J. Phys. Chem. 1987, 91, 3171-3178 er-level HF calculations, we have carried out calculations a t the 4-31G level with full geometry optimization. The results obtained are in good accord with the experimental data. The approach used is a reasonable compromise to obtain a reasonably accurate analytical torsional potential function for this molecule. W e have obtained good agreement with experimental geometry parameters as well as with the measured values for the barrier. As pointed out above, it is possible that the computed geometry may not be
3171
accurate since we did not include polarization-type functions in the calculations. If so, then the experimental geometry is in error.
Acknowledgment. The authors thank Mr. B. G. Sumpter and Ms. Gillian Lynch for helpful discussions. This work was supported by the US.Army Research Office. Registry No. HONO, 7782-77-6.
Electronic States and Nature of Bonding of the RuC Molecule by Ait-Electron ab Initio HF-CI Calculations and Equilibrium Mass Spectrometric Experiments Irene Shim,* Department of Chemical Physics, Chemistry Department B, The Technical University of Denmark, DTH 301, DK-2800 Lyngby, Denmark
Heidi C. Finkbeiner, and Karl A. Gingerich* Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received: September 1 1 , 1986; In Final Form: February 5, 1987)
In the present work we present all-electron ab initio Hartree-Fock (HF) and configuration interaction (CI) calculations of 28 electronic states of the RuC molecule. The ground state of the RuC molecule has been determined as a 3A state. The molecule has two low-lying excited states, '2+and 'A. The electronic structure of the RuC molecule has been rationalized in a simple molecular orbital picture. The electronic spectra observed by Scullman and Thelin have been assigned as transitions between the 3A ground state and two close-lying excited states of 311and 3+ symmetry. The chemical bond in the RuC molecule is a triple bond composed of two x bonds and one u bond. The 5s electron of Ru hardly participates in the bond formation. It is located in a singly occupied nonbonding orbital. The chemical bond is polar with a charge transfer of 0.27e from Ru to C in the 3A ground state at the internuclear distance 3.09 au. Mass spectrometric equilibrium measurements over the temperature range 2086-2770 K have resulted in the selected dissociation energy Doo = 146.3 rl: 2.5 or 612.1 i= 10.5 kJ mol-' for RuC(g).
Introduction Platinum metals and platinum metal alloys are essential components of catalytic converters and also of catalysts for the important industrial processes of petrol refining as well as of coal gasification and liquefaction. In the action of such catalysts with carbon-containing gases the bond formation between the platinum metal and the carbon must play an important role. The knowledge of the nature of the bond between carbon and the metal in the smallest possible unit, namely the diatomic platinum metal carbide molecule, should therefore be of considerable basic scientific and also applied technological interest. In continuation of our theoretical and experimental investigations of diatomic carbides,'" we present here our detailed results for the R u C molecule. Reviously, the RuC molecule has been studied experimentally in optical s p e c t r o ~ c o p y and ~ ~ ~ the dissociation energy of the molecule has been derived from high-temperature, mass spectrometric equilibrium measurements.@ Both the optical spectra (1) Shim, I.; Gingerich, K. A. J . Chem. Phys. 1982, 76, 3833. (2) Shim, I.; Gingerich, K. A. J . Chem. Phys. 1984, 81, 5937. (3) Shim, I.; Gingerich, K.A. Sur!. Sci. 1985, 156, 623. (4) Scullman, R.; Thelin, B. Phys. Scr. 1971, 3, 19. (5) Scullman, R.; Thelin, B. Phys. Scr. 1972, 5, 201. (6) McIntyre, N. S . ; Auwera-Mahieu, A. Vander; Drowart, J. Trans. Faraday SOC.1968, 64, 3006. (7) Auwera-Mahieu, A. Vander: Peeters R.; McIntyre, N. S . ; Drowart, J. Trans. Faraday SOC.1970, 66, 809.
0022-3654/87/2091-317 1$01.50/0
TABLE I: Relative Energies (ir au) of the Lowest Lying Terms Originating from Different Orbital Configurations of the Ru Atom and Also of the Lowest Lying Terms of the C Atom'
state Ru 5F(4d)7(5s)' Ru 5D(4d)6(5s)2 Ru 3F(4d)8 c 3P(2s)2(2p)2 C lD(2~)~(2p)~ c IS(2s)2(2p)2
calcd
exptP
0.0000
0.0000
0.0458 0.0831
0.0319 0.0401
0.0000
0.0000
0.0573 0.1393
0.0463 0.0985
'The calculated energies are results of HF calculations. bCenter of gravity of each multiplet has been calculated from the data of Moore, C. E. Nutl. Bur. Srand. Circ. No. 467, 1952 and 1958, Vol. 1 and 3. and the dissociation energy of RuC have been reviewed by Huber and Herzberg.Io However, the available experimental data have given rise to only very limited information about the R u C molecule. Thus, the optical spectra4v5were too complex to be assigned, and the dissociation energy derived from the mass spectrometric data were in all cases based on third law evaluations of limited measurements utilizing estimated molecular constant^.^-^ In the present investigation we have performed all-electron Hartree-Fock (HF) and configuration interaction (CI) calcula(8) Gingerich, K. A. Chem. Phys. Letr. 1974, 25, 523. (9) Gingerich, K. A.; Cocke, D. L. Inorg. Chim. Acta 1978, 28, L171. (10) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979.
0 1987 American Chemical Societv
3172
Shim et al.
The Journal of Physical Chemistry, Vol. 91. No. 12, 1987
TABLE II: Total Enereies for the RuC Molecule Resulting from HF Treatments at the Internuclear Distance 3.09 au' no. of d
valence shell config
state
23n,'w
53.
'rI,'W 3n.w
3n In
3Z+
3n
SA
lr
5n,5w
'2+
32-
sc+ In 3n,3oc
'A 'Z+ 3A
26 4 1 1
3 3 4 4 4 4 3 2 3 2 2 2 2 3 3 4 3
5K
4 4 4 3 3 4 3 4 3 4 4 4 4 4 4 4 4 4 4 4
6~ 2 1
2 0 0 1
0 0 0 2 0 1
2 0 2 1 1 0
0 0
10u 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2
Ilu
0 2 2 2 2 1 2 1
2 1
2 1 1 2 2 2 2 2 2 2
12u 0 2 1
2 2 0 1 1
1 0 2 1 1
2 0 1 0 1
0
I
energy,b au
electrons on Ru
gross atomic charge
0.270401 0.199726 0.164525 0.134541 0.116466 0.105874 0.092604 0.088636 0.084856 0.080416 0.075101 0.058434 0.048 1 17 0.044791 0.041650 0.009048 0.004594 0,000 123 -0.01 2 367 -0.023249
16.07 16.25 16.50 16.52 17.44 16.92 17.11 16.97 17.22 16.45 16.91 16.57 16.45 16.96 16.65 17.30 16.88 17.57 16.94
0.33 0.45 0.28 0.26 0.47 0.29 0.37 0.29 0.60 0.20 0.43 0.56 0.20 0.47 0.32 0.37 0.22 0.30 0.24
"Also included are the gross atomic charges and the total number of d electrons on the Ru atom. bEnergy of RuC minus energy of the Ru and the C atoms, both in their ground terms. CThewave function represents a mixture of orbital angular momenta.
