A Time-Dependent Density Functional Theory Study of the Structure

Article pubs.acs.org/JPCA

A Time-Dependent Density Functional Theory Study of the Structure and Electronic Spectroscopy of the Group 7 Mixed-Metal Carbonyls: MnTc(CO)10, MnRe(CO)10, and TcRe(CO)10 Russell G. McKinlay and Martin J. Paterson* Institute of Chemical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland ABSTRACT: A detailed study of the structure, infrared, and electronic spectra of the mixed-metal group 7 carbonyls MnTc(CO)10, MnRe(CO)10, and TcRe(CO)10 is presented using density functional theory, and time-dependent density functional theory, with a variety of modern density functionals. Long-range corrected density functionals are needed to accurately model the transitions in such complexes, and through calibration with data for known bimetallic carbonyls, DFT and TD-DFT can be used to predict the behavior of their as yet elusive counterparts.

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INTRODUCTION We present a detailed study of structure and electronic spectra of the mixed-metal group 7 carbonyls MnTc(CO)10, MnRe(CO)10, and TcRe(CO)10. The equivalent group 7 bimetallics Mn2(CO)10, Tc2(CO)10, and Re2(CO)10 have already been extensively investigated both experimentally and theoretically for structure and spectroscopy.1−5 Modern laser-based experiments have shown that Mn2(CO)10 in particular displays rich ultrafast dissociative photochemistry after laser excitation, including nonadiabatic features such as conical intersections in the relaxation mechanisms of the two possible dissociation channels of the initial photoproducts formed, metal−carbonyl or metal−metal bond cleavage. Indeed, the theoretical photochemistry of a wider range of metal carbonyls has been extensively studied and reviewed.4,6−13 However, the mixedmetal bimetallics have received much less attention. This is surprising, as the ground-state structures of these carbonyls have no bridging ligands and a bond between two different transition metal atoms. Reports relating to them in the literature are comparatively rare, with MnRe(CO)10 the most studied of the three carbonyls, with synthesis, spectroscopy, and reactivity all investigated, in a review by Coville and Leins.14 Two recent papers have been published on the subject of the structure of MnRe(CO)10. The first by Tanjaroon et al.15 reported the experimental rotational spectrum with a reported rotational constant of 200.55 MHz for the Re185 isotopomer and 200.36 MHz for the Re187 isotopomer using a highresolution pulsed beam microwave spectrometer with density functional (B3LYP and BP86) and ab initio calculations (SCF) used to determine the nuclear quadrupole coupling constants and electric field gradients. The second paper by Palmer and co-workers16 reported in detail the possible equilibrium structures of MnRe(CO)10 using density functional theory, using both the B3LYP and the BP86 density functionals. Two different conformers of C4v symmetry were found in either © 2012 American Chemical Society

staggered or eclipsed geometries with respect to rotation around the metal−metal bond. The staggered conformation was found to be lower in energy by no more than 4.07 kcal mol−1, with interconversion between the two conformers thought to be readily accessible via one imaginary frequency in the eclipsed conformation that relates to internal rotation around the metal−metal bond. Reports on MnTc(CO)10 and TcRe(CO)10 are much less common with only one study reported in the literature by Michels and Svec from 198117 where the synthesis and characterization by infrared spectroscopy and mass spectrometry was discussed. At the present time, no report has been found in the literature relating to a theoretical study of the structure of MnTc(CO)10 or TcRe(CO)10 and the theoretical electronic spectra of any of these three complexes. This is surprising as one could hypothesize that the structural and spectral properties of all three should be quite similar. Given the number of studies on monometallic binary transition metal carbonyls,4,10−13,18 and Mn2(CO)10,19 as paradigm systems in inorganic chemistry, clearly further work on these mixed-metal systems is required. To investigate the structure and spectroscopy of these systems, we have used density functional theory (DFT) and time-dependent density functional theory (TD-DFT) with a range of well-known and more modern functionals including the meta-GGA functionals of Zhao and Truhlar20 and the coulomb attenuated B3LYP (CAM-B3LYP) functional of Handy and co-workers.21 The latter purports to include all of the benefits of the B3LYP hybrid functional while also including a better treatment of exchange interactions at long range, which in theory should improve the ability of TD-DFT to describe charge-transfer states.22−24 These states are prevalent in transition metal Received: July 26, 2012 Revised: August 20, 2012 Published: August 24, 2012 9295

dx.doi.org/10.1021/jp3073969 | J. Phys. Chem. A 2012, 116, 9295−9304

The Journal of Physical Chemistry A

Article

then used to generate the electronic spectrum of each carbonyl with TD-DFT using both basis sets and all three functionals for each, encompassing the first 60 vertical excited states. The infrared spectrum of each system was also generated, assigned, and discussed using the B3LYP functional and the SDD/6311G* basis set. The impact of (scalar) relativistic effects on our results for both structure and electronic spectroscopy was investigated by the inclusion of a cc-pVTZ basis set with three different types of SDD relativistic pseudopotentials for the system that has seen most experimental studies, MnRe(CO)10, accounting for zero-, quasi-, and full-relativistic effects. A cc-pVTZ DK (Douglas-Kroll) basis set was used on manganese37,38 along with a cc-pVTZ basis set on rhenium with the three pseudopotentials.34,39 Carbon and oxygen were treated with the all-electron cc-pVTZ basis set40 implemented within the Gaussian 09 code. As with the other calculations, the staggered conformer was optimized using this cc-pVTZ basis set and all three pseudopotentials, but using only the CAM-B3LYP functional. The eclipsed conformer was also optimized using this cc-pVTZ basis set, but using only the full-relativistic pseudopotential to compare the values of the barrier height between staggered and eclipsed conformers. The first 60 vertical excited states were also calculated with the cc-pVTZ basis set with the CAM-B3LYP functional and all three pseudopotentials. These results were compared to the results calculated using the other smaller basis sets. Finally, some reference calculations on the bimetallic binary carbonyl Mn2(CO)10 with D4d symmetry were also performed to check the accuracy of the LanL2DZ, SDD/6-311G*, and ccpVTZ DK basis sets with the CAM-B3LYP functional against previous studies of both structure and electronic spectroscopy for a system whose structure and photochemistry have been intensely studied in the past.41,42

