Theoretical studies of intramolecular electron transfer reactions: Distance and free energy dependences

Electron tunneling through a square potential energy barrier is used to calculate the distance-dependent factors of electron transfer (ET) processes in metal-monolayer-metal junctions, donors and acceptors dispersed in rigid organic glasses, intramolecular ET in rigid donorbridge—acceptor species in solution and redox centers attached to electrodes through adsorbed monolayers. This tunneling model of distancedependent non-adiabatic factors is incorporated in the intersecting state model (ISM). The result is a simple semiclassical theory which is used to calculate the rates of non-adiabatic ET reactions. When the electron is originally located in a π* molecular orbital of the donor and the reaction free energy is no lower than approximately −50 kJ mol⁻¹, no adjustable parameters are necessary to calculate the intramolecular ET rates from a donor, through a rigid bridge, to an acceptor. Such calculated rates are within an order of magnitude of the experimental values. The model can also account for the ET rates of more exothermic reactions provided that the value of an empirical parameter, which is constant for structurally related reactants and solvents of similar polarity, is estimated. The physical meaning of this parameter is related to the dynamics of the reactions. The profiles of the distance and free energy dependences of photoinduced ET rates are closely reproduced. The occurrence of distance-dependent non-adiabatic factors in intermolecular σ*-d ETs is rationalized.     

Photoinduced intra- and intermolecular electron transfer in solutions and in solid organized molecular assemblies

The present paper highlights results of a systematic study of photoinduced electron transfer, where the fundamental aspects of the photochemistry occurring in solutions and in artificially or self-assembled molecular systems are combined and compared. In photochemical electron transfer (ET) reactions in solutions the electron donor, D, and acceptor, A, have to be or to diffuse to a short distance, which requires a high concentration of quencher molecules and/or long lifetimes of the excited donor or acceptor, which cannot always be arranged. The problem can partly be avoided by linking the donor and acceptor moieties covalently by a single bond, molecular chain or chains, or rigid bridge, forming D-A dyads. The covalent combination of porphyrin or phthalocyanine donors with an efficient electron acceptor, e.g. fullerene, has a two-fold effect on the electron transfer properties. Firstly, the electronic systems of the D-A pair result in a formation of an exciplex intermediate upon excitation both in solutions and in solid phases. The formation of the exciplex accelerates the ET rate, which was found to be as fast as >10(12) s(-1). Secondly, the total reorganization energy can be as small as 0.3 eV, even in polar solvents, which allows nanosecond lifetimes for the charge separated (CS) state. Molecular assemblies can form solid heterogeneous, but organized systems, e.g. molecular layers. This results in more complex charge separation and recombination dynamics. A distinct feature of the ET in organized assemblies is intermolecular interactions, which open a possibility for a charge migration both in the acceptor and in the donor layers, after the primary intramolecular exciplex formation and charge separation in the D-A dyad. The intramolecular ET is fast (35 ps) and efficient, but the formed interlayer CS states have lifetimes in microsecond or even second time domain. This is an important result considering possible applications.     

Intramolecular dissociative electron transfer

Dissociative electron transfers (ET) are reactions in which the ET is associated with the cleavage of a sigma bond. Although a rather satisfactory amount of information is currently available on the intermolecular and heterogeneous dissociative ET reactions, less is known for the corresponding intramolecular processes, despite the relevance of these reactions in both chemistry and biochemistry. This tutorial review focuses on the most recent developments in this area, with particular emphasis on the reactions occurring in well-defined Donor-Spacer-Acceptor molecular systems. The goal is to provide the reader with the essential background to understand and possibly predict the feasibility and rates of these reactions, as well as to stimulate the application of the intramolecular dissociative ET concepts and related issues to still unexplored molecular systems.     

