C Alternately

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Ab initio Molecular Orbital Study of the First Four Si/C Alternately Substituted Annulenes Takako Kudo, Michael W. Schmidt, and Nikita Matsunaga J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02631 • Publication Date (Web): 07 May 2019 Downloaded from http://pubs.acs.org on May 7, 2019

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The Journal of Physical Chemistry

1

Ab initio Molecular Orbital Study of the First Four Si/C Alternately Substituted Annulenes Takako Kudo*, Michael W. Schmidt†, and Nikita Matsunaga‡ *Division of Pure and Applied Science, Graduate School of Science and Technology, Gunma University, Kiryu 376-8515, Japan. †Department of Chemistry, Iowa State University, Ames, Iowa 50011-2030, U.S.A. ‡Department of Chemistry & Biochemistry, Long Island University, Brooklyn, New York, 11201, U.S.A.

Abstract:

The ground and low-lying excited states of four alternating Si/C annulenes, HnSin/2Cn/2

with n=4, 6, 8 and 10, have been investigated by ab initio molecular orbital methods and compared to their all-carbon and all-silicon analogues.

In the ground state, all the Si/C-mixed annulenes except for

the largest 10-membered annulene (H10Si5C5) assume equal bond length structures by adopting a closed shell electronic structure in the possible highest symmetry.

For the largest H10Si5C5, the trend of the

bond-delocalization still remains but the circular structure is considerably distorted and non-planar due to severe angle strain.

In the low-lying singlet (S1) and triplet (T1) states, the geometry of the

compounds tends to be non-planar as the excitations produce silyl radical character.

Relative energies

of the T1 and S1 states of the 6-membered ring, compared to the respective ground states (S0), are higher than those of the 4- and 8-membered rings, suggesting a special stability for H6Si3C3.

The

planar rhombus shape of the formally anti-aromatic H4Si2C2 suggests synthetic effort is merited. Bonding analyses are given to support the conclusions reached on the basis of geometric structures and excited state energetics.

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Introduction Benzene is one of the most famous organic compounds, as the archetypal compound with special stability (aromaticity).1,2,3,4 Therefore, it is not surprising that a great deal of interest has been focused on the properties of analogous compounds of the heavier group 14 elements such as the all-silicon congener – hexasilabenzene (H6Si6).5,6,7,8,9,10,11,12,13,14,15,16,17

In spite of huge experimental efforts in

silicon chemistry, the hexasilabenzene derivative has not been synthesized.

According to previous

theoretical studies,10 its molecular framework is non-planar and chair-like with D3d symmetry, which is in sharp contrast to benzene.

To assist the possible synthesis of hexasilabenzene derivatives, we

recently proposed various theoretical ideas to increase their thermodynamic and kinetic stabilities by making use of substituent effects.17 Monosubstituted silabenzene is now well characterized experimentally,18,19,20,21,22,23 with some early theoretical results given in the references.24,25,26,27

For disilabenzene, para-disubstituted

silabenzene has been isolated in matrix,28 complexed with ruthenium,29 and embedded in larger ring systems.30

The ortho-disilabenzene has also been isolated for X-ray analysis.31

Interestingly,

coupled cluster calculations predict that the apparently unobserved meta isomer of disilabenzene is more stable than ortho by about 3 kcal/mol, and more stable than para by about 12 kcal/mol.32

We

have obtained similar results at the B3LYP/6-311G* level of calculations.33 Although the alternating mixed Si/C trisilabenzene (H6Si3C3) has not yet been isolated, it has been detected in a mass spectrometer.34

Theory predicts this congener has a planar structure and is

remarkably more stable than the other H6Si3C3 ring isomers.9,10,11,33,35

Our recent investigation of

the energy factors involved in the out of plane distortions of C6H6, Si6H6, and various alternating compounds H6X3Y3 confirms the special stability of H6Si3C3.33

We also have systematically

investigated the properties of the various different Si/C-mixed benzenes (containing 1 to 6 Si atoms) ACS Paragon Plus Environment

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3 and their major valence isomers such as fulvene, Dewar-benzene, benzvalene, prismane, and other ring structures mainly at the HF and DFT levels of theory.36

As a result, the stabilities of benzvalene and

prismane were found to increase as the number of Si atoms in the molecular skeleton increases.

It

was also noted36 that the Si/C-alternately mixed annulenes have some unique properties compared to the other Si/C-mixed compounds with different Si/C ratio or arrangement of Si and C atoms. The unique character found for the Si/C alternately substituted benzene suggested that other sizes of alternately mixed Si/C annulenes might be interesting, so the subject of this paper is to examine the alternating Si/C rings H4Si2C2, H6Si3C3, H8Si4C4 and H10Si5C5.

This paper's investigation of 4, 6, 8,

and 10 membered Si/C rings is similar in spirit to a theoretical comparison of the all-carbon rings of the same 4 sizes, due to Pierrefixe and Bickelhaupt.37

The key result of the present paper is that all three

of the smallest alternating rings tend to have equal bond distances and planar or nearly planar structures, akin to benzene, even for those rings which would normally be categorized as anti-aromatic due to having 4π or 8π electrons.

This behavior for the alternating Si/C rings is completely different

from that of the all-carbon and all-silicon analogues, whose contrasting results are also included in this paper.

Additionally, in order to deepen the knowledge for the electronic states of these compounds,

the S1 and T1 low-lying excited states of the four Si/C-alternately-mixed annulenes were systematically investigated, and also compared to the all-carbon and all-silicon analogues.

The information for the

excited states obtained in the present study gives more insight into their ground states. Throughout this paper, we use the terms 'aromatic' and 'anti-aromatic' as short hand for electron counts of 4n+2 or 4n π electrons, respectively.

These terms carry additional meanings, as is often

discussed,1-4 but are used here only in this simplest possible sense, although we also consider structure a key indicator.4

Salient references for the six membered rings have been given above, while the less

numerous references for the other ring sizes are given below, where each is discussed in turn.



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Computational Methods Geometry optimizations were performed for the S0, S1, and T1 states of alternating Si/C mixed annulenes for HnSin/2Cn/2 ring sizes n=4, 6, 8, and 10, using the aug-cc-pVDZ basis set.38,39

Most such

optimizations used the complete active space multi-configurational self-consistent field wave function,40 with an active space of nπ electrons in nπ orbitals (CASSCF(n,n); where n is the ring size). For comparison, the geometry of the all-carbon and all-silicon analogues for 4- and 6-membered ring structure were also optimized at the same level of theory.

For the larger all-carbon and all-silicon

rings, with 8 or 10 heavy atoms, second order perturbation theory (MP2)41 using the same aug-ccpVDZ basis set was carried out for the geometry optimizations for their ground states.

All optimized

structures were characterized as minima or transition states by normal mode analyses.

Single point

energy calculations on the CASSCF optimized geometries were carried out at the multi-reference second order perturbation (MRMP2) level42 of theory with the larger cc-pVTZ basis set38,39 for the S0, S1, and T1 states of every alternating ring, and the two smaller all-C and all-Si rings.

Furthermore,

CCSD(T)43,44 energy calculations using the aug-cc-pVDZ basis were performed for selected structures, as well as one CCSD(T) geometry optimization for H4Si2C2. For the ring sizes n=4 and 6, minimum energy crossing (MEX) point searches45 between the S0 and T1 states, as well as conical intersection (CON) searches46 between the S0 and S1 states were performed.

For both types of crossing point searches, the level of theory used was the same as

described above, i.e. CASSCF(n,n)/aug-cc-pVDZ.

However, the orbital optimization steps were

carried out with equally weighted state averaging of the two states during the conical intersection searches.

As with other stationary points, single point MRMP2/cc-pVTZ energy calculations were

carried out on both states at the MEX and CON points, averaging their two energies. Bonding analysis relies on the Kinetic Bond Order, recently introduced by Ruedenberg and ACS Paragon Plus Environment

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5 coworkers,47,48 which has been applied to a few chemical systems.49,50,51

Since kinetic energy is the

driving force for lowering the interatomic bonding energy,52 this portion of a complete energy analysis48 serves as a simple index of the extent of electron sharing (covalent bonding).

