4798
J. Phys. Chem. 1996, 100, 4798-4802
Electronic Structure of C28, Pa@C28, and U@C28 Ke Zhao and Russell M. Pitzer* Department of Chemistry, The Ohio State UniVersity, 120 West 18th AVenue, Columbus, Ohio 43210 ReceiVed: August 31, 1995; In Final Form: December 1, 1995X
Electronic structure calculations, including relativistic core potentials and the spin-orbit interaction, have been carried out on the C28, Pa@C28, and U@C28 species. Excitation energies, spin-orbit splittings, the electron affinity, and the ionization potential are computed for C28. The ground state of C28 is described well by the Hartree-Fock wave functions, but other states are not. The computed electron affinity and ionization potential are similar to those of C60. Strong metal-cage binding is found for Pa@C28 and U@C28, similar to that in U(C8H8)2. The ground electronic states depend on the order of the lowest-energy cage π* and metal 5f orbitals, with (π*)1 and (π*)1(5f)1 found to be the ground electronic configurations for the two complexes. U@C28 is found to be diamagnetic.
I. Introduction
TABLE 1: Protactinium Basis Set
A C28 peak was apparent in the mass spectra under carboncluster-generating conditions when fullerenes were first being studied.1,2 It was also noted that C32 was the smallest fullerene observed in laser “shrink-wrapping” experiments on larger fullerenes,3 so that C28 clusters could not be formed in this way. An early theoretical discussion4 of small carbon clusters showed that a Td C28 structure had some enhanced stability characteristics compared to other clusters of approximately the same size but that it would have an open-shell electronic structure. Semiempirical theoretical treatments by the MNDO5 and tight-binding molecular dynamics6 methods optimized structures with Td topology but distorted to C1 symmetry. These studies did not identify the electronic state. An ab initio selfconsistent-field (SCF) study of carbon clusters7 found the optimum fullerene-type structure to have Td symmetry, but with a cyclic polyacetylene C28 structure having lower energy. This study used a double-ζ (6s3p)/[3s2p] generally contracted basis set and identified the electronic state incorrectly. Interest in C28 clusters was greatly increased when it was found8 that endohedral C28 metal complexes, particularly U@C28, could be formed with quite high efficiency. Although no characterization experiments on pure samples have been reported, photoemission spectra8 on sublimed films containing U@C28 suggest a 4+ valence state. Laser shrink-wrapping experiments8 on larger clusters, such as U@C60, all led to U@C28 being the last structure before fragmentation. Accompanying ab initio SCF calculations8,9 showed the Td ground state to be (a1)1(t2)3 5A2 which was noted to be JahnTeller inactive. The basis set used was a double-ζ (7s3p)/[4s2p] segmented contraction set. Small energy lowerings were found with slight structural distortions, but calculations using density functional theory supported the Td geometry.9 A series of calculations of endohedral complexes has followed9-16 in which many elements have been considered for the central atom. In such studies which included geometry reoptimizations, the changes were small (CC bond distance changes of 0.04 Å maximum). A simple model was proposed9 that a Pauling electronegativity value of 1.54 or smaller was necessary for an atom to form a stable endohedral complex. In the present work, we carry out calculations on C28, Pa@C28, and U@C28. In order to treat complexes with heavy X
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4798$12.00/0
orbital exponents
contraction coefficients
2.811 0.8944 0.3746 0.1271
n ) 3 basis for 6s, 7s, 6d orbitals -0.083 003 6 -0.009 312 5 0.744 693 9 -0.032 325 7 0.358 889 9 0.524 189 1 0.008 380 3 0.607 544 2
0.0 0.0 0.0 1.0
4.038 1.741 0.8038 0.3146
n ) 4 basis for 6p, 7p, 5f orbitals 0.005 697 8 0.178 751 2 0.039 128 4 0.371 661 9 0.670 397 5 0.383 500 0 0.405 387 2 0.347 182 4
0.0 0.0 0.0 1.0