complexes but are a great weakness for TD-DFT. However, CAM-B3LYP has already been successfully applied to some systems, see, for example, refs 22−27, and it has also been demonstrated that it is the best performing functional for twophoton absorption, which can be much harder to describe than linear absorption due the functional needing to describe “virtual states” of varying character.28 We also present an assignment of the infrared spectra of each carbonyl using the B3LYP functional. IR spectroscopy is very important in the structural determination of such species; very few studies on the assignments of these spectra have been found in the literature.

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COMPUTATIONAL DETAILS The Gaussian 09 code29 was used to perform all calculations in which both the staggered and the eclipsed conformers of all three complexes were investigated using three different DFT functionals. The first is the three-parameter B3LYP hybrid functional of Becke, Lee, Yang, and Parr,30 which is one of the most commonly used DFT methods in modern electronic structure theory. The second is the M062X functional developed by Zhao and Truhlar20 that is a hybrid functional where the “2X” notation means it uses double the amount of Hartree−Fock exchange over its “M06” sister functional, at 54%. This hybrid meta-GGA functional is another “rung” up on the “Jacob’s ladder” of DFT functionals31 in that it involves the kinetic energy density in addition to the density and density gradient. Neither of these two functionals is designed to specifically deal with charge-transfer states in electronic spectroscopy. The third functional used in this article is the coulomb attenuated B3LYP (CAM-B3LYP) functional developed by Yanai, Tew, and Handy,21 which “switches on” the amount of exact Hartree−Fock exchange as the interelectronic distance increases. CAM-B3LYP has already been successfully applied to problems of charge-transfer states such as an investigation on the charge-transfer band in a zinc bacteriochlorin−bacteriochlorin complex by Kobayashi and Amos,23 and a study of temporary anion states in a range of first-row transition metal (Cr, Mn, Fe, Co) cyclopentadienyl carbonyl complexes by Cheng, Chang, and Shih.24 Because these states are predicted to be important for most metal carbonyls studied, it is included here. The use of M062X and CAM-B3LYP represents a chance to look at improvements over the B3LYP functional in two different ways when calculating the electronic excited states of transition metal complexes. By using M062X, we compare a hybrid GGA functional with a hybrid meta-GGA functional. Using CAM-B3LYP, we compare the addition of a long-range exchange correction. It may be argued that M06L is better suited to transition metal systems than M062X, but we use it here for the comparison stated above. Both staggered and eclipsed conformers were optimized using all three functionals including analytical frequency calculations to establish the presence of any imaginary vibrational frequencies. Two basis sets were used in all calculations, the Los Alamos effective core potential (ECP) double-ζ (LanL2DZ) basis set32,33 on all atoms ([Ne] 10 electron core) on the metals, and Dunning 95 double-ζ on all atoms with the standard frozen core electrons on each metal atom as implemented within the Gaussian 09 code, giving 224 basis functions. The second larger basis set is a mix of the SDD ECP core [Ne], [Ar], and [Kr]4d basis set on the manganese, technetium, and rhenium atoms, respectively,32,34,35 and the Pople 6-311G*36 basis set on carbon and oxygen, which has 439 basis functions in total. These optimized geometries were

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RESULTS AND DISCUSSION I. Structure. First, the results of the reference calculations on Mn2(CO)10 using the three basis sets and the CAM-B3LYP functional are shown in Table 1. These results are compared to Table 1. Bond Lengths (Å) of Mn2(CO)10 with Three Basis Sets in Order from the Smallest (LanL2DZ) to the Largest (cc-pVTZ DK) As Compared to Experiment for the LSD Exchange Functional Form basis sets bond length Mn−Mn Mn−CO axial Mn−CO equatorial

LanL2DZ

SDD/6311G*

cc-pVTZ DK

LSD

experiment

2.900 1.836 1.790

2.925 1.855 1.807

2.880 1.839 1.790

2.876 1.799 1.747

2.895 1.859 1.820

previous experimental43 and theoretical DFT3,19 studies. It can be seen that the values of the main three types of bond lengths, the Mn−Mn, the Mn−C equatorial, and the Mn−C axial, computed with CAM-B3LYP and the three basis sets used compare well to the experimental structure and with each other, with no more than a 0.04 Å difference between the experimental structure and the CAM-B3LYP results or between the CAM-B3LYP results themselves. This shows for the Mn2(CO)10 system at least the CAM-B3LYP results and the 9296



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Table 2. Energetics of All Optimized Geometriesa energy of conformer/au complex MnTc(CO)10

functional B3LYP M062X CAM-B3LYP

MnRe(CO)10

B3LYP M062X CAM-B3LYP

TcRe(CO)10


a

basis set

staggered

eclipsed

barrier to rotation/kcal mol−1

LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* cc-pVTZ (FR) LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G*

−1317.2763 −1319.0281 −1316.5661 −1318.3405 −1316.6562 −1318.4360 −1316.3252 −1316.5258 −1315.6058 −1315.8417 −1316.6562 −1318.4360 −2359.8522 −1292.5308 −1293.0759 −1291.7824 −1292.3558 −1291.9036 −1292.4715

−1317.2690 −1319.0217 −1316.5557 −1318.3314 −1316.6475 −1318.4286 −1316.3173 −1316.5193 −1315.5945 −1315.8323 −1316.6475 −1318.4286 −2359.8450 −1292.5244 −1293.0705 −1291.7732 −1292.3483 −1291.8964 −1292.4656

4.619 4.009 6.503 5.736 5.459 4.643 4.920 4.054 7.088 5.904 5.459 4.643 4.499 4.004 3.352 5.793 4.711 4.553 3.722

Energies are quoted in atomic units, and barrier to rotation values are in kcal mol−1.