tions to determine the electronic structure and the nature of bonding of the RuC molecule. We also report detailed equilibrium data for RuC, and we have utilized these data together with the calculated electronic states to obtain the dissociation energy of the molecule. Finally, we present the dissociation energy of RuC as derived in the present work together with a reevaluation of the mass spectrometric literature data. The HF calculations for the RuC molecule have been carried out in the Hartree-Fock-Roothaan formalism." The integrals have been calculated by using the program MOLECULE.'*For the HF calculations we have utilized the ALCHEMY program system,13and the CI calculations have been performed by using ALCHEMY in conjunction with the program ENERGY" for generating the symbolic energy expressions. The deformation density maps have been produced by using the program MOLPLOT, especially designed for plotting of orbitals, densities, and electrostatic potentials. I s Previously, a few of the results concerning the ground state of the RuC molecule were included in a comparative study with the molecules RhC and P d C 3 Theoretical Investigations A. Basis Sets and Atomic Calculations. The basis sets consisted of contracted Gaussian-type functions. For the Ru atom we have utilized Huzinaga's basis set16 with certain modifications as described in connection with the Ru2 molec~le.'~The primitive basis set for Ru (17s,l3p,8d) has been contracted to (10s,8p,5d) leading to a triple {expansion for the 4d orbital. For the C atom Huzinaga's (10s,6p) basis setla has been augmented by a d polarization function with exponent 0.75, and the primitive basis set has been contracted to (4s,3p,ld). In Table I we compare the relative energies of some low-lying terms of the Ru and the C atoms as derived in HF calculations (1 1) Roothaan, C. C. J. Rev. Mod. Phys. 1960, 32, 179. (12) Almlbf, J. Proceedings of the Second Seminar on Computational Problems in Quantum Chemistry; Max Planck Institute: Miinchen, W. Germany, 1973. (13) The ALCHEMY program system is written at IBM Research Laboratory in San Jose, CA, by P. S. Bagus, B. Liu, M. Yoshimine, and A. D.
McLean.
(14) Sarma, C. R.; Rettrup, S . Theor. Chim. Acta (Berlin) 1977, 46, 63. Rettrup, S.; Sarma, C. R. Ibid. 1977, 46, 73. (15) Johansen, H., private communication. ( 1 6 ) Huzinaga, S . J . Chem. Phys. 1977, 66, 4245. (17)Cotton, F. A,; Shim, I. J. Am. Chem. SOC.1982, 104, 7025. (18) Huzinaga, S. J . Chem. Phys. 1965, 42, 1293.
with the corresponding experimental data. It is noted that we obtain the right ordering of the terms, but the calculated splittings are larger than the experimental values. This is a well-known deficiency of HF calculations, and it has been studied in considerable detail at an early stage for the first-row transition-metal atoms.19 However, the quality of our basis set for the Ru atom is revealed by observing that our calculated splittings are in reasonable agreement with those derived in numerical HF calcuIations.20 B. HF Calculations on Selected States of the RuC Molecule. In 1971 and 1972 Scullman and Thelin4s5had already obtained UV spectra of the RuC molecule in the gas phase, but due to the complexity of the spectra it was not possible to assign the observed transitions fully. Therefore, until now, the symmetry of the electronic ground state of the RuC molecule had not been established with certainty. The high spin and orbital angular momenta of the Ru atom in its ground term give rise to numerous possibilities for ground-state assignments of the RuC molecule. Thus, coupling of angular momenta of the Ru atom in its SF ground term with those of the C atom in its 3P ground term gives rise to septet, quintet, triplet, and singlet states of the symmetries 2+(2), E-( I ) , II(3), A(3), 9(2), r ( l ) , where the numbers in parentheses are the number of states generated within each symmetry. If, in addition, the low-lying excited terms of each atom are taken into account, the number of possible candidates for the electronic ground state of RuC increases significantly. However, from our previous work on the RhC molecule2 we note that the ground state as well as the low-lying excited states of this molecule can be rationalized by using a simple molecular orbital picture. The results for the RhC molecule reveal that the interaction occurs between a C atom in the ( ~ S U ) ~ ( ~ P O ) ' ( ~ P K ) ' configuration and a Rh atom in the (4du)1(4d~)3(4d6)4(5su)' configuration. For the RhC molecule the lowest lying fully occupied valence molecular orbitals are two u orbitals and a K orbital. The u orbitals are mixtures of the 2su and the 2pu of C with the 4du of Rh while the T orbital is the 4da of Rh with approximately 33% admixture of the 2pn from C . The higher lying valence orbitals, which are partly occupied in some of the states considered, are the metal 4d6 orbital followed by a u orbital which is mainly a mixture of the 5su of Rh and the 2pu of C, and finally followed by a T orbital. (19) Claydon, C. R.; Carlson, K. D. J . Chem. Phys. 1968, 49, 1331. (20) Martin, R. L.; Hay. P. J. J . Chem. Phys. 1981, 7.5, 4539.
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3173
Bonding of the RuC Molecule
TABLE I11 Mulliken Population Analyses of the Valence Orbitals of the RuC Molecule in the Ground 3A State and in the First Excited 'Z+ Statea
orbital analyses atomic populn state 3A
orbital 100 lla 12a 57T 26
total
'E+
1Oa
11a 5K 26
total
Ru
C
0.42 0.85 0.78 2.34 3.00 43.22 0.42 0.97 1.94 4.00 43.13
1.54 1.03 0.16 0.91 0.00
overlap vopuln 0.03 0.12 0.06 0.75 0.00
Ru S
0.03 0.03 0.68 0.00 0.00
5.69 1.55 0.88 1.27
0.03 0.15 0.79
0.00
0.00
0.00 0.00
5.74
1.13
8.07
1.10
8.72 0.03 0.06
C
P
d
0.03
0.38
0.08
0.80
0.04 0.03
0.09 2.68 3.00 16.94 0.38
0.00
18.09 0.02 0.11 0.02 0.00
18.06
0.88
2.31 4.00 17.57
occup
1.53 0.28
0.80
-0.01 0.00
0.20 1.25
0.00
0.00
0.00
3.85 1.55 0.24
2.33 0.02 0.70 1.64
0.00 0.01
0.00
0.00
2.41
0.05
0.00 0.00
3.85
no.
