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 c...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.展开更多
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 ...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.展开更多
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 th...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.展开更多
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 bon...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.展开更多
The concept of resonance-assisted hydrogen bonds(RAHBs)highlights the synergistic interplay between theπ-resonance and hydrogen bonding interactions.This concept has been well-accepted in academia and is widely used ...The concept of resonance-assisted hydrogen bonds(RAHBs)highlights the synergistic interplay between theπ-resonance and hydrogen bonding interactions.This concept has been well-accepted in academia and is widely used in practice.However,it has been argued that the seemingly enhanced intramolecular hydrogen bonding(IMHB)in unsaturated compounds may simply be a result of the constraints imposed by theσ-skeleton framework.Thus,it is crucial to estimate the strength of IMHBs.In this work,we used two approaches to probe the resonance effect and estimate the strength of the IMHBs in the two exemplary cases of the enol forms of acetylacetone and o-hydroxyacetophenone.One approach is the block-localized wavefunction(BLW)method,which is a variant of the ab initio valence bond(VB)theory.Using this approach,it is possible to derive the geometries and energetics with resonance shut down.The other approach is Edmiston’s truncated localized molecular orbital(TLMO)technique,which monitors the energy changes by removing the delocalization tails from localized molecular orbitals.The integrated BLW and TLMO studies confirmed that the hydrogen bonding in these two molecules is indeed enhanced byπ-resonance,and that this enhancement is not a result ofσconstraints.展开更多
The interactions of complexes of XeOF_(2) and XeO_(3) with a series of different hybridization N-containing donors are studied by means of DFT and MP_(2) calculations.The aerogen bonding interaction energies range fro...The interactions of complexes of XeOF_(2) and XeO_(3) with a series of different hybridization N-containing donors are studied by means of DFT and MP_(2) calculations.The aerogen bonding interaction energies range from 6.5 kcal/mol to19.9 kcal/mol between XeO_(3) or XeOF_(2) and typical N-containing donors.The sequence of interaction for N-containing hy-bridization is sp^(3)>sp^(2)>sp,and XeO_(3)is higher than XeOF_(2).For some donors of sp^(2)and sp^(3) hybridization,the steric effect plays a minor role in the interaction with the evidence of reduced density gradient plots.The dominant stable part is the electrostatic interaction.In complex of XeO_(3),the weight of polarization is larger than dispersion,while the situation is opposite for XeOF_(2)complexes.Except for the sum of the maximum value of molecular electrostatic potential on Xe atom and minimum value of molecular electrostatic potential on N atom,the other five interaction parameters including the potential energy density at bond critical point,the equilibrium distances,interaction energies with the basis set superposition error correction,localized molecular orbital energy decomposition analysis interaction energies,and the electron charge density,show great linear correlation coefficients with each other.展开更多
A localized INDO method was used to calculate the ion [Fe_2 (CH_3) (CO) (Ph_2PCH_2PPh_2)- Cp_2]^+. Based on the analysis of the localized molecular orbitals (LMO), bond orders and contour maps, it was pointed out that...A localized INDO method was used to calculate the ion [Fe_2 (CH_3) (CO) (Ph_2PCH_2PPh_2)- Cp_2]^+. Based on the analysis of the localized molecular orbitals (LMO), bond orders and contour maps, it was pointed out that the LMO no. 20 corresponds to the coordination of C(1)-H(I) σbond to Fe(2) atom. Non occurrence of metal-metal bond between Fe(1) and Fe(2) atoms was found and the covalence of irons was numerated, which coincides with the value in ref 17.展开更多
The localized molecular orbitals and energy levels for four typical conjugated six-membered ring systems C_6H_6, C_3N_3H_3, B_3N_3H_6, and (B_3O_6)^(3-) as well as a non-aromatic reference molecule N_3Cl_6 have been ...The localized molecular orbitals and energy levels for four typical conjugated six-membered ring systems C_6H_6, C_3N_3H_3, B_3N_3H_6, and (B_3O_6)^(3-) as well as a non-aromatic reference molecule N_3Cl_6 have been calculated by using Edmiston-Ruedenberg energy localization technique under the CNDO/2 approximation in order to investigate the nature of aromaticity or quasi-aromaticity of the six-membered ring systems studied. The contour maps for π-type localized MO's (LMO) have been plotted to illustrate the bonding characteristics of the five ring systems studied. These LMO calculations show that for all the conjugated six-membered ring systems considered there exists local delocalization of π-bonds or three-centered and occasionally four-centered two-electron π-bonds in our terminology, and the cooperative effect among these π-bonds leading to the formation of a closed continuous x-conjugation system around the ring, which is necessary for the creation of aromaticity in the systems studied. We have been able to discuss the properties of these three-centered π-bonds in terms of the constituent atoms and electrons and the relevant orbitals involved.展开更多
