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Notes: Roothaan-Hartree-Fock (RHF) calculations are carried out for the ground states of the atoms from helium to xenon using a minimal basis set of Slater-type functions whose principal quantum numbers are allowed to take variationally optimal noninteger values. The resulting energies are substantially superior to those obtained previously under the usual restriction that principal quantum numbers be positive integers. The energy lowering relative to the single-zeta wave functions of Clementi and co-workers ranges from 0.0066 Eh in He to 11.2 Eh in Xe. Our results are superior to those obtained by Höjer using a minimal basis set of unconventional binomially screened basis functions. Noninteger principal quantum numbers benefit d-orbitals the most; physically realistic negative d-orbital energies are obtained in all cases including those transition-metal atoms for which a conventional single-zeta STF basis leads to positive d-orbital energies. © 1997 John Wiley & Sons, Inc.

Notes: An ab initio study on the reaction of the ground state (3D) and the excited state (1D) of Sc+ with methane was performed. Reaction channels on the singlet and triplet potential surface (PES) and the reaction mechanism are examined and discussed. Three regions of the potential surface was studied: the molecular complex, the C(SINGLE BOND)H insertion products, and the transition states for the reaction. Comparisons between singlet and triplet PESs show that the excited state (1D) of Sc+ has more reactivity with methane than does the ground state (3D) due to the spin quantum number conservation with the more stable insertion intermediate. © 1997 John Wiley & Sons, Inc.

Notes: The importance of the hybridization displacement charge (HDC) in describing molecular electrostatic potential (MEP) maps was demonstrated by studying six molecules; pyrazine N-oxide, para-nitropyridine, 5-nitropyrimidine, 3-nitropyridazine, N2, and N2O. It is shown that continuously distributed HDC-corrected Löwdin charges reproduce the MEP features of these molecules, most of which have competing electrophilic sites, in agreement with ab initio results. Further, it is found that for homonuclear diatomic molecules MEP minima can be located properly using HDC-corrected Löwdin (or HDC-corrected Mulliken) continuously distributed charges, but these features cannot be obtained using the conventional Löwdin (or Mulliken) charges. It was shown that the order of molecular electric field (MEF) values near the different electrophilic sites becomes changed when one moves away from the molecules. Thus, pyridine-type nitrogen atoms are the preferred binding sites close to the molecules, while at large distances, effects of oxygen atoms of the NO groups become dominant. © 1997 John Wiley & Sons, Inc.

Notes: Some types of atomic vibrations in a chain of the DNA type constructed of G-C pairs were studied. These are the atomic vibrations of the lateral groups of guanine and N(3)H(1)H(2) of cytosine connected by the hydrogen bond h-b-1 and the vibrations of the centers of masses of bases in the direction parallel to bonds h-b-i, i = 1-3. The vibrations mix partially due to the dependence of the energy of the bond h-b-1 on its length and split into two bands because of the interaction between neighboring base pairs. It was shown that the excitation of the bond h-b-1 results in the splitting off of the two local vibrations and in a small deformation of the chain in the vicinity of the pair with the localized hydrogen bond. The law of the dispersion of band vibrations, values of the split-off frequencies, and degree of poly(dG)-poly(dC) chain deformation were determined. © 1997 John Wiley & Sons, Inc.

Notes: Analytical solutions to the Yukawa-like screened Coulomb nuclear attraction and electron repulsion molecular basic integrals, as well as to the basic integrals required to compute the virial coefficient, over Gaussian basis functions, are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of molecular electronic structure. © 1997 John Wiley & Sons, Inc.

Notes: He I photoelectron (PE) spectra of four carboxylic acids and five esters are measured. Semiempirical and ab initio quantum chemical calculations are used for the interpretation of the spectra. The complex approach which uses empirically established relationships (the dependence of valence electron ionization energies on proton affinities in the gas phase, on the core level ionization energies, and on the structure) was developed. © 1997 John Wiley & Sons, Inc.

Notes: Simple molecular orbital calculations are employed in searching electronic parameters which may characterize the chemical carcinogens. Using frontier orbitals, the carcinogen-DNA bond formation is described as an electron transfer from the highest occupied molecular orbital (HOMO) of DNA to the lowest unoccupied molecular orbital (LUMO) of the carcinogen. Analysis of the DNA bases units shows that the electron donation occurs preferentially at the guanine site. The calculated low LUMO energy of several carcinogens indicate correctly the electrophilic character of these compounds. The difference between the carcinogen and the ultimate carcinogen is analyzed. Epoxides, free radicals, alkylating agents, and other metabolite forms are studied. A reasonable correlation is found between the LUMO energy and the carcinogenic function. © 1997 John Wiley & Sons, Inc.

Notes: The Gaussian expansions of the generalized relativistic effective core potential (GRECP) components are reported for elements Hg through Rn. The accuracy of the analytical GRECPs is estimated by calculations of atomic transition energies with the numerical one-configurational wave functions in comparison with Dirac-Fock calculations. The results of the corresponding calculations with the RECPs of other groups are also given. An “averaged error” in the reproduction of the transition energies without the change of the occupation number of the 5d-shell is an order of magnitude smaller than that for the RECPs of other groups. As is demonstrated for the transitions with the change of the occupation number of the 5d-shell in mercury, the largest absolute error of the GRECP is only 1.5-2 times smaller than that of the energy-adjusted pseudopotential (PP) or the RECP of Ross et al. with the same space of explicitly treated electrons. However, the dispersion of these errors is 19⋅10-4 au for the energy-adjusted PP, 35⋅10-4 au for the RECP of Ross et al. and only 4⋅10-4 au for the GRECP. One-configurational spin-averaged calculations of the molecular properties for HgH and HgH+ are carried out and compared with the corresponding results of Häussermann et al.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1107-1122, 1997