d 0.00 0.01 0.00
V
S
0.03
2.00 2.00
1.oo
0.03
4.00 3.00
0.06 2.00 2.00 4.00 4.00
0.03
"The calculations were performed in the HF approximation at the internuclear distance 3.09 au. TABLE IV: Spectroscopic Constants of Some Low-Lying Electronic States of the RuC Molecule As Derived in HF Calculations equilib dissocn vibnl state distance, au energy, eV freq, cm-I 3A 3.00 0.70 1198 '2+ 2.93 0.56 1268 1A 2.96 0.14 1242
5n
'2lr
3.57 3.29 3.29
0.01 -1.10
-1.92
290 746 746
Assuming that a similar molecular orbital picture is adequate for the R u C molecule implies that this molecule should have a IZ+ ground state and a 3A lowest excited state. In the present work we have performed HF calculations on these states as well as on numerous other states a t the experimental internuclear distance, 3.09 au, of the lowest lying state reported in Huber and Herzberg.Io Table I1 shows the results of the HF calculations. In this table we have presented the configuration of each state together with its total energy. In addition, we have included the total number of d electrons and the gross atomic charge on the R u atom. It is noted that the Ru atom acquires a significant positive charge in all the states considered. Furthermore, the variations in the number of the d electrons on R u indicate that states derived from the configurations (4d)6(5s)2, (4d)'(5s)l, and (4d)8 of Ru have been treated. Of all the states we investigated, only two have energies below the sum of the energies of the separated atoms a t the internuclear distance 3.09 au, namely the states 3A and l2+. The 3A state can be regarded as derived from the (4d)7(5s)' configuration, while the state originates from the (4d)* configuration of the Ru atom. This is reflected in the Mulliken population analyses of the two states shown in Table 111. The population analyses show that all the valence orbitals except the 26 orbitals are considerably delocalized. As was the case for the RhC molecule the main bonding orbitals for R u C in both the 3A and the l2+ states are the 5 n orbitals, which are mixtures of the 4dn of Ru with 2pn of C. The 10a and l l a orbitals are also bonding, and they are mixtures of the 4du of Ru with the 2s and 2pu of C. For the 'A state the 126 orbital can be identified as the 5 s orbital of Ru with some charge donated into the 2pu of C. In our earlier work3 the chemical bond in the R u C molecule was interpreted in terms of donation and backdonation of charge. In the HF approximation the chemical bond in the RuC molecule is essentially a triple bond composed of one u and two n bonds. Table IV shows the spectroscopic constants as derived on the basis of the HF calculations. The vibrational frequencies have been derived by fitting the bottom of the potential energy curves to harmonic potentials and the dissociation energies by subtracting the sum of the atomic H F energies from the molecular energy. states also the IA and It is noted that besides the 3A and the the slI states are bound relative to the free atoms. The nature of the IA state resembles that of the 3A state closely. In fact, the IA state should be regarded as derived from the 3A state just by
3.6 1
13.6
2.4
2.4
1.2
1.2
-.O
-.O
-1.2
-1.2
-2.4
-2.4
-3'6
i
1
-4.8 -4.8
-3.6
-3.6
-2.4
-1.2
0.0
1.2
2.4
3.6
1-4.8 4.8
Figure 1. Deformation density map for the 'A ground state of the RuC molecule at the internuclear distance 3.09 au. The superpositioned atomic charge densities from the (4d)'(5s)l configuration of Ru and the ( 2 ~ ) ~ ( 2 pconfiguration )* of C have been subtracted from the molecular charge density. Solid contours show enhanced electron charge relative to the superpositioned atoms, and dashed contours show diminished charge. The smallest contour value is 0.000625 e/au3. Adjacent contours differ by a factor of 2.
a change of the spin coupling, and this explains the close agreements between the equilibrium distances and the vibrational frequencies of these two states. The state is derivable from the 3A state by promotion of a 26 electron to the 6n orbital. Table IV reveals that this results in a considerable elongation of the equilibrium distance and lowering of the vibrational frequency. Figures 1 and 2 show the deformation density maps of R u C for the 3A ground state and the '2' first excited state a t the internuclear distance 3.09 au. They have been derived by subtracting the spherical averaged, superpositioned atomic charge densities from the charge density of the molecule in the 3A and in the '21' state, respectively. It is recognized that both states are considerably polarized and that the chemical bonds give rise to buildup of charges halfway between the nuclei. Furthermore, the finer details of the deformation density maps are consistent with the results presented in Table 11; that is, the stronger bond is formed in the 3A state and the larger charge transfer occurs in the l2+ state. Results of CI Calculations on the RuC Molecule. The C I calculations we performed allowed full reorganization within the valence shells of the RuC molecule, thus ensuring a correct description of the molecule in the dissociation limit. The calculations have been carried out in the subgroup C,, of the full symmetry
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
3174
Shim et al.
