Configuration-interaction energy derivatives in a fully variational formulation

A configuration-interaction energy function (Lagrange) which is variational in all variables, including the orbital rotational parameters, is constructed. When this Lagrangian is used for obtaining configuration-interaction derivatives, all the important simplifications which occur for derivatives of variational wave functions carry over in a straightforward way. In particular, the state and orbital rotational response parameters obey the 2n+1 rule and the Lagrange multipliers obey the somewhat stronger 2n+2 rule. The simplifications which are normally obtained by invoking the Handy-Schaefer technique are automatically incorporated to all orders. Simple expressions for energy derivatives up to third order are presented. The relationship between the numerical errors in the variational parameters and the errors in the calculated energy derivatives is discussed.     

Simplified reference wave functions for multireference perturbation theory

A number of simplifications in defining the reference wave functions used in multireference second-order M?ller-Plesset perturbation theory (MRMP2) calculations are studied. The usual multiconfigurational orbital optimization is avoided by using Hartree-Fock or Kohn-Sham orbitals; the complete configuration expansion in the active-space orbitals is replaced by a severely truncated expansion, and the spin-component-scaling idea is applied to the multireference perturbation expansion. We assess these approximations to the full procedure by calculating the barrier heights for 15 processes taken from the Zhao-Gonzalez-Garcia-Truhlar database. Our results suggest that reliable and relatively cheap reference wave functions for MRMP2 calculations can be obtained from the simplifications introduced here. We hope that this will enable the application of the MRMP2 method to a larger range of chemical systems.     

Variational principles for discontinuous wave functions and the independent particle model of electronic structure

Using the variational method advanced by McCavert and Rudge, we obtain the independent particle model variational principle for loge localized discontinuous wave functions. The transformation of the variational expressions into matrix form when the loge localized discontinuous orbitals are expanded in finite basis sets is discussed. The simplifications brought about by this new method in the evaluation of molecular integrals are indicated.     

Simulation of stochastic model processes in the theory of stark-broadening

Calculations following the Method of Model Microfields (MMM) are performed by simulating various model processes. The approach via simulations gives simplifications for the numerical evaluation of the line profile. Furthermore it is shown how to check with its help the validity of certain approximations introduced in the MMM and in general Stark-broadening theory. Results for Lyman-α are shown.     

聚合物口模挤出流动分析方法

综述挤出口模中聚合物熔体流动分析方法。着重讨论了包括有限差分法、有限元法和边界元法等在内的数值方法。并且对挤出口模流道几何形状简化和数学模型简化进行了评价     

Fast computer calculation of ESR and nonlinear spin response spectra from the fast motion to the rigid lattice limits

Fast computer simulation of the electron spin resonance and adiabatic rapid passage spectra of spin labels characterized by rotational correlation times ranging from the fast motion to the rigid lattice limits is demonstrated. Calculations are based upon a modification of the stochastic Liouville equation for the density matrix which explicitly includes interaction of the spins with applied radiation and modulation fields. Several mathematical simplifications of previous calculations are demonstrated, permitting computation with core and CPU requirements compatible with small computers.     

Gap equations for molecular systems

The gap equations for different Fukutome classes are derived in the formalism of second quantization. Compact orbital forms are given for the gap and related to energy difference of the new LUMO and HOMO , ?_LU –?_HO , obtained from the old RHF molecular orbitals. Approximate expressions are obtained by maximizing the average electron–electron repulsion energy. The simplifications obtained and possible applications to molecular systems are discussed and compared with the instability analysis of an RHF state.     

Electrostatic molecular potentials: Mulliken approximation

The electrostatic potential is calculated, in the LCAO framework, through Mulliken's approximation. An extremely simplified form of the potential expression is obtained, with a degree of accuracy comparable to a full ab initio treatment. Other related possible simplifications are also discussed.     

General principles of algebraic modelling of structural organic analysis

A general theory is developed for modelling structural organic analysis, based on Boolean algebra and the theory of semi-lattices with certain simplifications. A linear system of Boolean equations is suitable for expressing the exact relationship of compositional and experimental information. The concepts introduced, and their unambiguous limits of applicability are discussed in terms of abstract algebra.     

X-ray microanalysis of 1.5-10 μm particles in metallurgical research

The importance of particle X-ray microanalysis for contemporary metallurgical research has been accentuated. Corrections in the formulae for the geometric modelling method and simplifications in the calculation procedure are introduced. Conditions for successful application of the peak to background ratio method were outlined. Besides these two methods related to isolated particles a new extrapolation method for matrix embedded particles is developed and comments to the particle weight fraction estimation method for the same kind of particles are given.     

