Computational study of the structure, bonding and reactivity of selected helical metallocenes

Accepted Manuscript Computational study of the structure, bonding and reactivity of selected helical metallocenes U.E. Cázares-Larios, U.G. Reyes-Leaño, P.A. Castillo-López, K. PinedaUrbina, Z. Gómez-Sandoval PII: DOI: Reference:

S0020-1693(15)00455-7 http://dx.doi.org/10.1016/j.ica.2015.09.017 ICA 16692

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Inorganica Chimica Acta

Received Date: Revised Date: Accepted Date:

30 July 2015 19 September 2015 21 September 2015

Please cite this article as: U.E. Cázares-Larios, U.G. Reyes-Leaño, P.A. Castillo-López, K. Pineda-Urbina, Z. Gómez-Sandoval, Computational study of the structure, bonding and reactivity of selected helical metallocenes, Inorganica Chimica Acta (2015), doi: http://dx.doi.org/10.1016/j.ica.2015.09.017

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Computational study of the structure, bonding and reactivity of selected helical metallocenes. U.E. Cázares-Larios, U.G. Reyes-Leaño, P.A. Castillo-López, K. Pineda-Urbina*, Z. Gómez-Sandoval*. Facultad de Ciencias Químicas, Universidad de Colima, Carretera Colima-Coquimatlán Km. 9, Coquimatlán, Colima Col. C.P. 28400, México. * e-mail: [email protected]; [email protected].

Abstract: A series of helicoid metallocenes structures were studied in silico under the DFT framework. Their reactivity was explored by the dual Fukui function. An energy decomposition analysis was performed in order to gain insight into the interaction between the helix-like ligand and the metallic nuclei. Helical cobaltocene was highlighted as an interesting synthetic target through its peculiar response to ionization as well as its interaction and preparation energies. Keywords: DFT, Fukui function, EDA, metallocenes, helical ligands. 1) Introduction Kealy and Pauson introduced the ferrocene to the world over 60 years ago [1]. This molecule served as the cornerstone that opened up a whole new group of molecular systems for study, the metallocenes. Metallocenes have found their place in science with applications in asymmetrical catalysis, polymerization, antitumoral agents and malaria treatment, besides the basic contributions from studying their peculiar structure and bonding. Within the metallocenes, the helical ferrocene reported by Katz and Pesti in 1982 stands out as a very interesting synthesized structure [2]. This molecule contains a helical organic ligand formed by two cyclopentadiene rings linked by five fused benzene rings, bound on both ends to an iron atom. The resulting structure presents a conjugated chiral system which could display chiroptical activity and interesting electrical properties, besides the helix-like pattern of interest itself as it’s recurrently found in proteins, nucleic acids, polysaccharides and such [3][4][5][6][7]. There has been previous attempts to expand on this helicoid ferrocene like the proposal of a new structure with a similar but longer ligand, for example. Despite all this, there is surprisingly little information about this particular type of metallocene [8]. Due to the nature of the metal-ligand and ligandligand interactions, the electronic properties of a helical metallocene could vary just by changing the metal center, associated with the coordination sphere geometry and oxidation state. Hence, a group of helical metallocenes using Katz and Pesti’s ligand, along with the metals of the fourth period is proposed. Their structures and reactivity are compared to the available data from experimental sources and previous theoretical studies [9] [10] [11]. 2) Computational details Full structure optimizations, without symmetry constraints, were performed with the generalized gradient approximation (GGA) employing the exchange-correlation functional proposed by Becke and Perdew (BP86) [12][13]. All electrons were treated explicitly using the triple zeta valence plus polarization (def2-TZVP) basis set for all atoms as they are implemented in the ORCA code

[14][15][16]. In order to verify the optimized minima on the potential energy surface, a frequency analysis was performed. Having established the lowest energy stationary points for each molecule, a set of reactivity properties was calculated assuming a vertical ionization approximation. The same stationary points were used to calculate the Fukui functions employing ADPT with the BP86 functional, DZVP basis set and GEN-A2* auxiliary basis set on the deMon2k software [17][18][19][20][21][22]. EDA calculations were performed on the Amsterdam Density Functional (ADF) software [23][24][25][26]. They all used the BP86 functional and the TZ2P STO basis set. The ZORA approximation was employed in order to include relativistic effects. The images were rendered by the molecular visualizer Sinapsis, except for Figure 1, which was done with ChemCraft [27][28].Results and discussion A procedural exploration of different multiplicities was done for each proposed metallocene. Every helical system was optimized using four different spin multiplicities; 1, 3, 5 and 7 for compounds with an even number of electrons and 2, 4, 6 and 8 for the ones with an odd number of electrons. These results were used to select a single structure for each helical metallocene, based on two structural stability criterion: the lowest total energy and the largest HOMO-LUMO gap or SOMOLUMO gap (henceforth called HLG indistinctively). They are attached as supplementary material. The metallocenes’ selected structures fulfilled both criteria and their multiplicity and HLG are listed on Table 1. Table 1. Helical metallocene energy gap.

