On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

Third-order energy derivative corrections to the Kohn-Sham orbital hardness tensor

The third term in the Taylor expansion of the total energy functional around the number of electronsN is evaluated as the second-order derivative of orbital Kohn-Sham energies with respect to orbital occupancy. Present approach is an extension of an efficient algorithm to compute densityfunctional based orbital reactivity indices. Various energy derivatives used to approximate orbital reactivity indices are defined within the space spanned by the orbital occupation numbers and the Kohn-Sham one-electron energies. The third-order energy functional derivative has to be considered for singular hardness tensor ([η]). On the contrary, this term has negligible influence on the reactivity index values for atomic or molecular systems with positively defined hardness tensors. In this context, stability of a system in equilibrium state estimated through the eigenvalues of [η] is discussed. Numerical illustration of the Kohn-Sham energy functional derivatives in orbital resolution up to the third order is shown for benchmark molecules such as H₂O, H₂S, and OH⁻.     

Ab initio calculations on furan with a new computer program

Two ab initio calculations with different basis sets have been performed on the molecule furan, C₄H₄O. The calculations were done with a new computer program, REFLECT, which is presented. A preliminary analysis of the molecular wave functions has been made by looking at total and orbital energies and also by means of a population analysis. One inner shell ionization energy has been calculated by taking the difference in total energy for the molecule and the corresponding ion. The result is compared with the ionization energy obtained from Koopmans' theorem.     

Trap mechanism based on frontier molecular orbitals of additives in polyethylene insulators: A theoretical study and molecular design strategy

In this work, the energy gaps (E_g) of highest occupied orbitals and lowest unoccupied orbitals, trap energies (E_t(e) and E_t(h)) and excited energies of polyethylene model compound, typical defect compound, acetophonene, and 33 designed additives are obtained using density functional method at B3LYP/6–311+G(d, p) level. The correlation between trapping‐electrons (holes) abilities of additives and molecular frontier orbitals is established, and a new understanding for trap mechanism based on chemical molecular orbital levels is given for the first time which could be used to filter qualitative additives as voltage stabilizers of polyethylene. The role of trap energies and the energy gaps on discussing space charge accumulation and electric breakdown is analyzed in detail. A molecular design strategy for potential additives of cross‐linked polyethylene insulated high‐voltage cable is shown based on conjugation effect, substituents character, and polycyclic aromatic compounds. © 2015 Wiley Periodicals, Inc.     

Tuning of the electronic properties of H‐passivated armchair graphene nanoribbons by mild border oxidation: Theoretical study on periodic models

We report the results of a DFT study of the electronic properties, intended as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, of periodic models of H‐passivated armchair graphene nanoribbons (a‐GNRs) as that synthetized by bottom‐up technique, functionalized by vicinal dialdehydic groups. This material can be obtained by border oxidation in mild and easy to control conditions with ¹Δ_g O₂ as we reported in our previous paper (Ghigo et al., ChemPhysChem 2015, 16, 3030). The calculations show that the two models of border oxidized a‐GNRs (model A, 0.98 nm and model B, 1.35 nm wide) present LUMO and HOMO energies lowered by an extend roughly linearly dependent on the amount of oxygen chemically bound. The frontier orbital energy variations dependence on the % wt of oxygen bound are, for model A: ?0.12 eV for the LUMO and ?0.05 eV for the HOMO; for model B: ?0.15 eV (HOMO) and ?0.06 eV (LUMO). © 2016 Wiley Periodicals, Inc.     

The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach

Potential energy curves for inner-shell states of nitrogen and carbon dioxide molecules are calculated by inner-shell complete active space self-consistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged inner-shell states at multiconfigurational level. This is possible since the collapse of the wave function to a low-lying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of K-shell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N(2) are considerably high, which means that these states are strongly bound. Potential curves along ground state normal modes of CO(2) indicate the occurrence of Renner-Teller effect in inner-shell states.     

Theoretical study of ionization potentials in monosubstituted benzenes

Monosubstituted benzenes, in which the substituents participate in the π-electron system, are studied following a classification in two classes according to the π-electronic structure of the substituent. For this type of molecule, a relation is established between the nature of the substituent and, on the one hand, the energies of the two highest occupied molecular orbitals and, on the other hand, their respective differences. The two orbitals referred to above have π-character and belong to the a₂ and b₁ species if a C_2v point group is assumed. Simple symmetry arguments lead to the conclusion that the a₂ orbitals have, essentially, an intraring character, whereas the π-orbitals of the substituents do give an important contribution to the b₁ orbitals. Therefore, an a₂ electron must have a larger interaction with the benzene ring and a smaller kinetic energy, whereas a b₁ electron must have a larger interaction with the substituent and a larger kinetic energy. It is also expected that the changes in the π-electronic structure of the substituent must much more influence the variations on the b₁ energies and on the components of orbital energies associated with the substituent than the variations on the a₂ energies and on the intraring components of the orbital energies. A modified version of the MOPAC program was prepared to perform the decomposition of the orbital energies in their kinetic and potential energy components and these in their monocentric and bicentric terms. MNDO calculations on nine monosubstituted benzenes, using the modified MOPAC program, give good confirmation of the symmetry predictions and prove the consistency of the classification of the substituents that is introduced. © 1993 John Wiley & Sons, Inc.     

