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.

A Quick Estimate of the Correlation Energy for Alkanes

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.

Applications of Simple Estimation Scheme of Electron Correlation Energy to Strong Ionic Compounds

The calculation results of electron correlation energies of KF and （KF）2 were reported. The transferability of 1s^2 K , 1s^2 F and the inner core correlation effects of K and F in both K, K^＋, KF and F, F^-, KF systems were investigated respectively. The correlation energy contributions of K and F component to KF system were calculated. By applying the simple estimation scheme to the calculation of the correlation energy of the strong ionic compound KF and （KF）2, it was shown that such a powerful scheme could not only reach the chemical accuracy but also need little computational work.

The Parallel Calculation of the Ground-State Correlation Energy of Helium Atom

When we use Modified Configuration Interaction method(MCI) to calculate the correlation energy of double electron systems, for obtaining the higher precision, we always need huge calculations. In order to handle this problem, which will cost much CPU time and memory room if only using a single computer to do it, we now adopt the parallel multisection recurrence algorithm. Thus we can use several CPUs to get the ground state energy of a Helium atom at the same time.

Two Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A_2 Type Molecules

Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the to-tal correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of error, however, in this way, more than 90% of computational work can be saved. The most attractive result in present paper is that, in these two molecules the co-efficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A- to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 mole-cules would be very useful to estimate the correlation energies of large symmetrical molecules.

THE LINEAR CORRELATIONS BETWEEN ELECTRONIC TRANSITION ENERGY AND HAMMETT CONSTANTS FOR THE SUBSTITUTED PORPHYRIN-LIKE MACROCYCLE

The properties of absorption spectra are presented and the linear correlations of Hammett constants with the 0-0 transition energy(E_(o,o))of S_←S_o, and the ratios of oscillator strength(f/f)are used to probe the interactions betwee π-electron of aromatic maerocycles or metal ion of complexes with the sub- stituents on β-position of benzene ring for porphyrin-like maerocyclic compounds.

Changing Rules of Bonding Electron Pair Correlation Energies of CH_3X (X=F,OH,NH_2) Systems

The pair correlation energy of bonding electrons is used and analyzed in the cal- culation of CH and CY (Y = F, O, N) bonding electron pairs in CH3X (X = F, OH, NH2) isoelec- tronic systems based on intra- and interpair correlation energy results at both MP2-OPT2/6- 311++G(d) and MP2-OPT2/cc-pVtz levels with MELD program. Comparison of two set results shows that cc-pVtz and 6-311++G(d) give more correlation energy of valence electrons and innermost core electron pairs, respectively in these systems, resulting that the total correlation energy with cc-pVtz basis of each system is larger than that with 6-311++G(d). Investigations of pair correlation energy show that with the decrease of electronegativity of X atom and the increase of H atoms in these CH3X (X = F, OH, NH2) systems, the pair correlation energy of 1sC2 of the C atoms is transferable, and the correlation energy of CH bonding electron pair with little changes is of approximate transferability, while those of CY (CF, CO, CN) bonding electron pair decrease in a large extent from CH3F through CH3OH to CH3NH2 molecules. It is suggested that the study of pair correlation energy of bonding electrons will further deepen the understanding of electron corre- lation effect from traditional chemical bonding concept.

The Pionic Effect on the Binding Energy of Relativistic Particle-Hole Excitation in Nuclear Matter

The renormalization of pion-exchange nucleon self-energy in nuclear matter is doneby dispersion relation.The exchange and correlation energies(in the ring approximation)ofpion,σ and ω mesons are derived and used to calculate the binding energy of nuctear matter atzero temperature.We find that the pionic contribution to the binding energy fails to lift the highdensity end of the binding energy curve,that is,the binding energy can not saturate without adensity dependent correction to the σNN and ωNN coupling constants.But the binding energycan saturate in the relativistic Hartree approximation plus the exchange and correlation energiesof л meson.

Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of Helium

The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1s^(2), 1s2s, and 1s2p states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.

