A benchmark quantum chemical study of the stacking interaction between larger polycondensed aromatic hydrocarbons

Large-scale electronic structure calculations were performed for the interaction energy between coronene, C₂₄H₁₂ with circumcoronene, C₅₄H₁₈, and between two circumcoronene molecules, in order to get a picture of the interaction between larger graphene sheets. Most calculations were performed at the SCS-MP2 level but we have corrected them for higher-order correlation effects using a calculation on the coronene-circumcoronene system at the quadratic CI, QCISD(T) level. Our best estimate for the interaction energy between coronene and circumcoronene is 32.1?kcal/mol. We estimate the binding of coronene on a graphite surface to be 37.4 or 1.56?kcal/mol per carbon atom (67.5?meV/C atom). This is also our estimate for the exfoliation energy of graphite. It is higher than most previous theoretical estimates. The SCS-MP2 method which reproduces the CCSD(T) and QCISD(T) values very well for smaller aromatic hydrocarbons, e.g., for the benzene dimer, increasingly overestimates dispersion as the bandgap (the HOMO-LUMO separation) decreases. The barrier to the sliding motion of coronene on circumcoronene is 0.45?kcal/mol, and for two circumcoronene molecules 1.85?kcal/mol (0.018 and 0.034?kcal/mol per C atom, respectively). This means that larger graphenes cannot easily glide over each other.     

Theoretical investigation of structure and stability of oligomers of LiH,NaH, LiF,and NaF

The molecules Li_nH_n, Na_nH_n, Li_nF_n, n=1,..., 4, and NaF and Na₂F₂ are investigated by means of extended basis set SCF and CEPA-PNO computations. In analogy to the D _2h structure of dimers, it is found that trimers have a planar cyclic D _3h equilibrium geometry. For the tetramer of LiH and NaH, the D _4h structure has about the same energy as the 3-dimensional T _d structure, whereas the latter is definitely favoured for Li₄F₄. Correlation effects are investigated for the oligomerization of LiH and the dimerization of LiF. The effect of electron correlation on corresponding E turns out to be small (<4 kJ/mol), except for the case that the T _d tetramer is involved which has a rather large correlation energy.     

MC-SCF and CI calculations on four isomers of Si6H6

The four isomers of Si₆ H₆, hexasilabenzene ( 1 ), hexasilaprismane ( 2 ), hexasila-Dewar benzene ( 3 ), and tris-(disilanediyl) ( 4 ), have been investigated, using highly correlated wavefunctions in conjunction with a local pseudopotential approach. At the Hartree-Fock level 1 (D_6h), 2 (D_3h), and 3 (C_2v) are established as minima by means of the harmonic vibrational frequencies. Inclusion of the most important correlation corrections via CI however, provokes a significant puckering of 1 resulting in a D_3d structure, 7.1 kJ/mol below the planar conformer. The detailed analysis shows unambiguously that the propensity to puckering is due solely to the correlation contributions from the σ framework while correlation of the π electrons is of little relevance. Isomer 2 turns out to be the most stable of the investigated isomers lying 41 kJ/mol below 1 (D_3d). Isomers 3 and 4 are more than 100 kJ/mol higher in energy. The Si? Si bond energies of 1 and 2 are determined as 251 and 176 kJ/mol, respectively.     

Conformational preferences of 34 valence electron A2X4 molecules: An ab initio Study of B2F4, B2Cl4, N2O4, and C2O

Ab initio molecular orbital structures and energies of B₂F₄, B₂Cl₄, N₂O₄, and C₂O have been calculated for both perpendicular D_2d and planar D_2h rotamers. The experimental trend toward greater preference for the D_2d forms in going from B₂F₄ to B₂Cl₄ is reproduced. N₂O₄ favors the planar conformation, although the rotation barrier is overestimated at the theoretical levels used. The oxalate dianion is calculated to be more stable in the D_2d conformation; the experimental planar arrangement in the solid may be due to crystal packing forces. The preferences for one conformation over another are small; analysis indicates that different effects may predominate in each case: π stabilization for B₂F₄, hyperconjugation for B₂Cl₄, lone-pair interactions for N₂O₄, and electrostatic repulsions for C₂O.     