Study of photoelectron spectra of some XPY3 molecules (X = O,S and Y = Cl,Br) by the SCF-Xα-SW method

In this paper we extend our previous studies to investigate the ionization energies of some XPY₃ molecules (X = O, S and Y = Cl, Br). The calculated orbital energies agree very well with reported experimental ionization energies. The molecular orbital orderings obtained coincide with recent experimental orbital assignments. The results are also compared with previous ab initio and semiempirical calculations for OPCl₃, OPBr₃, SPCl₃, and SPBr₃ molecules. The comparison indicates that the present results show improved agreement with experiment and clarify certain ambiguities in the earlier assignments.     

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

Low‐lying equilibrium geometric structures of Al_nN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al₇N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Segmentation and additive approach: A reliable technique to study noncovalent interactions of large molecules at the surface of single‐wall carbon nanotubes

This investigation explores a new protocol, named Segmentation and Additive approach (SAA), to study exohedral noncovalent functionalization of single‐walled carbon nanotubes with large molecules, such as polymers and biomolecules, by segmenting the entire system into smaller units to reduce computational cost. A key criterion of the segmentation process is the preservation of the molecular structure responsible for stabilization of the entire system in smaller segments. Noncovalent interaction of linoleic acid (LA, C₁₈H₃₂O₂), a fatty acid, at the surface of a (10,0) zigzag nanotube is considered for test purposes. Three smaller segmented models have been created from the full (10,0)‐LA system and interaction energies were calculated for these models and compared with the full system at different levels of theory, namely ωB97XD, LDA. The success of this SAA is confirmed as the sum of the interaction energies is in very good agreement with the total interaction energy. Besides reducing computational cost, another merit of SAA is an estimation of the contributions from different sections of the large system to the total interaction energy which can be studied in‐depth using a higher level of theory to estimate several properties of each segment. On the negative side, bulk properties, such as HOMO‐LUMO (highest occupied molecular orbital ‐ lowest occupied molecular orbital) gap, of the entire system cannot be estimated by adding results from segment models. © 2016 Wiley Periodicals, Inc.     

Ab initioMO calculations on the acidities of water and methanol,and hydrogen bond energies of the conjugate ions with a water molecule

The acidities, deprotonation energies, of water and methanol were calculated by the use of the ab initio self-consistent-field (SCF ) molecular orbital (MO ) method with electron correlation computed by the thirdorder Møller–Plesset perturbation method and configuration interaction with double excitations. Zero-point vibrational energy correction translational energy change, and the PV work term were included to evaluate the accurate acidities. The calculated acidity difference including these corrections was 7 kcal/mol, which is somewhat smaller than the experimental ones (9.5–12.5 kcal/mol) recently determined. The hydrogen bond energies of the conjugate ions (OH^? and CH₃O^?) with a water molecule were calculated to be 2.3 kcal/mol near the Hartree–Fock limit; this energy only amounts to 25% of the (total) hydration energy difference between the two negative ions. The aqueous solvation effect on the acidity scale was discussed.     

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

Synthesis,characterization, thermal behavior,and DFT aspects of some oxovanadium(IV) complexes involving ONO-donor sugar Schiff bases

Seven new Schiff base complexes of oxovanadium(IV), [VO(L)(H₂O)], where H₂L = H₂bmpph-gls, H₂bumpph-gls, H₂iso-vmpph-gls, H₂pmpph-gls, H₂iso-bumpph-gls, H₂ampph-gls, and H₂vmpph-gls, have been synthesized by the reaction of VOSO₄·5H₂O and the said ligands in aqueous ethanol. The resulting complexes have been characterized on the basis of elemental analysis, vanadium determination, molar conductance, magnetic measurements, thermogravimetric (TG) analysis, infrared, electronic mass, and electron spin resonance studies. The thermal decomposition processes of one representative complex is discussed, and the order of reaction (n) and the activation energies (E_a) have been calculated from TG and differential TG curves. Molecular geometry optimizations, molecular surface electrostatic potentials, vibrational frequency calculations, bond lengths, bond angles and dihedral angles, and natural atomic charges obtained by natural bond orbital and Mulliken population analysis and calculations of molecular energies, highest occupied molecular orbital and lowest unoccupied molecular orbital were performed with the Gaussian 09 software package using density functional theory methods with Becke3–Lee–Yang–Parr (B3LYP) hybrid exchange–correlation functional and the standard 6-311G(+) basis set for (ampph-glsH₂) and LANL2DZ basis set for one of its complexes, [VO(ampph-gls)(H₂O)]. No imaginary frequency was found in the optimized model compounds, and hence it ensures that the molecule is in the lowest point of the potential energy surface, that is, an energy minimum. Finally calculated results were applied to simulate infrared spectra which show good agreement with observed spectra. Based on experimental and theoretical data, suitable square pyramidal structures have been proposed for these complexes.     

