The electronic modulation characteristics of efficient metal phosphide electrocatalysts can be utilized to tune the performance of oxygen evolution reaction(OER).However,improving the overall water splitting performan...The electronic modulation characteristics of efficient metal phosphide electrocatalysts can be utilized to tune the performance of oxygen evolution reaction(OER).However,improving the overall water splitting performance remains a challenging task.By building metal organic framework(MOF)on MOF heterostructures,an efficient strategy for controlling the electrical structure of MOFs was presented in this study.ZIF-67 was in-situ synthesized on MIL-88(Fe)using a two-step self-assembly method,followed by low-temperature phosphorization to ultimately synthesize FeP-CoP_(3)bimetallic phosphides.By combining atomic orbital theory and theoretical calculations(density functional theory),the results reveal the successful modulation of electronic orbitals in FeP-CoP_(3)bimetallic phosphides,which are synthesized from MOF on MOF structure.The synergistic impact of the metal center Co species and the phase conjugation of both kinds of MOFs are responsible for this regulatory phenomenon.Therefore,the catalyst demonstrates excellent properties,demonstrating HER 81 mV(η10)in a 1.0 mol L^(−1)KOH solution and OER 239 mV(η50)low overpotentials.The FeP-CoP_(3)linked dual electrode alkaline batteries,which are bifunctional electrocatalysts,have a good electrocatalytic ability and may last for 50 h.They require just 1.49 V(η50)for total water breakdown.Through this technique,the electrical structure of electrocatalysts may be altered to increase catalytic activity.展开更多
Accelerating the sluggish redox kinetics of lithium polysulfides(LiPSs)by electrocatalysis is essential to achieve high performance lithium-sulfur(Li-S)batteries.However,the issue of insufficient catalytic activity re...Accelerating the sluggish redox kinetics of lithium polysulfides(LiPSs)by electrocatalysis is essential to achieve high performance lithium-sulfur(Li-S)batteries.However,the issue of insufficient catalytic activity remains to be addressed.Herein,a strategy of modulating e_(g) orbitals through ligand engineering has been proposed to boost the catalytic activity of NiSe for rapid LiPSs redox conversion.The X-ray spectroscopic measurements and theoretical calculations reveal that partial substitution of Se with N disrupts the octahedral coordination of Ni atoms in NiSe,leading to the reduced degeneracy and upward shift of e_(g) orbitals of Ni 3 d states.As a consequence,the bonding strength of N-substituted NiSe(N-NiSe)with LiPSs is enhanced,which facilitates the interfacial charge transfer kinetics and accelerates the LiPSs redox kinetics.Therefore,the Li-S batteries assembled with N-NiSe present a high capacity of 682.6 mAh g^(-1) at a high rate of 5 C and a high areal capacity of 6.5 mAh cm^(-2)at a high sulfur loading of 6 mg cm^(-2).This work provides a promising strategy to develop efficient transition-metal based electrocatalysts for Li-S batteries through e_(g) orbital modulation.展开更多
In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the ...In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.展开更多
The outer valence electron momentum distributions of benzene are reinvestigated with theoretical calculations involving the vibrational effects.The results are compared with recent experimental measurements[Phys.Rev.A...The outer valence electron momentum distributions of benzene are reinvestigated with theoretical calculations involving the vibrational effects.The results are compared with recent experimental measurements[Phys.Rev.A 98042705(2018)].The significant discrepancies between theories and experiments in previous works have now been interpreted quantitatively,indicating that the vibrational motion in benzene molecule has noticeable influence on its electron momentum distributions.展开更多
Rehybridization of electronic orbitals in carbon nanotubes contains tilting angles of π orbital, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, etc. In this paper, we have obtained ana...Rehybridization of electronic orbitals in carbon nanotubes contains tilting angles of π orbital, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, etc. In this paper, we have obtained analytical formulas of tilting angle of π orbital relative to tube surface, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, separately, as well as the numerical results.展开更多
