Natural Bond Orbital Theory of Pseudo-Jahn-Teller Effects.

We describe a unified picture of symmetry-breaking electronic interactions that are usually described as "pseudo-Jahn-Teller (PJT) effects" and attributed to vibronic coupling but can also be associated with hyperconjugative donor-acceptor interactions in the framework of natural bond orbital (NBO) and natural resonance theory (NRT) analysis. We show how NBO/NRT descriptors offer a simplified alternative to the vibronic coupling picture of PJT effects that yields both improved cause-effect specificity and chemically enriched understanding of symmetry-breaking phenomena but with no necessary input from ground-state vibrational or excited-state electronic properties. Comparative NBO/NRT vs vibronic coupling analyses of PJT effects are illustrated for two well-known cases: trans-bending in Si2H4 and higher Group-14 homologues of ethylene and chain-kinking in cyclopentadienylideneketene (C5H4CCO) and related cumulene ketones. The conceptual and practical advantages of the NBO-based hyperconjugative approach may be expected to extend to numerous PJT-type symmetry-breaking phenomena throughout the chemical sciences.

Exploring the Origin of the Generalized Anomeric Effects in the Acyclic Nonplanar Systems.

Contrary to the published conclusions in the literature concerning the origin of the generalized anomeric relationships in open-chain nonplanar systems, its origin has remained an open question. In order to explore the origin of the generalized anomeric relationships in open-chain nonplanar systems, we assessed the roles and contributions of the effective factors on the conformational properties of methyl propargyl ether (1), methyl propargyl sulfide (2), and methyl propargyl selenide (3) by means of the G3MP2, CCSD(T), MP2, LC-ωPBE, and B3LYP methods and natural bond orbital (NBO) interpretations. We examined the contributions of the hyperconjugative interactions on the conformational preferences of compounds 1-3 by the deletions of the orbitals overlapping from the Fock matrices of the gauche- and anti-conformations. The trend observed for energy changes in the Fock matrices justify the variations of the gauche-conformations preferences going from compound 1 to compound 3, revealing that the hyperconjugative interactions are solely responsible for the generalized anomeric relationships in compounds 1-3. Accordingly, the conclusions published in the literature concerning the origin of the generalized anomeric effect in the acyclic nonplanar compounds should be revised by these findings. The Pauli exchange type repulsions (PETR) are in favors of the gauche-conformations and the variations of the PETR differences between the gauche- and anti-conformations of compounds 1-3 correlate well with their gauche-conformations preferences, revealing that the generalized anomeric relationships in compounds 1-3 have also the Pauli exchange-type repulsions origin. The resemblance between the preorthogonal natural bond orbitals (that are involved in the hyperconjugative interactions) and their corresponding molecular orbitals have been investigated.

Symmetry breaking in the planar configurations of disilicon tetrahalides: Pseudo-Jahn-Teller effect parameters, hardness and electronegativity.

CCSD(T), MP2, LC-BLYP, LC-ωPBE and B3LYP methods with the Def2-TZVPP basis set and natural bond orbital (NBO) interpretations were performed to investigate the correlations between the Pseudo-Jahn-Teller Effect (PJTE) parameters [i.e. vibronic coupling constant values (F), energy gaps between reference states (Δ) and the primary force constant (K0)], structural and configurational properties, global hardness, global electronegativity, natural bond orders, stabilization energies associated with electron delocalizations and natural atomic charges of disilicon tetrafluoride (1), disilicon tetrachloride (2), disilicon tetrabromide (3) and disilicon tetraiodide (4). All levels of theory showed the trans-bent (C2h) configurations as the energy minimum structures of compounds 1-4, and the flap angles between the X2Si planes and the Si=Si bonds in the distorted (C2h) configurations decrease from compound 1 to compound 4. The negative curvatures of the ground state electronic configurations and the positive curvatures of the excited states of the adiabatic potential energy surfaces (APESs) which resulted from the mixing of the ground Ag and excited B2g states are due to the PJTE (i.e. PJT(Ag + B2g) ⊗ b2g problem). Contrary to the usual expectation, with the decrease of the energy gaps between reference states (Δ), the PJTE stabilization energy, E(PJT), decreases from compound 1 to compound 4. The canonical molecular orbital (CMO) analysis revealed that the contributions of the ψ(HOMO)(b3u) and ψL(UMO)(b1u) molecular orbitals in the vibronic coupling constant (F) decrease from compound 1 to compound 4. This fact clearly justifies the decrease of the vibronic coupling constant (F) and the primary force constant (the force constant without the PJTE) values on going from compound 1 to compound 4, leading to the decrease of the negative curvatures of the ground state electronic configuration curves of their corresponding APESs. The results obtained showed that the stabilization energies associated with the mixing of the distorted donor π(Si-Si)(b(u)) bonding and acceptor σ(Si-Si)*(b(u)) antibonding orbitals along the b2g bending distortions decrease from compound 1 to compound 4. This fact reasonably explains the increase of the Si-Si natural bond orders (nbo) on going from compound 1 to compound 4. With the increase of the Si-Si natural bond orders, the corresponding E(PJT) decreases from compound 1 to compound 4. Importantly, the variations of the global hardness (η) differences (Δ[η(C2h) - η(D2h)]) do not correlate with the trend observed for their corresponding total energy differences, justifying that the configurational properties of compounds 1-4 do not obey the maximum hardness principle. Interestingly, the trans-bent (C2h) configurations of compounds 1-4 are more electronegative than their corresponding planar (D2h) forms and the variations of their global electronegativity (χ) differences (Δ[χ(C2h) - χ(D2h)]) succeed in accounting for the decrease of the E(PJT) stabilization energies for the D2h → C2h conversion processes on going from compound 1 to compound 4.

