where the second IP of the metal is very large, the binding energy of the 'Al state is much smaller than for the 3A2state. This is in contrast to Ca02and Sr02, where the much smaller second IPSproduce a IAl ground state. While it might seem surprising that the 0-0 bond length in the 'Al state of Mg02 is substantially longer than for either Ca02 or Sr02, it is consistent with the populations that indicate it is more ionic. The fact that MgOz is slightly more ionic than C a 0 2 or Sr02,
2 1 92 202 1
bend degenerate
asym
SYm
I
W.
I
W.
I
134
152
270
despite its larger IP, is probably due to the smaller covalent contribution to the bonding. For Ca02and SrOz, donation occurs into both the d and p orbitals of the metal atom, while for Mg02 only the s and p orbitals are sufficiently low-lying to be able to accept donation from the ligand. Thus, both the lower second IP of the metal and the presence of low-lying d orbitals in Ca and Sr contribute to the preference of the 'A, state over the 3A2state for CaOi and Sr02. For W2,there is some question as to whether a stable structure even exists for the 'Al state. Recently, Lee et ale2' reported the geometry and vibrational frequencies for the 'Al state of BeOz at the CCSD(T) level using a small basis set. However, with their basis set, we do not find a stationary point in this region using the MCPF method. At the CASSCF level (with 10 electrons in 7 active orbitals), there is also no singlet triangular structure, and the potential does not even show the inflection observed at the MCPF level. Adding more extensive correlation to this CASSCF using the ICACPF approach produces a minimum at a geometry similar to that of Lee et al. but with a barrier to formation of linear BeO, of less than 1 kcal/mol. Expanding the CASSCF space to 10 active orbitals also results in a stable 'Al state with a barrier of about 0.4 kcal/mol.28 Adding a diffuse p function to oxygen deepens the ICACPF well slightly. Thus, while improving the basis set and level of correlation treatment should stabilize the IAl state relative to the linear states, it is likely that only a shallow well exists for the 'Al state of Be02. Further, this state may be difficult to detect, because it is 40 kcal/mol below the asymptote
9262 The Journal of PhysicaJ Chemistry, Vol. 96, No. 23, 1992
and has only a small barrier to the linear state that is an additional 40 kcal/mol more stable. In Table 111, we summarize our CASSCF vibrational freOF,Mg02, and Ca02 We include quencies and intensitiesfor 02, the metal valence s and p and oxygen 2p orbitals and electrons in the active space. For example, this corresponds to eight electrons in six orbitals (eight in six) for 0,.For Oc,the CASSCF active space reduces to ( 5 in 4), because the rOx and rux orbitals are doubly occupied in all configurations. For the C, structures, this corresponds to a (10 in 10) active space. For the linear systems, an "extra" rgactive orbital is included 80 that the rgand ruorbitals are treated equivalently. The CASSCF frequencies for 0,and 0,are only slightly less than the experimental values, but this is a dramatic improvement over the SCF frequencies that are about 400 cm-' larger than experiment. In order to help calibrate the vibrational frequencies for the alkaline-earth metal superoxides, a similar treatment was performed for NaOz. The good agreement with e~periment~?~ for Na0, gives us confidence in our computed values, especially for the )A2state, where the bonding is primarily of M+Oz-character. To calibrate the 'Al state, the vibrational frequencies of CaOZwere computed at the CCSD(T) level; the agreement between the CASSCF and CCSD(T) is good-see Table 111. The 04 stretch in the singlet state of CaO, is much or for the 3Azstate of CaO, and lower in frequency than for 0,is predicted to be very strong. However, since the 04 stretching frequency is far from what was expected based on analogy with the alkali-metal superoxides and falls in the same frequency region as CaO and O,, it may have been observed, but not identified. The computed asymmetric Ca-O stretch for the 'Al state is in good agreement with the experimental va1ue.l For MgO,, our calculations favor a linear )E., ground state, but the structure is too low-lying to be definitively led out. The vibrational frequenciesmay therefore provide an alternative means of identifying the ground-state structure. For the )Xi state, we predict a strong asymmetric stretch at about 800 cm-'. Unfortunately, this may be difficult to observe, as it falls in the same 1-s region as the vibrations of Mg03. Experimentally