Article pubs.acs.org/JPCA
Molybdenum−Molybdenum Multiple Bonding in Homoleptic Molybdenum Carbonyls: Comparison with Their Chromium Analogues Yi Zhao,‡ Xuejun Feng,*,† Yaoming Xie,§ R. Bruce King,*,§ and H. F. Schaefer, III§ †
School of Petrochemical Engineering, Changzhou University, Changzhou 213164, P. R. China SINOPEC Research Institute of Petroleum Processing (RIPP), Beijing 100083, P. R. China § Center for Computational Chemistry and Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States ‡
S Supporting Information *
ABSTRACT: The binuclear molybdenum carbonyls Mo2(CO)n (n = 11, 10, 9, 8) have been studied by density functional theory using the BP86 and MPW1PW91 functionals. The lowest energy Mo2(CO)11 structure is a singly bridged singlet structure with a Mo− Mo single bond. This structure is essentially thermoneutral toward dissociation into Mo(CO)6 + Mo(CO)5, suggesting limited viability similar to the analogous Cr2(CO)11. The lowest energy Mo2(CO)10 structure is a doubly semibridged singlet structure with a MoMo double bond. This structure is essentially thermoneutral toward disproportionation into Mo2(CO)11 + Mo2(CO)9, suggesting limited viability. The lowest energy Mo2(CO)9 structure has three semibridging CO groups and a MoMo triple bond analogous to the lowest energy Cr2(CO)9 structure. This structure appears to be viable toward CO dissociation, disproportionation into Mo2(CO)10 + Mo2(CO)8, and fragmentation into Mo(CO)5 + Mo(CO)4 and thus appears to be a possible synthetic objective. The lowest energy Mo2(CO)8 structure has one semibridging CO group and a MoMo triple bond similar to that in the lowest energy Mo2(CO)9 structure. This differs from the lowest energy Cr2(CO)8 structure, which is a triply bridged structure. A higher energy unbridged D2d Mo2(CO)8 structure was found with a very short Mo−Mo distance of 2.6 Å. This interesting structure has two degenerate imaginary vibrational frequencies. Following the corresponding normal modes leads to a Mo2(CO)8 structure, lying ∼5 kcal/mol above the global minimum, with two four-electron donor bridging CO groups and a MoMo distance suggesting a formal double bond. All of the triplet Mo2(CO)n (n = 10, 9, 8) structures were found to be relatively high energy structures, lying at least 22 kcal/mol above the corresponding global minimum. The singlet−triplet splittings for the Mo2(CO)n (n = 10, 9, 8) structures are significantly higher than those of the Cr2(CO)n analogues. The Mo−Mo Wiberg bond indices confirm our assigned bond orders based on predicted bond distances.
1. INTRODUCTION The three homoleptic binuclear metal carbonyls Co2(CO)8, Fe2(CO)9, and Mn2(CO)10 are stable crystalline solids that have now been available commercially for a number of years (e.g., from Strem Chemical Co.). The formulas of all three of these binuclear metal carbonyls obey the 18-electron rule assuming a metal−metal single bond. the structures of all three of these metal carbonyls have been established by X-ray crystallography (Figure 1).
The next member of this series of binuclear metal carbonyls is the chromium carbonyl derivative Cr2(CO)11. However, neither this compound nor its molybdenum or tungsten analogues have been isolated. A theoretical study on Cr2(CO)11 leads to low-energy structures having either a single bridging carbonyl group or two semibridging carbonyl groups (Figure 2).1 Both of these Cr2(CO)11 structures have Cr−Cr distances suggesting the formal single bonds required to give the chromium atoms the favored 18-electron configurations. However, the lowest energy of these two Cr2(CO)11 structures, namely Cr2(μ-CO)(CO)10 (Figure 2), lies 1.7 kcal/mol higher in energy than separated Cr(CO)6 and Cr(CO)5 fragments. This accounts for the fact that Cr2(CO)11 has never been synthesized. Any reactions that might be expected to lead to Cr2(CO)11 instead give the very stable mononuclear Cr(CO)6. Simple binuclear chromium carbonyls appear to exist only if
Figure 1. Structures of the stable first-row binuclear transition-metal carbonyls.
Received: March 8, 2012 Revised: May 10, 2012 Published: May 11, 2012
© 2012 American Chemical Society
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exchange functional with the Perdew−Wang 91 gradientcorrelation functional.16 This MPW1PW91 functional has been shown to be better than the first-generation functionals for some heavy transition-metal compounds.17 The two DFT methods agree well in predicting the optimized geometries. The disparities between the two methods for most bond distances range from 0.01 to 0.04 Å. The Stuttgart double-ζ basis set with an effective core potential (ECP)18,19 was used for the molybdenum atoms. In this basis set the 28 core electrons for the molybdenum atoms are replaced by an effective core potential (ECP), and the valence basis set is contracted from (8s7p6d) primitive sets to (6s5p3d). The effective core approximation includes scalar relativistic contributions, which may become significant for the heavy transition-metal atoms. For the C and O atoms, the allelectron DZP basis sets are used. They are the Huzinaga− Dunning contracted double-ζ contraction sets20,21 plus a set of spherical harmonic d polarization functions with the orbital exponents αd(C) = 0.75 and αd(O) = 0.85. The DZP basis sets for C and O atoms may be designated as (9s5p1d/4s2p1d). Thus, for Mo2(CO)11, there are 402 contracted Gaussian functions. All of the computations were carried out with the Gaussian 03 program22 in which the default grid (75, 302) is chosen for evaluating integrals numerically. Low magnitude imaginary vibrational frequencies are known to be suspect owing to the significant limitations in the numerical integration procedures used in the DFT computations.23,24 In such cases, a finer (99, 590) grid was used to further check if the imaginary frequencies arise from numerical errors. The geometries of all structures were fully optimized using the two DFT methods independently. The harmonic vibrational frequencies were also obtained at the same levels. The corresponding infrared intensities were evaluated analytically as well. The infrared ν(CO) frequencies of the Mo2(CO)n derivatives (Table 1), which are particularly useful for characterizing metal carbonyl derivatives, were obtained using the BP86 functional, which has been found to predict ν(CO) vibrational frequencies closer to the experimental fundamental frequencies than the MPW1PW91 results.25
Figure 2. Low-energy Cr2(CO)11 structures found in the previous theoretical study.1
some of the carbonyl groups are replaced pairwise with a small bite bidentate phosphine ligand such as CH3N(PF2)2 (Figure 3). Thus, the known chromium derivative 2,3 [CH 3 N(PF2)2]3Cr2(CO)5 is formally a substitution product of Cr2(CO)11.
Figure 3. Structurally characterized pairwise substitution products of Cr2(CO)11 having three and four CH3N(PF2)2 bridges pairwise replacing carbonyl groups.