Notes: Molecular dynamics simulations of liquid formamide(HCONH2) were carried out using the GROMOS software. The formamide molecule is represented by all of its atoms with all internal degrees of freedom. In contrast to other simulations dealing with bulk properties, this study focuses on the interface liquid-vacuum for the first time. We show that the molecular plane is tilted out of the surface, exposing the HCO group to the vacuum.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1123-1131, 1997

Notes: The H2 interaction with the Pd dimer and trimer were studied using multiconfigurational self-consistent field (MC-SCF) calculations with the relativistic effective core potential (RECP); the correlation energy correction was included in the extended multireference configuration interaction (MRCI), variational and perturbative to second order. Here, we considered the Pd2 first six states: 3Σ+u, 1Σ+g, 3Πg, 3Δxy, 1Σ+u, and 3Σ+g. For them, the four geometrical approaches included were the side-on H2 toward Pd2, for the hydrogen molecule in and out the Pd dimer plane; the perpendicular end-on H2 toward Pd2; and the perpendicular end-on Pd2 to H2. The Pd2 ground state is 3Σ+u, which only captures H2 in the C2v end-on approach, softly relaxing the H(SINGLE BOND)H bond. The closed-shell 1Σ+g captures the H2 molecule in all the approaches considered: The side-on approach of this state presents deep wells and relaxes the H(SINGLE BOND)H bond, and the end-on approach captures H2 with a relatively longer H(SINGLE BOND)H distance and also a deep well. The 3Πg state was the only one which did not capture H2. For the triangular Pd3 clusters, H2 was approached in the C2v symmetry in and out of the Pd3 plane. In the triangular case, H2 was absorbed in both spin states, with deep wells and relaxing the H(SINGLE BOND)H distance. The linear Pd3 singlet and triplet states capture outside of the Pd3 and break the H(SINGLE BOND)H bond. © 1997 John Wiley & Sons, Inc.

Notes: We presented a calculation of the total and partial decay widths of vibrational predissociation (VP) of the HeI2 molecule for low initial vibrational excitations from the lowest van der Waals (vdW) state with total angular momentum J = 0. A time-dependent golden rule wave-packet method was employed in our numerical calculations for the decay widths. The computed total decay widths, lifetimes, and rates of VP are in fairly good agreement with those extrapolated from the experimental data available. Predicted total decay widths as a function of initial vibrational levels exhibit a highly nonlinear behavior. These results demonstrate that a quantum mechanical decay mode for low vibrational excitation remains as well. The total propagation time needed in the time-dependent golden rule wave-packet calculations is much shorter than is the lifetime of the predissociation of HeI2. It is shown that the final-state interaction between the fragments is important for determining the final rotational-state distribution (partial decay width). We find that the major peak position in the final rotational-state distribution shifts to lower rotational energy levels with increase of the initial vibrational quantum number, which is evidently different from that for higher vibrational levels. This fact can be clearly explained by the dependence of the amount of kinetic energy released to the product degrees of freedom on the initial vibrational state. © 1997 John Wiley & Sons, Inc.

Notes: An extension to the theory of Schrödinger equations has been made which enables the derivation of eigenvalues from a consideration of a very small part of geometric space. The concomitant unwanted continuum effects have been removed. The theory enables very convergent or “superconvergent” calculations. In the case of the helium ground state, E=-2.90372437703411987 Eh was obtained from 251 terms. The result is comparable to that from the largest variation calculations so far carried out reinforced by extrapolation techniques. The theory is extensible to atoms and molecules irrespectively of the number of electrons or nuclear centers. In these cases, the advantage of “superconvergent” calculations will be more pronounced than in the case of helium.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1065-1078, 1997

Notes: We calculate the resonant and antibound state energies for a Morse potential with a centrifugal barrier using Siegert boundary conditions. Starting with a complex wave number k (purely imaginary for bound and antibound states), we integrate numerically from the origin up to a matching point using Numerov's method. The inward integration is performed using the corresponding (first-order) Riccati equation. The complex eigenvalues are found by matching the two logarithmic derivatives. We find narrow shape resonances within the well, above the dissociation limit, and broad resonances above the centrifugal barrier. Antibound states are found even with J = 0. © 1997 John Wiley & Sons, Inc.

Notes: Numerical experiments with a nonlinear (λχ4) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ 〉 0), a threshold is reached at λ = λc when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. © 1997 John Wiley & Sons, Inc.

Notes: Testosterone (17β-hydroxy-4-androsten-3-one) was studied by the semiempirical AM1 and PM3 and ab initio STO-3G*, 3-21G*, and 6-31G* methods. The goals were to compare those methods and to know the electronic structure of the hormone. Full geometry optimization was performed, and two crystal conformers (T1 and T2), and experimental dipole moment in solution were used for comparison. One conformer with a dipole moment similar to the solvated conditions was generated. Total energy, entalphies, dipole moments, charges, electrostatic potentials, and highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbital (LUMO) were calculated. Root-mean-square (RMS) index of the theoretical molecules against T1 and T2 showed best results with the 3-21G* and 6-31G* methods, while AM1 gave better energies than PM3. Dipole moments were directed toward the OH group and the botton face of the A ring. The frontier orbitals were located along the C4-C5 π bond, particularly the LUMO was split between C4 and C5, predicting the action of enzymes at C5 yielding to 5α and 5β-reduced androgens. Electrostatic potentials might be also of biological importance since they are coincidental with the dipole-moment orientation. Finally, it is interesting that the solvatedlike conformer, its properties, and the OH group laid between the same group of T1 and T2 and with a total energy between the crystals and the gas phase or in vacuo conditions. This results might also explain the biology of testosterone and use them to model the hormone-receptor interaction. © 1997 John Wiley & Sons, Inc.