MgO, , structure with a Mg-O has been interpreted) as having a C symmetric stretch of 681 cm-' and an asymmetric stretch of 427 cm-I. Our computed asymmetric stretch of 406 cm-'is consistent with experiment, but assigning our 540-cm-' frequency to the Mg-O symmetric stretch for the )A2state would imply an error that is much larger than found for either CaO, or N a 0 2 We note that our computed symmetric stretch is in the same spectral region as the 575- and 499-cm-' peaks that were assigned to unknownisomers of MgO,. Thus, unfortunately, the experimental vibrational frequencies do not provide unambiguous information regarding the identity of the ground-state structure. Additional experimental studies of MgO2 would be very desirable. Relativistic effects are potentially important for the heavier systems, especially for Sr02. Therefore, we have estimated the mass velocity and Darwin contributions using perturbation the~ r y . ,The ~ effect of relativity is best observed from Table I1 by comparing the entries with the values in parentheses that contain these COrrtCtiOflS. The relativistic binding energies computed using eq 1 are expected to be more accurate as the number of metal valence electrons in the superoxide is closer to that in the ionic rather than in the neutral fragments. Therefore, we focus on the results computed in this manner. For CaO,, the effect of relativity on the binding energy of the )A2state is small. For the 'Al state, which contains some doubly ionic character, relativistic contributions reduce the binding energy slightly. For Sr02,the trends are similar, but the effects are larger. The reduction in the binding energy of the 3A2state due to relativity may be due to the polarization of the 5s-like orbital which reduces the Sr 5s population and increases the 5p population. Because the relativistic effect is smaller for the 5p than for the 5s orbital, such a polarization causes relativistic effects to decrease De. An accurate determination of the relativistic contributions requires a very flexible one-particle basis set in the core. Uncertainties of 1-2 kcal/mol may therefore be likely in the SrO, relativistic corrections to the binding energies.
Bauschlicher et al. TABLE IV: De Values (kd/mol) of the State of Caw neutral ion De Computed Using the '2+ State 83.9 88.2 MCPF CCSD(T) 89.5 92.0 De Computed for the )II State and Then Corrected Using the
Experimental )II Separationb 91.4 95.1 MCPF expt' 95.9 i 1.6 "The results under "neutral* are to Ca('S) + O()P), while those under "ion" use an approach analogous to that defined by eq 1. Reference 29. Reference 30. Because of the absence of accurate binding energies for the alkaline-earth metal superoxides, we conclude the discussion with recommended De values and estimates of their reliability. On the basis of previous studies1' of the alkali-metal superoxides, we suspect that basis set saturation beyond the ptesent very large basis sets will increase the De values by only a small amount. Therefore, it is unlikely that further basis set saturation will increase the De values of the alkaline-earth metal superoxides by more than 2 f 2 kcal/mol. We suspect that the largest remaining error in the calculations is due to limitations in the treatment of electron correlation. Therefore, we performed several calibration calculations to allow us to estimate the remaining errors. We have performed calculations on the state of CaO, as the bonding in this state is analogous to that in the 'Al state of the alkaline-earth metal superoxides. The De values are summarized in Table IV. Because the )II state is well described by a single reference configuration, an accurate De value can be computed for the 'V state by computing an accurate De value for the 311 state using an equation analogous to eq 1 and then adjusting it This apusing the accurate experimental )II-lX+ ~eparation.)~ proach yields a value that lies within the experimental error ban." Directly computing the De value of the '2' state using "eq 1" produces a De value for CaO that is substantially less. Because the bonding in the alkaline-earth metal superoxides is similar to that in the monoxides, it is likely that our calculations favor the 3A2state over the 'Al state. This contention is supported by the magnitude of the electron correlation, which at the MCPF for all of the alkaline-earth metal level varies as 'Al > 3A2> superoxides. At the CCSD('f) level, the binding energy of the 'Al state of CaO, to neutral fragments is 2.0 kcal/mol larger than at the MCPF level. The binding energy computed via eq 1 is still 1.5 