The localized molecular orbitals (LMOs) of certain quasi-aromatic organic and inor- ganic molecules with six-membered rings have been calculated by virtue of the ab initio method using STO-3G and 4-31G basis sets as w...The localized molecular orbitals (LMOs) of certain quasi-aromatic organic and inor- ganic molecules with six-membered rings have been calculated by virtue of the ab initio method using STO-3G and 4-31G basis sets as well as the CNDO/2 method. It is shown that there exists extensively-delocalized p-pπ bonding in these quasi-aromatic systems. The localized pictures of the π-type LMOs for the heterocyclic and homocyclic systems from the σ-π localization scheme are discussed. The Generator Orbital approach is utilized to account for the bonding patterns.展开更多
Within the localized molecular orbital description,the intra- and interorbital pair correlation energies calculated with the coupled cluster doubles (CCD) theory have been obtained for methane,ethane,propane,butane,is...Within the localized molecular orbital description,the intra- and interorbital pair correlation energies calculated with the coupled cluster doubles (CCD) theory have been obtained for methane,ethane,propane,butane,isobutane,pentane, isopentane and neopentane using the 6-31G * basis set. The results showed the quantitative transferability of pair correlation energies and gross orbital correlation energies within this series of molecules. Based on the gross orbital correlation energies of five sample alkanes (butane,isobutane,pentane,isopentane and neopentane),we have derived a simple linear relationship to estimate the CCD correlation energy for an arbitrary large alkane. The correlation energy predicted by this simple relationship remarkably recovers more than 98.9% of the exact CCD correlation energy for a number of alkanes containing six to eight carbon atoms. The relative stability of less branched isomers can be correctly predicted.展开更多
The molecular orbitals for B4H4, B4F4, B4Cl4, B4Br4 and B4I4 have been calculated by using all-electron or effective core potential ab initio method at the self-consistent field level using basis sets with diffuse and...The molecular orbitals for B4H4, B4F4, B4Cl4, B4Br4 and B4I4 have been calculated by using all-electron or effective core potential ab initio method at the self-consistent field level using basis sets with diffuse and polarization functions. The boron-boron and boron-halide (-hydrogen) distances of these cage compounds are optimized with three kinds of basis sets constrained to a tetrahedral symmetry. According to the localization scheme of Boys, four three-centered two-electron (3c2e) B-B-B bonds localized on each of the faces of the B4 tetrahedron are derived for B4X4 clusters. The HOMO-LUMO energy gaps, atomization energies and Mulliken overlap populations of these compounds indicate that the stabilities of the clusters decrease in the sequence of B4F4 > B4Cl4, B4H4 > B4Br4 > B4I4.展开更多
BEPCII has two rings each with an injection system. The injection system of each ring consists of two kicker magnets and a septum magnet. The injection layout of two rings is the same. Both two kickers would kick the ...BEPCII has two rings each with an injection system. The injection system of each ring consists of two kicker magnets and a septum magnet. The injection layout of two rings is the same. Both two kickers would kick the beam in horizontal plane. The betatron phase advance in the horizontal plane between two kickers is designed exactly 180° in order to reduce the perturbation to the circulating beams during injection. In fact, the residual orbit oscillation will originate because of the existence of a variety of errors. The Librea Electron BPM processor is used to acquire the beam position data in turn-by-turn mode and to analyze the residual orbit oscillation. According to the measurement results, minimization of the residual orbit oscillation can be done by adjusting the peak field strength and trigger timing delay of two kickers. With very small residual orbit oscillation the two beams can keep collision condition during the injection.展开更多
To investigate the substituent effect on x-electron delocalization of the N-benzylideneaniline （NBA）, the vertical resonance energies △E^V（θ） of eleven substituted NBAs were separated into n and a parts at the B...To investigate the substituent effect on x-electron delocalization of the N-benzylideneaniline （NBA）, the vertical resonance energies △E^V（θ） of eleven substituted NBAs were separated into n and a parts at the B3LYP/6-311G（d） level of the Density Functional Theory （DFT）. When substituted with an electron-releasing group --OH, the calculated △E^V（θ） of NBA was increased, indicative of more resonance destabilization than the mother molecule. However, when substituted with an electron-withdrawing group -NO2, the calculated △E^V（θ） values indicated less resonance destabilization. The most destabilizing effect was observed especially when the -OH group located at the ortho-position of the aromatic ring in the fragment -N=CH-Ar. For most of the substituted NBA molecules, it was the destabilized a framework that determined the destabilizing feature of the vertical resonance energy, instead of the stabilized n system. When the -NO2 substituent at the para-position of the aromatic ring of the -N=CH-Ar group, the π system had the highest stabilizing effect while the σ framework exhibited the highest destabilizing effect. While the -NO2 substituent was at the para-position of the left aromatic ring （At-）, the NBA had the least vertical resonance energy value.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11174175)the Tsinghua University Initiative Scientific Research Program,China
文摘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.