Notes: Two alternative dehydration reactions C(OH)4 → (HO)2CO + H2O and C(OH)4 + H2O → (HO)2CO + 2H2O are studied by ab initio Becke3LYP/6-311 + G** and MP2/6-31G** methods. Calculated energy and geometry characteristics of intermediates and transition states predict a catalytic effect of one water molecule and the exothermism of the transformations. Relevant HF/6-311 + G**, HF/6-31G**, HF/6-31G, and HF/3-21G calculations were performed for comparison. © 1997 John Wiley & Sons, Inc.

Notes: Restricted geometry optimizations at the ab initio SCF level with the 3-21G basis set were employed to investigate the conformation space of flavone acetic acid (FAA) and its related compounds. All the conformations are produced from a conformation which is, according to our previous work, probably the active conformation in terms of antitumor activity shown by these compounds. Detailed studies on FAA were carried out while only brief discussions are made on the analogs. The main results obtained are that (1) FAA is a very flexible molecule, e.g., with the energy barrier up to about 3 kcal mol-1 from the reference conformation, the important torsional angle τ1 can change from 27.0° to 117.0°, τ2 from -168.0° to 2.0°, and τ3 from -50.0° to 30.0°; (2) the hydrogen-bonding effect plays an important role in determining lower-energy conformations; (3) among all the FAA conformations considered, some are active and some are inactive; (4) it seems that the analogs will have similar behavior to FAA when the torsional angle τ3 is restricted to the values which are around the equilibrium values; and (5) the hypothesis put forward previously has been further developed in this work. Now, we postulate that efficient charge transfers will lower the energy and that proper charge transfers will activate the molecule. There are mainly two different types of charge transfer corresponding to two different types of conformation, which are specified in this article. © 1997 John Wiley & Sons, Inc.

Notes: We compare geometry configurations, vibrational properties, and electronic structures of (HF)2 in a free state and inside argon atom shells Arn. For the first stage, molecular dynamics calculations for the (HF)2 · Ar62 heterocluster are performed with the help of model potentials HF(SINGLE BOND)HF, Ar(SINGLE BOND)Ar, and Ar(SINGLE BOND)HF. Then, ab initio quantum chemistry analysis is carried out for the smaller systems (HF)2 · Ar15 and (HF)2 · Ar6 when keeping the argon atoms closest to the trapped dimer. We conclude that the hydrogen-bonded complex (HF)2 gains some extra stability inside the argon shells, originating primarily from a decrease of intermolecular distance RFF. Electronic structure calculations are in accord with the changes in dynamical properties, namely, a noticeable increase in the vibrational frequency assigned to the F(SINGLE BOND)F stretching mode (+25 cm-1) and decrease in rms deviations for the corresponding coordinate δFF. In addition to these changes, the argon atoms of the nearest solvent shell donate a small fraction of electron charge which is spent for an increase of population of the antibonding orbital σ*Hf(SINGLE BOND)Ff of the free monomer unit and shift orbital energies primarily of the lone-pair fluorine species. These shifts are greater than the changes due to geometry alterations and the possible inaccuracies of the calculation scheme. © 1997 John Wiley & Sons, Inc.

Notes: An analysis of the anisotropic Heisenberg model is carried out by solving the Bethe ansatz solution of the model numerically as a function of the anisotropy parameter for finite N. A brief introduction to the limit of the infinite chain is presented. The energy for a few special limiting cases of the anisotropy parameter in the Hamiltonian are worked out. Numerical results for finite cycles as well as for the infinite chain are given. Comparison can then be made with the case of finite increasing N. © 1997 John Wiley & Sons, Inc.

Notes: The MELD program is employed to evaluate the Slater average potential v(r) felt by an electron at the point r within an atom. The characteristic radius R of the atom is then defined by the classical turning point equation v(R) = -I, where I denotes the first ionization potential of the atom. The atomic radii defined in this way have a close correlation with the van der Waals atomic radii. © 1997 John Wiley & Sons, Inc.

Notes: Highly accurate upper bounds for several 2Pe states of the Li isoelectronic series obtained by extensive Hylleraas-Cl calculations are given. The best value for the 22Pe state (1s2p2) of Li is -5.21373920 au. The evaluation of the occurring integrals is given explicitly. Additionally, we present some expectation values and isotope energies of the Li isoelectronic series. © 1997 John Wiley & Sons, Inc.

Notes: An efficient expansion method for the evaluation of VB matrix elements is introduced. The overlaps of VB wave functions of N electrons can be treated as algebrants, i.e., generalized determinants, of N × N matrices. An algebrant can be expanded with subalgebrants of lower orders in a successive way. By choosing Rumer spin bases and appropriately arranging the expansion, it is found that the number of unique subalgebrants involved in the expansion increases in a quite moderate way with N. In contrast to the traditional symmetric group approach, which explicitly utilizes all N! representation matrices, the new strategy incorporates the group theoretical factors in a simple way in the successive expansion. As only the unique subalgebrants are further expanded, the computational effort required by the new strategy scales in a very acceptable manner with the increasing number of electrons. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 245-259, 1997

Notes: Characters of irreducible representations (irreps) of the symmetric group corresponding to the two-row Young diagrams, i.e., describing transformation properties of N-electron eigenfunctions of the total spin operators, have been expressed as explicit functions of the number of electrons N and of the total spin quantum number S. The formulas are useful in various areas of theory of many-electron systems, particularly in designing algorithms for evaluation of spectral density moments. © 1997 John Wiley & Sons, Inc.