kcal/mol larger than the MCPF value. Thus, the CaO, results are parallel to those of CaO, but the differences between the MCPF and CCSD(T) values are smaller for CaO, than for CaO. Using the CaO results for calibration, it is clear that we are underestimating the binding energy of the 'Al state at the CCSD(T) level even using eq 1. On the basis of the difference between the MCPF and CCSD(T) levels of theory and the CaO calibration calculations, we estimate that the correlation contribution to the binding energy is underestimated at the MCPF level by about 2 f 2 kcal/mol. Therefore, our best estimate for the CaO, binding energy is obtained by adding 4 f 4 kcal/mol to the MCPF binding energy (that includes a correction for relativistic effects). Because the bonding in Ca02 and SrOl is very similar, we apply the same procedure to SrO, but increase the uncertainty to f6 kcal/mol to account for the uncertainty in the relativistic correction. Thus, our recommended De values are 54 i 4 and 54 f 6 kcal/mol for Ca0, and SrOz, respectively. The bonding in the ?Z; state has no obvious analogue in the diatomic molecule, and furthermore, eq 1 cannot be unambiguously applied. Therefore, to calibrate the effects of electron correlation, we have studied the 3Z- state of Be02 at both the CCSD(T) and ICACPF levels of tieor,. For the CCSD(T) calculation, we use the same procedure as for the MCPF and correct the symmetry-broken binding energy using the MRCI+Q separation between the relevant stat=. The MCPF binding energy falls between the CCSD and CCSD(T) values, as for many other systems that are well described by a single configuration. The
Alkaline-Earth Metal Superoxides Be02 through S r 0 2 CCSD(T) De value is 2.5 (4.0) kcal/mol smaller than the MCPF(CCSD) result. This reflects the larger correlation energy in Be O2 than in BeO,; the SCF binding energy is 124.2 kcal/mol. We also performed CASSCF/ICACPF calculations for Be02 Because we are using a CASSCF-based approach, we directly compute the binding energy of the '2; state rather than using the symmetry-broken approach. A (10 in 12) active space was employed, similar to that used to compute the Mg02 vibrational frequencies. The Be 1s electrons are not correlated to reduce the size of the calculation (at the MCPF level, Be 1s correlation increases the binding energy by 1.5 kcal/mol). The occupations associated with t h w determinants with coefficients greater than 0.01 in the CASSCF wave function are included in the reference space for the ICACPF calculation. This ICACPF calculation yields a binding energy of 85.6 kcal/mol, which, when corrected for Be 1s correlation, leads to a binding energy of 87.1 kcal/mol. The CCSD(T) and ICACPF calculations suggest that the MCPF De value is too large by about 2 and 1 kcal/mol, respectively. Because of the small difference between the CCSD and CCSD(T) and the CCSD(T) and ICACPF De values, it is likely that higher levels of correlation treatment will reduce the binding energy by about the same amount, as basis set improvements will increase it; thus, our best estimate for the binding energy is the MCPF value, or 88 f 4 kcal/mol. On the basis of the BeO, 32;calculations, the best binding energy for the '2; state of Mg02 is the MCPF result computed to neutral fragments. On the basii of previous work, our best value for the 3A2state of Mg02 is obtained using eq 1. Thus, at the MCPF level, the 32;state is only 2.6 kcal/mol below the 'A2 state. To better assess the effects of electron correlation, CASSCF/ ICACPF calculations were performed for the 32-and 3A2states of Mg02 using the larger basis sets and a CASSbF active space analogous to that used for the vibrational frequencies. A threshold of 0.01 was used for reference selection in the ICACPF calculations. The Mg 2s and 2p electrons were not correlated, because Mg inner-shell correlation increased the separation by only 0.5 kcal/mol at the MCPF level. At the ICACPF level, the separation is 3.5 kcal/mol (3.0 kcal/mol when corrected for Mg inner-shell correlation based on the MCPF results). This is in excellent agreement with the value deduced from the MCPF calculations. Thus, our calculations support the assignment of a 32-ground state for Mg02. However, in light of the very smal! energy difference between the 32-and 3A2states and the fact that the experimental vibrational hequencies cannot be correlated with either structure, this conclusion is not definitive. Assuming a 32; ground state, our best estimate of the binding energy is 25 f 4 kcal/mol, which is arrived at in the same manner as for Be02.
+
v.
