Are the Dmh Symmetric Hxq Rings with 4n + 2 σ-Electrons and

Single-point energies (for the H6 system only) were evaluated at the ..... Abstract published in Advance ACS Abstracts, July 1, 1996. ...... J. K., An...
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J. Phys. Chem. 1996, 100, 12299-12304

12299

Are the Dmh Symmetric Hxq Rings with 4n + 2 σ-Electrons and Hydrogen Clusters Aromatic? Haijun Jiao,† Paul von Rague´ Schleyer,*,† and Mikhail N. Glukhovtsev*,†,‡ Computer-Chemie-Centrum, Institut fu¨ r Organische Chemie, UniVersita¨ t Erlangen-Nu¨ rnberg, Henkestrasse 42, D-91054 Erlangen, Germany, and Institute of Physical and Organic Chemistry, RostoV UniVersity, 194/3 Stachki AVenue, RostoV on Don, 344104, Russian Federation ReceiVed: April 5, 1996X

The Dmh symmetric Hxq rings, H5- (D5h, D4h), H5+ (C2V), H6 (D6h, D5h), H7+ (D7h, D6h), H82+/2- (D8h), H9+ (D3h), H9- (D9h, D8h), and H10 (D10h, D9h) are considered as possible analogs of the Hu¨ckel 4n + 2 electron aromatic annulene systems. While aromatic character (due to ring current effects) is indicated by the magnetic susceptibility exaltations (Λ) and large magnetic susceptibility anisotropies, χanis (derived from IGLO computations of the magnetic properties), most of these hydrogen ring systems are higher order saddle points. The exceptions are transition structures: H6 (D6h), which can be compared with benzene, and H10 (D10h) which is even less favorable energetically. On the basis of energetic, structural, and magnetic criteria, aromaticity can result from cyclic delocalization of σ- as well as π-electrons. On the basis of the diamagnetic exaltations, “spherical aromaticity” is illustrated by H62- and H8, both with Oh symmetry and eight σ-electrons as well as H42+ with Td symmetry and only two σ-electrons, even though these species are artificial, higher order saddle points. The Hu¨ckel 4n electron antiaromatic H3- (D3h), H4 (D4h), H5+ (D5h, D4h), and H8 (D8h) triplet states have been computed. Both H4 (D4h) and H8 (D8h) have negative (unfavorable) energies of concert relative to two H atoms and the appropriate number of H2 molecules.

Introduction Hexagonal H6 has been identified by numerous theoretical investigations as the transition state for the degenerate exchange of three H2 molecules.1-10 The experimental investigations, although extensive, are inconclusive.11-19 The energy of H6 (D6h) is ca. 30 kcal/mol lower than 2H2 + 2H (i.e., a process involving dissociation of a hydrogen molecule). Can this quite large “energy of concert”20 be ascribed to the aromatic character of the benzene-like H6 ring?1 Is the six σ-electron delocalization in hexagonal H6 comparable with the six π-electron delocalization of benzene? Are other hydrogen rings with imposed Dmh symmetry and with 4n + 2 σ-electrons delocalization generally useful as models for understanding aromaticity? Evans pointed out the relationship between the electronic structures of the Diels-Alder transition state and benzene in 1938.21 Recently, we have verified the aromatic character of several pericyclic transition structures by computing their magnetic properties.22-26 Both Hu¨ckel (six electron) and Mo¨bius (eight electron) transition structures are aromatic according to the geometric and the energetic as well as the magnetic criteria.27,28 The key molecular orbitals are neither pure π nor pure σ, but have hybrid character. We now characterize Dmh Hxq ring systems with only σ orbitals using the same criteria of aromaticity.27,28 The “energy of concert” (defined as the difference between a concerted, symmetric mechanism and a nonconcerted biradical alternative) provides a measure of the aromatic stabilization energy (ASE) of transition states.20 The magnetic criteria involve abnormal chemical shifts and anisotropies as well as magnetic susceptibility exaltations (Λ, ppm cgs). This exaltation is the difference (Λ ) χM - χM′) between the measured bulk magnetic susceptibility (χM) and the value (χM′) deduced by additivity †