Angular parameters of the overlap integrals of f-orbitals

Angular parameters are calculated for these integrals for - and -types in the complexes MX₆ (O_h and D_3h symmetry), MX₈ (O_h, D_4d, D_2d, D_6h, C_2V, and D_3h), and MX₉ (D_3h). Examples are given of the use of the angular parameters in considering coordination compounds of the lanthanide elements: stabilization energy of the addend field and geometry of the compounds in the ground and excited states.     

Quantum chemical study of the structure of tetrasilacyclobutadiene,its dication,and dianion

MINDO/3 calculations have indicated the instability of the D _2h planar geometrical configuration of tetrasilacyclobutadiene relative both to pyramidalization of the silicon atoms with the formation of a nonplanar C _2h structure and acoplanarization of the silicon skeleton leading to a C _s nonplanar bicyclic structure. Such distortions are also characteristic for the D _4h structure of the tetrasilabicyclobutadiene dianion. The dication of tetrasilabicyclobutadiene has D _2d nonplanar symmetry, similar to that for the dication of cyclobutadiene.Physical and Organic Chemistry Research Institute, Rostov State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 6, pp. 23–32, November–December, 1989.     

Some continuous geometry transitions and the consequences for a transition‐metal atom

By considering a transition‐metal ion in the field of some symmetrically placed ions, we illustrate the consequences of a continuous change of the structure of the ligands on the energies of the 3d electrons of the transition‐metal atom. Both a rigorous mathematical derivation and an analysis based on group theory are presented. For six ions surrounding the transition‐metal atom, a continuous D_∞h → D_3d → O_h→ D_3d→ D_6d transition is observed, whereas for four ions, a continuous D_{∞ h}→ D_2d→ T_d→ D_2d→ D_4d transition results. Although the two systems possess many similarities, interesting differences are found as well. Finally, we demonstrate that when including orbital interactions between the ligands and the transition‐metal atom, quantitative differences occur. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

<Emphasis Type="Italic">Ab initio</Emphasis> structural study of M(mda)<Subscript>2</Subscript> complexes (M = Be,Mg, Ca; mda = C<Subscript>3</Subscript>O<Subscript>2</Subscript>H<Subscript>3</Subscript>)

The structure of M(mda)₂ (M = Be, Mg, Ca; mda = C₃O₂H₃) bis-complexes was investigated by the ab initio Hartree-Fock method and by including electron correlation in terms of second order Möller-Plesset perturbation theory; for calculations we used triple-zeta valence basis sets complemented with polarization functions. Two most probable geometrical nuclear configurations (D _2h and D _2d ) are considered for each molecule. The structure with two mutually orthogonal chelate ligands (D _2d symmetry) corresponds to the potential energy surface (PES) minimum. The planar D _2h configuration corresponds to the first order saddle point on PES; consequently, its relative energy determines the height of the barrier to the D _2d D _2h D _2d intramolecular rearrangement. Correlation equations that relate the calculated values of equilibrium internuclear distances, force constants, and rearrangement barrier heights to the value of the ionic radius of the metal atom have been obtained. These correlations were employed to evaluate the molecular constants for Sr(mda)₂ and Ba(mda)₂. The theoretical data are compared with the available experimental literature data.Original Russian Text Copyright © 2004 by V. V. Sliznev, S. B. Lapshina, and G. V. GirichevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 611–623, July–August, 2004This revised version was published online in April 2005 with a corrected cover date.     

Dicyclohepta[ijkl,uvwx]rubicene with Two Pentagons and Two Heptagons as a Stable and Planar Non‐benzenoid Nanographene