Table 3. Selected Geometrical Parameters of All Carbonyls Studied in the Staggered Conformationa geometrical parameter/Å complex MnTc(CO)10


MnRe(CO)10


TcRe(CO)10


basis set

M−M

M1−COax

M2−COax

M1−COeq

M2−COeq

LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* cc-pVTZ (NR) cc-pVTZ (QR) cc-pVTZ (FR) LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G*

3.045 3.064 2.980 2.993 2.976 3.001 3.044 3.079 2.978 3.005 2.977 3.016 2.967 2.983 2.986 3.127 3.152 3.033 3.053 3.068 3.097

1.843 1.862 1.871 1.899 1.831 1.853 1.844 1.863 1.874 1.900 1.833 1.853 1.831 1.835 1.835 1.997 2.006 1.995 2.002 1.990 1.999

2.000 2.009 1.995 2.001 1.993 2.001 1.996 2.023 1.987 2.012 1.989 2.016 2.058 2.010 2.004 1.994 2.021 1.986 2.013 1.986 2.014

1.796 1.814 1.811 1.831 1.788 1.806 1.798 1.816 1.816 1.834 1.790 1.808 1.790 1.791 1.791 1.944 1.949 1.933 1.931 1.941 1.945

1.939 1.944 1.928 1.929 1.937 1.941 1.934 1.959 1.924 1.947 1.932 1.956 1.997 1.944 1.939 1.936 1.960 1.926 1.948 1.934 1.957

a

All numbers are given in angstroms. The subscript numbers 1 and 2 for each M−CO bond correspond to the metals in the order they are written in the table.

basis sets used are accurate for studying the molecular structure of such a carbonyl. The main results of all geometry optimizations for both staggered and eclipsed conformations of all three carbonyls are shown in Tables 2, 3, and 4. Both energetic and geometrical parameter results are presented, Table 2 for energetics and Tables 3 and 4 for staggered and eclipsed geometrical parameters, respectively. All results are compared to previously reported experimental and theoretical results where applicable.

The structures of each conformer are pictorially presented in Figure 1. It was found that the staggered conformation was lower in energy than the eclipsed conformation. Analytical frequency calculations showed that the staggered conformation was a valid minimum, and that the eclipsed conformation was a first-order saddle point with one imaginary vibrational frequency. This frequency relates to rotation around the metal−metal bond for interconversion to the staggered conformation. These results 9297



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Table 4. Selected Geometrical Parameters of All Carbonyls Studied in the Eclipsed Conformationa geometrical parameter/Å complex MnTc(CO)10


MnRe(CO)10


TcRe(CO)10


basis set

M−M

M1−COax

M2−COax

M1−COeq

M2−COeq

LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* cc-pVTZ (FR) LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G* LanL2DZ SDD/6-311G*

3.168 3.188 3.117 3.123 3.093 3.118 3.166 3.198 3.110 3.131 3.093 3.128 3.099 3.232 3.254 3.157 3.168 3.167 3.193

1.843 1.863 1.870 1.899 1.832 1.854 1.843 1.863 1.873 1.900 1.833 1.854 1.837 1.997 2.007 1.996 2.003 1.990 1.999

2.000 2.008 1.997 2.002 1.992 2.001 1.996 2.022 1.988 2.013 1.989 2.016 2.005 1.994 2.021 1.987 1.919 1.986 2.014

1.792 1.810 1.802 1.821 1.784 1.801 1.794 1.811 1.808 1.824 1.786 1.803 1.783 1.937 1.942 1.920 2.014 1.934 1.938

1.933 1.937 1.916 1.916 1.930 1.934 1.929 1.952 1.915 1.936 1.926 1.949 1.931 1.931 1.954 1.917 1.937 1.928 1.951

a

All numbers are given in angstroms. The subscript numbers 1 and 2 for each M−CO bond correspond to the metals in the order they are written in the table.

results presented here. The value of the Mn−Re bond length measured in the crystal structure is also in reasonable agreement with the presented results, with the shortest bond length of 2.967 Å with CAM-B3LYP and the cc-pVTZ (nonrelativistic pseudopotential) basis set and the longest bond length with our results of 3.07 Å with B3LYP and the SDD/6-311G* basis set. Here, the smaller LanL2DZ basis set gives shorter bond lengths than the SDD/6-311G* basis set, and the Mn−Re bond lengths match well with the crystal structure. From this, it can be seen that the Mn−Tc bonds are generally shorter and Tc−Re bond generally longer than Mn−Re bonds, but this can be understood due to the relative size of the two metal atoms in the complexes. If the lengths of the M−M bond are compared between both staggered and eclipsed conformations, the bonds in the eclipsed conformation are slightly longer, but the difference is negligible; for example, the Mn−Re bond length calculated with B3LYP and the SDD/6-311G* basis set was 3.07 Å for the staggered conformation and 3.17 Å for the eclipsed conformations. This is a difference of 0.1 Å, and in almost all cases the difference between M−M bond lengths never exceeds this value of difference. The effect of the ccpVTZ basis is that it also compares very well with the crystal structure bond lengths in general, and that the small basis sets also fare well as compared to the larger triple-ζ one. The effect in going from a non- to quasi- to fully relativistic pseudopotential is that the bond lengths are lengthened, but the difference in bond lengths when quasi- and fully relativistic pseudopotentials are used is very small indeed. The barrier going from staggered to eclipsed conformers with the cc-pVTZ basis set and fully relativistic pseudopotential is 4.499 kcal mol−1, which is comparable both with the results of Palmer and co-workers and with the smaller basis sets used here. This shows that the effects on structure when relativistic effects are taken into account for rhenium are rather small as compared to the smaller basis sets, which do not explicitly account for these relativistic effects.

