Theoretical studies on the multiple metalemetal bonds in the bimetallic molecules and the ultrashort VeMn bonds in the complexes Hua Dong a , Qingyong Meng a,1 , Bo-Zhen Chen a, * , Yan-Bo Wu b a School of Chemistry and Chemical Engineering, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049, PR China b Institute of Molecular Science, Key Laboratory of Chemical Biology and Molecular Engineering of the Education Ministry, Shanxi University, Taiyuan, Shanxi Province 030006, PR China article info Article history: Received 26 March 2012 Received in revised form 18 July 2012 Accepted 21 July 2012 Keywords: Multiple metalemetal bonds CASSCF CASPT2 NBO abstract The present work analyzed the multiple bimetallic bond of CreCr, VeMn, VeTc, NbeMn, CreMo, MoeMo, and NbeTc using the multiconfiguration second-order perturbation theory (CASPT2) in conjunction with treating the relativistic effects by calculating the spineorbit coupling and using ANO-RCC basis set and the DKH Hamiltonian. The bimetallic bond length, natural bond order (NBO), effective bond order (EBO), formal shortness ratio (FSR) values, and Mulliken charge populations are calculated using the multiconfigurational methods. Our calculations indicate that the VeMn molecule has smaller bond length value and larger FSR value than other heterobimetallic molecules, and the VeMn bimetallic core could be considered as a good candidate to investigate the multiple heterobimetallic bonds in complexes. And then the VMn(NHCHNH) 2 and VMn(NHCHO) 2 molecules were chosen as two models to study the influences of the ligands using the CASSCF and BP86 methods. The steric hindrances and electronic effects of the substituent groups on the ligands were considered by calculating four kinds of complexes with 2-aminopyridine, 2-hydroxypyridine, amidinate, and guanidinate as ligands using the BP86, BPW91, and B3LYP methods. On the basis of our calculations, we would conclude that the ligands with the O or N atom coordinated to the VeMn core could elongate the VeMn bond significantly. The steric hindrances from the substituent groups on the ligands could shorten the VeMn bond to a certain extent and the electronic effects of the substituents could elongate or shorten the VeMn bond depending on the properties and the positions of the substituents on the ligands. But it may be unfeasible to contract the bimetallic bond length in complex to a certain limit as that in the bimetallic molecule. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction The nature of the interactions governing chemical bonds has fascinated chemists for a long time [1,2]. Recently, the bond order and in particular the possibility of multiple bonding between transition metals, with a maximum of six owing to the overlap among s, d and even f orbitals, contained in a complex have been highlighted [3e6]. For finding the ultrashort bimetallic bond with high bond order, extensive experimental [7e12] and theoretical [13e17] studies on the multiple bond and ultrashort metalemetal distances of the bichromium and other homobimetallic compounds have been reported in the literature, following the pioneer synthesis experiments of Ar 0 CrCrAr 0 with fivefold CreCr bonding, where Ar 0 indicates C 6 H 3 -2,6(C 6 H 3 -2,6-Pr 2 i ) 2 and Pr i indicates isopropyl, carried out by Nguyen et al. [7] in 2005. Recently, La Macchia et al. [17] investigated the electronic configuration of several bichromium (homobimetallic) species with ligands using nitrogen to coordinate the metal centers. According to their CASPT2 (for optimizing the CreCr and Creligand distances) and B3LYP (for optimizing other degrees of freedom) calculations, La Macchia et al. [17] showed that the correlation between the CreCr bond length and the effective bond order (EBO) is strongly affected by the nature of the ligand, as well as by the steric hindrance due to the ligand structure. Here we shall discuss whether the two factors suggested by La Macchia et al. [17] affect the heterobimetallic compounds [18] as in the case of CreCr bond? Since Group 6 elements can form the maximum bond order between d-block elements, the hetero- bimetallic molecules composed by the elements of Groups 5 and 7, such as VeMn, VeTc, MneNb, and NbeTc, may be the candidates for the heterobimetallic core with multiple bonds in the complexes. Ten out of their 12 valence electrons can be used to form the * Corresponding author. Tel.: þ86 10 8825 6129. E-mail address: [email protected](B.-Z. Chen). 1 Present address: Theoretische Chemie, Physikalisch-Chemische Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany. Contents lists available at SciVerse ScienceDirect Journal of Organometallic Chemistry journal homepage: www.elsevier.com/locate/jorganchem 0022-328X/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jorganchem.2012.07.035 Journal of Organometallic Chemistry 717 (2012) 108e115
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Journal of Organometallic Chemistry 717 (2012) 108e115
a School of Chemistry and Chemical Engineering, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049, PR Chinab Institute of Molecular Science, Key Laboratory of Chemical Biology and Molecular Engineering of the Education Ministry, Shanxi University, Taiyuan,Shanxi Province 030006, PR China
a r t i c l e i n f o
Article history:Received 26 March 2012Received in revised form18 July 2012Accepted 21 July 2012
0022-328X/$ e see front matter � 2012 Elsevier B.V.http://dx.doi.org/10.1016/j.jorganchem.2012.07.035
a b s t r a c t
The present work analyzed the multiple bimetallic bond of CreCr, VeMn, VeTc, NbeMn, CreMo, MoeMo,and NbeTc using the multiconfiguration second-order perturbation theory (CASPT2) in conjunction withtreating the relativistic effects by calculating the spineorbit coupling and using ANO-RCC basis set and theDKHHamiltonian. The bimetallic bond length, natural bondorder (NBO), effective bondorder (EBO), formalshortness ratio (FSR) values, andMulliken charge populations are calculatedusing themulticonfigurationalmethods. Our calculations indicate that the VeMnmolecule has smaller bond length value and larger FSRvalue than other heterobimetallic molecules, and the VeMn bimetallic core could be considered as a goodcandidate to investigate the multiple heterobimetallic bonds in complexes. And then the VMn(NHCHNH)2and VMn(NHCHO)2 molecules were chosen as twomodels to study the influences of the ligands using theCASSCF and BP86 methods. The steric hindrances and electronic effects of the substituent groups on theligandswere considered by calculating four kinds of complexeswith 2-aminopyridine, 2-hydroxypyridine,amidinate, and guanidinate as ligands using the BP86, BPW91, and B3LYP methods. On the basis of ourcalculations, wewould conclude that the ligandswith the O or N atom coordinated to the VeMn core couldelongate the VeMn bond significantly. The steric hindrances from the substituent groups on the ligandscould shorten the VeMn bond to a certain extent and the electronic effects of the substituents couldelongate or shorten the VeMn bond depending on the properties and the positions of the substituents onthe ligands. But it may be unfeasible to contract the bimetallic bond length in complex to a certain limit asthat in the bimetallic molecule.