atoms, we use relativistic core potentials,17,18 the corresponding spin-orbit operators,17,18 and the spin-orbit configurationinteraction (CI) method.19,20 The basis sets used for carbon,21 (4s4p)/[2s2p], and uranium,22 (4sd4pf)/[3sd3pf], are as used previously, and a protactinium basis set was developed of the same type as the uranium basis set (Table 1). All are of approximately double-ζ quality. Computer programs from the COLUMBUS system22,23 were used. The C28 calculations were done to investigate excited states, negative ion states, and positive ion states. All studies used a C28 structure very close to that of ref 9. In going to U@C28 calculations, we expected that the electronic structure would be quite analogous to that of uranocene.22 Four of the uranium atom’s six valence electrons would be used to fully occupy the half-occupied a1 and t2 C28 MOs. The C28 π MOs would mix heavily with the unoccupied uranium 6d orbitals and to a lesser extent with the 5f orbitals, causing strong bonding and reducing the net charge transferred. The remaining two uranium valence electrons would be in a (5f)2 configuration, giving probably a triplet, paramagnetic ground state. Much of this came out in the U@C28 results, but the unanticipated part was that a C28 π* MO was of sufficiently low energy to give a (π*)1(5f)1 ground state. The Pa@C28 studies were then undertaken to study the relative energies of these MOs in even simpler electronic states. A brief account of the U@C28 results was included in a review paper24 on actinocenes and actinofullerenes. II. C28 The simple model8 for C28 that we have found to be very useful is that of a perfect tetrahedron with four carbon atoms at the vertices and a hexagon of carbon atoms, analogous to benzene, located on each of the four faces. The hexagons are © 1996 American Chemical Society
Electronic Structure of C28, Pa@C28, and U@C28
J. Phys. Chem., Vol. 100, No. 12, 1996 4799
TABLE 2: C28 5A2 MOs MO
main component
occupation no.a
IVO orbital energy (hartree)
5e 8t2 5t1 9t2 5a1 6e 10t2 6t1
hexagon π (e1g) hexagon π (e1g) hexagon π (e1g) vertex π vertex π hexagon π* (e2u) hexagon π* (e2u) hexagon π* (e2u)
4 6 6 3 (9/4) 1 (3/4) 0 0 0
-0.624 359 -0.610 871 -0.495 347 -0.336 457 -0.332 957 -0.122 941 -0.086 261 -0.051 510
a
Numbers in parentheses are those used in the IVO calculation.
TABLE 3: Partial Gross Atomic Populations of 5A2 C28 MOs C1
C2
C3
MO
s
p
s
p
s
p
5e 8t2 5t2 9t2 5a1
0.00 0.08 0.00 0.07 0.04
0.03 0.39 0.08 1.98 0.81
-0.10 -0.14 -0.49 0.00 0.00
1.36 3.51 4.32 0.18 0.03
0.05 -0.11 -0.26 -0.11 -0.01
2.66 2.27 2.35 0.88 0.12
TABLE 4: Total Gross Atomic Populations and Atomic Charges for 5A2 C28 atom
s
p
total
charge
C1 C2 C3
1.328 1.122 1.174
2.607 2.891 2.834
3.935 4.013 4.008
+0.065 -0.013 -0.008
displaced radially outward to give an approximately spherical cluster. Each hexagon, by the benzene analogy, has a closedshell electronic structure, leaving four unpaired electrons in π-like orbitals on the vertices. Combining these vertex π orbitals into MOs with parallel spins gives the (a1)1(t2)3 5A2 ground state. The higher-energy SCF MOs determined for the ground state are given in Table 2. C1 designates the (four) vertex carbon atoms, C2 the (twelve) carbon atoms bonded to C1 atoms, and C3 the other (twelve) carbon atoms. The four sets of benzenelike HOMOs (e1g) form the basis for a representation which reduces to E + T2 + T1 in Td symmetry, with the corresponding C28 MOs being 5e, 8t2, 5t1, which are split by hexagon-hexagon interactions into this energy order. Our MO numbering differs from that of other authors due to our use of core potentials. The benzene-like LUMOs (e2u) split similarly into E + T2 + T1 (6e, 10t2, 6t1) so that the LUMO for C28 is the π* 6e MO. The half-full MOs are 5a1 and 9t2 and are mainly on the C1 atoms. The character of these MOs is evident from the partial gross atomic populations (Table 3); the total populations are given in Table 4 and show the C1 atoms to be slightly positive and the other atoms slightly negative. For the spin-orbit CI calculation, it was necessary to truncate the set of virtual orbitals, so we used the improved virtual orbital (IVO) procedure25 to increase the utility of the virtual orbitals retained; in doing so, one-fourth of an electron was removed from each half-occupied MO. The active MOs in the CI were then chosen to be 5t1, 9t2, 5a1 (occupied) and 6e, 10t2, 6t1 (unoccupied). A singles and doubles spin-orbit CI (CISD) within these restrictions had approximately 48 000 terms in the D2 symmetry actually used in the calculations. The results are given in Table 5. The 5A2 ground state is represented well by the SCF wave function in the CI (94.3%). The spin-orbit interaction splits it into E + T1 double-group terms. Since half-filled shells give no first-order spin-orbit splitting, the main (5a1)1(9t2)3 part of the wave function contributes nothing directly and the splitting (less than 0.01 meV) comes from the CI mixing.
