Electronic structures of the alkali-containing buckminsterfullerenes (A∂C60) (A = Li, Na, K, Rb, Cs) and the halogen-containing buckminsterfuller

Journalof MolecularStructure (Theochem), 282 (1993) 187-191 0166-1280/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

187

Electronic structures of the alkali-containing buckminsterfullerenes (AX& (A = Li, Na, K, Rb, Cs) and the halogen-containing buckminsterfullerenes (Ha&) (H = F, Cl, Br, I) Da-Ren Zhang”, Ji-An Wubpc, Ji-Min Yan*ld ‘Research Center for Eco-Environmental Sciences, Academia Sinica, Beijing 100085, People’s Republic of China ‘Institute of Semiconductor, Academia Sinica, Beijing 100083, People’s Republic of China ‘Laboratory for Quantum Optics, Academia Sinica, Shanghai 201800, People’s Republic of China ‘Institute of Chemistry, Academia Sinica. Beijing 100080, People’s Republic of China (Received 20 October 1992) Abstract (A = Li, Na, K, Rb, Cs) and (HZ,) The geometrical parameters and electronic structures of C M),(AX,) (H = F, Cl, Br, I) have been calculated by the EHMO/ASED (atom superposition and electron delocalization) method. When putting a central atom into the Cso cage, the frontier and subfrontier orbitals of (AX,) (A = Li, Na, K, Rb, Cs) and (HdC&) (H = F, Cl) relative to those of C M) undergo little change and thus, from the viewpoint of charge transfer, A (A = Li, Na, K, Rb, Cs) and H (H = F, Cl) are simply electron donors and acceptors for the C, cage respectively. Br is an electron acceptor but it does influence the frontier and subfrontier MOs for the Cso cage, and although there is no charge transfer between I and the Cm cage, the frontier and subfrontier MOs for the Cso cage am obviously influenced by I. The stabilities AEx (AEx = (Ex+ Ecrn)- E~x~,,) follow the sequence I < Br < None < Cl < F < Li < Na < K < Rb < Cs while the cage radii r follow the inverse sequence. The stability order and the cage radii order have been explained by means of the (exp-6-l) potential.

Introduction

The football-like Cso molecule had been suggested by chemists in the 1970s [1,2], but it stimulated intense interest only after the discovery of the compound in experiments in 1985 [3]. Besides Cso itself, extracage complexes and intracage complexes have also been discovered experimentally [4-lo]. Cso and its complexes have very interesting and useful properties, which have promoted many experimental and theoretical investigations. * Corresponding

author.

The determination of the electronic structure of the Cm molecule is a very interesting problem and the structure has been calculated by both ab initio and semiempirical methods [ 1 l- 161. In addition, the electronic structures of intracage complexes are unprecedented in chemistry, so they have a strong attraction for chemists. The intracage complex, in which an atom X is trapped inside the cage, is written as (XdC& by means of Smalley’s symbol [17]. In this paper, the EHMO/ASED (atom superposition and electron delocalization) method [18-201 was used to optimize the geometries of the Cm, the alkali-containing C& (AdC6s)

188

D.-R. Zhang et al./J. Mol. Struct. (Theo&m)

(A = Li, Na, K, Rb, Cs) and the halogen-containing Cm (HBC.&) (H = F, Cl, Br, I) molecules and to calculate their electronic structures. The stabilities of the complexes and the interactions between Cso and guest atoms were investigated. Computational

method and electronic structure of

the buckminsterfullerene

Cso

The semiempirical EHMO/ASED method is a direct improvement of the EHMO method with ASED-MO theory suggested by Anderson and co-workers [18-201, in which the repulsive interaction is taken into account. The repulsive energy acting on b for any a-b pair of atoms in a molecule is given by ‘%@b)

=

zb

Za/Rb [

Pa(r)/k

-

-

Rbidr

J

1 (1)

where Z, r and R are the nuclear charge of the atom, the electron coordinate and the nuclear coordinate respectively. The off-diagonal elements of the hamiltonian are modified, so that the hamiltonian has the form Hii = -(VSIP)i