The first step

is to localize the π active orbitals of an MCSCF wavefunction, which in the present case produces one p-like molecular orbital on each C or Si atom of the ring. Then, the KBO is simply the product of the off diagonal density matrix element (bond order53) times the corresponding kinetic energy integral, for any pair of these p-shaped orbitals.48

The KBO is conventionally multiplied by 0.1 to compensate for

the absence of the much more difficult to evaluate two electron interference terms.47

More negative

values of the KBO typify greater covalency. All calculations were performed with the GAMESS electronic structure code.54,55

Results and Discussion

This section gives geometric and energetic results first for rings with 6 atoms, and then 4 atoms, followed by data for the 8 and 10 atom rings.

In each molecule's subsection, the ground states for the

alternating Si/C rings are compared to the all-carbon case, and the all-silicon case.

Naïve trust in the

famous 4n+2 rule predicts aromaticity only for the 6 and 10 atom rings, but the results for alternating rings will prove much more interesting.

Excited state results are then presented for each ring size.

Two final subsections compare excited states and bonding properties of the various ring sizes to each other.

1. The 6-membered ring compound (H6Si3C3) Figure 1 shows the CASSCF(6,6)/aug-cc-pVDZ optimized geometries of the Si/C-alternatelymixed benzene (1,3,5-trisilabenzene, H6Si3C3) in the ground (S0) and several low-lying excited singlet ACS Paragon Plus Environment


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6 and triplet states. just as for benzene.

Alternating trisilabenzene has an equal-bond planar structure in the ground state,10 Because there are Si and C atoms in alternating positions, the molecular

symmetry is not D6h but rather D3h (so the designation for the S0 state is 1A1').

For comparison, the

optimized geometries at the same level of theory for benzene (H6C6) and hexasilabenzene (H6Si6) in the S0, T1 and S1 states are depicted in Figure 2.

As seen in the Figure, and as is already well known,8,10

hexasilabenzene has a non-planar chair type structure in the ground state.

Hence, the S0 structure of

the Si/C-alternately-mixed benzene resembles benzene more closely than the all-silicon analogue. However, it is noteworthy that all three benzene analogues (H6C6, H6Si3C3 and H6Si6) adopt an equalbond structure in their ground states. In the T1 state of the Si/C-mixed benzene, two localized Si-C double bonds appear, as shown in Figure 1, therefore, T1 looks like a cyclohexadiene structure.

Interestingly, the same thing is observed

in the cases of benzene and hexasilabenzene, but only the all-carbon analogue remains planar.

The T1

structure of hexasilabenzene is similar to its S0, remaining chair-type with C2 (3B) symmetry, while one Si-H bond is significantly out-of plane for the Si/C-mixed benzene, which makes the molecular symmetry Cs (3A’).

This is explained by the excitation of an electron into an MO localized on the

corresponding Si atom, to produce local silyl radical character, which then drives a pyramidalization at that Si atom. In the S1 state (1B2u), the molecular skeleton of benzene remains highly symmetric, planar D6h just like its ground state, as shown in Figure 2.

It is interesting to note that S1 of hexasilabenzene also has

an equal-bond structure, and remains nonplanar with Cs (1A”) symmetry. On the other hand, three different Si-C bond lengths are found for the S1 of the Si/C-mixed benzene (C2, 1B), suggesting the Si/C-mixed benzene in the S1 state resembles neither benzene nor hexasilabenzene. However, it is found that the Si/C-mixed benzene almost takes an equal-bond structure in the S2 state with Cs symmetry (A”) as shown in Figure 1. ACS Paragon Plus Environment

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7 In the higher T2 and S3 states, the Si/C-mixed benzene has been located with decidedly non-planar structures, as seen in Figure 1. To summarize the geometries of the six membered rings, in both their ground and low-lying T1 states, the structures of the Si/C-mixed and the all-carbon and all-silicon analogues are all similar, within each species.

As expected, the degree of non-planarity for these three is in the order H6C6
H6Si6.

This reflects the special stability of benzene due to

aromaticity in the S0 state, but also suggests moderate stability for the S0 state of the Si/C-alternatelymixed benzene. The frontier molecular orbitals of the Si/C-mixed benzene are compared with those of benzene in Figure 3.

All of them are π orbitals and are qualitatively the same in both molecules, despite the

differences in the molecular symmetry. Incidentally, the frontier molecular orbitals of hexasilabenzene (not shown) are almost identical to those of benzene, and have π character even though the molecular skeleton is not planar. The minimum energy crossing (MEX) point (S0/T1 crossing) for the six-membered ring compound has a structure similar to that of the T1 state, as shown in Figure 1. assumes a tetrahedral bond angle.

The silicon in the Cs plane

The MEX point also occurs energetically close to the T1 state, just

3.4 kcal/mol above it, at the MRMP2/cc-pVTZ level of theory. On the other hand, the conical intersection (CON) between the S0 and S1 states has a quite different structure from either state.

The

structure of CON assumes a conformation with one of the silicon atoms positioned significantly above ACS Paragon Plus Environment


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8 the plane of the ring and so represents a considerable geometrical deviation from the S1 state, for which all heavy atoms are nearly in plane.

All-carbon atoms have nearly sp2 hybridization bond angles,

while the silicon atoms are closer to tetrahedral angles.

Energetically, CON is located about 9.1

kcal/mol above the S1 state minimum.

2. The 4-membered ring compound (H4Si2C2) A 1984 Gordon group paper56 considering various isomers with this formula found that for 4 membered rings, only the alternating isomer was a minimum on the potential surface.

It should be

noted that the findings in the 1984 paper suffer from the use of a very small 3-21G basis set, especially in incorrectly predicting alternating double and single bond distances in a planar ring.

The same set of

isomers were considered in 1998 at the DFT level of theory by the Maier group,57 whose matrix isolation experiments detected three isomers with this formula, but not the 4-membered ring which is of interest here. ring.

Like the present work, that paper57 predicts four equal SiC distances in the alternating

A compound with adjacent doubly bonded Si atoms in a four membered ring has recently been

isolated,58 by including its two adjacent carbon atoms into a 6-atom carbon ring, as part of a bicyclic C6Si2 8π electron system.

Thus, no parent or substituted alternating H4Si2C2 appears to be known in

the laboratory. The all-carbon ring cyclobutadiene is usually cited as the archetypal antiaromatic compound, and so has an enormous literature, for which we reference only a single review article.59

The all-silicon ring

tetrasilacyclobutadiene is now known,60 with bulky substituents, whose X-ray structure is discussed just below, and which has drawn both a published commentary61 and theoretical modeling.62

Even

more recently, another Si4 ring has been prepared,63 but with its two diagonally opposite Si atoms also contained in exo 4-membered rings (SiN2C).

Synthetic strategies other than bulky substitution or

affixing external ring systems include charge adjustment, since either +2 or -2 formal charges create an ACS Paragon Plus Environment

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9 aromatic electron count.

A dianionic Si4 system complexed to a Ru metal center was reported in

2009,64 and some modeling of Si4-2 complexes with two alkali metals has been performed.65

A

dicationic Si4 ring66 is found by X-ray crystallography to be rhombus shaped due to two opposing Si atoms being contained in an exo SiN2C ring, with its four central Si atoms entirely planar. Incidentally, the planarity of the dicationic Si4 ring is in agreement with the prediction of planarity for dicationic hexasilabenzene due to decreased π repulsion.33 Figure 4 shows the CASSCF(4,4)/aug-cc-pVDZ optimized geometries of the alternately Si/C substituted cyclobutadiene (1,3-disilacyclobutadiene, H4Si2C2), while those obtained at the same level of theory are depicted in Figure 5 for the all-carbon and all-silicon analogues. for the S0, T1 and S1 states of all three rings.

Geometries are given

Note that the H4Si2C2 heavy atom skeleton is planar at

the CASSCF(4,4) level, with four equal SiC distances, and with the H atoms just barely out of plane: the Si1Si2C3H7 torsion angle is 160.7°.

Note that the combination of its small ring size and the angle

CSiC being greater than 90° means the diagonal Si-Si distance of 2.35 Å is equal to a typical Si-Si single bond distance, but the C-C distance is long, at 2.67 Å.