Most of the C28 excited states have large CI mixing (Table 5), including both the first excited state (3T1) at 0.25 eV excitation energy and the second excited state (1E, 0.37 eV). Since MOs optimized for the ground state were used for the excited states, we repeated the calculations with MOs optimized for the average of the configuration (5a1)1(9t2)3. With these MOs, the 5A2 CI energy is 0.69 eV higher and the excitation energies are 0.80 eV (3T1) and 1.20 eV (1E), showing both that the former MOs are better for all three states and that the CI is too restricted, probably most seriously in the active space, to make the results nearly equivalent. The lowest electric-dipoleallowed state, 5T1, was computed to lie at 2.58 eV. It is 85.8% (5t1)5(5a1)1(9t2)4 in character. The near degeneracy of the 5a1 and 9t2 MOs means that there are nearly degenerate ways to remove or add electrons to C28. SCF, IVO, and CI calculations analogous to those done for C28 were performed for C28+1 and C28-1. The states used for the determination of MOs were (5a1)1(9t2)2 4T1 for C28+1 and (5a1)1(9t2)4 4T1 for C28-1. The other candidate for C28+1, (5t1)5(5a1)1(9t2)3 6T2, could not be handled correctly by our SCF program in the D2 symmetry necessary for use in the CI program (but could be handled in Td symmetry). The results of these calculations are given in Table 5. For C28+1, the ground state at the SCF level, 6T2, becomes the second excited state at the CI level, with the 4T1 state becoming the ground state. The physical difference is whether the electron is removed from a hexagon MO (5t1, giving 6T2) or a vertex MO (9t2, giving 4T1). Besides the three excited states of C28-1 shown in Table 5, there is a fourth one, 2T1, at -1.02 eV relative to C28. All the other C28-1 states were found to be unbound with respect to C28. Only the 4A2 state is electric-dipole-allowed from the ground 4T1 state. Our computed C28 electron affinity (2.02 eV) is probably too low due to our limited correlation energy treatment, and our computed ionization potential (9.23 eV) is too high (7.8 eV, measured by the charge-transfer bracketing technique26). The electron affinity and ionization potential of C28 are not greatly different from those of C60 (2.6527 and 7.64 eV28) despite the qualitative difference in electronic structure.26 The 4T1 ground states of both C28 ions are Jahn-Teller active, but due to the strongly bonded character of the cage, we do not expect large distortions. It is interesting that the same MO shell (9t2) is both the donor and acceptor of electrons in the formation of the C28 ions. III. Pa@C28 The Pa@C28 complex has not been studied experimentally yet, but should be stable.9 It is expected to have a simple openshell electronic structure. If four of the five Pa valence electrons (5f26d17s2) move to the C28 cage to pair up its four unpaired electrons, then there will be one unpaired electron and the question of interest is whether it occupies a metal orbital (5f or 6d)29 or a cage π* orbital. The C28 structure used for Pa@C28 was the same as was used for C28 itself. It had been noted9 that the center-to-hexagon distance in C28 is very close to the metal-to-ring distance in uranocene, so we felt that any substantial change in structure is unlikely. To determine MOs for use in the spin-orbit CI calculations, we carried out SCF calculations with one electron in a π* orbital, (6e)1 2E, and with one electron in a 5f orbital, (7a1)1 2A1, (10t2)1 2T2, (5t1)1 2T1, (7a1, 10t2, 5t1)1 (average). The 2E was the lowest in energy. Spin-orbit CI calculations were done using both MOs from the (6e)1 SCF calculation and the (5f, average)1 SCF calculation. The latter gave lower total energies for all states of interest, so we present only those results.
