Aromaticity of ionic structures: Investigation and application of NICS value and 4n + 2 rule

At DFT/B3LYP/6‐31G** theoretical level, C₆H and C (n = 0, ?2, and +2), C₆H and C (n = 0, ±2, ±4, and ±6), C₆H (n = 0–6), as well as C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures were investigated. Comparing NICS values of C₆H and C (n = 0, ?2, and +2), we discovered that C₆H, C₆H were antiaromatic, and C₆H₆, C₆, C, C had aromaticity with negative NICS values. According to research of C₆H and C (n = 0, ±2, ±4, ±6), C₆H (n = 0–6), we sustained that their σ and π orbit were different and the locations of electrons were difficult to confirm in ionic structures. Thus, neither 4n + 2 rule nor NICS values can precisely estimate the aromaticity of ionic structures. Besides, through WBI (NBO) research of C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures, we found that C₆H₆ was easy to accept electrons, contrarily, C₆ was prone to bestowing electrons. Moreover, C₆H₆ took the symmetrical carbon atoms form feeble interaction or bond, and C₆ used all carbon atoms to impact with other atom. C₆H₆ generated two contrapuntal single bonds with oxygen, sulfur, and nitrogen atoms, whereas C₆ molecule formed double bond with oxygen and nitrogen atoms, two conjoint single bonds with sulfur atom. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ab initio MO calculations of hyperfine coupling constants. A basis set study for 19F, 35Cl, 19F,and 35Cl

Hyperfine coupling constants (HFCC ) of the ¹⁹F and ³⁵Cl atoms and the ¹⁹F and ³⁵Cl radical anions have been calculated by the unrestricted Hartree–Fock (UHF ) method using polarization and diffuse functions with contracted double-zeta as well as uncontracted basis sets. The A_dip values are fairly insensitive to changes in the basis set and show good accordance with experimental and other theoretical studies. The isotropic HFCCS a_N of ¹⁹F, ¹⁹F, and ³⁵Cl show strong dependence on d functions and the state of contraction of the s, p set. Spin-projected UHF wave functions lead to better agreement with experiment.     

Probing the ultrafast photoelectron spectra of Br2 molecule

The time‐dependent‐wave‐packet method is applied to study the ionization of Br₂ molecule with four ionization processes. The ground state absorption makes the photoelectron to be left in the three final ionic states: Br (X²∑), Br (A²∏_u), and Br (B²∑), and each population of these ionic states is related with the laser intensities. The information of the dissociation can be got by analyzing the photoelectron features of the transient wave packet, which also suggests that an ionization process occurs during the dissociation, and the Br atoms that mainly resulted from the dissociation of Br₂ (C¹∏_u) are ionized at later time delays as the dissociation is nearly complete. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The role of d orbitals in tetrahedral hybrid orbitals of oxy-ions

The hybrid orbitals of tetrahedral oxy-ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO, PO, SO, ClO, and decrease in order of GeO, AsO, SeO, BrO. The bond strengths are also obtained for these ions. The hybrid Orbital of VO, CrO, and MnO are of the type d³s as the result of calculation.     

Dipole,quadrupole, octupole,and dipole–dipole–quandrupole polarizabilities and second hyperpolarizabilities at real and imaginary frequencies for helium in the 23S state: Dispersion-energy coefficients for interactions between He(23S) and H(12S), He(11S), He(23S), or H2(X1∑g+)

We have determined the dynamic dipole (α₁), quadrupole (α₂), octupole (α₃), and dipole–dipole–quadrupole (B) polarizabilities and the second hyperpolarizability tensor (γ) for the helium atom in its lowest triplet state (2³S). We have done so for both real and imaginary frequencies: in the former case, for a range of frequencies (ω) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss–Legendre grid running from zero to ?ω = 20 E_h. We have also determined the dispersion-energy coefficients C₆, C₈, and C₁₀ for the systems H(1²S)? He(2³S), He(1¹S)? He(2³S), and He(2³S)? He(2³S) and the C, C, C, C, and C coefficients for the interaction He(2³S)? H₂(X¹∑). Our values of the higher-order multipolar polarizabilities and of γ for the 2³S state of helium are, we believe, the first to be published. © 1993 John Wiley & Sons, Inc.     

