Study of chemical bonding in H2 and HF molecules: Wave function and density functional theory (DFT) parameters approach

Balint Kurti's Fourier grid Hamiltonian method is employed to obtain the molecular wave function and equilibrium bond length for H₂ and HF molecules. The density functional theory parameter, namely, the chemical hardness (η) value, was determined for some diatomic hydride molecules using this wave function and the results are found to be in good agreement with the values obtained from the ab initio HF–SCF method. A new formula for chemical hardness (η=1/2Dr, where D is the proportionality constant and r is the internuclear distance) is introduced in binding energy and change of hardness equations to determine the chemical hardness and chemical potential values for different bond lengths. The binding energy and change of hardness values are calculated for H₂, H, H, HF, HF⁺, and HF⁻ molecules and the bond stability is discussed. Finally, the concept of an atom in a molecule is examined in the context of DFT parameters and comparison is made between an atom in a molecule and the isolated atom. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 662–669, 2000     

Theoretical study of electrical and electrochemical properties of cyclopentanepentaone and its dicyanomethylene derivatives

Theoretical studies on anions of 1,2‐dihydroxycyclopentenetrione (croconic acid, H₂C₅O₅) and the whole series of dicyanomethylene derivatives in gas phase and in dimethyl formamide (DMF) solution are carried out using density functional theory (DFT) and self‐consistent reaction field (SCRF)‐DFT method at the B3LYP theory level for the first time. Natural bond orbital (NBO) analyses indicate that π‐electron delocalization in the series is quite strong. Based on the most stable conformations, linear correlations are observed between the oxidation potential measured by cyclic voltammetry and the highest occupied molecular orbital (HOMO) energy as well as ionization potential (Ip), which supports experimental results that systematic substitution of the oxygen atoms in the C₅O structure with C(CN)₂ groups causes a shift of both the oxidation potentials E and E toward more positive values. The correlations are also observed between experimental diffusion coefficient D and E_bind calculated in gas phase and DMF solution, the experimental electrochemical reducing potentials (E_R) and the electron affinity (Ea). © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Charge distributions and chemical effects. XXXIV. Concepts involved in an approximate,but accurate,description of bond energies

The concepts underlying the definition of bond energies in terms of potentials at the nuclei are outlined. The theory is rooted, first, in a definition of the energy, E_i, of “atom” i in the molecule in terms of the potential energy, V(i, mol), of nucleus Z_i in the field of all the electrons and nuclei of the molecule: E_i = K V(i, mol). The K parameter, which is not required to be a constant in the derivation of the energy expression describing the contribution of an ij bond, turns out to be virtually constant for each atomic species—a situation which is exploited in numerical applications. Second, the Hellmann—Feynman theorem is applied in the calculation of the derivative, δΔE/δZ_i, of the atomization energy, ΔE, using (i) the exact quantum-chemical definition of ΔE and (ii) the view that ΔE is the sum of bond energy contributions, ε_ij, plus a small interaction between nonbonded atoms. The individual bond energies derived in this manner necessarily depend on local charges at the bond-forming atoms. Numerical applications illustrate how this new bond-energy formula provides a simple link between typical saturated, olefinic, acetylenic, and aromatic hydrocarbons.     

Leading‐order behavior of the correlation energy in the uniform electron gas

We show that, in the high‐density limit, restricted Møller‐Plesset (RMP) perturbation theory yields E = π^?2(1 ? ln 2) ln r_s + O(r) for the correlation energy per electron in the uniform electron gas, where r_s is the Seitz radius. This contradicts an earlier derivation which yielded E = O(ln|ln r_s|). The reason for the discrepancy is explained. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Density functional study of S(N) 2 substitution reactions for CH(3) Cl + CX(1) X(2•-) (X(1) X(2) = HH, HF, HCl, HBr, HI, FF, ClCl, BrBr, and II)