Figure 1. Optimized geometries of the staggered and eclipsed C4v transition states for all carbonyls studied.

agree with the findings of Palmer and co-workers who reported this only for MnRe(CO)10. The difference in energy between staggered and eclipsed conformations is very small in all cases and similar in magnitude to the results of Palmer and co-workers. The barrier to rotation is also very small and never more than 7.1 kcal mol−1 in all cases, although it is smaller in the other two carbonyls than in MnRe(CO)10 in the order of MnRe(CO)10 > MnTc(CO)10 > TcRe(CO)10. The larger basis set gives a slightly lower barrier to rotation in all cases. CAM-B3LYP should have similar properties and predict similar results for ground-state structures and energetics as B3LYP, and here the energy values predicted by CAM-B3LYP and B3LYP are closer to one another than those values predicted by M062X. The barriers to rotation reported by Palmer and co-workers of 3.82 and 4.07 kcal mol−1 for B3LYP and BP86, respectively, for MnRe(CO)10 are comparable to the results presented here where with the LanL2DZ basis set the barrier was 4.92 kcal mol−1 and with the SDD/6-311G* basis set it was 4.05 kcal mol−1. The crystal structure of MnRe(CO)10 was reported by Rheingold and co-workers44 who measured an Mn−Re bond length of 2.96 Å with a space group of I2/a. Each individual molecule in the complex was found to have C4v symmetry in the staggered conformation, which is in accordance with the 9298



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One last consideration in terms of structure are the rotational constants of these complexes. These have been calculated in the paper by Tanjaroon and co-workers15 discussed earlier. Calculations with B3LYP with the SDD/6-311G* basis set are 210.84, 192.49, and 188.87 MHz for MnTc(CO)10, MnRe(CO)10, and TcRe(CO)10, respectively. The rotational constant is almost 8 MHz lower than the best values reported by Tanjaroon, but our values are in reasonable agreement with this value. A reduction in rotational constant is observed going from MnTc(CO)10 to TcRe(CO)10. II. Infrared Spectroscopy. The infrared spectra of all three carbonyls are presented in Tables 5−7 using the B3LYP

Table 7. Infrared Spectrum Assignments for TcRe(CO)10 Using B3LYP and the SDD/6-311G* Basis Set

Table 5. Infrared Spectrum Assignments for MnTc(CO)10 Using B3LYP and the SDD/6-311G* Basis Set frequency/ cm−1 55, 56 102, 107, 425 103 94, 147 541 96, 110, 667 391, 611, 627 395 404, 420, 568 459 462 476, 682 2056 2061, 2073 2092 2111, 2187

symmetry

assignment

E, E E, A1, A1

C−M−M−C antisymmetric bending mode C−Tc−C symmetric bending mode

B2 A1, A1 E E, E, E E, E, A1

C−Mn−C symmetric bending mode M−M symmetric stretching mode C−Tc−C antisymmetric bending mode C−Mn−C antisymmetric bending mode C−Tc−C antisymmetric stretching mode

A1 E, E, E

C−Mn−C symmetric stretching mode C−Mn−Tc−C antisymmetric bending mode

A1 E A1, A1 E A1, A1

Tc−C stretching mode C−Mn−C antisymmetric stretching mode Mn−C stretching mode C−O antisymmetric axial stretching mode Mn−C−O, Tc−C−O only antisymmetric stretching mode C−O symmetric axial stretching mode C−O symmetric breathing mode

E A1, A1

symmetry

55, 57, 85, 98 94 95, 102 110, 544, 602, 610 144 388 410, 427 450, 474 569, 462, 667, 681 475 2053, 2056 2071, 2113, 2187 2088

E, E, E, A1 A1 E, E E, E, E, A1

C−Mn−C M−M symmetric stretching mode C−Mn−Re−C antisymmetric bend C−Re−C antisymmetric bending mode

A1 E E, E A1, A1 E, E, E, A1

C−Mn−C antisymmetric bending mode C−Re−C antisymmetric stretching mode C−Mn−Re−C antisymmetric bending mode Re−C stretching mode C−Mn−C antisymmetric bending mode

A1 E, A1 A1, A1, A1

Mn−C stretching mode C−O antisymmetric stretching mode C−O symmetric breathing mode

E

Mn−C−O, Re−C−O only antisymmetric stretching mode

symmetry

assignment

51, 53, 128 82, 100, 410, 539, 613, 636 87 89, 96, 98, 376, 542, 604, 608 389, 394

E, E, A1 E, E, E, E, E, A1 A1 E, A1, E, A2, E, E, A1 E, E

426

E

427 452 473 2053, 2054, 2087, 2128 2068

A1 A1 A1 A1, E, E, A1

C−Tc−Re−C asymmetric bend C−Tc−C antisymmetric bending mode Tc−Re stretching mode C−Re−C antisymmetric bending mode C−Re−C antisymmetric stretching mode C−Tc−Re−C antisymmetric bending mode C−Tc−C symmetric stretching mode C−Re−C symmetric stretching mode Tc−C stretching mode C−O antisymmetric modes