TABLE V: Comparison of the Spectroscopic Constants, Le., Vibrational Frequencies, we, Equilibrium Distances, r e and Transition Energies, T,, of Some Low-Lying States of RuC As Obtained in HF Calculations and in CI Calculations Based on Molecular Orbitals Optimized for the 3A, sll, and 'Et States. Reswctivelv"
results of HF
state 3A
mol orbitals optimized for
'A
HF
TI
CI CI CI HF
eV
'A 'A
CI CI CI HF CI CI CI
1Zt
T,,b
5n
'z+
0.00 0.00 0.00 0.00
IZ+
0.14
'A
0.55
5n
0.53 0.32 0.56 0.66 0.72 0.52 0.69 2.16 1.59 1.38
7z+
'A 3A 5rI
TZ+
5n
c1 CI CI
'A
TI 7Z+
re
au 3.00 3.13 3.28 3.31 2.93 3.20 3.36 3.33 2.96 3.08 3.28 3.37 3.57 3.72 3.72 3.78
we,
cm-' 1198 890 888
769 1268 917 950 851
1242
occupn 67r 0.00
0.09 0.21 0.23 0.00
0.12 0.25 0.27
888
0.00 0.10
830 711 290 373 203 355
0.23 0.26 1.00 1.04 1.12 1.13
overlap
gross atomic
populn 1.10
charge 0.24 0.24 0.26 0.42 0.30 0.3 1 0.37 0.44 0.22
1.11
1.05 0.78 1.13 1.16 1.10 0.85
1.12 1.13 1.05 0.8 1
0.90 0.91 0.62
0.21
0.24 0.38 0.32 0.37 0.51
S
number of P
8.73 8.74 8.76 8.66 8.07 8.10 8.12 8.16 8.77 8.77 8.79 8.73 8.75 8.79 8.73
18.09 18.14 18.17 18.05 18.06 18.19 18.20 18.08
d
16.94 16.88 16.80 16.87 17.57 17.40 17.31 17.31
18.14
16.88
18.14
18.17 18.06 18.28
16.88 16.80 16.80 16.65
18.30
16.54 16.61
18.15
"Also included are the occupation of the 6 8 orbital, the overlap population, the gross atomic charge, and the total number of s, p, and d electrons on Ru at the internuclear distance 3.09 au. bThe total enerlgy, Ee, of the 'A state as derived in HF calculations is -4478.813681 au. The total enemies of the 'A state derived in the CI calculations based on orbitals optimized for the states 'A, 511, and 7Zeare -4478.845 514, -4478.895 262, and :4478.893 732 au, respectively. -3.6
-1.8 4.0
*--
,'
-2.4
-1.2
0.0
1.2
2.9
3.6
4.8 1.0
_ _ _ - - - - --. _
,'
3.6
2.4
1.2
-.o -1.2
-2.4
-3.6
-4.0
-4.8
--._ ---_____---3.6
-2.1
-1.2
0.0
1.2
2.4
3.6
-4.8 4.8
Figure 2. Deformation density map of the 'Z* first excited state of the
RuC molecule at the internuclear distance 3.09 au. The superpositioned atomic charge densities from the (4d)7(5s)' configuration of Ru and the ( 2 ~ ) ~ ( 2configuration p)~ of C have been substracted from the molecular charge density. Solid contours show enhanced electron charge relative to the superpositioned atoms, and dashed contours show diminished charge. The smallest contour value is 0.000625 e/au3. Adjacent contours differ by a factor of 2. group C,, of the RuC molecule. The number of configurations included within each symmetry species of C, reaches 270 for the quintet states, 858 for the triplet states, and 672 for the singlet states. Analogous to our work on the RhC molecule2 we have chosen to describe all the low-lying states of the RuC molecule in performing CI calculations by using just one set of molecular orbitals. In the search for an appropriate set of such orbitals we have performed C I calculations on some of the low-lying electronic states utilizing selected sets of the molecular orbitals that have been optimized for the states presented in Table 11. In Table V we compare some of the results obtained. The C I calculations utilizing the molecular orbitals optimized for the 3A ground state have revealed that the virtual 6 a orbitals achieve a significant population. Therefore Table V also includes results from C I calculations based on molecular orbitals optimized for a 511 state that has a single electron in the 6a orbital, and for a 'Z+ state
with two electrons in the 6a orbital. The spectroscopic constants presented in Table V have been derived by fitting the calculated energies either to Morse potentials or to harmonic potentials. First of all it is noted that the sequence of the low-lying electronic states is independent of the choice of molecular orbitals used in the CI calculations, and, in addition, the calculated spectroscopic constants are in reasonable agreements. Table V also contains the overlap population, the gross atomic charges, and the total numbers of s, p, and d electrons on Ru resulting from the various CI calculations a t the internuclear distance 3.09 au. The total numbers of s, p, and d electrons on Ru indicate that the electronic configuration of Ru is not very sensitive to the choice of optimized orbitals. However, the overlap populations and the gross atomic charges on Ru reveal that the RuC molecule becomes appreciably more ionic when the CI calculations are based on the orbitals optimized for the 'Z+ state than on those optimized for the 3A or the sII states. Taking this into consideration along with the fact that the lowest total energy of the 3A ground state has been obtained utilizing the sII orbitals we have chosen to present the detailed results of the CI calculations based on the orbitals optimized for the 511 state. The molecular orbitals have been optimized for the 511state at the internuclear distances 2.80, 3.00, 3.09, 3.30, 3.60, 4.20, and 5.00 au, and the resulting orbitals have been utilized in C I calculations allowing full reorganization within the valence shells of the molecule as described above. The potential energies obtained in the CI calculations have been fitted to Morse curves, and in Figure 3 we present the potential energy curves for 28 electronic states of the RuC molecule. Comparing with the states expected due to coupling of angular momenta of the atoms, it is interesting to note that the states approaching the ground term atoms are a septet, a quintet, a triplet, and a singlet state of each of the symmetries Zt,II, A, and a. Of the states of the symmetries Z- and r that should also approach this dissociation limit only the 3Z- and the SFstates are within the energy range covered by the CI calculations. The potential energy curves for these 3Zand 5rstates must exhibit barriers at internuclear distances larger than 5 au in order to approach the right dissociation limit. The equilibrium distances, the vibrational frequencies, and the transition energies derived by fitting the potential energies to the Morse curves are reported in Table VI. Also presented are the dissociation energies determined as differences between the energies of the RuC molecule at the equilibrium distances and the sum of the HF energies of the atoms. This procedure is consistent because the CI wave functions include only molecular correlation that vanish in the dissociation limit.
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3175
Bonding of the R u C Molecule
E (a.3+4478a.u.
TABLE VII: Valence Shell Configurations of the Electronic States of the RUC Molecule As Derived in CI Calculations at Distances Close to the Calculated Equilibrium Distances of the Individual States distance, occupation of natural orbital
state
-.EO
I ~ A
TI 'A
1
In 'n 'a -i'
'A
'Z'
3*
'A 'A
'x- 'n '1' 'n 'a 'rl
1'2+ 'Z'
I 3n
TI
15II 7 2+
X ll 'a 'A 'X'