A reason for the instability of Cr2(CO)11 relative to mononuclear Cr(CO)n fragments, including the very stable Cr(CO)6, may relate to the high coordination numbers of seven and eight required for the chromium atoms in the most stable structures (Figure 2). However, the unsaturated Cr2(CO)n (n = 10, 9, 8) derivatives are also unknown experimentally, even though structures with lower chromium coordination numbers are possible. In this case, however, the chromium−chromium multiple bonds require more than one orbital from each chromium atom involved. Theoretical studies on the unsaturated Cr2(CO)n structures4 predict a doubly bridged structure5 for Cr2(CO)10 and triply bridged structures with formal CrCr triple bonds6,7 for Cr2(CO)9 and Cr2(CO)8. Because of the need for relatively high metal coordination numbers in the M2(CO)11 structures (Figure 2), the heavier congeners of chromium, namely molybdenum and tungsten, might be expected to form M2(CO)11 derivatives that are more favorable with respect to fragmentation into M(CO)6 and M(CO)5. Such considerations suggested a theoretical study of the molybdenum derivatives Mo2(CO)n (n = 11, 10, 9, 8) for comparison with the Cr2(CO)n derivatives reported in the previous papers.1,4−7 The results from this investigation are discussed in the present paper.
3. DISCUSSION 3.1. Mo2(CO)11. Two energetically low-lying structures were found for Mo2(CO)11 (Figure 4 and Table 2), namely, the singlet Cs structure 11S-1, and the singlet C2v structure 11S-2. The Cs singly bridged Mo2(CO)11 structure 11S-1 is the global minimum with all real vibrational frequencies. It has one bridging CO group and 10 terminal CO groups. The Mo−Mo bond distance for 11S-1 of 3.343 Å (BP86) or 3.305 Å (MPW1PW91) is close to the experimental value of the Mo− Mo single bond distance of 3.235 Å in (η5-C5H5)2Mo2(CO)6, determined by X-ray crystallography.26 We thus interpret the Mo−Mo bond in the Mo2(CO)11 structure 11S-1 to be the formal single bond required to give both molybdenum atoms the favored 18-electron configuration. The second Mo2(CO)11 structure 11S-2 has C2v symmetry and two semibridging carbonyl groups and is predicted to lie only 0.6 kcal/mol (MPW1PW91) or 1.2 kcal/mol (BP86) in energy above 11S-1 (Figure 4 and Table 2). Structure 11S-2 has one small imaginary vibrational frequency, namely 26i cm−1 (MPW1PW91) or 37i cm−1 (BP86). This imaginary vibrational frequency is not removed using the finer (99, 590) integration grid. Following the corresponding normal mode leads to the
2. THEORETICAL METHODS Density functional theory (DFT) appears to be a powerful and effective computational tool to study organotransition metal chemistry.8−14 In this connection, two different density functional theory (DFT) methods were used in the present study. The first DFT method is the BP86 method, which uses Becke’s 1988 exchange functional (B) with Perdew’s 1986 gradient corrected correlation functional (P86).15 The second DFT method is a newer generation functional, MPW1PW91, which is a combination of the modified Perdew−Wang 5699
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Table 1. Carbonyl ν(CO) Frequencies (in cm−1) Predicted by the BP86 Method for the Mo2(CO)n (n = 11, 10, 9, 8) Structures structure 11S-1 (Cs) 11S-2 (C2v)
10S-1 (C2h) 10S-2 (C2) 10T-3 (C2) 10T-4 (C2h) 9S-1 (Cs) 9S-2 (C3v) 9S-3 (Cs) 9T-4 (Cs) 8S-1 (C1) 8S-2 (C2h) 8S-3 (D2d) 8T-4 (C2) 8T-5 (D2d)
Table 2. Bond Distances (in Å), Total Energies (E, in hartree), Relative Energies (ΔE, in kcal/mol), LUMO− HOMO Gaps (in eV), and Numbers of Imaginary Vibrational Frequencies (Nimg) for the Mo2(CO)11 Structures
carbonyl ν(CO) frequenciesa Mo2(CO)11 1853 (198),b 1959 (449), 1962 (34), 1972 (762), 1984 (430), 1988 (2783), 1988 (2224), 1997 (22), 2003 (188), 2048 (1232), 2086 (7) 1932 (43), 1941 (272), 1957 (751), 1960 (445), 1975 (2097), 1990 (0), 1991 (2428), 2001 (573), 2004 (549), 2049 (1093), 2086 (61) Mo2(CO)10 1904 (0), 1926 (1294), 1950 (0), 1967 (0), 1969 (1474), 1983 (2725), 1988 (1003), 1994 (0), 2043 (1213), 2076 (0) 1915 (102), 1920 (210), 1936 (1037), 1949 (1191), 1952 (462), 1992 (2056), 2001 (638), 2005 (528), 2023 (1271), 2079 (224) 1921 (26), 1933 (460), 1961 (221), 1968 (6), 1971 (2315), 1978 (366), 1982 (1104), 1986 (1404), 2008 (2644), 2071 (1) 1894 (0), 1903 (562), 1960 (0), 1970 (0), 1972 (1806), 1975 (554), 1986 (2542), 1987 (0), 2010 (2947), 2070 (0) Mo2(CO)9 1923 (207), 1939 (191), 1941 (834), 1953 (1711), 1967 (332), 1976 (1537), 1993 (554), 2016 (2016), 2063 (89) 1902 (17), 1907 (280), 1907 (280), 1947 (1261), 1947 (1261), 2000 (2336), 2007 (696), 2007 (696), 2067 (486) 1770 (310), 1827 (583), 1944 (1), 1965 (1250), 1970 (555), 1976 (2825), 1980 (434), 2023 (1208), 2064 (77) 1923 (207), 1939 (190), 1941 (834), 1953 (1711), 1967 (333), 1976 (1536), 1993 (554), 2016 (2016), 2063 (89) Mo2(CO)8 1897 (231), 1910 (779), 1919 (536), 1945 (1235), 1962 (258), 1968 (1504), 2001 (2381), 2043 (35) 1775 (0), 1787 (859), 1937 (0), 1943 (1706), 1947 (0), 1969 (2862), 2015 (983), 2048 (0) 1930 (415), 1930 (415), 1956 (0), 1957 (1344), 1962 (2124), 1962 (2124), 2009 (1277), 2048 (0) 1858 (147), 1867 (618), 1937 (71), 1957 (1051), 1961 (1927), 1964 (318), 1993 (2782), 2035 (37) 1934 (8), 1934 (8), 1953 (0), 1954 (723), 1957 (2413), 1957 (2413), 1989 (1640), 2039 (0)
method BP86
MPW1PW91
parameter
11S-1 (Cs)
11S-2 (C2v)
E ΔE LUMO−HOMO Nimg Mo−Mo E ΔE LUMO−HOMO Nimg Mo−Mo
−1383.788 12 0.0 2.5 0 3.343 −1383.233 73 0.0 4.1 0 3.305
−1383.786 51 1.2 2.5 1(37i) 3.427 −1383.232 94 0.6 4.1 1(26i) 3.393
Figure 5. Four optimized Mo2(CO)10 structures. Distances are in angstroms.