CODC~USiOM Electronic structura and binding energies have been determined for the 'A, and 'Al triangular structures and the linear symmetric '2; structure of the alkaline-earth metal superoxides Be through Sr. The ground states for Be02 and Mg02 are predicted to be 'Z-,while Ca02and Sr02are predicted to have 'Al ground states. Vigrational frequencies and intensities are computed for comparison with values determined from matrix isolation studies. Our values for CaOl compare favorably with experiment, thereby corroborating a lAl ground state. For Mg02, however, it is not possible to unambiguously identify the theoretical vibrational frequencies for either the 'A2 or 32;states with the recOm"mnded experimental values. Additional experimental studies of MgO, would therefore be very worthwhile. Recommended theoretical De values are given with an assigned uncertainty of 4 kcal/mol(6 kcal/mol for S a 2 ) . The error bars are larger than for the alkali-metal superoxides due to greater complexity of the bonding. We recommend that these De values be adopted until definitive experimental determinations become available, Acknowledgment. M. Sodupe gratefully acknowledges a Fulbright fellowship. We acknowledge helpful discussions with John Plane. We also thank Gustavo Scuseria for providing us with a copy of his open-shell CCSD(T) program.
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9263
Appendix This appendix gives the details of our one-particle basis sets. All even-tempered functions used in this work are of the form a, = paofor n = 0, k, with a @ of 2.5 unless otherwise noted. A f? of 2.5 is d when even-tempered diffuse functions are added. A. Be. The s primiitive set is the 13s set of Partridgd2 op timized for the IS state. An even-tempered diffuse s function is added. The seven tightest functions are contracted based on the SCF 1s orbital. The p basis set consists of the 7p functions for the 'P state supplemented with an even-tempered diffuse function. Four even-tempered d and two even-tempered f functions are added with ao(d) = 0.05 and %(f) = 0.22. In addition, two tight d functions (2.5 and 8.5) and two tight f functions (1.4 and 3.44) are added. The p, d, and f functions are uncontracted. B. Mg. The s and p primitive sets are taken from the ( 2 0 ~ 1 2 ~ ) set of Partridge33optimized for the IS state. A general contraction based on the atomic SCF calculations is used to contract the 14 tightest s exponents to 2 functions and the 8 tightest p functions to 1 function. The three supplemental p functions optimized3' for the 3P state are added as well as an even-tempered diffuse s and p function. Seven even-tempered d functions with q = 0.0237 and six even-tempered f functions with = 0.028 are added. The d functions are uncontracted, while the f functions are contracted to four functions using the atomic natural orbital (ANO) pro~ e d u r e . ' ~The f A N 0 is based on the average natural orbitals for the 'S and 3Pstates correlating two electrons. The f functions with exponents of 1.1,0.1776, and 0.071 are then uncontracted. C. Ca. The s and p primitives are taken from the (20s12p) set 0ptimized3~for Ca 'S.Using a general contraction, the tightest 15 s and 10 p functions are contracted to 3 s and 2 p functions based on the atomic Is, 2s, 3s,2p, and 3p orbitals. To this, the three supplemented p functions optimized32for the 'P state and eight even-tempered d and six even-tempered f functions are added. A j3 of 2.7 is used for the d and f functions; ao(d) = 0.027 and ao(f)= 0.0324. The d and f functions are contracted using the A N 0 procedure based on the average natural orbitals for the 'S, 3P, and 3D states correlating two electrons. The three A N 0 d functions are supplemented by uncontracting the outermost function and that with an exponent of 0.53 1. The single f A N 0 function is supplemented by uncontracting the outermost function and that with an exponent of 0.6377. D. Sr. The all-electron Sr basis set is derived from the (26s16plOd) set of Partridge and FaegrLs5 Four s orbitals, three p orbitals, and one d orbital are contracted based on the SCF