4800 J. Phys. Chem., Vol. 100, No. 12, 1996
Zhao and Pitzer
TABLE 5: C28, C28-1, and C28+1 Relative Energies species C28
C28-1
C28+1
a
principal configurations 5a1 9t2 5t1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5
1 1 0 2 0 2 1 1 0 2 1 1 2 2 1 2 0 1 1
3 3 4 2 4 2 3 4 5 3 4 4 3 3 2 1 3 2 3
∆E (CI, eV)
Γ-S state
no. of spin-orbit states
total spin-orbit ∆E (meV)
0.943 0.467 0.242 0.234 0.360 0.357 0.233 0.853 0.399 0.256 0.202 0.597 0.225 0.780 0.906 0.412 0.281 0.210 0.957
5A a 2 3 T1
2 4
0.00 0.08
0.00 b
0.00 0.25
1
E
1
-
b
0.37
4T a 1 2T 2
4 2
0.10 0.00
2
E
1
4A
2 4T a 1 2T 2
6T
2
-0.84 b
-2.02 -1.84
-
b
-1.40
1 4 2
0.24 0.09
0.23 9.61 b
-1.23 9.23 9.50
6
0.09
8.58
9.53
b
State used to obtain MOs. Not calculated.
TABLE 6: Pa@C28 (5f)1 Configuration MOs MO 4e 8t2 9t2 4t1 5e 5t1 10t2 6a1 7a1 11t2 6t1 6e 7t1 12t2 13t2 8a1 7e a
∆E (SCF, eV)
weights
main component(s) hexagon π (e1g), Pa 6d hexagon π (e1g), Pa 6d C28 σ C28 σ C28 σ hexagon π (e1g), Pa 5f vertex π, Pa 5f vertex π, Pa 5f Pa 5f Pa 5f Pa 5f hexagon π* (e2u) hexagon π* (e2u) hexagon π* (e2u) Pa 6d C28 π* Pa 6d
occupation no.a
IVO orbital energy (hartree)
4 6 6 6 4 6 6 2 1/7 (0) 3/7 (0) 3/7 (0) 0 0 0 0 0 0
-0.802 055 -0.771 419 -0.762 584 -0.745 508 -0.722 610 -0.613 110 -0.560 979 -0.530 836 -0.229 345 -0.220 921 -0.205 993 -0.190 530 -0.098 862 -0.086 616 -0.048 683 -0.036 947 -0.022 988
Numbers in parentheses are those used in the IVO calculation.
The MOs for Pa@C28 are given in Table 6. In comparing to the C28 MOs, note that the 4e and 8t2 hexagon π MOs have mixed heavily with Pa 6d orbitals and have dropped in energy below some C28 σ MOs. The 5t1 hexagon π MO and the 10t2 and 6a1 vertex π MOs have mixed with 5f orbitals to a lesser extent and retain their positions as a group. Similar mixing with 4f orbitals occurs in
[email protected] The Pa 5f orbitals are split slightly but will be rearranged by the spin-orbit interaction. The numbering of the MOs in Pa@C28 compared to that in C28 is affected by the insertion of the Pa 6s (a1) and Pa 6p (t2) MOs at low energy. Since the electronic structure has one electron outside closed shells, the IVOs are the same as the virtual orbitals from the SCF calculation. The population analysis by MO is in Table 7, and the total gross atomic populations are in Table 8. Note that the large mixing of Pa orbitals into C28 MOs (0.71 (7s), 0.36(7p), 3.68 (6d), 2.64 (5f)) has made the charge on the Pa atom negative. This value of the atomic charge relates more to the extent of metal-cage bonding than it does to the oxidation number. The active MOs for the CI were (5t1-hexagon π), (10t2, 6a1vertex π), (7a1, 11t2, 6t1-5f), (6e, 7t1, 12t2-hexagon π*), (13t2, 7e-6d), and (8a1-π*). The reference configurations were all those of the types (6e)1 and (5f)1. All single excitations were used as well as selected double excitations.