An Amati-Like Correlation for Short Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are by far the most powerful explosions in the universe. Over the past two decades, several GRB energy and luminosity correlations were discovered for long gamma-ray bursts, which are bursts whose observed duration exceeds 2 seconds. One important correlation, the Amati relation, involves the observed peak energy, Ep,obs, in the vFv spectrum and the equivalent isotropic energy, Eiso. For many years, it was believed that the Amati correlation applied only to long GRBs. In this paper, we use a recent data sample that includes both long and short GRBs to re-examine the issue of whether the Amati correlation applies to long GRBs only. Our results indicate that although short bursts do not follow the Amati relation in the strict sense, they do exhibit a correlation between the intrinsic peak energy, Ep,i, and Eiso that is very similar to the Amati relation but with a different normalization and slope. The paper also discusses the physical interpretation of this correlation in the context of the internal shock model.

Energy consumption hierarchical analysis based on interpretative structural model for ethylene production

Interpretative structural model(ISM) can transform a multivariate problem into several sub-variable problems to analyze a complex industrial structure in a more efficient way by building a multi-level hierarchical structure model. To build an ISM of a production system, the partial correlation coefficient method is proposed to obtain the adjacency matrix, which can be transformed to ISM. According to estimation of correlation coefficient, the result can give actual variable correlations and eliminate effects of intermediate variables. Furthermore, this paper proposes an effective approach using ISM to analyze the main factors and basic mechanisms that affect the energy consumption in an ethylene production system. The case study shows that the proposed energy consumption analysis method is valid and efficient in improvement of energy efficiency in ethylene production.

The Wave Function with Symplectic Symmetry and Its Application

The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination.

Fixed-node Quantum Monte Carlo: A Novel Approach

In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the traditional fixed-node quantum Monte Carlo method is only the zero order approximation of the eigenvalue of the energy. But when using our novel method, in the case of only increasing less computing amounts (<1%), we can obtain conveniently the first order approximation, second order approximation, and so on. We have calculated the values of the zero, first and second approximation (0, 1 and 2) of the energies of 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O using this novel method. The results indicate that for 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O it needs only the second order approximation to obtain electronic correlation energy with over 97%. This demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.

Basis Set Extrapolation for the High Resolution Spectroscopy

Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the levels of MP2, RI-MP2, and CCSD （T） with Dunnings sequential correlation consistent basis sets. A two point basis set extrapolation scheme for correlation energies to the complete basis set limit based on only DZ （double-zeta） and TZ （triple-zeta） results is presented and analyzed. We show that this basis set extrapolation scheme reduces the computational cost by two to three orders of magnitude to obtain the same accuracy as simpler extrapolations from higher order basis set computations.

A Brief Review of the Amati Relation for GRBs

Gamma-ray bursts (GRBs) are the most powerful explosions in the universe. Alt-hough the exact mechanism behind these explosions remains elusive, GRBs hold great promise as cosmological probes for two main reasons: they have been observed up to very high redshift (z > 9), and their gamma-ray emission is unencumbered by any intervening dust. Several GRB energy and luminosity indicators have been discovered. These indicators correlate an observable quantity, like the intrinsic peak energy, Ep,i, in the spectrum of a burst to an unobservable parameter like the equivalent isotropic energy, Eiso, or the isotropic peak luminosity, Lp,iso. This paper provides a brief review of one of these energy and luminosity indicators, the Amati relation, and discusses its potential use as a cosmological probe.

Modeling of kinetic characteristics of alkaline-surfactant-polymer-strengthened foams decay under ultrasonic standing wave