Universita¨t Erlangen-Nu¨rnberg. Rostov University. Current address: Department of Chemistry, Wayne State University, Detroit, MI 48202. X Abstract published in AdVance ACS Abstracts, July 1, 1996. ‡

S0022-3654(96)01031-3 CCC: $12.00

on the basis of an increment system.29,30 In this paper the χ values are obtained from IGLO calculations.31 “Aromatic” transition structures generally have symmetries as high as possible. Although Dmh symmetry is imposed on the Hxq ring systems considered here, only two of these are true transition structures with only one imaginary frequency; the rest are higher order saddle points. The same is true of cluster Hxq systems which were examined to see if they demonstrated “spherical aromaticity”.27,32 For comparison, the Hu¨ckel 4n electron antiaromatic H3- (D3h), H4 (D4h), and H5+ (D5h, D4h) as well as H8 (D8h) triplet states have been computed. Computational Methods All geometries were optimized initially at the MP2/6311++G(d,2p) and more recently at the Becke3LYP/6-311++G(d,3pd) levels (the basis sets correspond to 311+G(2p) and 3-11+G(3pd), respectively, for hydrogen)33 with the GAUSSIAN 92/DFT program.34 Frequencies and zero point energies were computed at these levels. While the usual scaling factor of 0.97 was applied to the MP2 data,35 no scaling appears to be necessary for the Becke3LYP frequencies (the computed value is almost the same as the experimental). The MP2 geometries were used for the magnetic property computations. Single-point energies (for the H6 system only) were evaluated at the QCISD(T)/6-311++G(d,2p) using MP2 geometries and the CCSD(T,E4T)/6-311++G(d,3pd)//Becke3LYP/6-311++G(d,3pd)33 levels. Figure 1 summarizes the optimized geometries as well as 1H chemical shifts computed at the IGLO/II,31 GIAO-MP2/TZP, and GIAO-HF/TZP levels.36 Current interest in the performance of density functional methods37 prompted our reexamination of the simplest hydrogen species with the Becke3LYP functional. This calibration (summarized in Table 1) reveals truly excellent agreement with the best experimental and prior ab initio data. Results and Discussion Aromaticity of the D6h H6 Structure. In agreement with the earlier theoretical investigations,1,2,4-7,9,10 hexagonal H6 with © 1996 American Chemical Society

12300 J. Phys. Chem., Vol. 100, No. 30, 1996

Jiao et al.

Figure 1. The MP2(fc)/6-311++G(d,2p) and Becke3LYP/6-311++G(d,3pd) (given in italics) optimized geometries and the calculated 1H chemical shifts at the GIAO-HF/TZP, GIAO-MP2/TZP, and IGLO/II levels using the MP2 geometries.

TABLE 1: Calculated Total (E, Hartrees) and Zero-Point Energies (ZPE, the Number of Imaginary Frequencies in Parentheses, NIMAG), Activation Energies (Ea, kcal/mol), Atom Distances (R, Å), Vibrational Frequencies (W, cm-1 for H2), and Dissociation Energy (D0°) of H2 as well as Proton Affinity (PA) levels

H2

H6 (D3h)

H6 (D6h)

E, MP2/6-311++G(d,2p) ZPE(NIMAG)a R (Å) E, Becke3LYP/6-311++G(d,3pd) ZPE (NIMAG) R (Å) E, QCISD(T)/6-311++G(d,2p)c E, CCSD(T)d V (cm-1) D0° (kcal/mol) PA (kcal/mol, 0 K) PA (kcal/mol, 298 K) Ea (MP2)j Ea (QCISD(T))j Ea (Becke3LYP/6-311++G(d,3pd)k Ea (CCSD(T))k

