An ab initio effective potential for two particles in the field of the core: a reduction of (N + 2)-electron problem to two-electron problem

We have used many-body Green function theory and the two-electron Bethe—Salpeter equation to derive an approximate two-electron position space hamiltonian eigenvalue equation for two electrons in the presence of a closed shell core. The resulting effective hamiltonian is nonlocal, energy independent, hermitian and nonadiabatic. It includes all the core—valence, valence—valence exchange effects, core screening effects and electron—electron correlation effects. If a closed form solution of the equation is difficult because of the need to construct the hamiltonian, a semi-empirical approach can be taken which expresses much of the hamiltonian in terms of known properties of the core. A semi-empirical analysis of this effective hamiltonian is shown to give well-known phenomenological effective hamiltonians and the connections to them. Thus this work can also be viewed as a theoretical justification and extension of the two-electron model potential or pseudopotential theories.     

Solution of large configuration mixing matrices arising in partitioning technique and applications to the generalized eigenvalue problem

A method is presented that can be used (a) to determine the several lowest eigenvalues and eigenvectors of large symmetric matrices, (b) to solve the generalized eigenvalue problem associated with energy-dependent operators, that arises in computations involving energy-dependent many-body Green's functions and in the evaluation of the true parameters of the effective valence shell hamiltonian, and (c) to directly evaluate the matrices associated with resolvent operators. The applicability to large configuration mixing calculations arises when the N-electron basis functions can be easily broken down to a few dominant configurations (the primary block) and their complement. Using the partitioning technique, the effective hamiltonian within the primary block is directly evaluated. The method is extended to evaluation of the dynamical polarizability tensor, which effectively contains the contributions from all of the eigenstates of a hamiltonian matrix, without the necessity of explicitly calculating its eigenvalues and eigenvectors.     

A note on the importance of d orbitals in the calculation of effective interactions and the excitation spectra of atoms and molecules

The focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the ³P → ¹D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.     

Analysis of exact valence shell hamiltonian: Nonclassical terms and molecular based parameters

The exact valence shell effective hamiltonian is analyzed for one- and two-valence orbital systems using a second quantized formulation. The exact solutions of the exact effective hamiltonian are used, to display the meaning of each of its terms. The well-known α_υ = ?I_p and γ_υυ = I_p ? A_f relations are provided a molecular basis for certain special cases, thereby enabling molecular definitions for molecular “integrals” and allowing the determination of the molecule and bond length dependence of traditional semi-empirical “integrals”. It is shown how the presence of nonclassical terms in the effective hamiltonian destroys the pairing symmetry of alternate hydrocarbons.     

电负性研究Ⅰ.建立元素电负性标度的有效核电荷数方法

通过价层电离能、价键轨道能量用有效核电荷数法建立了周期表中 90种元素的电负性新标度。χ=0 .41 2 3 -EV,该式表明电负性值与价键轨道能量的绝对值的平方根成正比 ,所得数值是一套无量纲的相对参数。元素电负性值随价态的升高与元素非金属性的增强相对应 ,元素电负性的大小不仅与单个成键电子有关 ,而且也与参加价键作用的多个电子甚至整个价层都有紧密的联系。氢的元素电负性值不同于Pauling值、等于 1 .52。用 1 6种氢化物中键的额外离子能Δ′对 (χA-χB) 2 作图 ,两者之间确实具有良好的线性关系。本方法充分体现了目前公认的三大电负性标度的优点 ,该标度同时也是价层电子在价键状态下的一种能量标度 ,是对元素周期律的定量描述和反映。     

A derivation of the exact pi-electron hamiltonian

The exact pi-electron hamiltonian is derived from the full many-electron Schrödinger equation. The derivation employs techniques which also enable the development of open shell generalized perturbation theory. The parameters occurring in the pi-hamiltonian are therefore amenable to calculation using the approximate theories and methods of Sinano?lu, Nesbet, Kelly, etc. To a good approximation, the pi-hamiltonian is found to be generally consistent with its customarily assumed form.     

