The assignment of peroxo stretching frequencies for Molybdenum and Tungsten complexes is studied by DFT and MP2 calculations. We found that M06 functional is unsuitable for assignment of Mo=O and O–O stretches in CpMo(
IR spectroscopy is an important characterization technique in chemistry and it has been extensively employed in various subdisciplines of chemistry such as organic, inorganic, and organometallic chemistry. In this work, we are interested in the assignment of vibrational modes (Mo/W=O and O–O stretching modes) in Molybdenum and Tungsten complexes which are efficient catalysts in epoxidation and oxidation [
We had been working on the use of Molybdenum based catalyst in both epoxidation [
During the course of our study, we found that not all Minnesota density functionals are suitable for the assignment of Mo=O stretching and O–O stretching in Molybdenum and Tungsten complexes which contain these groups. We also found that some literature assignments of asymmetric and symmetric Mo=O stretching frequencies to observed bands in the IR spectrum do not agree with those calculated with modern DFT functionals. Relevant results would be presented in the rest of this work.
All calculations were performed with Gaussian 09 A.02 or C.01 [
Def2SVP, def2SVPD, def2TZVP, def2TZVPD, and def2QZVPD basis sets [
The DFT functionals employed in this study are Minnesota series [
Frequency calculations were performed at the default atmosphere and temperature as implemented in Gaussian. Default convergence criteria and integration grid were used, unless otherwise stated. For tighter convergence criteria and larger integration grid, the keywords “opt=tight” and “int=ultrafine” were used in Gaussian 09.
For the study of solvent effect, two approaches were adopted. For explicit solvation, three solvent molecules (acetonitrile or water) were added. For implicit solvation model, the PCM model implemented in Gaussian 09 was used. Geometries optimization and frequencies calculations for explicit solvation are the same as in the gas phase calculations. For implicit solvation model, optimization and frequencies calculations are performed with PCM via the keywords “scrf=(solvent=acetonitrile).” Note that, for water, tighter convergence criteria and larger integration grid were specified via “opt=tight” and “int=ultrafine,” in addition to “scrf=(solvent=water).”
The isotopes used for frequency calculations are the default in Gaussian 09 unless otherwise stated.
Geometries for
Anharmonic correction is generally neglected in this study. We attempted to fit the calculated harmonic frequencies to the fundamental frequencies observed experimentally.
3D images of optimized geometries are created with CYLview v1.0.562 beta [
Synthesis and characterization of CpMo(
During the course of our study, we explored the use of M06 functional as recommended by Zhao and Truhlar for transition metal [
In our calculations, the geometry optimization and subsequent frequency analysis were performed with M06 functional and the family of basis sets defined by Weigend and Ahlrichs [
Key vibrational modes and their calculated frequencies.





640.35, 625.81  635.75, 616.86 
OOP C–H bending of Cp  849.88, 829.84, 818.68  847.10, 830.87, 821 

1032.34  1028.21 
Inplane C–H bending of Cp  1038.02  1039.12 

1041.44  1040.97 
Key vibration modes and their respective frequencies calculated at M06 with various basis sets.
Vibration mode  Expt.^{[a]}  M06/def2SVP  M06/def2SVPD  M06/def2TZVP  M06/def2TZVPD 


951  1042.41  1029.76  1028.21  1027.07 

877  1036.81  1038.37  1040.97  1040.26 
OOP bending C–H of Cp  N/A  813.94  821.31  830.87  826.03 

565  637.30  626.28  635.75  634.37 
620.86  609.96  616.86  615.79 
^{[a]}Based on assignment based on the work of AlAjlouni et al. [
Illustrating the conformation differences.
The normal modes of various key vibrational modes listed in Table
Normal modes associated with MoO(
800–850 cm^{−1} bending modes that are associated with the Cp ring for
The normal modes associated with the bending of Cp ring are shown in Figure
The various isotopes of Molybdenum have negligible effect on the frequencies. The difference is generally less than 10 cm^{−1}; therefore, we would not be considering the effect of isotope in the calculations.
The effects of size of basis sets on the vibrational modes of interest and their frequencies are tabulated in Table
When the numerical accuracy is increased by employing a larger integration grid and tighter convergence criteria as implemented in Gaussian 09, the Mo=O stretch and O–O stretch become strongly coupled and assignment of frequency is ambiguous. However, at M06/def2TZVP Mo=O stretch and O–O stretch remain decoupled.
Systematic error in calculated IR frequencies calculated by theoretical methods such as
In order to ascertain that the reversed order of O–O stretch and Mo=O stretch frequencies when the M06 functional was used is not sensitive to the choice of basis set (other than the Weigend and Aldrich ones used), calculations were performed with the two variants of the LANL2 basis set for Molybdenum and the 6311+G(d,p) or ACCT basis set for carbon, hydrogen, and oxygen atoms. As can be seen from Table
Results at M06 with various basis sets as indicated in the table.
Basis set 