2189

A1

A1

Tc−C−O, Re−C−O only antisymmetric stretching mode C−O symmetric breathing mode

could be expected. The spectra produced here for MnRe(CO)10 broadly agree with those previously produced for this carbonyl. This includes an E symmetry band at 2088 cm−1 from our results, which is at 2087 cm−1 in the study by Tanjaroon et al. and at 2017 cm−1 in the experimental study by Flitcroft et al. referenced above. The IR spectra of the other two carbonyls are broadly similar to that of MnRe(CO) 10, a conclusion shared by the experimental study of Michels and Svec referenced above. The spectra in all three cases consist of two main collections of bands, the lower between 500 and 700 cm−1 relating to M−C bending vibrational modes and another group of bands between 2000 and 2200 cm−1 that relate to C−O stretching vibrational modes. One minor consideration that can be drawn from analysis of the C−O stretching region is that six C−O stretching vibrations are present for each carbonyl, while in the experimental IR spectra measured by Michels and Svec only three such stretching bands are observed. It appears that while three vibrations for each species are strong, three others are either weak and buried or are hidden by the stronger bands. Further experimental study would be needed to confirm which or either hypothesis is true. It does appear however that the same effect occurs in each carbonyl. III. Electronic Spectroscopy. The results of the reference calculations on the experimental bands46,47 of Mn2(CO)10 with the CAM-B3LYP functional and the LanL2DZ, SDD/6-311G*, and cc-pVTZ DK basis sets as compared to a previous CASSF/ CASPT2 study by Kühn and co-workers4 are presented in Table 8. It can be seen that all three basis sets used with CAMB3LYP give reasonably similar results for these three bands, although the CASPT2 results are closer in this case. A small blue-shift is also observed in going from the smallest (LanL2DZ) to the biggest (cc-pVTZ) basis set used here. What can also be seen is that the results with the LanL2DZ basis set do not agree very well with the experimental value for the excitation energy of the third excited state in the table. For this system, this can be explained by the fact that the smaller size of this basis set limits its ability to accurately model higher energy (>6 eV) excited states. What this does show is that the smaller basis sets used here do agree reasonably well with the largest triple-ζ basis sets used for Mn2(CO)10 for the prediction of electronic excited states. Through this we believe that the

Table 6. Infrared Spectrum Assignments for MnRe(CO)10 Using B3LYP and the SDD/6311G* Basis Set frequency/cm−1

frequency/cm‑1

assignment

functional and the SDD/6-311G* basis set. The IR spectra and analysis have been reported before for MnRe(CO)10,15,45 and the spectra of MnTc(CO)10 and TcRe(CO)10 have also been produced.17 All three spectra are very similar with only minor differences in the position and type of signal in the spectra that 9299



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Table 8. Comparison of Experimental Excitation Energies of Mn2(CO)10 with CASSCF and CASPT2 from CAM-B3LYP with Three Basis Sets of Increasing Sizea CAM-B3LYP

a

state symmetry

character

CASSCF

CASPT2

expt.

LanL2DZ

SDD/6-311G*

cc-pVDZ DK

E1 B2 E1

π→σ* σ→σ* σ→π*CO

5.22 (0.03) 4.69 (0.92) 6.11 (0.24)

3.27 (0.03) 3.40 (0.92) 5.37 (0.24)

3.31 3.39 6.09

3.71 (0) 3.82 (0.54) 5.61 (0)

3.62 (0) 3.87 (0.52) 5.89 (0.0005)

3.80 (0) 4.03 (0.51) 6.00 (0.0035)

Oscillator strengths are in parentheses.

well as selected important dark states, are presented in Tables 10−16 for the purposes of assigning these states to the experimental bands. Table 14 presents these states for MnRe(CO)10 using the CAM-B3LYP and the cc-pVTZ basis set with all three types of pseudopotential used. The first band in the spectrum was assigned as a metal− metal transition due to its lower energy position in the spectrum counting it out as a MLCT state, according to Levenson and Gray. This is because the effort required to excite metal electrons away from a ligand orbital increases relative to the effective nuclear charge of the metal, it was argued.49 An A1 symmetry band transition with large oscillator strength of ∼0.3 or higher dominates the lower part of the theoretical spectra in all cases. The excitation energies of this transition for MnRe(CO)10 are ∼3.70 and ∼4.0 eV for the LanL2DZ and SDD/6-311G* basis set, respectively, which is in good agreement with the σ→σ* band of the experimental spectrum. This state is also present when using the cc-pVTZ basis sets, with an excitation energy of around 4.0 eV for each pseudopotential used. This is quite close to the band in the experimental spectrum, with the effect of going from a non- to quasi- to full-relativistic pseudopotential a general increase in excitation energy by a small amount, no more than 0.2 eV, and very little difference between the results computed using the quasi- and fully relativistic pseudopotentials for all states. Figure 2 shows the orbitals that are involved in this transition. The subsequent bands present more of a challenge to assign. In the experimental spectrum, the next two bands were assigned as MLCT bands; however, both were poorly resolved, which is a common feature of such complexes. The remaining allowed transitions reported here are mainly classified as MLCT states. Keeping MnRe(CO)10 in mind, the experimental spectrum splits the third band into two parts called A and B. This band lies between 4.46 and 4.67 eV in energy, and part A of the third band was assigned as a σ→π* character MLCT state, and such transitions are present in our results in the correct energy region, especially with the M062X functional,

two smaller basis sets can be used for the study of the electronic excited states of the other three group 7 bimetallics. Andrea and co-workers48 have reported the experimental ultraviolet photoelectron spectrum of MnRe(CO)10 where the metal−metal σ and π interactions were specifically studied for this spectrum, as at the time these interactions between manganese and rhenium pentacarbonyls were not known. They concluded that a “simple” σ bond was present between both metal fragments via their 3dz2 orbitals and further more the bond was similar to its monometallic analogue Mn2(CO)10. Levenson and Gray49 have also studied the electronic spectrum of MnRe(CO)10 in detail along with its bimetallic analogues of manganese, rhenium, and technetium. The spectral data from this study are given in Table 9. They identified four main bright Table 9. Experimental Spectral Data for the Main Bands MnRe(CO)10 at 77 K in a 6:1 Mixture of Isopentane and 3Methylpentane from Reference 19a excitation energy/eV

molar absorptivity/cm2 mol−1

assignment

3.96 (3.84) 4.46 4.67 6.41

20 100 (14 900) 11 400 8900 86 600

σ→σ* σ→π* dπ→π* M→π*

Excitation energies have been converted from cm−1 to eV. Numbers in parentheses relate to measurements taken at 300 K.