Ab initio calculation of the effective valence shell hamiltonian of carbon: Simultaneous treatment of neutral and ion states

The n = 2 effective valence shell hamiltonian, $\text{H}$^v, of carbon is evaluated through second order using ³P Hartree—Fock orbitals (5s4p) with added d functions to provide results within a few percent of the spd convergence limits. The calculated $\text{H}$^v is employed to evaluate the n = 2 valence states of C, C^?, C⁺, C²⁺ and C³⁺ with an average deviation of the 21 excitation energies, ionization potentials and electron affinity from experimental values of 0.32 eV. Three-electron parts of $\text{H}$^v contribute substantially to a number of these excitation energies.     

Approximate molecular orbital theory: the ese mo formalism.: III. Parametrization for all- or valence-electron calculation using accurate STF bases for molecules containing 1st, 2nd,and 3rd row atoms. SO2 results

The key components of a completely theoretical parametrization of the essential-structural-elements molecular orbital (ESE MO) formalism using Slater-type AO basis in the LCAO SCF procedure are discussed. Special attention is paid to the problem of separability into core and valence parts of the total molecular wavefunction, including the case where valence functions strongly overlap neighbouring core orbitals. The use of Huzinaga and Cantu effective hamiltonian is proposed. The parametrization is tested in relation to the SO₂ molecules. The role of sulphur 3d functions in bonding as predicted by the present ESE MO calculations and ab initio calculations are compared. The present parametrization appears to adequately handle both the core/valence separation, and the diffuse higher valence sulphur 3d functions in this system.     

The adiabatic approximation for coupled oscillators

The adiabatic approximation is applied to determine the quantum states of coupled oscillators described by a generalized Hénon-Heiles hamiltonian. Comparison with exact quantum and other results show that numerically calculated adiabatic energy levels are accurate even for excited states.     

The Effective Hamiltonian and Electron Correlation Energy

An effective,hermitian hamiltonian is derived in amodel space. Its perturbation expressions to third order approximation are given.The correlation energy is also given to the third order approximation.The effective hamiltonian deviates form the actual one by the presence of acorrelation operator.The cprrelation operatop is given in an explicit form.     

Model calculation of weak and medium strong linear hydrogen bonded systems

The model hamiltonian with two coupling constants between the low and high frequency vibrations of a linear AH?B system is studied. The results show that the wave functions and energy levels of this hamiltonian obtained by exact diagonalisation can be adequately approximated by the wave functions and energy levels of a harmonic “effective hamiltonian”. The experimental spectrum of (CH₃)O?HCl in the stretching region was reconstituted by means of this model.     

The calculation of London coefficients by the variation-perturbation method

The London coefficients for the dispersion interaction between LiLi, BeBe and LiBe are calculated by the variation-perturbation method using the whole atomic hamiltonian as H₀ and the Hartree-Fock approximation for the upper turbed wavefunction ?₀. A single excited valence configuration with optimized orbital exponents gives accurate results for Li, whereas comparable accuracy for Be is obtained when part of the valence correlation energy in the ground as well as in the excited state is accounted for through a limited configuration interaction.     

基态原子价壳层电子能级连接性指数与元素的电负性

构建了基态原子价壳层电子能级连接性指数(^mVEI),m=0,1,2,…，它对基态原子实现唯一性表征，其中^0VEI,^1VEI对原子具有良好的结构选择性，以^0VEL,^1VEL，价壳层电子总离子化能(ΣniEi)和总从电子数(Σni)为基本参数，定义了元素的电负性：X~N=0.444067+1.190653(1-1.32775/Σni)(^0VEI)-3.154675(^1VEI)+0.134591.(ΣniEi/Σni)。用上式给出了周期表中主族元素、副族元素及惰性元素的电负性。结果表明，新电负性标度X~N与目前流行的Pauling标度颇为一致。进一步从价轨道能级连接性指数确定了碳原子的sp,sp^2,sp^3杂化轨道的电负性。     

电负性研究(Ⅱ)—氢的电负性

氢的电负性值是氢元素性质的重要参数，１９３２年Pauling犤１～３犦定量确定氢的相对电负性值等于２．１，１９６１年Allred犤４，５犦用更准确的实验数据对Paul－ing电负性标度进行了修正，氢的电负性值被确定为２．２，目前这两个数值都在采用。元素的电负性值是与元素的性质紧密相关的，一个合适的电负性标度应该至少反映所有重要元素的电负性值，氢的化合物比任何其它元素都多，理应有一个基本的准确电负性值，然而一些电负性标度中却缺乏这样的数据。在Murphy等四人犤６犦最近发表的论文中，对Pauling电负性标度又进行了深入考查与…     