a
Infrared intensities (km/mol) are given in parentheses. bThe bridging carbonyl ν(CO) frequencies are listed in bold.
structure 11S-1. This suggests the formal double bond required to give both molybdenum atoms in 10S-1 the favored 18electron configuration. No relevant experimental examples of MoMo double bonded species appear to have been characterized structurally. The Mo2(CO)10 structure 10S-2 with C2 symmetry lies 6.3 kcal/mol in energy above 10S-1 (Figure 5 and Table 3). Structure 10S-2 has a significant imaginary vibrational frequency of 116i cm−1 (BP86) or 78i cm−1 (MPW1PW91). This imaginary vibrational frequency is not removed using the finer (99, 590) integration grid. Following the corresponding normal mode leads to 10S-1. The MoMo distance in 10S-2 of 2.979 Å (BP86) or 3.047 Å (MPW1PW91) can also be considered as a formal double bond to give both Mo atoms the 18-electron configurations. The triplet Mo2(CO)10 structures lie at significantly higher energies than the lowest energy singlet structures. Thus, the C2 unbridged triplet structure 10T-3 lies 22.6 kcal/mol (BP86) or 23.2 kcal/mol (MPW1PW91) above 10S-1 (Figure 5 and Table 3). The MoMo distance for this triplet structure is 2.947 Å (BP86) or 2.910 Å (MPW1PW91), suggesting a formal double bond to give each Mo atom the favored 18-electron configuration. The two unpaired electrons for the triplet spin state of 10T-3 reside in this MoMo double bond, which is a
Figure 4. Two optimized Mo2(CO)11 structures. Distances are in angstroms.
global minimum 11S-1. The Mo−Mo single bond distance in 11S-2 of 3.427 Å (BP86) or 3.393 Å (MPW1PW91) is slightly longer than that in 11S-1. 3.2. Mo2(CO)10. Four structures are found for Mo2(CO)10 (Figure 5 and Table 3). The global minimum 10S-1 of Mo2(CO)10 is a C2h singlet structure with two semibridging carbonyl groups. For these semibridging CO groups the short Mo−C distances are 2.064 Å (BP86) or 2.052 Å (MPW1PW91) and the long Mo−C distances are 2.642 Å (BP86) and 2.671 Å (MPW1PW91). The MoMo distance of 3.046 Å (BP86) or 3.012 Å (MPW1PW91) in 10S-1 is ∼0.3 Å shorter than the Mo−Mo single bond in the Mo2(CO)11 5700
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Table 3. Bond Distances (in Å), Total Energies (E, in hartree), Relative Energies (ΔE, in kcal/mol), LUMO−HOMO Gaps (in eV), and Numbers of Imaginary Vibrational Frequencies (Nimg) for the Mo2(CO)10 Structures method BP86
MPW1PW91
parameter
10S-1 (C2h)
10S-2 (C2)
10T-3 (C2)
10T-4 (C2h)
E ΔE LUMO−HOMO Nimg Mo−Mo E ΔE LUMO−HOMO Nimg Mo−Mo
−1270.414 71 0.0 1.3 0 3.046 −1269.892 90 0.0 2.8 0 3.012
−1270.404 74 6.3 1.5 1(116i) 2.979 −1269.882 71 6.3 3.0 1(78i) 3.047
−1270.378 77 22.6 2.2 0 2.947 −1269.856 39 23.2 3.8 0 2.910
−1270.377 86 23.2 1.7 0 2.930 −1269.854 57 23.8 3.4 1(19i) 2.908
σ + 2/2π bond, similar to that in dioxygen or the organometallic27−29 (η5-C5H5)2Fe2(μ-CO)3. Such a double bond consists of two one-electron orthogonal π “half-bonds” containing the unpaired electrons. Another triplet Mo2(CO)10 structure 10T-4 with C2h symmetry lies 23.2 kcal/mol (BP86) or 23.8 kcal/mol (MPW1PW91) above 10S-1 (Figure 5 and Table 3). Structure 10T-4 has two semibridging carbonyl groups. The MoMo distance in 10T-4 of 2.930 Å (BP86) or 2.908 Å (MPW1PW91), while slightly shorter than that in 10T-3, still can correspond to a MoMo double bond to give each Mo atom favored 18-electron configurations. As in 10T-3, the two unpaired electrons in 10T-4 reside in the two π half-bonds of a σ + 2/2π type double bond. 3.3. Mo2(CO)9. Three singlet and one triplet Mo2(CO)9 structures are found (Figure 6 and Table 4). The Cs singlet
MoMo triple bond distance of 2.448 Å in (η 5 C5H5)2Mo2(CO)4, determined by X-ray crystallography.30 The C3v singlet Mo2(CO)9 structure 9S-2 lies 2.7 kcal/mol (BP86) or 4.6 kcal/mol (MPW1PW91) in energy above 9S-1 (Figure 6 and Table 4). Structure 9S-2 is a genuine minimum with no imaginary vibrational frequencies. Like 9S-1, structure 9S-2 has three semibridging CO groups. However, unlike 9S-1, all three semibridging CO groups in 9S-2 have their short Mo− C bonds to the same molybdenum atom. The MoMo distance in 9S-2 is 2.698 Å (BP86) or 2.692 Å (MPW1PW91) and is similar to that in 9S-1 and can likewise correspond to the formal triple bond required to give each Mo atom the favored 18-electron configuration. A third singlet Mo2(CO)9 minimum 9S-3 lies 8.6 kcal/mol (BP86) or 8.9 kcal/mol (MPW1PW91) above 9S-1 (Figure 6 and Table 4). Structure 9S-3 is found to have one normal twoelectron donor bridging carbonyl and one four-electron donor bridging η2-μ-CO carbonyl. The latter is characterized by a short Mo−O distance of ∼2.5 Å and a very low ν(CO) frequency of 1770 cm−1 (Table 1). The MoMo distance of 3.101 Å (BP86) or 3.074 Å (MPW1PW91) in 9S-3 is longer than those in 9S-1 and 9S-2. This suggests the formal double bond to give each Mo atom the favored 18-electron configuration in a Mo2(CO)9 structure with one four-electron donor bridging group. The lowest energy triplet Mo2(CO)9 structure 9T-4 is a high-energy structure, lying 28.9 kcal/mol above the global minimum 9S-1. Like structures 9S-1 and 9S-2, structure 9T-4 has three semibridging CO groups. The MoMo distance of 2.752 Å (BP86) or 2.742 Å (MPW1PW91) in 9T-4 is ∼0.1 Å longer than the MoMo distances in 9S-1 and 9S-2. It can be interpreted as a strong formal double bond, thereby giving each molybdenum atom in 9T-4 the 17-electron configuration for a binuclear triplet. 3.4. Mo2(CO)8. Five low-lying structures (three singlets and two triplets) are found for Mo2(CO)8 (Figure 7 and Table 5). The global minimum 8S-1 has a semibridging CO group exhibiting a relatively low ν(CO) frequency of 1897 cm−1 (Table 1), as well as seven terminal CO groups. The MoMo distance of 2.670 Å (BP86) or 2.675 Å (MPW1PW91) in 8S-1 is very close to that in 9S-1 and 9S-2 and likewise can be interpreted as a formal triple bond. This gives one of the Mo atoms in 8S-1 the favored 18-electron configuration but the other Mo atom only a 16-electron configuration. The Mo atom in 8S-1 with the 16-electron configuration is probably the “left” Mo atom in Figure 7, since it appears to have a gap in its coordination sphere.