Notes: The geometries and S-H, S-S, and S-C bond dissociation energies for hydrogen sulfide, hydrogen disulfide, methanethiol, dimethyl disulfide, and dimethyl disulfide were calculated with both ab initio (ROHF and MP2), hybrid (BHandH, BHandHLYP, Becke3LYP and Becke3P86), and nonlocal (BLYP and BP86) density functional theory (DFT) methods. In all studies the 6-31 + G(d) basis set is used. The computed results are compared to the experimentally obtained values, targeting the selection of a suitable ab initio or DFT method for the study of these systems. © 1997 John Wiley & Sons, Inc.

Notes: The mechanism and kinetics for the decomposition of β-hydroxypropaldehyde, primary and secondary β-hydroxyketones, were studied by using ab initio RHF/6-31G and RHF/6-31G* methods. The activation barriers of these reactions were refined to be 39.57, 40.10, and 36.80 kcal mol-1 at the MP2/ /RHF/6-31G* level, respectively. The calculated results show that each decomposition is a concerted process with hydrogen transferring and bond breaking via a six-membered cyclic transition state. The thermal rate constants of the decomposition of primary and secondary β-hydroxyketones were obtained by calculating microcanonical probability fluxes through each transition state. It is theoretically confirmed that methyl substitution at the hydroxyl carbon of β-hydroxyketones causes a small enhancement in rates. The theoretical investigations of the mechanism and the rate constants are in agreement with the experimental results. © 1997 John Wiley & Sons, Inc.

Notes: The method of o(4, 2) operator replacements is generalized. As a result, the series whose limiting values when the variable goes to  +∞ should correspond to the two-electron atom energies now have rational coefficients. This generalization allows one also to compute the series for the case of singlet S symmetry, a case which could not be considered in the previous original formulation of the method. Series with rational coefficients for the helium singlet and triplet S ground-state energy are calculated up to order 41 and 45, respectively. Moreover, symbolic computations also allow one to give the first few coefficients of these series for arbitrary values of the nuclear charge Z. Finally, a new method for analytic continuation to the limit  +∞ is presented for the energies of the helium singlet and triplet ground states.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1079-1089, 1997

Notes: A few simple atom-transfer reactions (i.e., Ȧ+X-A→A-X+Ȧ) are studied by quantum mechanical ab initio methods. Emphasis is given to the detailed analysis of density matrices rather than to the energetics. Results reveal that during these reactions a small free valence always develops on the migrating atom at the transition state. The barriers in these reactions arise from the greater extent of bond cleavage in the reactant than that of bond formation in the transition state. Analysis of bond orders estimated from bond lengths using Pauling's relation also leads to the fact that the bond-cleavage process is more advanced than is the bond-formation process in these reactions.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1099-1106, 1997

Notes: In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.

Notes: In this communication, the application of the transmission line modelling (TLM) technique to the solution of the differential Riccati equation is described. A comparison is made between the TLM, fourth-order Runge-Kutta and the first-order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equation is second-order. It is found that, when the system is underdamped, the fourth-order Runge-Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM method yields results that are closest to the analytical solution. Finally, a discussion is presented of the effects of errors in the TLM solution of the Riccati equation on the accuracy of the solution to the continuous Kalman filter estimation equation.

Notes: The paper describes the influence of contact area on the service life of dynamically loaded gears with a crack in a tooth root. Numerical results obtained with the finite element method using the program package BERSAFE are compared with the experimental results obtained on the universal testing machine INSTRON 1255. Numerical and experimental results are in good agreement. The analysis shows that the contact area directly influences the speed and direction of the crack propagation and the service life of the gear with a crack in a tooth root.

Notes: Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented.

Notes: A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.

Notes: In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.

Notes: We examine a method to impose boundary conditions on arbitrary boundaries, introduced to make domains of infinite extent finite for the purpose of numerical calculations, when a finite element discretization based on linear, bilinear or trilinear elements is used, in one, two or three dimensions, respectively. In particular, we look at the so-called ‘free’ boundary condition, which consists in retaining the boundary integrals generated by the weighted-residuals formulation along the open boundaries and adding them to the stiffness matrix. We show that this procedure is exactly equivalent to imposing on the boundary nodes a Sommerfeld radiation condition in one dimension, and a slightly modified form of the Sommerfeld boundary condition in two and three dimensions. We also show that the procedure is not applicable to the purely elliptic case.

Notes: Recent advances in planar mesh generation of arbitrary domains incorporate methods for placing points as well as connecting them into a triangulation. Postprocessing techniques such as Laplacian smoothing and mesh relaxation enhance the shape of triangles in these meshes but do not address the construction of meshes near boundaries or provide a criterion to determine the number of interior points of the initial triangulation. The paper addresses these issues by investigating the construction of degree-6 triangulations, the primary goal of the mesh relaxation method.

Notes: The paper presents a distributed computing approach for concurrent finite element analysis of truss structures. The client-server model of distributed computation is applied to the plane frame finite element algorithm and implemented on SUN workstations. The remote procedure call combined with the ability to create threads of computation allows one to efficiently implement distributed and concurrent programs. The present approach is demonstrated through a typical truss structure to illustrate the details of the implementation. This approach can be used for very large finite element systems.

Notes: This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov-Galerkin) method, explicit forward Euler pseudo-temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.

Notes: A posteriori error estimation for typical Euler-Bernoulli beam bending problems is developed using a recovery operator based on a smoothing technique that is applied in the context of one-dimensional fourth-order problems. The development exploits a discrete superconvergence property of the ‘bending moments’ of the trial space interpolant of a polynomial solution of sufficiently low degree at certain Gauss points, and the superconvegence property of the energy norm difference of the trial space interpolant (of the weak solution) and the finite element approximation. An asymptotically exact error estimator is developed.

