Stabilization of Binuclear Chromium Carbonyls by Substitution of

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Stabilization of Binuclear Chromium Carbonyls by Substitution of Thiocarbonyl Groups for Carbonyl Groups: Nearly Linear Structures for Cr2(CS)2(CO)9 Zhong Zhang,† Qian-shu Li,*,†,‡ Yaoming Xie,§ R. Bruce King,*,†,§ and Henry F. Schaefer III§ Center for Computational Quantum Chemistry, South China Normal UniVersity, Guangzhou 510631, People’s Republic of China, Institute of Chemical Physics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China, and Department of Chemistry and Center for Computational Chemistry, UniVersity of Georgia, Athens, Georgia 30602 ReceiVed: July 20, 2009; ReVised Manuscript ReceiVed: October 15, 2009

The chromium carbonyl thiocarbonyls Cr(CS)(CO)n (n ) 5, 4, 3) and Cr2(CS)2(CO)n (n ) 9, 8, 7, 6) were studied by density functional theory (DFT). The expected octahedral structure was found for the known Cr(CS)(CO)5. The structures for the unsaturated derivatives Cr(CS)(CO)n (n ) 4, 3) are derived from the octahedral Cr(CS)(CO)5 by removal of one or two carbonyl groups, respectively. The lowest energy structures for the binuclear derivatives Cr2(CS)2(CO)n (n ) 9, 8, 7, 6) all contain four-electron donor bridging η2-µ-CE (E ) O, S) groups. For the formally saturated Cr2(CS)2(CO)9, no chromium-chromium bond is then required to give the chromium atoms the favored 18-electron configuration. This leads to a uniquely linear Cr-C-OfCr arrangement or bent Cr-C-SfCr arrangement (C-SfCr angle of ∼110°) with a long clearly nonbonding Cr · · · Cr distance. A similar structural feature is found in the known stable arene-chromium carbonyl thiocarbonyl (η6-MeC6H5)Cr(CO)2[CSfCr(CO)5]. The lowest energy structures for the formally unsaturated Cr2(CS)2(CO)n (n ) 8, 7, 6) are predicted to have one (n ) 8) or two (n ) 7, 6) four-electron donor η2-µ-CS groups with a Cr-Cr single bond (n ) 8 and 7) or CrdCr double bond (n ) 6) to give both chromium atoms the favored 18-electron configuration. The lowest energy structures for the binuclear Cr2(CS)2(CO)n (n ) 9, 8, 7, 6) are all predicted to be stable with respect to fragmentation into mononuclear Cr(CS)(CO)m in contrast to the homoleptic Cr2(CO)11. This suggests that there is a reasonable chance that at least some of the binuclear Cr2(CS)2(CO)n (n ) 9, 8, 7, 6) derivatives will be synthesized as stable or at least detectable molecules. 1. Introduction The first-row transition metal binuclear metal carbonyls Co2(CO)8 (ref 1), Fe2(CO)9 (ref 2), and Mn2(CO)10 (ref 3) are all stable commercially available compounds that are commonly used starting materials for the synthesis of more complicated carbonyl derivatives of these metals. These three binuclear metal carbonyls all have metal-metal distances consistent with formal single bonds leading to the favorable 18-electron configuration for both metal atoms. Extending this series of homoleptic binuclear metal carbonyls to the left in the Periodic Table predicts Cr2(CO)11 to have the favored 18-electron configuration for both chromium atoms like Co2(CO)8, Fe2(CO)9, and Mn2(CO)10. However, Cr2(CO)11 has never been synthesized or even characterized spectroscopically in low-temperature matrices. This is consistent with theory showing that Cr2(CO)11 is thermodynamically unstable with respect to dissociation into Cr(CO)6 + Cr(CO)5 fragments.4 Recent studies5 of the binuclear iron carbonyl thiocarbonyls Fe2(CS)2(CO)n predict the thiocarbonyl group to behave quite differently from the carbonyl group in binuclear derivatives, particularly when the thiocarbonyl group bridges two metal atoms in the unsaturated derivatives Fe2(CS)2(CO)n (n ) 6, 5, 4). More specifically, four-electron donor thiocarbonyl groups bonded as η2-µ-CS groups through both the sulfur and the carbon atoms are frequently energetically preferred over * Corresponding author. E-mail: [email protected]. † South China Normal University. ‡ Beijing Institute of Technology. § University of Georgia.

metal-metal multiple bonding. Similar four-electron donor η2µ-CO groups are much rarer in the chemistry of binuclear metal carbonyls with (diphos)2Mn2(CO)4(η2-µ-CO) being the original example.6,7 This tendency of bridging thiocarbonyl groups to function as four-electron donor η2-µ-CS groups suggests that binuclear chromium carbonyl derivatives in which some of the CO ligands have been replaced by CS ligands might be more thermodynamically stable toward dissociation than the corresponding homoleptic carbonyls. The only known chromium carbonyl thiocarbonyl containing only CO and CS ligands is Cr(CS)(CO)5, which was first prepared by Dombek and Angelici8 in 1973 by the reaction of Cr(CO)52- with SdCCl2. This is a very stable molecule having a structure derived from the octahedrally coordinated Cr(CO)6 by the replacement of one CO group with a CS group.9 Furthermore, photolysis of Cr(CS)(CO)5 in CH4 matrices at 20 K has been reported by Poliakoff10 to give two isomers of the unsaturated Cr(CS)(CO)4, identified by their ν(CO) frequencies. These isomers have been assigned square pyramidal structures with the CS group in an apical position in one isomer and in a basal position in the other isomer. Despite the existence of Cr(CS)(CO)5 as a stable molecule and Cr(CS)(CO)4 in low temperature matrices, binuclear chromium derivatives containing only CO and CS groups have not yet been synthesized. This Article reports a theoretical investigation of chromium carbonyl thiocarbonyls. The mononuclear derivatives Cr(CS)(CO)n (n ) 5, 4, 3) were first studied to provide a comparison with the experimental results. Binuclear compounds of the type Cr2(CS)2(CO)n (n ) 9, 8, 7, 6) with a 1:1 Cr/CS ratio were then considered because such compounds are the most likely

10.1021/jp9068587  2010 American Chemical Society Published on Web 12/04/2009

Stabilization of Binuclear Chromium Carbonyls

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TABLE 1: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Frequencies (Nimg) for the Five Cr(CS)(CO)4 Structures B3LYP BP86

-E ∆E Nimg -E ∆E Nimg

14-1 (C4V)

14-2 (Cs)

14-3T (C2V)

14-4T (C3V)

14-5 (Cs)

1934.22760 0.0 0 1934.46196 0.0 0

1934.22569 1.2 0 1934.45924 1.7 0

1934.20777 12.4 0 1934.43566 16.5 0

1934.20620 13.4 0 1934.43319 18.1 0

1934.16313 40.5 0 1934.39702 40.8 0

TABLE 2: ν(CO) and ν(CS) Stretching Frequencies (cm-1) and Infrared Intensities (km/mol, in parentheses) Predicted by the BP86 Method for the Mononuclear Cr(CS)(CO)n (n ) 5, 4, 3) Derivatives ν(CO)

ν(CS) 1294 (a1, 798)

expt.8

Cr(CS)(CO)5 2067 (a1, 231), 2001 (b2, 0), 1994 (a1, 715), 1982 (e, 1559), 1982 (e, 1559) 2091 w, 2023 m, 1997 vs

14-1 (C4V) expt.10 14-2 (Cs) expt.10 14-3T (C2V) 14-4T (C3V) 14-5 (Cs)

Cr(CS)(CO)4 2048 (a1, 120), 1986 (b2, 0), 1962 (e, 1728), 1962 (e, 1728) 2081.4 (a1), 2016.3 (b2), 1982.3 (e) 2040 (a′, 345), 1978 (a′, 690), 1960 (a′′, 1722), 1952 (a′, 738) 2069.3 (a′), 2011.3 (a′), 1975.6 (a′′), 1949.3 (a′) 2032 (a1, 258), 1967 (a1, 229), 1966 (b2, 1090), 1957 (b1, 1697) 2023 (a1, 416), 1973 (e, 1023), 1973 (e, 1023), 1965 (a1, 659) 2037 (a′, 272), 1965 (a′, 576), 1956 (a′′, 1658), 1952 (a′, 705)