1.16280 6.5 (0) 0.736 (0.741)b 1.18003 6.3 (0) 0.742 1.17084 1.17253 4416.08,e 4530.45f (4401.21)b 103.82g 103.92b 98.93e,h 100.17b 100.17g 101.29i 0.0 0.0 0.0 0.0

3.48845 19.5(6) 0.737, 3.833

3.37739 26.3 (1) 0.982 3.40288 25.5 (1)

3.51259

3.40288 3.41034

0.0 0.0

69.8-71.3 68.7-70.4 60.2-62.1 67.2-68.1

a Scaled by 0.97, ref 35. b Experimental results, ref 39a. c Using the MP2/6-311++G(d,2p) geometries. d At CCSD(T,E4T)/6-311++G(d,3pd)/ /Becke3LYP/6-311++G(d,3pd) geometries. e At Becke3LYP/6-311++G(d,3pd). f At MP2/6-311++G(d,2p). g At Becke3LYP/6-311++G(d,3pd)+ZPE(Becke3LYP/6-311++G(d,3pd). h The G2 value (0 K) is 99.00 kcal/mol, ref 39b. i Experimental results, ref 46, G2 value (298 K) is 100.17 kcal/mol, ref 39b. j Corrected for thermal energy (MP2/6-311++G(d,2p) over the 1200-1800 K range. k Corrected for thermal energy (Becke3LYP/6-311++G(d,3pd) over the 1200-1800 K range.

equal bond lengths is the authentic transition state [one imaginary frequency, 2640i (MP2), 2499i (Becke3LYP) cm-1] for hydrogen exchange. The MP2 H-H separation, 0.982 Å, is in the 0.985 ( 0.003 Å range found earlier (HF, MP4, CI

levels using various basis sets).1,2,4-7 The Becke3LYP separation, 0.991 Å, is nearly the same, for example, as the distance (0.981 Å, MP2(full)/6-31G*) in the transition state for H2 elimination from 1,4-cyclohexadiene.38

Dmh Symmetric Hxq Rings

J. Phys. Chem., Vol. 100, No. 30, 1996 12301

TABLE 2: Calculated Magnetic Properties (ppm cgs) and Wiberg Bond Index (WBI) for D6h Symmetric H6 Compared with Those for Benzene system

χanis

Λ

C6H6 (D6h) H6 (D6h)

-62.9 -21.7

b

-13.4 -9.4

b

δLia

WBI

-6.6 -5.4

1.440c 0.443

b

In the C6V symmetric complex with Li+ (using MP2(fc)/6311G++(d, 2p) geometry). b See ref 30. c See ref 41. a