� 2012 Elsevier B.V. All rights reserved.
1. Introduction
The nature of the interactions governing chemical bonds hasfascinated chemists for a long time [1,2]. Recently, the bond orderand in particular the possibility of multiple bonding betweentransition metals, with a maximum of six owing to the overlapamong s, d and even f orbitals, contained in a complex have beenhighlighted [3e6]. For finding the ultrashort bimetallic bond withhigh bond order, extensive experimental [7e12] and theoretical[13e17] studies on the multiple bond and ultrashort metalemetaldistances of the bichromium and other homobimetalliccompounds have been reported in the literature, following thepioneer synthesis experiments of Ar0CrCrAr0 with fivefold CreCr
bonding, where Ar0 indicates C6H3-2,6(C6H3-2,6-Pr2i )2 and Pri
indicates isopropyl, carried out by Nguyen et al. [7] in 2005.Recently, La Macchia et al. [17] investigated the electronic
configuration of several bichromium (homobimetallic) species withligands using nitrogen to coordinate themetal centers. According totheir CASPT2 (for optimizing the CreCr and Creligand distances)and B3LYP (for optimizing other degrees of freedom) calculations,La Macchia et al. [17] showed that the correlation between theCreCr bond length and the effective bond order (EBO) is stronglyaffected by the nature of the ligand, as well as by the sterichindrance due to the ligand structure.
Here we shall discuss whether the two factors suggested by LaMacchia et al. [17] affect the heterobimetallic compounds [18] as inthe case of CreCr bond? Since Group 6 elements can form themaximum bond order between d-block elements, the hetero-bimetallic molecules composed by the elements of Groups 5 and 7,such as VeMn, VeTc, MneNb, and NbeTc, may be the candidatesfor the heterobimetallic corewithmultiple bonds in the complexes.Ten out of their 12 valence electrons can be used to form the
H. Dong et al. / Journal of Organometallic Chemistry 717 (2012) 108e115 109
multiple bonds, leaving one electron of each atom free to sharea bond with the surrounding ligand. The choice of the ligand isa crucial parameter that allows keeping the transition metals in thelowest possible oxidation state, at the same time maximizing thenumber of valence electrons available for the formation of multiplebonds. Since the overlap of (nþ 1) s and nd orbitals (n¼ 3 or 4), theheterobimetallic system could form two s, a pair of p, and a pair ofd bonding orbitals and corresponding antibonding orbitals.
As for now, the main target in the chemistry of bimetallicmultiple-bonded species is the design of the compounds with themetalemetal interactions closest to the limit imposed by thebimetallic molecule [19,20]. The bimetallic bonds studied in thepresent work are formed from 5 or 6 unpaired electrons on each ofthe atoms (for Group 5, 6, or 7). Although the bimetallic multiplebond is difficult to quantify theoretically because of the crowded-ness of electrons in the bonding region, the CASPT2 [21,22] andCASSCF [23] calculations have yielded a series of molecularparameters in good agreement with the experimental values [19].The electronic structure of these bimetallic molecules can betherefore well described at the CASPT2 level of theory [19].
In the present computational work, we investigate the multiplebond and ultrashort distance of the bimetallic molecules and themetalemetal center of the heterobimetallic compounds using theCAS (including CASPT2 and CASSCF) and DFT (including BP86[24,25], BPW91 [24.26], and B3LYP [27,28]) methods. The geome-tries of seven bimetallic molecules (CreCr, VeMn, VeTc, NbeMn,CreMo, MoeMo, and NbeTc) are optimized at the CASPT2 levelin conjunction with treating the relativistic effects [29e31]. Thebond order (BO) values of these seven molecules at their optimizedgeometries were calculated. Because of its short bond length, wechoose the VeMn bond as the studying model. For studying theeffect of the ligand to the VeMn bond, geometries of two modelmolecules in the VMn(XYZ)2 type, i.e. VMn(NHCHNH)2 (denoted asmolecule 1) and VMn(NHCHO)2 (denoted as molecule 2), areoptimized using the CASSCF and BP86 methods. And then thegeometries of four kinds of complexes containing the VeMn coredesigned based on the model molecule 1 or 2 will be optimizedusing the BP86, BPW91, and B3LYP methods [24e28,32e34]. Theeffects of ligands and the substituent groups on the ligands to theVeMn bond will be discussed.