a

states, each of different character including a σ→σ* state, which had the lowest energy of the four at 3.96 eV in low temperature (77 K) solvent. The nature of this state and its contribution toward the reactive photochemistry of these complexes will be discussed later. All spectra presented here contain a large density of states within a relatively small spectral range between 3 and 6 eV and most show little or no oscillator strength, even though A1 and E symmetry transitions are allowed for one-photon absorption, and all spectra contain a large number of transitions with such symmetry. All transitions with non-zero oscillator strength, as

Table 10. Selected Allowed Transitions for MnTc(CO)10 with the LanL2DZ Basis Seta MnTc(CO)10/LanL2DZ B3LYP excitation energy/eV 3.58 3.65 4.20 4.40 4.62 4.83 4.99 a

(σ→π*CO) (σ→σ*) (σ→π*) (π→π*) (σ→σ*) (π→π*) (σ→σ*)

M062X f 0 0.3900 0.0140 0.0260 0.0510 0.0301 0.0330

excitation energy/eV 3.32 3.74 4.12 4.22 4.66 4.85 5.25

(σ→π*CO) (σ→σ*) (σ→π*) (σ→π*) (σ→σ*) (σ→σ*) (σ→σ*)

CAM-B3LYP f 0 0.4600 0.0220 0.0120 0.0130 0.0280 0.0401


(σ→π*CO) (σ→σ*) (σ→π*) (π→π*) (σ→σ*) (π→π*) (σ→σ*)

f 0 0.4900 0.0260 0.0509 0.0230 0.0140 0.0350

Oscillator strength, f, is given next to each transition, and the assignment of each state is given in parentheses next to the excitation energy. 9300



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Table 11. Selected Allowed Transitions for MnTc(CO)10 with the SDD/6-311G* Basis Seta MnTc(CO)10/SDD 6-311G* B3LYP

a

M062X

CAM-B3LYP

excitation energy/eV

f


f


f

3.78 (σ→π*CO) 3.802 (σ→σ*) 4.408 (σ→π*) 4.62 (π→π*) 4.75 (σ→σ*) 5.0042 (π→π*) 5.14 (σ→σ*)

0 0.4200 0.0140 0.0320 0.0307 0.0350 0.0140

3.38 (σ→π*CO) 3.91 (σ→σ*) 4.33 (σ→π*) 4.43 (σ→π*) 4.78 (σ→σ*) 5.504 (π→π*) 5.807 (π→π*)

0 0.4600 0.0230 0.0120 0.0250 0.0390 0.0580

4.018 (σ→π*CO) 3.87 (σ→σ*) 4.73 (σ→π*) 5.109 (σ→σ*) 5.16 (π→π*) 5.44 (π→π*) 5.56 (σ→σ*)

0 0.5100 0.0210 0.0360 0.0210 0.0210 0.0180

Oscillator strength, f, is given next to each transition, and the assignment of each state is given in parentheses next to the excitation energy.

Table 12. Selected Allowed Transitions for MnRe(CO)10 with the LanL2DZ Basis Seta MnRe(CO)10/LanL2DZ B3LYP

a

M062X

CAM-B3LYP


f


f

3.68 (σ→π*CO) 3.71 (σ→σ*) 4.309 (π→π*) 4.801 (π→π*) 4.83 (π→π*) 4.99 (σ→σ*) 5.46 (σ→π*)

0 0.3700 0.0390 0.0180 0.0102 0.0104 0.0108

3.88 (σ→π*CO) 3.89 (σ→σ*) 4.37 (σ→π*) 5.048 (σ→σ*) 5.12 (π→π*) 5.608 (π→π*) 5.83 (σ→π*)

0 0.4300 0.0180 0.0520 0.0209 0.0310 0.0307


(σ→π*CO) (σ→σ*) (σ→π*) (π→π*) (σ→σ*) (π→π*) (σ→π*)

f 0 0.4600 0.0130 0.0403 0.0100 0.0230 0.0330


Table 13. Selected Allowed Transitions for MnRe(CO)10 with the SDD/6-311G* Basis Seta MnRe(CO)10/SDD 6-311G* B3LYP

a

M062X

CAM-B3LYP


f


f


f

3.83 (σ→π*CO) 3.802 (σ→σ*) 4.47 (π→π*) 4.84 (σ→π*) 4.96 (π→π*)

0 0.3800 0.0405 0.0140 0.0280

3.89 (σ→π*CO) 3.9882 (σ→σ*) 4.4314 (σ→π*) 4.5381 (σ→π*) 4.8328 (π→π*) 5.0403 (σ→σ*) 5.2943 (π→π*)

0 0.4200 0.0120 0.0160 0.0110 0.0204 0.0560

4.10 (σ→π*CO) 3.9091 (σ→σ*) 4.8188 (π→π*) 4.9745 (π→π*) 5.2271 (σ→σ*) 5.434 (π→π*) 6.0107 (σ→σ*)

0 0.4700 0.0140 0.0410 0.0202 0.0230 0.0240


Table 14. Selected Allowed Excited States for MnRe(CO)10 with the CAM-B3LYP Functional and the cc-pVTZ Basis Set with All Three Pseudopotentials Accounting for No (NR), Quasi (QR), and Full (FR) Relativistic Effects on Rhenium MnRe(CO)10/CAM-B3LYP/cc-pVTZ NR ECP excitation energy/eV 4.14 4.07 4.94 5.00 5.50 5.64

(σ→π*CO) (σ→σ*) (π→π*) (π→π*) (σ→σ*) (π→π*)

QR ECP

FR ECP

f


f

0 0.3500 0.0310 0.0100 0.0150 0.0030

4.32 (σ→π*CO) 4.13 (σ→σ*) 4.82 (π→π*) 5.19 (π→π*) 5.49 (σ→σ*) 5.82 (π→π*) 6.203 (σ→σ*)