Metal Multiplicity HLG (kcal/mol) Sc Ti V Cr Mn Fe Co Ni Zn

2 1 4 1 2 1 2 3 1

11.39 15.25 26.07 17.28 24.35 33.29 13.30 11.30 53.34

The HLG calculated for some of the selected structures is small –probably as a consequence of their extended conjugation– which certainly sets them up as challenging synthetic targets. However, there has been successful experimentations on systems with HLG of similar magnitude and there are at least two established approaches for their synthesis [29][30][31]. Moreover, the HLGs calculated for the helical vanadocene and helical manganocene are closer to the HLG calculated for the experimentally available helical ferrocene suggesting that a similar approach to their synthesis is not out of the question. The bond lengths between the metal and the Cp rings were analyzed for the selected structures and are listed on Table 2 (use Figure 1 for reference).

Table 2. Metallocene bond lengths, average bond lengths and standard deviations.

Bond C1-M C2-M C3-M C4-M C5-M C6-M C7-M C8-M C9-M C10-M
 σ

Sc 2.446 2.399 2.429 2.415 2.440 2.449 2.401 2.429 2.414 2.441 2.426 0.017

Ti 2.328 2.320 2.365 2.301 2.283 2.328 2.320 2.366 2.302 2.283 2.319 0.028

V 2.290 2.306 2.301 2.209 2.220 2.290 2.305 2.301 2.210 2.220 2.265 0.042

Cr 2.168 2.240 2.258 2.115 2.076 2.167 2.240 2.257 2.115 2.076 2.171 0.070

Metal Mn Fe* 1.934 2.070 1.931 2.079 1.982 2.087 1.938 2.008 1.945 2.017 1.934 2.055 1.931 2.084 1.982 2.104 1.938 2.007 1.946 2.013 1.946 2.052 0.019 0.036

Fe 2.073 2.090 2.098 2.005 2.021 2.073 2.092 2.101 2.006 2.020 2.057 0.038

Co 2.088 2.116 2.210 2.036 2.029 2.087 2.115 2.210 2.036 2.029 2.095 0.066

Ni 2.131 2.230 2.301 2.171 2.095 2.130 2.230 2.302 2.172 2.096 2.185 0.073

Zn 2.582 2.028 2.554 3.059 3.101 2.582 2.028 2.554 3.059 3.101 2.664 0.393

* Experimental data from [32].

Figure 1. Helical metallocene general structure.

Theoretical bond lengths from the helical ferrocene concord nicely with the experimental data from [32]. The deformation of the helical zincocene’s structure is evident from looking at the rather large standard deviation of its C-Zn bond lengths. There is an evident trend in the bond lengths, where the helical manganocene system has the shortest average C-M bond length and this number gets larger as you move farther away from manganese on the periodic table.

Average C-M bond length (Å)

2.426

2.320

Sc

Ti

2.265

V

2.171

Cr

1.946

Mn

2.058

2.096

2.186

2.665

Fe

Co

Ni

Zn

Helical-metalocene

Figure 2. Average C-M bond length in angstrom of each helical metallocene with their respective standard deviation.

There is a direct correlation between the reported effective ionic radii of the metals and the average bond length of the metallocenes (Figure 3) [33]. Scandium was omitted from the effective ionic radii graph as there is no data available for its oxidation state 2+. 1 0.95 0.9 0.85 0.8 0.75 0.7

Sc

Ti

V

Cr

Normalized average Bond Length

Mn

Fe

Co

Ni

Zn

Normalized effective ionic radii

Figure 3. Normalized average bond lengths and effective atomic radii.

A first approach towards the characterization of the proposed helical metallocenes’ local reactivity was done with the Fukui function. The Fukui function is a tool which predicts the change of the electronic density due to a change in the number of electrons of a system. Formally, the Fukui function is the derivative of the electron density with respect to the number of electrons at a fixed external potential [34][35][36][37].