Role of angular electron pair correlation in stabilizing C

A pseudo‐potential that was successfully employed in an earlier study by the Compton group is used to describe the binding of a single electron to a C₆₀ molecule to form C. Then, the interaction of a second electron with the C anion is treated in two manners. First, as performed in the earlier Compton study, a mean‐field (i.e., Hartree–Fock) approach is used to estimate the C‐to‐C energy difference for the singlet state of the dianion and, much as in the earlier study, this dianion is predicted to be unstable by ∼0.4 eV. Second, for this same singlet state, a configuration interaction wave function is employed that allows for the angular correlation of the two excess electrons, allowing them to avoid one another by moving on opposite sides of the C₆₀ skeleton. The energy of the dianion is lowered by 0.3 eV when angular correlation is included, suggesting that the singlet dianion is unstable with respect to electron loss by only ∼0.1 eV. A Coulomb barrier (>1 eV high) and angular momentum barriers then combine to trap electrons of singlet C from detaching, thus producing the very long observed lifetimes. In addition, the energy of the lowest triplet state of C is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Host-guest preorganization and complementarity: A molecular mechanics and molecular dynamics study of cation complexes of a cyclic urea-anisole spherand

Molecular mechanics and molecular dynamics calculations were carried out in vacuo for 1 and for the complexes of 1 with alkali metal cations and t-BuNH. The calculations identify perching and nesting conformations of the complexes not available from X-ray data. For the Li⁺ ? 1 complex, the MD simulations identify a new global minimum not found by the molecular mechanics calculation. In general, the net favorable ion-spherand complexation energy is due to the offset of the unfavorable reorganization energy of the spherand by the overwhelmingly favorable electrostatic component of the ion-spherand interaction energy. The host is least preorganized for the binding of Li⁺ and, even in its complexed conformation, presents the least steric complementarity to this ion. The complexation energy becomes significantly more favorable due to a large increase in the electrostatic complementarity of the ion binding site when the spherand adopts its complexed conformation. Correction of the calculated complexation energy by the experimental free energy of ion aqueous desolvation leads to results in line with the findings of Cram and co-workers that K⁺ is the most, and Li⁺ the least, favorably bound by 1 .     

Theoretical evidence of d‐orbital aromaticity in anionic metal X (X = Sc,Y, La) clusters

The equilibrium geometries, total electronic energies, and vibrational frequencies for singlet, triplet, and quinted states of three all‐metal X (X = Sc, Y, and La) anions and nine relevant neutral singlet MX₃ (M = Li, Na, K, X = Sc, Y, La) clusters are investigated with four density functional theory (DFT) and correlated ab initio methods B3LYP, B3PW91, MP2, and CCSD(T). To our knowledge, the theoretical study on these clusters composed of the transition metal Sc, Y, La is first reported here. The calculated results show that for the X clusters the singlet states with trigonal D_3h structures are the lowest energetically, while the neutral singlet MX₃ clusters each have two stable isomers: one trigonal pyramidal C_3v and one bidentate C_2v structures with the pyramidal C_3v isomer being ground state. In addition, we calculate the resonance energies (RE) and nucleus‐independent chemical shift (NICS) for the singlet trigonal X rings and show that these singlet trigonal X rings exhibit higher degree of aromaticity. The detailed molecular orbital (MO) analyses reveal that the singlet trigonal X anions have one delocalized σ‐type and one delocalized π‐type MOs, which follow the 4n + 2 electron counting rule, respectively and play an important role in rendering these species two‐fold aromaticity. Here, an explicit theoretical evidence is given to prove that the contribution to the two‐fold aromaticity of the singlet trigonal X (X = Sc, Y, and La) rings originates primarily from the d‐orbital bonding interactions of these component transition metal X atoms. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Sigma,pi, and delta wavefunction forms for the hydrogen molecule

Using variational Monte Carlo methods, we examine simple, explicitly‐correlated trial wavefunction forms for the X¹Σ, B¹Σ, a³Σ, b³Σ, I¹Π_g, C¹Π_u, i³Π_g, c³Π_u, J¹Δ_g, and j³Δ_g states of the hydrogen molecule. The energies produced by our best wavefunctions are slightly above the best values in the literature. When we combine our trial wavefunction forms with the generalized Feynman‐Kac path integral method, our results are in excellent agreement with the best nonrelativistic values for these systems except for the I¹Π_g state. Our best energy for this state, ?0.65951554(6), is lower by several microhartrees than that obtained by Wolniewicz [J Mol Spectrosc 1995, 169, 329]. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Explicit expression of the franck–condon factors in terms of the potentials of the two states

The calculus of the overlap integral for two states represented by the vibrational wave functions ψ and ψ is reduced to that of the Franck–Condon integral ?(0, x) = ∫ ψψ (t) dt. It is proved that for “numerical potentials” (as well as for a Dunham potential), this integral is given on each interval by a simple analytic expression in terms of the two potentials. The Franck–Condon factors are well determined by “coupling constants” related uniquely to the coordinates of the turning points of the potentials. An application to the band system BII? XΣ of Nα₂ is compared with the usual numerical methods.     