Mo=O/Å  

Mo  NonMo  
LANL2TZ(f)  6311 + G(d,p)  1000.02  1027.54  −27.52  1.669 
ACCT  1011.06  1040.92  −29.86  1.669  


LANL2DZmod  6311 + G(d,p)  987.63  1022.78  −35.15  1.695 
ACCT^{[a]}  1010.59  1040.99  −30.4  1.684 
^{[a]}Invoked via the keyword “augccpVTZ” in Gaussian 09.
Nevertheless, the problem could lie in the functional and could be largely independent of the basis set. Therefore, we optimized the geometry of
Mo=O and O–O stretching, and Cp’s C–H OOP bending frequencies for




Mo=O/Å  O–O/Å  

M06L  980.21  963.92  +16.29  828.80  1.685  1.430 
M06  1028.21  1040.97  −12.76  830.87  1.670  1.408 
M062X  1076.74  1060.31  +16.43  847.72  1.658  1.412 
PBE0  1043.41  1031.92  +11.49  842.94  1.669  1.414 
B3LYP  1017.40  977.41  +39.99  840.90  1.681  1.437 
B3PW91  1030.09  1009.12  +20.97  839.89  1.675  1.422 
MP2/def2SVP  952.02  894.69  +57.33  816.75  1.708  1.457 
MP2/def2SVPD  936.88  871.31  +65.57  820.09  1.714  1.469 
MP2/def2TZVP  954.83  920.28  +34.55  826.25  1.711  1.459 
Expt.  951^{a}  877^{a}  +74  1.728  1.271 
^{a}Based on assignment based on the work of AlAjlouni et al. [
Mo=O and O–O stretching, and Cp’s C–H OOP bending frequencies for



Mo=O^{[a]}/Å  O–O^{[a]}/Å  

M06L  976.99  967.87  9.12  1.685  1.427 
M06  1028.87  1044.62  −15.75  1.669  1.404 
M062X  1084.30  1065.57  18.73  1.656  1.409 
Expt.  952.7^{[b]}  1.689  1.440 
^{[a]}Bond lengths are taken from the work of Hauser et al. [
Mo=O and O–O stretching, and Cp’s C–H OOP bending frequencies for



Mo=O/Å  O–O/Å  

M06L  981.10  963.24  17.86  1.678  1.430 
M06  1032.38  1040.76  −8.38  1.662  1.406 
M062X  1085.37  1066.20  19.17  1.649  1.410 
Expt.  881  842  39  1.771  1.352 
Bond lengths and IR frequencies are taken from the work of Galakhov et al. [
It is likely that the assignment made by M06 is erroneous; therefore, it is not recommended for assignment of Molybdenum complexes which contain both Mo=O and O–O groups.
From Table
Two other peroxo complexes were calculated: they are
From Table
Calculated frequencies for complex
Geometries and vibrational frequencies of CpMoO_{2}CH_{3}
Mo=O stretching and Cp’s C–H OOP bending frequencies for





M06L/def2TZVP  946.29  973.92  27.63 
M06/def2TZVP  982.01  1013.78  31.77 
M062X/def2TZVP  1017.38^{[a]}  1059.88^{[a]}  42.5 
PBE0/def2TZVP  996.75  1027.54  30.79 
B3LYP/def2TZVP  975.30  1004.35  29.05 
CAMB3LYP/def2TZVP  1006.55  1042.96  36.41 
B3PW91/def2TZVP  985.68  1015.36  29.68 
wB97xD/def2TZVP  1006.62  1044.62  38 
MP2/def2SVP  928.80  899.36  −28.64 
MP2/def2SVPD  903.11  884.42  −18.69 
MP2/def2TZVP  923.48  903.53  −19.95 
Experimental^{[b]}  918  887  −31 
^{[a]}Tight convergence criteria and ultrafine integration grid were used due to a low imaginary frequency when optimized with default setting. ^{[b]}Assignment based on the work of Legzdins et al.; see [
In this case, we believe that MP2 does not give reliable assignment even with the def2TZVP basis set. The reasons are discussed in the following paragraphs.
Firstly, the work of Butcher et al. on Molybdenum(VI) dihalide dioxide complexes assigned the lower 905 cm^{−1} to the asymmetric Mo=O stretch and the higher 940 cm^{−1} to the symmetric Mo=O stretch [
Secondly, when testing MP2 with def2SVP, def2SVPD, def2TZVP, and def2TZVPD on
Results of asymmetric and symmetric Mo=O stretches for
Methods 




MP2/def2SVP  828.52  808.83  19.69 
MP2/def2SVPD  772.78  768.95  3.83 
MP2/def2TZVP  810.13  799.53  10.6 
MP2/def2TZVPD  786.31  789.21  −2.9 
MP2/def2QZVPD  783.53  789.82  −6.29 
CCSD(T)/def2SVP^{[a]}  839.60, 840.17, 840.27  872.13  −32 (840–872) 
M06L/def2SVP  843.69  874.91  −31.22 
M06L/def2SVPD  818.43  860.74  −42.31 
M06L/def2TZVP  817.71  864.85  −47.14 
M06L/def2TZVPD  807.75  863.15  −55.4 
^{[a]}The optimized geometry does not have a
Results of asymmetric and symmetric Mo=O stretches for variuos Molydbenum and Tungsten complexes. See Figure
Complex  Label 

