Canonical Molecular Orbitals Research Articles

Quantitative Characteristics of Qualitative Localized Bonding Patterns

Patterns of localized and delocalized chemical bonding obtained using the recently proposed adaptive natural density partitioning (AdNDP) provide a qualitative description of electronic structure but miss any quantitative information. Descriptors, such as the electron localization function (ELF), provide quantitative characteristics of bonding and can enhance the usefulness of qualitative patterns. In the present study, we used ELF and a related construct, charge-density-weighted ELF (ELF rho), to characterize localized and delocalized bonding in a variety of systems. It is demonstrated that ELF rho yields a more detailed description than ELF when used to analyze bonding in aromatic, conflicting aromatic, and antiaromatic systems. Both canonical molecular orbitals (CMOs) and localized multicenter two-electron (nc-2e) bonds obtained in the latter case by AdNDP localization are used to calculate ELF rho.

Comparison of configuration interaction expansions based on different orbital transformations

The characteristics of CI expansions based on different types of orbitals (all obtained from the same basis set) are compared in a series of calculations on the water molecule. The orbitals compared include canonical SCF molecular orbitals, natural orbitals, and two other types related to these. The comparisons include energy and property convergence and the distribution of magnitudes of the off-diagonal elements of the Hamiltonian matrix and of the eigenvector components. The implications of the results are discussed.

Carbo-siloles, Part 1: A Theoretical Study

The ring carbo-mer of silole, termed as carbo-silole, was investigated at the DFT level of theory (B3PW91/6-31G**) and compared to its carbo-cyclopentadiene and carbo-cyclopentadienone analogues. The electronic delocalization of these species and their parent molecules is analyzed indirectly from their optimized geometry, and directly from their canonical and NBO molecular orbitals by comparison of the HOMO-LUMO gaps. All criteria indicate that the π electron systems of carbo-silole and carbo-cyclopentadiene are delocalized to a similar extent, in particular through a π − σ* AH2 conjugation (A = C, Si). The cyclic component of the delocalization, i.e., aromaticity, has been more directly appraised by calculation of NICS values at the center of the rings: the latter definitely confirm that in contrast to carbo-cyclopentadienone (NICS = −8.1 ppm), both carbo-silole (NICS = −1.1 ppm) and carbo-cyclopentadiene (NICS = +2.4 ppm) are non-aromatic. The electron affinity is significantly increased by carbo-merization of silole (from 0.25 to 1.95 eV), suggesting that the carbo-silole ring might be a relevant unit for the design of functional materials. Studies of the carbo-silolylium cation show that its aromaticity is comparable to that of the long studied carbo-cyclopentadienyl analogue.

Substituent effects on conformational preference inα-substitutedα-fluorophenylacetic acid methyl ester model systems for chiral derivatizing agents

In connection with study of chiral derivatizing agents (CDAs) for NMR determination of absolute configuration of organic compounds, factors controlling the conformational preference between syn- and anti-forms in α-substituted α-fluorophenylacetic acid methyl ester (FC(X)(Ph)COOMe) model systems were theoretically investigated. Substituents X at the stereogenic carbon atom were X = H, CCH and CH3, the electronic and steric properties of which were significantly different from each other. The model system with X = CCH and that with X = CH3 were found to be possible candidates for fluorine-containing CDAs. The syn conformation is stable compared with the anti one by 0.7 kcal mol−1 for the ester with X = CCH. On the other hand, the anti conformation is stable compared with the syn one by 0.5 kcal mol−1 for the ester with X = CH3. Both natural bond orbital (NBO) analysis and deletion of selected orbitals based on the donor–acceptor NBO scheme were adopted for semi-quantitative estimation of factors responsible for the conformational preference as well as a qualitative inspection of occupied canonical molecular orbitals (MOs). It was shown that [σ–(σ* + π*)(CO)] and [σ–σ*(Ph) and π(Ph)–σ*] hyperconjugations are the main factors controlling the conformational preferences between the syn and anti conformations. Other types of effects such as electrostatic effects were also investigated. The role of the fluorine atom was also clarified. Copyright © 2009 John Wiley & Sons, Ltd.

