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3 Larger Rings: Preference for Small Rings

3 Larger Rings: Preference for Small Rings

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300



S. Inagaki



Density functional calculations showed transitions from planar to nonplanar

structures at n = 5 with increasing size of Aln and Gan clusters [47]. Both Si and

Al tend to build three-dimensional structures rather than two- or one-dimensional

structures, except for n = 3 or 4 [48].

The planar cyclic P5− anion isoelectronic with cyclopentadienyl anion has been

prepared in the form of M+P5− salts (M = Li, Na) by Baudler et al. [49]. The pentaphosphole anion P5− favors planar D5h geometry [50] while the most stable structure

of P5+ is square-pyramidal [51]. The negatively charged pentamers Sb5 and Bi5 are

planar rings [52, 53].



2.4  Regular Octahedrons of M6 Clusters

There are Wade rules for metal clusters, [3, 4] which have been extended by Teo

[54, 55], Mingos [56, 57], and Jemmis [58, 59]. These general rules give only a

single number of electrons for a given polyhedron to be stabilized. The valence

electron rules for the three- and four-membered metal rings in the singlet states

(Sects. 2.1, 2.2) suggested that there could be more than one number of electrons. A valence electron rule was recently proposed for the regular octahedron of

high-row representative elements in the singlet states [8].

Atomic orbitals are separated into the s-orbitals, the radial (r), and tangential (t)

p-orbitals (Scheme 2) [7]. The Hückel theory was applied to the s-orbitals, the

radial (r), and tangential (t) p-orbitals of the regular octahedron. The qualitative

energy levels (Scheme 5) [8] show that the number of valence electrons is 6N+ 14

for the closed-shell structures when all the s-orbitals are occupied by two electrons.

The t1u pr-orbitals at the nonbonding level are allowed to interact with the bonding

pt-orbitals of the same symmetry and are raised in energy above the nonbonding level. The upper limit of the number of electrons is 26 (N = 2).

The M6 clusters with 6N + 14 (N = 0–2) valence electrons assume regular octahedrons, whereas those with the other numbers of valence electrons do not.

The 6N + 14 (N= 0–2) valence electron rule was supported by the results of the

calculations of the M6 clusters of the third and fourth row elements at the

UB3LYP/6-31 + G(d) (Table 3) [8]. The regular octahedrons were located as

the energy minima for the 14 (N= 0) electron systems, Mg62− and Ca62−, for the 20

(N= 1) electron system, Al62−, and for the 26 (N= 2) electron systems, Si62− and

Ge62−. No energy minima were located for the regular octahedrons with 6N+ 14

(N≥ 3) or the other numbers of valence electrons than 6N + 14.

The 6N + 14 valence electron rule is based on the assumption that neighboring

pr-orbitals interact with each other more strongly than neighboring pt-orbitals, or that

the a1g pr-orbital is lower in energy than the t2g pt-orbitals (Scheme 5). When the interactions occur to a similar degree, the octahedral geometry of the 20 (N= 1) electron systems

is unstable. When the interaction between the pt-orbitals is stronger, the regular octahedron prefers 18 and 20 (N= 0, 1) valence electron systems. The relative magnitudes of

the interactions between the pr- and pt-orbitals depend on the atoms.



Orbitals in Inorganic Chemistry



301



Table 3  Number of valence electrons and regular octahedronsa

14



16



18



20



22



24



26



28



30



32



34



36



38



Mg62−

+

Ca62−

+



Al62+

Ga62+

-



Al6

Ga6

-



Al62−

+

Ga62−

-



Si62+

Ge62+

-



Si6

Ge6

-



Si62−

+

Ge62−

+



P62+

As62+

-



P6

As6

-



P62−

As62−

-



S62+

Se62+

-



S6

Se6

-



S62−

Se62−

-



a

The success and the failure in locating the regular octahedral geometries as energy minima at the

UB3LYP/6-31 + G(d) levels are denoted by the plus (+) and minus (−) signs, respectively



t1g

eg

t2u

t1u



26



20

14



a1g



t1u



t2g



eg

t1u



s



a1g











Scheme 5  Orbital energy levels of the regular octahedron



The Al62− and Ga62+ dianions have 20 (= 6 × 1 + 14) valence electrons and satisfy

the 6N + 14 valence electron rule. The Al62− dianion possesses an Oh geometry [60].

