Unmasking the Optimal Isomers of Ti2C84: Ti2C2@C82 Instead of Ti2

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C: Physical Processes in Nanomaterials and Nanostructures 2

84

2

2

82

2

84

Unmasking the Optimal Isomers of TiC : TiC@C instead of Ti@C

Yao-Xiao Zhao, Meng-Yang Li, Rui-Sheng Zhao, Pei Zhao, Kun Yuan, Qiao-Zhi Li, and Xiang Zhao J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 30 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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The Journal of Physical Chemistry

Unmasking the Optimal Isomers of Ti2C84: Ti2C2@C82 instead of Ti2@C84§

Yaoxiao Zhao, Mengyang Li, Ruisheng Zhao, Pei Zhao,Kun Yuan, Qiaozhi Li, Xiang Zhao*

Institute for Chemical Physics & Department of Chemistry, School of Science, State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China

§

Dedicated to Professor Takeshi Akasaka on the occasion of his 70th birthday.

*Corresponding author: E-mail :[email protected] Phone:+86 29 8266 5671 Fax:+86 29 8266 8559

1

ACS Paragon Plus Environment

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ABSTRACT Up to now, the controversies over the stable structures of endohedral di-metallofullerenes M2Cn whether M2@Cn or M2C2@Cn-2 have continued ceaselessly. Herein, in order to disclose the optimal structures of Ti2C84, density functional theory combined with statistical thermodynamic analysis is performed in detail and it turns out that IPR C82 with Ti2C2 inserted win overwhelmingly and perform close-shell electronic structure after our detailed analysis. Furthermore, the stimulation of UV-vis-NIR absorption spectra of thermodynamics preferred isomers under PCM models shows better accordance to the experimental spectra to reconfirm our result again. And 13C NMR spectra of three more stable isomers are performed for further investigations on geometry structures. Last but not least, the electronic structures and various interactions of thermodynamically optimum structures are further revealed.

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■ INTRODUCTION Great efforts have been devoted to endohedral metallofullerenes (EMFs) containing one or more metal ions or even metal clusters in fullerene cages due to EMFs’ novel structures and fascinating electronic properties together with their progressive applications in versatile fields including electronics, magnetism, medicine, materials science1-5 after the successful synthesis and separation of La@C82 in 1991.6 Especially endohedral di-metallofullerenes(di-EMFs), of which the inner moieties possess two metal atoms in fullerenes, have attracted comprehensive attentions since Sc2C86 was identified as metal carbide clusterfullerene (CCFs) Sc2C2@C84 rather than initially proposed Sc2@C86 by Shinohara and co-workers.7 Its carbide nature was later further confirmed by the same group utilizing

13

C NMR combined with synchrotron

X-ray structural studies. Likewise, di-EMFs based on the Group III and Group IV metal atoms, to date, have achieved excellent progress, for instance, Er2C2@C82,8 Gd2C2@C2n(2n=88–92),9,10

Y2C2@C2n(2n=82,84,92,100),11-16

Ti2C2@C78,17-20

Dy2C2@C82,21 Tm2C2@C82,22 Tb2C2@C82,23 Sc2C2@C8224-29 and mixed metal carbide clusterfullerene ErYC2@C82,30 all of which are proven to be CCFs. An increasing number of facts have proved that much attention to the structural determination of di-EMFs with large carbon cages should be paid, such as Ti2C80,17-20 Sc2C82,31 and so on, in that their simple endohedral forms M2@Cn may not fulfill the stable geometry structure and closed-shell electronic configuration rule (CSECR). To attain stabilities on geometry and electronic structures, it is likely that some of these di-EMFs would prefer to the structures of M2C2@Cn–2.18 In fact, numerous di-EMFs reported before 3