2. Computational technical details
2.1. CAS calculations
The multiconfigurational quantum-chemical approaches[29e31], such as the CASPT2 and CASSCF methods, have been wellestablished to describe the metalemetal multiple bonds. Witha CASSCF wave function constituting the reference function, theCASPT2 calculations which included the dynamic electron-correlation energy were performed to compute the first-orderwave function and the second-order energy in the full CI space.The relativistic effects were treated in two steps [29e31]: (i) thescalar terms which were included in the basis set generation andused to determine wave functions and energies (including staticand dynamic correlation effects) and (ii) the spineorbit (SO)coupling which was treated in a configuration interaction modelusing the CASSCF wave functions as the basis sets.
In the present work, the CAS (CASSCF and CASPT2)calculations for the seven bimetallic molecules were performedusing the MOLCAS v7.4 quantum chemistry software package [35].A relativistic atomic natural orbital (ANO-RCC) basis set[10s10p8d6f4g2h] [36e39] was used for the scalar relativistic effect[ANO-RCC were contracted using the DouglaseKrolleHess (DKH)Hamiltonian and MOLCAS package would automatically recognize
this and turn on the DKH option when ANO-RCC was used]. TheSO coupling was then included by allowing the CASSCF wave-functions to mix under the influence of the SO Hamiltonian usingthe RASSI method [29e31]. In these CAS calculations, 12 electronswere active and the active space included the two s, a pair of p, anda pair of d bonding orbitals and two s*, a pair of p*, and a pair of d*antibonding orbitals. The level shift option of 1.5 and imaginaryshift option of 0.5 were used in the RASSCF and CASPT2 subprogramof MOLCAS [40,41], respectively. In all the CASPT2 calculations, theweight values of the CASSCF reference functions in the first-orderwave functions were all larger than 0.85.
For studying the multiple bond in the bimetallic molecules, wefirstly optimized the bond length values of seven bimetallic mole-cules: CreCr, MoeMo, VeMn, VeTc, NbeMn, CreMo, and NbeTc atthe relativistic CASPT2 level and then calculated the natural bondorder (NBO) and EBO of these seven bimetallic molecules using theCASSCF wavefunctions at the respective CASPT2 optimized geom-etries (denoted as CAS NBO and CAS EBO).
The geometries of model molecules 1 and 2 in the Cs symmetrywere optimized at the CASSCF level using the Gaussian 09 program[42]. In the CASSCF calculations for 1 and 2, 12 electrons were activeand the active space included all of the 3d and 4s orbitals of V andMn atoms.
2.2. DFT calculations
The hybrid functionals with the B3LYP [27,28] functional asa well-known example have been found to give unreliable resultsfor transitionmetal chemistry [34], while the pure functionals, suchas BP86 [24,25] and BPW91 [24,26] could give more quantitativeresults [34]. Therefore, in the present work, the BP86 methodcarried out with the Gaussian 09 program [42] was used to opti-mize the geometries of the twomodel molecules and the four kindsof complexes. Frequency analysis calculations at the BP86 levelwere then performed to ensure the absence of imaginaryfrequencies for all the species and produce the zero-point energies(ZPEs). However, for comparing the difference of different DFTmethods, the same calculations were performed at the BPW91 andB3LYP levels for the model molecules and the complexes, whoseresults were given in the Supporting information.
In all of the DFT and CASSCF calculations implemented byGaussian 09, we used the LanL2DZ and 6-31G** basis sets for thetransition metal and themain-group atoms, respectively. This set ofthe LanL2DZ together with the 6-31G** basis set was denoted as“ECP” in the following text.
The BP86 NBO calculations for the metalemetal bond wereapplied to all of the above molecules (including the bimetallicmolecules, model molecules, and complexes) using the CASPT2geometries of the bimetallic molecules, the CASSCF and BP86geometries of model molecules, and the BP86 geometries of thecomplexes. These NBO calculations were carried out using the NBO3.0 package [43] included in the Gaussian 09 program [42].
For comparing the metalemetal distances, we calculated theformal shortness ratio (FSR) [2] of the MeM0 bond (M and M0
representing two metal atoms in this work), which was defined asFSR ¼ R(M e M0)/(rM þ rM0), where R(MeM0) is the bond length ofMeM0, and rM and rM0 are atomic radii [44,45] of M and M0,respectively. In the present work, the FSR values were calculated byusing two kinds of atomic radii data [44,45], which are denoted asFSR(S) and FSR(C) from the atomic radii of Slater [44], and Clementiet al., [45] respectively.
For evaluating the accuracy of the present DFT calculations, wereoptimized the two complexes containing the CreCr core (deno-ted as 3 and 4, see the left column of Table S7 of Supportinginformation for their structures) at the BP86/ECP, BPW91/ECP, and
H. Dong et al. / Journal of Organometallic Chemistry 717 (2012) 108e115110
B3LYP/ECP levels. The geometries of complexes 3 and 4 were alsooptimized at the B3LYP-CAS/DZP level by La Macchia et al. [17] Forcomplex 3, both of present and previous [17] calculations wereperformed on a simplified molecule 3a, instead of the experimentalsynthesis structure 3b [8]. As shown in Table S7, except the presentB3LYP results, the theoretical results of the CreCr distances are inreasonable agreement with experiment. The BP86 and BPW91CreCr distances of 3a and 4 are about 0.04 Å smaller than experi-mental values [8,9] of 3b and 4, respectively. The results for theCreCr distances given by La Macchia et al. [17] are 0.06 Å for 3a and0.02 Å for 4 larger than the corresponding experimental values[8,9]. Thus, the present BP86 and BPW91 calculations are consid-ered more accurate than the B3LYP calculations.