Energetic Criteria. The 3H2 exchange barrier via H6 (D6h) is 68.8 kcal/mol at RQCISD(T)/6-311++G(d,2p)//MP2/6311++G(d,2p), 76.0 kcal/mol with ZPE correction (zero-point vibration energies) at 0 K and 68.7-70.4 kcal/mol corrected for thermal energy over the 1200-1800 K range. The corresponding Becke3LYP/6-311++G(d,3pd) values, 60.3, 67.0, and 60.2-62.1 kcal/mol, are 8-9 kcal/mol lower than the RQCISD(T) results. At the CCSD(T)/6-311++G(d,3pd) level using the Becke3LYP/6-311++G(d,3pd) geometries, the computed energies (67.3, 74.0, and 67.2-68.1 kcal/mol) are very close to the RCISD(T) results. At Becke3LYP/6-311++G(d,3pd) + ZPE (Becke3LYP/6-311++G(d,3pd)), the calculated dissociation energy of H2 into two H radicals of 103.63 kcal/mol agrees very well with the measured value (103.31 kcal/mol)39a and that (104.3 kcal/mol) at RQCISD(T)/6-311++G(d,2p)//MP2(fc)/6311++G(d,2p). The Becke3LYP computed vibrational frequency, dissociation energy, diatomic distance, and proton affinity of H2 are in excellent agreement with the experimental results (Table 1). The energy of concert for H6 is 37.2 kcal/mol (at 0 K), based on the energy difference between the computed exchange barrier and the energy of a alternative process involving the participation of two H radicals in the (2H2 + 2H) exchange reaction. Hence, the H6 transition state is aromatic to a quite large extent energetically.22-26 Magnetic Criterion. The IGLO/II magnetic susceptibility exaltation of H6 of -9.5 ppm cgs (relative to 3H2) may be compared with the benzene value, -13.4 (IGLO/II;40 the experimental value30 is -13.7 ppm cgs). The magnetic susceptibility anisotropy (χanis) is quite large in planar aromatic systems, e.g., benzene (-62.9), furan (-36.2), pyrrole (-41.8), and thiophene (-46.4) at IGLO/II29,40 (the corresponding experimental values are -59.7, -38.7, -42.4, and -50.1).42 Although similar, the calculated χanis for H6 is quite negative (-21.7), whereas for H2 it is only -0.3. The large difference in χanis (-20.8) between H6 and 3H2 also points to the pronounced aromatic character of H6. Li chemical shifts are also useful to probe for ring current effects.24,43,44 In the C6V complex of H6 with Li+, the calculated δLi+ of -5.4 ppm (compare with -6.6 ppm in the benzeneLi+ complex40) also demonstrates the existence of ring currents of six σ-electron delocalization as well as the aromatic character of H6 (Table 2). The C6V symmetric H6Li+ also has a large magnetic susceptibility anisotropy of -23.9 and a magnetic susceptibility exaltation of -7.1. In the corresponding energy minimum complex of Li+ with 3H2 (H6Li+, D3), the calculated δLi+ (+1.8) and χanis (-0.5) as well as Λ (+0.3) are in sharp contrast to the C6V H6Li+ results. Aromaticity of Other Hxq Ring and Cluster Systems. Besides H6, we have calculated the energies and magnetic properties of other Hxq rings and their noncyclic isomers as well as the Oh symmetric H62-, H8, and Td symmetric H42+ (note that the dianions serve only as model systems and improvement of the computational level of theory would lead to solutions corresponding to the monoanions plus a separated electron). The total energies, the zero-point vibrational energies, and the

TABLE 3: Calculated Total Energies (Hartrees) and Zero-Point Energies (kcal/mol) as Well as the Number of the Imaginary frequencies (NIMAG, in Parentheses) at both MP2 and Becke3LYP Levels MP2(fc)/ 6-311++G(d,2p)

Becke3LYP/ 6-311++G(d,3pd)

Hxq

symmetry

Etot

ZPEb (NIMAG)

Etot

ZPE (NIMAG)

H HH2 H3+ H3+ H42+ H5+ H5H5H5H6 H6 H6 H6Li+ H6Li+ H7+ H7+ H7+ H7+ H7+ H82+ H8 H62H82H9H9H9+ H10 H10 H10

Kh Kh D∞h D3h D∞h Td C2V D5h D4h D∞h D6h D3h D5h D3 C6V D7h D6h C2V D3h D∞h D8h Oh Oh D8h D9h D8h D3h D10h D9h D5h

-0.49880a -0.50958 -1.16280 -1.33129 -1.26359 -1.03407 -2.50650 -2.77845 -2.69137 -2.83963 -3.37739 -3.48845 -3.27637 -10.74975 -10.62747 -3.60827 -3.54010 -3.67699 -3.60637 -3.61640 -3.47149 -4.38140 -3.01221 -4.26001 -5.06476 -4.87783 -4.84639 -5.62237 -5.44877 -5.81411