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were confirmed as CCFs afterwards.27 Lately, the theoretical work of Sc2@C70 was queried because hybrid density functional method B3LYP without long-range correction used in that work may overestimate the energy of the isomers, the critical temperature in the temperature-relative abundance curve of the series is overestimated and the result is questionable according to Zhao’s work in 2017.32 Note that these phenomena do not mean that all the isomers of M2Cn are in the form of M2C2@Cn-2. Hereon, an illustration that dimetallic actinide endohedral metallofullerenes U2@Ih(7)-C80 has been verified experimentally as conclusive isolatable product in a recent paper has no choice but to be mentioned.33 Recently, the structures of Ti2C84 isomers catch our violent attention. The reasons why we focus on Ti2C84 system are as follows. I) In view of Ti and Sc atoms, the radiuses of them are similar to some extent, and Sc2C84 isomers were proofed in the form of Sc2C2@C82. Thus it is questionable whether the form of Ti2C84 isomers is Ti2C2@C82 instead of Ti2@C84 like Sc2C84 isomers. II) There are numerous studies on di-EMFs, however, these studies on di-EMFs with Ti encaged are relatively insufficient. As yet only Ti2C80 and Ti2C84 have been reported as isolatable EMFs. Ti2C80, the most abundant Ti-fullerene extracted,34 turned out to be (Ti2C2)6+@C786with stable closed-shell electronic configuration, among which the valence of Ti is +4 by DFT calculations.18 In addition, it is reported that three Ti2@C84 isomers have been isolated and characterized by laser-desorption time-of-flight mass spectrometry and UV-vis-NIR absorption spectra. And the results indicate that Ti2C84 acquiesces in the form of Ti2@C84 and the valence of Ti is less than +2,34 which are less evidences. 4


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Herein, a systematic theoretical study, density functional theory (DFT) calculations combined with statistic thermodynamic analysis, on Ti2C84 system is exerted to uncover the most stable structures, which are thermodynamically preferred. The main interactions between titanium atoms and carbon atoms relating to titanium and electronic characteristics of the most stable isomers were further investigated.

■CALCULATION METHODS The ionic model of EMFs has been extensively accepted in general. Initial fullerene cages with pentagon adjacencies (PAs) less than three, C824- for Ti2C2@C82 and C846for Ti2@C84, were fully screened based on semi-empirical molecular orbital method AM1. Then the selected fullerene cages, of which relative energies were less than 52.0 kcal/mol for C824- and less than 31.5 kcal/mol for C846- observing or violating isolated-pentagon rules (IPRs), were re-optimized on basis of B3LYP/6-31G(d). Next, B3LYP/3-21G*~Lanl2dz,

B3LYP/6-31G(d)~Lanl2dz

and

wB97XD/6-31G(d)~Lanl2dz methods were exerted on full optimizations of Ti2C2@C82 and Ti2@C84 isomers without any symmetry limit, and the relative energies of EMFs were re-evaluated on M06/6-31G(d)~Lanl2dz levels (3-21G* and 6-31G(d) considering split-valence polarized are just used for carbon atoms and Lanl2dz is used for Ti atoms). To ensure the stationary points as local minima, vibration frequency analyses were conducted at wB97XD/6-31G(d)~Lanl2dz level. Based on the relative energies and partition functions of isomers, thermodynamic analysis considering the entropy-enthalpy was carried out to determine the stable isomers thermodynamically. In addition, UV-vis-NIR absorption spectra, which are 5



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sensitive to cage structures, were simulated under the PCM model with carbon disulfide solvent at room-temperature on basis of wB97XD/6-311G(d,p)~Lanl2dz method.

13

C NMR spectrums of three EMFs also were performed to authenticate

themselves by same wB97XD/6-311G(d,p)~Lanl2dz method. For further exploration of electronic features and interactions between inner clusters and outer fullerene cages, NBO analysis and quantum theory of atom in the molecule (QTAIM)35 were carried out, and bond critical points (BCPs) with their parameters, density of all electrons, Laplacian of electron density, ellipticity of electron density were searched and calculated. There are general opinions that the outer cages and inner moieties act major ionic interactions companied with a few covalent interactions. Then, Mayer bond orders (MBOs) between metal atoms and directly relevant non-metal atoms of fullerene cages or inner clusters were calculated. The DFT calculations above were performed with Gaussian 09 program packages.36 The analyses of interactions between metal and non-metal atoms were carried out with MULTIWFN.37

■RESULTS AND DISCUSSION The thermodynamic stabilities for Ti2C84 series The stabilities' sequences of C824- and C846- cages were decided with their relative energies based on AM1 and part of them were listed in Table S1 and S2 of supporting information (SI). And the results of optimizations on hollow fullerene cages with relative energies and the gaps between highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs), were also shown in Table S3 and S4 of SI, which indicates that C3v(39717)-C82, C2v(39718)-C82, Cs(39715)-C82, 6