The near planarity of H4Si2C2 found at

the CASSCF level was checked by additional CCSD(T)/aug-cc-pVDZ optimizations (see Figure S1), which found that even the hydrogen atoms become coplanar, namely the torsion angle Si1Si2C3H7 becomes 180.0°, with r(SiC)=1.798 and r(SiSi)=2.377 Å.67 The all-carbon cyclobutadiene is the archetypal anti-aromatic compound with 4π electrons, and consequently adopts a rectangular bond-alternating structure in the S0 state.59

On the other hand, the

all-silicon analogue, tetrasilacyclobutadiene, has been isolated with two different bulky substituents by Suzuki and Matsuo et al.60

The X-ray structures have a non-planar rhombus akin to that shown in

Figure 5 for the all hydrogen substitution, but considerable steric repulsion among the bulky substituents60 makes the molecular skeleton in the laboratory compound flatter than that found here for the simple prototype H4Si4.

It is not surprising that the silicon compound does not have an alternating ACS Paragon Plus Environment


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10 bond structure involving localized double bonds, as is the case for the carbon analogue, because silicon does not prefer unsaturated bonds.

Instead, H4Si4 avoids anti-aromaticity by pyramidalization at all

four silicon atoms. Thus, the diamond-shape structure for H4Si2C2 resembles the all-silicon analogue only in having all bonds equal, and resembles the all-carbon analogue only in being planar.

Clearly the nearly planar,

equal-bond structure found for the anti-aromatic H4Si2C2 warrants further attention. The frontier molecular orbitals at idealized geometries for H4C4 and H4C2Si2 are compared in Figure 6.

The

idealized geometries are taken as a square planar shaped (D4h) geometry for cyclobutadiene and a planar diamond-shaped (D2h) structure for the Si/C case (all hydrogens in the heavy atom plane).

The

equilibrium structure of cyclobutadiene in the ground state is actually strongly rectangular (D2h) after distorting to alternating double and single bond distances, while the hydrogen atoms of the Si/C-mixed analogue are not quite planar (C2h), as noted above.

But, Figure 6 is convenient to explain the

different electronic structure of these two molecules.

As seen in the Figure, the highest orbitals of

cyclobutadiene with D4h symmetry are degenerate, and so become singly occupied MOs (SOMOs). The electronic state for the single occupancy is doubly degenerate, leading to Jahn-Teller distortion and subsequent collapse to a closed shell rectangular-shaped structure with D2h symmetry, which is the well known ground state of cyclobutadiene.59

In contrast, the molecular symmetry of the Si/C-alternately-

mixed congener is already lowered to D2h, as the skeleton consists of two different elements, with very different electronegativities and different atomic sizes.

Therefore, the HOMO is a non-degenerate

filled orbital largely centered on the carbon atoms, which makes it possible for the molecule to keep equal bond lengths.

For the case of H4Si4, the idealized D4h molecular skeleton is subject to the same

Jahn-Teller instability as H4C4, but distorts in a different manner, to a considerably non-planar geometry.

This avoids forming any localized double bond, in favor of pyramidalization, which is a

typical behavior for silicon. It is quite interesting that these three different 4π e- system find three ACS Paragon Plus Environment

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11 different ways to shed their anti-aromaticity! Turning to excited states, for the T1 state (Cs, 3A”) of the Si/C-mixed compound, two unequal Si-C bonds appear in the Si2C2 skeleton, and one Si-H bond is significantly out-of-plane as is also the case for the T1 state of the Si/C-mixed benzene (compare Figures 1 and 4).

This may be explained by the

same localized Si pyramidalization as discussed above for the T1 state of the Si/C-mixed 6-membered ring.

However, for the S1 state, an equal-bond rhombic structure, similar to the S0 state, is obtained

again, but its C2 axis now passes through different heavy atoms than in S0.

An equal-bond structure in

the S1 state is also found for H4C4 whose skeleton is square planar as shown in Figure 5.

For H4Si4,

the molecular shape is an alternating-bond structure in both the T1 and S1 states, and the Si4 skeleton in T1 is considerably non-planar, whereas near planarity is found for the S1 state. On the other hand, the Si2C2 skeleton of the Si/C-mixed analogue is almost planar in all three states.

Therefore, this

compound is rather close to the carbon analogue for molecular planarity in the low-lying electronic states, including the ground state. Table 2 summarizes the energies of the T1 and S1 states relative to that of the S0 of H4Si2C2 together with those of the all-carbon and all-silicon analogues.

It is noteworthy that at the CASSCF(4,4)/aug-

cc-pVDZ level both T1 and S1 are lower than the S0 in energy for the Si/C-mixed compound. However, the order of stability is reversed once dynamical electron correlation is included, at the MRMP2/cc-pVTZ level, so indeed the state labeled S0 is the lowest.68

As for the case of the 6-

membered ring, the relative stability of the ground state also increases for the all-silicon ring, but not for the all-carbon analogue when dynamical correlation effects are included via MRMP2 calculations. The relative energy of T1 compared to the ground state increases in the order, H4C4 < H4Si2C2 < H4Si4, which suggests the anti-aromaticity of the all-carbon compound in its ground state geometry is largest. However, the S1 state relative to S0 is lowest in the Si/C-alternately mixed compound. Crossing point geometries for H4Si2C2 are also given in Figure 4. ACS Paragon Plus Environment

The MEX point between the S0


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12 and T1 states of H4Si2C2 has D2h symmetry, with the four SiC bonds equal in length, and so is even more symmetrical than the S0 and T1 states.

In comparison to the S0 state, the MEX bond lengths for

the Si-C bonds are elongated, but are intermediate to the two unique SiC distances found in the T1 state geometry. theory. Si atoms.

The MEX point’s energy lies 7.6 kcal/mol above T1 at the MRMP2/cc-pVTZ level of

The CON point between S0 and S1 has Cs symmetry, with the mirror plane containing the two The Si-C bond lengths are all stretched compared to both the parent S0 and S1 state

geometries, and the SiCSi angle is larger than 90, unlike S0 or S1.

The relative energy of CON

compared to S1 is 24.5 kcal/mol, which is much greater than the energy gap found between MEX and T1.

The energy gaps to reach MEX from T1 or CON from S1 for the 4-membered ring systems are

thus about double the analogous differences found in the 6-membered ring systems.

3. The 8-membered ring compound (H8Si4C4) Figure 7 shows the CASSCF(8,8)/aug-cc-pVDZ optimized geometry of the alternating Si/C substituted cyclooctatetraene (1,3,5,7-tetrasilacyclooctatetraene, H8Si4C4) in the ground (S0) and several additional low-lying excited singlet and triplet states.

In spite of this 8π e- system being

formally anti-aromatic, the ground state molecule has an equal-bond planar structure!

In contrast, the

carbon analogue, cyclooctatetraene (COT = H8C8) takes D2d symmetry with alternating single and double bond lengths, and is far from planar, as shown in Figure S2.

Note that planar C8 systems do

exist, as part of larger systems, and strategies for creating these are reviewed by Boldyrev.69 Moreover, at the MP2/aug-cc-pVDZ level, it is found that the analogous D2d symmetry structure of the all-silicon analogue, H8Si8, has 4 imaginary frequency modes, and collapses to a polyhedral octasilacuneane (C1) as shown in Figure S2.

This result is quite reasonable, as silicon atoms prefer to

form saturated bonds instead of any unsaturated bonds.

Even for Si6 systems, prismanes and other 3-

dimensional structures have lower energies than simple rings with π bonds.7 ACS Paragon Plus Environment

Therefore, for the S0

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13 structure, the equal bond length and planar Si/C mixed compound, H8Si4C4, resembles neither the allcarbon analogue nor the all-silicon analogue, which is noteworthy. The frontier molecular orbitals of the Si/C-alternately-mixed analogue (D4h) are compared to the octagonal-shaped (D8h) COT in Figure 8.

As already noted, the D8h structure is not a minimum for

COT, but it is useful to examine this idealized planar structure to see why the 8π e- mixed compound can be equal-bond and planar.

As was discussed for four membered rings above, COT cannot remain

in a degenerate electronic state, leading to an alternating-bond structure with D2d symmetry after JahnTeller distortion.

On the other hand, the corresponding two orbitals of the Si/C-mixed compound are

split into a non-degenerate HOMO and LUMO, and the former orbital (electron density concentrated primarily on carbon atoms) is filled. As seen in Figure 7, the molecular structure of the Si/C-mixed compound becomes non-planar in the low-lying excited states, especially at the Si-H bonds.

Interestingly, although the structure of the

S1 (Cs, 1A”) state is non-planar, the deviation from the plane of the 8-membered ring is only 9.6 degrees.