13-1 (Cs) 13-2 (Cs) 13-3T (Cs) 13-4T (Cs) 13-5T (Cs) 13-6 (C2V)

2018 1999 2003 2009 2017 2015

15-1 (C4V)

Cr(CS)(CO)3 (a′, 149), 1941 (a′′, 1835), 1934 (a′, 680) (a′, 835), 1943 (a′, 751), 1922 (a′′, 962) (a′, 595), 1959 (a′′, 1205), 1946 (a′, 965) (a′, 254), 1944 (a′, 715), 1931 (a′′, 1908) (a′, 657), 1953 (a′, 1777), 1924 (a′, 613) (a1, 362), 1959 (a1, 855), 1934 (b2, 1953)

binuclear chromium carbonyl thiocarbonyls to be synthesized from the known Cr(CS)(CO)5. Computational studies on the homoleptic binuclear chromium carbonyls Cr2(CO)n (n ) 11, 10, 9, 8) have previously been reported.4,11-14 2. Theoretical Methods Electron correlation effects were considered using density functional theory (DFT) methods, which have evolved as a practical and effective computational tool, especially for organometallic compounds.15-23 Two DFT methods were used in this study. The first functional is the popular B3LYP method, which is the hybrid HF/DFT method using a combination of the three-parameter Becke exchange functional (B3) with the Lee-Yang-Parr (LYP) generalized gradient correlation functional.24,25 The other DFT method used in the present Article is BP86, which combines Becke’s 1988 exchange functional (B) with Perdew’s 1986 gradient corrected correlation functional method (P86).26,27 It has been noted elsewhere that the BP86 method may be somewhat more reliable than B3LYP for the type of organometallic systems considered in this Article.28-30 Our DZP basis sets used for carbon, oxygen, and sulfur add one set of pure spherical harmonic d functions with orbital exponents Rd(C) ) 0.75, Rd(O) ) 0.85, and Rd(S) ) 0.70 to the standard Huzinaga-Dunning-Hay contracted DZ sets.31-33 The C and O basis sets are designated as (9s5p1d/4s2p1d), and the S basis set is designated as (12s8p1d/6s4p1d). For Cr, in our loosely contracted DZP basis set, the Wachters primitive set34 is used augmented by two sets of p functions and one set of d functions, contracted following Hood, Pitzer, and Schaefer,35 and designated (14s11p6d/10s8p3d). For Cr(CS)(CO)5, Cr(CS)(CO)4, Cr(CS)(CO)3, Cr2(CS)2(CO)9, Cr2(CS)2(CO)8, Cr2(CS)2(CO)7, and Cr2(CS)2(CO)6, there are 237, 207, 177, 444, 414, 384, and 354 contracted Gaussian functions, respectively, in the basis sets.

1253 vs 1283 (a1, 630) 1276 (a′, 762) 1240 (a1, 412) 1268 (a1, 689) 1033 (a′, 107) 1271 1262 1251 1235 1239 1261

(a′, 532) (a′, 743) (a′, 744) (a′, 420) (a′, 784) (a1, 785)

The geometries of all structures were fully optimized using the B3LYP/DZP and BP86/DZP methods. Vibrational frequencies were determined by evaluating analytically the second derivatives of the energy with respect to the nuclear coordinates. The corresponding infrared intensities were also evaluated analytically. All of the computations were carried out with the Gaussian 03 program,36 exercising the fine grid option (75 radial shells, 302 angular points) for evaluating integrals numerically,37 while the tight (10-8 hartree) designation is the default for the self-consistent field (SCF) convergence. In the search for minima using all currently implemented DFT methods, low magnitude imaginary vibrational frequencies are suspect because of significant limitations in the numerical integration procedures used in the DFT computations. Thus, all imaginary vibrational frequencies with a magnitude less than 50i cm-1 are considered questionable and are given less weight in the analysis.37-39 Therefore, we do not always follow such low imaginary vibrational frequencies. The optimized structures, including their predicted ν(CO) and ν(CS) frequencies, are listed in Tables 1-12 and depicted in Figures 1-8. Each Cra(CS)a(CO)b structure is designated as abc, where a is the number of chromium atoms (the same as the number of CS groups), b is the number of CO groups, and c orders the structures according to their relative energies. Triplet structures are indicated by T. Thus, the lowest energy structure of Cr2(CS)2(CO)9 is designated 29-1. 3. Results 3.1. Structures of Mononuclear Derivatives. 3.1.1. Cr(CS)(CO)5. Only a single structure was found for Cr(CS)(CO)5, 15-1 (Figure 1), which is a genuine minimum with all real vibrational frequencies. The Cr-C(S) distance in 15-1 is predicted to be 1.885 Å (B3LYP) or 1.879 Å (BP86), and the C-S bond length

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Figure 1. Optimized structures of Cr(CS)(CO)5 and Cr(CS)(CO)4. In Figures 1-8, the upper distances were predicted by the B3LYP method and the lower distances by the BP86 method.

Figure 2. Optimized structures of Cr(CS)(CO)3.

is found to be 1.554 Å (B3LYP) or 1.566 Å (BP86). The Cr-C(O) distance of 1.943 Å (B3LYP) or 1.927 Å (BP86) to the carbonyl trans to the thiocarbonyl group is predicted to be somewhat longer than the Cr-C(O) distance of 1.924 Å (B3LYP) or 1.909 Å (BP86) to the carbonyl groups cis to the thiocarbonyl group. This is consistent with a larger trans effect of a thiocarbonyl group relative to a carbonyl group. Direct comparison of these distances with the experimental X-ray crystal structure9 for Cr(CS)(CO)5 is not feasible because disorder in the crystal structure scrambles the CO and CS groups, so that the experiment gives only average values of the nonequivalent distances. Attempts to optimize alternative structures of Cr(CS)(CO)5 with the CS group bonded to the chromium through both the carbon and the sulfur atoms in a “side-on” manner all led back to structure 15-1. 3.1.2. Cr(CS)(CO)4. All five structures found for Cr(CS)(CO)4 are predicted to be genuine minima because they have no imaginary vibrational frequencies. The global minimum of Cr(CS)(CO)4, the C4V structure 14-1, can be derived from the Cr(CS)(CO)5 structure 15-1 by loss of the carbonyl group trans to the thiocarbonyl group with concurrent shortening of the Cr-C(S) distance to 1.811 Å (B3LYP) or 1.800 Å (BP86). The slightly higher energy Cs structure 14-2 of Cr(CS)(CO)4 at 1.2 kcal/mol (B3LYP) or 1.7 kcal/mol (BP86) above 14-1 can also be derived from 15-1, but by loss of a carbonyl group cis rather than trans to the thiocarbonyl group. The closeness in the predicted energies of 14-1 and 14-2 suggests a potentially fluxional system. However, in low temperature matrix ultraviolet photolysis studies of Cr(CS)(CO)5, both of these Cr(CS)(CO)4 isomers were observed as indicated by the closeness of our predicted ν(CO) frequencies to those reported in the experimental work.10 The slightly lower energy of the Cr(CS)(CO)4 structure 14-1, in which the “missing” carbonyl group is trans to the thiocarbonyl ligand, relative to 14-2, in which the “missing” carbonyl group is cis to the carbonyl ligand, is consistent with a slightly higher trans effect of the thiocarbonyl ligand relative to the carbonyl ligand. Two essentially degenerate triplet trigonal bipyramidal structures for Cr(CS)(CO)4 are predicted (Figure 1 and Table 1), 14-3T with the thiocarbonyl group in an equatorial position and 14-4T with the thiocarbonyl group in an axial position. The