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Cs(51365)-C84 and D2(51589)-C84 possess lower relative energies. Then full optimizations of Ti2C84 isomers with their relative energies and gaps between HOMOs or single occupied molecular orbitals (SOMOs) and LUMOs were performed on B3LYP/3-21G*~Lanl2dz and B3LYP/6-31G(d)~Lanl2dz (shown in Table S5 of SI), respectively. It turns out that singlet Ti2C2@Cs(39715)-C82, Ti2C2@C2v(39718)-C82 and Ti2C2@C2(39714)-C82 with lower relative energies and high gaps are thermodynamically supported isomers based on B3LYP/3-21G*~Lanl2dz. Instead, quintet

Ti2@D2(51590)-C84,

Ti2C2@Cs(39715)-C82

are

quintet

Ti2@Cs(51578)-C84

thermodynamically

favorable

and

isomers

singlet based

on

B3LYP/6-31G(d)~Lanl2dz. Therefore, the results are controversial. As all know, the long-range interactions play an important role in the stabilities of Sc2C2@C2n isomers,32 thus these isomers, of which relative energies are lower based on Table S5, were

re-optimized

interactions.

on

Results

wB97XD/6-31G(d)~Lanl2dz of

relative

wB97XD/6-31G(d)~Lanl2dz

level

energies were

for

shown

considering

long-range

EMFs

basis

in

on Table

1,

of and

M06/6-31G(d)~Lanl2dz was applied as single-point calculations in order to re-ensure energies due to the special characters of Ti atoms (also shown in Table 1). It’s clear that

the

relative

energies

from

Table

S5

and

Table

1

obtained

via

wB97XD/6-31G(d)~Lanl2dz, M06/6-31G(d)~Lanl2dz and B3LYP/3-21G~Lanl2dz are almost in harmony with each other and all of them reveal that Ti2C2@C82 isomers are a little preferred than Ti2@C84. So it is demonstrated that the long-range interactions between inner clusters and fullerene cages also play rather significant 7



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Table 1 Relative energies (ΔE, in kcalꞏmol-1) and HOMO-LUMO gaps (in eV) of Ti2C84 isomers based on wB97XD/6-31G(d)~Lanl2dz and M06/6-31G(d)~Lanl2dz. Isomer

Multiplicity

PA

wB97XD/6-31G(d) ∆E

M06/6-31G(d) ∆E

Gap

Ti2C2@Cs(39715)-C82

singlet

0

0.0

0.0

1.93

Ti2C2@C2v (39718)-C82

singlet

0

4.0

1.3

1.77

Ti2C2@C3v (39717)-C82

triplet

0

4.8

11.7

2.22

Ti2C2@ C3v (39717)-C82

singlet

0

5.1

1.7

2.65

Ti2C2@C2v(39718)-C82

triplet

0

8.0

15.0

1.51

Ti2C2@C2v(39718)-C82

quintet

0

9.0

24.8

1.46

Ti2C2@ C3v (39717)-C82

quintet

0

9.7

26.9

1.23

Ti2C2@Cs(39715)-C82 Ti2@C1(51383)-C84 Ti2C2@C2(39714)-C82 Ti2@D2(51590)-C84 Ti2@C1(51580)-C84 Ti2@C1(51383)-C84 Ti2C2@Cs(39713)-C82 Ti2@C1(51483)-C84 Ti2@D2(51590)-C84 Ti2@D2(51589)-C84 Ti2C2@C2(39714)-C82 Ti2@D2d(51591)-C84 Ti2@C1(51482)-C84 Ti2C2@Cs(39715)-C82 Ti2@D2d(51591)-C84 Ti2@D2d(51591)-C84 Ti2@Cs(51583)-C84 Ti2C2@C2v(39705)-C82 Ti2@Cs(51578)-C84 Ti2@Cs(51578)-C84

triplet

0

13.9

20.0

1.60

quintet

1

15.1

47.1

1.05

triplet

0

15.6

17.4

1.62

quintet

0

15.9

24.7

1.17

septet

0

16.2

— 24.1 8.6 33.6 39.6 31.7 10.8 38.2 31.5 11.1 22.7 40.5 41.7 17.2 46.4 37.5

— 1.62 1.47 1.22 1.22 1.30 1.67 1.12 1.12 1.80 1.13 1.25 1.31 1.88 1.08 1.10

triplet

1

16.3

singlet

0

18.9

quintet

1

19.0

septet

0

19.5

quintet

0

19.6

singlet

0

19.6

septet

0

19.9

quintet

1

20.2

singlet

0

20.5

triplet

0

20.7

quintet

0

21.1

septet

0

22.3

singlet

1

22.5

septet

0

26.0

quintet

0

29.6

a. septet Ti2@C1(51580)-C84 could not be converged.