Coordination control of intramolecular electron transfer in boronate-bridged zinc porphyrin-diimide molecules

Three sets of dyads, in which a zinc-porphyrin (ZP) electron donor is connected to an aromatic diimide electron acceptor,either pyromellitimide (PI) or naphthalene-1,8:4,5-tetracarboxylic acid diimide (NI), via a boronate-ester bridge, a piperidine bridge, and a 1,3-dioxolane bridge, respectively, were prepared for the purpose of control of intramolecular electron transfer (ET) by acid-base reactions at the connecting bridge. Boronate-ester bridge is a Lewis acidic site and confers a chance to regulate intramolecular ET reaction upon base coordination. This has been demonstrated by suppression of photoinduced ET from ZP to PI or NI in highly electron-pair donating solvents or upon addition of a fluoride anion. To extend this strategy to control of ET-path selectivity, we prepared triad 18, which consists of a ZP donor bearing NI and PI acceptors at similar distances through a boronate-ester bridge and an acetal bridge, respectively. Photoexcitation of 18 in a free form led to intramolecular ET from (1)()ZP preferentially to NI, but the ET path was completely switched toward PI in F(-)-coordinated form without a serious drop in the rate, constituting a novel ET-switching molecular system.     

Ab initio study of long-range electron transfer between biphenyl anion radical and naphthalene

After the separation of the donor, the acceptor, and the σ-type bridge from the π-σ-π system, the geometries of biphenyl, biphenyl anion radical, naphthalene, and naphthalene anion radical are optimized, and then the reorganization energy for the intermolecular electron transfer (ET) at the levels of HF/4-31G and HF/DZP is calculated. The ET matrix elements of the self-exchange reactions of theπ-σ-π systems have been calculated by means of both the direct calculation based on the variational principle, and the transition energy between the molecular orbitals at the linear coordinateR = 0.5. For the cross reactions, the ET matrix element and the geometry of the transition state are determined by searching the minimum energy splitting Δ_min along the reaction coordinate. In the evaluation of the solvent reorganization energy of the ET in solution, the Marcus’ two- sphere model has been invoked. A few of ET rate constants for the intramolecular ET reactions for the π-σ-π systems, which contain the biphenylyl as the donor and both biphenylyl and naphthyl as the acceptor, have been obtained. Project supported by the National Natural Science Foundation of China (Grant Nos. 29706104 and 29573112), the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University.     

Endothelin receptors in gastrointestinal smooth muscle

Endothelins (ETs) are a family of peptides with 21-amino-acid residues. ET-1 was identified as a potent vasoconstrictor produced by vascular endothelial cells. Three distinct isoforms of ET, i.e. ET-1, ET-2 and ET-3, have been found to exist in a variety of tissues. ET was later found to cause contraction as well as relaxation of smooth muscle in many physiologic systems. In the gastrointestinal tract, ET causes contraction and/or relaxation of the esophagus, stomach, ileum and colon. In the hepatobiliary system, ET causes contraction of the portal vein, hepatic stellate cells, gallbladder and common bile duct. In mammalian species, two classes of ET receptors, ET(A) and ET(B), have been cloned. ET(A) receptors have higher affinities for ET-1 and ET-2 than ET-3, while ET(B) receptors have the same affinities for ET-1, ET-2 and ET-3. In the gastrointestinal system, ET causes smooth muscle contraction through interaction with ET(A) receptors, ET(B) receptors or both ET(A) and ET(B) receptors, depending on the tissues and species. In addition to contraction, ET causes smooth muscle relaxation through interaction with ET(A) receptors or ET(B) receptors. At the present time, there are no studies showing that ET causes smooth muscle relaxation through interaction with both ET(A) and ET(B) subtypes. ET induces contraction in most of the non-sphincter muscle except the fundus of the stomach. On the other hand, ET causes relaxation and contraction in the lower esophageal and internal anal sphincters. ET may play an important role in the control of human gastrointestinal motility and portal vein pressure.     

Electron Transfer around a Molecular Corner

The distance dependence of electron transfer (ET) is commonly investigated in linear rigid rod‐like compounds, but studies of molecular wires with integrated corners imposing 90° angles are very rare. By using spirobifluorene as a key bridging element and by substituting it at different positions, two isomeric series of donor‐bridge‐acceptor compounds with either nearly linear or angled geometries were obtained. Photoinduced ET in both series is dominated by rapid through‐bond hole hopping across oligofluorene bridges over distances of up to 70 Å. Despite considerable conformational flexibility, direct through‐space and through‐solvent ET is negligible even in the angled series. The independence of the ET rate constant on the total number of fluorene units in the angled series is attributed to a rate‐limiting tunneling step through the spirobifluorene corner. This finding is relevant for multidimensional ET systems and grids in which individual molecular wires are interlinked at 90° angles.     

Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores

Enhanced two-photon-absorbing (2PA) systems with triplet cores are currently under scrutiny for several biomedical applications, including photodynamic therapy (PDT) and two-photon microscopy of oxygen. The performance of so far developed molecules, however, is substantially below expected. In this study we take a detailed look at the processes occurring in these systems and propose ways to improve their performance. We focus on the interchromophore distance tuning as a means for optimization of two-photon sensors for oxygen. In these constructs, energy transfer from several 2PA chromophores is used to enhance the effective 2PA cross section of phosphorescent metalloporphyrins. Previous studies have indicated that intramolecular electron transfer (ET) can act as an effective quencher of phosphorescence, decreasing the overall sensor efficiency. We studied the interplay between 2PA, energy transfer, electron transfer, and phosphorescence emission using Rhodamine B-Pt tetrabenzoporphyrin (RhB-PtTBP) adducts as model compounds. 2PA cross sections (sigma2) of tetrabenzoporphyrins (TBPs) are in the range of several tens of GM units (near 800 nm), making TBPs superior 2PA chromophores compared to regular porphyrins (sigma2 values typically 1-2 GM). Relatively large 2PA cross sections of rhodamines (about 200 GM in 800-850 nm range) and their high photostabilities make them good candidates as 2PA antennae. Fluorescence of Rhodamine B (lambda(fl) = 590 nm, phi(fl) = 0.5 in EtOH) overlaps with the Q-band of phosphorescent PtTBP (lambda(abs) = 615 nm, epsilon = 98 000 M(-1) cm(-1), phi(p) approximately 0.1), suggesting that a significant amplification of the 2PA-induced phosphorescence via fluorescence resonance energy transfer (FRET) might occur. However, most of the excitation energy in RhB-PtTBP assemblies is consumed in several intramolecular ET processes. By installing rigid nonconducting decaproline spacers (Pro10) between RhB and PtTBP, the intramolecular ETs were suppressed, while the chromophores were kept within the F?rster r0 distance in order to maintain high FRET efficiency. The resulting assemblies exhibit linear amplification of their 2PA-induced phosphorescence upon increase in the number of 2PA antenna chromophores and show high oxygen sensitivity. We also have found that PtTBPs possess unexpectedly strong forbidden S0 --> T1 bands (lambda(max) = 762 nm, epsilon = 120 M-1 cm-1). The latter may overlap with the laser spectrum and lead to unwanted linear excitation.     

Molecular Gears: From Solution to Surfaces

This review highlights the major efforts devoted to the development of molecular gears over the past 40 years, from pioneering covalent bis-triptycyl systems undergoing intramolecular correlated rotation in solution, to the most recent examples of gearing systems anchored on a surface, which allow intermolecular transmission of mechanical power. Emphasis is laid on the different strategies devised progressively to control the architectures of molecular bevel and spur gears, as intramolecular systems in solution or intermolecular systems on surfaces, while aiming at increased efficiency, complexity and functionality.     

Photoinduced electron transfer between quinones and amines in micellar media: Tuning the Marcus inversion region

Electron transfer (ET) rates between quinone acceptors and amine donors in micellar media show Marcus inversion behavior on correlating with the free energy changes of the ET reactions. The onset of Marcus inversion in these systems is seen to be tuned by about 0.25 eV by changing the type of the micelle. The results are rationalized on the basis of two-dimensional ET theory where ET occurs along intramolecular coordinate with non-equilibrium configuration along solvation coordinate. Maximum ET rates are seen to vary by about one order of magnitude in different micelles, and are attributed to the micelle-dependent changes in the separations of the interacting quinone–amine pairs. Tunings of Marcus inversion and ET rates by changing micellar microenvironments have been observed and suggested to have useful implications in different applied areas.     

Low-temperature electronic transport through macromolecules and characteristics of intramolecular electron transfer

Long-distance electron transfer (ET) plays an important part in many biological processes. Also, fundamental understanding of ET processes could give grounds for designing miniaturized electronic devices. So far, experimental data on the ET mostly concern ET rates which characterize ET processes as a whole. Here, we develop a different approach which could provide more information about intrinsic characteristics of the long-range intramolecular ET. A starting point of the studies is an obvious resemblance between ET processes and electric transport through molecular wires placed between metallic contacts. Accordingly, the theory of electronic transport through molecular wires is applied to analyze characteristics of a long-range electron transfer through molecular bridges. Assuming a coherent electron tunneling to be a predominant mechanism of ET at low temperatures, it is shown that low-temperature current-voltage characteristics could exhibit a special structure, and the latter contains information concerning intrinsic features of the intramolecular ET. Using the Buttiker dephasing model within the scattering matrix formalism, we analyze the effect of dephasing on the electron transmission function and current-voltage curves.     