Polycyclic aromatic hydrocarbons with hexagons/pentagons or hexagons/heptagons have been intensively investigated in recent years, but those with simultaneous presence of hexagons, pentagons and heptagons remain rare. In this paper, we report dicyclohepta[ijkl,uvwx]rubicene ( DHR ), a non‐benzenoid isomer of dibenzo[bc,kl]coronene with two pentagons and two heptagons. We developed an efficient and scalable synthetic method for DHR by using Scholl reaction and dehydrogenation. Crystal structure of DHR shows that the benzenoid rings, two pentagons and two heptagons are coplanar. The bond lengths analysis and the ICSS(1)zz and LOL‐π calculations indicate that the incorporation of two formal azulene moieties has an effect on the conjugated structure. The π‐electrons of benzenoid and pentagon rings are more delocalized. Cyclic voltammetry studies indicate that DHR shows multiple oxidation and reduction potentials. Interestingly, DHR exhibits unusual S₀ to S₂ absorption and abnormal anti‐Kasha S₂ to S₀ emission. Moreover, crystals of DHR exhibit semiconducting behaviour with hole mobility up to 0.082 cm² V^?1 s^?1.     

Jahn–Teller Effect in Circulenes: X‐ray Diffraction Study of Coronene and Corannulene Radical Anions

Single‐crystal X‐ray diffraction studies of two polyaromatic radical anions crystallized as sodium salts, namely [Na(DME)₃]⁺[C₂₀H₁₀^?] ( 1 ) and [Na(DME)₃]⁺[C₂₄H₁₂^?] ( 2 ) are reported. This allowed the first structural evaluation of Jahn–Teller (JT) effects for monoreduced circulenes and a comparison between bowl‐shaped corannulene and planar coronene. The C_s and D_2h symmetrical distortions are found to fit the experimental data for C₂₀H₁₀^.? and C₂₄H₁₂^.?, respectively. The continuous symmetry measure (CSM) analysis was carried out to provide a quantitative measure of the JT distortions in 1 and 2 . In addition, the X‐ray crystallographic results were fully supported by DFT calculations.     

Theory of spin triplet ground states ind 6 transition metal compounds and the effect of high-energy states on the nature of the ground state

The formation of spin triplet, quintet, and singlet ground states within the 3d ⁶ electron configuration is investigated inD _4h , andD _3d symmetries employing irreducible tensor operator methods. Significant differences in the possible ground states are encountered between a complete CI and spin-orbit interaction treatment and an approximate calculation within the cubic⁵ T ₂,¹A₁,³ T ₁, and³ T ₂ parents.     

Boron rings containing planar octacoordinate iron and cobalt

The boron rings containing planar octacoordinate transition metals, D _8h FeB₈ ²⁻, CoB₈ ⁻ and CoB₈ ³⁺, C _2v FeB₈, D _2h CoB₈ ⁺ and CoB₈, are optimized with all real vibrational frequencies at the B3LYP/6–311+G* level of the theory. The D _8h FeB₈ ²⁻ and CoB₈ ⁻ isomers are global minima, while D _8h CoB₈ ³⁺ is only local minimum. The electronic structure character of these systems is revealed by natural bond orbital (NBO) analysis, showing that the boron rings containing planar octacoordinate transition metals have stability and aromaticity with six π electrons. The aromaticity is confirmed by nucleus independent chemical shifts (NICS) calculations. Supported by the specialized research fund for the doctoral program of higher education (20060007030)     

The ionization energies of bridged [14]annulenes and of dicyclohepta[cd,gh] pentalene

The ionization energies J_J, of 1,6;8,13-alkanediylidene-[14]annulenes ( 2 to 5 ) and of dicyclohepta[cd,gh]pentalene ( 1 ) have been determined by photoelectron spectroscopy, using HeI radiation. The data are interpreted in terms of Koopmans' theorem (J_J = ?ε_J) on the basis of correlation diagrams and with the help of simple molecular orbital models. If the bridge is an ethane-, propane- or butane-diylidene group, the π-orbital sequence, in descending order of orbital energies, is (in C_2v): b₁, b₂, a₂, a₁. The sequence is due to a complicated and not uniquely definable interplay of inductive, conjugative and homoconjugative effects. A detailed analysis of these effects suggests that the effective angle of twist between two consecutive basis-AOs 2p_μ, 2p_ν of the peripheral π-system should be smaller than the twist angles θ_μν determined by X-ray analysis, i.e. that the pi;-ribbon adjusts elastically and is no longer locally orthogonal to the σ-frame. In the non-alternant hydrocarbon 1 of symmetry D_2h, the sequence is 2b_2g, 3b_1u, 2b_3g, 1a_u, 2b_1u. The sequence 3b_1u above 2b_3g, _i.e. the reverse of b₂ above a₁ in the bridged [14]annulenes, is explained as being due to the interaction of the semilocalized perimeter orbitals b_1u and b_3g with the bonding (π(B_1u))and antibonding (π*(B_3g)) orbital of the central double bond. In 2 the replacement of the two latter orbitals by the Walsh-orbitals of the cyclopropane moiety leads to the sequence b₁, b₂, a₁, a₂. From the data observed for 1 to 5 and for 1,6-methano-[10]annulene [11], a crude estimate for the orbital energies of the hypothetical all-cis D_10h-[10]- and D_14h-[14]annulenes can be derived.     