TABLE 7: Partial Gross Atomic Populations for (5f)1 Pa@C28 MOs C1 MO
C2
s
p
s
C3 p
s
Pa p
s
p
4e 0.00 0.12 0.14 1.07 0.34 1.54 0.00 0.00 0.13 0.69 0.35 2.19 0.09 1.44 0.00 0.00 8t2 0.06 0.57 0.03 2.10 0.18 2.17 0.00 0.87 9t2 0.00 1.74 0.03 3.27 0.00 0.96 0.00 0.00 4t1 5e 0.00 0.26 0.00 0.93 0.24 2.52 0.00 0.00 0.00 0.09 -0.40 3.66 -0.30 2.28 0.00 0.00 5t1 10t2 -0.10 1.53 -0.03 0.85 -0.47 3.62 0.00 0.00 6a1 -0.06 1.31 -0.01 0.20 -0.06 0.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 7a1 0.00 0.04 0.00 0.02 0.00 0.01 0.00 0.00 11t2 0.00 0.00 0.00 0.01 0.00 0.04 0.00 0.00 6t1
d
f
0.79 1.07 0.00 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.66 0.61 0.14 0.13 0.36 0.38
TABLE 8: Total Gross Atomic Populations and Atomic Charges for (5f)1 Pa@C28 atom
s
p
C1 C2 C3 Pa
1.21 1.21 1.14 2.71
2.68 2.73 2.76 6.36
d
3.68
f
total
charge
3.64
3.89 3.94 3.90 15.40
+0.11 +0.06 +0.10 -2.40
TABLE 9: Pa@C28 Electronic States principal configurations 1
(6e) (10t2)5(6e)1(11t2)1 (11t2)1 (12t2)1 (11t2)1 (12t2)1 (7a1)1 (6t1)1 (6t1)1 (7t1)1 (7t1)1 (6t1)1 (7a1)1
weight 0.782 0.081 0.657 0.178 0.603 0.225 0.754 0.157 0.422 0.395 0.360 0.313 0.170
principal character
double-group state
∆E (eV)
π*
G3/2
0.000
5f
G3/2
1.702
5f
E5/2
1.811
5f
E1/2
2.223
5f
G3/2
2.497
5f
E1/2
2.521
The resulting energy levels and principal wave function components are shown in Table 9. The ground state is (6e)1 G3/2, and the first excited state is (11t2-5f)1 G3/2 at 1.70 eV. The rest of the (5f)1 states follow, going up to 2.52 eV. All of the (5f)1 states have appreciable mixing of hexagon π* character. The CI based on (6e)1 MOs gave a first excitation energy of 2.70 eV to an excited state which was principally hexagon π* in character.
Electronic Structure of C28, Pa@C28, and U@C28
J. Phys. Chem., Vol. 100, No. 12, 1996 4801
TABLE 10: U@C28 (5f)2 Configuration MOs MO
main component(s)
occupation no.a
IVO orbital energy (hartree)
4e 8t2 9t2 4t1 5e 5t1 10t2 6a1 7a1 11t2 6t1 6e 7t1 12t2 7e
hexagon π (e1g), U 6d C28 σ hexagon π (e1g), U 6d C28 σ C28 σ hexagon π (e1g), U 5f vertex π, U 5f vertex π, U 5f U 5f U 5f U 5f hexagon π* (e2u) hexagon π* (e2u) U 6d U 6d
4 6 6 6 4 6 6 2 2/7 (1/7) 6/7 (3/7) 6/7 (3/7) 0 0 0 0
-0.801 87 -0.774 72 -0.771 61 -0.745 26 -0.722 74 -0.620 02 -0.568 30 -0.535 47 -0.369 14 -0.355 26 -0.347 64 -0.190 06 -0.100 07 -0.095 34 -0.045 64
a
Numbers in parentheses are those used in the IVO calculation.