Notes: We discuss a two-step superposition method for calculating linear elastic stress intensity factors. The procedure requires the solution to the full cracked problem and the solution to a problem on the same mesh assuming the singularity due to a crack tip in an infinite region. We show that this is equivalent to the well known subtraction of singularity method if the two solutions are characterized by crack tip stress. The advantages of our procedure are that no modifications need to be made to a standard computer program and that once one singular solution is available on a given cracked mesh, solutions with different boundary conditions on the same mesh may be obtained in one step without including any singular crack effects. The mesh required to represent the singular crack tip field may also be studied independently of the complete problem. The additional computational cost of a two-step procedure is minimal since the solution matrix from step one may be reused with a new right-hand side. Numerical experiments using the boundary element method demonstrate the high accuracy and simplicity of the superposition approach.

Notes: The effect of upwinding on iterative performance of convection-diffusion problems is investigated. An analysis of the iterative method considered here leads to a criterion for selecting the optimal upwinding parameter to improve iterative performance for a class of two-dimensional convection-diffusion problems. Supporting numerical experiments are presented.

Notes: A numerical method is presented for the analysis of dynamic interaction between rigid wheel and flexible beam. In contrast to traditional approaches, the wheel nominal motion as well as the contact force are considered here as unknowns. The correct contact force between the wheel and the beam is computed by iteratively reducing the constraint error towards zero, and a simple time integration is employed for the solution of equations of motion. Convergence of the iterative scheme is analysed, and numerical simulations are conducted to demonstrate the accuracy of the solution.

Notes: The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well.

Notes: The integral transform method is employed in the analytical solution of the non-classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.

Notes: Because of the earth's curvature, all existing channels have a curvature. E. Zeidler gave an existence and uniqueness proof for permanent heavy and capillar-heavy waves in such circular shaped channels. Based on this proof and on a general computational method for constructing the solutions numerically, the case of permanent heavy waves in circular-shaped channels is considered in this work.

Notes: In this paper, I discuss the convergence and divergence rates for a class of generalized matrix multisplitting relaxation methods in a detailed manner. In particular, when the coefficient matrix is an L-matrix, I obtain several sufficient and necessary conditions ensuring the convergence of these methods.

Notes: An independent refinement and integration procedure is developed to couple together independently modelled (global and local) regions in a single analysis. The finite element models can have different levels of refinement and the nodes along the interface between them need not coincide with one another. A spline interpolation function that satisfies the linear isotropic plate-bending differential equation is used to relate the local model interface nodal displacements to the global model interface displacements. The proposed independent refinement and integration procedure is validated by applying it to problems involving in-plane and out-of-plane deformations.

Notes: Both the logarithmic and derivative kernel integrations for potential problems, solved with quadratic isoparametric boundary elements, contain quartic functions of the integration parameter. It is shown that such functions can be written as the product of two quadratic functions with real coefficients. The derivative kernel integration is then represented as the sum of two integrals, which can be evaluated analytically. The logarithmic kernel integration can be similarly split but needs a Taylor series expansion of the Jacobian of the integration to enable analytical integration. The use of this Taylor series expansion means that the method presented is limited to problems involving weakly curved elements.

Notes: In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick.

Notes: The determination of the dynamic response of plate and shell structures is carried out employing a discrete representation of the continuum, associated with an explicit integration scheme in the time domain. Comparisons with experimental results certify the accuracy and reliability of the proposed method.

Notes: Constraints arise naturally in the context of rigid inclusions, incompressibility, inextensible fibres and deformed finite elements. Typical methods for handling constraints in the governing matrix equation include Lagrange multipliers, penalty weights and elimination of variables. Each procedure has a particular undesirable feature. Proposed here is an approach in which each constraint is handled directly and sequentially through a modification of the rows and columns of the governing matrix and force vector. Positive definiteness, symmetry and the dimensions of the matrix remain unchanged. Elementary examples involving both the static and dynamic response of a bar are given to illustrate the procedure.

Notes: The focus of the present work is directed towards the construction of a family of special finite elements for the numerical solution of the Reissner-Mindlin plate problem. The model describes the deformation of a plate when transverse shear deformation is taken into account. The model is widely used for thin to moderately thick plates. Despite its simple formulation, the numerical approximation is not straightforward. When standard low-order finite elements are used for the approximation the solution degenerates very rapidly for small thickness (locking phenomenon). To overcome such behaviour, non-standard formulations of the problem are usually combined with low-order finite elements to weaken or possibly eliminate the locking of the numerical solution.In recent years high-order finite elements have been introduced and successfully applied in several fields. Previously we have constructed a family of hierarchic high-order finite elements to solve the Reissner-Mindlin problem in its plain formulation. The locking was strongly reduced but was still active for very thin plates. Meanwhile some mixed-interpolated finite elements have been developed and shown to be locking free. In this paper we combine the two approaches, namely, the hierarchic high-order elements and the mixed-interpolated elements. The result is a family of special finite elements that exhibits both properties of convergence and robustness.

Notes: The paper reveals the conditions under which the approximations of the normal vector and global coordinates of interior points of two segments on a smooth contour can fail using the C1-continuous Overhauser elements. A new continuous modelling of the normal vector is developed using the standard Lagrange elements. The derivation is consistent with the assumptions employed in the boundary element method formulations of potential problems. Test numerical examples are considered in order to analyse the accuracy of the approximations based on the use of standard C0-continuous elements, Overhauser C1-continuous elements and the proposed ‘smooth’ C0 elements.

