Assessment of delocalized and localized molecular orbitals through electron momentum spectroscopy

Recently, there was a hot controversy about the concept of localized orbitals, which was triggered by Grushow＇s work titled ＂Is it time to retire the hybrid atomic orbital？＂ [J. Chem. Educ. 88, 860 （2011）]. To clarify the issue, we assess the delocalized and localized molecular orbitals from an experimental view using electron momentum spectroscopy. The delocalized and localized molecular orbitals based on various theoretical models for CH4, NH3, and H20 are compared with the experimental momentum distributions. Our results show that the delocalized molecular orbitals rather than the localized ones can give a direct interpretation of the experimental （e, 2e） results.

Conformation effects on the molecular orbitals of serine

This paper calculates the five most stable conformers of serine with Hartree-Fock theory, density functional theory （B3LYP）, Moller-Plesset perturbation theory （MP4（SDQ）） and electron propagation theory with the 6-311＋＋G（2d,2p） basis set. The calculated vertical ionization energies for the valence molecular orbitals of each conformer are in agreement with the experimental data, indicating that a range of molecular conformations would coexist in an equilibrium sample. Information of the five outer valence molecular orbitals for each conformer is explored in coordinate and momentum spaces using dual space analysis to investigate the conformational processes, which are generated from the global minimum conformer Serl by rotation of C2-C3 （Ser4）, C1 C2 （Ser5） and C1-O2 （Set2 and Ser3）. Orbitals 28a, 27a and 26a are identified as the fingerprint orbitals for all the conformational processes.

APPLICATION OF MOLECULAR ORBITAL THEORY TO ANALYSIS OF PHASE STABILITY FOR ALLOYS

The critical _d vahues ( _ ) of the γ/(γ+σ).γ/(γ+μ) and γ/(γ+γ') phase boundaries in some ternar alloy phase diagrams at various temperatures are calculated by averaging the _d values of sererai selected characteristic points at the phase boundaries.Approxmate equations for the temperature dependence of the critical _d of γ/(γ+σ).γ/(γ+μ) and γ/(γ+γ') phase boundaries are established.The accuracy of the analysis is discussed in detail. It is found for the first time that the average value of the bond order _ at the phase boundaries ts also approximatelr a constant and therefore a critical average bond order _ like - can be introduced for the analysts of phase stability

Electronic Couplings for Singlet Oxygen Photosensitization and Its Molecular Orbital Overlap Description

The reaction of triplet fusion,also named triplet-triplet annihilation,has attracted a lot of research interests because of its wide applications in photocatalytic,solar cells,and bioimaging.As for the singlet oxygen photosensitization,the reactive singlet oxygen species are generated through the energy transfers from photosensitizer(PS)to ground triplet oxygen molecule.In this work,we computed the electronic coupling for singlet oxygen photosensitization using the nonadiabatic coupling from the quantum chemical calculation.Then we utilized the molecular orbital(MO)overlaps to approximate it,where the MOs were computed from isolated single molecules.As demonstrated with quantitative results,this approach well describes the distribution of the coupling strength as the function of the intermolecular distance between the sensitizer and O_(2),providing us a simple but effective way to predict the coupling of triplet fusion reactions.

Role of highest occupied molecular orbitals in molecular field-free alignment by a femtosecond pulse

This paper studies the molecular rotational excitation and field-free spatial alignment in a nonresonant intense laser field numerically and analytically by using the time-dependent SchrSdinger equation. The broad rotational wave packets excited by the femtosecond pulse are defined in conjugate angle space, and their coefficients are obtained by solving a set of coupled linear equations. Both single molecule orientation angles and an ensemble of O2 and CO molecule angular distributions are calculated in detail. The numerical results show that, for single molecule highest occupied molecular orbital （HOMO） symmetry σ tends to have a molecular orientation along the laser polarization direction and the permanent dipole moment diminishes the mean of the orientation angles; for an ensemble of molecules, angular distributions provide more complex and additional information at times where there are no revivals in the single molecule plot. In particular, at the revival peak instant, with the increase of temperature of the molecular ensemble, the anisotropic angular distributions with respect to the laser polarization direction of the πg orbital gradually transform to the symmetrical distributions regarding the laser polarization vector and for two HOMO configurations angular distributions of all directions are confined within a smaller angle when the temperature of the molecular ensemble is higher.