TABLE 11: Partial Gross Atomic Populations for (5f)2 U@C28 MOs C1 MO
s
C2 p
s
C3 p
s
4e 0.00 0.12 0.08 1.08 0.18 0.13 0.57 0.19 2.19 0.36 8t2 0.09 0.78 0.21 2.34 0.03 9t2 0.00 1.74 0.03 3.27 0.00 4t1 5e 0.00 0.26 0.00 0.94 0.20 0.00 0.09 -0.36 3.63 -0.27 5t1 10t2 -0.09 1.53 -0.03 0.84 -0.48 0.00 6a1 -0.05 1.30 -0.01 0.19 0.00 0.01 0.00 0.00 0.00 7a1 0.00 0.02 0.00 11t2 -0.01 0.05 0.00 0.00 0.00 0.04 -0.01 6t1
U p
s
p
d
f
1.74 2.31 1.47 0.96 2.52 2.25 3.57 0.48 0.01 0.04 0.05
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.22 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.81 0.01 1.02 0.00 0.08 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.72 0.66 0.15 0.27 0.76 0.78
The G3/2 ground state will be Jahn-Teller active, particularly with respect to E vibrations since it is mostly of 2E character, but this is probably a dynamical Jahn-Teller effect since the cage atoms are strongly bonded. The G3/2 g values are calculated to be 2.004 44 and 2.008 54, both larger than the free-electron value, but subject to vibronic averaging. IV. U@C28 The U@C28 complex has been synthesized with substantial yield compared to both other metallofullerenes and empty fullerenes, suggesting that the uranium atom may nucleate fullerene formation.8 The fact that shrink-wrapping C60 gives C32 and shrink-wrapping U@C60 gives U@C28 also suggests strong stabilization of fullerenes by uranium.8 The principal question regarding the electronic structure is whether the two unpaired electrons are in (π*)2, as suggested by Pa@C28, in (5f)2 by analogy with uranocene, or in (π*)1(5f)1. SCF calculations were carried out on the lowest (π*)2 and (π*)1(5f)1 states and on several (5f)2 states. The lowest energy was for a (5f)2 state, followed by a (π*)1(5f)1 state and then by several more (5f)2 states. Accordingly, an SCF calculation on the average of all (5f)2 states was done to provide MOs for the CI calculations. The (π*)1(5f)1 MOs could not be used in a CI calculation directly because the SCF calculation had to be done in Td symmetry but the CI calculation had to be done in D2 symmetry. The MOs from the lowest (π*)2 state were retained for possible CI use also. The higher-energy MOs from the (5f)2 SCF-IVO calculations are shown in Table 10, their population analysis is shown in Table 11, and the gross atomic populations and atomic charges are shown in Table 12. The MO results are generally very similar to those for Pa@C28. Both the strong mixing of C28 π orbitals with metal orbitals and the resulting population analysis negative charge on uranium remain. This negative charge
Figure 1. Energy levels of U@C28.
TABLE 12: Total Gross Atomic Populations and Atomic Charges for (5f)2 U@C28 atom
s
p
C1 C2 C3 U
1.21 1.22 1.14 2.67
2.70 2.76 2.79 6.08
d
3.07
f
total
charge
3.67
3.91 3.98 3.93 15.49
+0.09 +0.02 +0.07 -1.49
TABLE 13: U@C28 Electronic States principal configuration
principal character
double-group state
∆E (eV)
(7a1)1(6e)1 (7a1)1(6e)1 (7a1)1(6e)1 (11t2)1(6e)1 (11t2)1(6e)1 (11t2)1(6e)1 (11t2)1(6e)1 (11t2)1(6e)1 (11t2)1(6e)1 (11t2)1(6e)1 (7a1)1(11t2)1 (7a1)1(11t2)1
(5f)1(π*)1
E T1 T2 A1 T1 T2 A2 E T1 T2 E T1
0.000 0.030 0.038 0.266 0.275 0.293 0.295 0.305 0.306 0.334 0.553 0.590
(5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)1(π*)1 (5f)2 (5f)2
(-1.49) varies less than 0.1 for the (π*)1(5f)1 and (π*)2 sets of MOs. After some experimentation, the active MOs for the spinorbit CI calculation were chosen to be the 5t1 through 7e MOs from Table 10. The reference configurations were chosen to be all those of the types (5f)2 and (6e)1(5f)1. A CI calculation just among the reference configurations gave a (5f)2 ground state. Adding all single excitations gave a (6e)1(5f)1 ground state with the (5f)2 states all becoming excited states. The spin-orbit CI program did not have the capacity to add all double excitations so we could only add a selected subset of them. The final results are shown in Table 13 and Figure 1. The groupings of states in Figure 1 are characteristic of a strong ligand field. At higher energy, the grouping is less clear. The lowest group of states is for the (7a1-5f)1(6e-π*)1 configuration and gives double-group states (in energy order) E (majority singlet), T1, and T2 (both majority triplet). All three states are composed of approximately 61% of the main