3. Results and discussion
3.1. CAS studies on the bimetallic molecules
In the present section, we focus on the ultrashort MeM0
distances and multiple bonds of the seven bimetallic molecules.We optimized the bond lengths of the CreCr, MoeMo, VeMn,VeTc, NbeMn, CreMo, and NbeTc molecules using the CASPT2method in conjunction with treatments of the relativistic effects.The CAS NBO and EBO of these seven bimetallic molecules at theseoptimized geometries were then calculated. Table 1 gives the bondlengths, NBOs, EBOs, and FSRs of these bimetallic molecules. It canbe found from Table 1 that NBO values are very close to theirrespective EBO values.
3.1.1. The same row bimetallic molecules: CreCr, VeMn, MoeMo,and NbeTc
As shown in Table 1, the present CASPT2 CreCr bond length(1.650 Å) is in reasonable agreement with the previous CASPT2value (1.660 Å) [31] and experiment (1.679 Å) [46], and the presentCAS EBO value (4.1) is also close to the previous calculated one (4.5)[31]. By comparing the calculated bond length, NBO, EBO, and FSRvalues of VeMnwith those of CreCr, one can find that these valuesof VeMn are all close to the corresponding values of CreCr. Thissimilar feature implies the same multiple-bond characteristic ofthese two bonds. Likewise, by a comparison between the NbeTcand MoeMo molecules (see Table 1) we could also conclude that
Table 1The computational geometries of the metalemetal molecules at the CASPT2/ANO-RCC level (bond lengths are given in Å), together with the natural bond order(NBO) and effect bond order (EBO). The formal shortness ratio (FSR) values calcu-lated by using two kinds of atomic radii data are also given. Values in parenthesesare the BP86/ECP NBO values using theoretical and experimental geometries.
MeM0 R(MeM0) NBO EBO FSR(S), FSR(C)a
The bimetallic molecules with the same row elementsCreCr 1.650 4.9 (6.0) 4.1 0.59, 0.50
a The FSR(S) values are calculated by using the atomic radii data from reference[44] and the FSR(C) from reference [45].
b Reference [31].c The experimental value, see reference [46].d The optimized geometry at the CASSCF/ANO-RCC level.
both have the similar multiple bond characteristic. However, theFSR values of MoeMo and NbeTc are larger than those of CreCr andVeMn, while the BO values of MoeMo and NbeTc are also largerthan those of CreCr and VeMn.
From theoretical point of view, in the CreCr and MoeMomolecules the much larger (nþ1)s valence orbital generates anses (one sg) molecular orbital with a considerably larger bondlength than the nd-nd (one sg, a pair of pu, and a pair of dg)molecular orbitals [31]. This bond length-unbalance between theses and ded valence orbital interactions, which will be abbreviatedto “the ses vs ded unbalance” in the subsequent text, weakens theded interactions and makes the sg(ses) bonding orbital withnonbonding feature at the equilibrium geometry [19,31]. Therefore,the CreCr molecule has a smaller EBO value of 4.1 than the idealvalue of 6.0 for such bimetallic molecule with 12 valence electrons.The MoeMo molecule, however, has the EBO value of 5.4 which ismore near the ideal value (6.0). One reason for the enhancement ofthe MoeMo EBO value is the relativistic effects which play animportant role in making the 5s and 4d orbitals more equal in sizefor the second row transition metals [31]. This equivalency in sizeconsiderably enhances the strength of the metallic bond.
Although the ses (ded) interactions between the two differentatoms are weaker than those between the two same atoms, the sesand ded unbalances in the VeMn and NbeTc molecules should besimilar to those in the CreCr and MoeMo molecules, respectively,and still are an important factor for the metalemetal bond prop-erties (bond length and NBO). Thus, the bond length and NBOvalues of VeMn (NbeTc) are close to the corresponding values ofCreCr (MoeMo).
3.1.2. The different row bimetallic molecules: VeTc, NbeMn, andCreMo
The bond length values of 1.825, 1.880, 1.861 Å for the VeTc,NbeMn, and CreMo molecules, respectively, are all larger thanthose of CreCr (1.650 Å) and VeMn (1.670 Å). However, all the FSRvalues for the VeTc, NbeMn, and CreMo bonds are only slightlylarger than those for the CreCr and VeMn bonds. As shown inTable 1, the VeTc, NbeMn, and CreMo molecules have the similarbond length, EBO, NBO, and FSR values, which imply that the threemolecules have similar multiple characters.
3.1.3. Discussion on the multiple biatomic bonds in the bimetallicsystems
Surprisingly, the BP86 NBO value for each of the CreCr, VeMn,VeTc, NbeMn, and CreMo molecules is larger than the CAS NBOvalue. As shown in Table 1, the BP86 NBO calculations at the CreCrgeometries of 1.650, 1.660, and 1.679 Å predicted by differenttheoretical levels and experiment give the same NBO value of 6.0.Our CAS NBO and EBO values at the CASPT2 CreCr optimizedgeometry are 4.9 and 4.1, respectively. For VeMn, the BP86 NBOcalculations at the optimized geometries of 1.670 and 1.649 Å (seeTable 1) predicted by different theoretical levels also give the sameNBO value of 5.7. The reasons, why there exist such differencesbetween CAS NBO and BP86 NBO at the same geometries, may bethat current DFT functionals lack nondynamical correlation whichis probably important for such bimetallic molecules. Just as Rooset al. [31] mentioned, the DFT methods (including BP86) are notsuitable for calculating the properties (such as bond length andNBO) of the bimetallic molecules. The CAS NBO values for thebimetallic molecules may be more credible than the BP86 NBOvalues for the bimetallic molecules.