Local σ– π mixing in C 60 buckminsterfullerene

The local σ– π mixing phenomenon in C 60 buckminsterfullerene is quantified. To accomplish this, the localized orbitals spanning the space of fullerene’s σ and π systems were orthogonalized and projected onto canonical molecular orbitals. The results show that there exist π-type molecular orbitals which possess ∼10% σ character and vice versa. This strong mixing can be considered as a new evidence that contributes to the unconventional properties of fullerenes. The localized analysis detected bond bending for both σ and π bonds which were deviated from their framework for nearly 14 degrees. Also, several localized aspects of the π system shows two types of π bonds while the σ bonds are fairly equivalent.

Aromaticity of Ni bis-dithiolenes complexes

The Ni bis-dithiolene complexes with D 2h symmetry were predicted to be stable at B3LYP/6-311++G(d) level. The analyses of nature bond orbital and nucleus-independent chemical shift (NICS) at B3LYP/6-31G(d) and GIAO-B3LYP/6-31G(d) level revealed the aromatic character of the Ni bis-dithiolene complexes. The total isotropic NICS (NICS iso) at the ring center [NICS(0) iso] has main contribution from the molecular orbitals (MOs) within the molecular plane according to the analysis of canonical MO (CMO) contributions to NICS. The π MOs have large contribution to the NICS iso at 1 Å above the ring center [NICS(1) iso]. Both analyses of CMO and nature local MO (NLMO) predict that the Ni–S σ bonds weaken the aromaticity of the Ni(S 2C 2H 2) and Ni(bdt) 2 complexes. The three d atomic orbitals with lone pair electrons of the Ni atom and the delocalized π bond among S–C–C–S have large contribution to the NICS(0) iso and NICS(1) iso in Ni(S 2C 2H 2) and Ni(bdt) 2 according to the analyses of NLMO. The C–C π bond has large contribution to the NICS( n) iso ( n = 0 or 1) in Ni(S 2C 2H 2) 2, while the delocalized S–C π bond has large contribution to the NICS( n) iso ( n = 0 or 1) in Ni(bdt) 2.

Application of a “charge-averaged” second order multireference perturbation theory strategy to the study of a model Mixed-Valence compound

A new proposed second order Multireference Perturbation Theory (MRPT) approach (termed NEVPT2(av)), based upon the use of state-averaged canonical molecular orbitals instead of the state-specific canonical ones, is applied to the study of a model Mixed-Valence compound. Such strategy has already been shown, on the basis of some preliminary calculations reported in a previous paper, to be able to overcome the inadequacy of a standard second order MRPT treatment for such MV systems. In order to test the validity and the firmness of the NEVPT2(av) methodology, an investigation is carried out, using basis sets of various size and two different active spaces. The reliability of the method is fully confirmed by the good agreement achieved with the results of highly-correlated Multireference Configuration Interaction (MRCI) computations recently published.

Conformation-Specific Raman Bands and Electronic Conjugation in Substituted Thioanisoles

Nonresonant Raman spectra and conformational stability are studied for thioanisole (TA) and substituted analogues [4-XTA, X = NO(2) (1), CN (2), H (3), CH(3) (4), and NH(2) (5)] at the 4-position. The ring-substituent (SCH(3)) vibrational modes of out-of-plane bending and torsional types are calculated to have strong Raman scattering activities only for the vertical conformers. Agreement between observed and calculated Raman spectra is analyzed numerically. The conformational stability of the SCH(3) rotation changes systematically to the electron-withdrawing character of the substituents. The rotational barrier is calculated satisfactorily by B3LYP/6-31++G(d,p) calculations, whereas the second- to fourth-order Møller-Presset perturbation theory and coupled-cluster with single- and double-excitation calculations tend to overestimate conformational energy barriers with respect to coplanar forms. The coplanar form is obtained for 1 and 2, whereas the vertical conformer is favorable for 4 and 5. The origin of the conformational energy difference, DeltaE, is demonstrated on the basis of canonical molecular orbitals and natural bond orbitals (NBOs) of the ground state. The natural bond orbital interaction between a nonbonding n(S) orbital of the S atom and a pi orbital of the benzene ring is shown to stabilize the coplanar form predominantly. A linear relationship is obtained between the energy of the highest occupied molecular orbitals and DeltaE. The n(S)-pi interaction energy, E(2), based on the NBO representation and the Hammet constants also change linearly with respect to DeltaE.