former lies above the global minimum 14-1 by 12.4 kcal/mol (B3LYP) or 16.5 kcal/mol (BP86), whereas the latter is 13.4 kcal/mol (B3LYP) or 18.1 kcal/mol (BP86). A relatively high energy Cr(CS)(CO)4 structure 14-5 with a “side-on” thiocarbonyl group bonded to the chromium atom through both its carbon and its sulfur atom (Figure 1 and Table 1) was found at 40.5 kcal/mol (B3LYP) or 40.8 kcal/mol (BP86) relative to the global minimum 14-1. The nature of the “sideon” bonding of the thiocarbonyl group in 14-5 is indicated a short Cr-S distance of 2.485 Å (B3LYP) or 2.467 Å (BP86) in addition to a long Cr-C distance of 2.375 Å (B3LYP) or 2.285 Å (BP86). 3.1.3. Cr(CS)(CO)3. Three singlet and three triplet structures were found for Cr(CS)(CO)3 (Figure 2 and Table 3). The global minimum 13-1, which is a singlet with no imaginary vibrational frequencies, has a “sawhorse” structure derived from the octahedral Cr(CS)(CO)5 structure 15-1 (Figure 1) by removing two adjacent carbonyl groups, including the carbonyl group trans to the thiocarbonyl group. The next lowest energy structure of Cr(CS)(CO)3, 13-2 at 1.6 kcal/mol (B3LYP) or 2.3 kcal/mol (BP86) above 13-1, also has a “sawhorse” structure derived from the 15-1 structure by the loss of two adjacent terminal carbonyl groups. However, for 13-2 both of the carbonyl groups lost from 15-1 are carbonyl groups trans to other carbonyl groups so that the pair of trans ligands in the resulting sawhorse consists of one carbonyl and one thiocarbonyl group. The two triplet Cr(CS)(CO)3 structures 13-3T and 13-4T are similar to the singlet structures 13-2 and 13-1, respectively, but lie at the higher energies of 8.2 kcal/mol (B3LYP) or 16.4 kcal/mol (BP86) for 13-3T and 9.0 kcal/mol (B3LYP) or 15.9 kcal/mol (BP86) for 13-4T. None of these first four structures of Cr(CS)(CO)3 is predicted to have any imaginary vibrational frequencies. The remaining two Cr(CS)(CO)3 structures, 13-5T and 13-6 (Figure 2 and Table 3), have approximate square planar coordination of the chromium atom. These structures may be derived from the octahedral structure 15-1 of Cr(CS)(CO)5 (Figure 1) by removing a pair of antipodal carbonyl ligands. The triplet Cr(CS)(CO)3 structure 13-5T lies 8.9 kcal/mol (B3LYP) or 19.3 kcal/mol (BP86) above 13-1, whereas the singlet Cr(CS)(CO)3 structure 13-6 lies at 12.4 kcal/mol (B3LYP) or 19.2 kcal/mol (BP86) above 13-1.



TABLE 3: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Vibrational Frequencies for the Six Cr(CS)(CO)3 Structures B3LYP BP86


13-1 (Cs)

13-2 (Cs)

13-3T (Cs)

13-4T (Cs)

13-5T (Cs)

13-6 (C2V)

1820.83877 0.0 0 1821.06732 0.0 0

1820.83617 1.6 0 1821.06364 2.3 0

1820.82567 8.2 0 1821.04121 16.4 0

1820.82447 9.0 0 1821.04200 15.9 0

1820.82465 8.9 0 1821.03660 19.3 1 (15i)

1820.81898 12.4 0 1821.03674 19.2 0

TABLE 4: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Vibrational Frequencies (Nimg) for the Five Cr2(CS)2(CO)9 Structures with End-On Bridging CO or CS Groups B3LYP BP86


29-1 (Cs)

29-2 (C4V)

29-3 (C1)

29-4 (C1)

29-5 (Cs)

29-6 (C1)

3981.85980 0.0 0 3982.33532 0.0 0

3981.85948 0.2 0 3982.33522 0.1 0

3981.85711 1.7 0 3982.33211 2.0 0

3981.85713 1.7 0 3982.33214 2.0 0

3981.85781 1.2 0 3982.33681 -0.9 0

3981.85383 3.7 0 3982.33231 1.9 0

The infrared ν(CO) frequencies of the terminal carbonyl groups in the Cr(CS)(CO)n (n ) 5, 4, 3) derivatives fall in the range 2070-1920 cm-1 (Table 2), with the lower values in this range appearing for the derivatives with fewer carbonyl groups to compete for the metal electron density. The infrared ν(CS) frequencies of the terminal thiocarbonyl groups in the Cr(CS)(CO)n (n ) 5, 4, 3) derivatives fall in the somewhat narrower range of 1295-1235 cm-1. However, the novel “side-on” bonded thiocarbonyl group in 14-5 is predicted to have an unusually low ν(CS) frequency of 1033 cm-1. 3.2. Structures of Binuclear Derivatives. 3.2.1. Cr2(CS)2(CO)9. A total of six structures were found to be genuine minima with all real vibrational frequencies for Cr2(CS)2(CO)9 within 5 kcal/mol of the global minimum 29-1 (Figure 3 and Tables 4 and 5). These structures all have two octahedrally

coordinated chromium atoms bridged by an end-on CE (E ) O or S) group bonded to one chromium atom through its carbon atom and to the other chromium atom through the chalcogen atom (O or S). A related end-on bridging thiocarbonyl group has been found experimentally in (η6-MeC6H5)Cr(CO)2[CSfCr(CO)5], which is stable enough to be isolated and characterized by X-ray crystallography.40 The experimental Cr-C, C-S, S-Cr distances, and Cr-C-S angle of 1.747 Å, 1.604 Å, 2.486 Å, and 110.4°, respectively, in (η6MeC6H5)Cr(CO)2[CSfCr(CO)5] can be compared to the corresponding values of 1.85 Å, 1.58 ( 0.01 Å, 2.58 ( 0.08 Å, and 109.7 ( 0.5°, predicted in this research for the related Cr2(CS)2(CO)9 structure 29-5. The shorter Cr-C and Cr-S distances and longer C-S distances in (η6-MeC6H5)Cr(CO)2[CSfCr(CO)5] relative to those in structure 29-5 can relate

Figure 3. The five Cr2(CS)2(CO)9 structures with end-on bridging CO or CS groups.

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TABLE 5: ν(CO) and ν(CS) Stretching Frequencies and Infrared Intensities Predicted for the Cr2(CS)2(CO)9 Structuresa ν(CO) 29-1 (Cs) 29-2 (C4V) 29-3 (C1) 29-4 (C1) 29-5 (Cs) 29-6 (C1)

a

ν(CS)

2066 (a′, 362), 2042 (a′, 4), 2005 (a′, 322), 2001 (a′, 831), 1991 (a′′, 1855), 1985 (a′′, 1), 1961 (a′, 1279), 1960 (a′′, 999), 1949 (a′, 1748) 2067 (a1, 12), 2042 (a1, 1), 2007 (b2, 0), 1990 (e, 1877), 1990 (e, 1877), 1986 (b1, 0), 1961 (e, 987), 1961 (e, 987), 1948 (a1, 1084) 2066 (a, 343), 2035 (a, 451), 2004 (a, 288), 2000 (a, 780), 1990 (a, 1743), 1977 (a, 330), 1959 (a, 1166), 1958 (a, 185), 1952 (a, 2388) 2065 (a, 231), 2035 (a, 491), 2004 (a, 274), 2001 (a, 749), 1990 (a, 1806), 1977 (a, 426), 1959 (a, 1067), 1958 (a, 229), 1952 (a, 2343) 2075 (a′, 512), 2034 (a′, 160), 2014 (a′′, 68), 2011 (a′, 820), 1997 (a′, 1492), 1996 (a′′, 1738), 1983 (a′, 122), 1962 (a′′, 922), 1952 (a′, 988) 2067 (a, 5), 2042 (a, 622), 2014 (a, 60), 1999 (a, 1392), 1997 (a, 1603), 1979 (a, 131), 1955 (a, 1009), 1952 (a, 761), 1948 (a, 1142)

1298 (a′, 680), 1283 (a′, 939) 1299 (a1, 620), 1282 (a1, 1495) 1299 (a, 833), 1278 (a, 538) 1297 (a, 778), 1278 (a, 641) 1283 (a′, 815), 1221 (a′, 1171) 1307 (a, 408), 1198 (a, 1736)

Bridging carbonyl and thiocarbonyl frequencies are in bold print.