Wade rules are not applicable to the stable Oh geometry of Al62−. The instability of

the Oh geometry of Ga62+ in disagreement with the rule can be attributed to similar

magnitudes of the interaction between the pr-orbitals and that between the ptorbitals which gives a very small HOMO-LUMO gap [8].

According to the 6N+ 14 valence electron rule, the regular octahedron is not stable

for 18 (= 4 + 14) electron systems. The most stable forms of Al6 [47, 48, 61] and Ga6

[47] were calculated to be distorted octahedrons. However, the result of the calculation

by Pettersson et al. [62] showed the regular octahedron as the most stable structure of

Al6, suggesting a reverse ordering of the strength of the neighboring pt- and pr-orbital

interactions or the energy levels of the a1g pr-orbitals above the t2g pt-orbitals.

The 24 (10 + 14) electron systems cannot be of Oh geometry. Honea et al. [12]

prepared and isolated Si6 by low-energy deposition into a solid nitrogen matrix, and

showed by Raman spectroscopy that the octahedron is distorted, in agreement with



302



S. Inagaki



the rule. The tetragonal bipyramid (D4h symmetry) was computed by Zhao and

Balasubramanian as the ground states of the Si6 [63]and Ge6 clusters [64], in accord

with the suggested experimental assignments by Fuke et al. [65, 66].

For 26 (6 × 2 + 14) electron systems, a regular octahedron (Oh) is predicted to be

stable. However, the Ge62− dianion has been observed to assume a distorted octahedron (D4) in [{(CO)5Cr}6Ge6]{P(C6H5)4}2) [67]. The distortion may be caused by the

effects of the ligands and cannot be taken as evidence against the prediction.

The octahedron is classified into the closo-structure by Wade [3,4]. Closostructures with n skeletal atoms are stable when they have 4n+ 2 valence electrons.

Wade’s rules predict that the 26 (= 4 × 6 + 2) valence electrons could stabilize the

regular octahedrons since n is 6 for the octahedron. This prediction is contained in

our 6N + 14 (N= 2) valence electron rule. Our rule also predicts the stability of

octahedral metal clusters with the other numbers (14 and 20) of valence electrons.



3  Pentagon Stability

For hydrocarbons, six-membered rings are thermodynamically preferred whether

they are saturated or unsaturated. Cyclohexane is free from ring strain. Benzene is

stabilized by cyclic delocalization of six p electrons. Here we show that fivemembered rings are more stable in a class of molecules. This is termed pentagon

stability. We apply the pentagon stability to understanding some interesting chemical phenomena of five-membered ring molecules and to designing some polycyclic

molecules stable with little ring strain.



3.1  Theory

The orbital phase theory (Chapter “An Orbital Phase Theory” by Inagaki in this

­volume) shows that some saturated cyclic molecules with lone pairs on the ring

n



in phase



in phase



σ*



σ*

in phase



Scheme 6  Phase continuity of the n, s, and s orbitals for cyclic delocalization of a lone pair



Orbitals in Inorganic Chemistry



303



atoms could prefer the five- to six-membered ring [68]. Cyclic delocalization of the

lone pair electrons on the five-membered ring atoms through the vicinal s bonds is

favored by the orbital phase properties (Scheme 6). The resulting stability is

outstanding in the saturated phosphorus five-membered rings in the puckered

conformation (Scheme 7). The five-membered ring molecule 1 has a negative ring

strain energy [68–70]. The stability of the five- relative to six-membered phosphorus rings was also noted elsewhere [71].