Picene, which attracts the great interest of researchers, not only can be used to fabricate thin film transistors with high hole mobilities, but also is the parent material of a new type organic superconductor. Here, ...Picene, which attracts the great interest of researchers, not only can be used to fabricate thin film transistors with high hole mobilities, but also is the parent material of a new type organic superconductor. Here, we investigate the electronic properties of individual picene molecules directly adsorbed on Cu（111） surface by a combination of experimental scanning tunneling microscopy/spectroscopy measurements and theoretical calculations based on the density functional theory. At low coverage, the picene molecules exhibit mono-dispersed adsorption behavior with the benzene ring planes parallel to the surface. The highest occupied state around -1.2 V and the lowest unoccupied state around 1.6 V with an obvious energy gap of the singly adsorbed picene molecule are identified by the dI/dV spectra and maps. In addition, we observe the strong dependence of the dI/dV signal of the unoccupied states on the intramolecular positions. Our first-principles calculations reproduce the above experimental results and interpret them as a specific molecule-substrate interaction and energy/spatial distributions of hybrid states mainly derived from different molecular orbitals of picene with some intermixing between them. This work provides direct information on the local electronic structure of individual picene on a metallic substrate and will facilitate the understanding the dependence of electron transport properties on the coupling between molecules and metal electrodes in single-molecule devices.展开更多
Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this...Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.展开更多
In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it...In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.展开更多
The frontier orbitals HOMO and LUMO of the fullerene C_(60) has been given in a system of 60 motion-coordinates, of which each origin is at each C atom of fullerene C_(60) and each z-axis is in the direction perpendic...The frontier orbitals HOMO and LUMO of the fullerene C_(60) has been given in a system of 60 motion-coordinates, of which each origin is at each C atom of fullerene C_(60) and each z-axis is in the direction perpendicular to C_(60)'S spherical surface. In this motion-coordinate system the HOMO and LUMO of fullerene C_(60) obviously display characteristics of spherical n-molecular orbitals π_n. The Fenske-Hall quantum-chemical method is used in calculation for the electronic structure of the fullerene C_(60).展开更多
Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GET...Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.展开更多
The valence state of C atoms and the structure of molecular orbitals of the (Buckminster)Fullerene C_(60)have been demonstrated. It has been shown that when a motion-coordinate system is adopted, in which the coordina...The valence state of C atoms and the structure of molecular orbitals of the (Buckminster)Fullerene C_(60)have been demonstrated. It has been shown that when a motion-coordinate system is adopted, in which the coordinate origin is at every C atom, the z axis is in the direction of the normal and the (x,y) axes are in the direction of tangents of C_(60)'s spherical surface, 240 valence atomic orbitals of C_(60) can be divided into two groups. All (P_x, P_y)atomic orbitals named as Pt ones and all the other P_z atomic orbitals named as p. ones, That is to say that if we name the molecular orbital linearly combined of P_t atomic orbitals as σ_t and the molecular orbital linearly combined of P_n atomic orbitals as π_n, the 240 valence molecular orbitals are of the property of σ_t-π_n separability. It has also been shown that the frontier and nearby frontier molecular orbitals are π_n ones, and therefore the essential physical and chemical properties of C_(60) are determined by its π_n molecular orbitals.展开更多
An enzyme is a kind of protein with catalytic activity and long chain,and its structure and shape are determined by the hybridized state of atomic orbital.The fractal dimension(D_f)is closely related to the hybridizat...An enzyme is a kind of protein with catalytic activity and long chain,and its structure and shape are determined by the hybridized state of atomic orbital.The fractal dimension(D_f)is closely related to the hybridization,e.g.D_f=2ln2/ln[2(1+α/(1-α))]for the spa type, where a denotes the fraction of the s orbital in the hybridized molecular orbital.This relationship and the five fractal theorems introduced by the present paper play an important role in the investigations of the model of imitative enzyme.展开更多
We performed density functional theory (DFT) calculations for ribonucleotides and active triphosphate metabolites of candidate drugs against Coronavirus disease 2019 (Covid-19). Frontier orbitals (highest occupied mol...We performed density functional theory (DFT) calculations for ribonucleotides and active triphosphate metabolites of candidate drugs against Coronavirus disease 2019 (Covid-19). Frontier orbitals (highest occupied molecular orbital and lowest unoccupied molecular</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">orbital) at optimized structure of each molecule were obtained. T-705RTP (active triphosphate metabolite of favipiravir) and cytidine triphosphate (CTP) have similar shapes of frontier orbitals. We also obtained similar shapes of frontier orbitals among dihydroxy GS-441524 triphosphate (GS-441524 is an active triphosphate metabolite of remdesivir) and adenosine triphosphate (ATP). From a theoretical </span><span style="font-family:Verdana;">viewpoint, we suggest T-705RTP is a CTP analogue and dihydroxy GS-441524</span><span style="font-family:Verdana;"> triphosphate is an</span></span><span style="font-family:""> </span><span style="font-family:Verdana;">ATP analogue.展开更多
