The direct CI method. A detailed analysis

A thorough analysis of the direct CI method as applied to the case of a general set of reference configurations coupled to all single and double substitutions is presented. It is pointed out that there is no single strategy which proves optimal under all circumstances. A variety of procedures are therefore presented together with rules to enable the selection of the most favourable under a given circumstance. Much emphasis has been placed on organizing the calculations via a series of matrix multiplications, which enables a vector or array processing computer to be used to best effect. Some consideration is given to using an atomic integral (rather than molecular integral) driven scheme for some interactions, thus removing the necessity for a complete transformation of the molecular integrals to a molecular orbital basis, and the advantages and disadvantages of so doing are discussed. Improved procedures for carrying out both full and partial transformations of the molecular integrals are described. A number of test case calculations involving configuration lists of the order of 10⁴ to 10⁵ have been analysed in detail, to give a clear picture of the cost of the various interaction types which arise, and indicating that integrals carrying two external molecular orbital indices account for approximately 60 per cent of the cost in typical cases. Typically, a calculation involving 10⁵ configurations requires approximately two minutes of CRAY-1 computer time, allowing for ten iterations of the diagonalization procedure. The cost of the calculations are found, somewhat surprisingly, to be approximately linear in the dimension of the configuration space, indicating that calculations involving 10⁶ configurations are now quite feasible.     

Substituent effects on gas-phase acidities of formic acid and its silicon and sulphur derivatives R − M(= X)XH(M = C., Si; X = O,S; R = H,F, CI,OH, NH2 and CH3)

Ab initio molecular orbital methods at the CBS-Q level of theory have been used to study the effect of substituent (F, Cl, NH₂, OH and CH₃) on the gas-phase acidities of formic acid, HCOOH, its silicon and sulphur derivatives R-M(= X)XH(M = C., Si; X = 0, S; R = F, Cl, OH, NH₂ and CH₃). For formic acid and its thio and dithio derivatives the acidity changes upon substitution are irregular and depend on both the type of substituent, position and degree of replacement of oxygen atoms by sulphur atoms. For sila carboxylic acids and their thio and dithio derivatives the calculated acidities regularly increase in the order: R-SiOOH < R-Si(=S)OH ? R-Si(=O)SH < R-SiSSH(R = H, F, Cl, OH, NH₂ and CH₃). The chloro derivatives are the strongest among the acids studied. The highest gas phase acidity (1277.6 kJmol^?1) has been calculated for ClC(=S)OH.     

Molecular relativistic electric field gradient calculations suggest revision of the value of the nuclear electric quadrupole moment of 127I

Relativistic ab initio methods are used to compute the electric field gradient at the iodine nucleus in nine different closed-shell diatomic molecules. Combining these theoretical electric field gradients with experimental nuclear quadrupole coupling constants gives a consistent value of the nuclear quadrupole moment of ¹²⁷I of—696(12)millibarn. We argue that this value is more precise than the current standard value of the nuclear quadrupole moment of ¹²⁷I and recommend adjusting the reference value accordingly. The precision of this determination is still determined by technical limitations in the theoretical work, in particular the neglect of the two-electron Gaunt interaction in the Hamiltonian and correlation contributions beyond those described at the CCSD(T) level of theory, but the errors are reduced relative to the theoretical work that underlies the current standard value of this nuclear quadrupole moment. As a secondary study we also considered the calculation of the small electric field gradient at the gold nucleus in the AuI molecule and conclude that this computation remains a challenge for theoreticians.     

Experimental and theoretical study of the far-infrared spectra of HCl dissolved in liquid Ar,Kr, and Xe

New experimental results are reported on the relative absorption intensity distribution in the FIR spectra of HCl dissolved in liquefied Ar, Kr, and Xe at several temperatures along the liquid—vapour coexistence curve. These are treated further by applying a previously developed quantum-statistical spectral theory, which accounts for the line mixing and memory effects. Theoretical spectra are given in terms of the anisotropic potential time autocorrelation functions obtained from classical MD simulations using several empirical analytical potentials with density-adjusted well depths. Globally fair agreement between the theoretical and experimental spectra is demonstrated, except in the high frequency wings, where the theory underestimates the observed intensities. The choice of a particular radial form for the anisotropic HCl/RG potentials is found to be not critical for reproducing the experimental absorption profiles.     

On the Use of the Modelling System GAMS at an Energy Study Centre

Mathematical programming models play an important role in theenergy policy studies performed for a variety of clients bythe Netherlands Energy Research Foundation. Initially, modelswere built with the use of software tools developed in-house.Limitations imposed by these tools, coupled with an increaseddemand for various policy studies, prompted a switch to a differentsoftware technology which resulted in the choice of the GeneralAlgebraic Modelling System (GAMS). The new software technologygreatly improved not only the model development process butalso the reliability and flexibility associated with the useof models. Despite these improvements, further extensions inmodelling technology are needed in order to guarantee that amodelling system can also function effectively as an efficientdecision support system.     

CHARGE ACCUMULATION IN THE REACTION CENTER OF PHOTOSYSTEM 2

Abstract— The significance of the accumulation of positive charge in the reaction center of the oxygen-evolving system of photosynthesis is discussed. Many experiments on delayed and prompt fluorescence are explained by the electric field caused by positive charges on the various components at the oxidizing side of the photosystem 2 reaction center. A molecular model for this reaction center is proposed.     

On a Class of Similarity Solutions of the Equation ut(|u|m-1ux)x with m -1

Self similar solutions of the one-dimensional porous-medium equation are studied in thispaper. These solutions emerge from initial values that consistof two onstant states: one non-positive for x < 0 and onenon–negative for x > 0. With a diffusivity of the form we consider, for m > 0 sign-change solutions, and for m m (–1,0] non-negativesolutions.The method we use is based on a transformation whichmaps the ordinary differential equation for f into a singularelliptic boundary-value problem with Dirichlet conditions. Specialattention is given to the behaviour of f near zero. We alsopresent a number of numerical results.     

The onset of thermal runaway in partially insulated or cooled reactors

The conditions for the onset of thermal runaway in partiallyinsulated or cooled reactors are investigated. The temperaturein the reactor is taken to satisfy a nonlinear elliptic equationand the reaction is modelled by an Arrhenius heat generationterm with finite activation energy. To determine the onset ofthermal runaway, the method of matched asymptotic expansionsis used to derive expressions for the critical Frank-Kamenetskiiparameter _c() for reactors containing either a small coolingrod or having a small cooling patch on their boundary. The theoryused to determine _c() is an extension of the results of Wardand Keller (1991). These previous results of Ward and Kellerare also extended to the case of finite activation energiesby using a numerical scheme to evaluate the coefficients inthe asymptotic results for _c(). In some special cases, the asymptoticexpansions for _c() are compared with numerical results for _c(),and clear agreement is found.