As shown above, the 4se4s interaction has nonbonding featureat the geometries of CreCr and VeMn molecules [19,31]. If the 4selectron is (partially) removed, the CreCr and VeMn bonds in thebimetallic complexes may still maintain high bond order and short
H. Dong et al. / Journal of Organometallic Chemistry 717 (2012) 108e115 111
bond length as that in the bimetallic molecules. This can be done byadding an electronegative ligand (L) to each metal atom anddifferent substituents on the ligand. Thus, the bond length of thebimetallic core could depend mainly on: (i) the effectiveness in theremoval of the 4s electrons and (ii) the steric hindrance of thesubstituent on the ligand. It is not surprising to consider point (i) asthe electronic effect from the ligands themselves and point (ii) asthe mechanic effect from the substituent on the ligand.
As mentioned above, there are several theoretical studies on thechemical bond of the homobimetallic molecules (including CreCr[19,31], MoeMo [31], WeW [20,31], UeU [16], and other homo-bimetallic systems based on actinides elements [31]) using theCASPT2 method in conjunction with treatments of the relativisticeffects. Many groups [13e15] have reported the DFT studies on thecomplexes with the CreCr, MoeMo, or UeU core (homobimetalliccore). Although the synthesis and properties of the hetero-bimetallic complexes have been reported in the literatures [18],there is no theoretical study on the multiple heterobimetallic bondin the complexes.
In the following sections, we will focus on the ultrashort(multiple) VeMn bond (one kind of the heterobimetallic bonds) inthe complexes considering the similar characteristic betweenVeMn and CreCr.
3.2. CASSCF studies on the two model molecules
For studying the effect of the ligands on the VeMn bond, twomolecules, VMn(NHCHNH)2 (denoted as molecule 1) andVMn(NHCHO)2 (denoted as molecule 2) were chosen as the modelmolecules to calculate the property of the VeMn bonds incomplexes using the CASSCF and BP86 methods. Table 2 gives thestructures and partial geometry parameters, such as R(VeMn),R(VeL), and R(MneL) of 1 and 2. The FSR, BP86//CASSCF NBO,and BP86 NBO values for the VeMn bond are also shown in Table 2.
As shown in Table 2, the BP86 bond length and NBO values ofVeMn are in reasonable agreement with the CASSCF correspondingvalues. The VeMn distances in 1 and 2 (1.739 and 1.755 Å,
Table 2The computational geometries of the VMn(NHCHNH)2 (1) and VMn(NHCHO)2 (2)model molecules at the CASSCF/ECP level (bond lengths are given in Å), togetherwith the BP86/ECP NBO values of the VeMn bonds at these CASSCF geometries. Theformal shortness ratio (FSR) values calculated by using two kinds of atomic radii dataof the V and Mn atoms are also given. The BP86/ECP geometries and NBOs are alsogiven in italic.
Species Geometry parameters FSR(S),FSR(C)a
NBO
R(VeMn) R(VeN) R(MneN) R(VeO) R(MneO)
C1N1
V Mn
N2
N1C2
N2
HH
H
H
HH1
1.739 2.157 2.039 e e 0.63,0.52
4.4
1.735 2.019 1.932 e e 0.63,0.52
4.1
C1N1
V Mn
O1
O2C2
N2
H
H
H
H21.755 2.174 2.042 2.106 1.984 0.64,
0.534.4
1.735 2.028 1.935 1.980 1.920 0.63,0.52
4.2
a The FSR(S) values are calculated by using the atomic radii data from reference[44] and the FSR(C) from reference [45].
respectively) at the CASSCF level are both larger than that in theVeMn molecule (1.670, 1.649 and 1.655 Å at the CASPT2, CASSCF,and BP86 levels, respectively). It is noted that the BP86 NBO valuesof the VeMn bonds in 1 and 2 (both equal to 4.4) are much smallerthan the unreliable BP86 NBO of the VeMn molecule (6.0), andslightly smaller than the credible CAS NBO (4.6) (see Tables 1 and2). The BP86 NBO calculations for the complexes may be reliablebecause the electronic wave functions of such complexes have thesingle-configurational feature.
The Mulliken charge calculations predict that each bimetalliccore in 1 and 2 has a charge of 1.410 and 1.437e, respectively, at theCASSCF/ECP level, and 1.102 and 1.104e at the BP86/ECP level (seethe Supporting information). Such phenomenon implies that theligands of the model molecules have effectiveness in the removal ofthe 4s electrons. Indeed the VeMn core could (partially) lose the 4selectrons to form the valence bond between the metal and ligandsand at the same time obtain lone pair electrons from the ligands toform the coordination bond. The lone pair electrons of the ligandsshould move to the antibonding of the VeMn core, resulting thatthe VeMn distances (the BO values) in model molecules are larger(smaller) than the bond length of VeMn molecule.
It is noted that the VeMn bond length values in 1 and 2 (1.739and 1.755 Å, respectively) are both larger than that in the VeMnmolecule (1.649 Å) at the CASSCF level, which indicates that theligands with the O or N atom coordinated to the VeMn core couldelongate the VeMn bond significantly. However, the bond ordersare similar to the VeMn molecule (see Tables 1 and 2), just as weexpected. In the following section we will consider the sterichindrance (using the calculated relative energies (DE) to quantifythe steric hindrance) of the substituent on each class of the modelligands.
3.3. DFT studies on the VeMn bonds in the complexes
In the present section, we will consider the VeMn distance infour kinds of complexes. The VeMn distances and the NBO and FSRvalues of the VeMn bond at the BP86/ECP level are given anddiscussed. Those at BPW91/ECP and B3LYP/ECP levels are onlygiven in the Supporting information.