roles in the stabilities of Ti2C2@C2n series. This phenomenon is same with Sc2C2@C2n and Sc2@C2n+2. The reason why B3LYP/3-21G*~Lanl2dz method performs a little better but B3LYP/6-31G(d)~Lanl2dz behaves worse is that both the basic set of 3-21G* and B3LYP method possess little deviation, so they offset. Lastly, the energies based on wB97XD/6-31G(d)~Lanl2dz and HOMO-LUMO gap values based on B3LYP/3-21G*~Lanl2dz, due to the overestimation of gap values with wB97XD 8


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methods, were employed. To ensure that these energies are local minima, the frequency

calculations

of

them

were

also

implemented

on

wB97XD/6-31G(d)~Lanl2dz level and there is no imaginary frequency for our optimized

structures.

Ti2C2@Cs(39715)-C82

The

results

possesses

from

lowest

Table energy

1

states

followed

that

singlet

by

singlet

Ti2C2@C2v(39718)-C82 and tripletTi2C2@C3v(39717)-C82. These three isomers, all in the form of Ti2C2@C82 instead of acknowledged Ti2@C84, are recognized as the relative stable individuals. Notably, the entropy-enthalpy interchange plays a vital role in the stabilities of fullerenes supported by both experimental and theoretical research. In order to unambiguously determine the structures of Ti2C84 isomers, entropy-enthalpy must be taken into considerations. Hence, the result of thermodynamic analysis demonstrates that entropy-enthalpy effect was performed on fourteen isomers whose relative energies are lower than 16.2kcalꞏmol-1 based on Table 1. The abundance of Ti2C84 isomers was calculated at fullerene-formation temperature because the potential energy could not absolutely decide the thermodynamic stabilities of EMFs. As we can see Figure S1 in SI, the concentration of numerous isomers including Ti2@C1(51383)-C84 with higher potential energies is nearly close to zero at whole range of temperature and it turns out that our standard energy was selected are reasonable. So we can just ignore isomers with lower even near zero abundance in whole fullerene-formation temperatures and a new curve of Ti2C84 isomers in same level is shown in Figure 1 without isomers with lower abundance in Figure S1. Ti2C2@Cs(39715)-C82 is the most abundant isomer at absolute zero degree, 9



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Figure 1 Relative concentration of Ti2C84 isomers with lower energy in the range of fullerene-formation temperature. but its abundance decrease sharply with ascending temperature. On the contrary, the abundance

of

Ti2C2@C2v(39718)-C82,

Ti2C2@C3v(39717)-C82

and

Ti2C2@C2(39714)-C82 increases with raising temperature. The highest abundance of Ti2C2@C2v(39718)-C82 was around 6.22% at 1600K. Although Ti2C2@C2(39714)-C82 possesses some larger abundance, its triplet electronic structure which performs free radical-like with unpaired electron on fullerene cage, with spin electronic density shown in Figure S2 of SI, is seriously unstable. Another remarkable isomer is Ti2C2@C3v(39717)-C82, of which abundance rises rapidly up to 56.26% at 2000K and possesses

dominant

Ti2C2@Cs(39715)-C82

role at

at 1200K.

long-range But

the

temperature relative

after

energies

exceeding of

singlet

Ti2C2@C3v(39717)-C82 with higher relative energies is over 0.3kcalꞏmol-1, which is ignorable, compared with its triplet from Table S5 and Table 1, so the singlet isomer of Ti2C2@C3v(39717)-C82 satisfying stable closed-shell electronic configuration rule is more easily acceptable.