In view of the growing interest in molecular orbitals (MOs) encountered in certain complex oxides, we review some of their properties from the band theory perspective and provide detailed examples based on real materi...In view of the growing interest in molecular orbitals (MOs) encountered in certain complex oxides, we review some of their properties from the band theory perspective and provide detailed examples based on real materials. Our discussion includes some technical aspects of identifying MOs in electronic structure calculations and considers cases when MOs can be both orthogonal and non-orthogonal. We also describe orthonormalization of MOs, a procedure converting them into Wannier functions, and discuss the problem of Wannier functions possibly being rather spatially extended and how using MO, rather than atomic orbital, based effective Hamiltonians might be a better choice in describing certain strongly correlated systems as well as systems with strong electron-phonon coupling. Furthermore, we address the problem of strongly correlated MOs and how it can be treated in band theory calculations.展开更多
In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the ...In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the forces, we show a few instances displaying typical fresh orbitals. Aside from the common theoretical foundation, the specifics of the orbitals are given by the solution of corresponding equations of motion. These are coupled nonlinear differential equations. Solving these equations numerically, utilizing a Computer Algebra System such as Mathematica is conducive to the orbits. Simulation of the orbitals provides a visual understanding about the motion under the influence of the generalized noncentral forces.展开更多
The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric ...The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric geometry at impact energy of 2.5 keV plus binding energy. The ionization bands have been assigned in detail via the high accuracy SACCI general-R method calculation and the experimental momentum profiles are compared with the theoretical ones calculated by Hartree-Fock and B3LYP/aug-cc-pVTZ（C,H）6-311G？？（I）. The spin-orbit coupling effect and intramolecular orbital interaction have been analyzed for the outermost two bands, which are assigned to the iodine 5p lone pairs, using NBO method and non-relativistic as well as relativistic calculations. It is found that both of the interactions will lead to the observed differences in electron momentum distributions. The experimental results agree with the relativistic theoretical momentum profiles, indicating that the spin-orbit coupling effect dominates in n-propyl iodide molecule.展开更多
This paper calculates the five most stable conformers of serine with Hartree-Fock theory, density functional theory （B3LYP）, Moller-Plesset perturbation theory （MP4（SDQ）） and electron propagation theory with the...This paper calculates the five most stable conformers of serine with Hartree-Fock theory, density functional theory （B3LYP）, Moller-Plesset perturbation theory （MP4（SDQ）） and electron propagation theory with the 6-311＋＋G（2d,2p） basis set. The calculated vertical ionization energies for the valence molecular orbitals of each conformer are in agreement with the experimental data, indicating that a range of molecular conformations would coexist in an equilibrium sample. Information of the five outer valence molecular orbitals for each conformer is explored in coordinate and momentum spaces using dual space analysis to investigate the conformational processes, which are generated from the global minimum conformer Serl by rotation of C2-C3 （Ser4）, C1 C2 （Ser5） and C1-O2 （Set2 and Ser3）. Orbitals 28a, 27a and 26a are identified as the fingerprint orbitals for all the conformational processes.展开更多
Basing on the DFT calculations we propose the new theoretical model which describes both the surface tension σ of the short chain n-alkanes at their normal boiling points and their reaction rate constants with hydrox...Basing on the DFT calculations we propose the new theoretical model which describes both the surface tension σ of the short chain n-alkanes at their normal boiling points and their reaction rate constants with hydroxyl radicals OH<span style="white-space:nowrap;">•</span> (at 297 ± 2 K) on the basis of their molecular orbital electronic characteristics. It has been shown that intermolecular dispersion attraction within the surface liquid monolayer of these compounds, as well as their reaction rate constants k with OH<span style="white-space:nowrap;">•</span> radicals are determined by the energies <em>E<sub>orb</sub></em> of the specific occupied molecular orbitals which are the same in the determination of both the above physico-chemical characteristics of the studied n-alkanes. The received regression equations confirm the theoretically found dependences between the quantities of σ and k and the module |<em>E<sub>orb</sub></em>|. For the compounds under study this fact indicates the key role of their electronic structure particularities in determination of both the physical (surface tension) and the chemical (reaction rate constants) properties.展开更多