3.3.1. The steric hindrance effect of the substituent groupFour kinds of complexes with the substituted 2-aminopyridine
(pa), 2-hydroxypyridine (po), amidinate (ad), and guanidinate(gd) were chosen in the presentwork since these ligands were usedin the experimental [5e12] and theoretical [13e17] studies on theultrashort CreCr bond. The pa, ad, and gd complexes were used toinvestigate the steric hindrance effect of the substituent groups onthe VeMn bond while the po complexes were used to explore theelectronic effect. The structures of all of the complexes calculated inthis work are listed in Table 3. The BP86/ECP NBO, FSR, and VeMnbond length values of the pa, po, ad, and gd complexes are listed inTables 4e6. From Tables 2 and 3, one can easily find that 1 is themodel structure for the pa, ad, and gd complexes, while 2 is modelfor the po complexes. Shortening of VeMn bond by the sterichindrance of the bridging coordination and the role of thesubstituent groups in stabilizing VeMn distance are summarized inFig. 1. Here we would not make the detailed description for Fig. 1.
Considering that the bond energies of VeL and MneL arenearly constant, the energy difference between the complex andits corresponding fragments (DE), which is formulated asDE¼ E(complex)þ E(H2)� E(VeMn)� 2� E(ligandmolecule) for paand po complexes and DE ¼ E(complex) þ 2 � E(H2) � E(VeMn) �2 � E(ligand molecule) for ad and gd complexes, should be a keyparameter to quantify the steric hindrance, that is, the more negativeDE value, the smaller the steric hindrance is. The calculated DE values
Table 4Computational geometry parameters (bond lengths are given in Å) and DE (given inkcal/mol) with zero-point energy (ZPE) correction for molecules pa1epa7 at thelevels of BP86/ECP, together with the NBO and FSR values for the VeMn bonds at thesame theoretical level.
Name Geometry FSR(S),FSR(C)a
NBO DE
R(VeMn)
R(VeN1)
R(VeN2)
R(MneN1)
R(MneN2)
pa1 1.731 2.055 1.989 1.948 1.920 0.63,0.52
4.1 �115.01
pa2 1.729 2.059 1.993 1.955 1.927 0.63,0.52
4.1 �111.22
pa3 1.725 2.060 1.994 1.960 1.932 0.63,0.52
4.0 �108.43
pa4 1.724 2.122 2.010 2.031 1.981 0.63,0.52
4.1 �77.52
pa5 1.734 2.061 2.010 1.964 1.952 0.63,0.52
4.0 �105.02
pa6 1.733 2.065 2.004 1.965 1.943 0.63,0.52
4.0 �100.45
pa7 1.719 2.132 2.016 2.042 1.988 0.63,0.52
4.1 �75.03
a The FSR(S) values are calculated by using the atomic radii data from reference[44] and the FSR(C) from reference [45].
Table 5Computational geometry parameters (bond lengths are given in Å) and DE (given inkcal/mol) with ZPE correction for molecules po1epo11 at the level of BP86/ECP,together with the NBO and FSR values for the VeMn bonds at the same theoreticallevel.
a The FSR(S) values are calculated by using the atomic radii data from reference[44] and the FSR(C) from reference [45].
Table 3Structures of the four classes of complexes with different ligands and substituents.
Complexes Name Substituent groups
R1 R2 R3 R4 R5
N1C1
R1
R2
R3
R4
N2R5
MnV
N4N3C2
R1
R2
R3
R4
R5
pa1 H H H H Hpa2 Me H H H Mepa3 Et H H H Etpa4 t-Bu H H H t-Bupa5 Vinyl H H H Vinylpa6 Ph H H H Phpa7 t-Bu H OH H t-Bu
R1 R2 R3 R4
N1C1
R1
R2
R3
R4
O1
MnV
N2O2C2
R1
R2
R3
R4
po1 H H H Hpo2 OH H H Hpo3 H H OH Hpo4 OH H OH Hpo5 H OH H Hpo6 H H H OHpo7 NO2 H H Hpo8 H H NO2 Hpo9 NO2 H NO2 Hpo10 H NO2 H Hpo11 H H H NO2
R R0
N1C1
N2R
R'
R
V Mn
N1 N2R C2 R
R'
ad1 H Had2 t-Bu Had3 t-Bu Mead4 2,6-Et-Ph Had5 2,6-Et-Ph Me
R R0
N1C1
N2R
N
R
V Mn
N1 N2R C2 R
NR'R'
R' R'
gd1 H Hgd2 t-Bu Hgd3 t-Bu Megd4 2,6-Et-Ph Hgd5 2,6-Et-Ph Me
H. Dong et al. / Journal of Organometallic Chemistry 717 (2012) 108e115112
are listed inTables 4e6 (the BP86 results) and Supporting information(theBPW91andB3LYP results). All theDEvalueswere correctedby theZPEs. From Tables 4 and 6, we can obtain the following orders of DE:pa1 < pa2 < pa3 wpa5 < pa6 < pa4 wpa7 and ad1 < ad2 < ad5wad4< ad3, which are consistent with the steric hindrance order ofH <Me < VinylwEt < Ph< t-Buw2,6-diethylphenyl, indicating ourassumption is reasonable.
