Valency and molecular structure

Valency is defined for each molecular orbital. The molecular orbital valency values are shown to be a good measure of the bonding nature of the molecular orbital. Comparisons are made with photoelectron spectral studies and Mulliken overlap population analysis.The variation of molecular valency and molecular orbital valency with bond angle is studied. It is found that for all the molecules presently considered, energy is linearly related to valency and that the molecular valency reaches a maximum at the equilibrium bond angle. It is also shown that the molecular orbital valency can serve as a quantitatively reliable ordinate for Mulliken-Walsh diagrams.     

An animated visualization of orbital angular momentum and spin‐orbit coupling

This paper presents an approach toward visualizing a complex orbital based on animation using a time‐dependent phase factor. This makes orbital angular momentum clearly visible, in a way that reflects the nature of the orbital angular momentum wavefunction. Visualization of this quantity is also useful for examining the effects of spin‐orbit coupling (SOC), in which higher orbital angular momentum states are admixed into the orbital; in this case, however, scaling of one phase‐component is needed. The phase orientation of a complex orbital, which is generally not guaranteed by the SCF procedure, must be considered when doing this. The method of visualization presented here may prove useful when analyzing properties where SOC is important, such as magnetic resonance parameters. Animated visualizations are performed, and compared with the method of phase‐colored isosurfaces, first for a model p‐orbital to explain the idea, and then for the singly‐occupied molecular orbitals of two small doublet radicals.     

The orbital relaxation energy for single and double ionizations from valence shells of CH4, NH3, H2O and HF

The orbital relaxation energy is defined for single and double ionizations of valence electrons, and is calculated for CH₄, NH₃, H₂O and HF molecules with the ab initio SCF method. It is shown that the orbital relaxation energy for the ionization from a bonding orbital is about half of that for a non-bonding orbital, and the orbital relaxation energy for the double ionization is about double of that for the single ionization. This result gives a theoretical foundation for the empirical method of interpret Auger electron spectra by using experimental single ionization potentials.     

Orbital Interaction and the Mulliken-Walsh Diagram for AH2 Systems

We define θ- (or R-) bonding (or antibonding) character of the molecular orbitals according to the slopes of the orbital energy curves when the internuclear angle (or internuclear distance) is varied. So far the slope of the orbital curve has only been accounted for by the qualitative argument based on two factors: the orbital overlap and the s-p mixing. We employ the bond orbitals instead of the usual atomic orbitals as the basis set to analysis the character of the molecular orbitals. The Fock matrix in the bond orbital basis can then quantitatively account for the effects of both the overlap and s-p mixing factors. Our analysis also show that a third factor, the orbital interaction, is essential to account for both the “typical” and “abnormal” behavior of the slopes.     

Magnetic structure and orbital ordering in tetragonal and monoclinic KCrF(3) from first-principles calculations

KCrF(3) has been systematically investigated by using the full-potential linearized augmented plane wave plus local orbital method within the generalized gradient approximation and the local spin density approximation plus the on-site Coulomb repulsion approach. The total energies for ferromagnetic and three different antiferromagnetic configurations are calculated in the high-temperature tetragonal and low-temperature monoclinic phases, respectively. It reveals that the ground state is the A-type antiferromagnetic in both phases. Furthermore, the ground states of the two phases are found to be Mott-Hubbard insulators with the G-type orbital ordering pattern. In addition, our calculations show the staggered orbital ordering of the 3d(x(2) ) and 3d(y(2) ) orbitals for the tetragonal phase and the 3d(z(2) ) and 3d(x(2) ) orbitals for the monoclinic phase, which is in agreement with the available data. More importantly, the relationship between magnetic structure and orbital ordering as well as the origin of the orbital ordering are analyzed in detail.     