Theoretical study of one‐electron bonds in a series of high‐spin lithium–beryllium–hydrogen clusters: “Valence shell single‐electron repulsion” rule and electron localization function analysis

A series of high‐spin clusters containing Li, H, and Be in which the valence shell molecular orbitals (MOs) are occupied by a single electron has been characterized using ab initio and density functional theory (DFT) calculations. A first type (⁵Li₂, ⁿ⁺¹LiH_n+ (n = 2–5), ⁸Li₂H) possesses only one electron pair in the lowest MO, with bond energies of ～3 kcal/mol. In a second type, all the MOs are singly occupied, which results in highly excited species that nevertheless constitute a marked minimum on their potential energy surface (PES). Thus, it is possible to design a larger panel of structures (⁸LiBe, ⁷Li₂, ⁸Li, ⁴LiH⁺, ⁶BeH, ⁿ⁺³LiH (n = 3, 4), ⁿ⁺²LiH (n = 4–6), ⁸Li₂H, ⁹Li₂H, ²²Li₃Be₃ and ²²Li₆H), single‐electron equivalent to doublet “classical” molecules ranging from CO to C₆H₆. The geometrical structure is studied in relation to the valence shell single‐electron repulsion (VSEPR) theory and the electron localization function (ELF) is analyzed, revealing a striking similarity with the corresponding structure having paired electrons. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Redshifts and blueshifts of OH vibrations

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlations between these quantities, are presented for a water molecule and an OH^? ion in a uniform electric field of varying field strength. It is explained why a bound H₂O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH^? ion either a downshift or an upshift. The frequency-field variation is well accounted for by the expression Δν_OH ∝ ?E_∥·(dμ/dr_OH + 1/2 · ?μ/?r_OH). A frequency maximum occurs at the field strength where ?μ/?r_OH ～ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/dr_OH is negative (this is the situation for OH^?), and (2) the maximum frequency falls at a negative field when dμ/dr_OH is positive (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/dr_OH and ?μ/?r_OH. Correlation curves between the external linear force constant, k^ext, and r_OH,e are closely linear over the whole field range studied here, whereas the frequency vs. r_OH,e and force constants vs. r_OH,e correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the v vs. r_OH,e curves has a slope of ～ ?16,000 cm^?1/Å. © 1993 John Wiley & Sons, Inc.     

Possibility of proton passage through all metal aromatic Al42− ring in HAl4−

We report theoretical investigations on HAl in which the proton can move through the Al ring similar to umbrella inversion. The potential energy for the motion is a double well, with an activation barrier of 4.45 kcal/mol. We find that excitation to v = 6 vibrational levels should lead to easy passage of H⁺ through the ring. After considering the tunnelling effect, inversion rate at 298 K is calculated using transition state theory and is found to be 1.3 × 10¹⁰/s^?1. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Reaction mechanism of platinum dimer cation with ammonia based on the relativistic density functional study

The gas‐phase reactions between Pt and NH₃ have been investigated using the relativistic density functional approach (ZORA‐PW91/TZ2P). The quartet and doublet potential energy surfaces of Pt + NH₃ have been explored. The minimum energy reaction path proceeds through the following steps: Pt(⁴Σ_u) + NH₃ → q‐1 → d‐2 → d‐3 → d‐4 → d‐Pt₂NH⁺ + H₂. In the whole reaction pathway, the step of d‐2 → d‐3 is the rate‐determining step with a energy barrier of 36.1 kcal/mol, and exoergicity of the whole reaction is 12.0 kcal/mol. When Pt₂NH⁺ reacts with NH₃ again, there are two rival reaction paths in the doublet state. One is degradation of NH and another is loss of H₂. In the case of degradation of NH, the activation energy is only 3.4 kcal/mol, and the overall reaction is exothermic by 8.9 kcal/mol. Thus, this reaction is favored both thermodynamically and kinetically. However, in the case of loss of H₂, the rate‐determining step's energy barrier is 64.3 kcal/mol and the overall reaction is endothermic by 8.5 kcal/mol, so it is difficult to take place. Predicted relative energies and barriers along the suggested reaction paths are in reasonable agreement with experimental observations. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Symmetry breaking and its influence on the correlation energy for CF and CF ions