10


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Thus,

singlet

Ti2C2@Cs(39715)-C82,

Ti2C2@C2v(39718)-C82

are

proofed

as

Ti2C2@C3v(39717)-C82

thermodynamic

stable

isomers

and at

1000K-3500K rather than Ti2@C84 detected by UV-vis-NIR absorption spectra which is misunderstood in experiments. The conclusion that the thermodynamic stabilities of EMFs seriously rely on temperature and entropy-enthalpy effect has been revealed for the second time and a higher attention to these isomers with higher spin multiplicities larger than 1 or 2 should be paid. It is well known to all that UV-vis-NIR spectra is sensitive to the structure of fullerene cage and its electronic structure.34 In order to deeply clarify the conflicting ideas on the structure of Ti2C84 isomers, simulated UV-vis-NIR spectra of Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82 were exerted under the PCM model with carbon disulfide solvent and based on wB97XD/6-311G(d, p)~Lanl2dz level at room temperature to compare with those obtained in experiment (shown in Figure 2 with 0.25eV, 0.35eV and 0.20eV half-width at half-height of spectra). It is found that the UV-vis-NIR spectra of Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82 are almost similar with these in experiments (shown in FigureS3 of SI), which is another stauncher

poof

that

the

isomers

luckily

caught

in

experiment

are

Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82 instead of Ti2@C84. UV-vis-NIR

spectra

of

Ti2C2@Cs(39715)-C82,Ti2C2@C3v(39717)-C82

and

Ti2C2@C2v(39718)-C82 with 0.1eV half-width at a half-height of spectra are also 11



Page 12 of 28

shown in Figure 2 in top right to provide the detailed distinguished information about themselves with others. UV-vis-NIR absorption peaks of Ti2C2@C3v(39717)-C82, which are detected at around 600nm, 712nm and 850nm in experiment, can also be searched out in our calculations. Other characteristic peaks and absorption bands, at around 620nm and 400-450nm, are also searched out companied with some fingerprint peaks, and these cannot be searched out by experiments in the past due to the insufficient purity of samples and the limited experiment conditions. Although UV-vis-NIR spectra of Ti2C2@C2v(39718)-C82 and Ti2C2@Cs(39715)-C82 are similar to each other, both of which possess three absorption bands and are still a few differences to distinguish with each other. The absorption bands in UV-vis-NIR

Figure 2 Simulated UV-vis-NIR spectra of a)Ti2C2@C3v(39717)-C82, b)Ti2C2@C2v(39718)-C82 and c) Ti2C2@Cs(39715)-C82. (Three spectra are simulated with 0.35 eV, 0.20 eV and 0.25 eV half-width and their spectra with 0.10 eV half-width are embedded on the top right). spectra of Ti2C2@C2v(39718)-C82 lie in around 400-580, 580-900 and 900-1200nm and their absorption peaks are at round 520, 650 and 1100nm, which also can be used for distinguishing themselves. While Ti2C2@Cs(39715)-C82 owns three absorption bands at around 400-450, 450-650 and 650-1000nm and two conspicuously characteristic peaks at around 500 and 800nm. These inimitable absorption bands and peaks of Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2v@C2v(39718)-C82 12


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would provide valuable information for further experimental investigation with improving technologies and more detailed methods. The

13

C

NMR

of

Ti2C2@Cs(39715)-C82,

Ti2C2@C3v(39717)-C82

and

Ti2C2v@C2v(39718)-C82 NMR can be used as an effective method to verify molecule structures, in our work, but there is a shielding action with outer cages for Ti2C2 inner moieties. So only

13

C

NMR spectra can meaningfully be carried out to clarify the structures of fullerene cages after entrapping Ti2C2 moieties.

13

C NMR spectrums of three thermodynamic

optimum isomers are shown in Figure 3. After our considerate analysis, it is evident that the symmetries of these three fullerene cages, C3v(39717)-C82, C2v(39718)-C82 and Cs(39715)-C82, have changed from initial symmetries, C3v, C2v and Cs respectively, to C1 without exception, which can be in favor of 82 equal-intensity peaks. The degree of deformations for fullerene cages with Ti2C2 compared with its initial hollow cages are accordance with the sequences for EMFs based on relative energies seeing from Table 1. In other word, the larger deformations for fullerene cages mean EMFs with higher relative energies for Ti2C2@C3v(39717)-C82, C2@C2v(39718)-C82 and Ti2C2@Cs(39715)-C82; thus, the energies of deformation occupy considerable proportion in the energies of whole molecule at least in this work. Although C1 point group is for C3v(39717)-C82, C2v(39718)-C82 and Cs(39715)-C82 after entrapping Ti2C2, there are still a fewer unique features to differentiate themselves from the others and these are our except for future experimental study. As