  =    However, the Fukui function is ill-defined due to a derivative discontinuity and as a result it is redefined as two one-sided derivatives [38][39][40][41].  ±  = 

±

 



On the KS-DFT framework, the Fukui functions can be derived as [42]   = |  

  = | 

| |



+    

!  +   

| | ,  | | 

where  are the exact Kohn-Sham orbitals. The second term of these equations is a correction from the relaxation of the inner orbitals due to the ionization of the system. This relaxation term has been calculated by analytical methods that employed linear response theory [20][21][22][43][44][45]. As is, the Fukui function is a tool able to predict predisposition towards electrophiles (  ) and nucleophiles (  ). In this work, the Fukui dual descriptor ( " ) is used in order to display both electrophile and nucleophile regioselectivity in a single image.  "  =    −    This descriptor will take high values in places appropriate to react with nucleophiles and low values where an electrophile interaction is favored by the electronic structure. The Fukui dual descriptor was calculated for every selected system and is presented as a plot over an isodensity. These images utilize a color ramp that goes from low values of  "  in blue to high values of  "  in red.

Figure 4. Colored isodensity for the Fukui dual descriptor of helical metallocenes. a) Sc. b) Ti. c) V. d) Cr. e) Mn. f) Fe. g) Co. h) Ni. i) Zn.

The Fukui dual descriptor images show a trend where the function has both its lowest and highest values around the metallic nucleus. In addition to this, there is a general trend where the first, third and fifth benzene rings present high values of  "  on the outer side of the spiral while the second and fourth benzene rings have high values of  "  on the inner side of the spiral, with the sole exception of the helical cobaltocene. That molecule’s  "  indicates a predisposition towards both electrophiles and nucleophiles on the ligand’s cyclopentadienyl rings and both the first and fifth benzene rings.

Energy decomposition analysis (EDA) allows to quantify electrostatic and orbital contributions to a given interaction in order to characterize it as ionic or covalent. However, the setup is arbitrary because of the inability to split the Hamiltonian into orbital and electrostatic contributions. Morokuma, Ziegler and Rauk have already adapted this energy partition scheme for use in DFT. In this study, two fragments were defined, a metallic nucleus (M) and the ligand (L) in order to analyze the interaction energy (Δ%&' ) between them. This energy is the difference between the

molecule’s energy (%()) and the sum of the fragments’ energies (%( + %)) using the molecule’s geometry. The interaction energy can be further broken down into: Δ%&' = Δ%*+,'-' + Δ%.-/+ + Δ%01

Where Δ%*+,'-' stands for the energy of the electrostatic attraction between both fragments and is calculated under a constant electron density distribution. The second term, Δ%.-/+ , takes into

account the exchange repulsion, kinetic repulsion and overlap repulsion. The last term, Δ%01 , stands for the molecular orbitals’ energy that stabilize the system. Along the way, the preparation energy (Δ%20*2) is also computed. This is the difference between the energy of the molecule ML and the sum of the energies of the optimized fragments M and L calculated separately. The sum of Δ%20*2 and Δ%&' is the energy needed to break apart both fragments, dissociation energy (−3* ). The results of the EDA study are listed on the table: Table 3. Energy-decomposition analysis of metallocenes 45 − 67 87 9 (M=Sc-Zn) at BP86/TZ2P/ZORA. All values are in kcal/mol. Term

Sc

ΔE;<=

-586.07

-639.55

-678.59

-733.36

-740.87

-795.07

-782.51

-748.35

-684.15

254.27

298.82

303.83

368.58

683.11

415.42

320.40

205.61

116.05

ΔEBABC=?=

-413.29 (49.2%)

-438.57 (46.7%)

-452.57 (46.1%)

-483.85 (43.9%)

-571.18 (40.1%)

-514.26 (42.5%)

-498.00 (45.2%)

-466.02 (48.9%)

-470.84 (58.8%)

ΔEDEF

-427.05 (50.8%)

-499.80 (53.3%)

-529.85 (53.9%)

-618.09 (56.1%)

-852.79 (59.9%)

-696.22 (57.5%)

-604.90 (54.8%)

-487.94 (51.1%)

-329.37 (41.2%)

-159.02

-139.75

-148.74

-115.27

111.93

-98.84

-177.60

-260.41

-354.79

5.33

20.65

26.02

7.54

31.79

18.93

14.99

18.50

22.46

580.34

618.90

652.57

725.82

709.08

776.14

767.52

729.85

661.69

ΔE>?@A;