? . I
30'a
5@
'n
SA
?z+
-
l'Z+
7n
'A
'I*
7@
7A '2-
23n 25II 2'A
'A
-.go
3
2
4
5 R (a.u.)
Figure 3. Potential energy curves for 28 electronic states of the RuC
molecule as derived from CI calculations. (The states are labeled according to increasing values of T,from left to right.) TABLE VI: Spectroscopic Constants for the Low-Lying Electronic States of the RuC Molecule As Derived in CI Calculations state re, au we, em-' De, eV T,, eV 888 2.92 0.00 1'A 3.28
1'2' 'A 'cp I*
1'n
15n 72+
1
'n
5@
5A 52+
1'2'
7n 7*
7A
'z-
2311 2'II 2'A 5r
212+ 21n 33n 233 23z+ 43n 3'A
3.36 3.28 3.47 3.64 3.41 3.72 4.23 3.93 4.08 3.97 4.34 4.10 4.46 4.37 4.58 3.53 3.63 3.79 4.11 3.94 3.98 3.75 3.80 3.83 3.79 3.57 4.16
950 830 531 608 436 203 427 369 414 419 424 414 474 430 469 546 531 524 478 433 485 470 392 366 399 536 285
I'II
2.39 2.20 1.65 1.59 1.57 1.35 1.34 1.30 1.29 1.25 1.24 1.20 1.19 1.18
0.96 0.91 0.84 0.78 0.73 0.51 0.45 0.28 0.26 0.18
0.13 0.08
-0.02
0.53 0.72 1.27 1.33 1.35 1.57 1.58 1.63 1.63 1.67 1.68 1.72 1.73 1.74 1.97 2.01 2.08 2.15 2.19 2.41 2.47 2.64 2.66 2.74 2.79 2.85 2.94
Table VI1 reveals the configurations of the electronic states through the occupations of the natural orbitals a t those of the internuclear distances that are closest to the calculated equilibrium distances of the individual states. Table VI11 contains the Mulliken population analyses of the 3A ground state as well as of the 'E+ first excited state a t the internuclear distance 3.09 au. The configurations presented in Table VI1 indicate that the low-lying electronic states of the RuC molecule can be rationalized on the basis of a simple molecular orbital picture. Thus, the sequence of the low-lying states is consistent with a molecular orbital diagram where the lowest lying valence orbital is the 10u orbital followed by the 57r orbital and by the 11u orbital. The higher lying valence orbitals are the 26 orbital followed by the 12u orbital and finally by the 6 a orbital. The 26 and the 12u orbitals should be almost degenerate, since the exchange energy
212+ 21n 3'n 23cp 232+ 4% 33A
au 3.3 3.3 3.3 3.3 3.6 3.3 3.6 4.2 3.6 3.6 3.6 4.2 4.2 4.2 4.2 4.2 3.6 3.6 3.6 4.2 4.2 4.2 3.6 3.6 3.6 3.6 3.6 4.2
IOU
1.99 2.00 2.00 2.00 1.99 2.00 1.99 2.00 1.99 1.99 1.99 2.00 2.00 2.00 2.00 2.00 1.99 1.99 1.99 1.99 1.98 1.99 1.99 1.99 1.99 1.99 1.99 1.98
Ilu 1.97 1.95 1.97 1.91 1.80 1.91 1.86
12u 1.02 0.09 1.02 0.09 0.21 0.10 1.01
1.00
1.00
1.79 1.08 1.94 1.18 1.33 1.70
0.28 0.93
1.00
2.00 1.97 1.90 1.08
1.53 1.87 1.53 1.93 1.74 1.30 1.28 1.72 1.78
1.05
0.83 0.67 1.00 1.00 1.00
1.96 1.04 0.99 1.48 1.11 0.56 0.89 0.98 0.95 0.77 0.97 1.16
57r 3.74 3.72 3.70 3.80 3.64 3.81 3.76 3.78 3.64 3.57 2.82 3.66 3.44 3.00 3.00 2.00 3.67 3.66 3.70 2.90 2.87 3.56 3.62 3.36 3.62 3.49 3.70 3.07
67r 0.28 0.33 0.31 1.20 1.36 1.19 1.23 2.00 1.36 1.44 1.19 1.98 1.91 2.00 2.00 2.00 0.37 1.14 1.30 1.12 1.17 1.51 1.23 1.01 1.38 1.00 1.27 1.23
26 3.00 3.91 3.00 3.00 2.99 2.99 2.15 2.22 2.95 3.00 3.00 2.36 2.64 2.30 3.00 3.00 2.04 2.27 2.94 2.98 3.00 2.84 2.33 2.93 2.77 3.47 2.35 2.78
apparently causes the 3A and the IA states both with the approximate configuration (lO~)~(1lo)~(12~)'(5a)~(26)~ to respectively fall below and above the energy of the 'E+ ( 1 0 ~ ) ~ (1 1 ~ ) ~ ( 5 x ) ~ ( state. 26)~ The configurations of the next higher lying states, 3@, I@, and 1311 as well as of 1111 are approximately ( 1 0 ~ ) ~ ( 1 1 ~ ) ~ ( 5 7 r ) ~ (2~5)~(6a)'. This indicates that these states are derived from the 3A and the IA states by excitation of an electron from the 12u to the 67r orbital. The 1511state, which has a lower energy than the l ' I I state, as well as the states 2311 and 2III all arise from the approximate configuration ( ~ O U 11 ) ~~)~(57r)~(26)~( ( 12u)I(67r)'. Thus, these states are derived by excitation of an 26 electron in the 3A or 'A states into the 6 7 orbital. The 2311 and the 2'II states are quite high up in energy, but apparently the recoupling that occurs in the 1511state causes the energy of this state to drop below that of the 1'II state. In order to reach the ' E and the higher lying states, excitations out of the low-lying valence orbitals, 11u and 57r, have to be taken into account. Altogether it is noted that the calculated electronic structure of the R u C molecule implies that orbital energy differences and exchange coupling energies due to different spin couplings are of the same order of magnitude. For the 3A ground state as well as for the 'A low-lying excited state, the occupations of the natural orbitals are almost identical over the entire range of internuclear distances considered. The occupations of the Sa orbitals decrease while those of the 6 a increase as the internuclear distance increases, but for all distances the sum of the occupations in the 57r and 6a orbitals adds up to approximately 4. For the '2' state the populations of the u valence orbitals change significantly as functions of the internuclear distance. This, in combination with the changes occurring in the R and 6 orbitals, reflects that a change of configuration has to occur in order for the IE+ state to approach the right dissociation limit. For the 3A ground state and the 'Z+ first excited state Table VI1 reveals that the 10u and 1 1u orbitals are mixtures of the 4du of R u with the 2s and 2pu of C. The 12u orbital is primarily the 5s orbital of R u but with some charge donated into the 2pu of C. The 57r and 67r orbitals are mixtures of the 4d7r of Ru with the 2pa of C, but in this case back-donation of charge gives rise
3176
Shim et al.
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
TABLE VIII: Mulliken Population Analyses of the Valence Orbitals of the RuC Molecule in the 3A Ground State as well as in the Excited State"
First
orbital analyses state 3A
6a
atomic populn Ru C 0.81 1.14 1.31 0.53 0.79 0.20 0.96 2.10 0.12 0.11
26
3.00
0.00
0.00
1Oa
43.21 0.60 0.74
5.74 1.36 1.08 0.01 1.24 0.11
1.04 0.04 0.14 0.82 -0.02
0.00
5.82
orbital IOU
lla 12a 5a total lZ+
lla 12a 57r 6a 26 total
0.05
1.74 0.16 3.92 43.08
overlap
populn 0.04 0.14 0.01 0.74 -0.01
S
0.01
0.07 0.69 0.00 0.00 0.00
Ru P 0.00 0.10
0.09
d 0.82 0.42 0.09 2.41 0.07 3.00 16.80 0.57 0.67
0.00
0.0 1
0.12 0.04
2.04
0.03 0.07 0.04 0.00
8.76 0.03 0.06 0.04
18.17
0.00
0.00 0.00 0.00
1.10
8.12
18.20
0.00
0.01
0.00
0.1 1
3.92 17.31
S
0.95 0.87 -0.01 0.00 0.00 0.00
3.84 1.28 0.53 0.00 0.00 0.00 0.00
3.85
C P
0.21 0.51 0.22 1.30 0.10 0.00
2.38 0.10 0.61 0.01 1.62 0.10
occupn d
no.