-(-) 6.3 (0) 12.7 (0) 9.3 (2) 6.6 (3) 22.0 (0) 14.8 (2) 11.3 (2) 15.4 (2) 25.5 (1) 18.9 (6) 19.6 (4) 24.2 (0) 27.3 (1) 26.7 (2) 27.7 (3) 30.8 (0) 20.9 (8) 30.8 (4) 21.7 (6) 28.8 (5) 6.2 (9) 19.5 (3) 32.0 (2) 23.2 (9) 39.0 (0) 39.7 (2) 34.7 (6) 31.6 (14)

-0.50226 -0.53416 -1.18003 -1.34725 -1.28499 -1.05511 2.54693 -2.84619 -2.76604 -2.89991 -3.44395 3.54010 -3.34525 -10.85383 -10.74599 -3.68056 -3.60988 -3.73443 -3.67947 -3.69099 -3.55489 -4.45950 -3.09951 -4.37983 -5.18014 -4.99556 -4.92122 -5.74052 -5.56665 -5.89992

-(-) -(-) 6.5 (0) 12.5 (0) 9.2 (2) 6.5 (3) 21.2 (0) 14.5 (2) 10.3 (3) 15.9 (0) 25.6 (1) 18.9 (6) 19.7 (4) 23.9 (0) 27.5 (1) 27.1 (2) 27.7 (3) 30.4 (0) 22.6 (6) 26.5 (6) 21.7 (6) 32.1 (3) 6.2 (9) 18.9 (3) 32.3 (3) 22.8 (9) 38.5 (0) 42.1 (1) 34.7 (6) 31.6 (16)

a

At HF/6-311++G(d,2p). b Scaled by 0.97, see ref 35.

number of imaginary frequencies (NIMAG) are summarized in Table 3. The calculated magnetic properties and relative energies are given in Table 4. These species include H3+ (D3h), H42+ (Td), H5+ (C2V), H7+ (C2V), and H9+ (D3h) with two delocalized electrons, H5- (D4h, D5h), H7+ (D6h, D7h), H6 (D5h), and H82+ (D8h) with six delocalized electrons as well as H82(D8h), H9- (D8h, D9h), and H10 (D9h, D10h) with 10 delocalized σ-electrons. Both H62- and H8 (Oh) are eight delocalized electron systems. In the species with six delocalized σ-electrons, H5- (D4h, D5h), H7+ (D6h, D7h), H6 (D5h) and H82+ (D8h) are highly aromatic molecules. The degree of aromaticity of H5- (D4h and D5h) is indicated by their magnetic susceptibility exaltations (Λ’s) of -10.3 (D5h) and -12.9 (D4h) relative to their linear isomer. Both D5h and D4h H5- have nearly the same χanis (-21.7 and -20.6) as H6 (D6h′ -21.7). In comparison with their linear isomer, the Λ’s of the D7h (analogous to the tropylium ion) and D6h H7+ are -8.5 and -7.3. Even the D5h H6 (with a hydrogen in the center of the ring) is aromatic, with Λ ) -10.3 and χanis ) -19.6. In going from six to 10 delocalized electron systems, dramatic differences in the magnetic properties are found between the D8h species, H82+ and H82-. Both are aromatic, but the 10electron H82- has a much larger χanis and Λ than the six-electron H82+ (Table 4). Both D9h and D8h H9- are aromatic with large Λ’s of -41.6 and -40.2 (based on 4H2 + H-). Like D3h H6, the magnetic susceptibility of D5h H10 is the same as 5H2, whereas the D10h and D9h isomers are aromatic. They not only have large Λ (-40.0 and -37.0 ppm cgs) but also large χanis (-98.7 and -80.1 ppm cgs).