Imaging Molecular Orbitals of Single Picene Molecules Adsorbed on Cu（111） Surface： a Combined Experimental and Theoretical Study

Picene, which attracts the great interest of researchers, not only can be used to fabricate thin film transistors with high hole mobilities, but also is the parent material of a new type organic superconductor. Here, we investigate the electronic properties of individual picene molecules directly adsorbed on Cu（111） surface by a combination of experimental scanning tunneling microscopy/spectroscopy measurements and theoretical calculations based on the density functional theory. At low coverage, the picene molecules exhibit mono-dispersed adsorption behavior with the benzene ring planes parallel to the surface. The highest occupied state around -1.2 V and the lowest unoccupied state around 1.6 V with an obvious energy gap of the singly adsorbed picene molecule are identified by the dI/dV spectra and maps. In addition, we observe the strong dependence of the dI/dV signal of the unoccupied states on the intramolecular positions. Our first-principles calculations reproduce the above experimental results and interpret them as a specific molecule-substrate interaction and energy/spatial distributions of hybrid states mainly derived from different molecular orbitals of picene with some intermixing between them. This work provides direct information on the local electronic structure of individual picene on a metallic substrate and will facilitate the understanding the dependence of electron transport properties on the coupling between molecules and metal electrodes in single-molecule devices.

Quasi-aromaticity in Cluster Chemistry Ⅲ. Localized Molecular Orbital Study on Electron-rich Cobalt-sulfur Cluster Compounds[Co_6(μ_3-X)_8L_6]￣(n+)(X=S,Se;L=PPh_3,PEt_3,CO;n=0,1)

The localized molecular orbitals and energy levels for [Co_6 (μ_3-S)_8 (PH_3)_6]￣(n+)(n=0, 1) as model molecules of the electron-rich [Co_6 (μ_3-S)_8 (PPh_3)_6]￣(n+) (n=0,1) cluster compounds have been calculated by using Edmiston-Ruedenberg energy localization scheme under the spin-unrestricted CNDO/2 approximation. It is shown that the cluster skeletons of these two isostructural molecules consist of the edge-localized two-centered two-electron (Co-S) bonds plus a pair of the skeleton electrons delocalized on the whole cluster core,leading an extra stability of the cluster core.The one-electron oxidation for the neutral molecule gives rise to a one-electron σ (Co-Co) bond.which further resonates among the three diagonal lines of the {Co_6} octahedron. The comparison between [Co_6 (μ_3-S)_8(PPh_3)_6] and [Co_6(μ_3-CO)_8(CO)_6]￣(4-) indicates that the latter possesses face-localized bridging-bonds which are further delocalized on the whole surface of the cluster octahedron by the back-donation bonds from the lone electron pairs on the Co atoms to the capping carbonyl CO ligands. The structural features of the series of the [Co6(μ_3-X)_8L_6]￣(n+)(X =S, Se; L=PPh_3,PEt_3, CO;n=0, 1) cluster compounds are briefly rationalized on the basis of the localization description as well.

Crystal Structure and Molecular Orbital Calculation of(1R,2S)-N-Methylephedine Benzoate Hydrochloride

The title compound was synthesized and its crystal structure was determined. C_(13)H(21)NO_2·HCl, orthorhombic, space group P2_12_12_1 with dimensions:a =10. 635(2), b=26.942(6), c=6.193(2), V=1774.5(8),Z=4,Mr=319. 83 and Dc=1.20g/cm￣3. The final residual factor R=0.048, Rw=0.062. The C atoms except those in rings has a distorted tetrahedron structure.The dihedral angle between the phenyl rings in the molecule is 74. 56°. There is no bond between HCl and ester.The molecules join each other by van der Waals force. Its molecular orbital calculations were carried out by means of extended Huckel molecular orbital method.

Bonding Energy of a Molecular Orbital(Ⅱ)——Ab initio Calculation

Calculation of the bonding energy of a molecular orbital for a series of small molecules has been carried out by using ab initio STO-3G method. The results obtained demonstrate that the concept of the molecular orbital bonding energy is applicable for judging whether a molecular orbital is bonding, nonbonding or antibonding besides Mulliken overlap criterion.

LOCALIZED MOLECULAR ORBITAL STUDY ON ELECTRONIC STRUCTURES OF BOWL-SHAPED AROMATIC HYDROCARBONS

The localized molecular orbitals for typical bowl-shaped circulenes are obtained by the use of INDO-LMO method. It is found that these bowl-shaped circulenes with strained π-electron systems are still aromatic and the rim π-bonds with larger localization form reactive regions for formation of buckminsterfullerene.