orbitals. The outermost six s, four p, and two d primitives are uncontracted. Three even-tempered diffuse p and four diffuse d functions are added. The three contracted f functions are those obtained from two-term fits% to Slater 4f functions with exponents of 2.25 and 0.90;the exponents of the tighter 4f function were uncontracted. E. 0. For oxygen, we employ the (13sSp6d4f)/[5~5p2dlfl A N 0 basis set3' determined from the average natural orbitals of 0 and 0-.This basis is augmented by an additional diffuse s function with an orbital exponent of 0.076 666. This is the same oxygen basis set used in our recent study" of the alkali-metal superoxides. References and Notes (1) Auk, B. S.; Andrews, L. J . Chem. Phys. 1975,62, 2312. (2) Andrews, L.; Auk, B. S. J . Mol. Specrrosc. 1977, 68, 114. (3) Andrews, L.; Prochaska, E. S.; Ault, B. S. J . Chem. Phys. 1978,69,* 556. (4) Thomas, D. M.; Andrews, L. J. Mol. Specrrosc. 1974, 50, 220. (5) Andrews, L. J . Chem. Phys. 1%9, 50,4288. Andrews, L. J . Phys. Chem. 1969,73,3922. Andrews, L. J. Chem. Phys. 1971,54,4935. Andrew, L.; Hwang, J.-T.; Trindle, C. J. Phys. Chem. 1973, 77, 1065. (6) Adrian, F. J.; Cochran, E. L.; Bowers, V. A. J. Chem. Phys. 1973.59, 56. (7) Celotta, R. J.; Bennett, R. A.; Hall, J. L.; Siegel, M. W.; Levine, J. Phys. Rev. A 1972, 6, 631. (8) Ault, B. S.; Andrews, L. J . Mol. Specfrosc. 1977, 65, 437. (9) Langhoff, S.R.; Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1986, 84, 4474. (10) Plane, J. M. C. Personal communication.
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J. Phys. Chem. 1992,96,9264-9268
(1 1) Partridge, H.; Bauschlicher, C. W.; Sodupe, M.;Langhoff, S. R. Chem. Phys. Lert. 1992,195, 200. (12) Chong, D. P.; Langhoff, S.R. J. Chem. Phys. 1986,84,5606. See also: Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J. Chem. Phys. 1985,82, 890. (13) Bartlett, R. J. Amu. Rev. Phys. Chem. 1981,32,359. Raghavachari, K.; Trucks, G.W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (14) Wcmer, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803. Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514. (15) Gdanitz, R. J.; Ahirid, R. Chem. Phys. Lett. 1988, 143,413. (16) Dunning, T. H. J. Chem. Phys. 1971,55,716. (17) McLean, A. D.; Chandler, G. S.J. Chem. Phys. 1980, 72, 5639. (18) Pettersson, L. G. M.; Siegbahn, P. E. M.;Ismail, S.Chem. Phys. 1983,82, 355. (19) R m , B.; Veillard, A,; Vinot, G. Theor. Chim. Acta 1971, 20, 1. (20)Moore, C. E. Atomic energy levels; US. National Bureau of Standards (US.) Circular No. 467; National Bureau of Standards: Washington, DC, 1949. (21) Huber, K. P.; Herzberg, G.Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (22) MOLECULE-SWEDEN is an electronic structure program system written by J. Almlbf, C. W. Bauphlicher, M. R. A. Blomberg, D. P. Chong, A. Heiberg, S.R. Langhoff, P.-A. Malmqvist, A. P. Rendell, B. 0. Roos, P.
E. M.Siegbahn, and P. R. Taylor. (23) TITAN is a set of electronic structure programs written by T. J. Lee, A. P. Rendell, and J. E. Rice. (24) Scuseria, G. E. Chem. Phys. Lett. 1991, 176, 27. (25) SIRIUS is an MCSCF program written by H. J. Jenscn, H. k e n , and J. Olsen; ABACUS is an MCSCF energy derivatives program written by T. Helgaker, H. J. Jensen, P. Jsrgenscn, J. Olscn, and P. R. Taylor. (26) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. Knowles, P. J.; Wemcr, H.-J. Chem. Phys. Lerr. 1985, 115, 259. (27) Lee,T. J.; Kobayashi, R.; Handy, N. C.; Amos, R. D. J. Chem. Phys. 1992, 96, 8931. (28) Taylor, P. R. Personal communication. (29) Martin, R. L. J . Phys. Chem. 1983,87, 750. See also: Cowan, R. D.; Griffin, D. C. J . Opt. Soc. Am. 1976,66, 1010. (30) Field, R. W. J. Chem. Phys. 1974, 60, 2400. (31) Irvin, J. A.; Dagdigian, P. J. J. Chem. Phys. 1980, 73, 176. The vibrational frequency is from ref 21. (32) Partridge, H. J . Chem. Phys. 1989, 90,1043. (33) Partridge, H. J. Chem. Phys. 1987,87,6643. (34) AlmlBf, J.; Taylor, P. R. J. Chem. Phys. 1987, 86, 4070. (35) Partridge, H.; Faegri, K. Theor. Chfm.Acta 1992, 82, 207. (36) Bauschlicher, C. W.; Partridge, H.; Langhoff, S. R. Chem. Phys. 1990, 148, 57.