Figure 6. Four optimized Mo2(CO)9 structures. Distances are in angstroms.
structure 9S-1, with three semibridging CO groups and six terminal CO groups, is the global minimum. For the semibridging CO groups, two have their short Mo−C bonds to one molybdenum atom, whereas the third has its short Mo− C bond to the other molybdenum atom. The MoMo distance of 2.641 Å in 9S-1, predicted by both the BP86 and MPW1PW91 methods, is ∼0.4 Å shorter than the MoMo double bond distance in 10S-1. This suggests a formal triple bond in 9S-1, thereby giving each Mo atom the favored 18electron configuration. However, this presumed MoMo triple bond in 9S-1 is ∼0.2 Å longer than the experimental 5701
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Table 4. Bond Distances (in Å), Total Energies (E, in hartree), Relative Energies (ΔE, in kcal/mol), LUMO−HOMO Gaps (in eV), and Number of Imaginary Vibrational Frequencies (Nimg) for the Mo2(CO)9 Structures method BP86
MPW1PW91
parameter
9S-1 (Cs)
9S-2 (C3v)
9S-3 (Cs)
9T-4 (Cs)
E ΔE LUMO−HOMO Nimg Mo−Mo E ΔE LUMO−HOMO Nimg Mo−Mo
−1157.042 20 0.0 0.7 0 2.641 −1156.553 33 0.0 3.2 0 2.641
−1157.037 87 2.7 2.1 0 2.698 −1156.545 91 4.6 3.8 0 2.692
−1157.028 49 8.6 1.6 0 3.101 −1156.539 14 8.9 3.3 0 3.074
−1156.995 85 28.9 0.7 0 2.752 −1156.507 08 28.9 2.3 0 2.742
The C2h singlet Mo2(CO)8 structure 8S-2 lies 5.4 kcal/mol (BP86) or 3.9 kcal/mol (MPW1PW91) above 8S-1 (Figure 7 and Table 5). Structure 8S-2 has two four-electron donor bridging carbonyls, as indicated by the short Mo−O distances of 2.741 Å (BP86) and two very low ν(CO) frequencies at 1775 and 1787 cm−1 (BP86). The MPW1PW91 method predicts somewhat longer 3.073 Å Mo−O distances to these carbonyl groups. The MoMo distance of 3.148 Å (BP86) or 3.004 Å (MPW1PW91) in 8S-2 is ∼0.4 Å longer than that of the MoMo triple bond in 8S-1 and close to that of the Mo Mo double bond in 10S-1. This suggests a formal double bond, thereby giving each Mo atom the favored 18-electron configuration in a Mo2(CO)8 structure with two four-electron donor bridging CO groups. Another singlet Mo2(CO)8 structure 8S-3 has an even higher energy, lying 16.4 kcal/mol (BP86) or 19.3 kcal/mol (MPW1PW91) above 8S-1 (Figure 7 and Table 5). Structure 8S-3 has relatively high symmetry (D2d) and only terminal CO groups. The Mo Mo distance in 8S-3 of 2.615 Å (BP86) or 2.605 Å (MPW1PW91) suggests a formal quadruple bond to give each molybdenum atom the favored 18-electron configuration. Both BP86 and MPW1PW91 methods predict a pair of small imaginary vibrational frequencies (11i or 22i cm−1, respectively), which are not removed using the finer integration grid. By following the corresponding normal modes, the D2d structure 8S-3 collapses to the C2h structure 8S-2. In this collapse two of the terminal carbonyl groups in 8S-3 become four-electron donor bridging η2-μ-CO groups and the Mo−Mo distance lengthens from the presumed quadruple bond distance of ∼2.6 Å to the double bond distance of ∼3.1 Å. The lowest lying triplet Mo2(CO)8 structures have energies significantly above the lowest lying singlet structures, as was also found for Mo2(CO)9 and Mo2(CO)10 discussed above
Figure 7. Five optimized Mo2(CO)8 structures. Distances are in angstroms.