Periodic trends and complexation chemistry of tetravalent actinide ions with a potential actinide decorporation agent 5-LIO(Me-3,2-HOPO): A relativistic density functional theory exploration

A relativistic density functional theory (DFT) study is reported which aims to understand the complexation chemistry of An⁴⁺ ions (An = Th, U, Np, and Pu) with a potential decorporation agent, 5-LIO(Me-3,2-HOPO). The calculations show that the periodic change of the metal binding free energy has an excellent correlation with the ionic radii and such change of ionic radii also leads to the structural modulation of actinide–ligand complexes. The calculated structural and binding parameters agree well with the available experimental data. Atomic charges derived from quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) analysis shows the major role of ligand-to-metal charge transfer in the stability of the complexes. Energy decomposition analysis, QTAIM, and electron localization function (ELF) predict that the actinide–ligand bond is dominantly ionic, but the contribution of orbital interaction is considerable and increases from Th⁴⁺ to Pu⁴⁺. A decomposition of orbital contributions applying the extended transition state-natural orbital chemical valence method points out the significant π-donation from the oxygen donor centers to the electron-poor actinide ion. Molecular orbital analysis suggests an increasing trend of orbital mixing in the context of 5f orbital participation across the tetravalent An series (Th-Pu). However, the corresponding overlap integral is found to be smaller than in the case of 6d orbital participation. An analysis of the results from the aforementioned electronic structure methods indicates that such orbital participation possibly arises due to the energy matching of ligand and metal orbitals and carries the signature of near-degeneracy driven covalency.     

Coexistence of 1,3-butadiene conformers in ionization energies and Dyson orbitals

The minimum-energy structures on the torsional potential-energy surface of 1,3-butadiene have been studied quantum mechanically using a range of models including ab initio Hartree-Fock and second-order M?ller-Plesset theories, outer valence Green's function, and density-functional theory with a hybrid functional and statistical average orbital potential model in order to understand the binding-energy (ionization energy) spectra and orbital cross sections observed by experiments. The unique full geometry optimization process locates the s-trans-1,3-butadiene as the global minimum structure and the s-gauche-1,3-butadiene as the local minimum structure. The latter possesses the dihedral angle of the central carbon bond of 32.81 degrees in agreement with the range of 30 degrees-41 degrees obtained by other theoretical models. Ionization energies in the outer valence space of the conformer pair have been obtained using Hartree-Fock, outer valence Green's function, and density-functional (statistical average orbital potentials) models, respectively. The Hartree-Fock results indicate that electron correlation (and orbital relaxation) effects become more significant towards the inner shell. The spectroscopic pole strengths calculated in the Green's function model are in the range of 0.85-0.91, suggesting that the independent particle picture is a good approximation in the present study. The binding energies from the density-functional (statisticaly averaged orbital potential) model are in good agreement with photoelectron spectroscopy, and the simulated Dyson orbitals in momentum space approximated by the density-functional orbitals using plane-wave impulse approximation agree well with those from experimental electron momentum spectroscopy. The coexistence of the conformer pair under the experimental conditions is supported by the approximated experimental binding-energy spectra due to the split conformer orbital energies, as well as the orbital momentum distributions of the mixed conformer pair observed in the orbital cross sections of electron momentum spectroscopy.     

The role of excited Rydberg States in electron transfer dissociation

Ab initio electronic structure methods are used to estimate the cross sections for electron transfer from donor anions having electron binding energies ranging from 0.001 to 0.6 eV to each of three sites in a model disulfide-linked molecular cation. The three sites are (1) the S-S sigma(*) orbital to which electron attachment is rendered exothermic by Coulomb stabilization from the nearby positive site, (2) the ground Rydberg orbital of the -NH(3)(+) site, and (3) excited Rydberg orbitals of the same -NH(3)(+) site. It is found that attachment to the ground Rydberg orbital has a somewhat higher cross section than attachment to either the sigma orbital or the excited Rydberg orbital. However, it is through attachment either to the sigma(*) orbital or to certain excited Rydberg orbitals that cleavage of the S-S bond is most likely to occur. Attachment to the sigma(*) orbital causes prompt cleavage because the sigma energy surface is repulsive (except at very long range). Attachment to the ground or excited Rydberg state causes the S-S bond to rupture only once a through-bond electron transfer from the Rydberg orbital to the S-S sigma(*) orbital takes place. For the ground Rydberg state, this transfer requires surmounting an approximately 0.4 eV barrier that renders the S-S bond cleavage rate slow. However, for the excited Rydberg state, the intramolecular electron transfer has a much smaller barrier and is prompt.     