VALENCE STATE OF C AtOMS AND σ_t-η_n SEPARABILITY OF MOLECULAR ORBITALS IN THE (BUCKMINSTER)FULLERENE C_(50)

The valence state of C atoms and the structure of molecular orbitals of the (Buckminster)Fullerene C_(60)have been demonstrated. It has been shown that when a motion-coordinate system is adopted, in which the coordinate origin is at every C atom, the z axis is in the direction of the normal and the (x,y) axes are in the direction of tangents of C_(60)'s spherical surface, 240 valence atomic orbitals of C_(60) can be divided into two groups. All (P_x, P_y)atomic orbitals named as Pt ones and all the other P_z atomic orbitals named as p. ones, That is to say that if we name the molecular orbital linearly combined of P_t atomic orbitals as σ_t and the molecular orbital linearly combined of P_n atomic orbitals as π_n, the 240 valence molecular orbitals are of the property of σ_t-π_n separability. It has also been shown that the frontier and nearby frontier molecular orbitals are π_n ones, and therefore the essential physical and chemical properties of C_(60) are determined by its π_n molecular orbitals.

Quasi-aromaticity in Cluster Chemistry Ⅱ. Localized Molecular Orbital Studies on Co_6 (CO)_(14)^(4-) and Ni_2Co_4 (CO)_(14)^(2-) Cluster Anions

The energy-localized CNDO/2 molecular orbitals have been calculated for the cluster anions of [Co_6 (CO)_(14)]￣(4-) and [Ni_2Co_4 (CO)_(14)]￣(2-)in order to get a deeper insight into the nature of their skeletal bonding. The bonding characteristics of these hexanuclear carbonyl cobaltates are described from a localization bonding viewpoint. There are two typical M-CO bondings, one of which is formed by electron donation from the terminal and capping carbonyl ligands into the vacant hybrid orbitals on the metal atoms , leading to formation ofσ(C_t→Co) and σ(C_b→{Co_3})bonds. The other typical M-CO bonding is back donation of the lone d-electron pairs on the metal atoms into the carbonyl ligands, forming π(Co→C_t) bonds, σ(Co→{C_(b2)}) bonds and π(Co→{C_(b4)} ) bonds. It is found that there are no direct metalmetal bondings in the skeletons of these two cluster anions.The delocalization situation of the skeletal bonding electrons is briefly discussed.

Different Charging-Induced Modulations of Highest Occupied Molecular Orbital Energies in Fullerenes in Comparison with Carbon Nanotubes and Graphene Sheets

The highest occupied molecular orbital（HOMO） energies of fullerenes are found by quantitative first-principles calculations to be raised by negative charging, and the rising rate rank of the fullerenes is C60 >C70 >C80 >C90>C100 >C180. Then we compare fullerenes with carbon nanotubes（CNTs） and graphene sheets（GSs） and find that the increase of the HOMO energy of a fullerene is much faster than that of CNTs and graphene sheets with the same number of C atoms. The rising rate rank is fullerene>CNT>GS, which holds no matter what the number of C atoms is or which structure the fullerene isomer is. This work paves a new path for developing all-carbon devices with low-dimensional carbon nanomaterials as different functional elements.

Theoretical Study on the Molecular Orbital and Stabilization Energy of Substituted Lithium Carbene Cations

The stabilization energies of substituted lithium carbene cations were calculated by using ab initio molecular orbital theory, and the relationship between the stabilization energies and molecular orbitals was discussed. The substituents with pi donor engender strong stabilization to CH2Li+. The calculations show the Y-C* bond lengths of cations become shorter and H-Y bond lengths longer than those of corresponding neutral molecules.

Molecular Orbital Study on the Optimized Geometries and Spectroscopic Parameters of Borate Polyhedra

In this paper several methods including MNDO, multiple scattering Xa and ab initio self-consistent-field MO theories have been used to calculate the minimum energy geometries, force constants, vibrational frequencies, and 11B quadruple coupling constants of B-O polyhedra such as [BO3], [BO4], [OB2]and [OB3]. The results are in good agreement with the experimental and calculated values so far published by other authors.