H

P



H

P



P

P



HP



P



PH



P



PH



1



HP



P



P



P

HP P



P



P P



P



R



As



As



As



P

P

H



R2



NH2



NH2



1



R



OH



R



R2

R



R=



R



As



R



8



3



R



N



CH2CH2OH



N



N



S



S



9



P

P P



P



6



As



P



3



H



P



P



7



N



P



P

P



R



P



1



R



P



P



P



P

P



P



P



5



P P



P P



P



PH



P



P

H



P

P



P P



P



3



P



4



PH



P



P

P



PH



H

P



P



P



HP



P



P P



PH



P



P

P



P



P



PH



P



P



P



2



HP

P



P



P



HP



P



HP

HP



HP



P



S



10



Scheme 7  Cyclopentaphosphane and its related molecules



N



H



11



304



S. Inagaki



3.2  Applications

The stability of cyclopentaphosphanes (PR)5 is in agreement with some experimental

observations by Baudler [72–74]. The parent compound (PH)51 has been isolated

and characterized by spectroscopic methods, while the six-membered ring molecule

P6H6 is still unknown. The pentagon stability is in agreement with the Baudler rule

of the maximum number of five-membered ring units [72–74]. The strain energies

of 2 and 3 are negative [68]. Two stable conformers exist in solution [74]. The

derivatives are known. Many polycyclic phosphanes containing the five-membered

ring units are derived from the structure rule by Häser [75, 76]. The unknown polycyclic phosphanes 4–6 have low strain energies [68] due to having many puckered

pentagon units in them and can be synthetic targets. The low stability of the dodecahedron P20 (7) was suggested by the high strain energy due to its planar pentagon

units [68]. The relative stability of the five-membered rings is significant in the

saturated As ring molecules [77] but not in the saturated nitrogen ring molecules

[68] due to the greater energy gap between the n and s* orbitals.

A textbook error of the structure RAs = AsR of salvarsan, asphenamine, Ehrlich

606 [78] has been revised. The main component has a structure of a five-membered

As ring (8) [79], which is favored by the pentagon stability.

The pentagon stabilization has been found in a biochemical phenomenon [80].

The hydrogen on the thiazolium ring 9 (Scheme 7) is easily ionized to afford the

corresponding carbene 10, a key catalyst in enzymatic reactions for which thiamine

(vitamin B-1, 11) pyrophosphate is the cofactor. The pentagon stability is expected

to contribute to this unusual deprotonation. A lone pair generated on the carbon

atom in 10 can similarly delocalize through the vicinal C–N and C–S s bonds in a

cyclic manner.



H2NN=NNH2



HN=NNH2

12



13



14

R



HN=NNHNHN=NH



N

N



15



H

N



N

N



N

N



N



R



16

N



N



N



N



N

N



HN=NN=NH



N

17



Scheme 8  Hydronitrogens and polynitrogens



N

N

18



N

N



N

N



N

19



Orbitals in Inorganic Chemistry



305



4  Hydronitrogens and Polynitrogens

Nitrogen atoms can form molecules isoelectronic to hydrocarbons (Scheme 8).

Hydronitrogens NmHn are well known to have unique and useful properties. The

smallest hydronitrogen is ammonia (NH3) containing no N–N bond. Hydrazine

NH2NH2 and diazene NH=NH with one N–N bond (the former a single bond, the

latter a double) are widely used to reduce unsaturated functional groups in organic

molecules [81]. Hydronitrogens and/or their derivatives with the three nitrogen

atoms sequentially bonded (triazane NH2NHNH2, [82] triazene NH2NH=NH 12

[83] and hydrazoic acid HN3 [84], are known. For hydronitrogens with four nitrogen atoms sequentially bonded, 2-terazene NH2NH=NHNH213 [85] has been isolated. Tetrazane NH2NH2NH2NH2 [86] and tetrazadiene NH=NN=NH 14 [87] have

been postulated as reaction intermediates. The first pentazole was synthesized as a

phenyl derivative of 17 in 1954 [88]. Very recently, unstable HN5, the parent pentazolic acid, has been released in solution by the treatment of N-(p-anisyl)pentazole

with cerium(IV) ammonium nitrate [89].