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity

Orbital energies in Kohn-Sham density functional theory (DFT) are investigated, paying attention to the role of the integer discontinuity in the exact exchange-correlation potential. A series of closed-shell molecules are considered, comprising some that vertically bind an excess electron and others that do not. High-level ab initio electron densities are used to calculate accurate orbital energy differences, Deltavarepsilon, between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), using the same potential for both. They are combined with accurate vertical ionization potentials, I(0), and electron affinities, A(0), to determine accurate "average" orbital energies. These are the orbital energies associated with an exchange-correlation potential that averages over a constant jump in the accurate potential, of magnitude Delta(XC)=(I(0)-A(0))-Deltavarepsilon, as given by the discontinuity analysis. Local functional HOMO energies are shown to be almost an order of magnitude closer to these average values than to -I(0), with typical discrepancies of just 0.02 a.u. For systems that do not bind an excess electron, this level of agreement is only achieved when A(0) is set equal to the negative experimental affinity from electron transmission spectroscopy (ETS); it degrades notably when the zero ground state affinity is instead used. Analogous observations are made for the local functional LUMO energies, although the need to use the ETS affinities is less pronounced for systems where the ETS values are very negative. The application of an asymptotic correction recovers the preference, leading to positive LUMO energies (but bound orbitals) for these systems, consistent with the behavior of the average energies. The asymptotically corrected LUMO energies typically agree with the average values to within 0.02 a.u., comparable to that observed with the HOMOs. The study provides numerical support for the view that local functionals exhibit a near-average behavior based on a constant jump of magnitude Delta(XC). It illustrates why a recently proposed DFT expression involving local functional frontier orbital energies and ionization potential yields reasonable estimates of negative ETS affinities and is consistent with earlier work on the failure of DFT for charge-transfer excited states. The near-average behavior of the exchange-correlation potential is explicitly illustrated for selected systems. The nature of hybrid functional orbital energies is also mentioned, and the results of the study are discussed in terms of the variation in electronic energy as a function of electron number. The nature of DFT orbital energies is of great importance in chemistry; this study contributes to the understanding of these quantities.     

Cu(001)表面CO吸附单层结构和电子态的第一性原理研究

用密度泛函理论(DFT)研究了Cu(001)表面CO吸附单层的表面性质. 总能计算结果表明, 顶位结构总能最低, 相应位置的CO分子吸附能最大. 谷位吸附结构的衬底原子层间距相对于清洁表面的膨胀量约为10%, 从而导致了谷位吸附的不稳定性. 在顶位、桥位和谷位三个吸附结构中, C和Cu原子之间的距离dC-Cu分别为0.1868、0.1975和0.2231 nm, 对应的CO分子键长为0.1154、0.1165 和0.1175 nm. 计算了CO分子的态密度(DOS). 结果表明, 衬底与分子的作用主要是分子和金属轨道的杂化. 在吸附过程中, 电荷主要从碳原子的s轨道向p轨道转移. 在顶位、桥位和谷位吸附结构中, 每个碳原子内电荷的转移量分别为0.45e、0.54e 和0.55e. 衬底向吸附分子的电荷转移量不大, CO 吸附分子层为一绝缘层.     

Orbital deletion procedure and its applications

The orbital deletion procedure is introduced, which is suited to quantitatively investigating the electronic delocalization effiect in earboeations and boranes. While the routine, ab initio molecular orbital methods can generate wavefunetions for real systems where all electrons are delocalized, the present orbital deletion procedure can generate wavefunctions for hypothetical reference molecules where electronic delocalization effect is deactivated. The latter wavefunetion normlly corresponds In the most stable resonance structure in terms of the resonance theory. By comparing and analyzing the delocalized and the localized wavefunetions, one can obtain a quantitative and instinct pieture to show how electronic deloealizalion inside a molecule affects the molecular structure, energy as well as other physical properties. Two examples are detailedly discussed. The first is related to the hypercoujugation of alkyl groups in carbocations and a comparison of the order of stability of carbocations is made, T     

Basis set effects on frontier molecular orbital energies and energy gaps: a comparative study between plane waves and localized basis functions in molecular systems

In order to study the Kohn-Sham frontier molecular orbital energies in the complete basis limit, a comparative study between localized functions and plane waves, obtained with the local density approximation exchange-correlation functional is made. The analyzed systems are ethylene and butadiene, since they are theoretical and experimentally well characterized. The localized basis sets used are those developed by Dunning. For the plane-waves method, the pseudopotential approximation is employed. The results obtained by the localized basis sets suggest that it is possible to get an estimation of the orbital energies in the limit of the complete basis set, when the basis set size is large. It is shown that the frontier molecular orbital energies and the energy gaps obtained with plane waves are similar to those obtained with a large localized basis set, when the size of the supercell and the plane-wave expansion have been appropriately calibrated.     