Radial dependence of exterior electron distributions of molecular orbitals

A molecular surface is introduced to divide interior electron densities from exterior electron densities (EED). The radial distribution of EED (RADEED) is defined for each molecular orbital as a function of the distance from the molecular surface. Logarithmic plots of RADEED for NH₃ using various basis sets in ab initio MO calculations revealed some important features: (i) the Hartree-Fock limit for the orbital function tail may be suggested and thus qualities of basis sets can be discussed, and (ii) the slope of the curve shows the decay rate of the orbital which can be compared with the curve derived from the theoretical behavior of the long-range asymptotic form involving either the lowest ionization potential or the orbital energy of the highest occupied orbital.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Excited state properties,fluorescence energies,and lifetimes of a poly(fluorene‐phenylene), based on TD‐DFT investigation

The structural and electronic properties of fluorene‐phenylene copolymer (FP)_n, n = 1–4 were studied by means of quantum chemical calculations based on density functional theory (DFT) and time dependent density functional theory (TD‐DFT) using B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest singlet excited state. It was found that (FP)_n is nonplanar in its ground state while the electronic excitations lead to planarity in its S₁ state. Absorption and fluorescence energies were calculated using TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods. Vertical excitation energies and fluorescence energies were obtained by extrapolating these values to infinite chain length, resulting in extrapolated values for vertical excitation energy of 2.89 and 2.87 eV, respectively. The S₁ ← S₀ electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is distinguishing in terms of oscillator strength. Fluorescence energies of (FP)_n calculated from TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods are 2.27 and 2.26 eV, respectively. Radiative lifetimes are predicted to be 0.55 and 0.51 ns for TD‐B3LYP/SVP and TD‐B3LYP/SVP+ calculations, respectively. These fundamental information are valuable data in designing and making of promising materials for LED materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A systematic preparation of new contracted Gaussian-type orbital sets. VIII. MINI-1 and MIDI-1 sets for Ga through Cd

Minimal contracted Gaussian basis sets are presented for Ga through Cd. Characteristically these Gaussian-based minimal sets give far better d orbital energies than those by minimal STO basis sets. These new basis sets were tested on Br₂ for which a new benchmark calculation was also performed. The test result is satisfactory in that these basis sets produce good general agreement with the near Hartree–Fock calculation with respect to the molecular spectroscopic constants.     

Theoretical Investigations of the Effect of a Homologous Series of Anionic Surfactants on the Metabolism Bioactivity of Chromobacterium violaceum

Theoretical calculations were performed to obtain physicochemical properties associated with the effect of homologous anionic n-alkylsulfate surfactants on the metabolism of Chromobacterium violaceum. The quantitative experimental effects on the respiration process were those obtained from calorimetric data and were used to correlate the Structure–Activity–Relationship (SAR) of these compounds. Semiempirical AM1 and ab initio DFT levels, employing the set CEP-31G, were used for the theoretical calculations and were parameterized using the continuum-solvation model COSMO for solvent contributions. Chemometric analyses (HCA: hierarchical cluster analysis and PCA: principal component analysis) were used to correlate the physicochemical properties of these compounds and their biological activities. The results indicate that the biological activities of these compounds increase as the hydrocarbon chain length, volume, molar volume and exothermic enthalpy of formation (Δ_f H ^∘) increase; in contrast they decrease with decreases of the solvent effect (SE), ionization enthalpy (IE) and HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energies.     

Calculation of the kinetic energy release of charge separation processes

Kinetic energy release (KER) was studied by experimental methods and semiempirical (MNDO and AM1) molecular orbital calculations in the case of various charge separation processes: loss of a methyl ion from [CH₃? C₄? CH₃]²⁺, [CH₃? C₃? CH₃]²⁺ and [N,N-dimethyl-p-phenylenediamine]²⁺. It was found that the KER corresponding to the width of a dish-topped peak at half-height is very close to the mean KER of the process. The calculated potential energy curves of these reactions show significant reverse critical energies, a large part of which was found to be due, in agreement with conventional assumptions, to electric repulsion between the two separating singly charged products. The bond order between the two separating ions is nearly zero in the transition state, so exchange of internal energy between them is unlikely. These explain the good agreement between the (calculated) reverse critical energy and the measured kinetic energy release.