Fuzzy Symmetry Characteristics of Propadine Molecule

The fuzzy symmetry characteristics for the internal-rotation of propadine were analyzed using the fuzzy symmetry theory for molecule and molecular orbital (MO). In the process of rotation, three different symmetry point groups D_2h, D_2d, and D₂ were considered. Using the D_4h point group, which is the minimal point group including all symmetry elements of D_2h, D_2d, and D₂, we can analyze the fuzzy symmetry for this process. The elements included in D_4h point group can be classified to four subsets: (i) G0—it includes all the elements in D₂ point group, also belongs to all the above three point groups of D_2h, D_2d, and D₂; (ii) G1—it includes the elements in D_2h point group, but not in D_2d point group; (iii) G2—it includes the elements in D_2d point group, but not in D_2h point group; (iv) G3—it includes the elements in D_4h point group, but not in D_2h or D_2d point group. On the basis of the above four subsets, we analyzed the membership functions and the regularity of variation in MOs for the internal-rotation of propadine.     

Tetra-hydrides of the third-row transition elements: spin–orbit coupling effects on geometrical deformation in WH4 and OsH4

The dissociation energies of MH₄ (M =  La, Hf–Hg) were computed using full optimized reaction space (FORS) multi-configuration self-consistent field (MCSCF) and second-order multi-reference Møller–Plesset perturbation methods with the SBKJC basis sets augmented by a set of polarization functions (SBKJC(f,p)). It was shown that of the molecules examined, only four tetra-hydrides HfH₄, TaH₄, WH₄, and OsH₄ with T_d symmetry are lower in energy than the corresponding dissociation limits. For WH₄ and OsH₄, the potential energy surfaces from the D_4h to the T_d structure were explored from both theoretical calculations and symmetry arguments based on the pseudo-Jahn- Teller effect. As for WH₄, it is found that the ground state could be ³E_g, ³A_2g, or ³B_2g at the D_4h structure. The present calculations suggest that the ground state is ³E_g, and that this state is stabilized by the e_u deformation into a C_2v structure (³B₁) and then sequentially to the most stable T_d structure (³A₂). If the molecular system is promoted to the lowest ³B_2g state, the D_4h structure can directly deform into the most stable T_d structure along the b_2u vibrational mode. For OsH₄, the ground state (⁵B_1g) at the D_4h structure deforms into a D_2d structure and the resulting ⁵B₂ state strongly interacts with the lowest ³E and ¹A₁ states due to the spin-orbit couplings (SOCs). As a result, it was shown that the relativistic potential energy of the lowest spin-mixed state (ground state) monotonically decreases along the D_2d deformation path from the D_4h to the T_d structure.     

Dicyclohepta[ijkl,uvwx]rubicene with Two Pentagons and Two Heptagons as a Stable and Planar Non-benzenoid Nanographene

Polycyclic aromatic hydrocarbons with hexagons/pentagons or hexagons/heptagons have been intensively investigated in recent years, but those with simultaneous presence of hexagons, pentagons and heptagons remain rare. In this paper, we report dicyclohepta[ijkl,uvwx]rubicene ( DHR ), a non-benzenoid isomer of dibenzo[bc,kl]coronene with two pentagons and two heptagons. We developed an efficient and scalable synthetic method for DHR by using Scholl reaction and dehydrogenation. Crystal structure of DHR shows that the benzenoid rings, two pentagons and two heptagons are coplanar. The bond lengths analysis and the ICSS(1)zz and LOL-π calculations indicate that the incorporation of two formal azulene moieties has an effect on the conjugated structure. The π-electrons of benzenoid and pentagon rings are more delocalized. Cyclic voltammetry studies indicate that DHR shows multiple oxidation and reduction potentials. Interestingly, DHR exhibits unusual S₀ to S₂ absorption and abnormal anti-Kasha S₂ to S₀ emission. Moreover, crystals of DHR exhibit semiconducting behaviour with hole mobility up to 0.082 cm² V⁻¹ s⁻¹.     