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

AbstractWeinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N2 molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N2 molecule. For example, the magnitude of Fab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.

An insight into the general relationship between the three dimensional structures of enzymes and their electronic wave functions: Implication for the prediction of functional sites of enzymes

In this study, we explored the general relationship between the three-dimensional (3D) structures of enzymes and their electronic wave functions. Furthermore, we developed a method for the prediction of their functionally important sites. For this purpose, we first performed linear-scaling molecular orbital calculations for 112 nonredundant, non-homologous enzymes with known structure and function. In consequence, we showed that the canonical molecular orbitals (MOs) of the enzymes could be classified into three groups according to the degree of electron delocalization: highly localized orbitals (Group A), highly delocalized orbitals whose electrons are distributed over almost the whole molecule (Group B), and moderately delocalized orbitals (Group C). The MOs belonging to Group A are located near the HOMO-LUMO band gap, and thereby include the frontier orbitals of a given enzyme. We inferred that the MOs of Group B play a role in stabilizing the 3D structure of the enzyme, while those of Group C contribute to constructing the covalent bond framework of the enzyme. Next, we investigated whether the frontier orbitals of enzymes could be used for identifying their potential functional sites. As a result, we found that the frontier orbitals of the 112 enzymes have a high propensity to be colocalized with the known functional sites, especially when the enzymes are hydrated. Such a propensity is shown to be remarkable when Glu or Asp is a functional site residue. On the basis of these results, we finally propose a protocol for the prediction of functional sites of enzymes.

A Theoretical Study of the Photodetachment and Intramolecular Hydrogen-Bonding Energies of Hydrogen Maleate Anions

Three low-lying conformers of the hydrogen maleate anions (HMAs) regarding cis-HMA(HB) having the O-...HO intramolecular hydrogen bond (HB), cis-HMA(nHB) without the HB, and trans-HMA are studied by density functional theory (B3LYP) combined with natural bond orbital (NBO) and atoms-in-molecules (AIM) analyses. The photoelectron spectra of cis- and trans-HMA conformers recorded by Woo et al. (J. Phys. Chem. A 2005, 109, 10633) are reassigned on the basis of the present electron propagator theory calculations, indicating the significant energy differences between the Dyson orbitals and canonical molecular orbitals due to the electron-correlation and orbital relaxation effects considered in the electron propagator theory. The NBO associated with the natural resonance theory analyses and AIM electron topological study show that the strong O-...HO in cis-HMA(HB) has the remarkable characteristics of three-center four-electron hyperbond, and the bonding strength of ca. 30 kcal/mol is recommended with the reference calculations of the HO-...HOH complex. The further calculations for the microhydrated cis-HMA(HB) clusters indicate that the O-...HO bonding strength decreases in water solution.