Exploring the effect of aggregation-induced emission on the excited state intramolecular proton transfer for a bis-imine derivative by quantum mechanics and our own n-layered integrated molecular orbital and molecular mechanics calculations

We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonomethyl)-naphthalene-2-ol and 1-pyrenecarboxaldehyde. Especially, the density functional theory(DFT) and time-dependent density functional theory(TDDFT) methods for HNP monomer are introduced. Moreover, the "our own n-layered integrated molecular orbital and molecular mechanics"(ONIOM) method(TDDFT:universal force field(UFF)) is used to reveal the aggregation-induced emission(AIE) effect on the ESIPT process for HNP in crystal. Our results confirm that the ESIPT process happens upon the photoexcitation for the HNP monomer and HNP in crystal, which is distinctly monitored by the optimized geometric structures and the potential energy curves. In addition, the results of potential energy curves reveal that the ESIPT process in HNP will be promoted by the AIE effect. Furthermore, the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) for the HNP monomer and HNP in crystal have been calculated. The calculation demonstrates that the electron density decrease of proton donor caused by excitation promotes the ESIPT process. In addition, we find that the variation of atomic dipole moment corrected Hirshfeld population(ADCH) charge for proton acceptor induced by the AIE effect facilitates the ESIPT process. The results will be expected to deepen the understanding of ESIPT dynamics for luminophore under the AIE effect and provide insight into future design of high-efficient AIE compounds.

Plasma-Electrolysis of Dinitrophenol in Gas-Liquid Boundary and Interpretation Using Molecular Orbital Theory

The advanced oxidation of 2,4-dinitrophenol (DNP), 2,5-DNP, and 3,4-DNP in aqueous solution has been investigated using a multi-gas, dielectric barrier discharge. Dielectric barrier discharge was operated in the aqueous solution and gas boundary. The degradation was measured by high performance liquid chromatography (HPLC). The acceleration of the advanced-oxidation has been investigated by the combination of the anion exchange polymer membrane. The result indicated that the degradation pathways involve a rapid detachment of the nitro group and a slow opening of the aromatic-ring. The hydroxyl radical and the excited hydroxyl anion are responsible for the primary attack of the DNP with the production of dihydroxy-nitrobenzenes. The attack of hydroxyl radical occurs at the benzene ring carbon activated by the presence of a phenolic OH group and a nitro group. The result suggested that the reaction is dominated by a pseudo-first order kinetic reaction. The degradation process is interpreted using Molecular Orbital Theory.

A Band Theory Perspective on Molecular Orbitals in Complex Oxides

In view of the growing interest in molecular orbitals (MOs) encountered in certain complex oxides, we review some of their properties from the band theory perspective and provide detailed examples based on real materials. Our discussion includes some technical aspects of identifying MOs in electronic structure calculations and considers cases when MOs can be both orthogonal and non-orthogonal. We also describe orthonormalization of MOs, a procedure converting them into Wannier functions, and discuss the problem of Wannier functions possibly being rather spatially extended and how using MO, rather than atomic orbital, based effective Hamiltonians might be a better choice in describing certain strongly correlated systems as well as systems with strong electron-phonon coupling. Furthermore, we address the problem of strongly correlated MOs and how it can be treated in band theory calculations.

Quasi-aromaticity in Cluster Chemistry Ⅱ. Localized Molecular Orbital Studies on Co6 （CO）14 ￣（4-） and Ni2Co4 （CO）14 ￣（2-） Cluster Anions

The energy-localized CNDO/2 molecular orbitals have been calculated for the cluster anions of [Co6 （CO）14]￣（4-） and [Ni2Co4 （CO）14]￣（2-）in order to get a deeper insight into the nature of their skeletal bonding. The bonding characteristics of these hexanuclear carbonyl cobaltates are described from a localization bonding viewpoint. There are two typical M-CO bondings, one of which is formed by electron donation from the terminal and capping carbonyl ligands into the vacant hybrid orbitals on the metal atoms , leading to formation ofσ（Ct→Co） and σ（Cb→{Co3}）bonds. The other typical M-CO bonding is back donation of the lone d-electron pairs on the metal atoms into the carbonyl ligands, forming π（Co→Ct） bonds, σ(Co→{Cb2}) bonds and π(Co→{Cb4} ) bonds. It is found that there are no direct metalmetal bondings in the skeletons of these two cluster anions.The delocalization situation of the skeletal bonding electrons is briefly discussed.

Maximum Overlap Symmetry Molecular Orbital Calculation under CNDO／2 Approximation

A basic calculation procedure for the MOSMO method under CNDO/2 approximation is presented in this paper,and performed by using the same parameters as those used in the ordinary CNDO/2 LCAO-MO calculation.The calculated results on the whole are close to those obtained by use of the ordinary CNDO/2 LCAO-MO calculation,illustrating that the presented procedure is reasonable.Due to its simplicity,the presented calculation procedure may be feasible even in very large molecular s ystems.