Also, all the S1 Si-C bond lengths are equal and the 8 frontier MOs have π character as in the

ground state.

This is similar to the S1 of benzene and hexasilabenzene, and the S2 state of the Si/C-

alternately-mixed benzene as mentioned above. In contrast, the T1(Cs, 3A”) state has a partially alternating-bond structure. The energies of these excited states relative to that of the ground state of H8Si4C4 are summarized in Table 3.

Interestingly, S1 with the equal-bond structure is more stable than T1, both at the MRMP2

and CASSCF(8,8) levels.

As is for the case for the silicon containing 6- and 4-membered ring

compounds, the stability of the ground state relative to the low-lying excited states increases after inclusion of dynamical electron correlation effects.

4. The 10-membered ring compound (H10Si5C5) ACS Paragon Plus Environment


Page 14 of 42

14 According to the Hückel rule, an annulene with an equal-bond 10π e- (4n+2; n=2) electronic structure should be aromatic.

Nevertheless, for the all-carbon case H10C10, such a D10h symmetry

convex decagon is found not to be a minimum, but rather collapses to a twisted structure, according to a previous study of King et al.70 using CCSD(T) theory with various basis sets.

The second lowest

isomer is only about one kcal/mol higher in energy, and has a naphthalene-like structure in which bond alternation is observed as well.70

Our MP2 geometries for the two lowest energy annulenes using the

more flexible aug-cc-pVDZ basis are shown in Figure S3. King et al.,70 none of which are convex polygons.

A total of 5 ring isomers were located by

It is generally understood that the mismatch

between the 120° angles of sp2 hybridization and the 144° angle required in a perfect convex decagon drives the adoption of a few concave angles in these isomers, as well as deviations from planarity. Ring currents71 for all of King et al.’s [10]annulene isomers have been reported recently, and see also Boldyrev’s work on stabilization of planar C10 rings.69 In the case of the all-silicon analogue, H10Si10, the present MP2/aug-cc-pVDZ level geometry searches show that such twisted structures with a planar (2D) ring framework are further transformed into a three-dimensional (3D) polyhedral structure (see Figures S4 and S5). presented for the 8-membered ring silicon compounds noted just above.

This is akin to the results

The polyhedral structure is

found to be far more stable ( >100 kcal/mol at the MP2 level of theory) than other naphthalene-like (Naphth, Cs) or heart-shaped (Kokoro, C1) isomers, which are largely non-planar, too. For the largest Si/C-alternately-mixed compound in the present study, H10Si5C5, five ring isomers in the ground state have been located, as depicted in Figure 9.

As is true for H10C10, the planar equal-

bond D5h structure is found to have two imaginary frequency modes at the CASSCF(10,10)/aug-ccpVDZ level, and so is not a ring minimum.

Two of the five true minima found have naphthalene-like

structures, denoted Naphth(Cs) and Tctcc(Cs), and differ primarily in having their two internal H atoms on opposite or the same sides, respectively (the letters in Tctcc refer to trans or cis orientations at ACS Paragon Plus Environment

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15 consecutive SiC bonds).

Another two isomers with heart-shaped structures, Kokoro-Si(Cs) and

Kokoro-C(Cs), differ in having a silicon or carbon atom at the heart's cusp.

Finally, a nonsymmetric

isomer with a convex ring shape was found: this Convex isomer is nearly planar, with nearly equal bond lengths, and can be regarded as being derived directly from the idealized D5h decagon. In sharp contrast to the all-carbon rings, all five H10Si5C5 isomers have similar Si-C bond lengths, in all cases lying between 1.74 and 1.78 Å, and moreover, as seen in the insets of Figure 9, have much more planar geometries than have been reported for the all-carbon case.70 completely planar structure with moderately alternating Si-C bonds. CASSCF(10,10), MRMP2, and CCSD(T) are also shown in Figure 9.

In fact, Kokoro-Si has a

The energies for In ascending energy order, the

maximum bond alternation for Naphth is 0.011, Tctcc 0.015, Kokoro-Si 0.036, Kokoro-C 0.013, and Convex 0.029 Å.

The small extent of alternation in the mixed rings stand in sharp contrast to the all-

carbon or all-silicon analogues, but rather suggests some 4n+2=10 aromaticity.

This means that one

can readily identify some π character within the highest lying orbitals of all five isomers, and constructing the CASSCF(10,10) active space is simple. The relative energies of the isomers of H10Si5C5 at various calculation levels are fairly consistent, apart from an anomalously low MRMP2 energy for the Kokoro-Si isomer.

The CCSD(T) values

agree qualitatively with the CASSCF values, in predicting that the Napth isomer is the most stable, while the most ring-like convex isomer is the highest or close to it. All isomers occur in a narrow energy band, of 10 kcal/mol or so. Since the structures show that the mixed Si/C rings exhibit clear signs of some 10π e- aromaticity, the minimum of the T1 and S1 states for the Naphth isomer were located, and the results are displayed together with the S0 in Figure 10.

In contrast with the ground state, bond length alternation appears

and the 10-membered molecular skeletons are significantly non-planar in both T1 and S1 states. is the same trend found for all smaller sizes of the Si/C-alternately-mixed compounds. ACS Paragon Plus Environment

This

Additional T1


Page 16 of 42

16 states of other isomers such as Kokoro-Si (Cs) or Kokoro-C (Cs) were located, but were found to have higher MRPT2/cc-pVTZ energies than the triplet state of Napth.

Details for these additional states are

not reported here.

5. Overview of Excited States Table 4 summarizes the relative energies of the T1 and S1 states relative to the ground S0 states, for all the Si/C-alternating annulenes considered above.

All ring sizes have a S0 state dominated by a

single closed shell determinant, with singly excited open shell T1 and S1 states.

The largest excitation

energies occur for the benzene analogue H6Si3C3, suggesting a special stability for the ground state of the 6π system.

As one might expect, the smallest excitation energies occur in the 4 system H4Si2C2.

Note that the excitation to T1 is actually very similar for the 8 and 10 rings. The surface crossing points (MEX and CON) were located for the 4 atom and 6 atom rings.

The

MEX point for H4Si2C2 is at a high enough energy (~8 kcal/mol) to create a barrier to nonphotochemical decay pathways for T1 through surface crossings, but the corresponding value in H6Si3C3 is only ~3 kcal/mol.

More importantly, the CON points lie sufficiently above the equilibrium

geometries for S1 that optical spectroscopy involving S1 may be a useful way to characterize a successful synthesis of the S0 states of these two alternating rings.

Specifically, the CON points lie

~24 and ~9 kcal/mol above S1 for the 4 and 6 atom rings, respectively.

6. Electronic structure and bonding analysis Clearly the electronic structure of the "antiaromatic" 4 e- ring requires further comment.

As was

noted above, a 1984 paper56 using a very small unpolarized basis set found alternating bond lengths for this ring.

Optimization from that structure, still at the RHF level but with the present work's aug-

cc-pVDZ basis set leads to a symmetric planar molecule, with four equal SiC bond lengths, whose CH ACS Paragon Plus Environment

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17 bonds bend just a few degrees out of plane at the CASSCF theory level.

Use of the present basis set

also removes the UHF instability and multireference character reported in 1984.56

This may be

quantified by giving the occupation numbers of the four CASSCF/aug-cc-pVDZ  orbitals: the fully  bonding four center bu orbital is nearly filled at 1.980 e-, a formally * CC ag orbital holds 1.954 e- (but recall this is the long axis of the diamond shape), and the remaining two  active orbitals contain just 0.047 (bu) and 0.019 (bg) electrons.

As we noted above, this S0 state lies below the T1 and S1 states

after dynamical correlation is included via MCQDPT, and is predicted by CCSD(T) to be completely planar. In short, H4Si2C2 is a closed shell system, largely filling the two lowest orbitals shown in the MO diagram of Figure 6, and therefore a reasonable synthetic target. Table 5 presents a brief overview of the bonding in the first three mixed rings.

After localization

of the MCSCF active space  orbitals, one p-like orbital is found on each Si or C, and the electron occupancy of each is interpreted as a population of that orbital.

In all rings, the occupation number

(diagonal density matrix element) is greater for C than for Si, indicating that the  electrons are not equally distributed.