Symmetry-adapted-cluster/symmetry-adapted-cluster configuration interaction methodology extended to giant molecular systems: Ring molecular crystals

The symmetry adapted cluster (SAC)/symmetry adapted cluster configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states of molecules was extended to giant molecular systems. The size extensivity of energy and the size intensivity of excitation energy are very important for doing quantitative chemical studies of giant molecular systems and are designed to be satisfied in the present giant SAC/SAC-CI method. The first extension was made to giant molecular crystals composed of the same molecular species. The reference wave function was defined by introducing monomer-localized canonical molecular orbitals (ml-CMO's), which were obtained from the Hartree-Fock orbitals of a tetramer or a larger oligomer within the electrostatic field of the other part of the crystal. In the SAC/SAC-CI calculations, all the necessary integrals were obtained after the integral transformation with the ml-CMO's of the neighboring dimer. Only singles and doubles excitations within each neighboring dimer were considered as linked operators, and perturbation selection was done to choose only important operators. Almost all the important unlinked terms generated from the selected linked operators were included: the unlinked terms are important for keeping size extensivity and size intensivity. Some test calculations were carried out for the ring crystals of up to 10 000-mer, confirming the size extensivity and size intensivity of the calculated results and the efficiency of the giant method in comparison with the standard method available in GAUSSIAN 03. Then, the method was applied to the ring crystals of ethylene and water 50-mers, and formaldehyde 50-, 100-, and 500-mers. The potential energy curves of the ground state and the polarization and electron-transfer-type excited states were calculated for the intermonomer distances of 2.8-100 A. Several interesting behaviors were reported, showing the potentiality of the present giant SAC/SAC-CI method for molecular engineering.

Thiamin Deprotonation Mechanism. Carbanion Development Stabilized by the LUMOs of Thiazolium and Pyrimidylimine Working in Tandem and Release Governed by a H-Bond Switch

Our previous paper (J. Phys. Chem. A 2005, 109, 7606) using computed atomic charges, based on the quantum theory of atoms in molecules (QTAIM), on azolium models of thiamin diphosphate has shown that only sulfur acts as an effective electron sink in the formation of the thiamin carbanion intermediate. Herein we apply natural bond orbital (NBO) theory to the analysis of orbital contributions to canonical molecular orbitals (CMOs) of six abbreviated azolium analogs of the carbanion to better understand the unique function of sulfur. The NBO/CMO data provide a description of the origin of the first thiamin electron sink: sulfur performing in the sigma- and pi-orbitals of the transition state as well as in the carbanion, and its advantages due to low electronegativity and moderate size. At the next level of thiamin modeling, we include the six-membered pyrimidine ring to represent the prerequisite V-structure in the iminopyrimidine tautomeric form. This model is subjected to incremental deprotonation and MO decomposition. The 4'-pyrimidylimine moiety, in addition to being an internal base to abstract the C2 proton, also performs as the second electron sink. Thus, the LUMOs of the thiazolium and pyrimidylimine systems working in tandem stabilize the developing charges in these transient structures, with facilitation from their HOMOs. Further, the absence of detectable amounts of the C2 carbanion in 13C2-labeled thiamin-enzyme complex by NMR is explained. Both NBO analysis and the QTAIM topological electronic properties suggest the operation of a H-bonding scheme that leads to the formation of a cryptic C2 carbanion that is not accumulated. The shielding of the carbanion by the N4'-H hydrogen bond is weakened by N1'-H deprotonation. Consequently, prior return of the N1' proton to the nearby glutamate may be the switch for streaming a timed-release of the unstable C2 carbanion to the incoming substrate.

Pt-bridges in various single-strand and double-helix DNA sequences. DFT and MP2 study of the cisplatin coordination with guanine, adenine, and cytosine

In this study, various platinum cross-links in DNA bases were explored. Some of these structures occur in many cis/trans-platinated double-helixes or single-stranded adducts. However, in the models studied, no steric hindrance from sugar-phosphate backbone or other surroundings is considered. Such restrictions can change the bonding picture partially but hopefully the basic energy characteristics will not be changed substantially. The optimization of the structures explored was performed at the DFT level with the B3LYP functional and the 6-31G(d) basis set. Perturbation theory at the MP2/6-31++G(2df,2pd) level was used for the single-point energy and 6-31+G(d) basis set for the electron-property analyses. It was found that the most stable structures are the diguanine complexes followed by guanine-cytosine Pt-cross-links, ca 5 kcal mol(-1) less stable. The adenine-containing complexes are about 15 kcal mol(-1) below the stability of diguanine structures. This stability order was also confirmed by the BE of Pt-N bonds. For a detailed view on dative and electrostatic contributions to Pt-N bonds, Natural Population Analysis, determination of electrostatic potentials, and canonical Molecular Orbitals description of the examined systems were used.