Rigorous Interpretation of Electronic Wave Functions. 1. Electronic Structures of BH,, B,Hd, B9H7, and B& Jerzy Cioslowski* Department of Chemistry and Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306- 3006
and Michael L,McKee Chemistry Department, Auburn University, Auburn, Alabama 36849 (Received: June 8, 1992)
Electronic structures of the simplest boron hydrides, BH3, B2H6, B3H7,and B3H9,were investigated at the MP2/6-3lG(2d,p) level of theory using rigorous interpretive tools. The computed topological properties of electron density, localized natural orbitals, atomic charges, and covalent bond orders make it possible to unequivocally describe bonding in these molecules. In the BH3 and B2H6molecules, the bonding patterns are in agreement with the widely accepted notions of the B-H bonds and the B-H-B bridges. The 2102 isomer (in the styx terminology) of the B3H7molecule is best described as possessing an open B-B-B tricentric bond in addition to seven B-H bonds. There are no B-H-B bridges present in B3H7,although the atomic occupancies of the strongly occupied localized natural orbitals suggest a substantial degree of delocalization for two of the B-H bonds. In contrast, the 3003 isomer of the B3H9species has three B-H-B bridges together with six B-H bonds. In all of the systems under study, large ionicities of both the B-H and B-H-B bridges indicate that the hydrogen atoms have a strongly hydridic character.
Boron hydrides, also known as boranes, constitute a classical example of electrondeficientmolecules, Le., species in which there are fewer electrons than required to explain bonding with only conventional two-center bonds. Although the presence of the tricenter B-H-B bonds in molecules such as B2H6 has been postulated since the seminal work of Longuet-Higgins’ and is presently widely accepted by the chemical community, it can be uncovered only if localized molecular orbitals (LMOs) are used in the description of the electronic structures of boranes. In a series of Lipscomb and co-workers employed the Edmiston-Ruedenbergs and Foster-Boys6 localization produm to m e to the conclusion that only a few elementary types of LMOs are necessary to adequately account for chemical bonding in most boranes. These LMOs correspond to the conventional B-H and B-B bonds and the tricentric B-H-B and B-B-B bonds. The aforementioned calculations have been performed at the Hartrce-Fock (HF) level, and many of them used a semiempirical scheme for computation of the necessary twoelectron integrals. Therefore, the electron-correlation effects, which are well-known to be important (at least from the energetics point of view) in boranes? have not been included in the ensuing picture of the localized bonding. With the aim of alleviating this 0022-3654/92/2096-9264$03.00/0
deficiency, a new interpretation of the localized bonding in B2H6 has been recently put forward by Gerratt et a1.8 In contrast to the previous calculations, which involved a posteriori analysis of the computed wave functions, the new approach was based on an approximate spin-coupled electron-correlation theory in which minimization of the electronic energy results in one-electron wave functions (spin-orbitals) that spontaneously break the symmetry of a molecule under study. Such a theory, which is capable of recovering a substantial fraction of the correlation energy, affords LMOs directly. However, since the symmetry breaking at the oneelectron level is an obvious consequence of the projection of the Hamiltonian onto the Hilbert space of the allowed manyelectron Slater determinants (note that an unprojected Hamiltonian in the full CI method would not favor any particular form of spin-orbitals), it remains unclear whether the resulting LMOs indeed reflect the electronic structures of molecules rather than the underlying structure of the spin-coupling approximation. Among others, the controversial description of bonding in benzene that is obtained from the spin-coupled theory9raises more questions of this kind. Building upon the extensive body of work published previously by other researChers,lo recently we have proposed a set of rigorous interpretivetools for analysis of electronicwave functions.11J2The 0 1992 American Chemical Society