A systematic investigation on the S_N2 displacement reactions of nine carbene radical anions toward the substrate CH₃Cl has been theoretically carried out using the popular density functional theory functional BHandHLYP level with different basis sets 6‐31+G (d, p)/relativistic effective core potential (RECP), 6‐311++G (d, p)/RECP, and aug‐cc‐pVTZ/RECP. The studied models are CX¹X^2?? + CH₃Cl → X²X¹CH₃C^? + Cl^?, with CX¹X^2?? = CH₂^??, CHF^??, CHCl^??, CHBr^??, CHI^??, CF₂^??, CCl₂^??, CBr₂^??, and CI₂^??. The main results are proposed as follows: (a) Based on natural bond orbital (NBO), proton affinity (PA), and ionization energy (IE) analysis, reactant CH₂^?? should be a strongest base among the anion‐containing species (CX¹X^2??) and so more favorable nucleophile. (b) Regardless of frontside attacking pathway or backside one, the S_N2 reaction starts at an identical precomplex whose formation with no barrier. (c) The back‐S_N2 pathway is much more preferred than the front‐S_N2 one in terms of the energy gaps [ΔE(front)?ΔE(back)], steric demand, NBO population analysis. Thus, the back‐S_N2 reaction was discussed in detail. On the one hand, based on the energy barriers (ΔE and ΔE) analysis, we have strongly affirmed that the stabilization of back attacking transition states (b‐TSs) presents increase in the order: b‐TS‐CI₂ < b‐TS‐CBr₂ < b‐TS‐CCl₂ < b‐TS‐CHI < b‐TS‐CHBr < b‐TS‐CHCl < b‐TS‐CF₂ < b‐TS‐CHF < b‐TS‐CH₂. On the other hand, depended on discussions of the correlations of ΔE with influence factors (PA, IE, bond order, and ΔE), we have explored how and to what extent they affect the reactions. Moreover, we have predicted that the less size of substitution (α‐atom) required for the gas‐phase reaction with α‐nucleophile is related to the α‐effect and estimated that the reaction with the stronger PA nucleophile, holding the lighter substituted atom, corresponds to the greater exothermicity given out from reactants to products. © 2012 Wiley Periodicals, Inc. J Comput Chem, 2012     

DFT‐based QSAR study and molecular design of AHMA derivatives as potent anticancer agents

A quantitative structure–activity relationship (QSAR) of 3‐(9‐acridinylamino)‐5‐hydroxymethylaniline (AHMA) derivatives and their alkylcarbamates as potent anticancer agents has been studied using density functional theory (DFT), molecular mechanics (MM+), and statistical methods. In the best established QSAR equation, the energy (E_NL) of the next lowest unoccupied molecular orbital (NLUMO) and the net charges (Q_FR) of the first atom of the substituent R, as well as the steric parameter (MR₂) of subsituent R₂ are the main independent factors contributing to the anticancer activity of the compounds. A new scheme determining outliers by “leave‐one‐out” (LOO) cross‐validation coefficient (q) was suggested and successfully used. The fitting correlation coefficient (R²) and the “LOO” cross‐validation coefficient (q²) values for the training set of 25 compounds are 0.881 and 0.829, respectively. The predicted activities of 5 compounds in the test set using this QSAR model are in good agreement with their experimental values, indicating that this model has excellent predictive ability. Based on the established QSAR equation, 10 new compounds with rather high anticancer activity much greater than that of 34 compounds have been designed and await experimental verification. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Density functional theory study of geometry and stability of small Zrn (n = 2–10) clusters

Geometric structures, electronic properties, and stabilities of small Zr_n and Zr (n = 2–10) clusters have been investigated using density functional theory with effective core potential LanL2DZ basis set. For both neutral and charged systems, several isomers and different multiplicities were studied to determine the lowest energy structures. Many most stable states with high symmetry were found for small Zr_n clusters. The most stable structures and symmetries of Zr clusters are the same as the neutral ones except n = 4 and 7. We found that the clusters with n > 3 possess highly compact structures. The clusters are inclined to form the caged‐liked geometry containing pentagonal structures for n > 8, which is in favor of energy. From the formation energy and second‐order energy difference, we obtained that 2‐, 5‐, 7‐atoms of neutral and 4‐, 7‐atoms cationic clusters are the magic numbers. Furthermore, the highest occupied molecular orbital‐lowest unoccupied molecular orbital gaps display that the Zr₃, Zr₆, Zr, and Zr are more stable in chemical stability. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

CH bond dissociation energies,isolated stretching frequencies,and radical stabilization energy