13



Page 14 of 28

we can see, the major peaks of these isomers concentrate upon about 130.0-170.0ppm. There are three peaks (127.3, 129.1 and 129.8ppm), two peaks (127.8 and 129.0ppm)

Figure 3 Simulated 13C NMR spectra of Ti2C2@C3v(39717)-C82,Ti2C2@C2v(39718)-C82 and Ti2C2@Cs(39715)-C82. and one peaks (129.9ppm), are local in less than 130ppm for Ti2C2@C3v(39717)-C82, Ti2C2@C2v(39718)-C82 and Ti2C2@Cs(39715)-C82, respectively. Another feature to distinguish them is local at around 170ppm. It is clear that there is no peaks been local 14


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in larger than 170ppm for Ti2C2@C2v(39718)-C82. Although there are one peaks larger than 170ppm for Ti2C2@C3v(39717)-C82 and Ti2C2@Cs(39715)-C82, the peaks been local in 165.0-170.0ppm for Ti2C2@C3v(39717)-C82 are four, depicted as 166.7, 168.0, 169.1 and 169.3ppm, and only one peak (165.5ppm) for Ti2C2@Cs(39715)-C82 is local in 165.0-170.0ppm. Notably, these features of

13

C NMR stated above are very

conspicuous peaks to discern themselves but not only. Furthermore, the UV-vis-NIR absorption spectra for Ti2C2@C2v(39718)-C82 and Ti2C2@Cs(39715)-C82 are a little similar, so 13C NMR of their outer cages are another supplement evidence for further experiment investigation.

The geometrical structures of Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2v@C2v(39718)-C82 The geometrical structures of Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82 are shown in Figure 4 and the Cartesian coordinates of them are listed at the last of SI in order to have a 3D views. It is known to all that M2C2 clusters always exhibit two configurations, line-like which means four atoms in a line together with two carbon atoms in the middle and butterfly-like shapes which mean there is covalent bond between two carbon atoms and two metal atoms local at the two side of C-C bond. Different configurations of M2C2 in fullerene cages not only rely on the size of fullerene cages and M2C2 clusters but also depend on the type of M atoms. It is obvious that all of three Ti2C2 clusters perform butterfly-like shapes in their corresponding fullerene cages reflected in Figure 4. And these results are relevant to the interplay between Ti2C2 and C82 which will be specifically discussed 15



Page 16 of 28

Figure 4 Structures of a) Ti2C2@Cs(39715)-C82, b) Ti2C2@C3v(39717)-C82 and c) Ti2C2@C2v(39718)-C82 (C atoms of inner clusters are marked in yellow and C atoms of fullerene cages in gray; Ti atoms are marked in green). Table 2 Structural parameters of Ti2C2 cluster in the three isomers. dTi-Ca

dTi-cageb

dC-Cc

(Å)

(Å)

(Å)

Isomer

Dihedral angle of Ti2C2(deg)

Ti2C2@Cs(39715)-C82

145.7

1.993(Ti83-C85) 2.144(Ti83-C79) 1.960(Ti83-C86) 2.136(Ti84-C25) 2.002(Ti84-C85) 2.005(Ti84-C86)

1.345(C85-C86)

Ti2C2@C3v(39717)-C82

163.5


1.343(C85-C86)

Ti2C2@C2v(39718)-C82

154.6


1.343(C85-C86)

a

Distance between each titanium atom and each carbon atom in Ti2C2 cluster. bDistance between each titanium atom and the nearest carbon atoms of fullerene cages. cDistance between two carbons in Ti2C2 cluster. dDistance between carbide atoms and the nearest carbon atoms of fullerene cages.

later. The distances between two carbon atoms in Ti2C2 clusters are almost similar within three isomers seen from Table 2. Besides, there are similar structure parameters of Ti2C2 about the distances between Ti and C atoms of Ti2C2, which could be also detected from Table 2. But a law also must be noted that the dihedral angel of Ti2C2 would increase with increase of symmetry for initial fullerene cages detailing as 145.7, 154.6 and 163.5 (seen in Table 2) for Ti2C2@Cs(39715)-C82, Ti2C2@C2v(39718)-C82 and Ti2C2@C3v(39717)-C82 respectively. As it is concluded from dihedral angel of 16


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Ti2C2 and similar distances between Ti and C in Ti2C2 that the closest distance between Ti atoms and fullerene cages should be descending with increase of symmetry for initial fullerene cages, but the results are contrary seen from Table 2, which may be related to the strength of interactions between inner clusters and fullerene cages.