0.00
2.00 1.98 1.01 3.80 0.21 3.00
0.01 0.00
0.03 0.00 0.00
0.05 0.00
0.01 0.00
0.03
0.00
0.00 0.00
2.48
0.05
2.00 1.97 0.06 3.80 0.25 3.92
"The wave functions have been derived in CI calculations at the internuclear distance 3.09 au. to a small population in the 5 p r orbital of Ru. A similar qualitative description of the valence orbitals is also valid for the higher lying states of the R u C molecule, and therefore Table VI1 shows that the calculated electronic states arise from the Ru atom in the (4d)'(Ss)l configuration as well as in the configurations (4d)8 and (4d)6(5s)2. Analogous to our findings for the RhC molecule2 we assume that this does not represent a major problem with respect to the calculated relative energies of the electronic states of the R u C molecule. Comparison of Tables 111 and VI11 provides some justification of the procedure used, Le., describing all the low-lying states of the RuC molecule by performing CI calculations using just a single set of molecular orbitals. Thus, it is recognized that the description of the chemical bonds in the lowest lying states of the RuC molecule is not changed significantly by the CI calculation. The major contributions to the overlap population are due to the 5r and the 1 l a orbitals. The 12a orbital which is mostly the Ru 5 s is essentially nonbonding. Thus, the chemical bond in the RuC molecule is a triple bond composed of two r bonds and one a bond. The bond is polar with a total charge transfer of 0.27e from Ru to c. Spin-Orbit Coupling and Comparison with Electronic Spectra. In order to compare our results with the measured spectra by Scullman and Thelin4s5 we have performed an approximate treatment of the effect of the spin-orbit coupling on the low-lying states of the R u C qolecule utilizing the perturbational Hamiltonian H' = xl[(r,)l,ZpThe influence of the spin-orbit coupling on the electronic states of the RuC molecule is of course completely dominated by the Ru atom. Therefore, we have utilized the atomic spin-orbit coupling constant for R u together with the atomic populations on this atom as derived in the Mulliken population analyses at the internuclear distance 3.09 au to obtain the splittings of the molecular states a t this distance. The atomic coupling constant C(4d) for Ru has been obtained as 887 cm-' on the basis of the atomic spectra in Moore's Tables.2' In the present work we have explicitly treated the effect of spin-orbit coupling on the lowest lying triplet states of A, @, and II symmetry. In addition to the diagonal spin-orbit coupling effects we have also considered the off-diagonal effects caused by the nearby singlet states of the same space symmetries. In Table IX we show the vertical transition energies as calculated a t 3.09 au of the allowed transitions between the 3A ground state as well as the 'A and 'Z+ lowest excited states and the lowest lying 311,'II, 3@, and I @ states. Also included are the experimental values arranged according to our suggested assignments of the observed lines. The 3A ground state of the RuC molecule as determined in the present work is in agreement with Scullman and Thelin's sugg e s t i o ~based ~ ~ on their observation that the 7224-A system is (21) Moore, C . E. Natl. Bur. Stand. Circ. 1958, 3, No. 467
TABLE I X Vertical Transition Energies (eV) As Calculated at the Internuclear Distance 3.09 au, and Experimental Values Arranged according to Our Suggested Assignments of the Observed Lines in the Electronic Spectra of the RuC Molecule"
transition 3h-3A2
362-3~1 '64-'A3 3110-3A,
3n2-3~, 3rI,-3A2 'd3-IA2
1l-I -lZ+ &'A2
transition energy, eV calcd exptl 1.55 1.60 1.58 1.65 1.59 1.71 1.57 1.57 1.58 1.57 1.59 1.62 1.23 1.64 1.72
line designtn," 8, 7754 7499 or 7514 7224 7909 7884 7623
From ref 4.
consistent with a 394-3A3 transition. The 7884-A system possibly originates from a J 2-3 transition, and as noted from Table IX we have assigned this transition 3112-3A3. Scullman and Thelin4 have observed A doubling in the 7623-i% system arising from a state with R = 1. They suggest that it is the lower state that is A-doubled, but they also point out that it is difficult to settle which state is A-doubled due to the small splittings and the accuracy of the wavenumbers of the lines. Therefore, we suggest that the A-doubling occurs in the upper state leading to the tentative assignment 3rIl-3A2 of the 7623-A system. Furthermore, the relative intensities of the R and P branches of the 7623-A and possibly of the 7909-A systems indicate that these systems might originate from transitions with AA = -1. This supports our assignment of the 7909-A system as a 3110-3Al transition. All in all the observed lines of the electronic spectra of the RuC molecule are consistent with the results of our calculations that have predicted the transitions to occur between a 3A ground state and two close-lying states of 311and % symmetry.
Mass Spectrometric Investigations The mass spectrometric equilibrium measurements involving gaseous RuC were performed simultaneously with those of gaseous RhC.* The Ce-Rh-Ru-Os sample was mixed with excess graphite powder and placed inside a graphite Knudsen cell to ensure unit activity of carbon during the measurements. The graphite cell was inserted into a tantalum cell. The orifice diameter was 0.040 in. The energy of the ionizing electrons was 20 V, and the emission current was regulated a t 1.0 mA. The ions were accelerated through a potential of 4.5 kV and detected with a 20-stage electron multiplier whose entrance shield was maintained at a ca. -2 kV potential. Temperatures were measured by sighting a Leeds and Northrup optical pyrometer a t a black-body hole in the bottom
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3177
Bonding of the R u C Molecule TABLE X Gibbs Energy Functions, ( G o T- H o o ) / T ,and Enthalpy Increments, HOT - H o e for Gaseous RuC, Calculated according to Different Assumptions
-(GT - HoO)/ T,' J K-' HOT - HOo,' mol-' kJ mol-' 201.81 8.994 263.51 68.05 267.51 76.05 271.14 84.05 274.45 92.06 277.54 100.08 280.40 108.09 283.07 116.10
T. K
298 1800 2000 2200 2400 2600 2800 3000
-(GT
- HoO)/
T,bJ K-' mol-' 195.57 252.56 256.19 259.52 262.56 265.37 267.99 270.43
HOT
-
kJ mol-' 8.757 6 1.94 69.33 76.75 84.17 91.60 99.04 106.49 ~~~
~~~~~
Theoretical parameters, see text. Assumptions by McIntyre et al. (ref 6): 'Z', re = 1.61 A, we = 1050 cm-I. T/K 21300
26W
2LcQ
2200
I
I
I
I
0.2
R u (gl+C (Graphite ) = Ru C ( g i 031
O5 I
0.6
/
I
36
I
I
I
38
I
LO
I
I
,
L2
I
L.L
I
C
L6
,
+I L0
10LK/T
Figure 4. Plot of log K p vs. 1/T for Ru(g)
+ C(graph.) = RuC(g).