Notes: The paper describes a new numerical algorithm for pure advection at large Courant numbers. The DISCUS scheme uses an accurate and proven control volume algorithm (QUICKEST) within a Lagrangian treatment of advection. By being in sympathy with the information flow dictated by characteristic lines, the scheme performs exceedingly well at Courant numbers greater than one. In contrast to existing Lagrangian schemes which use the characteristics to determine the grid points from which concentrations are interpolated, in DISCUS the characteristics are used to determine the appropriate location for the control volume. The scheme is of comparable accuracy to Eulerian schemes at Courant numbers less than one, but it increasingly outperforms them as the Courant number increases. Indeed, the results reported illustrate the futility of using an Eulerian scheme at high Courant numbers.

Notes: The use of effective core potentials in the calculation of the geometrical parameters of the ferrocene molecule and its heavier analogs is reported. It is shown that a critical factor in these calculations is the efective core-core (ECC) potential and, in the absence of ECCs for first-row atoms that are involved in short bonds, calculations of the geometrical parameters are not reliable. Good agreement with experimental geometries may be obtained by using the Los Alamos ECPs for atoms of the second and higher rows of the periodic table at the MP2 level. DFT calculations have been performed and found to give numerical results comparable to MP2 in the same basis. © 1995 John Wiley & Sons, Inc.

Notes: In this article, we report an efficient computational procedure for electron scattering matrix elements in the previously developed cubic-grid Gaussian basis sets. The Green function matrix elements derived for the cubic-grid basis set are simpler and easier to calculate than are those available in the literature for conventional Gaussian basis sets. Special features of the cubic-grid basis sets may also be exploited for a very efficient computation of Coulomb and exchange integrals. Inelastic scattering amplitudes for vibrational excitations may be efficiently calcualted in the harmonic approximation by numerical differention of the T-matrix elements. © 1995 John Wiley & Sons, Inc.

Notes: Previously developed cubic-grid basis sets of various sizes were used for the calculation of cross sections for elastic and inelastic electron scattering by the He and Ne atoms and the H2O molecule by the T-matrix expansion method. The aim was to test the invariance of calculated cross sections with respect to the translation of the target molecule and to examine the effect of basis-set size on the results. We also present a simple procedure for accounting for long-range interactions from the part of space that lies outside the volume that contains the cubic-grid basis set. © 1995 John Wiley & Sons, Inc.

Notes: Atomic charge and momentum densities of 91 atoms (He—U) are classified in terms of their L1, L2, and entropic measures of distance from the densities of the preceding atoms. The relationship between these distances and the first ionization energies is also considered. © 1995 John Wiley & Sons, Inc.

Notes: The subject of this article is the self-consistent-field (SCF) treatment of low-lying molecular vibrations in molecules subject to solvent effects and light atom migration. The analyses use a Cartesian Gaussian basis and Gaussian functional expansions of potential energy operators. The objective of the work was to establish approximate and practical methods of analysis of vibrational degrees of freedom in molecules that build on and compare well with the highly accurate treatments of vibrations in small molecular systems of the past decade. An application to a system in which hydrogen bonding contributes the major anharmonic effect illustrates the method. © 1995 John Wiley & Sons, Inc.

Notes: This article presents methods for computing matrix elements with Cartesian Gaussian wave functions of potential energy operators that depend on functions of the form (r-r0)n exp[-a(r - r0)] as well as matrix elements of the class of polynomial many-body potentials developed by Murrell et al. The matrix elements arise in the analyses of anharmonic vibrations in molecules. © 1995 John Wiley & Sons, Inc.

Notes: The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of altemant cyclic polyenes (CH)N, (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Möbius) orbitals are used to perform energy extrapolations for N → ∞. © 1995 John Wiley & Sons, Inc.

Notes: General formalism for evaluation of multiparticle integrals involving J̌2 and J̌z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.

Notes: The molecular g-tensors for the molecules NO2, CO2-, C3H5, H2CO+, and NF3+ are calculated at the unrestricted Hartree-Fock (UHF) level using the Rayleigh-Schrödinger perturbation approach. All one-electron terms have been evaluated, including the relativistic mass correction, the one-electron spin-Zeeman gauge correction, and a second-order term involving the spin-orbit coupling and the orbital-Zeeman interaction. The relative importance of the first-order terms is found to be quite substantial. For first-row molecules, their total contribution is often of the same order of magnitude as of the second-order contribution, in some instances even larger. A study on the basis-set dependence of these g-tensors has been conducted. At this level, the most important basis-set criterion is shown to be a satisfactory description of the valence regions. Finally, the gauge dependence of these g-tensor calculations has been systematically studied. This dependence seems to be substantially reduced for basis sets which include polarization functions. © 1995 John Wiley & Sons, Inc.

Notes: A scaling procedure is used for the force constants generated by the SINDO1 method in internal coordinates to achieve better agreement with experimental frequencies of molecules. The procedure is subsequently used to calculate frequency shifts for adsorbed molecules. The results for CO2 and CO adsorption at NaCl cluster surfaces are in good agreement with experimental data. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio self-consistent-field calculations are reported for electronic states of beryllium clusters comprised of 93, 105, 111, and 123 atoms. The respective clusters correspond to coordination shells 12-15 of a central Be atom with internuclear separations derived from the lattice constants of the bulk metal. Ab initio effective core potentials have been employed to replace the 1 s electrons, thereby reducing the complexity of the calculations. In addition, use of the full D3h point group symmetry of the clusters results in a substantial reduction of the numbers of two-electron integrals that must be computed and processed. Binding energies, orbital energies, electric field gradient, nuclear-electrostatic potential, diamagnetic shielding constant, second moments, and Mulliken populations are calculated for selected electronic states. Calculated binding energies when compared among the different clusters as well as to smaller and larger fragments from earlier studies provide evidence for the onset of convergence to the Hartree-Fock limit of the bulk. Lowest-state ionization potentials are consistently above and agree to within 14% of the experimental workfunction. The net charge on the central beryllium atom decreases toward zero. The variability of observed bulklike behavior for the different properties indicates that the transition between cluster and bulklike behavior is not sharp and depends on the quantity of interest. © 1995 John Wiley & Sons, Inc.