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TABLE 4: IGLO/II//MP2(fc)/6-311++G(d,2p) Calculated Magnetic Susceptibility (χtot), Magnetic Susceptibility Anisotropy (χanis), Magnetic Susceptibility Exaltation (Λ, ppm cgs), and the Relative Energies (kcal/mol) at Becke3LYP and MP2 (in Parentheses) as Well as the Energy of Concert (Econ, kcal/mol at Becke3LYP) Hxq -

H H2 H3+ 2+

H4 H5+ H5H6 H7+

H82+ H8 H62H82H9H9+ H10 H6Li+ 1

symmetry

χtota

χanisb

Λ

Erel

Kh D∞h D3h D∞h Td C2V D5h D4h D∞h D6h D5h D3h D7h D6h C2V D3h D∞h D8h Oh Oh D8h D9h D8h D3h D10h D9h D5h C6V D3

-8.4 -4.0c -3.2 -3.6 -18.8 -6.3 -27.4 -30.0 -17.1 -21.5 -22.0 -12.1 -20.3 -19.1 -10.1 -11.1 -11.8 -23.9 -37.4 -56.2 -76.6 -66.0 -65.6 -13.9 -60.1 -57.1 -20.1 -19.8 -12.3

0.0 -0.3 -0.6 -0.6 0.0 -0.8 -21.7 -20.6 -1.0 -21.7 -19.6 -0.8 -24.6 -21.2 -0.8 0.0 -1.1 -32.9 0.0 0.0 -101.1 -97.6 -87.8 -0.8 -98.7 -80.1 -1.3 -23.9 -0.5

+0.4 0.0 -15.6d +1.4e -10.3 -12.9 0.0 -9.4 -19.0 0.0 -8.5 -7.3 +1.7 +0.7 0.0 -12.7f -21.4g -30.8h -47.8i -41.6j -40.2j +1.9k -40.0 -37.0 0.0 -7.1 +0.34

-35.8 (-39.0) 0.0 204.7 (201.5)d -45.9 (-43.9)e 32.3 (37.8) 78.4 (88.7) 0.0 67.0 (75.9) 123.1 (133.8) 0.0 30.5 (39.0) 75.5 (82.8) 0.0 26.7 (34.4) 23.4 (44.9) 112.6 (133.9)f 169.6 (171.9)g 200.0 (202.3)h 143.4 (155.9)i 52.8 (66.5)j 159.1 (186.4)j -50.5 (-48.4)k 110.5 (128.4) 212.2 (232.4) 0.0 71.3 (79.7) 0.0

Econ

72.0m 25.9m 37.2n -18.8n 121.0o 76.1o

-15.6p 66.0q -95.9r -39.2s 50.8t -55.5t -6.1u -107.8u

aχ b c d + e + tot ) (χ11 + χ33)/3. χanis ) χ11 - (χ22 + χ33)/2. Measured value of -3.98, ref 45. Relative to 2HHH - H2. Relative to HHH + H2. Relative to 2HHH+ + H2. g Relative to 4H2. h Relative to 2H2 + 2H-. i Relative to 3H2 + 2H-. j Relative to 4H2 + H-. k Relative to HHH+ + 3H2. l Relative to 3H2 + Li+. m Relative to H- + H2 + 2H. n Relative to 2H2 + 2H. o Relative to HHH+ + H2 + 2H. p Relative to 2HHH+ + 2H. q Relative to 3H + 2H. r 2H- + H + 2H. s 2H- + 2H + 2H. t Relative to HHH+ + 2H + 2H. u Relative 4H + 2H. 2 2 2 2 2 f