Approximate symmetry-breaking in the independent particle model of monocyclic completely conjugated polyenes

We examine the singlet stability of symmetry adapted, restricted Hartree-Fock (RHF) solutions and the implied symmetry breaking for various planar, π-electron systems with conjugated double bonds as described by the semiempirical Pariser-Parr-Pople Hamiltonian. In particular, we explore the energy and charge- density waves (CDWs) in various real and hypothetical structures that result by a systematic deformation of the nuclear framework: we start with a highly symmetric cyclic polyene C _N H _N having a nondegenerate ground state (N = 2n = 4ν + 2, ν = 1, 2,...), whose sites form a regular N-gon (D _Nh point group), and proceed to structures with lower symmetry (D _6h , D _3h , D _2h point groups), or with only the planar symmetry of the conjugated π-electron system (C _1h ). The objective of this study is to explore the phenomenon that could be referred to as a breaking of an approximate symmetry or an implied symmetry breaking.     

Studies of Fe2(CO)9 Formation in the Thermolysis of Fe(CO)5 Using Ab Initio Calculations of Fe(CO)5 and Fe(CO)4

Ab initio calculations using the GAMESS program package in the atomic basis TZV (Fe: (14s, 11p, 6d)/[10s, 8p, 3d]; C, O: (11s, 6p)/[5s, 3p]) were performed with account taken of the correlation with the second-order Möller–Plesset (MP2) perturbation theory to predict a new conformer Fe(CO)₄ (with D _4h symmetry). This conformer has a square planar configuration in the ground singlet electronic state and is a mild electrophile produced by dissociation of Fe(CO)₅ along the axial Fe–C bond. The process of nucleation of iron nanoparticles Fe(CO)₅ + Fe(CO)₄ Fe₂(CO)₉ is supposed to occur in two stages. The first stage is an orbital-controlled reaction which should be monitored as an increase in medium polarity and temperature. It should proceed with participation of only one of the stable conformers of the nucleophile Fe(CO)₅, namely, a mild conformer with square-pyramidal structure (C _4v ) rather than a hard but energetically more advantageous conformer with trigonal–bipyramidal structure (D _3h ). The structure of a prereaction complex was discussed.     

Carbometallic derivatives of hydroborons C2h and D5d: A list of substitution isomers

The problem of determining the number and type of X-substituted (where X represents certain substituents) carbometallic derivatives of hydroborons [Co(C₂B₉H₁₁)₂]⁻ C _2h and [Co(C₅B₆H₁₁)₂]⁻ D _5d (from apexes) was solved on the basis of G. Pólya’s theorem by means of combinatory analysis. The formulae of symmetry Z and generating functions of the number of achiral substitution isomers were determined. The family distributions of isomers (depending on the type and number of substituents) and the sites of possible substitution depending on the number m were determined. Mono and di-X-substituted isomers of [Co(C₅B₆H₁₁)₂]⁻ C _2h , as well as mono and di-X-substituted isomers of [Co(C₅B₆H₁₁)₂]⁻ D _5d , were identified. The procedure for plotting an additive model of calculating the properties of isomers of apical substitution of [Co(C₅B₆H₁₁)₂]⁻ D _5d was described on the basis of splitting of polygonal numbers (K ₃, K _TE, K ₅, and so on) of Pascal triangle, upon use of which there is no randomization in the choice of parameters of calculation model. The additive schemes containing 7 and 25 parameters for the calculation of properties of X-substituted carbometallic derivative of hydroboron [Co(C₅B₆H₁₁)₂]⁻ D _5d to various approximations were obtained.