Table 5. Bond Distances (in Å), Total Energies (E, in hartree), Relative Energies (ΔE, in kcal/mol), LUMO−HOMO Gaps (in eV), and Number of Imaginary Vibrational Frequencies (Nimg) for the Mo2(CO)8 Structures method BP86
MPW1 PW91
parameter
8S-1 (C1)
8S-2 (C2h)
8S-3 (D2d)
8T-4 (C2)
8T-5 (D2d)
E ΔE LUMO−HOMO Nimg Mo−Mo E ΔE LUMO−HOMO Nimg Mo−Mo
−1043.648 90 0.0 1.3 0 2.670 −1043.19334 0.0 2.9 0 2.675
−1043.631 15 5.4 1.2 1(28i) 3.148 −1043.17692 3.9 2.7 0 3.004
−1043.622 78 16.4 0.6 2(11i,11i) 2.615 −1043.16251 19.3 1.8 2(22i,22i) 2.605
−1043.613 76 22.0 0.9 0 2.672 −1043.15389 24.5 2.3 0 2.630
−1043.606 61 26.4 0.5 0 2.571 −1043.14763 28.9 2.0 0 2.569
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to give Mo2(CO)9 (9S-1) is similar at 26.3 kcal/mol (BP86) or 26.1 kcal/mol (MPW1PW91). The carbonyl dissociation energy of Mo2(CO)9 (9S-1) to give Mo2(CO)8 (8S-1) is even higher at 39.7 kcal/mol (BP86) or 39.0 kcal/mol (MPW1PW91). Table 6 also shows the energies for disproportionation reactions of the type Mo 2 (CO) n → Mo 2 (CO) n+1 + Mo2(CO)n‑1. The disproportionation of Mo2(CO)10 into Mo2(CO)11 + Mo2(CO)9 is essentially thermoneutral at −0.5 kcal/mol (BP86) or −0.6 kcal/mol (MPW1PW91). On this thermodynamic criterion, Mo2(CO)10 would not appear to be a promising synthetic objective. On the other hand, the disproportionation of Mo2(CO)9 to Mo2(CO)10 + Mo2(CO)8 requires 13.3 kcal/mol (BP86) or 13.0 kcal/mol (MPW1PW91), indicating that Mo2(CO)9 is favored toward such disproportionation. The energies for dissociation of Mo2(CO)n (n = 11, 10, 9, 8) into mononuclear fragments, i.e., reactions of the type Mo2(CO)n → Mo(CO)p + Mo(CO)q, where n = p + q, were also determined (Table 6). In order to obtain such data, the structures for the mononuclear Mo(CO)m (m = 6, 5, 4) were optimized by the same DFT methods used for the binuclear Mo2(CO)n derivatives. The binuclear chromium carbonyl Cr2(CO)11 was previously predicted to be disfavored with respect to dissociation into Cr(CO)6 + Cr(CO)5 fragments.1 An analogous dissociation of Mo 2 (CO)11 into Mo(CO) 6 + Mo(CO) 5 is essentially thermoneutral at 1.1 kcal/mol (BP86) or 1.4 kcal/mol (MPW1PW91), suggesting only marginal viability for Mo2(CO)11 (Table 6). This demonstrates that simply increasing the size of the central metal atom from chromium to molybdenum is not enough to stabilize the corresponding M2(CO)11 derivative. This is consistent with fact that none of the homoleptic M2(CO)11 (M = Cr, Mo, W) have been synthesized. The energies for the dissociation of the unsaturated binuclear molybdenum carbonyls Mo2(CO)n (n = 10, 9, 8) into mononuclear fragments increase with decreasing number of carbonyl groups. Thus, Mo2(CO)9 and Mo2(CO)8 lie much lower energetically than the analogous fragments with very large predicted fragmentation energies of ∼56 and ∼83 kcal/ mol, respectively (Table 6). The free energy changes ΔG are also listed in Table 6, and most of them are comparable with the corresponding ΔE values. 3.6. Natural Atomic Charges and Wiberg Bond Indices. Table 7 lists the natural charges on the molybdenum atoms and the Wiberg bond indices for the Mo−Mo bonds in the singlet Mo2(CO)n (n = 11, 10, 9, 8) structures using natural bond orbital (NBO) analyses.33 The natural charges on the Mo atoms become more negative as the number of carbonyl groups on the Mo atoms is increased by up to −1.1 (BP86) or −1.2 (MPW1PW91) in the Mo2(CO)11 structure 11S-1, in which each Mo atom is bonded to five terminal CO groups and one bridging CO group. This suggests that the π back-bonding from the filled Mo d orbitals to the CO ligand antibonding π* orbitals is not enough to remove all of the negative charge on the metal atom arising from the σ forward bonding. Previous studies on the Wiberg bond indices (WBIs) in metal−metal bonded derivatives suggest typical values of 0.2− 0.3 for unbridged formal metal−metal single bonds.34 The WBIs for the lowest energy Mo2(CO)n (n = 11, 10, 9, 8) structures (Table 7) are even lower for a given Mo−Mo formal bond order, possibly because the bridging CO groups in all of
(Figure 7 and Table 5). Thus, the triplet structure 8T-4 lies 22.0 kcal/mol (BP86) or 24.5 kcal/mol (MPW1PW91) above 8S-1. Structure 8T-4 has two bridging carbonyls exhibiting ν(CO) frequencies (BP86) of 1858 and 1867 cm−1 (Table 1), which, as expected, are significantly lower than the terminal ν(CO) frequencies. The MoMo distance in 8T-4 of 2.672 Å (BP86) or 2.630 Å (MPW1PW91) is very similar to that of the MoMo triple bonds in 8S-1, 9S-1, and 9S-2. Formulating 8T-4 with a MoMo triple bond leads to 17-electron configurations for both molybdenum atoms, consistent with a binuclear triplet. Another triplet Mo2(CO)8 structure 8T-5 has an even higher energy, lying 26.4 kcal/mol (BP86) or 28.9 kcal/mol (MPW1PW91) above 8S-1 (Figure 7 and Table 5). All eight CO groups in 8T-5 are terminal CO groups. Structure 8T-5 has D2d symmetry similar to the singlet structure 8S-3. The Mo Mo distance in 8T-5 of 2.571 Å (BP86) or 2.569 Å (MPW1PW91) is even shorter than that in 8S-3 and can likewise be interpreted as the formal quadruple bond required to give each molybdenum atom the favored 18-electron configuration. The triplet spin multiplicity in 8T-5 arises from its Mo Mo quadruple bond being of the σ + 2π + 2/2δ type with two single-electron δ half-bonds each containing an unpaired electron. A similar type of Fe Fe quadruple bond was postulated some years ago in the lowest energy triplet (η5C5H5)2Fe2(μ-CO) structure found by density functional theory.31 3.5. Dissociation Energies. Table 6 lists the predicted energies for loss of a carbonyl ligand from the binuclear Table 6. Energies and Free Energies (kcal/mol) for Carbonyl Dissociation and Disproportionation of Mo2(CO)n Derivatives after Zero-Point Vibrational Energy (ZPVE) Corrections BP86 Mo2(CO)11 (11S-1) → Mo2(CO)10 (10S1) + CO Mo2(CO)10 (10S-1) → Mo2(CO)9 (9S-1) + CO Mo2(CO)9 (9S-1) → Mo2(CO)8 (8S-1) + CO 2Mo2(CO)10 (10S-1) → Mo2(CO)9 (9S1) + Mo2(CO)11 (11S-1) 2Mo2(CO)9 (9S-1) → Mo2(CO)8 (8S-1) + Mo2(CO)10 (10S-1) Mo2(CO)11 (11S-1) → Mo(CO)6 + Mo(CO)5 Mo2(CO)10 (10S-1) → Mo(CO)6 + Mo(CO)4 Mo2(CO)10 (10S-1) → 2Mo(CO)5 Mo2(CO)9 (9S-1) → Mo(CO)5 + Mo(CO)4 Mo2(CO)8 (8S-1) → 2Mo(CO)4
MPW1PW91
ΔE
ΔG
ΔE
ΔG
26.9
16.8
26.7
16.3
26.3
15.6
26.1
16.1
39.7
30.7
39.0
28.8
−0.5
−1.1
−0.6
−0.2
13.3
14.9
13.0
12.7
1.1
−11.2
1.4
−11.1
42.5
30.3
39.5
27.3
15.9 57.8
4.7 47.3
15.9 54.6
4.7 43.3
86.4
75.1
80.4
69.2
molybdenum carbonyl derivatives Mo2(CO)n (n = 11, 10, 9) considering the lowest energy structures. The carbonyl dissociation energy from Mo 2(CO)11 (11S-1) to give Mo2(CO)10 (10S-1) and CO is substantial at 26.9 kcal/mol (BP86) or 26.7 kcal/mol (MPW1PW91) and similar to the experimental dissociation energies for Ni(CO)4, Fe(CO)5, and Cr(CO)6 of 27, 41, and 37 kcal/mol, respectively.32 This suggests that Mo2(CO)11 is a viable species at least toward carbonyl loss. The carbonyl dissociation of Mo2(CO)10 (10S-1) 5703
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Mo2(CO)8 Structure 8S-3. The molybdenum−molybdenum interaction in the unbridged Mo2(CO)8 structure 8S-3 (Figure 7 and Table 5) is characterized by an unusual short distance of 2.6 Å and high WBI of 1.2. This suggests the formal Mo Mo quadruple bond required to give both molybdenum atoms the favored 18-electron configuration. In order to get more evidence for this interesting formal quadruple bond the frontier molecular orbitals (MOs) of this Mo2(CO)8 structure were examined (Figure 8).