In this paper, we have declined the formalism of the method of the Modified Atomic Orbital Theory (MAOT) applied to the calculations of energies of doubly excited states 2<em>snp</em>, 3<em>snp</e...In this paper, we have declined the formalism of the method of the Modified Atomic Orbital Theory (MAOT) applied to the calculations of energies of doubly excited states 2<em>snp</em>, 3<em>snp</em>, and 4<em>snp</em> Helium-like systems. Then we also applied the variational procedure of the Modified Atomic Orbital Theory to the computations of total energies, excitation energies of doubly-excited states 2<em>snp</em>, 3<em>snp</em>, 4<em>snp</em> types of Helium-like systems. The results obtained in this work are in good agreement with the experimental and theoretical values available.展开更多
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
文摘The electronic modulation characteristics of efficient metal phosphide electrocatalysts can be utilized to tune the performance of oxygen evolution reaction(OER).However,improving the overall water splitting performance remains a challenging task.By building metal organic framework(MOF)on MOF heterostructures,an efficient strategy for controlling the electrical structure of MOFs was presented in this study.ZIF-67 was in-situ synthesized on MIL-88(Fe)using a two-step self-assembly method,followed by low-temperature phosphorization to ultimately synthesize FeP-CoP_(3)bimetallic phosphides.By combining atomic orbital theory and theoretical calculations(density functional theory),the results reveal the successful modulation of electronic orbitals in FeP-CoP_(3)bimetallic phosphides,which are synthesized from MOF on MOF structure.The synergistic impact of the metal center Co species and the phase conjugation of both kinds of MOFs are responsible for this regulatory phenomenon.Therefore,the catalyst demonstrates excellent properties,demonstrating HER 81 mV(η10)in a 1.0 mol L^(−1)KOH solution and OER 239 mV(η50)low overpotentials.The FeP-CoP_(3)linked dual electrode alkaline batteries,which are bifunctional electrocatalysts,have a good electrocatalytic ability and may last for 50 h.They require just 1.49 V(η50)for total water breakdown.Through this technique,the electrical structure of electrocatalysts may be altered to increase catalytic activity.
基金supported by the Natural Science Foundation of Jiangsu Province (BK20190814)the National Natural Science Foundation of China (11905154)+4 种基金the Suzhou Science and Technology Project-Prospective Application Research Program(SYG202109)the Gusu innovative and entrepreneurial talent(ZXL2019245)the Collaborative Innovation Center of Suzhou Nano Science&Technologythe 111 ProjectSuzhou Key Laboratory of Functional Nano&Soft Materials,Soochow University-Western University Centre for Synchrotron Radiation Research
文摘Accelerating the sluggish redox kinetics of lithium polysulfides(LiPSs)by electrocatalysis is essential to achieve high performance lithium-sulfur(Li-S)batteries.However,the issue of insufficient catalytic activity remains to be addressed.Herein,a strategy of modulating e_(g) orbitals through ligand engineering has been proposed to boost the catalytic activity of NiSe for rapid LiPSs redox conversion.The X-ray spectroscopic measurements and theoretical calculations reveal that partial substitution of Se with N disrupts the octahedral coordination of Ni atoms in NiSe,leading to the reduced degeneracy and upward shift of e_(g) orbitals of Ni 3 d states.As a consequence,the bonding strength of N-substituted NiSe(N-NiSe)with LiPSs is enhanced,which facilitates the interfacial charge transfer kinetics and accelerates the LiPSs redox kinetics.Therefore,the Li-S batteries assembled with N-NiSe present a high capacity of 682.6 mAh g^(-1) at a high rate of 5 C and a high areal capacity of 6.5 mAh cm^(-2)at a high sulfur loading of 6 mg cm^(-2).This work provides a promising strategy to develop efficient transition-metal based electrocatalysts for Li-S batteries through e_(g) orbital modulation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11072168 and 10872141)
文摘In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0402300).
文摘The outer valence electron momentum distributions of benzene are reinvestigated with theoretical calculations involving the vibrational effects.The results are compared with recent experimental measurements[Phys.Rev.A 98042705(2018)].The significant discrepancies between theories and experiments in previous works have now been interpreted quantitatively,indicating that the vibrational motion in benzene molecule has noticeable influence on its electron momentum distributions.
基金Project supported by the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No 20030532008)
文摘Rehybridization of electronic orbitals in carbon nanotubes contains tilting angles of π orbital, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, etc. In this paper, we have obtained analytical formulas of tilting angle of π orbital relative to tube surface, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, separately, as well as the numerical results.