Ultrafast proton-coupled electron-transfer dynamics in pyrene-modified pyrimidine nucleosides: model studies towards an understanding of reductive electron transport in DNA.

5-(Pyren-1-yl)-2'-deoxyuridine (PydU) and 5-(Pyren-1-yl)-2'-deoxycytidine (PydC) were used as model nucleosides for DNA-mediated reductive electron transport (ET) in steady-state fluorescence and femtosecond time-resolved transient absorption spectroscopy studies. Excitation of the pyrene moiety in PydU and PydC leads to an intramolecular electron transfer that yields the pyrenyl radical cation and the corresponding pyrimidine radical anion (dU.- and dC.-. By comparing the excited state dynamics of PydC and PydU, we derived information about the energy difference between the two pyrimidine radical anion states. To determine the influence of protonation on the rates of photoinduced intramolecular ET, the spectroscopic investigations were performed in acetonitrile, MeCN, and in water at different pH values. The results show a significant difference in the basicity of the generated pyrimidine radical anions and imply an involvement of proton transfer during electron hopping in DNA. Our studies revealed that the radical anion dC.- is being protonated even in basic aqueous solution on a picosecond time scale (or faster). These results suggest that protonation of dC.- may also occur in DNA. In contrast, efficient ET in PydU could only be observed at low pH values (< 5). In conclusion, we propose--based on the free energy differences and the different basicities--that only dT.- but not dC.- can participate as an intermediate charge carrier for excess electron migration in DNA.     

Modeling and computations of the intramolecular electron transfer process in the two-heme protein cytochrome c(4)

The di-heme protein Pseudomonas stutzeri cytochrome c(4) (cyt c(4)) has emerged as a useful model for studying long-range protein electron transfer (ET). Recent experimental observations have shown a dramatically different pattern of intramolecular ET between the two heme groups in different local environments. Intramolecular ET in homogeneous solution is too slow (>10 s) to be detected but fast (ms-μs) intramolecular ET in an electrochemical environment has recently been achieved by controlling the molecular orientation of the protein assembled on a gold electrode surface. In this work we have performed computational modeling of the intramolecular ET process by a combination of density functional theory (DFT) and quantum mechanical charge transfer theory to disclose reasons for this difference. We first address the electronic structures of the model heme core with histidine and methionine axial ligands in both low- and high-spin states by structure-optimized DFT. The computations enable estimating the intramolecular reorganization energy of the ET process for different combinations of low- and high-spin heme couples. Environmental reorganization free energies, work terms ("gating") and driving force were determined using dielectric continuum models. We then calculated the electronic transmission coefficient of the intramolecular ET rate using perturbation theory combined with the electronic wave functions determined by the DFT calculations for different heme group orientations and Fe-Fe separations. The reactivity of low- and high-spin heme groups was notably different. The ET rate is exceedingly low for the crystallographic equilibrium orientation but increases by several orders of magnitude for thermally accessible non-equilibrium configurations. Deprotonation of the propionate carboxyl group was also found to enhance the ET rate significantly. The results are discussed in relation to the observed surface immobilization effect and support the notion of conformationally gated ET.     

Ellagitannin Digestion in Moth Larvae and a New Dimeric Ellagitannin from the Leaves of Platycarya strobilacea

Ellagitannins (ETs) are plant polyphenols with various health benefits. Recent studies have indicated that the biological activities of ETs are attributable to their degradation products, including ellagic acid and its gut microflora metabolites, such as urolithins. Insect tea produced in the Guangxi region, China, is made from the frass of moth larvae that feed on the ET-rich leaves of Platycarya strobilacea. Chromatographic separation of the Guangxi insect tea showed that the major phenolic constituents are ellagic acid, brevifolin carboxylic acid, gallic acid, brevifolin, and polymeric polyphenols. Chemical investigation of the feed of the larvae, the fresh leaves of P. strobilacea, showed that the major polyphenols are ETs including pedunculagin, casuarictin, strictinin, and a new ET named platycaryanin E. The new ET was confirmed as a dimer of strictinin having a tergalloyl group. The insect tea and the leaves of P. strobilacea contained polymeric polyphenols, both of which were shown to be composed of ETs and proanthocyanidins by acid hydrolysis and thiol degradation. This study clarified that Guangxi insect tea contains ET metabolites produced in the digestive tract of moth larvae, and the metabolites probably have higher bioavailabilities than the original large-molecular ETs of the leaves of P. strobilacea.     