The quality of s-orbitals determined by least-squares fitting and constrained variational methods

Calculations of a wide range of position and momentum space properties of 23 orbital basis sets for atomic helium are performed to supplement our previous work. The combined results on 94 orbital basis sets are used to demonstrate that, as in the case of d-orbitals, the least squares error is not as discriminating as other information theoretic measures of overall quality for s-orbitals. Detailed comparisons suggest that constrained variation can improve the overall quality of the resulting orbital provided that the constraints are selected carefully to complement the bias inherent in the energy expectation value and the functional form of the basis functions.     

MNDO and MINDO/3 study of the reactivity of 3-pyrrolin-2-one tautomers and derivatives

MINDO/3 and MNDO methods have been applied to the study of the reactivity of 3-pyrrolin-2-one tautomers and derivatives. The different parameters that can influence the reactivity from the frontier molecular orbital point of view (atomic charge distribution, frontier orbital energy and frontier orbital reactivity indices) are compared and evaluated with respect to the experimental reactivity already known.     

相对论效应对Au和Fr电子结构影响的研究

介绍了Dirac,Desclaux等人发展的相对论多电子原子自洽场Dirac-Fock(MCDF)方法,并用相对论多电子原子MERECC-94程序计算了元素Au,Fr的电子结构。结果表明：尽管Fr的1s轨道相对论收缩效应比Au大,但因外壳层电子结构的不同,使Au的6s轨道的相对论收缩和稳定化效应比Fr和7s更明显。     

Electronegatlvity and the bonding character of Molecular Orbitals

The density-functional approach to Molecular Orbital theory shows that the chemical bonding potential is better described by orbital electronegativities than by ionization energies. This results from the fact that the electronic relaxation connected with ionization is not significant for the homolytic breaking of chemical bonds. Electronegativity, on the other hand, is an eigenvalue corresponding to the average potential seen by an electron as a molecular orbital changes into monocentric (atomic) orbitals.     

Inner and outer phases of antibonding orbitals of transition metal bonds: olefin metathesis

The frontier orbital theory is applied to ruthenium olefin metathesis. The formal [2+2] cycloaddition step, that is, the key step involved in the catalytic cycle of the reaction, is found to be favored by the phases of the HOMO and LUMO, in sharp contrast to [2+2] cycloaddition reactions between olefins. In the LUMO of transition metal part, a d-orbital overlaps out of phase with the vacant p-orbital of the carbene in the inner space of the metal–carbon π bond as is expected, but the remote lobe of the d orbital overlaps in phase in the outer space of the bond. This is a characteristic feature of the antibonding orbitals of transition metal bonds. The outer orbital phase plays more important role in the interaction.     

Effect of hyperconjugation on ionization energies of hydroxyalkyl radicals

On the basis of electronic structure calculations and molecular orbital analysis, we offer a physical explanation of the observed large decrease (0.9 eV) in ionization energies (IE) in going from hydroxymethyl to hydroxyethyl radical. The effect is attributed to hyperconjugative interactions between the sigma CH orbitals of the methyl group in hydroxyethyl, the singly occupied p orbital of carbon, and the lone pair p orbital of oxygen. Analyses of vertical and adiabatic IEs and hyperconjugation energies computed by the natural bond orbital (NBO) procedure reveal that the decrease is due to the destabilization of the singly occupied molecular orbital in hydroxyethyl radical as well as structural relaxation of the cation maximizing the hyperconjugative interactions. The stabilization is achieved due to the contraction of the CO and CC bonds, whereas large changes in torsional angles bear little effect on the total hyperconjugation energies and, consequently, IEs.