Foaming issues are encountered at the stages in crude oil production, transportation, processing, especially in chemical flooding enhanced oil recovery(EOR) oilfields. These accumulated foams would cause a lot of trouble for downstream operation. The destruction of foams under ultrasonic has been increasingly paying attention in the background of green oilfield development. This study focuses on the decay kinetic characteristics of alkaline-surfactant-polymer-strengthened foams under the ultrasonic standing wave.The performance of the diverse foams was characterized. A decay kinetic model incorporating the energy correlation was developed and validated. The factors that affect the decay kinetic characteristics were discussed. The results indicated that the collapse rate and the collapse volume fraction decreased when the foam size decreased, the gas-liquid ratio decreased and the surface tension increased. Ultrasonic standing wave parameters have a significant impact on the decay behavior of the foam. Both the ultrasonic frequency and ultrasonic amplitude were increased by 50%, the collapse volume fraction of foams increased by about 1.25 times in the identical irradiation time. The relative deviation between the measured results and the model prediction was less than 10%. The potential collapse mechanism was also explained using the principle of energy correlation of foam surface. This study is not only beneficial to provide a robust and rigorous way to defoam of produced liquid in the alkaline/surfactant/polymer(ASP)flooding EOR process but also meaningful to well understand the decay process of oil-based foams.

The Eiso-Liso Plane for Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are the most intense and powerful explosions in the universe. Based on their observed duration, they are traditionally divided into long bursts whose observed duration equals or exceeds 2 s, and short bursts whose observed duration is less than 2 s. Several GRB energy and luminosity correlations have been discovered for long gamma-ray bursts. Two important correlations are the Amati relation and the Yonetoku relation. The Amati relation is a correlation between the intrinsic peak energy, Ep,i, obtained from the νFν spectrum and the equivalent isotropic energy, Eiso, while the Yonetoku relation is a correlation between Ep,i and the peak isotropic luminosity, Liso. In this paper, we use a recent data sample that includes both long and short GRBs to compare these two correlations for the two groups of bursts. We also compare the Eiso-Liso plane for these two types of bursts. Our results indicate that both long and short bursts adhere to these two correlations but with different normalizations. We also find that the Eiso-Liso plane is similar for both types of GRBs but is shifted to lower values of Eiso for short GRBs.

Beyond-mean-field dynamical correlations for nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum

We extend the deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc)to go beyondmean-field framework by performing a two-dimensional collective Hamiltonian.The influences of dynamical correlations on the ground-state properties are examined in different mass regions,picking Se,Nd,and Th isotopic chains as representatives.It is found that the dynamical correlation energies(DCEs)and the rotational correction energies E_(rot) in the cranking approximation have an almost equivalent effect on the description of binding energies for most deformed nuclei,and the DCEs can provide a significant improvement for the(near)spherical nuclei close to the neutron shells and thus reduce the rms deviations of S_(2n) by≈17%.Furthermore,it is found that the DCEs are quite sensitive to the pairing correlations;taking ^(148)Nd as an example,a 10%enhancement of pairing strength can raise the DCE by≈37%.

The calculation of band gap energy in zinc oxide films

We investigated the optical properties of undoped zinc oxide thin films as the n-type semiconductor;the thin films were deposited at different precursor molarities by ultrasonic spray and spray pyrolysis techniques.The thin films were deposited at different substrate temperatures ranging between 200 and 500℃. In this paper, we present a new approach to control the optical gap energy of ZnO thin films by concentration of the ZnO solution and substrate temperatures from experimental data, which were published in international journals. The model proposed to calculate the band gap energy with the Urbach energy was investigated. The relation between the experimental data and theoretical calculation suggests that the band gap energies are predominantly estimated by the Urbach energies, film transparency, and concentration of the ZnO solution and substrate temperatures. The measurements by these proposal models are in qualitative agreements with the experimental data; the correlation coefficient values were varied in the range 0.96–0.99999, indicating high quality representation of data based on Equation（2）, so that the relative errors of all calculation are smaller than 4%. Thus, one can suppose that the undoped ZnO thin films are chemically purer and have many fewer defects and less disorder owing to an almost complete chemical decomposition and contained higher optical band gap energy.

Polaron Effect of a Two Electron Parabolic Quantum Dot

Polaron induced double electron in a quantum dot is investigated using the exact diagonalization techniques and the compact density-matrix approach. The dependence of nonlinear optical processes on the incident photon energies and the polaronic effect are brought out. The linear, third order non-linear optical absorption coefficients and the refractive index changes of singlet and triplet states as a function of photon energy are obtained with and without the inclusion of polaronic effect. It is found that the geometrical confinement and the effect of polaron have great influence on the optical properties of dots.