Table 7. Wiberg Bond Indices (WBI) for Mo−Mo Bond and Natural Charges on the Molybdenum Atoms for the Singlet Mo2(CO)n (n = 11, 10, 9, 8) Structures WBI of Mo− Mo bond
Mo− Mo bond distance
Mo− Mo bond order
BP86
0.07
3.343
1
CO
MPW1PW91
0.07
3.305
1
CO
BP86
0.14
3.427
1
MPW1PW91
0.15
3.393
1
BP86
0.13
3.046
2
MPW1PW91
0.14
3.012
2
BP86
0.26
2.979
2
MPW1PW91
0.24
3.047
2
BP86
0.33
2.641
3
MPW1PW91
0.32
2.641
3
BP86
0.47
2.698
3
MPW1PW91
0.45
2.692
3
BP86
0.22
3.101
2
MPW1PW91
0.22
3.074
2
BP86
0.34
2.670
3
2 semi CO 2 semi CO 2 semi CO 2 semi CO 2 semi CO 2 semi CO 3 semi CO 3 semi CO 3 semi CO 3 semi CO CO + η4-CO CO + η4-CO semi CO
MPW1PW91
0.32
2.675
3
semi CO
BP86
0.27
3.148
2
2 η4-CO
MPW1PW91
0.29
3.004
2
2 η4-CO
BP86
1.24
2.615
4
none
MPW1PW91
1.22
2.605
4
none
method 11S-1
11S-2
10S-1
10S-2
9S-1
9S-2
9S-3
8S-1
8S-2
8S-3
bridging groups
natural charges on Mo −1.097, −1.058 −1.206, −1.256 −2.158, −1.862 −2.281, −1.981 −0.977, −0.977 −1.066, −1.066 −1.498, −2.145 −1.541, −2.287 −0.934, −0.838 −1.051, −0.856 −1.111, −2.095 −1.147, −2.241 −1.236, −1.656 −1.311, −1.751 −0.705, −0.533 −0.723, −0.597 −1.037, −1.037 −1.081, −1.081 −1.188, −1.188 −1.258, −1.258
Figure 8. The frontier bonding molecular orbitals in the unbridged Mo2(CO)8 structure 8S-3 (Figure 7).
The bonding MOs from HOMO−2 down to HOMO−5 for 8S-3 correspond to the expected δ component, two orthogonal π components, and the σ component of a Mo Mo quadruple bond (Figure 8). However, the HOMO and HOMO−1 bonding MOs correspond to σ* antibonding and δ* antibonding components of the molybdenum−molybdenum interaction. These cancel out the σ and δ components of the presumed Mo Mo quadruple bond in the Mo2(CO)8 structure 8S-3, leaving only the two orthogonal π components for the molybdenum−molybdenum interactions. Thus the MoMo interaction in the Mo2(CO)8 structure 8S-3 appears not to be a true quadruple bond but instead an unusual double bond consisting only of two orthogonal π components. This is similar to the apparent Fe Fe quadruple bond in the unbridged Fe2(CO)6 structure with a predicted short iron−iron distance of 2.00 Å, which also appears really to be a pure π double bond consisting only of the two orthogonal π components.37 Such purely π double bonds clearly differ from the usual σ + π double bond found in familiar species such as ethylene. Purely π metal−metal double bonds, such as those in the unbridged Fe2(CO)6 and Mo2(CO)8 structures, appear to be unusually
these structures weaken the Mo−Mo bonds by multicenter bonding. This may relate to the difficulty in finding evidence for a direct iron−iron bond in Fe2(CO)9, which has a triply bridged Fe2(CO)6(μ-CO)3 structure.35 For Fe2(CO)6(μ-CO)3 an analysis of the domain-averaged Fermi holes suggests the presence of a three-center two-electron Fe2C bond rather than a direct Fe−Fe bond in the central Fe2(μ-CO)3 unit.36 For the binuclear molybdenum carbonyls Mo2(CO)n, the WBIs follow a consistent pattern with values of 0.07−0.15 for the Mo−Mo single bonds in the Mo2(CO)11 structures, 0.13−0.29 for Mo Mo double bonds, and 0.32−0.47 for the MoMo triple bonds in Mo2(CO)9 and Mo2(CO)8 structures. The essentially identical WBIs of ∼0.33 for the lowest energy structures of Mo2(CO)9 (9S-1) and Mo2(CO)8 (8S-1) supports the suggestion of a MoMo triple bond in the latter species, in accord with the MoMo bond distance. For the presumed Mo Mo quadruple bond in 8S-3 the WBI has the much higher value of 1.2. 3.7. Frontier Molecular Orbital Analysis of the Presumed Mo Mo Quadruple Bond in the Unbridged 5704
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into Mo2(CO)10 + Mo2(CO)8, which requires ∼13 kcal/mol. However, the synthesis of Mo2(CO)9 cannot involve unstable Mo2(CO)11 or Mo2(CO)10 as an intermediate. The best prospect for synthesizing Mo2(CO)9 involves finding a way to combine the very stable Mo(CO)6 with a reactive Mo(CO)3 fragment or combining reactive Mo(CO)5 and Mo(CO)4 fragments. Some interesting higher energy Mo2(CO)9 structures were discovered of types that have not yet been found for Cr2(CO)9 (Figure 6).6 The Mo2(CO)9 structure 9S-3 has a four-electron donor bridging η2-μ-CO group and a MoMo distance of ∼3.1 Å, corresponding to the formal double bond required to give each Mo atom the favored 18-electron configuration. The lowest energy triplet Mo2(CO)9 structure 9T-4 lies ∼29 kcal/ mol above the lowest energy structure 9S-1. This is another example of the large singlet−triplet splitting in the second row transition metal molybdenum. The highly unsaturated Mo2(CO)8 requires a formal Mo Mo quadruple bond for each Mo atom to have the favored 18-electron configuration. However, the lowest energy Mo2(CO)8 structure 8S-1 (Figure 7) was found to have a MoMo distance and WBI similar to the MoMo triple bond in the lowest energy Mo2(CO)9 structures. Thus, in 8S-1 only one of the Mo atoms has the favored 18-electron configuration; the other Mo atom can have only a 16-electron configuration. Structure 8S-1 has only a single semibridging CO group; the other seven CO groups are all terminal CO groups. This differs from the lowest energy Cr2 (CO) 8 structure,7 which is a triply bridged structure derived from the Cr2(CO)9 structure by removal of one of the terminal CO groups. A singlet D2d Mo2(CO)8 structure 8S-3, lying ∼18 kcal/mol above 8S-1, is found having Mo−Mo distances short enough (∼2.6 Å) to suggest the formal quadruple bond required to give each molybdenum atom in 8S-3 the favored 18-electron configuration. However, analysis of the frontier molecular orbitals of 8S-3 suggests that the molybdenum−molybdenum interaction is not a true σ + 2π + δ quadruple bond but instead a pure π MoMo double bond, consisting only of the two orthogonal π components. Structure 8S-3 has a pair of small imaginary vibrational frequencies. Following the corresponding normal modes leads to a C2h structure, 8S-2. Structure 8S-2, lying ∼5 kcal/mol above 8S-1, has two four-electron donor η2μ-CO groups and a MoMo distance of ∼3.1 Å, suggesting a formal double bond (Figure 7). A similar Cr2(CO)8 structure was found but at a higher energy (∼16 kcal/mol) above the global minimum.7 This may imply that Mo is a more oxophilic metal than Cr and thus more likely to form structures with four-electron donor bridging η2-μ-CO carbonyl groups in unsaturated metal carbonyl derivatives. The triplet Mo2(CO)8 structures (8T-4 and 8T-5 in Figure 7) are high-energy structures, lying more than 22 kcal/mol above the lowest energy singlet structures.