Charge transfer interaction in the effective fragment potential method

An approximate formula is derived and implemented in the general effective fragment potential (EFP2) method to model the intermolecular charge transfer interaction. This formula is based on second order intermolecular perturbation theory and utilizes canonical molecular orbitals and Fock matrices obtained with preparative self-consistent field calculations. It predicts charge transfer energies that are in reasonable agreement with the reduced variational space energy decomposition analysis. The formulas for the charge transfer gradients with respect to EFP translational and rotational displacements are also derived and implemented.

Dipole Correlation of the Electronic Structures of theConformations of Water Molecule Evolving Through theNormal Modes of Vibrations Between Angular (C2v) to Linear(D∝h) Shapes

In order to settle the issue of equivalence or non-equivalence of the two lone pairsof electrons on oxygen atom in water molecule, a quantum chemical study of the dipolecorrelation of the electronic structure of the molecule as a function of conformationsgenerated following the normal modes of vibrations between the two extremeconformations, C2v (∠HOH at 90o) and D∝h (∠HOH at 180o), including the equilibrium one,has been performed. The study invokes quantum mechanical partitioning of moleculardipoles into bond moment and lone pair moment and localization of delocalized canonicalmolecular orbitals, CMO’s into localized molecular orbitals, LMO’s. An earlier suggestion,on the basis of photoelectron spectroscopy, that one lone pair is in p-type and the other is ins-type orbital of O atom of water molecule at its equilibrium shape, and also the qualitative“Squirrel Ears” structure are brought under serious scrutiny. A large number ofconformations are generated and the charge density matrix, dipole moment of eachconformation is computed in terms of the generated canonical molecular orbitals, CMO’sand then Sinanoğlu’s localization method is invoked to localize the CMO’s of eachconformation and the quantum mechanical hybridizations of all the bonds and lone pairs onO center are evaluated in terms of the localized molecular orbitals. Computed datademonstrate that the electronic structures i.e. two bond pairs and two lone pairs and itshybridization status of all conformations of water molecule are straightforward in terms ofthe LMO’s. It is further revealed that the pattern of orbital hybridization changescontinuously as a function of evolution of molecular shape. The close analysis of thegenerated LMO’s reveals that one lone pair is accommodated in a pure p orbital and anotherlone pair is in a hybrid orbital in almost all conformations. One more important result of the present study is that, with the physical process of structural evolution from close angular shape to the linear transition state, the length of the σ (O–H) decreases and its strength increases as a monotone function of reaction coordinates. The bond length is shortest and the strength is largest at the transition state of structural inversion. Result of structural effect of the present study during the evolution of molecular conformations is quite consistent with the result of a very refined calculation that one physically significant feature of force field that the stretching force constants at the linear geometry are considerably larger than their equilibrium counter parts. The variation of bond strength and the hybridization of s and p orbitals on O atom center to form the σ (O–H) bond as a function of evolution of conformations is in accordance with Coulson’s prediction. The total dipole moment of all conformations is partitioned into the contribution from bonds and lone pairs and correlated in terms of the computed hybridization in lone pairs. The analysis of the variation of dipole moment as a function of angular to linear structural evolution reveals that the dipole moment of H2O molecule is not due to the bond moments only but a significant contribution comes from a lone pair. It is strongly established that the dipole moment of water molecule at and around the equilibrium geometry is not due to the bond moments only and the major part of the molecular dipole comes from the contribution of lone pair electrons. This necessitates the accommodation of a lone pair of electrons in a hybrid orbital on O atom. The computed LMO’s webbed with partitioned molecular dipole reveal that one lone pair is in a pure p- type orbital and the other lone pair is in a hybrid of s and p, and not in a pure s type orbital as suggested on the basis of photoelectron spectra. The possibility of qualitative “Squirrel Ears” structure is also ruled out. The problem of equivalence or non-equivalence of the two lone pairs of the O atom in water seems to have been finally resolved by the present quantum chemical calculation. An attempt of locating the origin of barrier to the physical process of inversion of water molecule is made in terms of energy partitioning method. It is found that the dipole can be used as a descriptor for the elucidation of electronic structure of molecules.