全氟烷基磺酸盐和全氟烷基磺酰亚胺盐的多相化催化研究

传统的Lewis酸催化剂在环境的压力下受到挑战,全氟烷基磺酸盐和全氟烷基磺酰亚胺盐作为均相、高效的Lewis酸催化剂在有机合成中受到人们的关注.为了简化分离操作,人们对全氟烷基磺酸盐和全氟烷基磺酰亚胺盐的多相化进行了研究,并已取得巨大进展.本文综述了全氟烷基磺酸盐和全氟烷基磺酰亚胺盐分别负载在有机载体、无机载体以及离子液体上的多相化催化最新研究进展,简要概括了其制备方法和催化活性,并对其催化应用前景进行了展望.     

Simulating Non-linear Chemical and Physical (CAP) Dynamics of Signal Amplification By Reversible Exchange (SABRE)

The hyperpolarization of nuclear spins by using parahydrogen (pH₂) is a fascinating technique that allows spin polarization and thus the magnetic resonance signal to be increased by several orders of magnitude. Entirely new applications have become available. Signal amplification by reversible exchange (SABRE) is a relatively new method that is based on the reversible exchange of a substrate, catalyst and parahydrogen. SABRE is particularly interesting for in vivo medical and industrial applications, such as fast and low-cost trace analysis or continuous signal enhancement. Ever since its discovery, many attempts have been made to model and understand SABRE, with various degrees of simplifications. In this work, we reduced the simplifications further, taking into account non-linear chemical and physical (CAP) dynamics of several multi-spin systems. A master equation was derived and realized using the MOIN open-source software. The effects of different parameters (exchange rates, concentrations, spin–spin couplings) on relaxation and the polarization level have been evaluated and the results provide interesting insights into the mechanism of SABRE.     

Determination of the activity of a molecular solute in saturated solution

Prediction of the solubility of a solid molecular compound in a solvent, as well as, estimation of the solution activity coefficient from experimental solubility data both require estimation of the activity of the solute in the saturated solution. The activity of the solute in the saturated solution is often defined using the pure melt at the same temperature as the thermodynamic reference. In chemical engineering literature also the activity of the solid is usually defined on the same reference state. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solute in the saturated solution (=ideal solubility) and the heat capacity difference between the pure supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures. The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one-third of the correct value.     

Dynamical analysis of correlated wavefunctions

A comparative dynamical analysis of several quasi-exact wavefunctions for helium has been carried out by computing their corresponding correlation coefficients. The aim is to use the resulting information to study the correlation included in approximate wavefunctions within the factor correlation model. Information about the possibility of making simplifications in the approximate wavefunctions and about the flexibility of the quasi-exact wavefunctions is also obtained.     

Transcorrelated calculations of homogeneous electron gases

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation.     

浆态床中合成气制二甲醚宏观动力学的研究(英文)

以液体石蜡为介质,在合成甲醇催化剂与甲醇脱水催化剂比例为5、催化剂浓度为10 g/300 mL液体石蜡,温度为250℃~280℃,压力为3 MPa~5 MPa,气体空速为4 000 mL/(g(h)~7 000 mL/(g(h)的条件下,建立了浆态床合成气制二甲醚宏观动力学模型。甲醇合成反应和甲醇脱水反应的活化能分别为14.06 kJ/mol和23.53 kJ/mol。甲醇当量生成速率和二甲醚生成速率的计算值与实验值的相对误差在10%和20%以内。     

Novel squalene-hopene cyclase inhibitors derived from hydroxycoumarins and hydroxyacetophenones

Squalene-hopene cyclase (SHC) is a useful model enzyme for predicting molecular interactions with oxidosqualene cyclase (OSC). Structure--activity relationships were investigated for numerous coumarin-derived inhibitors of SHC, and structural simplifications are suggested. Both umbelliferone and 2,4-dihydroxyacetophenone provide convenient starting nuclei for the design of SHC inhibitors. Derivatives bearing an omega-epoxyfarnesyl moiety or just a plain alkyl chain showed an inhibitory effect on a recombinant SHC from Alicyclobacillus acidocaldarius expressed in Escherichia coli.     

Viscosities of liquids, colloidal suspensions, and polymeric systems under zero or non-zero electric field

The viscosities of pure liquids, polymer solutions and melts, and colloidal suspensions under zero or non-zero electric field are surveyed in this paper and the focus is placed on the case that no electric field is applied. The free volume concept and Eyring's rate theory is used for deriving the viscosity equations of pure liquids, polymer solutions and melts, and colloidal suspensions. The derived equations are found to be more universal and could be reduced to many currently used equations under certain simplifications. Qualitatively, those derived equations are in consistent with experimental results, too.