of the tantalum cell. The pyrometer had previously been calibrated a t the melting point of gold, using N B S standard reference material 745. The ionic species were identified by their m / e ratios, isotopic abundances, and ionization efficiency curves. The measured ion intensities of Ru', RuC', Rh+, and RhC+ were treated by the third-law and the second-law methods to calculate the enthalpy of the reactions
+ C(graph.) = RuC(g) RhC(g) + Ru(g) = Rh(g) + RuC(g) Ru(g)
(1)
which are independent of the absolute pressure calibration of the instrument. The third-law reaction enthalpy is given by the expression AHOo = -RT In Kp(T) - TA[(GoT - H o e ) / T I ,where Kp(T) is the equilibrium constant, A[(GoT - Hoo)/TI is the Gibbs energy function change for the reaction, and B = 0 or 298.15 K. In evaluating the equilibrium constant Kp from the measured ion currents it was assumed for both reactions that the effective relative ionization cross sections and multiplier gains of reactants and products cancel each other. The second-law enthalpy is obtained from the log K,(T) vs. 1 / T plot. The thermodynamic functions needed in these calculations were taken from Hultgren et a1.22for Ru(g), Rh(g), and C(graph.), those for RhC were taken from Cocke and G i n g e r i ~ h . ~For ~ RuC(g) the values calculated in the present investigations were used. Here we have considered the electronic states 3A3, 3A2, 3Al, ' E, and 'A2 with the respective relative energies 0, 755, 1775, 5 157, and 68 13 cm-' together with the vibrational frequency 1039 cm-' and the internuclear distance 1.634 A. The latter values have been taken from Huber and Herzberg,lo and the reason for this choice is the strong evidence presented in the previous section that the lower state identified by the 7224-A system in Scullman and Thelin's work4s5 is indeed the 3A ground state of the RuC molecule. The calculated thermal functions are listed in Table (22) Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.; Kelley, K. K.; Wagman, D. D. Selected Values of the Thermodynamic Properties of the Elements; America1 Society of Metals: Metals Park, OH, 1973. (23) Cocke, D. L.; Gingerich, K. A. J . Chem. Phys. 1972, 57, 3654.
TABLE XI: Third-Law Enthalpies for the Reaction Ru(g) C(graph.) = RuC(g) over Ce-Rh-Ru-Os-Graphite System ion currents, A data set
no. 19 20 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 72 73 74 75 76 77 78 79 80 81 82
83 84 85 86 87 88 89 90 91
T, K 2191 2161 2235 2264 2293 2318 2340 2371 2394 2420 2330 2330 2276 2242 2217 2202 2194 2164 2151 2139 2107 2086 2443 2443 2273 2273 2427 2448 2518 2576 2576 2484 2266 2253 2279 2307 2356 2225 2191 241 1 2446 2459 249 1 2553 2553 2589 2609 2609 2609 263 1 263 1 2168 2362 2353 2325 237 1 2403 2435 246 1 2496 2525 2558 2585 2732 2770 2734
I(Ru+) 1.700 X lo-'' 1.068 X lo-" 2.800 X lo-" 3.900 X lo-" 6.100 X lo-" 9.120 X lo-" 1.386 X 2.070 X 3.280 X 4.690 X 1.290 X 1.500 X lo-'' 8.250 X lo-'' 4.900 X lo-" 4.050 X lo-" 3.200 X lo-" 2.500 X lo-'' 1.900 X lo-'' 1.520 X lo-" 1.245 X lo-'' 8.400 X 5.350 X 5.700 X 4.900 X 6.850 X lo-" 7.170 X lo-" 4.620 X 5.780 X 1.215 X 1.545 x 10-9 1.770 X 6.100 X 5.050 X lo-'' 4.750 X lo-'' 6.600 X lo-'' 9.300 X lo-'' 1.620 X 2.950 X lo-'' 1.800 X lo-'' 3.000 X 4.300 X 5.000 X 7.400 X 1 .DO x 10-9 1.125 X lo4 1.785 X 2.610 X 2.250 X 2.400 X 2.580 X 2.520 X 1.101 x lo-" 1.425 X 1.455 X 1.155 X 1.860 X 2.715 X 3.200 X 1O-Io 4.300 X 10-lo 6.800 X 9.300 X 1.200 x 10-9 1.395 X 2.720 X 2.600 X 2.400 X
+
I( RuC') 3.400 X 2.450 X 7.200 X 1.035 X lo-'' 1.830 X lo-" 2.770 X lo-'' 4.300 X lo-'' 6.700 X lo-" 1.140 X 1.686 X 4.150 X lo-'' 4.630 X lo-'' 2.300 X lo-'' 1.240 X lo-" 1.020 x lo-" 7.560 X 5.900 X 4.300 X 3.300 X 2.470 X 1.700 X 1.000 x 10-12 2.110 x 10-10 1.790 X 1.930 X lo-'' 1.950 X lo-'' 1.710 X 2.235 X 4.900 X 7.180 X 7.150 X 2.370 X 1.320 X lo-'' 1.140 X lo-'' 1.740 X lo-'' 2.700 X lo-'' 4.980 X lo-'' 6.750 X 4.050 X 1.020 x 10-10 1.596 X 1.830 X 2.860 X 5.400 X 5.000 X 8.100 X 1.250 X 1.080 x 10-9 1.110 x 10-9 1.185 X 1.144 X 2.550 X 4.300 X lo-" 4.600 X lo-" 3.400 X lo-'' 6.000 X lo-'' 9.090 X lo-" 1.080 X 1.620 X 2.660 X 3.750 X 5.450 X 6.000 X 1.365 X 1.440 x 10-9 1.425 x 10-9
X, together with those used in previous investigations. The measured ion currents, I(Ru+) and I(RuC+), used for calculating the enthalpies for reaction 1 are given in Table XI. A second-law plot is shown in Figure 4. The enthalpies for reaction 2 were obtained from the ion currents in Table XI and the ion currents in Table VI11 of ref 2 for Rh+ and RhC' for the same data set number. In Table XI1 we summarize the second-
3178 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
Shim et al.