The origin of the anomeric effect: probing the impacts of stereoelectronic interactions.

To gain further insight on the origin of the anomeric effect [stabilization energies associated with electron delocalization (SE), electrostatic models associated with the dipole-dipole interactions (EM) and Pauli exchange-type repulsions (PETR)], the correlations between SE, EM, PETR, bond-orders, donor and acceptor orbital energies and occupancies, structural parameters and configurational behavior of 2,3-difluoro-1,4-oxathiane (1), 2,3-dichloro-1,4-oxathiane (2), and 2,3-dibromo-1,4-oxathiane (3) as well as 2,5-difluoro-1,4-oxathiane (4), 2,5-dichloro-1,4-oxathiane (5), and 2,5-dibromo-1,4-oxathiane (6) were investigated by means of the complete basis set (CBS-4), hybrid density functional theory method (B3LYP/6-311+G**) and natural bond orbital (NBO) interpretations. The differences in the total energies among four possible configurations of compounds 1-6 do not correlate with the differences in their corresponding SE, EM or PETR values but can be controlled by their cooperative or uncooperative impacts. The results obtained showed that the SE has a determining impact on the structural properties of compounds 1-6 but fails to account solely for the variations of the energy differences between the configurations in compounds 1-6. The SE and PETR components are in favor of the (ax,ax) forms (the most stable configuration) going from compound 1 to compound 3 but the EM has the opposite impact; therefore, these factors have counterintuitive impacts on the configurational properties of compounds 1-3. Because there are no significant dipole moment values for the (ax,ax) and (eq,eq) forms of compounds 4-6, the energy differences between these forms can result from the conflict between the SE and PETR components. Therefore, the conclusions published previously in the literature about the origin of the anomeric effect should be reexamined.

Conformational behaviors of trans-2,3- and trans-2,5-dihalo-1,4-diselenanes. A complete basis set, hybrid-density functional theory study and natural bond orbital interpretations.

Complete basis set CBS-4, hybrid-density functional theory (hybrid-DFT: B3LYP/6-311+G**) based methods and natural bond orbital (NBO) interpretations have been used to examine the contributions of the hyperconjugative, electrostatic, and steric effects on the conformational behaviors of trans-2,3-dihalo-1,4-diselenane [halo = F (1), Cl (2), Br (3)] and trans-2,5-dihalo-1,4-diselenane [halo = F (4), Cl (5), Br (6)]. Both levels of theory showed that the axial conformation stability, compared to its corresponding equatorial conformation, decreases from compounds 1 → 3 and 4 → 6. Based on the results obtained from the NBO analysis, there are significant anomeric effects for compounds 1-6. The anomeric effect associated with the electron delocalization is in favor of the axial conformation and increases from compounds 1 → 3 and 4 → 6. On the other hand, dipole moment differences between the axial and equatorial conformations [Δ(µ(eq)-µ(ax)] decrease from compounds 1 → 3. Although Δ(µ(eq)-µ(ax)) parameter decreases from compound 1 to compound 3, the dipole moment values of the axial conformations are smaller than those of their corresponding equatorial conformations. Therefore, the anomeric effect associated with the electron delocalizations (for halogen-C-Se segments) and the electrostatic model associated with the dipole-dipole interactions fail to account for the increase of the equatorial conformations stability on going from compound 1 to compound 3. Since there is no dipole moment for the axial and equatorial conformations of compounds 4-6, consequently, the conformational preferences in compounds 1-6 is in general dictated by the steric hindrance factor associated with the 1,3-syn-axial repulsions. Importantly, the CBS-4 results show that the entropy difference (∆S) between the equatorial axial conformations increases from compounds 1 → 3 and 4 → 6. This fact can be explained by the anomeric effect associated with the electron delocalization which affects the C2-Se bond orders and increase the rigidity of the corresponding rings. The Gibbs free energy difference values between the axial and equatorial conformations (i.e. ΔG(ax-ax) and ΔG(eq-eq)) of compounds 1 and 4, 2 and 5 and also 3 and 6 have been calculated. The correlations between the anomeric effect, electrostatic model, ΔG(eq-ax), ΔG(ax-ax), ΔG(eq-eq), bond orders, dipole-dipole interactions, structural parameters and conformational behaviors of compounds 1-6 have been investigated.