Modulation of the electronic properties of conjugated polymers through design of polymer backbone

We present the results of valence effective hamiltonian (VEH) band structure calculations on stereoregular block copolymers of poly(thienylene vinylene) and poly(pyrrylene vinylene). We have examined the evolution of the electronic properties as a function of the extension and distribution of the block copolymer sequences. In both cases, the electronic-properties deviate from a linear evolution as a consequence of the localization of both HOCO and LUCO.     

Identify fine microstructure of multifarious iron oxides via O K-edge EELS spectra

Relying on the electron energy loss spectrum (EELS) of metallic elements to obtain microstructure analysis is an investigation method of the reaction mechanisms of transition metal oxides (TMOs) in catalysis, energy storage and conversion. However, the low signal from K shell owing to insufficient electron beam energy, and the complicated electronic structure in L shell of the metal element restrict the analysis of the coordination environment of the TMOs. Herein, density functional theory (DFT) calculation, Fourier transform (FT) and wavelet transform (WT) were employed to probe the relationship between the four individual peaks in O K-edge spectra of iron oxides and the microstructure information (chemical bonds and atomic coordination). The findings show that the peak amplitude ration is in a linear correlation with the valence state of Fe element, and that the coordination number obtained by radial distribution function (RDF) is favorably linearly correlative with that from the standard coordination structure model. As a result, the quantitative analysis on the change of valence state and atomic coordination in microstructure can be realized by EELS O K-edge spectra. This study establishes EELS O K-edge spectrum as a promising pathway to quantitatively analyze the valence state and atomic coordination information of TMOs, and offers an effective method to conduct microstructure analysis via the EELS spectra of the non-metal element.     

Optimization of parameters for an effective hamiltonian

A generally applicable, least-squares method that can be used to optimize the parameters of an effective hamiltonian matrix in any basis set is described. The technique is applied to the correlation of photoelectron spectra of saturated hydrocarbons.     

Electron Momentum Spectroscopy Investigation on Electronic Structure of Iso-dichloroethylene Valence Shell

Here an electron momentum spectroscopy study on the electronic structure of valence shell of iso-dichloroethylene molecule is reported. The experiment is carried out with a binary (e, 2e) spectrometer at incident electron energy of 1200 eV, employing noncoplanar symmetric arrangement. The binding energy spectra and electron momentum distributions (EMDs) of iso-dichloroethylene valence shell have been obtained. Theoretical EMDs are predicted with both Hartree-Fock and density functional theory methods, generally indicating good agreements with the measurement results. The interference effect is observed to significantly influence the EMDs of 2a₂ and 5b₂ Cl lone-pair orbitals.     

An efficient algorithm for energy gradients and orbital optimization in valence bond theory

An efficient algorithm for energy gradients in valence bond theory with nonorthogonal orbitals is presented. A general Hartree-Fock-like expression for the Hamiltonian matrix element between valence bond (VB) determinants is derived by introducing a transition density matrix. Analytical expressions for the energy gradients with respect to the orbital coefficients are obtained explicitly, whose scaling for computational cost is m(4), where m is the number of basis functions, and is thus approximately the same as in HF method. Compared with other existing approaches, the present algorithm has lower scaling, and thus is much more efficient. Furthermore, the expression for the energy gradient with respect to the nuclear coordinates is also presented, and it provides an effective algorithm for the geometry optimization and the evaluation of various molecular properties in VB theory. Test applications show that our new algorithm runs faster than other methods.     

Definitive variational principles for physical quantities

New variational principles are proposed that provide the upper and lower limits to the square of the modulus of the matrix element for a transition. The corresponding variational problems for maximum and minimum are formulated via functional of general form that are bilinear with respect to the hamiltonian. An analogous variational principle may be derived via a functional linear with respect to the hamiltonian for a transition to a state of lowest energy of the given symmetry type. In some cases the variational estimates of the square of the modulus involve passage to the limit. Errors due to inexact eigenfunctions and replacement of limiting values by specified values for the parameters are discussed.