to the weaker back-bonding capability of an η6-arene ligand relative to three carbonyl groups. This leads to stronger backbonding to the end-on linear bridging thiocarbonyl group in (η6MeC6H5)Cr(CO)2[CSfCr(CO)5] relative to that in the Cr2(CS)2(CO)9 structure 29-5. The four lowest energy Cr2(CS)2(CO)9 structures have a carbonyl group (rather than a thiocarbonyl group) bridging the two octahedral chromium fragments. These structures differ in the location of the thiocarbonyl groups on each chromium atom relative to the end-on bridging carbonyl group. In the global minimum 29-1, the end-on bridging group is the carbonyl group cis to the thiocarbonyl group and is coordinated through its oxygen atom to the other chromium atom trans to its thiocarbonyl group. The HOMO and LOMO energy difference in 29-1 is predicted to be 0.131 au (B3LYP) or 0.083 au (BP86), which is large enough to rationalize the preferred singlet configuration. Nevertheless, we also optimized this structure in the triplet spin state, but, as expected, the triplet spin state structure was found to lie at a high energy (26.4 kcal/mol) above 29-1. For this reason, we did not investigate other triplet structures for Cr2(CS)2(CO)9. The second lowest energy Cr2(CS)2(CO)9 structure 29-2 (Figure 3 and Table 4) is essentially degenerate (within 0.2 kcal/ mol) with 29-1. Structure 29-2 differs from structure 29-1 in that the carbon atom of the end-on bridging carbonyl is trans rather than cis to the thiocarbonyl group on the same chromium atom. This minor structural difference obviously makes very little difference in the total energy. The remaining end-on CO bridged degenerate Cr2(CS)2(CO)9 structures 29-3 and 29-4, at 1.9 ( 0.2 kcal/mol above 29-1, have the oxygen atom of the end-on bridging carbonyl group coordinated trans to a carbonyl rather than a thiocarbonyl group. For the four structures 29-1, 29-2, 29-3, and 29-4, the C-O distances in the end-on bridging carbonyl groups are predicted to be ∼1.161 Å (B3LYP) or ∼1.175 Å (BP86), which are slightly longer than the C-O distances of ∼1.155 Å (B3LYP) or ∼1.170 Å (BP86) in the terminal carbonyl groups. The Cr-O distances are predicted to be ∼2.210 Å (B3LYP) or ∼2.165 Å (BP86) consistent with a Cr-O single bond. The end-on bridging carbonyl groups in 29-1, 29-2, 29-3, and 29-4 exhibit slightly lower ν(CO) frequencies than do the terminal carbonyl groups at 1950 ( 2 cm-1 (Table 5). The end-on CS bridged Cr2(CS)2(CO)9 structures are 29-5 and 29-6 (Figure 3 and Table 4) with relative energies of 1.2

and 3.7 kcal/mol (B3LYP) or -0.9 and 1.9 kcal/mol (BP86), respectively, above 29-1. The bridging C-S distances are predicted to be ∼1.577 Å (B3LYP) or ∼1.590 Å (BP86), which are somewhat longer than the terminal C-S distances. The Cr-S distances to the end-on bridging thiocarbonyl groups in 29-5 and 29-6 are predicted to be ∼2.64 Å (B3LYP) or ∼2.55 Å (BP86) in accord with a Cr-S bond. Note that in contrast to the linear Cr-C-O-Cr units in the Cr2(CS)2(CO)9 structures with bridging CO groups, the Cr-C-S-Cr units in the Cr2(CS)2(CO)9 derivatives with bridging CS groups (29-5 and 29-6) are bent with Cr-S-C angles of ∼110° (Figure 3). We also tried to find singlet and triplet bridged Cr2(CS)2(CO)9 structures with a direct Cr-Cr bond. However, attempted optimization of such structures led instead to the above structures with end-on bridging CO or CS groups without a Cr-Cr bond. 3.2.2. Cr2(CS)2(CO)8. The two lowest energy unsaturated Cr2(CS)2(CO)8 structures (Figure 4 and Tables 6 and 7) have a single four-electron donor bridging η2-µ-CS group so that a formal single Cr-Cr bond is sufficient to give both chromium atoms the favored 18-electron configuration. Thus, in the Cs global minimum structure of Cr2(CS)2(CO)8 28-1, the Cr-Cr distance is predicted to be 3.182 Å (B3LYP) or 3.120 Å (BP86), suggesting a relatively weak formal single bond. Furthermore, the Cr-S distance in 28-1 is predicted to be 2.576 Å (B3LYP) or 2.569 Å (BP86). This suggests that the bridging CS ligand is a four-electron donor donating two electrons to the “left” chromium atom in Figure 5 through the CdS π-bond, in addition to the two electrons assigned to the “right” chromium atom through the usual CfCr σ-bond. The “right” chromium atom forms a dative CrfCr bond with the “left” chromium atom leading to an 18-electron configuration for each chromium atom. The second η2-µ-CS bridged Cr2(CS)2(CO)8 structure 28-2 has no point group symmetry and is predicted to lie 2.7 kcal/mol (B3LYP) or 2.9 kcal/mol (BP86) higher in energy than 28-1 (Figure 4 and Tables 6 and 7) with all real frequencies predicted by both methods. The Cr2(CS)2(CO)8 structure 28-2 is similar to 28-1 except that the terminal thiocarbonyl ligand is bonded to the chromium atom bonded to the sulfur rather than the carbon of the bridging η2-µ-CS group, the “right” chromium atom in Figure 5. The four-electron donor thiocarbonyl groups in 28-1 and 28-2 are predicted to exhibit ν(CS) frequencies at 1155 ( 5 cm-1 (Table 8). The C2h doubly thiocarbonyl bridged Cr2(CS)2(CO)8 structure 28-3 (Figure 4 and Table 6) lies 12.0 kcal/mol (B3LYP) or 10.4



Figure 4. The seven optimized Cr2(CS)2(CO)8 structures.

TABLE 6: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Vibrational Frequencies for Cr2(CS)2(CO)8 B3LYP BP86


28-1 (Cs)

28-2 (C1)

3868.49214 0.0 0 3868.97194 0.0 0

3868.48786 2.7 0 3868.96731 2.9 0

28-3 (C2h) 3868.47299 12.0 0 3868.95545 10.4 1 (29i)

kcal/mol (BP86) above 28-1 with no imaginary vibrational frequencies by B3LYP and only a single small imaginary vibrational frequency at 29i cm-1 by BP86. The bridging thiocarbonyl groups in 28-3 are predicted to be asymmetric with a short Cr-C distance of 1.894 Å (B3LYP) or 1.904 Å (BP86) and a long Cr-C distance of 2.464 Å (B3LYP) or 2.341 Å (BP86), accompanying predicted ν(CS) frequencies at 1202 and 1188 cm-1 (Table 7). The CrdCr distance in 28-3 is predicted to be 2.864 Å (B3LYP) or 2.797 Å (BP86), suggesting the formal double bond required to give both metal atoms the favored 18-electron configuration. Structure 28-5 for Cr2(CS)2(CO)8, at 17.3 kcal/mol (B3LYP) or 16.8 kcal/mol (BP86) above the global minimum 28-1, is similar to structure 28-3 except that the two bridging groups are carbonyl groups

28-4 (C2V)

28-5 (C2h)

28-6 (Cs)

28-7 (C2)

3868.47244 12.4 0 3868.95177 12.7 0

3868.46455 17.3 0 3868.94518 16.8 0

3868.46230 18.7 0 3868.93168 25.3 0

3868.46048 19.9 0 3868.93991 20.1 0

rather than thiocarbonyl groups (Figure 4 and Table 6). The bridging carbonyl groups in 28-5, like the bridging thiocarbonyl groups in 28-3, are unsymmetrical with short Cr-C distances of 1.949 Å (B3LYP) or 1.945 Å (BP86) and long Cr-C distances of 2.577 Å (B3LYP) or 2.443 Å (BP86). The high asymmetry of the bridging carbonyl groups in 28-5 leads to predicted ν(CO) frequencies of 1927 and 1915 cm-1, which are only slightly below the terminal ν(CO) frequencies (Table 7). The CrdCr distance in 28-5 is predicted to be 2.932 Å (B3LYP) or 2.839 Å (BP86), which, although somewhat longer than that for 28-3, still can correspond to the formal double bond, leading to the favored 18-electron configuration for both chromium atoms. The doubly carbonyl bridged Cr2(CS)2(CO)8 structure 28-7, at 19.9 kcal/mol (B3LYP) or 20.1 kcal/mol (BP86) above