3.3.2. VeMn distances in complexes with 2-aminopyridine and 2-hydroxypyridine as ligands
As shown in Fig. 1(a), the steric hindrance effect in the pacomplexes mainly comes from the extrusion interaction betweenR1 and R5 substituent groups (for the molecular structures seeTable 3) of the ligands. Comparing the geometries of pa1epa6given in Table 4, we find that the complex with t-Bu on R1 and R5(pa4) has the VeMn bond length of 1.724 Å, being the smallest one,which is in agreement with the pa4 complex having the largest DE
value. However the VeMn bond length of pa4 is only 0.007 Åsmaller than that of pa1 while the DE value of pa4 is 37.5 kcal/mollarger than that of pa1. This fact indicates that the larger sterichindrance only slightly shortens the VeMn distance. It is noted thatall the NBO values of the VeMn bonds in pa1epa6 are nearly equalto each other (4.0 or 4.1, see Table 4) and also equal to that in themodel molecule 1 (4.1, see Table 2).
Since pyridine cycle is a conjugated system, the strong electron-donating (withdrawing) group could influence the distribution ofthe electron on the VeMn core and the VeMn bond length. In pa7geometry, the VeMn distance (1.719 Å) is 0.005 Å smaller than thatin pa4 geometry, showing that the OH group on the para-positioncan shorten the VeMn bond. Such a result supplies a useful infor-mation for us to design the complexes with different electron-denoting (attracting) groups (see below). The NBO value of 4.1 forVeMn core in pa7 is equal to those values in pa4 and molecule 1 atthe BP86/ECP level.
As reference, one can find that VeMndistance (1.732 Å) in po1 isclose to that in 2 (1.735 Å) and pa1 (1.731 Å). Then the electron-donating OH group (po2epo6) and electron-attracting NO2 group(po7epo11) were chosen as the substituents on the pyridine cycle(see Table 3).
Table 6Computational geometry parameters (bond lengths are given in Å) and DE (given inkcal/mol) with ZPE correction for molecules ad1ead5 and gd1egd5 at the levels ofBP86/ECP, together with the NBO and FSR values for the VeMn bonds at the sametheoretical level.
a The FSR(S) values are calculated by using the atomic radii data from reference[44] and the FSR(C) from reference [45].
b The geometries of gd5 at the BP86/ECP level of theory are failed to optimize.
H. Dong et al. / Journal of Organometallic Chemistry 717 (2012) 108e115 113
Just as we expected, DE values of po1epo11 (except for po7 andpo9) only have smaller discrepancies, within 14 kcal/mol (seeTable 5). The slightly more negative DE values of po7 and po9should be attributed to the interaction between the O atom on theNO2 group and the metal atom V (Mn).
Although the influence of the OH group is not significant, thereare still some laws to follow by analyzing our calculation results. Asshown in Table 5, the VeMn bond lengths in po3 (1.735 Å) and po5(1.728 Å) are 0.003 Å larger and 0.004 Å smaller than that in po1,respectively, since the electron-donating group on meta-position isunfavorable for the electron delocalization of the OH group to theVeMn core (via the pyridine ring conjugated system), while the
N R1NR5
MnV
N NR1 R5
N R1O
MnV
N OR1
N NR
R'
R
V Mn
N NR R
R'
N NR
N
R
V Mn
N NR R
NR'R'
R' R'
a b
c d
Fig. 1. Shortening of the bimetallic bond by bridging coordination of 2-aminopyridine,2-hydroxypyridine, amidinate, and guanidinate. And the role of these ligands instabilizing ultrashort bimetallic distance. (a) In 2-aminopyridine, the “up-down”arrangement may cause interligand repulsion limiting the “compression” of the VeMndistance by the ligands. (b) In 2-hydroxypyridine, there is no such arrangement as in 2-aminopyridine. (c) In amidinates, an “up-up” arrangement allows R group to be putfurther down, aligning the N-centred lone pairs to provide shorter bimetallic bonds.(d) In guanidinates, the steric pressure on top of the ligand initiates a process thatpushes R group down, resulting in a further shortening of the VeMn distance.
electron-donating group on para-position is favorable for suchconjugation process. However, the VeMn bond length of po2(1.733 Å) is similar to that of po1 (1.732 Å). The reason may be thatthe weak interactions between metal and the OH group on ortho-position (the distances of VeO and MneO being 3.2 and 3.1 Å,respectively) induce the electron (of the OH group) being partiallymoved to the antibonding orbital of the VeMn core. Above analysiscould be supported by the Mulliken charge populations of theVeMn core in po1, po2, and po3 [the sum Mulliken charges of theVeMn core in po2 and po3 are 0.025 and 0.002 e smaller than thatin po1 (0.577e), see the Supporting information]. The complex po4has the VeMn bond length value of 1.730 Å, between the bondlength values of 1.733 Å in po2 and of 1.728 Å in po3, indicating thatabove discussions are reasonable. In po6, the distance between H ofthe OH group and O connecting with metal atom is 2.1 Å, indicatingthat there should be a weak interaction between them. This weakinteraction should weaken the Mn(V)eO bond and make theelectrons be more inclined to localize on the VeMn core, therefore,the VeMn distance in po6 becomes shorter than that in po1.
As shown in Table 5, the po7, po8, and po9 complexes havesignificantly larger VeMn bond lengths of 1.779, 1.740, and 1.840 Å,respectively, than that of po1. The reasons for the large VeMndistances in po7 and po9 should be twofold. Firstly, the NO2
group on the ortho- and para-position strongly delocalizes theelectrons of the VeMn core over the conjugate pyridine ring, whichindirectly elongates the VeMn bond. This is also the reason whypo8 has a larger VeMn distance than po1. Secondly, there exists theinteraction between the O atom on the NO2 group and the metalatom V (Mn), which weakens the VeMn bond, leading to muchlonger VeMn bonds in Po7 and Po9 than in others. The morepositive charge populations of the VeMn core in po7, po8, and po9(0.656e, 0.681e, and 1.076e respectively) than that in po1 (0.577e)imply these discussions being reasonable. It is also noted that theNO2 group on meta-positions (R2 and R4) do not have significantinfluence on the VeMn bond length.