Notes: The discrete variable representation method (DVR) is applied to the calculation of the J = 0 vibrational energy levels of the ground electronic state of nitrogen dioxide, a molecule which shows a large amplitude bending vibration. The Hamiltonian is expressed in Johnson hyperspherical coordinates and developed on a DVR basis set for each coordinate. A successive diagonalization-truncation method is applied which gives accurate values for the energy levels up to ≃ 7000 cm-1. © 1995 John Wiley & Sons, Inc.

Notes: A procedure for finding transition states ( TS) that does not require the evaluation of the second derivatives during the search is proposed. The procedure is based on connecting a series of points representing products Pi and reactants Ri and taking conservative steps along the difference vector from Pi toward Ri and from Ri toward Pi until the two points coalesce. Although the points Po and Ro represent the product and reactant specifically, other Pi and Ri are determined by minimization in hyperplanes perpendicular to Pi -1 and Ri-1. We apply this technique to six well-known potential functions and compare these results with those obtained from other well-known procedures. © 1995 John Wiley & Sons, Inc.

Notes: Potential energy curves for the ground and low-lying excited states of the AH2+ (A = Mg - Ar) dications have been calculated using high-level ab initio methods with large atomic orbital basis sets. Quasi-bound potential energy curves with local minima and deprotonation barriers have been found for most of the dications studied. The energies, tunneling lifetimes, and widths of the quasi-bound states have been calculated by numerical solution of the radial Schrodinger equation using the Numeov method. All these dications except ArH2+ have low-lying states which support quasi-bound vibrational states. The ArH2+ dication has a 2∏i potential energy curve with a minimum so shallow that it does not support any quasi-bound vibrational states. Results of our calculations are compared with previous ab initio calculations and available experimental data. © 1995 John Wiley & Sons, Inc.

Notes: A bond-energy formula deduced by means of the Hellmann-Feynman theorem is applied to selected simple hydrocarbons. The required potentials at the nuclei are calculated with the help of large basis-set expansions including polarization functions. The carbon-carbon bond energy of ethane is evaluated at ∼ 70 kcal mol-1. The CC bond energies of ethane, ethylene, acetylene, benzene, and cyclopropane are approximately in a ratio of 1: 2.0: 3.0: 1.65 1.0. Limitations and possible improvements in future applications of this energy formula are discussed. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio molecular orbital (MO) calculations with the 3-21G and 6-31G basis sets are carried out on a series of complexes of NH3 with Li+, C≡N-, LiCN, and its isomer LiNC. The BSSE-corrected interaction energies, geometrical parameters, internal force constants, and harmonic vibrational frequencies are evaluated for 15 species. Complexes with trifurcated (C3v) structures are calculated to be saddle points on the potential energy surfaces and have one imaginary frequency each. Calculated energies, geometrical parameters, internal force constants, and harmonic vibrational frequencies of the various species considered are discussed in terms of the nature of association of LiCN with ammonia. The vibrational frequencies of the relevant complexed species are compared with the experimental frequencies reported earlier for solutions of lithium cyanide in liquid ammonia. © 1995 John Wiley & Sons, Inc.

Notes: When two electronic potentials present an avoided crossing, the adiabatic approximation breaks down in the energy region near to the crossing. In particular, the correspondence between exact energy levels of the two-state system and the adiabatic levels of the lower and upper adiabatic potentials becomes ambiguous. This implies that the term “nonadiabatic effect,” used for the difference between exact and adiabatic energy eigenvalues, loses its meaning in the crossing regime unless an unambiguous way of assigning an adiabatic to an exact level is defined. This is important in order to investigate where nonadiabatic schemes, such as the generator coordinate approximation, fit in between the adiabatic approximation and quasi-exact approaches. © 1995 John Wiley & Sons, Inc.

Notes: The application of the Σ-separation method to the calculation of multicenter two-electron molecular integrals with Slater-type basis functions is reported. The approach is based on the approximation of a scalar component of the two-center atomic density by a two-center expansion over Slater-type functions. A least-squares fit was used to determine the coefficients of the expansion. The angular multipliers of the atomic density were treated exactly. It is shown that this approach can serve as a sufficiently accurate and fast algorithm for the calculation of multicenter two-electron molecular integrals with Slater-type basis functions. © 1995 John Wiley & Sons, Inc.

Notes: The intersystem crossing (ISC) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin-orbit coupling (SOC) in oxirane biradicals (ĊR′R″ - CRR* - Ȯ) is stressed through calculations where the spin-orbit matrix elements over the full Breit-Pauli SOC operator has been obtained in the singlet-triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin-orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin-orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(3P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.

Notes: We consider a crystal as partitioned into a localized molecular cluster (containing a defect or not) and an embedding region. Within the Hartree-Fock formalism, an expression is derived for an effective potential due to the embedding region of crystal. This potential is part of the cluster Fock operator and requires input from a perfect crystal calculation. Special features of the derivative are rigorous inclusion of cluster-embedding overlap and orthogonality between single-electron states of the embedding region and the function-space manifold of the cluster; physically correct normalization of the Fock eigenstates; and a nontrivial total-energy algorithm. Computational requirements are qualitatively compared with those for an isolated cluster. The method allows for intracluster (and intraembedding) correlation and can be adapted straightforwardly to local density functional approaches. Fundamental aspects of the embedding problem are addressed in a general formulation that is, nevertheless, oriented toward explicit calculations. © 1995 John Wiley & Sons, Inc.