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TABLE 7: ν(CO) and ν(CS) Stretching Frequencies (cm-1) and Corresponding Infrared Intensities Predicted for the Cr2(CS)2(CO)8 Structuresa ν(CO) 28-1 (Cs)

2064 (a′, 431), 2011 (a′, 847), 2003 (a′, 145), 1997 (a′, 855), 1992 (a′′, 1969), 1970 (a′, 615), 1968 (a′, 599), 1947 (a′′, 442) 2053 (a, 441), 2014 (a, 1533), 2000 (a, 625), 1998 (a, 868), 1979 (a, 1061), 1964 (a, 623), 1950 (a, 406), 1943 (a, 558) 2053 (ag, 0), 2026 (bu, 1554), 1988 (ag, 0), 1987 (bu, 763), 1984 (au, 2375), 1969 (ag, 0), 1968 (bu, 1059), 1951 (bg, 0) 2144 (a1, 638), 2098 (a1, 4), 2093 (a1, 1675), 2093 (b2, 865), 2082 (b1, 1859), 2020 (b1, 1323), 2018 (a1, 1104), 1999 (b2, 855) 2046 (ag, 0), 2017 (bu, 586), 1983 (au, 2404), 1973 (ag, 0), 1971 (bu, 1198), 1951 (bg, 0), 1927 (bu, 810), 1915 (ag, 0) 2054 (a′, 490), 2010 (a′, 700), 2007 (a′′, 633), 1993 (a′, 1120), 1945 (a′, 885), 1931 (a′′, 1014), 1919 (a′, 1297), 1891 (a′′, 262) 2044 (a, 666), 2014 (b, 1544), 1991 (a, 706), 1981 (b, 1098), 1970 (a, 91), 1965 (b, 572), 1925 (b, 1047), 1907 (a, 17)

28-2 (C1) 28-3 (C2h) 28-4 (C2V) 28-5 (C2h) 28-6 (Cs) 28-7 (C2) a

ν(CS) 1276 (a′, 600), 1160 (a′, 362) 1298 (a, 646), 1151 (a, 381) 1202 (bu, 585), 1188 (ag, 0) 1283 (a1, 1082), 1201 (b2, 383) 1289 (ag, 0), 1286 (bu, 1649) 1302 (a′, 750), 1261 (a′, 557) 1289 (a, 1035), 1260 (b, 72)


Figure 5. The four low-lying optimized Cr2(CS)2(CO)7 structures with four-electron donor η2-µ-CS groups.

TABLE 8: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Frequencies (Nimg) for the Cr2(CS)2(CO)7 Structures with Four-Electron Donor η2-µ-CS Groups 27-1 (Cs)

27-2 (C2V)

27-3 (Cs)

27-4 (Cs)

B3LYP -E 3755.12738 3755.12725 3755.12394 3755.12220 ∆E 0.0 0.1 2.2 3.3 Nimg 0 0 0 0 BP68 -E 3755.60358 3755.59906 3755.60102 3755.60018 ∆E 0.0 2.8 1.6 2.1 Nimg 0 0 0 0

28-1, with no imaginary vibrational frequencies, is similar to 28-5 except for the locations of the terminal thiocarbonyl groups. In 28-7, the bridging carbonyl groups exhibit ν(CO) frequencies at 1925 and 1907 cm-1 (Table 7). The Cr2(CS)2(CO)8 structure 28-4, at 12.4 kcal/mol (B3LYP) or 12.7 kcal/mol (BP86) above the global minimum 28-1 with no imaginary vibrational frequencies, has a very long Cr · · · Cr

distance of 4.530 Å (B3LYP) or 4.304 Å (BP86), indicating no direct chromium-chromium bonding (Figure 4 and Table 6). The two thiocarbonyl groups are both bonded to one chromium atom (the “right” chromium atom in Figure 4) through the carbon atom, with Cr-C distances of 1.865 Å (B3LYP) or 1.868 Å (BP86), and to the other chromium atom (the “left” chromium atom in Figure 5) through the sulfur atom, as indicated by the rather short Cr-S distances of 2.661 Å (B3LYP) or 2.540 Å (BP86). Thus, both thiocarbonyl groups in 28-4 are four-electron donors leading to the favored 18electron configuration for both chromium atoms, even in the absence of any chromium-chromium bonding. Alternatively, 28-4 can be regarded as an octahedral (bidentate)Cr(CO)4 chelate in which the bidentate ligand is octahedral Cr(CO)4(CS)2 chelating to the first chromium atom through its sulfur atoms. The thiocarbonyl groups in 28-4 are predicted to exhibit ν(CS) frequencies at 1283 and 1201 cm-1 (Table 7).



TABLE 9: ν(CO) and ν(CS) Stretching Frequencies (cm-1) and Corresponding Infrared Intensities Predicted for the 11 Cr2(CS)2(CO)7 Structuresa ν(CO) 27-1 (Cs) 27-2 (C2V) 27-3 (Cs) 27-4 (Cs) 27-5 (Cs) 27-6 (C2) 27-7 (C1) 27-8 (Cs) 27-9 (C2) 27-10 (Cs) 27-11 (C1) a

ν(CS)

2055 (a′, 122), 2014 (a′, 1479), 1993 (a′, 409), 1985 (a′′, 2262), 1980 (a′, 228), 1976 (a′, 809), 1952 (a′′, 93) 2057 (a1, 390), 2005 (b1, 599), 2002 (a1, 1917), 2000 (a1, 60), 1986 (b2, 1809), 1967 (a1, 207), 1924 (b2, 657) 2053 (a′, 958), 2007 (a′, 489), 1989 (a′, 681), 1985 (a′′, 1694), 1980 (a′, 652), 1939 (a′′, 440), 1853 (a′, 256) 2051 (a′, 373), 2012 (a′, 387), 1997 (a′, 1404), 1987 (a′, 880), 1986 (a′′, 1672), 1958 (a′, 352), 1940 (a′′, 423) 2037 (a′, 109), 2005 (a′, 2263), 1985 (a′′, 870), 1984 (a′, 1015), 1975 (a′, 439), 1973 (a′′, 411), 1927 (a′, 477) 2036 (a, 124), 2004 (b, 2386), 1985 (a, 952), 1985 (b, 816), 1975 (b, 459), 1975 (a, 401), 1917 (a, 457) 2041 (a, 448), 2004 (a, 1805), 1986 (a, 794), 1981 (a, 907), 1974 (a, 497), 1935 (a, 864), 1927 (a, 173) 2037 (a′, 71), 2004 (a′, 2150), 1988 (a′′, 677), 1981 (a′, 547), 1971 (a′′, 778), 1930 (a′′, 698), 1927 (a′, 310) 2039 (a, 140), 2003 (a, 1777), 1985 (a, 977), 1981 (a, 219), 1940 (a, 1034), 1933 (a, 604), 1928 (a, 211) 2051 (a′, 373), 2012 (a′, 387), 1997 (a′, 1404), 1987 (a′, 880), 1986 (a′′, 1672), 1958 (a′, 352), 1940 (a′′, 423) 2048 (a, 375), 2001 (a, 782), 1997 (a, 2106), 1975 (a, 990), 1971 (a, 1114), 1959 (a, 356), 1952 (a, 51)

1150 (a′, 474), 1119 (a′, 73) 1168 (a1, 273), 1140 (b1, 407) 1287 (a′, 871), 1169 (a′, 288) 1166 (a′, 306), 1129 (a′, 304) 1226 (a′, 190), 1214 (a′′, 722) 1229 (a, 208), 1221 (b, 711) 1293 (a, 729), 1217 (a, 339) 1290 (a′, 708), 1231 (a′, 524) 1294 (a, 265), 1288 (a, 1243) 1166 (a′, 306), 1129 (a′, 304) 1170 (a, 475), 1134 (a, 177)


TABLE 10: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Frequencies (Nimg) for the Final Seven Cr2(CS)2(CO)7 Structures B3LYP BP86


27-5 (Cs)

27-6 (C2)

27-7 (C1)

27-8 (Cs)

27-9 (C2)

27-10 (Cs)