ΔEC=BE;G ΔEHEBH 3

Ti

V

Cr

Mn

Fe

Co

Ni

Zn

The data obtained suggests that the metal-ligand interaction has a larger covalent contribution which goes from 50.8% for the scandium complex (Δ%01 = −427.05 PQRS/UVS) to 59.9% for the

manganese complex (Δ%01 = -852.79 kcal/mol). The sole exception was the zinc helicoidal metallocene where a larger ionic contribution was present (58.8%, Δ%*+,'-' = -470.84 kcal/mol).

This is reflected on the position of the zinc nucleus, which is the only metallic atom that lies just outside the space between the ligand’s cyclopentadienyls. The Δ%&' shows a trend that suggests that the W-orbitals overlap strengthens the interaction. The data goes from -586.07 kcal/mol for the helical scandocene to -795.07 kcal/mol for the helical ferrocene. The helical cobaltocene and helical manganocene present interaction energies of similar magnitude to the helical ferrocene’s, a system which has already been synthesized. Δ%.-/+ is a measure of the repulsion between free electron pairs, which destabilize the interaction between fragments. For the systems in study, this energy goes from 116.05 kcal/mol for the zinc molecule to 683.11 kcal/mol on the manganese complex. The latter is 267.69 kcal/mol larger than the Δ%.-/+ of the helical ferrocene, while the helical cobaltocene’s is 95.02 kcal/mol lower than the reference system. The sum of the electrostatic energy and the Pauli energy is called steric energy (Δ%,'*0 ) and it takes into account nucleus-electron attraction and electron-electron repulsion. This means that any steric energy lower than zero corresponds to an overall stabilizing attraction, while a positive value indicates an overall destabilizing repulsion. The helical manganocene is the only system in this study that has a steric energy value over zero (111.93 kcal/mol), suggesting a certain degree of instability in the complex. The overall data for steric energies correlates to the distances between the metallic nuclei and the helical fragment (Table 2).

900

Absolute energy value (kcal/mol)

800 700 600 500 400 300 200 100 0 Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Zn

Helical metallocene ΔE Pauli

ΔE elestat

ΔE orb

Figure 5. Pauli energy, electrostatic energy and orbital energy.

The Δ%20*2 goes from 5.33 kcal/mol for the scandium system, up to 31.79 kcal/mol for the helical manganocene compound. While all systems present small preparation energies, the lower values indicate a more feasible formation. The preparation energies for the helical manganocene and the helical cobaltocene are 68% larger and 21% lower than the helical ferrocene, respectively. The overall data indicates that all systems are viable for synthesis, averaging high interaction energies, larger attraction energies than the corresponding repulsive energies, as well as overall low preparation energies. However, the helical cobaltocene showed similar energies to the previously synthesized helical ferrocene and in some instances, even more favorable values. 4) Conclusions A number of unusual optoelectronic properties and electron transfer phenomena have already been demonstrated for similar compounds to the ones discussed on this paper. This properly sets them up as desirable products for synthesis in order to further study their possible applications. One should note that the helical cobaltocene’s Fukui functions expose a distinct response of the system towards electronic ionization, in contrast to the response observed on the rest of the helical metallocenes discussed in this work. This might be indicative of peculiar optoelectronic properties. Furthermore, the EDA study identify this system, along with helical manganocene and helical ferrocene as highly stable complexes, according to their interaction energies. The preparation energy and the corresponding Pauli’s repulsive energy further strengthen the case of the helical cobaltocene as a viable and interesting synthesis target. With previous evidence of

successful synthetic efforts on the helical ferrocene and similar structures, the pursuit for the proposed systems is up for grabs for adventurous chemists.

Acknowledgments The authors are grateful for financial support from CONACyT (CB 2008: 105721). UECL and UGRL gratefully acknowledge CONACyT for fellowships 218993 and 296351 respectively.

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Graphical abstract

Graphical abstract A series of helical-metallocene compounds was studied under the DFT framework in order to gain insight of its metal-ligand interactions by way of energy decomposition analysis; and its reactivity, using local Fukui functions.

Highlights • • •

DFT analysis of interesting helical metallocene structures were done. EDA described the helix-cobaltocene as a feasible synthetic target. Helix-Co’s Fukui function stands out from the rest of the systems in study.