 

Expt.  Calc.^{[a]}  Expt.  Calc.^{[a]}  
CpMo( 

951^{[b]}  973.92  N/A  N/A 
CpMo 

926^{[b]}  973.92  902^{[b]}  946.29 
CpMo 

920^{[d]}  973.16  887^{[d]}  944.71 


934^{[e]}  957.54^{[i]}  N/A  N/A 
CpMo( 

953^{[f]}  974.82  N/A  N/A 


949^{[b]}  961.45  N/A  N/A 
CpW 

943^{[b]}  981.20  899^{[b]}  941.29 


941^{[b]}  958.74  N/A  N/A 


963^{[g]}  979.34  N/A  N/A 


940^{[h]}  987.68  905  957.31 
^{[a]}Calculated at M06L/def2TZVP. ^{[b]}AlAjlouni et al.; see [
We then examined the Mo=O and O–O stretching frequencies in ten complexes containing Molybdenum or Tungsten by restricting the level of theory to M06L/def2TZVP based on the results presented in the previous section on
Results of O–O stretches for variuos Molybdenum and Tungsten complexes.
Complex^{[a]}  Label  O–O  Scaled (cm^{−1}) by  

Expt.  Calculated  Linear model^{[b]}  0.9613  0.9595^{[c]}  
CpMo( 

877^{[d]}  963.92  926.12  926.62  925.27 


884^{[e]}  953.84  914.14  916.93  915.59 
CpMo( 

930–950^{[f]}  958.05  919.14  920.97  919.63 


860^{[g]}  926.13  881.20  890.29  888.99 


868^{[g]}  923.74  878.36  887.99  886.70 


870^{[h]}  940.32  898.07  903.93  902.61 
951.49  911.35  914.67  913.34 
^{[a]}Refer to Table
We attempted to perform mode specific scaling for the Mo=O of complexes listed in Table
Attempt to perform linear regression on the data in Table
Kesharwani et al. reported a scaling factor for fundamentals of 0.9595 at M06L/def2TZVP [
RMSD of predicted fundamental frequency of Mo=O and O–O stretch.
Mo=O  O–O  

RMSD (cm^{−1}) at M06L/def2TZVP  40.45  80.72 


RMSD (cm^{−1}) scaled with linear model^{[a]}  15.05  41.75 


RMSD (cm^{−1}) scaled with a factor of 0.9613  15.43  44.66 


RMSD (cm^{−1}) scaled with a factor of 0.9595  15.49  43.38 
^{[a]}Linear equation is
The agreement between experimental O–O stretching frequencies and calculated ones is not as good as those of Mo=O. The unscaled RMSD is larger at 80.72 cm^{−1}. The RMSD is reduced by about 50% after scaling to about the same magnitude as the unscaled RMSD for Mo=O stretching and is larger than those reported by Kesharwani et al.
At this point, it would be prudent to discuss the validity of assigning IR bands that is in the range of 860–880 cm^{−1}. From the work of AlAjlouni et al., CpMo(
Work of Postel et al. demonstrated through isotopic substitution with ^{17}O that ^{16}O–^{16}O stretching of a Molybdenum complex is 898 cm^{−1} while the Mo=O is 914 cm^{−1} [
Cramer and coworkers observed a fairly linear relationship between O–O stretching frequencies and O–O bond length in a diverse of molecules [
Plot of O–O stretching frequencies against O–O bond length for complexes reported in this work.
With
The results are tabulated in Table
Calculated Mo=O and O–O stretching frequencies in gas phase, with explicit solvation and with implicit solvation via PCM.
Level of theory  Solvent 



M06L/def2TZVP  No  976.99  967.87 
Acetonitrile, PCM^{[a]}  944.48  959.34  
Acetonitrile, explicit^{[b]}  952.75  961.73  
Water, PCM^{[a],[c]}  960.28^{[d]}  
Water, explicit^{[b],[c]}  959.20  968.15 
^{[a]}Default implicit solvent of Gaussian 09 A.02 was used. ^{[b]}Three molecules of solvents were added. ^{[c]}Tight convergence criteria and ultrafine integration grid were used due to low imaginary frequency with default setting. ^{[d]}Mo=O stretch and O–O stretch are strongly coupled, and assignment is ambiguous and therefore not attempted.
In this work, we have demonstrated the unsuitability of M06 functional for assignment of O–O and Mo=O frequency in
Cyclopentadienyl ligand C_{5}H_{5}
Cp and its derivative, C_{5}R_{5}, where R could be any groups such as CH_{3} in
Density functional theory
Infrared
In plane
Out of plane
Polarizable continuum model
Root mean square deviation.
The author declares that there is no conflict of interests regarding the publication of this paper.
Choon Wee Kee acknowledged C.H Tan and NTU for funding and NUSHPC for generously providing free computational resources.