The interactions between inner clusters and fullerene cages Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2v@C2v(39718)-C82

for

To ascertain electronic structures, NBO analysis of these three molecules, Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82, has been employed shown in Table 3. It is clear that C atoms of Ti2C2 possess four electrons and Ti atoms lose two electrons of their 4s shell for the three EMFs in comparison with that of isolated Ti atom 3d24s2, revealing that C atoms own covalent interactions Table 3 Natural electron populations of Ti atoms and carbon atoms in Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2(39714)-C82. Isomers Ti2C2@Cs(39715)-C82

Atoms

Populations 0.15

3d2.834p0.284d0.075p0.09

Ti83

4s

Ti84

4s0.173d2.904p0.304d0.085p0.10

C85

2s1.172p3.013p0.023d0.01

C86

2s1.172p3.033p0.023d0.01

Ti2C2@C3v(39717)-C82

Ti83 Ti84 C85 C86

4s0.153d2.774p0.364d0.07 4s0.153d2.784p0.364d0.07 2s1.172p3.073s0.013p0.023d0.01 2s1.212p3.003s0.013p0.023d0.01

Ti2C2@C2v(39718)-C82

Ti83 Ti84 C85 C86

4s0.153d2.804p0.364d0.07 4s0.163d2.834p0.374d0.08 2s1.202p3.043s0.013p0.023d0.01 2s1.162p3.023p0.023d0.01

with others and the oxidation state of Ti should be Ti2+. In another word, every Ti atom shifts two electrons toward outer cage. In addition, the occupations of 3d, 4p and 4d, even 5p shells increase more or less, which can be explained by the electron back 17



Page 18 of 28

donation from the cage to the atomic orbital of Ti. The similar cases occur to two Ti atoms in Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82. So the electronic configurations of Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82 can be simply clarified as (Ti2C2)4+@C824-, but the interaction between inner moieties and C82 or between Ti and C atoms are complicated. To further explore electronic features and interactions between clusters and fullerene cages, QTAIM was carried out, and bond critical points (BCPs) with their parameters, density of all electrons, Laplacian of electron density, energy density and ratio of potential energy densities to Lagrangian kinetic energies, were searched with the wave function obtained from optimization on wB97XD/6-31G(d)~Lanl2dz level. Generally, the fullerene cages and inner moieties act major ionic interactions companied with a few covalent interactions. The results of BCPs which are circled in Figure S4 attract our interest, and bond paths are shown in Figure S4 and the parameters of BCPs are listed in Table 4. The values of the topological parameters of electronics densities ( electronics densities (

) and Laplacian

) of BCPs in Table 4 between C atoms in fullerene cages

and Ti atoms are small and positive, indicating that the ion interaction mainly occurs between inner cluster and fullerenes. atoms are larger and

between C atoms in inner cluster and Ti

of them are not very small, especially for the bond

between two C atoms of inner clusters, and these parameters mean that the covalent interactions between two carbon atoms of inner clusters is as important as ion 18


Page 19 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


interaction between carbon atoms of inner clusters and Ti atoms, which is unambiguously exposed. These can also be proofed by energy densities (HBCP) with negative or zero values and ratio of potential energy densities to Lagrangian kinetic energies (

) with slightly larger values, and three of

areeven

larger than 2 (shown in Table 4). Table 4 The parameters of BCPs, Mayer bond orders and delocalization index. Bonds

HBCP

MBO

δ

Ti2C2@C2(39718)-C82 C44-Ti84 0.074 C45-Ti84 0.076 C85-Ti84 0.101 C86-Ti84 0.111 C85-C86 0.337 C85-Ti83 0.108 C86-Ti83 0.111 C63-Ti83 0.077 Ti2C2@Cs(39715)-C82