Table 5 clearly shows that the formally aromatic 6 e- ring has the least positively

charged Si atom (its  charge is +0.25), whereas the 4 and 8 rings show a much greater +/- charge separation.

This is in keeping with the notion that the aromatic 6 ring should be more delocalized.

It also fits with the MO diagrams shown in Figure 6 and 8 where the orbitals occupied after the degeneracy is raised are localized on the more electronegative carbon atoms. Table 5 also reports nearest neighbor kinetic bond orders, which weight the bond order with the kinetic energy integral, to serve as a measure of the energy lowering due to covalent bonding.

All

three KBOs are negative, which is indicative of electron sharing between adjacent Si and C atoms. Since the ring bonding is delocalized, all ring KBOs are smaller than the two center  bond found in silene H2Si=CH2.

Clearly, the value for the aromatic 6 ring exceeds the 8 ring by a narrow margin,

and is considerably larger than the 4 formally anti-aromatic case. Again, this is consistent with the ACS Paragon Plus Environment


Page 18 of 42

18 6 ring being aromatic.

The cross ring KBO values are not large in the 6 or 8 atom rings, but are

appreciable in the 4-atom ring: KBO(CC)= -0.0136 and KBO(SiSi)= -0.0100 Hartree, similar in magnitude to the neighboring atom KBO(SiC)= -0.0096.

There is clearly overall net  bonding in the

four-atom ring.

Concluding Remarks In the present study, the properties of the ground and low-lying excited states of the 4, 6, 8, and 10 atom Si/C-alternately-mixed annulenes were investigated and compared with their all-carbon- and allsilicon analogues. In the ground S0 state, the 4-, 6-, and 8-membered Si/C-alternately-mixed annulenes all possess equal-bond planar structures.

This is remarkable since the all-carbon analogue cyclobutadiene has

alternating single/double bonds, and cyclooctatetraene, H8C8, has an alternating-bond non-planar structure. The present work finds the monocyclic structure of H8Si8 also collapses, to the polyhedral structure octasilacuneane.

On the other hand, the 4-membered all-silicon compound has an equal-

bond structure, albeit far less planar than H4Si2C2.

For the largest 10-membered Si/C compound, a

moderate tendency towards bond-delocalization is also seen, but the molecular structure cannot keep the highest symmetry, probably because of significant angle strain.

This is also in sharp contrast with

that the all-carbon analogue H10C10 which has a considerably non-planar and bond-alternating structure70 while the all-silicon analogue H10Si10 has a completely different polyhedral structure containing only Si-Si single bonds. In contrast with the ground state, the molecular geometries found for the S1 and T1 states of all four mixed rings tend to be non-planar, probably because of the silyl radical character caused by electronic excitation to orbitals mainly localized on the Si atoms.

This is a common feature for all ring sizes of

the Si/C-alternately-mixed annulenes, whether the π e- count is formally aromatic or anti-aromatic. ACS Paragon Plus Environment

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19 The energy of T1 and S1 relative to the S0 for the 6-membered ring is much greater than those of the other rings, suggesting a special stability (aromaticity) for the ground state of the 6 e- benzene-type compound. states.

But the 4 e- ring also has a closed shell S0 and moderately stable low lying T1 and S1

These interesting findings may give some insight into a deeper understanding of aromaticity.

The key result for experimentalists, who have invested a great deal of effort to synthesize the allsilicon rings, is to suggest that alternating compounds are worth similar laboratory effort.

Already the

Si3C3 ring is known as an intermediate, and its properties suggest kinetic stabilization with bulky groups at Si can lead to an isolable compound.

More remarkably, it seems that the antiaromatic but

nearly planar with four equal sides Si2C2 ring is worth similar synthetic effort.

We note that a 4

electron system based on Si2N2 is stable enough to form a crystal,72 with its nearly rhombus shaped ring containing two silylene atoms (which contribute zero  electrons) and two nitrogen  lone pairs. Si2C2 would presumably delocalize its  electrons better than this known compound, as all four of its atoms contribute 1 electron to the 4 system.



Page 20 of 42

20

Associated Content Supporting Information. Five figures showing additional molecular structures.

S1 shows CCSD(T) geometry optimizations for

H4Si2C2, S2 shows H8C8 and H8Si8, S3 gives H10C10 results, and finally S4 and S5 give the H10Si10 structures.

Author Information Corresponding Author T.K. E-mail: [email protected] Telephone: +81-277-30-1935 ORCID Takako Kudo: 0000-0002-3222-4549 Nikita Matsunaga: 0000-0002-4477-2999 Notes The authors declare no competing financial interest.

Acknowledgement TK was supported by a grant for female researchers in Gunma University. supported by the US National Science Foundation grant CHE-1565888.


MWS was

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21 Table 1. CASSCF(6,6)/aug-cc-pVDZ and MRMP2/cc-pVTZ//CASSCF(6,6)/aug-cc-pVDZa) relative energies (kcal/mol) and the molecular and electronic states symmetries of the 6-membered annulenes, H6C6, H6Si3C3 and H6Si6 in the ground (S0) and some low-lying electronic states.

H6C6

H6Si3C3

S0

(D6h, A1g)

0.0 (0.0)

(D3h, A1')

T1

(C2v, A1)

81.9 (87.2)

S1

(D6h, B2u) 109.5 (101.6)

H6Si6 0.0 (0.0)

(D3d, A1g)

(Cs, A')

47.6 (58.2)

(C2, B)

(C2, B)

69.3 (79.8)

(Cs, A”)

T2

(Cs, A'') 67.9 (60.6)

S2

(Cs, A'') 71.1 (79.8)

S3

(Cs, A')

0.0 (0.0)

25.3 (35.7) 37.6 (41.9)

91.4 (103.4)

a) The more accurate MRMP2 values are in parentheses.

Table 2. CASSCF(4,4)/aug-cc-pVDZ and MRMP2/cc-pVTZ//CASSCF(4,4)/aug-cc-pVDZa) relative energies (kcal/mol) and the molecular and electronic state symmetries of the 4-membered annulenes, H4C4, H4Si2C2 and H4Si4 in the ground S0 and excited T1 and S1 states.

H4C4

H4Si2C2

S0

(D2h, Ag)

0.0 (0.0)

(C2h, Ag)

T1

(D4h, B3g)

16.9 (7.3)

S1

(D4h, B1g)

58.3 (35.2)

H4Si4 0.0 (0.0)

(D2d, A1)

0.0 (0.0)

(Cs, A'') -1.3 (12.6)

(C2h, Bg)

14.9 (24.6)

(C2h, Bg)

(C2h, Bg)

10.0 (23.0)

-6.5 (13.2)

a) The more accurate MRMP2 values are in parentheses.



Page 22 of 42

22 Table 3. CASSCF(8,8)/aug-cc-pVDZ and MRMP2/cc-pVTZ//CASSCF(8,8)/aug-cc-pVDZa) relative energies (kcal/mol) and the molecular and electronic state symmetries of the 8-membered Si/Calternately mixed annulene, H8Si4C4 in the ground (S0) and some low-lying electronic states.

H8Si4C4 S0

(D4h, A1g)

0.0 (0.0)

T1

(Cs, A'') 36.1 (42.0)

S1

(Cs, A'') 26.4 (37.3)

T2

(C2, A)

64.3 (75.1)

T3

(Cs, A')

65.3 (77.6)

S2

(C2, A)

84.2 (77.7)

a) The MRMP2 values are in parentheses.

Table 4. CASSCF(n,n)/aug-cc-pVDZ and MRMP2/cc-pVTZ//CASSCF(n,n)/aug-cc-pVDZa) relative energies (kcal/mol) of the 4, 6, 8 and 10-membered Si/C-alternately mixed annulenes, HnSin/2Cn/2; n=4, 6, 8 and 10), in the S0, T1 and S1 electronic states. H4Si2C2

H6Si3C3

H8Si4C4

H10Si5C5

S0

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

T1

-1.3 (12.6)

47.6 (58.2)

36.1 (42.0)

38.4 (21.5)

S1

-6.5 (13.2)

69.3 (79.8)

26.4 (37.3)

56.0 (21.7)

a) The MRMP2 values are in parentheses.


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23

Table 5. CASSCF(n,n)/aug-cc-pVDZ populations and kinetic bond ordersa.