4802 J. Phys. Chem., Vol. 100, No. 12, 1996 configuration, with the next-most-important terms coming from 10t2 f 11t2 (π f 5f), 6e f 6t1 (π* f 5f), and 5t1 f 6t1 (π* f 5f) excitations, all involving spin mixing. With reference to the population analysis charge on the uranium atom from the (5f)2 SCF calculation, the main terms of this wave function move electron population to the cage, while the secondary terms have the effect of moving part of this electron population back to the metal atom. The E state is diamagnetic, and the T1 and T2 states have magnetic moments 0.554 and 0.553 Bohr magnetons, respectively. The next-lowest group of states is based on the (11t2-5f)1(6e-π*)1 configuration, and it is the third group of states, based on (7a1-5f)1(11t2-5f)1, that gives the lowest (5f)2 states. The lowest such double-group state is 0.553 eV above the ground state and has primarily triplet character. These calculations were repeated with the (π*)2 MOs, and the same ordering of (π*)1(5f)1 and (5f)2 groups of states was obtained, but with all of the total energies being higher. The order of the (7a1)1(6e)1 states was changed to T1, T2, and E with an energy spread of only 0.009 eV. Our spin-orbit CI program needs more capacity to be able to provide the level of correlation energy treatment we would like to have for these complexes. For U@C28, the principal question is whether a more accurate calculation would reverse the 0.553 energy difference. Since neither the (π*)1(5f)1 nor the (5f)2 pair has significant terms involving doubly occupied MOs, the total amount of correlation energy involved with these pairs is not large. An attempt was made to compute the binding energy of U@C28 by using the energies of isolated C28 and the U atom. The result was -1.28 eV (unbound). Accurate calculations of such binding energies are quite difficult and would require both geometry optimization and considerably more extensive correlation energy treatments. The chemical consequences for Pa@C28 and U@C28 of having a (π*)1 aspect of their electronic structure is that, due to having an unpaired electron in an exterior orbital, they should be more reactive than if their unpaired electrons were confined to interior 5f orbitals. Thus, dimerization and other reactions would presumably contribute to the difficulties of separation and spectroscopic study. U@C28+1 and U@C28-1 were studied to a lesser extent. SCF calculations gave (7a1-5f)1 as the ground E1/2 state of U@C28+1 and (π*)1(5f)2 followed closely by (π*)2(5f)1 as the low-energy states of U@C28-1. A short CI on the latter, using U@C28 MOs, gave a (7a1-5f)1(π*-6e)2 E5/2 state as the lowest state, followed by other states of (5f)1(π*)2 character. None of the calculations on the ions were comparable to those on the neutral, so we did not obtain values for the ionization potential or electron affinity. The preliminary calculations done were consistent with an ionization potential in the 4-5 eV range, as expected from a typical cage π* orbital,30 and an electron affinity less than that of C28, as would be expected for a cage with an open π* shell rather than open π shells. V. Conclusions Through moderate-level spin-orbit CI calculations, we have characterized the excited states, spin-orbit splittings, ionization potential, and electron affinity of C28. The ground 5A2 state is described well by a simple Hartree-Fock wave function and has a very small spin-orbit splitting. The lower excited states have heavy configuration mixing; the lowest is 3T1 at 0.25 eV and with larger spin-orbit splittings. The calculated ionization potential and the electron affinity are 9.23 and 2.02 eV, respectively. The ground state of Pa@C28 has one electron in a cage π* MO rather than a 5f MO as might have been expected. The