short and strong because the metal−metal distances can then be optimal for π bonding rather than a compromise between the optimum distances for σ and π bonding in the usual σ + π type of double bond. They can therefore masquerade for formal quadruple bonds. A similar frontier MO analysis of the niobium−niobium bonding in unbridged Nb2(CO)9 and Nb2(CO)8 structures with unusually short NbNb distances suggests σ + 2π triple bonding in these species rather than the formal quadruple and quintuple bonds, respectively, suggested by the 18-electron rule, short Nb−Nb distances, and relatively high WBI values.38
4. DISCUSSION The lowest energy structure for Mo2(CO)11, namely 11S-1 (Figure 4), is a singly bridged structure similar to the lowest energy Cr2(CO)11 structure.1 The dissociation energy of 11S-1 into Mo(CO)6 + Mo(CO)5 is essentially thermoneutral, requiring only ∼1 kcal/mol. This is an improvement over the dissociation of the corresponding Cr2(CO)11, which is exothermic by 5−13 kcal/mol, depending on the synthetic method. This appears to be an effect of the larger size of the Mo atom relative to Cr. Thus, Mo can more readily accommodate seven bonds in an M2(CO)10(μ-CO) structure than the smaller Cr atom. However, the essentially thermoneutral dissociation of Mo2(CO)11 into Mo(CO)6 and Mo(CO)5 makes it an unpromising synthetic objective. The lowest energy Mo2(CO)10 structure 10S-1 has two semibridging CO groups and a MoMo distance of ∼3.0 Å, corresponding to the formal double bond required to give both Mo atoms the favored 18-electron configuration (Figure 5). An analogous doubly semibridged structure was found to be the lowest energy structure for Cr2(CO)10 in previous work.5 The Mo2(CO)10 structure, unlike Mo2(CO)11, is clearly favored with respect to dissociation into two Mo(CO)5, requiring an energy of ∼16 kcal/mol. However, its disproportionation into Mo2(CO)11 + Mo2(CO)9 is essentially thermoneutral, likewise making Mo2(CO)10 an unpromising synthetic objective. The study of Cr2(CO)10 led to the discovery of both unbridged and doubly semibridged triplet structures, lying ∼10 kcal/mol above the singlet global minimum singlet structure.5 A similar pair of triplet structures 10T-3 and 10T-4 (Figure 5) was found for Mo2(CO)10, but at significantly higher energies, namely, ∼23 kcal/mol above the singlet global minimum. This larger singlet−triplet splitting for Mo2(CO)10 relative to Cr2(CO)10 can be related to the larger ligand field splittings of the heavier transition metals relative to their lighter congeners. The two lowest energy Mo2(CO)9 structures, 9S-1 and 9S-2 (Figure 6), lying within 5 kcal/mol, both have three semibridging CO groups. The MoMo distances of ∼2.6 Å in 9S-1 and 9S-2 correspond to the formal triple bonds required to give each Mo atom the favored 18-electron configuration. An analogous structure was previously found6 for Cr2(CO)9. Structures 9S-1 and 9S-2 differ only in the distribution of the three semibridging CO groups between the central MoMo unit relative to their short and long Mo− C bonds. Thermochemistry indicates that Mo2(CO)9, if it can be synthesized, may be a stable molecule. Thus, the loss of a CO group from Mo2(CO)9 to give Mo2(CO)8 requires ∼39 kcal/ mol, which is comparable to the 41 kcal/mol experimental CO dissociation energy of the stable Fe(CO) 5 (Table 6). Furthermore, Mo2(CO)9 is stable toward disproportionation
5. SUMMARY The lowest lying Mo2(CO)11 structure is a singly bridged singlet structure with a Mo−Mo single bond. This structure is essentially thermoneutral toward dissociation into Mo(CO)6 + Mo(CO)5, suggesting limited viability analogous to the similar Cr2(CO)11. The lowest lying Mo2(CO)10 structure is a doubly semibridged singlet structure with a MoMo distance corresponding to a formal double bond. This structure is essentially thermoneutral toward disproportionation into 5705
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Mo2(CO)11 + Mo2(CO)9, making it an unpromising synthetic objective. The thermodynamic sink in the Mo2(CO)n (n = 11, 10, 9, 8) system and thus a promising synthetic objective appears to be Mo2(CO)9. Thus, Mo2(CO)9 has a high CO dissociation energy of ∼39 kcal/mol, a significant disproportionation energy into Mo2(CO)10 + Mo2(CO)8 of ∼13 kcal/mol, and a high fragmentation energy into Mo(CO)5 + Mo(CO)4 of ∼56 kcal/ mol. The lowest lying Mo2(CO)9 structure is similar to the lowest lying Cr2(CO)9 structure with three semibridging CO groups and a short MoMo distance (2.64 Å), suggesting a formal triple bond.6 The lowest energy Mo2(CO)8 structure 8S-1 has one semibridging CO group and a MoMo triple bond similar to that in the lowest energy Mo2(CO)9 structure. This differs from the lowest energy Cr2(CO)8 structure, which is a triply bridged structure derived from the Cr2(CO)9 structure by loss of a carbonyl group. A higher energy singlet D2d Mo2(CO)8 structure 8S-3 has a Mo Mo distance short enough (∼2.6 Å) to be the formal quadruple bond, required to give each molybdenum atom the favored 18-electron configuration. However, analysis of the frontier molecular orbitals of 8S-3 suggests that the molybdenum−molybdenum interaction is not a true σ + 2π + δ quadruple bond but instead a pure π Mo Mo double bond, consisting only of the two orthogonal π components. Structure 8S-3 lies ∼18 kcal/mol above the global minimum 8S-1. Furthermore, 8S-3 is not a genuine minimum, since it has a pair of small imaginary vibrational frequencies. Following the corresponding normal modes leads to the C2h structure 8S-2 having two four-electron donor bridging η2-μCO groups and a MoMo distance of ∼3.1 Å, suggesting the formal double bond required to give each molybdenum atom the favored 18-electron configuration in a Mo2(CO)8 structure with two four-electron donor bridging carbonyl groups. Triplet Mo2(CO)n (n = 10, 9, 8) structures were also investigated. However, they were all found to be relatively high energy structures, lying at least 22 kcal/mol above the corresponding global minimum. The assigned Mo−Mo bond orders based on bond distances were confirmed by the predicted natural bond orbital (NBO) molybdenum−molybdenum bond orders.