基金This work was supported by the National Basic Research Program of China （No.2011CB921400）, the Strategic Priority Research Program （B） of the Chinese Academy of Sciences （No.XDB01020100）, the Key Research Program of the Chinese Academy of Sciences （No.KJCX2-EWJ02）, the Youth Innovation Promotion Association of the Chinese Academy of Sciences （No.2011322）, and the National Natural Science Foundation of China （No.21473174, No.21273210, and No.51132007）.
文摘Picene, which attracts the great interest of researchers, not only can be used to fabricate thin film transistors with high hole mobilities, but also is the parent material of a new type organic superconductor. Here, we investigate the electronic properties of individual picene molecules directly adsorbed on Cu（111） surface by a combination of experimental scanning tunneling microscopy/spectroscopy measurements and theoretical calculations based on the density functional theory. At low coverage, the picene molecules exhibit mono-dispersed adsorption behavior with the benzene ring planes parallel to the surface. The highest occupied state around -1.2 V and the lowest unoccupied state around 1.6 V with an obvious energy gap of the singly adsorbed picene molecule are identified by the dI/dV spectra and maps. In addition, we observe the strong dependence of the dI/dV signal of the unoccupied states on the intramolecular positions. Our first-principles calculations reproduce the above experimental results and interpret them as a specific molecule-substrate interaction and energy/spatial distributions of hybrid states mainly derived from different molecular orbitals of picene with some intermixing between them. This work provides direct information on the local electronic structure of individual picene on a metallic substrate and will facilitate the understanding the dependence of electron transport properties on the coupling between molecules and metal electrodes in single-molecule devices.
文摘Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.
文摘In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.
文摘The frontier orbitals HOMO and LUMO of the fullerene C_(60) has been given in a system of 60 motion-coordinates, of which each origin is at each C atom of fullerene C_(60) and each z-axis is in the direction perpendicular to C_(60)'S spherical surface. In this motion-coordinate system the HOMO and LUMO of fullerene C_(60) obviously display characteristics of spherical n-molecular orbitals π_n. The Fenske-Hall quantum-chemical method is used in calculation for the electronic structure of the fullerene C_(60).
文摘Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.
文摘The valence state of C atoms and the structure of molecular orbitals of the (Buckminster)Fullerene C_(60)have been demonstrated. It has been shown that when a motion-coordinate system is adopted, in which the coordinate origin is at every C atom, the z axis is in the direction of the normal and the (x,y) axes are in the direction of tangents of C_(60)'s spherical surface, 240 valence atomic orbitals of C_(60) can be divided into two groups. All (P_x, P_y)atomic orbitals named as Pt ones and all the other P_z atomic orbitals named as p. ones, That is to say that if we name the molecular orbital linearly combined of P_t atomic orbitals as σ_t and the molecular orbital linearly combined of P_n atomic orbitals as π_n, the 240 valence molecular orbitals are of the property of σ_t-π_n separability. It has also been shown that the frontier and nearby frontier molecular orbitals are π_n ones, and therefore the essential physical and chemical properties of C_(60) are determined by its π_n molecular orbitals.
文摘An enzyme is a kind of protein with catalytic activity and long chain,and its structure and shape are determined by the hybridized state of atomic orbital.The fractal dimension(D_f)is closely related to the hybridization,e.g.D_f=2ln2/ln[2(1+α/(1-α))]for the spa type, where a denotes the fraction of the s orbital in the hybridized molecular orbital.This relationship and the five fractal theorems introduced by the present paper play an important role in the investigations of the model of imitative enzyme.
文摘We performed density functional theory (DFT) calculations for ribonucleotides and active triphosphate metabolites of candidate drugs against Coronavirus disease 2019 (Covid-19). Frontier orbitals (highest occupied molecular orbital and lowest unoccupied molecular</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">orbital) at optimized structure of each molecule were obtained. T-705RTP (active triphosphate metabolite of favipiravir) and cytidine triphosphate (CTP) have similar shapes of frontier orbitals. We also obtained similar shapes of frontier orbitals among dihydroxy GS-441524 triphosphate (GS-441524 is an active triphosphate metabolite of remdesivir) and adenosine triphosphate (ATP). From a theoretical </span><span style="font-family:Verdana;">viewpoint, we suggest T-705RTP is a CTP analogue and dihydroxy GS-441524</span><span style="font-family:Verdana;"> triphosphate is an</span></span><span style="font-family:""> </span><span style="font-family:Verdana;">ATP analogue.