27-11(C1)

3755.11990 4.7 0 3755.59761 3.8 0

3755.11937 5.0 1 (80i) 3755.59701 4.1 1 (71i)

3755.11622 7.0 0 3755.59427 5.8 0

3755.11582 7.3 0 3755.59342 6.4 1 (53i)

3755.11248 9.4 1 (60i) 3755.59054 8.2 0

3755.10915 11.4 1 (21i) converts to 27-4

3755.11375 8.6 0 3755.59234 7.1 0

The Cr2(CS)2(CO)8 structure 28-6, at 18.7 kcal/mol (B3LYP) or 25.3 kcal/mol (BP86) above the global minimum 28-1, without any imaginary vibrational frequencies, is similar to 28-4, except that the bridging groups are carbonyl groups rather than thiocarbonyl groups. These bridging carbonyl groups are four-electron donor bridging carbonyl groups, as indicated by Cr-O distances in 28-6 of 2.560 Å (B3LYP) or 2.474 Å (BP86), and are slightly shorter than the comparable Cr-S distances in 28-4. 3.2.3. Cr2(CS)2(CO)7. The potential energy surface of Cr2(CS)2(CO)7 is more complicated than that of Cr2(CS)2(CO)8 with 11 optimized structures within 15 kcal/mol of the global minimum (Figures 5-7 and Tables 8, 9, and 10). The four lowest energy Cr2(CS)2(CO)7 structures, which have no imaginary vibrational frequencies, have at least one four-electron donor bridging thiocarbonyl group. This differs from the isoelectronic Cr2(CO)9, for which no structures with fourelectron donor carbonyl groups were found in a previous DFT study.12 The global minimum of Cr2(CS)2(CO)7, 27-1, and structure 27-2 at only 0.1 kcal/mol (B3LYP) or 2.8 kcal/mol (BP86) above 27-1 (Figure 5 and Table 8) have two four-electron donor bridging η2-µ-CS groups as indicated by Cr-S distances of ∼2.6 Å. The ν(CS) frequencies of these thiocarbonyl groups are predicted to be relatively low at 1144 ( 25 cm-1 (Table 9). In 27-1, the sulfur atoms of the thiocarbonyl groups are bonded to different chromium atoms, whereas in 27-2 the sulfur atoms of the thiocarbonyl groups are bonded to the same chromium atom. The CrdCr distances in structures 27-1 and 27-2 are reported to be 2.79 ( 0.02 Å by both methods.

The Cr2(CS)2(CO)7 structure 27-3, at 2.2 kcal/mol (B3LYP) or 1.6 kcal/mol (BP86) above 27-1 (Figure 5 and Table 8), has one bridging thiocarbonyl group and one bridging carbonyl group. The bridging thiocarbonyl group in 27-3 is suggested to be a four-electron donor by its predicted short Cr-S distance of 2.408 Å (B3LYP) or 2.414 Å (BP86) and exhibits a ν(CS) frequency of 1169 cm-1 (Table 9). However, the bridging carbonyl group in 27-3 is only a two-electron donor, as indicated by a long Cr · · · O distance, and exhibits a ν(CO) frequency at 1853 cm-1. The CrdCr distance in 27-3 of 2.994 Å (B3LYP) or 2.810 Å (BP86) is relatively long for the formal double bond required to give both chromium atoms the favored 18-electron configuration. The Cr2(CS)2(CO)7 structure 27-4, at 3.3 kcal/mol (B3LYP) or 2.1 kcal/mol (BP86) above 27-1 (Figure 5 and Table 8), is similar to that of 27-3 except that both bridging groups are thiocarbonyl groups. One of these thiocarbonyl groups is a fourelectron donor η2-µ-CS group, as indicated by a Cr-S distance of 2.426 Å (B3LYP) or 2.424 Å (BP86). However, the second thiocarbonyl in 27-4 is only a two-electron donor with a clearly nonbonding Cr · · · S distance. The ν(CS) frequencies of 1166 and 1129 cm-1 for these thiocarbonyl groups (Table 9) do not clearly distinguish between the four-electron and two-electron donor thiocarbonyl groups. The CrdCr distance of 2.816 Å (B3LYP) or 2.772 Å (BP86) can be interpreted as the formal double bond required to give both chromium atoms the favored 18-electron configuration. The triply bridged structures Cr2(CO)6(µ-CO)(µ-CS)2, 27-5 and 27-6 at 4-5 kcal/mol above 27-1 (Figure 6 and Table 10), may be derived from the triply bridged Cr2(CO)6(µ-CO)3

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Figure 6. The five optimized Cr2(CS)2(CO)7 structures with three bridging groups.

Figure 7. The remaining two Cr2(CS)2(CO)7 structures.

structure previously predicted by DFT12 by replacing two of the bridging CO groups with bridging CS groups. The very short CrtCr distances of 2.27 ( 0.01 Å are consistent with the formal triple bond needed to give both chromium atoms the favored 18-electron configuration. Structure 27-6 is predicted to have an imaginary vibrational frequency of ∼80i cm-1 with both methods. Following the corresponding normal mode led to structure 27-5. The three Cr2(CS)2(CO)7 structures 27-7, 27-8, and 27-9 are derived from 27-5 or 27-6 by replacement of one or both CS groups by bridging CO groups. The structures 27-7 and 27-8 with one bridging CS group and two bridging CO groups lie 6-7 kcal/mol above 27-1 and have CrtCr distances somewhat longer at 2.30 ( 0.02 Å than those in the doubly CS bridged and singly CO bridged structures 27-5 and 27-6. The Cr2(CS)2(CO)7 structure 27-9 with three CO bridges and two terminal CS groups lies at a slightly higher energy of 8-9 kcal/ mol above 27-1 and has a somewhat longer CrtCr distance of 2.32 ( 0.01 Å. However, all of the CrtCr distances in structures 27-5, 27-6, 27-7, 27-8, and 27-9 fall within a reasonable range for the formal triple bond required to give both chromium atoms the favored 18-electron configuration. The Cr2(CS)2(CO)7 structure 27-10 with two bridging thiocarbonyl groups (Figure 7 and Table 10) is predicted by the B3LYP method to lie 11.4 kcal/mol above 27-1 and to have a

tiny imaginary frequency of 21i cm-1. However, attempted optimization of 27-10 by the BP86 method leads instead to 27-4. The nonbonding Cr · · · S distances in 27-10 imply that the two bridging thiocarbonyl groups are formal two-electron donors rather than four-electron donors. The CrdCr distance of 2.562 Å can be interpreted as a formal double bond, thereby giving the chromium atom bearing four terminal carbonyl groups (the “left” chromium atom in Figure 7) the favored 18-electron configuration, but the chromium atom bearing only three terminal carbonyl groups a 16-electron configuration. The final Cr2(CS)2(CO)7 genuine minimum structure 27-11 (Figure 7 and Table 10) is at 8.6 kcal/mol (B3LYP) or 7.1 kcal/ mol (BP86) above 27-1. Structure 27-11 has two four-electron donor thiocarbonyl groups bridging the chromium-chromium bond. The Cr-Cr distance is predicted to be 2.955 Å (B3LYP) or 2.910 Å (BP86), corresponding to a formal Cr-Cr single bond. This is sufficient to give both chromium atoms the favored 18-electron configuration in light of the two four-electron donor bridging CS groups. We also optimized singly bridged Cr2(CS)2(CO)7 structures. However, their energies were found to be more than 30 kcal/ mol above the global minimum 27-1. Therefore, they are not discussed in this Article. 3.2.4. Cr2(CS)2(CO)6. Five structures were optimized for Cr2(CS)2(CO)6 (Figure 8 and Tables 11 and 12). The lowest energy Cr2(CS)2(CO)6 structure 26-1 has Cs symmetry and all real vibrational frequencies by either B3LYP or BP86. The two bridging groups in 26-1 are thiocarbonyl groups, indicated to be formal four-electron donors by their relatively short Cr-S distances of 2.433 Å (B3LYP) or 2.419 Å (BP86) for one of the thiocarbonyl groups and 2.717 Å (B3LYP) and 2.711 Å (BP86) for the other thiocarbonyl group. The predicted CrdCr distance of 2.746 Å (B3LYP) or 2.710 Å (BP86) in 26-1 corresponds to the formal double bond needed to give both chromium atoms the favored 18-electron configuration after considering the two four-electron donor bridging thiocarbonyl groups.