0 0.3800 0.0034 0.0059 0.0500 0.0062 0.0210

which has a σ→π* character allowed state with an excitation energy of 4.37 eV. However, CAM-B3LYP and B3LYP both fail to reproduce this state with the LanL2DZ basis set, CAMB3LYP not showing any σ→π* transition with oscillator strength greater than 0.01 and no such transition with B3LYP


(σ→π*CO) (σ→σ*) (π→π*) (π→π*) (σ→σ*) (π→π*) (σ→σ*)

f 0 0.3900 0.0032 0.0051 0.0490 0.0070 0.0180

with an excitation energy lower than 4.84 eV. With the SDD/6311G* basis set, generally the excitation energies of the equivalent states are blue-shifted as compared to those calculated using the LanL2DZ basis set. The excitation energies of the first σ→σ* band is a good example of this. The general 9301



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Table 15. Selected Allowed Transitions for TcRe(CO)10 with the LanL2DZ Basis Seta TcRe(CO)10/LanL2DZ B3LYP excitation energy/eV 3.97 3.83 4.43 5.25

a

(σ→π*CO) (σ→σ*) (π→π*) (π→σ*)

M062X

CAM-B3LYP

f


f


f

0 0.3800 0.0610 0.0150

4.49 (σ→π*CO) 4.102 (σ→σ*) 5.11 (σ→σ*) 5.16 (π→π*) 6.18 (σ→π*)

0 0.4060 0.0140 0.0970 0.0102

4.35 (σ→π*CO) 4.0098 (σ→σ*) 4.73 (π→π*) 4.89 (π→π*) 5.78 (π→σ*) 5.95 (π→π*) 5.95 (σ→π*)

0 0.4600 0.0180 0.0570 0.0260 0.0170 0.0107


Table 16. Selected Allowed Transitions for TcRe(CO)10 with the SDD 6-311G* Basis Seta TcRe(CO)10/SDD 6-311G* B3LYP

a

M062X


f

4.20 (σ→π*CO) 4.0058 (σ→σ*) 4.47 (π→π*) 4.65 (π→π*) 5.609 (π→σ*)

0 0.3900 0.0203 0.0605 0.0120

excitation energy/eV 4.75 4.28 5.19 5.42 6.32

(σ→π*CO) (σ→σ*) (π→π*) (π→π*) (σ→π*)

CAM-B3LYP f


f

0 0.4200 0.0310 0.0902 0.0150

4.60 (σ→π*CO) 4.18 (σ→σ*) 4.53 (π→σ*) 4.92 (π→π*) 5.13 (π→π*) 6.0008 (σ→π*) 6.303 (σ→π*)

0 0.4800 0.0107 0.0330 0.0520 0.0350 0.0110


Figure 3. Orbital transition for the third dπ→π* MLCT part B band in the spectra for all carbonyls studied. The dominant component of the time-dependent response eigenvector is around 0.460 in most cases. Orbitals shown here were produced using the CAM-B3LYP functional with SDD/6-311G* basis set for MnRe(CO)10.

Figure 2. Orbital transition for the early σ→σ* metal−metal band in the spectra for all carbonyls studied. The dominant component of the time-dependent response eigenvector in all cases is around 0.600. Orbitals shown here were produced using the CAM-B3LYP functional with SDD/6-311g* basis set for MnRe(CO)10.

The channel leading to the loss of CO ligands is also important in the photochemistry of transition metal complexes as argued previously, so identifying the low-lying states that are responsible for the asymmetric loss of carbonyls ligands would be useful. These states are dark states, and as seen for example in Figure 3, there is a degree of charge asymmetry observed in the allowed transitions of these complexes. To cause an M−CO bond to cleave, electron density can be transferred to the CO π* orbitals. One example of such a state is the 1B2 state present in all complexes. This state is dark and is an MLCT state that involves charge transfer from the metal σ bond to the π* orbitals of the carbonyl ligands. In almost all cases, the transfer of charge is asymmetric to the carbonyls ligands of the metal with the lowest atomic mass, for example, manganese in MnTc(CO)10. However, this state is rather mixed, and the state also includes a contribution from a transition to carbonyl π* orbitals that are more evenly spread across all carbonyl ligands in the complex. This appears to be dependent on basis set and density functional chosen, but no specific pattern on the mixing

features of the spectrum are the same using all three functionals with MLCT states dominating the higher energy part of the spectrum, although the ordering of the states is slightly different in each case. One would expect differences such as this in principle due to their differing abilities to treat charge-transfer states. Part B of the third band is assigned in the experimental spectrum as a dπ→π* character transition at around 4.67 eV. All functionals with either basis set predict such a transition with the CAM-B3LYP and M062X functionals most closely matching the experimental band with respective calculated excitation energies of 4.81 and 4.83 eV. Figure 3 pictorially represents the orbitals that are involved in this transition. The CAM-B3LYP results with the cc-pVTZ basis sets predict such a transition as well with excitation energies that are close to the CAM-B3LYP results, again with very little difference between the results computed with quasi- or fully relativistic pseudopotentials. 9302