文摘In view of the growing interest in molecular orbitals (MOs) encountered in certain complex oxides, we review some of their properties from the band theory perspective and provide detailed examples based on real materials. Our discussion includes some technical aspects of identifying MOs in electronic structure calculations and considers cases when MOs can be both orthogonal and non-orthogonal. We also describe orthonormalization of MOs, a procedure converting them into Wannier functions, and discuss the problem of Wannier functions possibly being rather spatially extended and how using MO, rather than atomic orbital, based effective Hamiltonians might be a better choice in describing certain strongly correlated systems as well as systems with strong electron-phonon coupling. Furthermore, we address the problem of strongly correlated MOs and how it can be treated in band theory calculations.
文摘In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the forces, we show a few instances displaying typical fresh orbitals. Aside from the common theoretical foundation, the specifics of the orbitals are given by the solution of corresponding equations of motion. These are coupled nonlinear differential equations. Solving these equations numerically, utilizing a Computer Algebra System such as Mathematica is conducive to the orbits. Simulation of the orbitals provides a visual understanding about the motion under the influence of the generalized noncentral forces.
文摘The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric geometry at impact energy of 2.5 keV plus binding energy. The ionization bands have been assigned in detail via the high accuracy SACCI general-R method calculation and the experimental momentum profiles are compared with the theoretical ones calculated by Hartree-Fock and B3LYP/aug-cc-pVTZ（C,H）6-311G？？（I）. The spin-orbit coupling effect and intramolecular orbital interaction have been analyzed for the outermost two bands, which are assigned to the iodine 5p lone pairs, using NBO method and non-relativistic as well as relativistic calculations. It is found that both of the interactions will lead to the observed differences in electron momentum distributions. The experimental results agree with the relativistic theoretical momentum profiles, indicating that the spin-orbit coupling effect dominates in n-propyl iodide molecule.
基金supported by the Doctoral Research Fund of Henan Normal University,China (Grant No. 525449)
文摘This paper calculates the five most stable conformers of serine with Hartree-Fock theory, density functional theory （B3LYP）, Moller-Plesset perturbation theory （MP4（SDQ）） and electron propagation theory with the 6-311＋＋G（2d,2p） basis set. The calculated vertical ionization energies for the valence molecular orbitals of each conformer are in agreement with the experimental data, indicating that a range of molecular conformations would coexist in an equilibrium sample. Information of the five outer valence molecular orbitals for each conformer is explored in coordinate and momentum spaces using dual space analysis to investigate the conformational processes, which are generated from the global minimum conformer Serl by rotation of C2-C3 （Ser4）, C1 C2 （Ser5） and C1-O2 （Set2 and Ser3）. Orbitals 28a, 27a and 26a are identified as the fingerprint orbitals for all the conformational processes.
文摘Basing on the DFT calculations we propose the new theoretical model which describes both the surface tension σ of the short chain n-alkanes at their normal boiling points and their reaction rate constants with hydroxyl radicals OH<span style="white-space:nowrap;">•</span> (at 297 ± 2 K) on the basis of their molecular orbital electronic characteristics. It has been shown that intermolecular dispersion attraction within the surface liquid monolayer of these compounds, as well as their reaction rate constants k with OH<span style="white-space:nowrap;">•</span> radicals are determined by the energies <em>E<sub>orb</sub></em> of the specific occupied molecular orbitals which are the same in the determination of both the above physico-chemical characteristics of the studied n-alkanes. The received regression equations confirm the theoretically found dependences between the quantities of σ and k and the module |<em>E<sub>orb</sub></em>|. For the compounds under study this fact indicates the key role of their electronic structure particularities in determination of both the physical (surface tension) and the chemical (reaction rate constants) properties.
文摘In this paper, we have declined the formalism of the method of the Modified Atomic Orbital Theory (MAOT) applied to the calculations of energies of doubly excited states 2<em>snp</em>, 3<em>snp</em>, and 4<em>snp</em> Helium-like systems. Then we also applied the variational procedure of the Modified Atomic Orbital Theory to the computations of total energies, excitation energies of doubly-excited states 2<em>snp</em>, 3<em>snp</em>, 4<em>snp</em> types of Helium-like systems. The results obtained in this work are in good agreement with the experimental and theoretical values available.
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.