The top half of the table

shows two center  bond properties for comparison to the three alternating rings at the bottom.

n(Si)

n(C)

KBO(SiC)

H2C=CH2

1.0

1.0

-0.0325b

H2Si=CH2

0.89

1.11

-0.0253

H2Si=SiH2

1.0

1.0

-0.0103b

H4Si2C2

0.53

1.47

-0.0096

H6Si3C3

0.75

1.25

-0.0167

H8Si4C4

0.62

1.38

-0.0156

a) Electron populations (n) are in units of electrons, and sum to the number of  e-.

Kinetic bond

orders are the product of the bond order () and the kinetic energy integral, and are in Hartree units. The KBO values have been scaled by the conventional factor of 0.1.47 b) These two entries are the  bond KBO(CC) and KBO(SiSi).



Page 24 of 42

24

Figure Captions Figure 1.

The CASSCF(6,6)/aug-cc-pVDZ optimized geometries, in Å and degrees, for H6Si3C3 in

the S0 and some low-lying excited states, together with the S0/T1 minimum energy crossing point and the S0/S1 conical intersection.

The numbers above the structures are the CASSCF(6,6)/aug-cc-pVDZ

and MRMP2/cc-pVTZ// CASSCF(6,6)/aug-cc-pVDZ (in parentheses) energies, relative to that in the S0 state, in kcal/mol. Figure 2. The CASSCF(6,6)/aug-cc-pVDZ optimized geometries of the H6C6 and H6Si6 in the S0, T1 and S1 states in Å and degrees. The numbers above the structures are the CASSCF(6,6)/aug-cc-pVDZ and MRMP2/cc-pVTZ// CASSCF(6,6)/aug-cc-pVDZ (in parentheses) energies relative to that in each S0 state in kcal/mol. Figure 3. The frontier molecular orbitals of benzene and 1,3,5-trisilabenzene. Figure 4. The CASSCF(4,4)/aug-cc-pVDZ optimized geometries of the H4Si2C2 in the S0, T1 and S1 states, and MEX and CON crossing points, with geometric data in Å and degrees. The numbers above the structures are the CASSCF(4,4)/aug-cc-pVDZ and MRMP2/cc-pVTZ// CASSCF(4,4)/aug-ccpVDZ (in parentheses) energies relative to that in each S0 state in kcal/mol. Figure 5. The CASSCF(4,4)/aug-cc-pVDZ optimized geometries of the H4C4 and H4Si4 in the S0, T1 and S1 states, in Å and degrees. The numbers above the structures are the CASSCF(4,4)/aug-cc-pVDZ and MRMP2/cc-pVTZ// CASSCF(4,4)/aug-cc-pVDZ (in parentheses) energies relative to that in each S0 state in kcal/mol. Figure 6. The frontier molecular orbitals of cyclobutadiene in the square-shape (D4h), and the rhombus shaped (D2h) Si/C-alternately-mixed analogue. Figure 7. The CASSCF(8,8)/aug-cc-pVDZ optimized geometries of H8Si4C4 in the S0 and some lowlying excited states, in Å and degrees. The numbers above the structures are the CASSCF(8,8)/aug-ccpVDZ and MRMP2/cc-pVTZ// CASSCF(8,8)/aug-cc-pVDZ (in parentheses) energies relative to that in the S0 state in kcal/mol.


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25 Figure 8. The frontier molecular orbitals of cyclooctatetraene (COT) in an equilateral octagonal shape (D8h), and the Si/C-alternately-mixed analogue (D4h). Figure 9. The CASSCF(10,10)/aug-cc-pVDZ optimized geometries for some isomers of H10Si5C5 in the S0 state, in Å and degrees. The numbers above the structures are the energies relative to that of Naphth for CASSCF(10,10)/aug-cc-pVDZ, MRMP2/cc-pVTZ// CASSCF(10,10)/aug-cc-pVDZ (in parentheses) and CCSD(T)/cc-pVTZ// CASSCF(10,10)/aug-cc-pVDZ (in italics), in kcal/mol. Figure 10. The CASSCF(10,10)/aug-cc-pVDZ optimized geometries of Naphth (H10Si5C5) in the S0, T1 and S1 states, in Å and degrees. The numbers above the structures are the CASSCF(10,10)/aug-ccpVDZ and MRMP2/cc-pVTZ// CASSCF(10,10)/aug-cc-pVDZ (in parentheses) energies relative to that in the S0 state in kcal/mol.



Page 26 of 42

26

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Silaaromaticity in Polycyclic Systems: A

J. Org. Chem. 2003, 68, 1168-1171.

(26) Jeevanandam, J.; Malar, E. J. P.; Gopalan, R.

Do Möbius Silabenzene and Möbius

Phosphabenzene Exist? Ab Initio MO and Density Functional Study of Electrocyclic Ring-Opening Reactions of Hetero-Dewar Benzenes Containing Silicon or Phosphorus Organometallics 2003, ACS Paragon Plus Environment


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28 22, 5454-5462. (27) Su, M-D. Mechanistic Study of the Photochemical Isomerization Reactions of Silabenzene. Organometallics 2014, 33, 5231-5237. (28) Maier, G.; Schöttler, K.; Reisenauer, H. P.

1,4-Disilabenzol - Dimethoxysilylen als Idealer

Synthesebaustein. Tetrahedron Letters 1985, 26, 4079-4082. (29) Dysard, J. M.; Tilley, T. D.; Woo, T. K. Ruthenium.

Silabenzene and Disilabenzene Complexes of


(30) Sen, S. S.; Roesky, H. W.; Meindl, K.; Stern, D.; Henn, J.; Stückl, A. C.; Stalke, D. Synthesis, Structure, and Theoretical Investigation of Amidinato Supported 1,4-disilabenzene. Chem. Commun. 2010, 46, 5873-5875. (31) Kinjo, R.; Ichinohe, M.; Sekiguchi, A.; Takagi, N.; Sumimoto, M.; Nagase, S. a Disilyne RSi≡SiR (R =

SiiPr[CH(SiMe

3)2]2)

Reactivity of

toward π-Bonds: Stereospecific Addition and a New

Route to an Isolable 1,2-Disilabenzene. J. Am. Chem. Soc. 2007, 129, 7766-7767. (32) Priyakumar, U.D.; Saravanan, D.; Sastry, G.N. Computational Study.

Isomers of Disilabenzene (C4Si2H6): A


(33) Nakamura, T.; Kudo, T.

The Planarity of the Heteroatom Analogues of Benzene: Energy

Component Analysis and the Planarization of Hexasilabenzene

J. Comput. Chem. 2019, 40, 581-

590. (34) Bjarnason, A.; Arnason, I.

Gas-Phase Reactions of M+ and [CpM]+ (M=Fe, Co, Ni) with

1,3,5-Trisilacyclohexane: First Evidence for the Formation of 1,3,5-Trisilabenzene Angew. Chem. Int. Ed. Engl. 1992, 31, 1633-1634. (35) King, R.A.; Vacek, G.; Schaefer, H.F. III

1,3,5-Trisilabenzene: Has it been Synthesized?

Mol. Struct.(THEOCHEM), 1995, 358, 1-14. (36) Nakamura, T.; Mesuda, A.; Kudo, T. their Major Valence Isomers

Theoretical Study for the Si/C-mixed Benzenes and

to be prepared for submission.

(37) Pierrefixe, S. C. A. H.; Bickelhaupt, F. M.

Aromaticity and antiaromaticity in the 4-, 6-, 8-,

and 10-Membered Conjugated Hydrocarbon Rings. J. Phys. Chem. A 2008, 112, 12816-12822. (38) Dunning, T.H.

Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The

Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007-1023. (39) Kendall, R.A.; Dunning, T.H.; Harrison, R.J.

Electron Affinities of the First-row Atoms

Revisited. Systematic Basis Sets and Wave Functions.

J. Chem. Phys. 1992, 96, 6796-6806.

(40) Schmidt, M. W.; Gordon, M. S. The Construction and Interpretation of MCSCF


J.

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29 Wavefunctions. Annu. Rev. Phys. Chem. 1998, 49, 233−266. (41) Aikens, C. M.; Webb, S. P.; Bell, R. L.; Fletcher, G. D.; Schmidt, M. W.; Gordon, M. S. A Derivation of the Frozen-orbital Unrestricted Open Shell and Restricted Closed Shell MP2 Analytic Gradient. Theor. Chem. Acc. 2003, 110, 233−253. (42) Hirao, K.