We have studied symmetry breaking in three open-shell systems: CF (D_2d and C_2v) and CF (D_3h) molecular ions. These different Hartree–Fock solutions are employed as starting points to calculate the correlation energy of these ions with perturbative, configuration interaction, and density functional methods. When symmetry-broken or symmetry-adapted wave functions are used, the correlation energy obtained with each method changes the order of stability of CF for a determined symmetry. Density functional methods produce higher correlation energies although they do not alter the order of stability of Hartree–Fock calculations. The behavior of correlation energy with different methods and the characteristics of the symmetry of wave functions are compared. A study of appearance energies for three different channels of the decomposition reaction of ionized carbon tetrafluoride are considered by using different methods with symmetry-broken or symmetry-adapted wave functions to calculate correlation energies. © 1994 John Wiley & Sons, Inc.     

Crossed-Molecular beam studies of the state-to-state reaction dynamics of charge transfer at low and intermediate energy

The microscopic, state-to-state reaction dynamics of charge transfer reactions are reviewed for the two system N(N₂, N₂)N and Ar⁺(N₂, Ar)N. The crossed molecular beam method demonstrates that the symmetric, molecular case proceeds by two mechanisms at low collision energy (< 0.7 eV). One of these involves an orbiting complex in which the total available energy is redistributed, essentially statistically. The second mechanism is a direct mechanism which involves nearly rectilinear trajectories and corresponds to exactly resonant charge transfer at low energy (0.7 eV) and charge transfer accompanied by vibrational excitation at higher energy (> 10 eV). The orbiting mechanism is dominant at low energies and disappears entirely with increasing collision energy. The unsymmetric, nearly resonant charge transfer reaction is direct at all energies. At very low collision energy (0.6 eV) and moderate collision energy (> 1.5 eV) the dominant reaction channel is the generation of N₂⁺(X² g, v = 1) with little rotational excitation. At 0.6 eV substantial angular scattering (including back-scattering) is observed; above 1.5 eV the trajectories are essentially rectilinear. At intermediate energies (0.8 < E < 1.3 eV) a very different mechanism is observed. All the energetically accessible vibrational states of N are formed, each with a preferred scattering angle at a given energy. Related experiments and theoretical models which rationalize some, but not all, of these results are described. The most intriguing puzzle is the “energy window” in which quantum-state specific, angular-specific reactive scattering is observed.     

Characteristic operators and unitarily invariant decomposition of hermitian operators

A set of characteristic operators {F} is proposed for performing the decomposition of p-particle Hermitian operators {D^p} to constitute irreducible components {D} of the unitary group D = FD^p, q = 0,1,2,…,p. For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p-particle Hermitian operators are obtained as a number of terms having invariant group-theoretical meaning.     

The effect of donor atoms on the complexation of alkali cations with spherands: A density functional investigation

Spherands are highly preorganized hosts composed of methoxy 1, fluoro 2, and cyano 3 benzene units attached to one another at their 2,6‐positions. Density functional theory calculations were used to investigate the complexation between these spherands and alkali metal ions (Li⁺, Na⁺, and K⁺) to understand the intrinsic factors affecting cation complexation. A comparison of binding energies for these spherands shows that, this order O? Me ? F ? CN. Although anisyl units are basically poor ligands for metal ions, the rigid placements of their oxygen during synthesis rather than during complexation are undoubtedly responsible for the enhanced binding and selectivity of the spherand. The ion–dipolar moiety interactions are found to be the main factors affecting the preference of external binding in the CN‐spherands. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The formation of Na+ and Na ions from Na*(2P) atoms near a tungsten surface. II. Extended diatomics-in-molecules models

Potential energy surfaces (PES ) for Na(²S, ²P) interacting with a tungsten surface partially covered with sodium ions are computed within the framework of the diatomics-in-molecules (DIM) method. A small number (1 to 10) of adsorbed sodium atoms are considered explicitly, the effect of the rest being taken into account through the fragment matrix elements in the DIM formulation. A physical model proposed previously to account for the experimental observation of Na⁺ and Na ions is supported by these calculations and, in addition, a new pathway to Na products is identified. The effect of including extra adsorbed atoms is discussed in terms of the molecular wave functions and a sensitivity analysis.     

Quantum chemistry study on B14, B,and B14H

The structure of B₁₄, B, and B₁₄H in octahedral symmetry has been investigated by ab initio calculations at the STO-3G and 4–31G levels. The relationship of molecular orbitals among them has been analyzed and it can be found that the number of valence bonding orbitals of high borane obeys the Wade rule. The similarities and difference between boron clusters and carbon clusters are also discussed. © 1994 John Wiley & Sons, Inc.