The Cr2(CS)2(CO)6 structure 26-2, at 5.9 kcal/mol above 26-1, is closely related to 26-1, because it has Cs symmetry and two bridging thiocarbonyl groups, indicated to be formal four-electron donor η2-µ-CS groups by short Cr-S distances of 2.541 Å (B3LYP) or 2.505 Å (BP86) and 2.694 Å (B3LYP) or 2.683 Å (BP86) (Figure 8 and Tables 11 and 12). Structure 26-2 has a small imaginary vibrational frequency of 46i cm-1 (B3LYP) or 42i cm-1 (BP86). Following the corresponding normal mode leads structure 26-2 to 26-1. A third structure for Cr2(CS)2(CO)6, 26-5 at the relatively high energy of 26.1 kcal/mol (B3LYP) or 18.8 kcal/mol (BP86) above 26-1, was found with two four-electron donor bridging thiocarbonyl groups, as indicated by relatively short Cr-S distances of 2.700 Å (B3LYP) or 2.520 Å (BP86). Structure 26-5 is a transition state with an imaginary vibrational frequency at 43i cm-1 (B3LYP) or a relatively large 303i cm-1 (BP86). Following the corresponding normal mode leads to 26-1. The remaining Cr2(CS)2(CO)6 structures are considerably higher in energy than structures 26-1 and 26-2, indicating that the structures with two four-electron donor bridging thiocarbonyl groups are particularly favorable. The Cr2(CS)2(CO)6 structure 26-3, at 18.5 kcal/mol (B3LYP) or 18.8 kcal/mol (BP86) above 26-1 (Table 12), is closely related to structures 26-1 and 26-2, except one of the four-electron donor bridging groups is a carbonyl rather than a thiocarbonyl group. The four-electron donor nature of this carbonyl group is indicated by a short Cr-O distance of 2.195 Å (B3LYP) or 2.189 Å (BP86) and an unusually low ν(CO) frequency at 1660 cm-1 (Table 12). The CrdCr distance in 26-3 of 2.725 Å (B3LYP) or 2.690 Å (BP86) is similar to the CrdCr distances in 26-1 and 26-2 and thus can indicate a formal double bond in 26-3 to give both chromium atoms the favored 18-electron configurations. The final Cr2(CS)2(CO)6 structure 26-4 (Figure 8 and Table 11) at 25 ( 0.4 kcal/mol above 26-1 has two bridging thiocarbonyl groups. The relatively long Cr-S distances in 26-4 indicate that these thiocarbonyl groups are formal donors of only two rather than four electrons. The CrdCr distance of ∼2.54 Å is consistent with a formal double bond leading to only 16-electron configurations for each chromium atom. 3.3. Dissociation Energies. Table 13 lists the bond dissociation energies (BDEs) in terms of the single carbonyl dissociation steps:

Cr(CS)(CO)m f Cr(CS)(CO)m-1 + CO (m ) 5, 4)

(1) Cr2(CS)2(CO)n f Cr2(CS)2(CO)n-1 + CO (n ) 9, 8, 7) (2) The BDEs for the loss of CO from the mononuclear Cr(CS)(CO)m derivatives (m ) 5, 4) are similar to or slightly higher than the 37 kcal/mol BDE for CO loss from Cr(CO)6.41 The BDEs for loss of CO from the binuclear Cr2(CS)2(CO)n derivatives (n ) 9, 8, 7) are significantly lower than that of mononuclear Cr(CS)(CO)m derivatives in the 22 ( 3 kcal/mol (B3LYP) or 24 ( 2 kcal/mol (BP86) range. Table 14 reports the energies of the dissociation of the lowest energy structures of the binuclear Cr2(CS)2(CO)n into mononuclear fragments by reactions of the type: Cr2(CS)2(CO)n f Cr(CS)(CO)x + Cr(CS)(CO)y (n ) x + y)

(3)

Figure 8. The five optimized Cr2(CS)2(CO)6 structures.

All of the binuclear Cr2(CS)2(CO)n derivatives are seen to be thermodynamically stable with respect to dissociation into mononuclear fragments. This suggests that they might be synthesized as stable or at least detectable molecules. Thus, a possible method for the synthesis of Cr2(CS)2(CO)9 might be the photolysis of Cr(CS)(CO)5 in a weakly donating solvent L to give a Cr(CS)(CO)4L derivative followed by displacement of the weakly bonded L ligand by another equivalent of Cr(CS)(CO)5. Of particular interest is the viability of Cr2(CS)2(CO)9 with respect to such dissociation as compared to the related Cr2(CO)11 predicted from a previous DFT study to be thermodynamically unstable with respect to dissociation into mononuclear fragments.4 Also, as the number of carbonyl groups is increased in the Cr2(CS)2(CO)n derivatives, the energy required for dissociation into mononuclear fragments decreases. The stability of the binuclear Cr2(CS)2(CO)n derivatives may relate to the stability of the four-electron donor bridging η2-µ-CS groups holding together the two chromium atoms. Structures containing analogous four-electron donor bridging η2-µ-CO groups were not found in the earlier studies4,11-14 on homoleptic Cr2(CO)n+2 derivatives. 4. Discussion The only structure found for the known mononuclear Cr(CS)(CO)5 was the known octahedral structure 15-1 (Figure 1). Direct comparison of the predicted Cr-C, C-O, and C-S distances in 15-1 with those found by X-ray diffraction9 was not possible, due to disorder involving randomness in the positions of the CO and CS groups leading to averaged Cr-C and CsE (E ) O, S) distances in the experimental structure. The singlet state structures for the unsaturated mononuclear derivatives Cr(CS)(CO)n (n ) 4, 3) are derived from the octahedral Cr(CS)(CO)5 structure 15-1 by loss of one or two carbonyl groups, respectively. This leads to two isomeric square

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TABLE 11: Total Energies (E in au), Relative Energies (∆E in kcal/mol), and Numbers of Imaginary Frequencies for Cr2(CS)2(CO)6 -E ∆E Nimg -E ∆E Nimg

B3LYP BP86

26-1 (Cs)

26-2 (Cs)

26-3 (Cs)

26-4 (Ci)

26-5 (Ci)

3641.76793 0.0 0 3642.24030 0.0 0

3641.75860 5.9 1 (46i) 3642.23096 5.9 1 (42i)

3641.73839 18.5 0 3642.21034 18.8 0

3641.72757 25.3 1 (18i) 3642.20109 24.6 1 (18i)

3641.72637 26.1 1 (43i) 3642.21034 18.8 1 (303i)

TABLE 12: ν(CO) and ν(CS) Stretching Frequencies (cm-1) and Corresponding Infrared Intensities Predicted for the Five Cr2(CS)2(CO)7 Structuresa ν(CO) 26-1 (Cs)

2037 (a′, 22), 2003 (a′, 1865), 1985 (a′, 608), 1976 (a′′, 1895), 1968 (a′, 362), 1948 (a′′, 216) 2038 (a′, 228), 2002 (a′, 726), 1997 (a′, 1371), 1985 (a′′, 1554), 1957 (a′, 404), 1943 (a′′, 569) 2027 (a′, 533), 1990 (a′, 1102), 1984 (a′, 305), 1970 (a′′, 2092), 1950 (a′′, 56), 1660 (a′, 290) 2020 (ag, 0), 1994 (au, 2640), 1970 (ag, 0), 1970 (au, 906), 1951 (au, 1613), 1943 (ag, 0) 2023 (ag, 0), 1992 (au, 2691), 1975 (ag, 0), 1965 (au, 2035), 1960 (au, 517), 1938 (ag, 0)

26-2 (Cs) 26-3 (Cs) 26-4 (Ci) 26-5 (Ci) a

ν(CS) 1143 (a′, 444), 1116 (a′, 8) 1153 (a′, 336), 1113 (a′, 94) 1294 (a′, 655), 1138 (a′, 489) 1185 (au, 491), 1163 (ag, 0) 1164 (ag, 0), 1148 (au, 374)