Multireference Møller-Plesset method. Chem. Phys. Lett. 1992, 190, 374-380.

(43) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479−483. (44) Bartlett, R. J.; Watts, J. D.; Kucharski, S. A.; Noga, J. Non- iterative Fifth-order Triple and Quadruple Excitation Energy Corrections in Correlated Methods. Chem. Phys. Lett. 1990, 165, 513−522. (45) Harvey, J. N.; Aschi, M. View.

Spin-forbidden Dehydrogenation of Methoxy Cation: a Statistical

Phys. Chem. Chem. Phys. 1999, 1, 5555-5563.

(46) Minezawa, N.; Gordon, M. S.

Optimizing Conical Intersections by Spin-Flip Density

Functional Theory: Application to Ethylene. J. Phys. Chem. A 2009, 113, 12749-12753. (47) West, A. C.; Schmidt, M. W.; Gordon, M. S.; Ruedenberg, K.

A Comprehensive Analysis in

Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. II. Strongly Correlated MCSCF Wave Functions.

J. Phys. Chem. A 2015, 119, 10360-10367.

(48) Note especially equation 3.14 within: West, A. C.; Schmidt, M. W.; Gordon, M. S.; Ruedenberg, K.

Intrinsic Resolution of Molecular Electronic Wave Functions and Energies in

Terms of Quasi-atoms and their Interactions. J. Phys. Chem. A 2017, 121, 1086-1105. (49) West, A. C.; Schmidt, M. W.; Gordon, M. S.; Ruedenberg, K.

A Comprehensive Analysis in

Terms of Molecule-Intrinsic, Quasi-Atomic Orbitals. III. The Covalent Bonding Structure of Urea. J. Phys. Chem. A 2015, 119, 10368-10375. (50) West, A. C.; Duchimaza-Heredia, J. J.; Gordon, M. S.; Ruedenberg, K.

Identification and

Characterization of Molecular Bonding Structures by ab initio Quasi-Atomic Orbital Analyses. J. Phys. Chem. A 2017, 121, 8884-8898. (51) Quasi-Atomic Bonding Analysis of Xe-containing Compounds. Ruedenberg, K.; Gordon, M. S.

Duchimaza-Heredia, J. J.;

J. Phys. Chem. A 2018, 122, 3442-3454.

(52) Schmidt, M. W.; Ivanic, J.; Ruedenberg, K.

Covalent Bonds are created by the Drive of

Electron Waves to Lower their Kinetic Energy through Expansion. J. Chem. Phys. 2014, 140, 204104/1-14, and see also references therein. (53) Chirgwin, B. H.

Summation Convention and the Density Matrix in Quantum Chemistry.

Phys.Rev. 1957, 107, 1013-1025.



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General Atomic and Molecular Electronic Structure System J. Comput. Chem. 1993, 14,

1347-1363. (55) Gordon, M.S.; Schmidt, M.W.

Advances in Electronic Structure Theory: GAMESS a Decade

Later, In Theory and Applications of Computational Chemistry: The First Forty Years; Dykstra, C. E.; Frenking, G.; Kim, K.S.; Scuseria, G.E. Eds., Elsevier: Amsterdam, 2005, pp 1167-1189. (56) Holme, T. A.; Gordon, M. S. ; Yabushita, S.; Schmidt, M. W.

Theoretical Studies of Cyclic

C2Si2H4 Molecules. Organometallics, 1984, 3, 583-586. (57) Maier, G.; Reisenauer, H. P.; Meudt, A.

Silylenes of the Elemental Composition C2H4Si2:

Generation and Matrix-Spectroscopic Identification. Eur. J. Org. Chem. 1998, 1291-1295. (58) Ishida, S.; Misawa, Y.; Sugawara, S.; Iwamoto, T.

Benzodisilacyclobutadienes: 8π electron

Systems with an Antiaromatic Silicon Ring. Angew. Chem.Int. Ed. 2017, 56, 13829-13832 (59) Bally, T.; Masamune, S.

Cyclobutadiene.

Tetrahedron 1980, 36, 343.

(60) Suzuki, K.; Matsuo, T.; Hashizume, D.; Fueno, H.; Tanaka, K.; Tamao, K.

A Planar

Rhombic Charge-separated Tetrasilacyclobutadiene. Science 2011, 33, 1306-1309 (61) Jutzi, P.

Low-valent Silicon in Formally Antiaromatic Four-membered Ring Systems.

Angew. Chem. Int. Ed. 2011, 50, 9020-9022. (62) Yang, Y-F.; Cheng, G-J.; Zhu, J.; Zhang, X.; Inoue, S.; Wu, Y-D.

Silicon-containing formal

4π-electron 4-membered Ring Systems: Antiaromatic, Aromatic, or Nonaromatic?

Chem. Eur. J.

2012, 18, 7516-7524. (63) Zhang, S-H.; Xi, H-W.; Lim K. H.; So, C-W. Ring.

An Extensive n, π, - electron Delocalized Si4

Angew. Chem. Int. Ed. 2013, 52, 12364-12367.

(64) Takanashi, K.; Lee, V. Ya.; Sekiguchi, A.

Tetrasilacyclobutadiene and Cyclobutadiene

Tricarboylruthenium Complexes: [4-(tBu2MeSi)4]Ru(CO)3 and [4-(Me3Si)4]Ru(CO)3. Organometallics 2009, 28, 1248-1251. (65) Kim, S.; Wang, S. Schaefer, H. F.

Structures, Energetics, and Aromaticities of the

Tetrasilacycclobutadiene Dianion and Related Compounds: (Si4H4)-2, (Si4H4)-22Li+, (Si4(SiH3)4)22Li+,

(Si4(SiH3)4)-22Na+, (Si4(SiH3)4)-22K+.

J. Phys. Chem. A 2011. 115, 5478-5487.

(66) Inoue, S.; Epping, J. D.; Irran, E.; Driess, M,.

Formation of a Donor-stabilized

Tetrasislscyclobutadiene Dication by a Lewis Acid Assited Reaction of an N-heterocyclicl Chorlo Silylene.

J. Am. Chem. Soc. 2011, 133, 8514-8517.

(67) For the S0 of the H4Si2C2, another structure more stable than the C2h by 7-8 kcal/mol was also


Page 31 of 42 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


31 obtained at the CASSCF(4,4)/aug-cc-pVDZ and CASSCF(12,12)/aug-cc-pVDZ levels of theory. The structure is similar to the C2h but the symmetry is lower Ci (Ag state).

However, it was found

to be less stable than the C2h at the single point calculation at the MRMP2/cc-pVTZ level on the CASSCF(4,4) geometry. Furthermore, the Ci becomes C2h upon CCSD(T)/aug-cc-pVDZ geometry optimizations. Therefore, we have adopted the C2h structure as the S0 of the H4Si2C2. (68) There is another four-membered ring triplet state with non-alternating CC-SiSi structure (shown in Figure S1) with similar energetics (12.7 kcal/mol) to the T1 and S1 states found here. (69) Gribanova, T. N.; Minyaev, R. M.; Minkin, V. I.; Boldyrev, A. I.

Metalcarbonyl Analogues

of Annelated Cyclooctatetraene and Cyclodecapentaene Derivatives with a Planar Core Cycle: a Quantum Chemical Study. Phys. Chem. Chem. Phys. 2018, 20, 27830-27837. (70) King, R.A.; Crawford. T.D.; Stanton, J.F.; Schaefer, H.F. III.

Conformations of

[10]Annulene: More Bad News for Density Functional Theory and Second-Order Perturbation Theory

J. Am. Chem. Soc. 1999, 121, 10788-10793.

(71) Dimitrova, M.; Sundholm, D.

The Aromatic Character of [10]Annulenes and

Dicupra[10]Annulenes from Current Density Calculations. Phys. Chem. Chem. Phys. 2018, 20, 1337-1346. (72) Ghadwal, R. S.; Roesky, H. W.; Propper, K.; Dittrich, B.; Klein, S.; Frenking, G.

A Dimer of

Silaisonitrile with Two-coordinate Silicon Atoms. Angew. Chem. Int. Ed. 2011, 50, 5374-5378.