Understanding Substituent Effects on 29Si Chemical Shifts and Bonding in Disilynes. A Quantum-Chemical Analysis

The 29Si chemical shifts in substituted disilynes have been analyzed by quantum-chemical studies using a detailed breakdown of paramagnetic contributions into couplings of occupied and virtual canonical molecular orbitals. The results give indications of substituent effects on shielding and confirm the importance of energy denominators in the equation for σp in symmetrical substituted disilynes (H3SiSiSiSiH3 and H3CSiSiCH3) on their chemical shifts. In the unsymmetrical substituted disilyne H3CSiSiSiH3 the energy denominators are identical for both sites and thus cannot explain the widely different chemical shifts. It turns out that the asymmetric charge distribution (reflected in both occupied and virtual MOs and sampled by the PSO matrix elements) allows more efficient couplings at the methyl-substituted silicon side. Furthermore, shielding values in disilynes depend strongly on the size of the trans-bent angle φ, as indicated clearly by analyses of the 29Si chemical shifts in the model H3SiSiSiSiH3 at selected values of φ. Small changes in φ influence the 29Si shielding values appreciably. At lower values of φ, couplings between bonding and virtual MOs exhibit stronger deshielding caused by significantly lower energy denominators.

A localized molecular-orbital assembler approach for Hartree–Fock calculations of large molecules

We describe an alternative fragment-based method, the localized molecular-orbital assembler method, for Hartree-Fock (HF) calculations of macromolecules. In this approach, a large molecule is divided into many small-size fragments, each of which is capped by its local surroundings. Then the conventional HF calculations are preformed on these capped fragments (or subsystems) and the canonical molecular orbitals of these systems are transferred into localized molecular orbitals (LMOs). By assembling the LMOs of these subsystems into a set of LMOs of the target molecule, the total density matrix of the target molecule is constructed and correspondingly the HF energy or other molecular properties can be approximately computed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations with double-zeta and polarized double-zeta basis sets demonstrate that the present approach is able to reproduce the conventional HF energies within a few millihartrees for a broad range of molecules.

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.

Theoretical Revisit of Regioselectivities of Diels−Alder Reactions: Orbital-Based Reevaluation of Multicentered Reactivity in Terms of Reactive Hybrid Orbitals

When reactions proceed under kinetic control, stereoselectivities are determined from energetic properties of the transition state (TS). Orbital interaction at the TS plays a significant role in determining reactivity and selectivity, because it is directly related to lowering of the activation barrier. However, the orbital interaction at the TS cannot be represented only in terms of the frontier orbitals at the reactant state. A reactive hybrid orbital (RHO) that is localized at the reaction site is used to represent the orbital around the relevant TS in terms of a combination of the canonical molecular orbitals (MOs). This representation can make comparison of reactivities and selectivities among molecules of different sizes feasible. In this paper, the regioselectivities of Diels-Alder cycloaddition reactions of a monosubstituted butadiene and a dienophile (a monosubstituted ethylene) are investigated in terms of several parameters such as reactivity index and stabilization index, which are obtained on the basis of the newly developed multicentered version of the RHO method. These values can also be compared with the corresponding parameters defined on the basis of the frontier orbitals. Predictions of the regioselectivities based on the RHOs are consistent with experimental observations, while those based on the frontier orbitals are unreliable. This is because the RHO is superior to the frontier orbital as a descriptor of the orbital participating in orbital interactions around the TS.