TABLE 13: Bond Dissociation Energy (kcal/mol) for Successive Removal of Carbonyl Groups from the Lowest Energy Structures of Cr(CS)(CO)m (m ) 5, 4) and Cr2(CS)2(CO)n (n ) 9, 8, 7) B3LYP

BP86

37.8 37.8 24.5 22.7 19.3

42.7 42.3 22.7 25.8 22.6

Cr(CS)(CO)5 f Cr(CS)(CO)4 + CO Cr(CS)(CO)4 f Cr(CS)(CO)3 + CO Cr2(CS)2(CO)9 f Cr2(CS)2(CO)8 + CO Cr2(CS)2(CO)8 f Cr2(CS)2(CO)7 + CO Cr2(CS)2(CO)7 f Cr2(CS)2(CO)6 + CO

TABLE 14: Energies (Units in kcal/mol) for Dissociation of the Binuclear Complexes Cr2(CS)2(CO)n into Two Mononuclear Cr(CS)(CO)x Fragments Considering the Lowest Energy Structures Cr2(CS)2(CO)9 Cr2(CS)2(CO)8 Cr2(CS)2(CO)8 Cr2(CS)2(CO)7 Cr2(CS)2(CO)6

f f f f f

Cr(CS)(CO)5 Cr(CS)(CO)4 Cr(CS)(CO)5 Cr(CS)(CO)4 Cr(CS)(CO)3

+ + + + +

Cr(CS)(CO)4 Cr(CS)(CO)4 Cr(CS)(CO)3 Cr(CS)(CO)3 Cr(CS)(CO)3

B3LYP

BP86

9.8 23.2 23.1 38.3 56.7

10.1 30.1 29.7 46.6 66.3

pyramidal structures for Cr(CS)(CO)4 (Figure 1). One of these structures (14-1) has the CS group in the apical position, and the other such structure (14-2) has the CS group in a basal position. The Cr(CS)(CO)4 generated by photolysis of Cr(CS)(CO)5 in CH4 matrices at 20 K10 appears to be a mixture of isomers 14-1 and 14-2 as indicated by comparison of the experimental and calculated ν(CO) frequencies (Table 2). Two triplet state trigonal bipyramidal structures were also found for Cr(CS)(CO)4. One of these structures (14-3T) has the CS group in an equatorial position, and the other such structure (14-4T) has the CS group in an axial position. A singlet Cr(CS)(CO)4 structure with the thiocarbonyl group bonded endon as a four-electron donor (14-5) through both the carbon and the sulfur atom is predicted to be a high energy structure at ∼40 kcal/mol above the global minimum 14-1. The structures for the even more unsaturated Cr(CS)(CO)3 have “sawhorse” coordination by removing two cis carbonyl groups from the octahedral Cr(CS)(CO)5 15-1 (e.g., structures 13-1, 13-2, 13-3T, and 14-4T in Figure 2) or nearly square planar coor-

dination by removing two trans carbonyl groups from 15-1 (e.g., structures 13-5T and 13-6 in Figure 2). A feature common to the low energy structures of the binuclear Cr2(CS)2(CO)n (n ) 9, 8, 7, 6) is the presence of a four-electron donor bridging η2-µ-CS thiocarbonyl group. An analogous η2-µ-CO carbonyl group is not found in any of the corresponding Cr2(CO)n+2 structures previously studied by DFT.4,11-14 The presence of a four-electron donor bridging thiocarbonyl group in Cr2(CS)2(CO)9 means that no chromiumchromium bond is required to give both chromium atoms the favored 18-electron configuration. In this case, the four-electron donor CO or CS group is important so that these Cr2(CS)2(CO)9 structures (e.g., 29-1, 29-2, 29-3, 29-4, 29-5, and 29-6) have an essentially collinear Cr-CsOfCr or bent Cr-CsSfCr unit with very long clearly nonbonding Cr · · · Cr distances. Interestingly enough, these two types of structures for Cr2(CS)2(CO)9 are fluxional in energy. The Cr2(CS)2(CO)9 structures with features similar to those in the structures previously predicted4 for Cr2(CO)11 are predicted to have small imaginary vibrational frequencies and significantly higher energies than the structures with four-electron donor bridging CO or CS groups. Therefore, they are not discussed in this Article. The lowest energy structures for the unsaturated Cr2(CS)2(CO)n (n ) 8, 7) have one or two four-electron donor bridging η2-µCS groups, respectively. In such structures, a Cr-Cr single bond is sufficient to give both chromium atoms the favored 18electron configuration. In the Cr2(CS)2(CO)8 structures with a single η2-µ-CS group (e.g., structures 28-1 and 28-2 in Figure 4), this Cr-Cr single bond distance is ∼3.1 Å. However, the presence of two bridging four-electron donor η2-µ-CS groups in the lowest energy Cr2(CS)2(CO)7 structures 27-1 and 27-2 (Figure 5) shortens this Cr-Cr single bond distance to 2.82 ( 0.05 Å. The previous DFT study on Cr2(CO)9 predicted triply bridged Cr2(CO)6(µ-CO)3 structures to be the lowest energy structures.12 Analogous Cr2(CS)2(CO)7 structures were found, 27-5, 27-6, 27-7, and 27-8 in Figure 6, but at higher relative energies. Such structures are predicted to have relatively short CrtCr distances in the range 2.30 ( 0.04 Å, consistent with the formal triple

Stabilization of Binuclear Chromium Carbonyls bond required to give both chromium atoms the favored 18electron configuration when all of the carbonyl and thiocarbonyl groups are formal two-electron donors. The low energy structures for Cr2(CS)2(CO)6 (26-1, 26-2, and 26-5 in Figure 8) also have two four-electron donor η2-µ-CS groups. However, in addition to this structural feature, a CrdCr double bond is required to give both chromium atoms the favored 18-electron configuration. The CrdCr distances in these Cr2(CS)2(CO)6 structures fall in the range 2.70 ( 0.05 Å and are significantly shorter than the Cr-Cr distances of 2.82 ( 0.05 Å assigned to formal single bonds in the Cr2(CS)2(CO)7 derivatives with two η2-µ-CS groups discussed above. Thus, the chromium atoms in the Cr2(CS)2(CO)6 structures 26-1, 262, and 26-5 can each attain the favored 18-electron configuration with the two four-electron donor η2-µ-CS groups and a formal CrdCr double bond. A similar combination of two four-electron donor η2-µ-CO groups and a formal FedFe double bond was previously predicted by DFT42 for the lowest energy structure of the highly unsaturated Fe2(CO)6. Acknowledgment. We are indebted to the 111 Project (B07012) and the National Natural Science Foundation (20873045 and 20973066) of China as well as the U.S. National Science Foundation (Grants CHE-0749868 and CHE-0716718) for support of this research. Supporting Information Available: Tables S1-S6: Theoretical harmonic vibrational frequencies for Cr(CS)(CO)5 (1 structure), Cr(CS)(CO)4 (5 structures), Cr(CS)(CO)3 (6 structures), Cr2(CS)2(CO)9 (6 structures), Cr2(CS)2(CO)8 (7 structures), Cr2(CS)2(CO)7 (11 structures), and Cr2(CS)2(CO)6 (5 structures) using the BP86 method. Tables S6-S47: Theoretical Cartesian coordinates for Cr(CS)(CO)5 (1 structures), Cr(CS)(CO)4 (5 structures), Cr(CS)(CO)3 (6 structures), Cr2(CS)2(CO)9 (6 structures), Cr2(CS)2(CO)8 (7 structures), Cr2(CS)2(CO)7 (11 structures), and Cr2(CS)2(CO)6 (5 structures) using the B3LYP method. Complete Gaussian 03 reference (ref 36). This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Mond, L.; Hirtz, H.; Cowap, M. D. J. Chem. Soc. 1910, 57, 798. (2) Dewar, J.; Jones, H. O. Proc. R. Soc. 1907, 79A, 66. (3) Brimm, E. O.; Lynch, M. A., Jr.; Sesny, W. J. J. Am. Chem. Soc. 1954, 76, 3831. (4) Richardson, N. A.; Xie, Y.; King, R. B.; Schaefer, H. F. J. Phys. Chem. 2001, 105, 11134.

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Stabilization of Binuclear Chromium Carbonyls by Substitution of

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