However, because of the dependence on ring size,27 the magnetic criteria of aromaticity is not directly comparable with H3+, H5+ (a C2V complex of H2 with cyclic H3+), and H7+ (a C2V complex of 2H2 cyclic H3+) as well as H9+ (D3h complex of 3H2 with cyclic H3+); indeed, D3h H3+ has nearly the same χtot as the linear HHH+ isomer; even the former is about 40 kcal/mol more stable than the latter. At MP2(fc)/6-311++G(d,2p), D10h H10 has two imaginary frequencies (NIMAG ) 2), but it becomes a transition state with only one imaginary frequency (NIMAG ) 1) at Becke3LYP/6-311++G(d,3pd), and this transition state has a “negative” energy of concert of -6.1 kcal/mol indicating that the concerted reaction is less favorable energetically than the biradical alternative (Table 4). In contrast to other species which are higher order saddle points (more than one imaginary frequencies, see Table 3) and have even more unfavorable energies, H3+ (D3h), H5+ (C2V),47 H7+ (C2V), and H9+ (D3h)48 are all energy minima on the potential surface of all, the sequential H2 complexation energies are -10.1 kcal/ mol for H3+ (D3h) (to form H5+, C2V), -2.0 kcal/mol (to give H7+, C2V), and -2.7 kcal/mol (to give H9+, D3h) at Becke3LYP/ 6-311++G(d,3pd)+ZPE(Becke3LYP/6-311++G(d,3pd). Similar results were reported by Schaefer.48 In addition, both the eight σ-electron Oh symmetric H8 and H62- species have large Λ’s, -21.4 and -30.8 ppm cgs, and can be considered to be “spherical aromatics”.27,32 Of course, the anisotropies are zero because of the symmetry. Likewise, the Td H42+ with only two σ-electrons49 has a large magnetic susceptibility exaltation of -15.6 ppm cgs. There are no direct correlation between the calculated energies of concert (Econ, Table 4) and the magnetic susceptibility exaltations (Λ) for the Dnh hydrogen rings and hydrogen clusters. For example, D5h H5- (-10.3), D6h H6 (-9.4), and D7h H7+

(-8.5) have nearly the same Λ’s, but their energies of concert of 72.0, 37.2, and 121.0 kcal/mol are quite different. On the other hand, aromatic H6 (D5h), H82+ (D8h), H62- (Oh), H82- (D8h), and H10 (D9h) have “negative” energies of concert which indicate that they are higher in energy than their corresponding systems with two hydrogen radicals. H6 and H10 rings comprised of H2 molecules also were optimized in D3h and D5h symmetry, respectively. These led to the large separations and negligible interaction energies expected from van der Waals complexes. Not only the energies but also the magnetic susceptibilities and anisotropies of these “rings” were identical with those of the same number of H2 molecules. Furthermore, these “rings” were computed to have large numbers of (tiny) imaginary frequencies (partly an artifact of the standard optimization limits employed). As no effort was made to find the “true” van der Waals (H2)n complexes in this work, the results are not reported. Antiaromatic 4n σ Electron Dmh Hxq Triplet Systems. As discussed above, Dmh symmetric Hxq rings with 4n + 2 σ-electron can be considered as possible analogs of the Hu¨ckel aromatic annulene systems. Are, however, there 4n σ electron Dmh Hxq analogs of the Hu¨ckel antiaromatic systems? Table 5 summarizes the calculated energies for the Hxq triplet states. The optimized geometries of these systems are shown in Figure 2. H3- (D3h) and H4 (D4h) triplets each have two imaginary frequencies both at MP2 and at Becke3LYP/6-31G*. The triplet H3- (D3h) has a positive (favorable) energy of concert of 34.9 kcal/mol relative to 2H + H-, whereas H4 (D4h) has a negative energy of concert and is 31.3 kcal/mol higher in energy than 2H + H2 at Becke3LYP. The D3h H3- triplet is 15.9 kcal/mol higher in energy than the open-chain triplet isomer at Becke3LYP/ 6-311++G(d,3pd)+ZPE(Becke3LYP/6-311++G(d,3pd)). The

Dmh Symmetric Hxq Rings

J. Phys. Chem., Vol. 100, No. 30, 1996 12303

TABLE 5: Total Energies (Hartrees), Zero-Point Energies (kcal/mol), and Number of Imaginary Frequencies (NIMAG) [in Square Brackets] and Energy of Concert (Econ, kcal/mol) for Triplet States Hxq -