TABLE XII: Summary of Reaction Enthalpies, in kcal mol-' (kJ mol-') no. of
second law third law temp data sets AHo T" AHO, AH', AH0298 reaction range, K Ru(d + 2086-2770 66 18.7 f 0.4 22.2 f 0.4 25.2 f 0.3 25.6 f 0.3 C(graph) = (78.4 f 1.5)d (93.0 f 1.5) (105.5 f 1.2) (107.3 f 1.2) Ruck) RhC(g) + Ru(g) 2086-2770 56 -8.9 f 0.5 -10.7 f 0.5 -7.6 f 0.4 -7.6 f 0.4 = RuC(g) + (-37.1 f 2.2) (-45.0 f 2.2) (-31.9 f 1.5) (-31.7 f 1.5) Rh(g) T = 2380 K. *Using AHf,o[C(g)]= 169.6 f 0.5 kcal mol-' or 709.6 f 2.1 kJ mol-', ref 22. 'Using Do,(RhC) dValues in parentheses are in kJ mol-' units.
TABLE XIII: Comparison of Reaction Enthalpies Involving RuC with Literature Datao no. of
reaction Ru(g) + C(graph) = RuC(g)
Rh(g) + R u ( d = R u c k ) + Rh(d
temp range, K 2084-21 52
data sets
-9.2 f 2.0 146.6 f 2.0' (-38.3 f 8.4) = 137.4 f 0.9 kcal mol-', ref 2.
AHoo,kcal
second law
4
third law 18.6 f 0.8
17.5 2635-2145 2086-2770
66
2552-2785 2086-2770
6 56
18.8 f 0.2
3
24.1 f 0.4 (22.2 f 0.4) -7.1 (-10.7
Doo(RuC), kcal mol-' 145.9 f 2.0'
AHOo
(selected) 23.7 f 1.9 (99.3 f 8.0)
f 0.8 f 0.5)
18.4 f 0.5 (25.2 f 0.3)' -14.7 f 0.3 -15.5 f 0.6 (-7.6 f 0.4)'
ref 6 7 8 this work
9 this work
"Thermal functions for RuC(g) based on ref 6. 'Values in parentheses obtained with thermal functions for RuC(g) used in this investigation. and third-law enthalpies of reactions 1 and 2. A comparison of the enthalpies of reactions 1 and 2 with the corresponding literature data is given in Table XIII. The present investigation is by far the most extensive equilibrium study of gaseous RuC, and the only one in which reliable second- and third-law reaction enthalpies have been measured. The importance of simultaneous second- and third-law evaluations for this molecule becomes apparent if we focus on the comparatively large difference in the second- and third-law reaction enthalpies when using the estimated literature for the thermal functions of RuC(g) and on the respective comparisons shown in Table XI11 for the thermal functions of the present investigation. The better agreement between second- and third-law enthalpies is obtained when using the thermal functions calculated in the present investigation. However, the discrepancy of 3 kcal mol-' between the second and third law values appears large in view of the very small respective standard deviations of 0.5 or 0.4 and 0.3 or 0.4 for reactions 1 and 2. The small standard deviations for the third-law values indicate the absence of systematic errors in the Gibbs energy and enthalpy functions over the temperature range. The small standard deviations for the second-law reaction enthalpies are unusual and result from the numerous data measured over a large temperature range. Several factors may contribute to the observed enthalpy difference by the application of the second and third laws of thermodynamics. These can be inaccuracies in the Gibbs energy functions or enthalpy increments, inappropriate choice of ionization cross sections in absence of generally valid rules, possible temperature dependence of ionization cross sections, or instrument factors. Assuming that such factors about equally affect the second- and the third-law enthalpy values, we base our selected value for the dissociation energy of RuC on the average of the second- and third-law enthalpies of reactions 1 and 2. The average AHDO= -9.2 f 2.0 kcal mol-' for reaction 2 combined with the dissociation energy of RhC, 137.4 kcal mol-' (ref 2) yields Doo(RuC) = 146.6 kcal mol-'. The average, moo = 23.7 f 1.9 kcal mol-' for reaction 1 combined with AHf,,[C(g)] = 169.6 0.5 kcal mol-' yields Doo (RuC) = 145.9 kcal mol-'. The average of these two values yields the selected value of Doo (RuC) as 146.3 f 2.5 kcal mol-] or 612.4 f 10.5 kJ mol-'.
*
Conclusions In the present work we have reported results of theoretical as well as of experimental investigations of the RuC molecule. The electronic structure and nature of bonding of the molecule have been elucidated through all-electron ab initio HF-CI calculations,
and the dissociation energy has been determined from high-temperature mass spectrometric equilibrium measurements. The calculational results have revealed that the RuC molecule has a 3A ground state and two low-lying excited states of ]Z+ and 'A symmetries, respectively. The observed transitions of lowest energies in the electronic spectra of the RuC molecule have been assigned as transitions between the 3A ground state and two close-lying states of symmetry 3rI and 3@. The calculations also show that the electronic structure of the low-lying electronic states of the RuC molecule can be rationalized in terms of a simple molecular orbital picture. The valence orbitals that are only partly occupied in the 3A ground state as well as in the low-lying 'A state are the almost degenerate 26 and 12u orbitals. The next higher lying orbital is the 6 n orbital which becomes populated in the 3rI and 3@ states observed in the electronic spectra. The chemical bond between the Ru and the C atoms is a triple bond composed of one u bond and two n bonds. The u bond arises from combination of the d a orbital of Ru with the su and pu of C. The a bonds make the largest contributions to the total overlap population and they are combinations of the d a on Ru with the pn on C. The 5s orbital of Ru is hardly participating in the formation of the bond. This orbital is part of a singly occupied, nonbonding orbital from which a charge donation to the 2pu orbital of C occurs. The chemical bond in the RuC molecule is polar with a total charge transfer of 0.27e from Ru to C in the 3A ground state a t the internuclear distance 3.09 au. The triple bond nature of the chemical bond of the RuC molecule revealed in our calculations is in very good agreement with the high value of the dissociation energy, Doo= 612.1 f 10.5 kJ mol-', determined from our mass spectrometric measurements.
Acknowledgment. The major part of the computations has been performed a t the Computing Service Center at Texas A&M University. The computational work in Denmark has been performed a t UNI-C, the Technical University of Denmark, and supported by the Danish Natural Science Research Council. I. S. acknowledges the Royal Danish Academy of Sciences and Letters for awarding the Niels Bohr fellowship. The work at Texas A&M University has been supported by the National Science Foundation under Grant CHE-8219476 and by the Robert A. Welch Foundation under Grant A-387. The authors also appreciate the support by a N A T O Grant RG. 85/0448 for international collaboration in research. Registry No. RuC, 12012-13-4.