Natural bond orbital, nuclear magnetic resonance analysis and hybrid-density functional theory study of σ-aromaticity in Al2F6, Al2Cl6, Al2Br6 and Al2I6.

Natural bond orbital (NBO), nuclear magnetic resonance (NMR) analysis and hybrid-density functional theory based method (B3LYP/Def2-TZVPP) were used to investigate the correlation between the nucleus-independent chemical shifts [NICS, as an aromaticity criterion], σ Al(1)-X2(b) → σ*Al(3)-X4(b) electron delocalizations and the dissociation energies of Al2F6, Al2Cl6, Al2Br6 and Al2I6 to 2AlX3 (X = F, Cl, Br, I). The results obtained showed that the dissociation energies of Al2F6, Al2Cl6, Al2Br6 and Al2I6 decrease from Al2F6 to Al2I6. Like aromatic molecules, these compounds have relatively significant negative NICSiso(0) values. Clearly, based on magnetic criteria, they exhibit aromatic character and make it possible to consider them as σ-delocalized aromatic species, such as Möbius σ-aromatic species. The σ-aromatic character which is demonstrated by their NICSiso(0) values decreases from Al2F6 to Al2I6. The NICSiso values are dominated by the in-plane σ22 (i.e., σyy, the plane containing halogen atoms bridged) chemical shift components. The increase of the NICSiso values explains significantly the decrease of the corresponding dissociation energies of Al2F6, Al2Cl6, Al2Br6 and Al2I6. Importantly, the NBO results suggest that in these compounds the dissociation energies are controlled by the stabilization energies associated with σ Al(1)-X2(b) →σ*Al(3)-X4(b) electron delocalizations. The decrease of the stabilization energies associated with σ Al(1)-X2(b) →σ*Al(3)-X4(b) electron delocalizations is in accordance with the variation of the calculated NICSiso values. The correlations between the dissociation energies of Al2F6, Al2Cl6, Al2Br6 and Al2I6, σ Al(1)-X2(b) →σ*Al(3)-X4(b) electron delocalizations, natural atomic orbitals (NAOs) and NICSiso values have been investigated.

Pseudo Jahn-Teller effect and natural bond orbital analysis of structural properties of tetrahydridodimetallenes M2H4, (M = Si, Ge, and Sn).

The structural properties of ethene (1) and tetrahydridodimetallenes M(2)H(4) [M = Si (2), Ge (3), and Sn (4)] have been examined by means of CCSD(T)/Def2-TZVPP, MP4(SDTQ)/Def2-TZVPP, and B3LYP/Def2-TZVPP levels of theory and natural bond orbital analysis (NBO) interpretations. The results obtained showed the expected planar ground state structure for compound 1 (D(2h) symmetry) but trans-bent ground state structures for compounds 2-4 (C(2h) symmetry). The distortions of the high-symmetry configurations of compounds 2-4 are due to the pseudo Jahn-Teller effect (PJTE), which is the only source of instability of high-symmetry configurations in nondegenerate states. The distortions are due to the mixing of the ground A(g) and excited B(2g) states [i.e., HOMO(B(3u)) → LUMO + 3(B(1u)) for compound 1, HOMO(B(3u)) → LUMO + 2(B(1u)) for compound 2, and HOMO(B(3u)) → LUMO + 1(B(1u)) for compounds 3 and 4]. Importantly, the higher-lying B(1g), B(2u), and B(2g) states are not involved in the PJT interactions. The energy gaps between reference states (Δ) in the undistorted configurations decrease from compound 1 to compound 4, and the PJT stabilization energies increase. Therefore, the primary force constant of the ground state in the Q((b2g)) direction (K(0)) decreases from compound 1 to compound 4. This fact can be justified by the valence isoelectronic systems of these compounds (having similar vibronic coupling constants, F). For the purpose of more chemical transparency, the NBO results were analyzed, and their relation to the PJT interactions has been revealed. The NBO analysis showed that stabilization energy associated with π(M-H) (b(u)) → σ*(M═M) (b(u)) electron delocalization (i.e., the mixing of the distorted b(u) molecular orbitals along the b(2g) bending distortions) increases from compound 1 to compound 4. Also, by using the hybridized orbitals obtained, an n parameter is defined. The NBO results revealed that the n values in the mean hybrid orbitals (sp(n)) increase from compound 1 to 4. The correlations between the PJT stabilization energies, bond orders, n values, π(M-M) → σ*(M═M) electron delocalizations, and structural parameters of compounds 1-4 have been investigated.