(2)

Hij = l.l25(Hii + Hjj)Sijexp (-0.13R’)

(3)

where VSIP is the valence-state ionization potential, R’ is the internuclear distance and Sij is the overlap integral. The EHMO/ASED method can predict molecular geometry and some other properties [ 18-201. We used this method to optimize the geometries and to calculate the electronic structure

282 (1993) 187-191

C60,(AdC60) (A = Li, Na, K, Rb, Cs) and (HdC@) (H = F, Cl, Br, I). The VSIPs are taken from experimental tabulations [21] and the orbital exponents, except for those of C, which are taken from those used for graphite and diamond [30], are taken from SCF atomic wavefunctions [22,23]. Parameters used here are shown in Table 1. Css is made up of 12 five-membered C rings and 20 six-membered C rings possessing It, symmetry, so that there are two kinds of bond lengths, long bond lengths for five-six ring fusion and short bond lengths for six-six ring fusion, which need to be optimized. The optimized bond lengths and those obtained by other calculations and experiments are given in Table 2. For (ABC& and (H&&) molecules, the same bond lengths are optimized when the A (A = Li, Na, K, Rb, Cs) or H (H = F, Cl, Br, I) atoms are kept at the center of the cage. From Table 2 it can be seen that the bond lengths obtained by the EHMO/ASED method are in good agreement with the experimental values. The symmetries and degeneracies of energy levels obtained by the EHMO/ASED method are consistent with those obtained by other methods. Table 3 presents the energy levels of frontier orbitals and some other orbitals. The shake-up spectra of the X-ray photoemission of Cso indicated that the lowest electronic transition is 1.9 eV [15], which can be explained on the basis of monopole transition. In the distribution of energy levels given here, HOMO(4HJ + LUMO(ST,,) is symmetry forbidden, so the lowof

Table 1 Orbital exponents (C) and ionization potentials (VSIP) (eV) Li c VSIP

c VSIP

0.6396 5.392

Na 0.8358 5.139

K 0.8738 4.341

Rb

CS

0.9969 4.180

1.0605 3.890

C

F

Cl

Br

I

1.8174 1.7717 16.59 11.26

2.5638 2.5500 37.85 17.42

2.3561 2.0387 24.54 12.97

2.6382 2.2570 23.80 11.85

2.6807 2.3223 20.61 10.45

D.-R. Zhang et aI.lJ. Mol. Struct. (Theochem)

Table 2 Calculated and experimental Method

X-Ray 13C NMR STO-3G DZ basis set 4-31G MNDO IND0/2 EHMO/ASED

original C,; (3) there is a long distance between the center atoms and the C atoms on the Cm cage. The energy of the p atomic orbitals of Br (see Table 1) is close to that of the HOMO for Cm, so there is a greater influence on the frontier and subfrontier molecular orbitals of original Ca. The energy of the p atomic orbitals of I (see Table 1) is between those of the HOMO and LUMO for Cm, so there is the greatest influence on the frontier and subfrontier molecular orbitals of original Cso. In Table 5 the stabilities AEx (AE= (Ex+ EC,) - EfxBc,)), gaps and charges of the center atoms for (AXha) (A = Li, Na, K, Rb, Cs) and (HaC& (H = F, Cl, Br, I) are presented. From the data in Table 5, it is shown that the stability order when an atom is put into the center of the (?,a cage is as follows:

bond lengths of CW Ref.

Bond length (A)

189

282 (1993) 187-191

Short

Long

1.388

1.432

24

1.400 1.376 1.369 1.370 1.400 1.398 1.389

1.450 1.465 1.453 1.450 1.474 1.451 1.457

25 11 12 16 13 14 This work

e&-lying allowed transition is HOM0(4H,) + LUMO + 1(2T,,) and its value is 2.2eV, which is in quite good agreement with experiment. The results presented in Table 3 show that the EHMO/ASED method is basically feasible for Ca systems.