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of this σ→π*CO state is apparent. Details of this state for all systems are given in Tables 10−16. B3LYP at higher energies provides a poor description of the spectrum with very few transitions with oscillator strength over 0.01. Higher up in energy from the third band, there is a mixture of allowed states of different character. Surrounding these allowed states, there is a large number of forbidden excited states. What can also be seen in general is that the impact on these results for MnRe(CO)10 when accounting for relativistic effects on rhenium appears to be minimal with respect to the smaller basis sets used. A range of states with different chemical character are present in the electronic spectrum of MnRe(CO)10 with similar results from the cc-pVTZ basis set regardless of the pseudopotential used as compared to the two smaller basis sets. The net effect is a blue-shift in the value of the excitation energies of each state going from the smallest to largest basis set, with a small increase again in going from a non- to a quasi- to a full-relativistic pseudopotential. The difference in results between quasi- and fully relativistic pseudopotentials is almost nothing. The overall pattern of states is also the same. This shows that results computed using the two smaller basis sets can be looked upon confidently in that the lack of relativistic effects on rhenium does not have a detrimental effect to the accuracy of the results for all three mixed-metal carbonyls studied here. The calculated spectra of MnTc(CO)10 are quite similar to the spectra of MnRe(CO)10 with the main features broadly the same. The lower part of the spectra in all cases are dominated with a σ→σ*A1 symmetry transition with large oscillator strength. The next transition higher in energy is in all almost cases calculated to be a σ→π* MLCT state. Higher in energy from this state, MLCT states continue to dominate the spectra with σ→σ* metal centered states also present that involve a transition from the HOMO σ-orbital to higher lying metal σ* orbitals. When compared to MnRe(CO)10, the excitation energies of the allowed states are lower for MnTc(CO)10, which is most notably seen in the excitation energy values for the initial σ→σ* intense band. The low energy part of the calculated spectra of TcRe(CO)10 is very similar to those of the other two carbonyls studied here including the intense σ→σ* metal centered state, which is present with all functionals and basis sets, and the excitation energy for this state higher than the equivalent state in MnRe(CO)10. However, at higher energies, both B3LYP and M062X functionals fail to show many MLCT states with oscillator strength greater than 0.01. This shows that a longrange exchange correction, such as in CAM-B3LYP, is required to accurately reproduce higher energy MLCT states. The large difference in electron affinity between technetium and rhenium (39 kJ mol−1) could also be a contributing factor to this behavior. There is still a large density of forbidden states and states with weak oscillator strengths, but this highlights the inability in this example of hybrid functionals that are not corrected for long-range exchange to accurately predict the presence of charge-transfer states of any type in experimental spectra. Indeed, only CAM-B3LYP, which is designed to better describe charge-transfer states than B3LYP, predicts a range of charge-transfer states throughout the spectral range investigated here of π→σ*, π→π*, and σ→π* character. Such a pattern favorably compares with the other two complexes studied here and with the experimental spectrum of MnRe(CO)10. No evidence is seen of σ→π* allowed transition from the CAM-

B3LYP results for TcRe(CO)10, which is predicted to be band 3A in the experimental spectrum of MnRe(CO)10 and is present in the theoretical spectra of both MnRe(CO)10 and MnTc(CO)10. However, π→π* states are present at higher energies, which is in accordance with the experimental 3B band of MnRe(CO)10 and the theoretical spectra of MnTc(CO)10. As no experimental electronic spectrum of either MnTc(CO)10 or TcRe(CO)10 has ever been reported in the literature, these assignments are tentative at the moment, but due to the close structural similarities between all three complexes studied here, it can be argued that the theoretical spectra presented here should be close to the experimental electronic absorption spectra of MnTc(CO)10 and TcRe(CO)10. Indeed, it is the availability of the CAM-B3LYP functional, able to describe a variety of CT states, that gives one confidence in assigning these electronic spectra for the first time.

■

CONCLUSIONS Density functional theory has been used to study the structural features and electronic absorption spectra of the group 7 mixedmetal bimetallic carbonyl complexes MnTc(CO)10, MnRe(CO)10, and TcRe(CO)10 using the B3LYP, M062X, and CAM-B3LYP functionals and a range of basis sets. In all cases, the favored ground-state structure of all three carbonyls was found to be a C4v symmetry staggered conformation with respect to rotation along the metal−metal bond. Another conformer that is close in energy to the staggered conformation was also found, which was also of C4v symmetry but eclipsed with respect to rotation around the metal−metal bond. This eclipsed conformation was calculated to be a first-order saddle point using analytical frequency calculations with one imaginary frequency that corresponded to rotation around the metal− metal bond. The barrier to rotation and therefore interconversion to the staggered conformation were found to be low, and in all cases no more than 7.10 kcal mol−1. The electronic absorption spectra were calculated for each complex and compared to an experimental spectrum for MnRe(CO)10. The theoretical spectra for MnRe(CO)10 were found to be in good agreement with the experimental spectrum with many spectral features the same. The spectra of the other two complexes were predicted to be similar to that of MnRe(CO)10 with only CAM-B3LYP able to give a qualitative description of the spectra of all three carbonyls. One of the dark states responsible for population of the π*CO orbitals in all complexes that could contribute to the loss of a single or multiple CO ligand has also been identified and discussed. From a perspective of the reactive photochemistry of these complexes, the most intense σ→σ* transition would be similar to that present in the spectroscopy of Mn2(CO)104, the population of which causes homolytic bond cleavage and ultrafast photochemistry of the type already described for other binary transition metal carbonyls such as Cr(CO)6 and Fe(CO)5 involving Jahn−Teller degeneracies.12,13,50−55 For these species, the photochemistry should be more complex as there will be two different monometallic fragments involved in the subsequent reactive photochemistry. The impact of relativistic effects for both structure and electronic spectroscopy was investigated by the use of a ccpVTZ basis set with a mixture of relativistic pseudopotentials on rhenium in MnRe(CO)10. It was found that relativistic effects had a minimal impact on these results both for structure and for the range of electronic excited states exhibited by these carbonyls. This showed that the two smaller basis sets used 9303



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here gave still gave an accurate and balanced description of the structure and electronic excited states of these carbonyls without accounting for relativistic effects on the second and third row transition metal atoms in these systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the EPSRC for funding through grant EP/F01709X and the European Research Council (ERC) for funding under the European Union’s Seventh Framework Programme (FP7/ 2007-2013)/ERC Grant No. 258990.

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A Time-Dependent Density Functional Theory Study of the Structure

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