Photo-induced electron transfer study of rhenium(I) bipyridyl complexes with covalently linked phenothiazine donor through different bridge

A novel rhenium(I) bipyridyl complex 1a, [(4,4’-di-COOEt-bpy)Re(CO)₃(py-NHCO-PTZ)PF₆] and a model 1b, [(4,4’-di-COOEt-bpy)Re(CO)₃(py-PTZ)PF₆] (bpy is 2, 2’-bipyridine, py-NHCO-PTZ is phenothiazine-(10-carbonyl amide) pyridine and py-PTZ is 10-(4-picolyl) phenothiazine) were synthesized. Their photo-induced electron transfer (ET) reaction with electron acceptor methyl viologen (MV²⁺) in acetonitrile was studied by nanosecond laser flash photolysis at room temperature. Photoexcitation of 1 in the presence of MV²⁺ led to ET from the Re moiety to MV²⁺ generating Re(II) and methyl viologen radical (MV^·+). Then Re(II) was reduced either by the charge recombination with MV^·+ or by intramolecular ET from the attached PTZ, regenerating the photosensitizer Re(I) and forming the PTZ radical at 510 nm. In the case of 1b, the absorption for PTZ radical can be observed distinctly accompanied intermolecular ET, whereas not much difference at 510 nm can be detected for 1a on the time scale of the experiments. This demonstrates that the linking bridge plays a key role on the intramolecular ET in complex 1.     

Charge-localized naphthalene-bridged bis-hydrazine radical cations

Electron transfer (ET) in four symmetrically substituted naphthalene-bridged bis-hydrazine radical cations (1,4; 1,5; 2,6; and 2,7) is compared within the Marcus-Hush framework. The ET rate constants (k(ET)) for three of the compounds were measured by ESR; the 2,7-substituted compound has an intramolecular ET that is too slow to measure by this method. The k(ET) values are significantly dependent upon the substitution pattern of the hydrazine units on the naphthalene bridge but do not correlate with the distance between them. This is contrary to an assumption that is frequently made about intervalence compounds that the bridge serves only as a spacer that fixes the distance between the charge-bearing units. The internal vibrational and solvent portions (lambda(v) and lambda(s)) of the total reorganization energy (lambda) have been separated using solvent effects on the intervalence band maximum, resulting in a lambda(v) that is the same, 9900 cm(-1), for the differently substituted naphthalenes. This is in accord with the general assumption that lambda(v) is primarily dependent upon the charge bearing unit and not the bridge. However, the trends in lambda(s) cannot be explained by dielectric continuum theory.     

On the Hopping Efficiency of Nanoparticles in the Electron Transfer across Self‐Assembled Monolayers

Redox reactions of solvated molecular species at gold‐electrode surfaces modified by electrochemically inactive self‐assembled molecular monolayers (SAMs) are found to be activated by introducing Au nanoparticles (NPs) covalently bound to the SAM to form a reactive Au–alkanedithiol–NP–molecule hybrid entity. The NP appears to relay long‐range electron transfer (ET) so that the rate of the redox reaction may be as efficient as directly on a bare Au electrode, even though the ET distance is increased by several nanometers. In this study, we have employed a fast redox reaction of surface‐confined 6‐(ferrocenyl) hexanethiol molecules and NPs of Au, Pt and Pd to address the dependence of the rate of ET through the hybrid on the particular NP metal. Cyclic voltammograms show an increasing difference in the peak‐to‐peak separation for NPs in the order Au<Pt<Pd, especially when the length of the alkanedithiol increases from octanedithiol to decanedithiol. The corresponding apparent rate constants, k_app, for decanedithiol are 1170, 360 and 14 s^?1 for NPs of Au, Pt and Pd, respectively, indicating that the efficiency of NP mediation of the ET clearly depends on the nature of the NP. Based on a preliminary analysis rooted in interfacial electrochemical ET theory, combined with a simplified two‐step view of the NP coupling to the electrode and the molecule, this observation is referred to the density of electronic states of the NPs, reflected in a broadening of the molecular electron/NP bridge group levels and energy‐gap differences between the Fermi levels of the different metals.     