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REFERENCES
(1) Richardson, N. A.; Xie, Y.; King, R. B.; Schaefer, H. F. J. Phys. Chem. A 2001, 105, 11134. (2) King, R. B.; Lee, T. W. Inorg. Chem. 1982, 21, 319. (3) Newton, M. G.; King, R. B.; Lee, T.-W.; Norskov-Lauritzen, L.; Kumar, V. Chem. Commun. 1982, 101. (4) King, R. B.; Xie, Y.; Schaefer, H. F.; Richardson, N. A.; Li, S. Inorg. Chim. Acta 2005, 358, 1442. (5) Li, S.; Richardson, N. A.; Xie, Y.; King, R. B.; Schaefer, H. F. Faraday Discuss. 2003, 124, 315. (6) Li, S.; Richardson, N. A.; King, R. B.; Schaefer, H. F. J. Phys. Chem. A 2003, 107, 10118. (7) Li, S.; King, R. B.; Schaefer, H. F. J. Phys. Chem. A 2004, 108, 6879. (8) Ziegler, T.; Autschbach, J. Chem. Rev. 2005, 105, 2695. (9) Bühl, M.; Kabrede, H. J. Chem. Theory Comput. 2006, 2, 1282. (10) Brynda, M.; Gagliardi, L.; Widmark, P. O.; Power, P. P.; Roos, B. O. Angew. Chem., Int. Ed. 2006, 45, 3804. (11) Sieffert, N.; Bühl, M. J. Am. Chem. Soc. 2010, 132, 8056. (12) Schyman, P.; Lai, W.; Chen, H.; Wang, Y.; Shaik, S. J. Am. Chem. Soc. 2011, 133, 7977. (13) Adams, R. D.; Pearl, W. C.; Wong, Y. O.; Zhang, Q.; Hall, M. B.; Walensky, J. R. J. Am. Chem. Soc. 2011, 133, 12994. (14) Lonsdale, R.; Olah, J.; Mulholland, A. J.; Harvey, J. A. J. Am. Chem. Soc. 2011, 133, 15464. (15) (a) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (b) Perdew, J. P. Phys. Rev., B 1986, 33, 8822. (16) Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664. (17) Zhao, S.; Wang, W.; Li, Z.; Liu, Z. P.; Fan, K.; Xie, Y.; Schaefer, H. F. J. Chem. Phys. 2006, 124, 184102. (18) Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1993, 85, 441. (19) Bergner, A.; Dolg, M.; Kuechle, W.; Stoll, H.; Preuss, H. Mol. Phys. 1993, 80, 1431. (20) Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. (21) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (22) Frisch, M. J. et al. Gaussian 03, Revision C 02; Gaussian, Inc.: Wallingford, CT, 2004 (see the Supporting Information for the complete reference). (23) Jacobsen, H.; Ziegler, T. J. Am. Chem. Soc. 1996, 118, 4631. (24) Martin, J. M. L.; Bauschlicher, C. W.; Ricca, A. Comput. Phys. Commun. 2001, 133, 189. (25) Feng, X.; Gu, J.; Xie, Y.; King, R. B.; Schaefer, H. F. J. Chem. Theor. Comput. 2007, 3, 1580. (26) Huang, J. S.; Dahl, L. F. J. Organomet. Chem. 1983, 243, 57. (27) Caspar, J. V.; Meyer, T. J. J. Am. Chem. Soc. 1980, 102, 7794. (28) Hooker, R. H.; Mahmoud, K. A.; Rest, A. J. Chem. Commun. 1983, 1022. (29) Hepp, A. F.; Blaha, J. P.; Lewis, C.; Wrighton, M. S. Organometallics 1984, 3, 174. (30) Huang, J. S.; Dahl, L. F. J. Organomet. Chem. 1983, 243, 57. (31) Wang, H.; Xie, Y.; King, R. B.; Schaefer, H. F. Inorg. Chem. 2006, 45, 3384. (32) Sunderlin, L. S.; Wang, D.; Squires, R. R. J. Am. Chem. Soc. 1993, 115, 12060. (33) Weinhold, F.; Landis, C. R. Valency and Bonding: A Natural Bond Order Donor-Acceptor Perspective; Cambridge University Press: Cambridge, England, U. K., 2005. (34) Wang, H.; Xie, Y.; King, R. B.; Schaefer, H. F. J. Am. Chem. Soc. 2006, 128, 11376. (35) Reinhold, J.; Hunstock, E.; Mealli, C. New J. Chem. 1994, 18, 465. (36) Ponec, R.; Lendvay, G.; Chaves, J. J. Comput. Chem. 2008, 29, 1387. (37) Jemmis, E. D.; Pathak, B.; King, R. B.; Schaefer, H. F. Chem. Commun. 2006, 2164. (38) Tang, L.; Luo, Q.; Li, Q.-s.; Xie, Y.; King, R. B.; Schaefer, H. F. J. Chem. Theor. Comput. 2012, 8, 862.
ASSOCIATED CONTENT
S Supporting Information *
Tables S1−S15 [the harmonic vibrational frequencies (in cm−1) and their infrared intensities (in km/mol) for Mo2(CO)n (n = 11, 10, 9, 8)], Tables S16−S30 [the optimized geometries for Mo2(CO)n (n = 11, 10, 9, 8)], and complete Gaussian 03 reference (ref 22). This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (R.B.K.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, and the U.S. National Science Foundation (Grants CHE1057466 and CHE-1054286). 5706
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