0.212 0.252 0.278 0.247 -0.852 0.268 0.282 0.238

-0.019 -0.021 -0.034 -0.043 -0.387 -0.039 -0.041 -0.219

1.266 1.247 1.326 1.408 3.227 1.369 1.366 1.270

0.328 0.277 0.907 0.965 1.215 0.971 0.950 0.297

0.000 0.006 1.116 0.055 0.031 0.049 1.160 0.002

C25-Ti84 0.078 C17-Ti84 0.076 C85-Ti84 0.108 C86-Ti84 0.106 C85-C86 0.335 C86-C70 0.010 C85-Ti83 0.109 C86-Ti83 0.121 C79-Ti83 0.077 Ti2C2@C3v(39717)-C82

0.254 0.231 0.263 0.288 -0.835 0.031 0.299 0.250 0.234

-0.022 -0.021 -0.040 -0.037 -0.383 0.001 -0.038 -0.050 -0.022

1.257 1.262 1.378 1.338 3.201 0.865 1.338 1.444 1.269

0.312 0.344 0.951 0.932 1.201 0.000 0.961 0.994 0.299

0.000 0.001 0.053 1.326 1.163 0.042 1.270 0.056 1.154

0.226 0.221 0.288 0.034 0.036 -0.846 0.252 0.271 0.219

-0.020 -0.048 -0.031 0.001 0.001 -0.385 -0.042 -0.033 -0.022

1.264 1.464 1.299 0.826 0.837 3.216 1.401 1.325 1.282

0.293 0.993 0.926 0.000 0.000 1.224 0.940 0.925 0.310

0.001 0.058 0.027 0.000 0.000 1.147 1.153 0.044 0.055

C40-Ti83 C85-Ti83 C86-Ti83 C18-C85 C19-C85 C85-C86 C85-Ti84 C86-Ti84 C81-Ti84

0.075 0.116 0.099 0.010 0.010 0.335 0.110 0.100 0.076

There is a common phenomenon which is always queried that only one theory or method is applied on a certain object. Mayer bond orders (MBOs) can quantitatively be measured with the number of electron pairs shared between two atoms. In addition, MBOs between metal atoms and directly relevant non-metal atoms of fullerene cages or inner clusters were calculated in order to further verify the interplay between inner 19



Page 20 of 28

clusters and fullerene cages (shown in Table 4). MBOs of C86-C85 are larger than one, informing that strong covalent interaction of C86-C85 in three isomers. And MBOs of bonds between C atoms of inner clusters and Ti atoms possess large values close to 1, which emphasizes that there is strong covalent interaction between them. Subsequently, the results disclose that little covalent interaction also exists between clusters and fullerene cages since the MBOs between C atoms of fullerene and Ti atoms are over 0.27.

■CONCLUSIONS To conclude, thermodynamic stable structures of Ti2C84 are obviously proven as singlet Ti2C2@Cs(39715)-C82, Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82, of which electronic configurations could be simplified as (Ti2C2)4+@(C82)4-, rather than Ti2@C84 by DFT combined with thermodynamic analysis in this work. Compared with UV-vis-NIR absorption spectra experimentally, simulated UV-vis-NIR absorption

spectra

under

PCM

model

of

Ti2C2@Cs(39715)-C82,

Ti2C2@C3v(39717)-C82 and Ti2C2@C2v(39718)-C82 combined with

13

C NMR of

fullerene cages play a significant role in the structural reconfirmation of three isomers, which will provide valuable information for further investigation. It is amazing that covalent interactions between Ti atoms and C atoms in Ti2C2 are as significant as ion interactions in three isomers, which differs from Sc2C2 clusters in fullerene cages. Nevertheless, the interactions between the metal atoms and the C atoms in fullerene cages performed significant ion interactions combined with little covalent interactions. That is to say, the interactions between the inner clusters and outer fullerene cages 20


Page 21 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


belong mainly to ion interactions.

■ ACKNOWLEDGMENTS This work has been financially supported by the National Natural Science Foundation of China (21773181, 21573172).

■Supporting information Detailed relative concentration, spin electronic density, structures, UV-vis-NIR of experiment and topology of BCPs (Fig.S1-S5); relative energies of fullerene cages and Ti2C84 isomers (Table S1-S7); Cartesian coordinates of three stable structures in last.

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Graphical Abstracts Thermodynamic stability of Ti2C2@C82 exceeds Ti2@C84. The interactions between metal and non-metal atoms of cages and inner clusters are exposed distinguishably.

28


Unmasking the Optimal Isomers of Ti2C84: Ti2C2@C82 Instead of Ti2

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