An earlier correlation between isolated CH stretching frequencies, v, and experimental CH bond dissociation energies, in hydrocarbons, fluorocarbons, and CHO compounds, is updated. A stabilization energy, E, which reflects only the properties of the radical, is defined by the deviation of a point from the above correlation. E values for a variety of radicals are listed and discussed. In H? C? N and H? C? O compounds E is low or negligible, due to the low v found in these compounds. The conventional definition of E_S then represents a serious misnomer, which distracts attention from the probable source of discrepancies between experimental and ab initio values of DH°(C? H), namely, the parent molecules. Stereo electronic effects concerned with the breaking of CH bonds are predicted in a variety of situations. Some experimental determinations of DH°(C? H), viz., in C₂H₄, HCOOH, CH₃CHO, CH₃NH₂, are considered to be probably in error. Schemes for partitioning energies of atomization into ‘standard’ or ‘intrinsic’ bond energies are criticized.     

Structure and stability of B6, B,and B clusters

We investigated various isomers of B₆, B, and B clusters with ab initio [Hartree–Fock (HF), MP2)] and density functional theory (DFT) methods. Ten B₆ isomers, 6 B isomers, and 6 B isomers are determined to be local minima on their potential energy hypersurfaces by the HF, B3LYP, B3PW91, and MP2 methods. Fourteen of these structures are first reported. The most stable neutral B₆ cluster is the capped pentagonal pyramid (C_5v), in agreement with the results reported previously. Hexagon B (C_2h) isomer and fan‐shaped B (C_2v) isomer are found to be the most stable on the cationic and anionic energy hypersurfaces, respectively. Natural bond orbital analysis suggests that there are three‐centered bonds in the most stable B₆ neutral and ionic clusters. The multicentered bonds are responsible for the special stability of the lowest‐energy isomer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 269–278, 2003     

The structures,thermochemistry, and electron affinities of hydrogenated silicon clusters Si6Hn/Si6H (n = 3–14)

The hydrogenated silicon clusters structures, electron affinities, and dissociation energies of the Si₆H_n/Si₆H (n = 3?14) species have been systematically investigated by means of three density functional theory (DFT) methods. The basis set used in this work is of double‐ζ plus polarization quality with additional diffuse s‐ and p‐type functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. Three different types of energy separations presented in this work are the adiabatic electron affinity (EA_ad), the vertical electron affinity (EA_vert), and the vertical detachment energy (VDE). The first Si? H dissociation energies D_e (Si₆H_n→ Si₆H_n?1+H) for the neutral Si₆H_n and D_e (Si₆H→Si₆H+H) for the anionic Si₆H species have also been reported. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Ionic atmosphere effects on the energetics of thermal and optical electron-exchange reactions: Application to ferrocenium-ferrocene self exchange

A treatment of ionic-atmosphere effects upon symmetrical electron-transfer reactions resulting from added electrolyte is outlined. Relationships are derived on the basis of the extended Debye-Huckel model for the increase in the activation free energy, ΔG_ia*, associated with reorganization of the ionic atmosphere for homogeneous-phase reactions involving a pair of spherical reactants with varying internuclear distance R. Similar relationships apply to the energetics of symmetrical optical electron transfer, since the increase in the optical transition energy, ΔE, should equal the corresponding ionic atmosphere reorganization energy, E; under the anticipated linear response conditions, E = 4ΔG_ia*. The predicted ΔG_ia* (and hence ΔE) values increase sharply with increasing R, as a consequence of the diminished “sharing” of the ionic cloud surrounding the donor and acceptor sites under these conditions. Outer-sphere electrochemical reactions, featuring a single “near-isolated” reactant, are predicted to feature substantially larger ΔG_ia* values than for homogeneous processes proceeding with the reaction partners in contact. The influence of more specific “ionic atmosphere” effects upon ΔG_ia*, especially involving reactant-electrolyte ion pairing, is also discussed. Unlike that of the nonspecific ionic atmosphere, the nuclear reorganization process associated with counterion transport between donor and acceptor sites coupled with electron transfer is nonlinear in nature, so that E ≠ 4ΔG_ia*. Some recent experimental data for electrolyte effects upon the rate constants for ferrocenium-ferrocene self exchange and related systems are examined in the light of these considerations.     