文摘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.
文摘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.
文摘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.
文摘The concept of resonance-assisted hydrogen bonds(RAHBs)highlights the synergistic interplay between theπ-resonance and hydrogen bonding interactions.This concept has been well-accepted in academia and is widely used in practice.However,it has been argued that the seemingly enhanced intramolecular hydrogen bonding(IMHB)in unsaturated compounds may simply be a result of the constraints imposed by theσ-skeleton framework.Thus,it is crucial to estimate the strength of IMHBs.In this work,we used two approaches to probe the resonance effect and estimate the strength of the IMHBs in the two exemplary cases of the enol forms of acetylacetone and o-hydroxyacetophenone.One approach is the block-localized wavefunction(BLW)method,which is a variant of the ab initio valence bond(VB)theory.Using this approach,it is possible to derive the geometries and energetics with resonance shut down.The other approach is Edmiston’s truncated localized molecular orbital(TLMO)technique,which monitors the energy changes by removing the delocalization tails from localized molecular orbitals.The integrated BLW and TLMO studies confirmed that the hydrogen bonding in these two molecules is indeed enhanced byπ-resonance,and that this enhancement is not a result ofσconstraints.
基金financially supported by the China Postdoctoral Science Foundation(No.2020M682154)。
文摘The interactions of complexes of XeOF_(2) and XeO_(3) with a series of different hybridization N-containing donors are studied by means of DFT and MP_(2) calculations.The aerogen bonding interaction energies range from 6.5 kcal/mol to19.9 kcal/mol between XeO_(3) or XeOF_(2) and typical N-containing donors.The sequence of interaction for N-containing hy-bridization is sp^(3)>sp^(2)>sp,and XeO_(3)is higher than XeOF_(2).For some donors of sp^(2)and sp^(3) hybridization,the steric effect plays a minor role in the interaction with the evidence of reduced density gradient plots.The dominant stable part is the electrostatic interaction.In complex of XeO_(3),the weight of polarization is larger than dispersion,while the situation is opposite for XeOF_(2)complexes.Except for the sum of the maximum value of molecular electrostatic potential on Xe atom and minimum value of molecular electrostatic potential on N atom,the other five interaction parameters including the potential energy density at bond critical point,the equilibrium distances,interaction energies with the basis set superposition error correction,localized molecular orbital energy decomposition analysis interaction energies,and the electron charge density,show great linear correlation coefficients with each other.
文摘A localized INDO method was used to calculate the ion [Fe_2 (CH_3) (CO) (Ph_2PCH_2PPh_2)- Cp_2]^+. Based on the analysis of the localized molecular orbitals (LMO), bond orders and contour maps, it was pointed out that the LMO no. 20 corresponds to the coordination of C(1)-H(I) σbond to Fe(2) atom. Non occurrence of metal-metal bond between Fe(1) and Fe(2) atoms was found and the covalence of irons was numerated, which coincides with the value in ref 17.
文摘The localized molecular orbitals and energy levels for four typical conjugated six-membered ring systems C_6H_6, C_3N_3H_3, B_3N_3H_6, and (B_3O_6)^(3-) as well as a non-aromatic reference molecule N_3Cl_6 have been calculated by using Edmiston-Ruedenberg energy localization technique under the CNDO/2 approximation in order to investigate the nature of aromaticity or quasi-aromaticity of the six-membered ring systems studied. The contour maps for π-type localized MO's (LMO) have been plotted to illustrate the bonding characteristics of the five ring systems studied. These LMO calculations show that for all the conjugated six-membered ring systems considered there exists local delocalization of π-bonds or three-centered and occasionally four-centered two-electron π-bonds in our terminology, and the cooperative effect among these π-bonds leading to the formation of a closed continuous x-conjugation system around the ring, which is necessary for the creation of aromaticity in the systems studied. We have been able to discuss the properties of these three-centered π-bonds in terms of the constituent atoms and electrons and the relevant orbitals involved.