Polynitrogens Nm are recently of great interest as high-energy density materials

[90, 91]. The high-energy content arises from an unusual property of nitrogen: its

single and double bond energies are considerably less than one-third and two-thirds,

respectively, of its triple bond energy. Therefore, the decomposition of polynitrogen

species to N2 is accompnanied by a large release of energy. Beyond N2, N3−, N3+

[92], N4+ [93], and diazidyl N6− complex [94] have been spectroscopically detected as

short-lived species. Hexazine N618 isoelectronic to benzene was suggested to be a

product of photochemical reductive elimination of cis-diazidobis(triphenylphosphine)

platinum(II) in solution at 77 K [95].

The chemistry of hydronitrogens [96] and polynitrogens [90, 91] is still less

advanced than the chemistry of hydrocarbons. Unknown hydronitrogens may also

be of potential utility as the known hydronitrogens suggest. There are many questions to be answered about the chemical and physical properties of hydronitrogens

and polynitrogens. In this section, we briefly review the chemistry of some hydronitrogens and polynitrogens, including the fundamental nature of chemical bonding

between the nitrogen atoms and recent advances.



4.1  Triazene HN=NNH2 and 2-Tetrazene H2NN=NNH2

The delocalization of lone pair electrons on NH2 group to an adjacent N=N bond

was suggested by some calculations [97] to be appreciable in triazene 12 and

2-tetrazene 13. The N–N single bond is shorter than the isolated N–N single bond

in NH2NH2. The N=N bond is longer than in NH=NH. The n–p conjugation

stabilizes hydronitrogens.

There are six p electrons in 13. The delocalization of six p electrons in the four

p-orbitals of the linear conjugation is disfavored by the orbital phase discontinuity



306



S. Inagaki



(Sects. 2.1 and 3.1 in Chapter “A Orbital Phase Theory” by Inagaki in this volume)

[98, 99]. The n–p conjugation is weaker relative to that in 12 where a similar

phase restriction is absent. In fact, the rotational barriers about the single RNHNH=bond have been obseved to be lower for derivatives of 13 than for those of

12 [100].



4.2  Tetraazabutadiene (Tetrazadiene) HN=NN=NH

The geometry optimization and the analysis of electronic structure [97] suggested that

the single N–N bond could be unusually weak in tetraazabutadiene (tetrazadiene) 14.

n



HN

N



HN

s*



s*



N



N



N

n



HN



NH

n

N

N



s*

4



3



5



N



N



N

2



N



3



5

1



N

H



N

H



s*



n

N



N

N

N



N

2



1



N

N



N



s*

4



s*



N



N



N



N

N



n



n



N



Scheme 9  Electron donation from lone pairs weakening the single bond



The sN–N-bond is weakened by the acceptance of electrons in the antibonding orbital

sN–N* from geminal lone pairs on the inner nitrogen atoms as well as vicinal lone

pairs on the terminal nitrogen atoms (Scheme 9). The electron donation from the

geminal lone pairs occurs more readily in unsaturated hydronitrogens than in saturated ones.The interaction between sp2 orbitals on the same atom is stronger than that

between sp3orbitals since sp2 has a high s-character [97] (For the importance of the

interaction between the geminal σ-bonds, see Chapter “Relaxation of Ring Strain” by

Naruse and Inagaki in this volume).

Hexaaza-1,5-dienes RN=NNRNRN=NR, derivatives of 15 [96], are unusual

high-energy molecules. Very recently, Cowley, Holland, and co-workers [101]

fairly well stabilized the dianion RN6R2−16 as a ligand in a transition metal complex. These species are stabilized by such conjugations as those in allyl anions,

which are special conjugations of the n-p conjugations.



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