An Ab initio theoretical investigation on the geometrical and electronic structures of BAun−/0 (n = 1–4) clusters

An ab initio theoretical investigation on the geometrical and electronic structures and photoelectron spectroscopies (PES) of BAu_n^?/0 (n = 1–4) auroboranes has been performed in this work. Density functional theory and coupled cluster method (CCSD(T)) calculations indicate that BAu (n = 1–4) clusters with n‐Au terminals possess similar geometrical structures and bonding patterns with the corresponding boron hydrides BH. The PES spectra of BAu (n = 1–4) anions have been simulated computationally to facilitate their future experimental characterizations. In this series, the T_d BAu anion appears to be unique and particularly interesting: it possesses a perfect tetrahedral geometry and has the highest vertical electron detachment energy (VDE = 3.69 eV), largest HOMO‐LUMO gap (ΔE_gap = 3.0 eV), and the highest first excitation energy (E_ex = 2.18 eV). The possibility to use the tetrahedral BAu unit as the building block of Li⁺[BAu₄]^? ion‐pair and other [BAu₄]^?‐containing inorganic solids is discussed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A theoretical study of electronic and vibrational properties of neutral,cationic, and anionic B24 clusters

The equilibrium geometries, electronic and vibrational properties, and static polarizability of B₂₄, B, and B clusters are reported here. First‐principles calculations based on density functional theory predict the staggered double‐ring configuration to be the ground state for B₂₄, B, and B, in contrast to the quasi‐planar structure observed in small neutral and ionized B_n clusters with n ≤ 15. Furthermore, the (4 × B₆) tubular structure is found to be relatively stable in comparison to the 3D cage structure. The presence of delocalized π and multicentered σ bonds appears to be the cause of the stability of the double‐ring and tubular isomers. For the ground state of B₂₄, the lower and upper bound of the electron affinity is 2.67 and 2.81 eV, respectively, and the vertical ionization potential is 6.88 eV. Analysis of the frequency spectrum of the double‐ring and tubular isomers reveals the characteristic vibrational modes typically observed in carbon nanotubes. The corresponding IR spectrum also reflects the presence of some of these characteristic modes in the neutral and ionized B₂₄, suggesting that double‐ring and tubular structures can be considered as the building blocks of boron nanotubes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Dipole,quadrupole, octupole,and dipole–octupole polarizabilities at real and imaginary frequencies for H,HE, and H2 and the dispersion-energy coefficients for interactions between them

We have calculated certain dynamic polarizabilities (for both real and imaginary frequencies) for H, He, and H₂ and the dispersion-energy coefficients for long-range interactions between them. We have done so in a sum-over-states formalism with explicitly electron-correlated wave functions to describe the states. To be precise, we have determined the dipole (α₁), quadrupole (α₂), and octupole (α₃) polarizabilities of H and He for real frequencies (ω) in a range between zero and the first electronic-transition frequency and for imaginary frequencies (iω) on a 32-point Gauss-Legendre grid running from zero to ?ω = 20 E_h, and for H₂, we have found the dipole (α), quadrupole (C), and dipole–octupole (E) polarizability tensors for the same real and imaginary frequencies. The dispersion-energy coefficients, obtained by combining the sum-over-states for-malism for the polarizabilities with analytic integration over ω, gave values of C₆, C₈, and C₁₀ for the atom–atom systems; C, C, C, C, and C for the atom–diatom systems; and C₆, C and C for the H₂? H₂ system. Nearly all the results are considered to be more reliable than those hitherto published and some have been obtained for the first time, e.g., C(iω), E(ω), and E(iω) for H₂ and C, C, and C for the H? H₂ system. © 1993 John Wiley & Sons, Inc.     

A method to calculate the one‐electron reduction potentials for nitroaromatic compounds based on gas‐phase quantum mechanics

Nitroaromatic compounds (NACs) are widespread environmental contaminants, and the one‐electron reduction potential (E) is an important parameter used in modeling their environmental fate. We have identified a method that is both accurate and efficient to predict E values for NACs, using gas‐phase quantum mechanics (QM) calculations combined with empirical correlations. First, the adiabatic electron affinity (EA) at 0 K is calculated using the B98/MG3S method, and the predictions are scaled by a factor of 0.802 to account for systematic errors in the density functional calculations. Second, the E values are predicted from a linear correlation between E and EA. Using this method, E values were predicted with a mean absolute deviation from measured values of 0.021 V for the 14 NACs used to obtain the correlation and 0.029 V for six additional NACs. This represents a substantial improvement in accuracy over predictions by other QM methods, which are affected by large errors in solvation or aqueous‐phase calculations for some compounds. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010.