3.3.3. VeMn distances in complexes with amidinate andguanidinate as ligands
As shown in Table 6, the VeMn distance in each gd complex issmaller than that in the corresponding ad complex, as the largersteric hindrance between R and R0 groups in gd complex than thatin ad complex. The BP86/ECP VeMn distance in gd1 (1.726 Å) issmaller than that in ad1 (it is just themodel molecule 1, see Table 2)at both the CASSCF (1.739 Å) and BP86 (1.735 Å) levels. The ad3 andgd3 molecules have the shorter VeMn distance of 1.719 and1.718 Å, respectively, as there exist a large volume of spherical t-Buon the R position and a methyl on the R0 position. It is a littlesurprising that the VeMn bond length values of ad4, gd4, and ad5(1.733, 1.723 and 1.730 Å, respectively) are larger than that of ad3and gd3 (1.719 and 1.718 Å, respectively). By checking the BP86geometries of ad4, gd4, and ad5, we find that the dihedral anglebetween the 2,6-diethylphenyl plane and the VMnNCN-cycle planeis near 90.0�, which imply that the H atom (for the case of ad4 andgd4) or methyl group (for the case of ad5) locate far from the 2,6-diethylphenyl. Therefore, taking the cases of ad5 vs ad3 as anexample, the repulsion between 2,6-diethylphenyl and methylgroups (for the case of ad5) is weaker than that between t-Bu andmethyl groups (for the case of ad3), which is a reason for the longerVeMn bond in ad5 than that in ad3.
The DE differences of 70.64 and 47.57 kcal/mol of ad1 vs ad3 andad1 vs ad5 imply that there exists steric hindrance in the ad3 andad5molecules. But the VeMn bond length difference between ad1and ad3 (ad5) is not so significant. The effect of the steric hindranceon shortening the VeMn distance is also tiny as the case of pacomplexes.
H. Dong et al. / Journal of Organometallic Chemistry 717 (2012) 108e115114
From the calculation results and above analysis, we couldconclude that the VeMn bond length values of the complexesshould be larger than that of the VeMn molecule because of theinteraction between the VeMn core and the ligands. The ligandswith the N and O atoms coordinated to the V or Mn atom have thesimilar influences on the VeMn bond. Maybe it is possible to obtainthe shorter VeMn bond if less electronegative atoms coordinatewith the VeMn core. The substituent groups on the ligands (due tosteric hindrances or electronic effects) also have influences on theVeMn bond length, but less significant than that of the ligands. Thesteric hindrances from the substituents on the ligands couldshorten the VeMn bond to some extent, while the electronic effectsmay shorten or lengthen the VeMn bond depending on the prop-erties and positions of the substituent groups. But it may beunfeasible to contract the bimetallic bond length in complex toa certain limit as that in the bimetallic molecule.
4. Conclusions
In the present work, we analyzed the multiple bimetallic bondsin seven diatomic molecules: CreCr, VeMn, VeTc, NbeMn, CreMo,MoeMo, and NbeTc using the CASPT2 method in conjunction withtreatment of the relativistic effects by using the SO coupling andANO-RCC basis set for scalar part. The bimetallic bond lengths,NBOs, EBOs, FSRs, and Mulliken charge populations of these sevenbimetallic molecules are calculated. The calculation results indicatethat the VeMn molecule has smaller bond length and larger FSRvalue than other heterobimetallic molecules, and the VeMnbimetallic core could be considered as a good candidate to inves-tigate the multiple heterobimetallic bonds in complexes.
The geometries and NBO values of two model molecules andfour kinds of complexes containing the VeMn core were calculatedusing the CASSCF and BP86 methods. The steric hindrances andelectronic effects of the substituent groups on the four ligands(substituted 2-aminopyridine, 2-hydroxypyridine, amidinate andguanidinate) were investigated using the BP86, BPW91, and B3LYPmethods. On the basis of our calculations, we would conclude thatthe VeMn bonds in the complexes maintain high bond ordersimilar to that in VeMnmolecule. The VeMn bond length values ofthe complexes with the N and O atoms coordinated to the V or Mnatom are larger than that of the VeMn molecule because of theinteraction between the VeMn core and the ligands. Maybe it ispossible to obtain the shorter VeMn bond if less electronegativeatoms coordinate with the VeMn core. The substituent groups onligands also have influences on the VeMn bond length, but lesssignificant than that of ligands. Therefore, it may bemore necessaryto find an effective ligand structure than make great effort to seeka large volume substituent in designing and synthesizing bimetalliccomplexes with short bonds in experiment, which could save thematerial and obtain obvious effect.
Three kind of DFT methods produced different results. Theresults from the BPW91 functional are all close to those from BP86functional, and the VeMn bond length from B3LYP functional forthe model molecules and complex are all shorter than those of bothBP86 and BPW91. According to our calculations for the complexes 3and 4, the present BP86 and BPW91 calculations are closer toexperiment and the previous B3LYP-CAS calculations than theB3LYP calculations.
Acknowledgements
We appreciate the financial support provided by the Foundationof the Graduate University of Chinese Academy of Sciences for thiswork. Y.-B. Wu appreciates the financial support provided byNational Natural Science Foundation of China through Contract No.
21003086 and Provincial Natural Science Foundation of Shanxithrough Contract No. 2009021016-3.
Appendix A. Supplementary material
Supplementary data related to this article can be found online athttp://dx.doi.org/10.1016/j.jorganchem.2012.07.035.
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