The Journal of Physical Chemistry 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

S0#(D3h,#A1'):0.0(0.0) 1.473

T1#(Cs,#A’):47.6(58.2)#

Page 32 of 42

S1#(C2,#B):69.3(75.4)%

1.875

1.766

1.782 1.834

1.736

1.855

1.822

1.083

C2"Si4"C3%=%111.9% Si5"C1"Si6%=%120.1%%

C"Si"C%=%121.0% Si"C"Si%=%119.0%

T2#(Cs,#A”):67.0(60.6)#

C2"Si4"C3%=%120.2% Si5"C1"Si6%=%126.7%

S2#(Cs,#A”):71.1(79.8)#

S3#(Cs,#A’):91.4(103.4)# 1.873

1.830

1.857 1.791

1.792

1.831

1.866

1.831

1.763

C2"Si4"C3%=%105.7% Si5"C1"Si6%=%115.7%

C8"Si6"C7%=%114.0% Si5"C9"Si4%=%%123.2%

MEX(Cs):52.8(61.6)#

C8"Si6"C7%=%110.8% Si5"C9"Si4%=%%122.5%

CON(C1):80.3(84.5)# 1.487

1.888 1.746

1.828

1.872

1.889

1.829

1.822 1.803

C2"Si4"C3%=%109.2% Si5"C1"Si6%=%122.2%%

1.764 1.084

C"Si"C%=%88.5,117.8,110.9% Si"C"Si%=%125.6,115.6,119.3%

Figure 1 ACS Paragon Plus Environment

Page 33 of 42 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


S0#(D6h,#A1g):#0.0(0.0)#

T1#(C2v,#A1):#81.9(87.2)

1.399

S1#(D6h,#B2u):#109.4#(101.6) 1.437

1.471

&H6C6

1.362 1.471 1.081

1.079

C2#C1#C3&=&119.0& C1#C2#C4&=&120.5&

S0#(D3d,#A1g):0.0(0.0)#

T1#(C2,#B):#25.3(35.7) 2.348

2.275

&H6Si6

2.239 2.348

1.483

Si4#Si1#Si6&=&114.9& Si1#Si6#Si2&=&114.9&

S1#(Cs,#A”):#37.6(41.9)

2.348

2.324

2.239 2.348

SI4#Si3#Si5&=&111.5&& Si1#Si4#Si3&=&116.2&

1.487

Si4#Si1#Si6&=&113.9& Si1#Si6#Si2&=&113.5&

Figure 2



E

H6C6 (D6h)

H6Si3C3 (D3h)

Figure 3


Page 34 of 42

Page 35 of 42 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


S0#(C2h,#Ag):#0.0(0.0)#

T1#(Cs,#A”):#E1.3(12.6)#

S1#(C2h,#Bg):#E6.5(13.2)# C2#axis 1.080

C2#axis

1.780

1.780

1.476

1.476

1.474

1.491 1.078

1.080

C3"Si1"C4%=%87.3% C3"Si2"C4%=%94.5% Si1"C4"Si2%=%89.1% Si2"C4"Si1"C3%=%1.1%

C"Si"C%=%97.7% Si"C"Si%=%82.3% Si2"C4"Si1"C3%=%0.0%

MEX(D2h):#18.1(20.2)#

C3"Si1"C4%=%90.3% Si1"C3"Si2%=%89.7% Si1"C4"Si2%=%89.7% Si1"C4"Si2"C3%=%0.0%

CON(Cs):#22.2(37.7)#

1.080

1.086

1.839 2.656

2.582

1.831

1.075

%H4Si2C2

1.457

1.831

1.481

2.566

2.350%

1.885

1.771

1.501

1.860

1.870

1.489

2.815 1.870

1.860 1.086

C"Si"C%=%87.6% Si"C"Si%=%92.4%

C"Si"C%=%81.0,80.4% Si"C"Si%=98.0%

Figure 4



Page 36 of 42

S0#(D2h,#Ag):0.0(0.0)# T1#(D4h,#B3g):#16.9(7.3)# S1#(D4h,#A1g):#58.3(35.2)# 1.450

1.443

1.550

%H4C4%

1.357

1.076

1.077

1.076

S0#(D2d,#A1):#0.0(0.0)% T1#(C2h,#Bg):#14.9(24.6) S1#(C2h,#Bg):#10.0(23.0)# 2.382

%H4Si4%

2.264

2.332 2.326

%3.099%

1.481 2.356 1.481

Si1"Si3"Si2%=%83.3% Si1"Si3"Si2"Si4%=%37.8%

Si2"Si3"Si1%=%86.5% Si1"Si4"Si2%=%90.5% Si1"Si4"Si2"Si3%=18.4%

Si2"Si3"Si1%=%90.0% Si1"Si4"Si2%=%90.0% Si1"Si4"Si2"Si3%=0.0%

Figure 5


Page 37 of 42 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


LUMO

split%

E Degenerate%SOMOs

H4C4 (D4h)

HOMO

H4Si2C2 (D2h)



S0#(D4h,#A1g):#0.0(0.0)# 1.755

T1#(Cs,#A”):#36.1(42.0)% S1#(Cs,#A”):#26.4(37.3)# 1.843 1.740

1.088

1.809

1.475

1.770

C"Si"C%=%133.9% Si"C"Si%=%136.1%

T2#(C2,#A):#64.3(75.1)# 1.772 1.842 1.842 1.772

C"Si"C%=%123.1,131.8% Si"C"Si%=%140.4%

Page 38 of 42

1.789 1.778 1.789 1.789 1.789

C"Si"C%=%120.8,131.4% Si"C"Si%=%138.1,139.8%

C"Si"C%=%129.2% Si"C"Si%=%139.9%

T3#(Cs,#A’):65.3(77.6)# S2#(C2,#A):#84.2(77.7)% 1.842 1.772 1.772 1.842

1.778 1.813 1.863 1.789

C"Si"C%=%124.4,131.3% C"Si"C%=%123.3,127.6% Si"C"Si%=%140.5% Si"C"Si%=%129.3,135.9%

Figure 7


Page 39 of 42 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


LUMO

E

split Degenerate%SOMOs

H8C8 (D8h)

HOMO

H8Si4C4 (D4h)

Figure 8



D5h:#9.8#(0.6)9.5

Naphth(Cs):#0.0#(0.0)#0.0

Page 40 of 42

Tctcc(Cs):#5.4#(4.7)#5.5 1.773

1.770 1.759

1.753

1.762

1.759

1.759

1.758 1.764

1.759

1.763

1.475 1.092

Not%an%equilibrium%structure C"Si"C%=%140.0% C"Si"C%=%126.1,128.5,130.8% Si"C"Si%=%121.7,124.5,126.6% Si"C"Si%=%179.5%

C"Si"C%=%125.0,131.0,131.9% Si"C"Si%=%124.5,126.2,134.3%

%%KokoroESi(Cs):#3.7#(E9.9)#0.5 %KokoroEC(Cs):#0.4#(3.3)#2.1

1.752

1.762

1.772 2.667

3.078 1.752

1.772 1.757 1.740

1.747 1.747

1.762

1.776 1.755 1.753

C1:#4.1#(8.6)&10.2

1.770

C"Si"C%=%130.7%~%142.3% Si"C"Si%=%115.6%~%153.4%

1.749

1.758 1.754

C"Si"C%=%123.0,136.5,144.6% Si"C"Si%=%124.8,126.0,152.0%

Figure 9.


1.748

1.748 1.747

1.747

1.748

1.747 1.747

1.747

C"Si"C%=%139.1%~%139.5% Si"C"Si%=%142.9%~%146.7%

Page 41 of 42 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


%T1#(Cs,#A’):#38.4#(21.5)##

##S0#(Cs,#A’):#0.0(0.0)###

1.840

1.770 1.759

1.762

#S1#(Cs,#A”):#56.0(21.7)###

1.741

1.759

1.804

1.763

C"Si"C%=%126.1,128.5,130.8% Si"C"Si%=%121.7,124.5,126.6%

1.773

1.731

1.773

1.863

1.754

C"Si"C%=%113.2,120.2,127.7% Si"C"Si%=%126.9,132.4,133.8%

1.850

C"Si"C%=%111.3,121.2,129.6% Si"C"Si%=%126.2,132.2,136.8%


1.785


planar&equal&bonds?&

C4H4"≠" C6H6"="

≠"Si4H4"

4π"e,""

≠"Si6H6" 6π"e,""

TOC graphic


Page 42 of 42

C Alternately

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