On the covalent character of rare gas bonding interactions: a new kind of weak interaction.

At the averaged quadratic coupled-cluster (AQCC) level, a number of selected rare gas (Rg) containing systems have been studied using the quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO), and several other analysis methods. According to the criteria for a covalent bond, most of the Rg-M (Rg = He, Ne, Ar, Kr, Xe; M = Be, Cu, Ag, Au, Pt) bonds in this study are assigned to weak interactions instead of van der Walls or covalent ones. Our results indicate that the rare gas bond is a new kind of weak interaction, like the hydrogen bond for example.

Structural evidence of anomeric effects in the anesthetic isoflurane.

The conformational and structural properties of the inhalational anesthetic isoflurane (1-chloro-2,2,2-trifluoroethyl difluoromethyl ether) have been probed in a supersonic jet expansion using Fourier-transform microwave (FT-MW) spectroscopy. Two conformers of the isolated molecule were identified from the rotational spectrum of the parent and several (37)Cl and (13)C isotopologues detected in natural abundance. The two most stable structures of isoflurane are characterized by an anti carbon skeleton (τ(C(1)-C(2)-O-C(3)) = 137.8(11)° or 167.4(19)°), differing in the trans (AT) or gauche (AG) orientation of the difluoromethyl group. The conformational abundances in the jet were estimated from relative intensity measurements as (AT)/(AG) ≈ 3:1. The structural preferences of the molecule have been rationalized with supporting ab initio calculations and natural-bond-orbital (NBO) analysis, which suggest that the molecule is stabilized by hyperconjugative effects. The NBO analysis of donor-acceptor (LP → σ*) interactions showed that these stereoelectronic effects decrease from the AT to AG conformations, so the conformational preferences can be accounted for in terms of the generalized anomeric effect.

Stereoelectronic interaction effects on the conformational properties of hydrogen peroxide and its analogues containing S and Se atoms: an ab initio, hybrid-DFT study and NBO analysis.

Ab initio molecular orbital (MP2/6-311+G**//MP2/6-31G+G**) and hybrid-density functional theory (B3LYP/6-311+G**//MP2/6-311+G**) methods and NBO analysis were used to study the stereoelectronic interaction effects on the conformational properties of hydrogen peroxide (1), hydrogen disulfide (2) and hydrogen diselenide (3). The results showed that the Gibbs free energy difference (G(T)-G(S)) values at 298.15K and 1atm between the skew (S) and trans (T) conformations (DeltaG(T-S)) increase from compound 1 to compound 2 but decrease from compound 2 to compound 3. The C conformations of compounds 1-3 are less stable than their S and T conformations. Based on these results, the racemization processes of the axial symmetrical (C(2) symmetry) conformations of compounds 1-3 take place via their T conformations. Based on the optimized ground state geometries using the MP2/6-311+G** level of theory, the NBO analysis of donor-acceptor (bond-antibond) interactions revealed that the stabilization (resonance) energy associated with LP(2)M2-->sigma*(M3-H4) electronic delocalization for the S conformations of compounds 1-3 are 1.35, 5.94 and 4.68 kcal mol(-1), respectively. There is excellent agreement between the variations of the calculated DeltaG(T-S) and stabilization (resonance) energies associated with LP(2)M2-->sigma*(M3-H4) electronic delocalization for the S conformations of compounds 1-3. The correlations between resonance energies, orbital integrals, dipole moments, bond orders, structural parameters and conformational behaviors of compounds 1-3 have been investigated. Test were made of complete basis set methods (CBS-QB3, CBS-4 and CBS-Q), the first two gave results essentially indistinguishable from those we used, but the CBS-Q results were in disagreement with experimental and other theoretical results.

Prediction of toxicity of nitrobenzenes using ab initio and least squares support vector machines.

A quantitative structure-property relationship (QSPR) study is suggested for the prediction of toxicity (IGC50) of nitrobenzenes. Ab initio theory was used to calculate some quantum chemical descriptors including electrostatic potentials and local charges at each atom, HOMO and LUMO energies, etc. Modeling of the IGC50 of nitrobenzenes as a function of molecular structures was established by means of the least squares support vector machines (LS-SVM). This model was applied for the prediction of the toxicity (IGC50) of nitrobenzenes, which were not in the modeling procedure. The resulted model showed high prediction ability with root mean square error of prediction of 0.0049 for LS-SVM. Results have shown that the introduction of LS-SVM for quantum chemical descriptors drastically enhances the ability of prediction in QSAR studies superior to multiple linear regression and partial least squares.