Notes: An efficient procedure for third-order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self-energy expressions that are suitable for large molecules are empolyed. The outer-valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self-energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C72- with a 231 atomic orbital basis and for Zn(C5H5)2 with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.

Notes: The intermolecular potentials for the X 2σ and A2Π states of Li… Ar were studied by a variety of multiconfiguration, single-configuration, and perturbation methods (CASPT2). The A 2Π excited state was calculated to have a well depth of 811 cm-1 at an internuclear separation of 2.59 Å, in excellent agreement with the 810 cm-1 derived from experimental data. A smaller well of 77 cm-1 was found for the X 2σ ground state at an intermolecular separation of 4.8 Å. These results are in better agreement with experimental results than were the previously reported pseudopotential calculations. The comparison of CI calculation with the CAPST2 results shows that the latter is able to give good results for interacting metal-rare gas systems. © 1995 John Wiley & Sons, Inc.

Notes: This article is a brief review of the work formalism of electronic structure, its recent developments, and the results of its application to spherically symmetric and nonspherical density atoms. The formalism, which is founded in Schrödinger theory, is derived by physical arguments based on Coulomb's law. The fundamental quantity in the formalism is the pair-correlation density that constitutes the nonlocal quantum-mechanical source charge distribution giving rise to both a local potential representing electron correlations as well as the electron interaction energy. The potential is the work done to move an electron in the force field of the pair-correlation density and the energy the interaction energy between the electronic and pair-correlation densities. (For systems for which the curl of the force field may not vanish, the potential is obtained from the irrotational component of the field, the solenoidal component being neglected). The differential equation governing the system is a Sturm-Liouville equation, and as such, the exact wave function can in principle be obtained as an infinite linear combination of Slater determinants of the self-consistently determined spin-orbitals of the occupied and virtual states. The correctness of the interpretation for the local potential representing electron interaction is evidenced as follows: In the Pauli-correlated and central field approximations, ground-state energies of atoms (2 He -86Rn) lie within 50 ppm of those of Hartree-Fock theory, differing by less than 10 ppm for atoms with Z 〉 35. The densities thus generated clearly exhibit atomic shell structure and also satisfy the Kato-Steiner electron-nucleus cusp condition to 2 ppm. Another attribute of the formalism is that the asymptotic structure of the potential (when both Pauli and Coulomb correlations are considered) is that of the Pauli-correlated approximation. This is rigorously the case as shown for the He atom for which the potential vanishes in the classically forbidden region, the potential there being the exchange potential. As such, it is meaningful to compare the highest occupied eigenvalue of the differential equation in the Pauli-correlated approximation to experiment. A comparison for atoms and atomic ions of this eigenvalue to experimental ionization potentials and electron affinities show them to be consistently superior to the corresponding eigenvalue of Hartree-Fock theory. Transition energies determined from eigenvalue differences are also superior to those obtained from total energy calculations via Hartree-Fock theory when compared to experiment. Further, by considering the carbon atom in one of its degenerate ground states for which the curl of the field due to the Fermi hole does not vanish, it is shown that the solenoidal component of the field is negligible and two orders of magnitude smaller than is the irrotational component. Thus, the approximation of obtaining a path-independent potential for nonspherical density systems from the irrotational component of the field is accurate. Finally, Coulomb correlation effects can be incorporated within the work formalism in practice via the configuration interaction approximation. The self-consistent orbitals thus obtained explicitly incorporate the effects of both Pauli and Coulomb correlations in their structure because the source charge from which they are generated is a pair-correlation density. Furthermore, these orbitals possess the correct asymptotic structure since they are also generated by a potential that is local. The work formalism also provides a physical interpretation for the local potential representing electron correlations of Kohn-Sham density functional theory. Further, the exchange potential of the work formalism satisfies analytically two requisite conditions of the Kohn-Sham theory exchange potential. These are the scaling requirement and the sum rule relating the exchange energy to its functional derivative. The work formalism also leads to a deeper understanding of electron correlations in various approximations within Kohn-Sham theory. For example, it can be rigorously shown that the pair-correlation density in the local density approximation contains a term proportional to the gradient of the density. Thus, in contrast to the Kohn-Sham theory interpretation that electron correlations in this approximation are those of the uniform electron gas assumed valid locally, we learn that the nonuniformity of the electronic density is, in fact, explicitly accounted for by the approximation. This then explains the accuracy of the approximation. © 1995 John Wiley & Sons, Inc.

Notes: The aziridine analogues of the epoxide metabolites of carcinogenic polycyclic aromatic hydrocarbons have greater mutagenic potency than the epoxides. Like their well-studied analogues, the aziridines undergo a pH-dependent decomposition that leads to a reactive carbocation intermediate. In aqueous solution the nucleophile with which the carbocation generally reacts is water. The kinetics of this pH-dependent reaction have been experimentally characterized by others. Although the effect of DNA on this reaction has not been studied, we hypothesize that, like their epoxide analogues, the aziridine derivatives of polycyclic aromatic hydrocarbons undergo a DNA-catalyzed reaction leading through a carbocation to either a DNA-adduct or a hydrolysis product. Using Poisson-Boltzmann calculations in conjunction with Metropolis Monte Carlo simulations and energy-minimized conformations, we predict the DNA-dependence of the acidcatalyzed decomposition of the K-region aziridine, phenanthrene[9,10]imine. © 1995 John Wiley & Sons, Inc.