红光发射分子转子的设计与合成

粘度对细胞微环境的维持非常重要。检测细胞内的粘度一般采用分子转子,而目前大多数的分子转子发射波长较短,不利于生物成像,为此我们设计了基于扭转分子内电荷转移(TICT)机理,通过共轭双键连接吸电子基和给电子基的红光发射的分子转子2-(2-(4-氨基苯乙烯基)-4-H-吡喃-4-亚基)-丙二腈(DCM-NH_2)。DCM-NH_2的最大发射波长为631 nm,属于远红光,能有效减少生物背景,提高成像信噪比。该探针对粘度有很好的响应,具有非常宽的线性响应范围(0.6~458.6 c P),同时也具有较高的灵敏度。     

Energy and electron transfer in beta-alkynyl-linked porphyrin-[60]fullerene dyads

Three porphyrin-fullerene dyads, in which a diyne bridge links C(60) with a beta-position on a tetraarylporphyrin, have been synthesized. The free-base dyad was prepared, as well as the corresponding Zn(II) and Ni(II) materials. These represent the first examples of a new class of conjugatively linked electron donor-acceptor systems in which pi-conjugation extends from the porphyrin ring system directly to the fullerene surface. The processes that occur following photoexcitation of these dyads were examined using fluorescence and transient absorption techniques on the femtosecond, picosecond, and nanosecond time scales. In sharp contrast to the photodynamics associated with singlet excited-state decay of reference tetraphenylporphyrins (ZnTPP, NiTPP, and H(2)TPP), the diyne-linked dyads undergo ultrafast (<10 ps) singlet excited-state deactivation in toluene, tetrahydrofuran (THF), and benzonitrile (PhCN). Transient absorption techniques with the ZnP-C(60) dyad clearly show that in toluene intramolecular energy transfer (EnT) to ultimately generate C(60) triplet excited states is the dominant singlet decay mechanism, while intramolecular electron transfer (ET) dominates in THF and PhCN to give the ZnP(*+)/C(60)(*-) charge-separated radical ion pair (CSRP). Electrochemical studies indicate that there is no significant charge transfer in the ground states of these systems. The lifetime of ZnP(*+)/C(60)(*-) in PhCN was approximately 40 ps, determined by two different types of transient absorption measurement in two different laboratories. Thus, in this system, the ratio of the rates for charge separation (k(CS)) to rates for charge recombination (k(CR)), k(CS)/k(CR), is quite small, approximately 7. The fact that charge separation (CS) rates increase with increasing solvent polarity is consistent with this process occurring in the normal region of the Marcus curve, while the slower charge recombination (CR) rates in less polar solvents indicate that the CR process occurs in the Marcus inverted region. While photoinduced ET occurs on a similar time scale in a related dyad 15 in which a diethynyl bridge connects C(60) to the para position of a meso phenyl moiety of a tetrarylporphyrin, CR occurs much more slowly; i.e., k(CS)/k(CR) approximately equal to 7400. Thus, the position at which the conjugative linker is attached to the porphyrin moiety has a dramatic influence on k(CR) but not on k(CS). On the basis of electron density calculations, we tentatively conclude that unfavorable orbital symmetries inhibit charge recombination in 15 vis a vis the beta-linked dyads.     

取代1-氯蒽醌中分子内卤键的电子密度拓扑分析

运用量子化学密度泛函B3LYP方法,在6-311＋＋G（d,p）基组水平上对邻位和间位取代1-氯葸醌的分子内卤键进行了研究．用电子定域函数和“分子中的原子,,理论对分子内卤键的性质进行了电子密度拓扑分析．通过对计算得到的密度矩阵进行σ-π兀分离,得到了π-键的键径和分子图,并讨论了。电荷密度和兀电荷密度对卤键的影响．结果表明,键鞍点和环鞍点处的电子密度拓扑性质均可作为衡量分子内卤键强度的量度．键鞍点和环鞍点处的电荷密度P越大,键鞍点与环鞍点的距离越大,卤键强度越大．除σ电荷密度外,π电荷密度对分子内卤键的性质也有明显影响．