A& < AEBr < AENone < AEcr < AEF < AELi < AENa < AEK < AE,,

Calculation results and discussion

< AEa

From the viewpoint of charge transfer, on putting A (A = Li, Na, K, Rb, Cs) and H (H = F, Cl, Br, I) into the center of the C60 cage (see Tables 4 and 5), A (A = Li, Na, K, Rb, Cs) is just an electron donor and H (H = F, Cl) is just an electron acceptor for the Cm cage, Br is an electron acceptor for the Cti cage but it will have little influence on the frontier and subfrontier molecular orbitals for the Cm cage, and for I, although there is no charge transfer from I to the Cbo cage, the frontier and subfrontier molecular orbitals for the Cm cage are obviously influenced. The optimized bond lengths and cage radii of (AXso) (A = Li, Na, K, Rb, Cs) and (HXso) (H = F, Cl, Br, I) are given in Table 6. Generally speaking, there is only a small influence on the radius of the Cbo cage when an atom A (A = Li, Na, K, Rb, Cs) or H (H = F, Cl, Br, I) is put into

Table 4 presents the calculation results of (AXa) (A = Li, Na, K, Rb, Cs) and (HBC& (H = F, Cl, Br, I) including the symmetries, energies and occupations of the frontier and subfrontier orbitals. From Table 4 it can be seen that the symmetries and energies of the frontier and subfrontier molecular orbitals for original Cm are only slightly affected when the A (A = Li, Na, K, Rb, Cs) or H (H = F, Cl, Br, I) atom, except Br and I, is put into the C6a cage. This is explained by three reasons: (1) the symmetries of the s atomic orbitals for the center atoms do not match with the symmetries of the frontier and subfrontier molecular orbitals of original C,; (2) the energies of the valence atomic orbitals for the center atoms are far from the energies of the frontier and subfrontier molecular orbitals of Table 3 Some energy levels (eV) of valence molecular orbitals of Cm Order

HO-3 1

HO-30

.a.

Energy level Symmetry

-24.08

-23.73 17’1,

. .. . ..

‘As

HO-1

HOMO

LUMO

-12.47

-12.45

4%

7Hi?

-11.81 4%

HO-2

LU+I

Lu+2

...

-10.21

-9.60

5T1,

27’1,

-8.39 8Hs

... .‘.

190

D.-R. Zhang et al/J. Mol. Strut. (Theochem) 282 (1993) 187-191

Table 4 Symmetries, energies and occupations Center atom

of the frontier and subfrontier orbitalsa

HOMO- 1

HOMO

LUMO

LUMO + 1

S

E

0

s

E

0

s

E

0

None

7Hs

-12.446

10

4H,

-11.806

10

5T1,

-10.213

Li

7Hs

-12.448

10

4H,

-11.798

10

5T1,

-10.225

Na K

7Hs 7Hs

-12.450 -12.456

10 10

4H, 4H,

-11.794 -11.794

10 10

5T1, 5T1,

Rb cs F

7Hs 7Hs 7Hs

-12.460 -12.461 -12.446

10 10 10

4H, 4H, 4H,

-11.792 -11.793 -11.803

10 10 9

5T1, 5T1,

Cl

7Hs

-12.446

10

4H,

-11.805

9

Br I

5T1, 4Hu

-11.820 -11.796

6 10

4H, 5T1,

-11.804 -10.383

9 5

a S = symmetry; E = energy; 0 = occupation;

HOMO

and LUMO

the center of its cage, but it is interesting to see that the cage radius r’ exhibit an inverse order with their stabilities:

For the original C& without a center atom, the short bond length, the long bond length and the radius have their optimum values on a minimum balance point. When an atom A (A = Li, Na, K, Rb, Cs) or H (H = F, Cl, Br, I) is put into the center of the C6s cage, a new interaction takes place betwen the A (or H) atom and the C atoms Table 5 Stabilities, gaps and charges of center atoms for (A@C,) and (W&O) Center atom