Zhao and Pitzer energy difference is 1.70 eV. Strong mixing was found between cage MOs and metal orbitals, suggesting strong binding. The magnetic moments show moderate spin-orbit contributions. The U@C28 complex has a (π*)1(5f)1 diamagnetic ground state as opposed to (π*)2 or (5f)2, the latter being common in uranium organometallic complexes. The lowest (5f)2 state is found to be 0.553 eV higher. As with Pa@C28, the C28 π MOs mix heavily with the metal orbitals, suggesting strong binding, consistent with the experimentally observed high yields. U@C28+1 is expected to have a (5f)1 ground state rather than (π*)1, and U@C28-1 is expected to have a (5f)1(π*)2 ground state. Acknowledgment. This work was supported by Cray Research Inc. and by the Ohio Supercomputer Center, where the calculations were carried out on Cray YMP equipment. We thank Drs. G. Scuseria and R. Smalley for very useful discussions and for providing information in advance of publication. References and Notes (1) Zhang, Q. L.; O’Brien, S. C.; Heath, J. R.; Liu, Y.; Curl, R. F.; Kroto, H. W.; Smalley, R. E. J. Phys. Chem. 1986, 90, 525-528. (2) Cox, D. M.; Trevor, D. J.; Reichmann, K. C.; Kaldor, A. J. Am. Chem. Soc. 1986, 108, 2457-2458. (3) Curl, R. F.; Smalley, R. E. Science 1988, 242, 1017-1022. (4) Kroto, H. W. Nature 1987, 329, 529-531. (5) Bakowies, D.; Thiel, W. J. Am. Chem. Soc. 1991, 113, 37043714. (6) Zhang, B. L.; Wang, C. Z.; Ho, K. M.; Xu, C. H.; Chan, C. T. J. Chem. Phys. 1992, 97, 5007-5011. (7) Feyereisen, M.; Gutowski, M.; Simons, J.; Almlo¨f, J. J. Chem. Phys. 1992, 96, 2926-2932. (8) Guo, T.; Diener, M. D.; Chai, Y.; Alford, M. J.; Haufler, R. E.; McClure, S. M.; Ohno, T.; Weaver, J. H.; Scuseria, G. E.; Smalley, R. E. Science 1992, 257, 1661-1664. (9) Guo, T.; Smalley, R. E.; Scuseria, G. E. J. Chem. Phys. 1993, 99, 352-359. (10) Ha¨berlen, O. D.; Ro¨sch, N. J. Phys. Chem. 1992, 96, 9095-9097. (11) Ha¨berlen, O. D.; Ro¨sch, N.; Dunlap, B. I. Chem. Phys. Lett. 1992, 200, 418-423. (12) Ro¨sch, N.; Ha¨berlen, O. D.; Dunlap, B. I. Angew. Chem., Int. Ed. Engl. 1993, 32, 108-110. (13) Li, Z.-q.; Gu, B.-l.; Han, R.-s. Chem. Phys. Lett. 1993, 207, 4144. (14) Pederson, M. R.; Laouini, N. Phys. ReV. B 1993, 48, 2733-2737. (15) Jackson, K.; Kaxiras, E.; Peterson, M. R. Phys. ReV. B 1993, 48, 17556-17561. (16) Tuan, D. F.-t.; Pitzer, R. M. J. Phys. Chem. 1995, 99, 9762-9767; 1995, 99, 15069-15073. (17) Pacios, L. F.; Christiansen, P. A. J. Chem. Phys. 1985, 82, 26642671. (18) Ermler, W. C.; Ross, R. B.; Christiansen, P. A. Int. J. Quantum Chem. 1991, 40, 829-846. (19) Pitzer, R. M.; Winter, N. W. J. Phys. Chem. 1988, 92, 3061-3063. (20) Ermler, W. C.; Ross, R. B.; Christiansen, P. A. AdV. Quantum Chem. 1988, 19, 139-182. (21) Wallace, N. W.; Blaudeau, J. P.; Pitzer, R. M. Int. J. Quantum Chem. 1991, 40, 789-796. (22) Chang, A. H. H.; Pitzer, R. M. J. Am. Chem. Soc. 1989, 111, 25002507. (23) Shepard, R.; Shavitt, I.; Pitzer, R. M.; Comeau, D. C.; Pepper, M.; Lischka, H.; Szalay, P. G.; Ahlrichs, R.; Brown, F. B.; Zhao, J. G. Int. J. Quantum Chem., Symp. 1988, 22, 149-165. (24) Chang, A. H. H.; Zhao, K.; Ermler, W. C.; Pitzer, R. M. J. Alloys Compd. 1994, 213/214, 191-195. (25) Hunt, W. J.; Goddard, W. A. Chem. Phys. Lett. 1969, 3, 414-418. (26) Bach, S. B. H.; Bruce, J. E.; Ramanathan, R.; Watson, C. H.; Zimmerman, J. A.; Eyler, J. R. In On Clusters and Clustering: From Atoms to Fractals; Reynolds, P. J., Ed.; North Holland: New York, 1993; pp 5968. (27) Wang, L. S.; Conceicao, J.; Jin, C.; Smalley, R. E. Chem. Phys. Lett. 1991, 182, 5-11. (28) Lichtenberger, D. L.; Rempe, M. E.; Gogosha, S. B. Chem. Phys. Lett. 1992, 198, 454-460. (29) Edelstein, N.; Kot, W. K.; Krupa, J.-C. J. Chem. Phys. 1992, 96, 1-4. (30) Chang, A. H. H.; Ermler, W. C.; Pitzer, R. M. J. Chem. Phys. 1991, 94, 5004-5010.
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