基金Project supported by the National Natural Science Foundation of China the Foundation of the State Key Laboratory of Structural Chemistry of China
文摘The localized molecular orbitals (LMOs) of certain quasi-aromatic organic and inor- ganic molecules with six-membered rings have been calculated by virtue of the ab initio method using STO-3G and 4-31G basis sets as well as the CNDO/2 method. It is shown that there exists extensively-delocalized p-pπ bonding in these quasi-aromatic systems. The localized pictures of the π-type LMOs for the heterocyclic and homocyclic systems from the σ-π localization scheme are discussed. The Generator Orbital approach is utilized to account for the bonding patterns.
基金ProjectsupportedbytheNationalNaturalScienceFoundationofChina (No .2 0 0 73 0 2 0 )
文摘Within the localized molecular orbital description,the intra- and interorbital pair correlation energies calculated with the coupled cluster doubles (CCD) theory have been obtained for methane,ethane,propane,butane,isobutane,pentane, isopentane and neopentane using the 6-31G * basis set. The results showed the quantitative transferability of pair correlation energies and gross orbital correlation energies within this series of molecules. Based on the gross orbital correlation energies of five sample alkanes (butane,isobutane,pentane,isopentane and neopentane),we have derived a simple linear relationship to estimate the CCD correlation energy for an arbitrary large alkane. The correlation energy predicted by this simple relationship remarkably recovers more than 98.9% of the exact CCD correlation energy for a number of alkanes containing six to eight carbon atoms. The relative stability of less branched isomers can be correctly predicted.
基金Project supported jointly by the National Natural Science Foundation of China and the Foundation of State Key Laboratory of Structural Chemistry.
文摘The molecular orbitals for B4H4, B4F4, B4Cl4, B4Br4 and B4I4 have been calculated by using all-electron or effective core potential ab initio method at the self-consistent field level using basis sets with diffuse and polarization functions. The boron-boron and boron-halide (-hydrogen) distances of these cage compounds are optimized with three kinds of basis sets constrained to a tetrahedral symmetry. According to the localization scheme of Boys, four three-centered two-electron (3c2e) B-B-B bonds localized on each of the faces of the B4 tetrahedron are derived for B4X4 clusters. The HOMO-LUMO energy gaps, atomization energies and Mulliken overlap populations of these compounds indicate that the stabilities of the clusters decrease in the sequence of B4F4 > B4Cl4, B4H4 > B4Br4 > B4I4.
文摘BEPCII has two rings each with an injection system. The injection system of each ring consists of two kicker magnets and a septum magnet. The injection layout of two rings is the same. Both two kickers would kick the beam in horizontal plane. The betatron phase advance in the horizontal plane between two kickers is designed exactly 180° in order to reduce the perturbation to the circulating beams during injection. In fact, the residual orbit oscillation will originate because of the existence of a variety of errors. The Librea Electron BPM processor is used to acquire the beam position data in turn-by-turn mode and to analyze the residual orbit oscillation. According to the measurement results, minimization of the residual orbit oscillation can be done by adjusting the peak field strength and trigger timing delay of two kickers. With very small residual orbit oscillation the two beams can keep collision condition during the injection.
基金Project supported by the National Natural Science Foundation of China （No. 204720feng88）.
文摘To investigate the substituent effect on x-electron delocalization of the N-benzylideneaniline （NBA）, the vertical resonance energies △E^V（θ） of eleven substituted NBAs were separated into n and a parts at the B3LYP/6-311G（d） level of the Density Functional Theory （DFT）. When substituted with an electron-releasing group --OH, the calculated △E^V（θ） of NBA was increased, indicative of more resonance destabilization than the mother molecule. However, when substituted with an electron-withdrawing group -NO2, the calculated △E^V（θ） values indicated less resonance destabilization. The most destabilizing effect was observed especially when the -OH group located at the ortho-position of the aromatic ring in the fragment -N=CH-Ar. For most of the substituted NBA molecules, it was the destabilized a framework that determined the destabilizing feature of the vertical resonance energy, instead of the stabilized n system. When the -NO2 substituent at the para-position of the aromatic ring of the -N=CH-Ar group, the π system had the highest stabilizing effect while the σ framework exhibited the highest destabilizing effect. While the -NO2 substituent was at the para-position of the left aromatic ring （At-）, the NBA had the least vertical resonance energy value.