Stabilitya

Gap

Charge

(ev)

(ev)

(lel)

None Li Na K Rb cs F Cl Br I

8.0773 9.2486 15.8200 19.8097 26.2554 5.6078 1.0488 -0.1458 -0.4013

a AEx = (Ex + Ecm) - E(XGJC,)

1.5935 0.6192 0.6227 0.6306 0.6366 0.5976 1.5847 1.5869 1.5835 0.1405

1 1 1 1 1 -1 -1 -1 0

s

E

0

0

2Tls

-9.597

1

2T1,

-9.605

0 0

-10.226 -10.206

1 1

2T1, 2T1,

-9.603 -9.575

0 0

1 1 0

2T1s 2T1, 2T1s

-9.558 -9.554

6Tlu

-10.194 -10.192 -10.219

0 0 0

6Tlu

-10.218

0

2T1,

6Tl”

-10.220 -10.242

0 0

2T1s 2T1,

6Tl”

-9.602 -9.602 -9.605 -9.629

0 0 0 -

given here denote original ones of C,.

on the Cm cage, and then the short bond length, the long bond length and the radius will reach new optimum values on a new minimum balance point. The distance between the center atom and the C on the Cm cage is nearly the sum of their van der Waals radii, so the interaction between them can be described with the (expd-1) formula [26,27], in which the exp( - r) term means the repulsion interaction owing to the overlap of the electron cloud, the rm6 term means the dispersion interaction and the r-l term means the coulomb interaction. The coulomb interaction is attractive in the case considered here. A new minimum balance point is the result of a balance among all the bond interactions of the 60 C atoms on the Cso cage and between the (exp-6-l) interactions of the 60 C atoms on the Cso cage and the center atom. The larger the radius of the center atom, the larger the overlap repulsion and the dispersion attraction between the C on the C6e cage and the center atom, while their coulomb interaction is always the same, except for I. For I, there is no coulomb interaction between the center atom and the C atoms on the Cso cage because of its neutro-electricity. When the coulomb attraction plus the dispersion attraction is larger than the overlap repulsion, r6

and rfI < r&,,, (A = Li, Na, K, Rb, Cs; H = F, Cl)

D.-R. Zhang et al./J. Mol. Struct.

Table 6 Optimized (H@C&

(Theochem)

282 (1993)

bond lengths and cage radii of (A@C,)

187-191

and

(eV)

Center

Bond length (A)

Cage

atom

Short

Long

radius (A)

None Li Na K Rb CS F Cl Br I

1.3887 1.3901 1.3897 1.3851 1.3822 1.3816 1.3896 1.3895 1.3900 1.3941

1.4568 1.4527 1.4498 1.4463 1.4432 1.4428 1.4557 1.4563 1.4562 1.4550

3.5492 3.5440 3.5390 3.5294 3.5218 3.5207 3.5483 3.5491 3.5494 3.5512

When the overlap repulsion is larger than the coulomb attraction plus the dispersion attraction, 4 > &Xle

(H = Br, I)

The stability order mentioned above can also be explained by the (exp-6-l) interaction just given. Conclusions

We conclude that the EHMO/ASED method can provide a useful approximation to the Cso systems for their geometrical parameters and electronic structures. The frontier and subfrontier orbitals, the bond lengths and cage radii, and the stabilities of (Aa&,) (A = Li, Na, K, Rb, Cs) and (Hd&,) (H = F, Cl, Br, I) relative to, those of CsO present a certain order, which can be explained by the (exp-6-l) interactions. Acknowledgements

This work was supported by the National Natural Science Foundation of China and we thank Professor Alfred B. Anderson for the helpful discussion about the EHMO/ASED program. References 1 Z. Yoshida and E. Osawa,.Aromaticity, Kyoto, 1971.

Kagakudojin,

191

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