H3 H3H3H4 H5+ H5+ H8

symmetry

MP2(fc)a [ZPEc (NIMAG)]

Becke3LYPb [ZPE (NIMAG)]

Econd

D3h D∞h C∞V D4h D5h D4h D8h

1.54816 [1.0 (2)] 1.59016 [6.5 (1)] 1.59647 [7.7 (0)] 2.09455 [8.9 (2)] 2.30707 [12.4 (0)] 2.27620 [8.9 (2)] 4.38184 [32.0 (0)]

1.59631 [1.2 (2)] 1.63297 [8.3 (0)]

34.9 (24.7)e

2.13840 [8.8 (2)] 2.35381 [10.8 (2)] 2.32863 [8.5 (4)] 4.47719 [25.8 (2)]

-31.3 (-44.3)f 41.4 (25.3)g 23.3 (6.6)g -48.2 (-79.5)h

a Using the 6-311++G(d,2p) basis set. b Using the 6-311++G(d,3pd) basis set. c Scaled by 0.97, see ref 35. d At Becke3LYP/6311++G(d,3pd)+ZPE(Becke3LYP/6-311++G(d,3pd)) and MP2/6-311++G(d,2p)+ZPE(MP2(fc)/6-311++G(d,2p)) given in parentheses. e Relative to 2H + H-. f Relative to 2H + H2. g Relative to 2H + HHH+ (linear). h Relative to 2H + 3H2.

energies of concert relative to two H atoms and the appropriate number of H2 molecules. Acknowledgment. This work was supported by the Fonds der Chemischen Industrie, the Deutsche Forschungsgemeinschaft, and the Convex Computer Corporation. We also thank Prof. W. Kutzelnigg and Dr. U. Fleischer (Bochum) for helpful suggestions as well as the Shanxi Normal University (China) for a scholarship to H. Jiao and the Alexander von Humboldt Stiftung for a research fellowship to M. N. Glukhovtsev. References and Notes

Figure 2. The MP2/6-311++G(d,2p) and Becke3LYP/6-311++G(d,3pd) (in italics) optimized geometries for the triplet states of H3(D3h, D∞h, C∞V), H4 (D4h), H5+ (D5h, D4h), and H8 (D8h).

potential energy surfaces of H5+ (D5h, D4h) and of H8 (D8h) change from level to level. At MP2, both the H5+ (D5h) and H8 (D8h) triplets are energy minima (NIMAG ) 0), but become higher order saddle points (NIMAG ) 2) at Becke3LYP (Table 5). The D4h H5+ triplet has NIMAG ) 2 at MP2 and NIMAG ) 4 at Becke3LYP. The Becke3LYP energies of concert are favorable for both H5+ triplets, e.g., 41.4 (H5+, D5h) and 23.3 kcal/mol (H5+, D4h), but unfavorable for the triplet D8h H8 (-48.2 kcal/mol). Conclusions (1) The hexagonal H6 transition state for hydrogen exchange is aromatic according to the applicable criteria: energetic (large energy of concert) and magnetic (large magnetic susceptibility exaltation and anisotropy). The aromaticity of H6 (D6h) is supported by upfield Li+ chemical shift (δLi ) -5.4) in the C6V H6LI+ complex. (2) The D10h H10 also is a transition state with large diamagnetic susceptibility exaltation and anisotropy but has a negative (less favorable) energy of concert. On the basis of the magnetic criteria, the other Dmh symmetric Hxq rings (H5-, H7+, H82+/2-, H9-, and H10) and spherical H8 (Oh) and H62(Oh) as well as H42+ (Td) are aromatic species, but these do not represent chemically viable stationary points and also are very high in energy. Hence, delocalized Hxq (Dmh) systems have only limited applicability as models for understanding aromaticity. (3) In contrast to the aromatic H6 (D6h), both the antiaromatic H4 (D4h) and H8 (D8h) triplets have large negative (unfavorable)

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