SCF discrete-variational Xα calculations of the NH4Cl Auger spectrum

Formalism for calculations of the singlet and triplet Auger energies within the Xα model is presented. Using this method the KVV Auger spectrum of NH₄Cl is calculated and the theoretical intensities are determined within a one-center approximation. The calculated spectrum reproduces quite well all the main features observed for solid NH₄Cl. A new interpretation of the spectrum is suggested.     

The use of inner projections of the polarization propagator to study different contributions to the magnetic shielding tensor. I. Proton deshielding by steric compression

A new method for studying different contributions to the magnetic shielding tensor is proposed. These contributions come from different molecular fragments, which are defined through a localization procedure. They are obtained by means of inner projections of the polarization propagator onto the subspace defined by the chosen molecular fragment. To illustrate the utility of this method, results are presented for the proton desheilding effect of steric crowding. Different degrees of approximation both in the polarization propagator formalism and in the ground state wave function can be used. Results presented in this paper were obtained at the INDO level, within the CHF scheme. Good agreement with experimental values is obtained.     

Estimation of activity coefficients at different temperatures by using the mean spherical approximation

A method of estimating activity coefficients for a variety of electrolytes at different temperatures is presented. The MSA approximation is used to calculate the activity coefficients from experimental data available in the literature. This strategy provides suitable results within a wide range of temperatures, electrolyte stoichiometries and concentrations of investigated solutions.     

Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies

The recently presented linear-response function for Mukherjee's multireference coupled-cluster method (Mk-MRCC) [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044115 (2012)] is employed to determine vertical excitation energies within the singles and doubles approximation (Mk-MRCCSD-LR) for ozone as well as for o-benzyne, m-benzyne, and p-benzyne, which display increasing multireference character in their ground states. In order to assess the impact of a multireference ground-state wavefunction on excitation energies, we compare all our results to those obtained at the single-reference coupled-cluster level of theory within the singles and doubles as well as within the singles, doubles, and triples approximation. Special attention is paid to the artificial splitting of certain excited states which arises from the redundancy intrinsic to Mk-MRCC theory and hinders the straightforward application of the Mk-MRCC-LR method.     

Calculation of indirect nuclear spin-spin coupling constants within the regular approximation for relativistic effects

A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.     

Electrical double layer interactions for spherical charge regulating colloidal particles

A new way of linearising the Poisson-Boltzmann equation is presented which is capable of producing accurate answers for moderately high surface charge and surface potentials. Unlike the Debye-Hückel approximation, the linearisation is based on the fact that electric potential variation, rather than the magnitude of the potential itself, remains small between two charged plates at close separation. The method can be applied quite generally to any type of surface. The cases of constant surface charge, the constant surfaceppotential and charge regulating systems are considered as examples. The results for constant charge and potentials as high as 5 μC/cm² and 200 mV are within 7% of the exact answers for plate separations of one Debye length or less. In contrast, the Debye-Hückel approximation produces answers that are at least an order of magnitude too large, for the same problems. The application of the method to the problem of calculating the electrostatic forces between charge regulated spherical particles is also addressed in some detail.     

Shape-invariance approach and Hamiltonian hierarchy method on the Woods–Saxon potential for <Emphasis Type="Italic">ℓ</Emphasis> ≠ 0 states

An analytically solvable Woods–Saxon potential for ? ≠ 0 states is presented within the framework of Supersymmetric Quantum Mechanics formalism. The shape-invariance approach and Hamiltonian hierarchy method are included in calculations by means of a translation of parameters. The approximate energy spectrum of this potential is obtained for ? ≠ 0 states, applying the Woods–Saxon square approximation to the centrifugal barrier term of the Schrödinger equation.     

Finite expansion of the inverse matrix in the polarization propagator method

 An alternative theoretical approach to the polarization propagator based on a new finite expansion of a finite-dimensional matrix is presented. The general equations for such an expansion are derived and the validity conditions stated. This method is used to accomplish an approximate scheme for the self-energy of the particle–hole propagator within the superoperator formalism. Within this scheme each contribution includes corrections to infinite order in electronic interaction and so describes collective effects in a natural way. Individual contributions can be interpreted as describing the propagation of the interaction through a particular subset of electronic excitations. Comparison with other known approximation levels, such as the random-phase approximation, is also analyzed. Received: 14 February 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation

An approach to treat static correlation within a density-functional framework is presented. To that end, a multiconfiguration optimized effective potential (MCOEP) method is derived. In contrast to standard multiconfiguration self-consistent field (MCSCF) methods and previous combinations of MCSCF procedures with density-functional theory, the MCOEP method yields well-defined physically meaningful orbital and eigenvalue spectra. In addition to the electronic ground state also excited electronic states can be described. The MCOEP method is implemented invoking the localized Hartree-Fock approximation, leading to a multiconfiguration localized Hartree-Fock approach. Applications of the new method to the dissociation of the hydrogen molecule and the isomerization of ethene and cyclobutadiene show that it is capable of describing situations that are characterized by strong static correlation.     

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strength-dependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N(6) to N(5). Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Mo?ller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.     

Calculations of molecules,clusters, and solids with a simplified LCAO-DFT-LDA scheme

A simplified LCAO-DFT-LDA scheme for calculations of structure and electronic structure of large molecules, clusters, and solids is presented. Forces on the atoms are calculated in a semiempirical way considering the electronic states. The small computational effort of this treatment allows one to perform molecular dynamics (MD ) simulations of molecules and clusters up to a few hundred atoms as well as corresponding simulations of condensed systems within the Born-Oppenheimer approximation. The accuracy of the method is illustrated by the results of calculations for a series of small molecules and clusters. © 1996 John Wiley & Sons, Inc.     

The centrifugally decoupled exponential distorted wave (CDEDW) approximation for the calculation of rotationally inelastic molecular collision cross se

A new approximate method is presented for the rapid calculation of rotationally inelastic molecular collision cross sections. The method is called the centrifugally decoupled exponential distorted wave (CDEDW) approximation and involves the combination of two well known approximations. The first approximation is the neglect of the off-diagonal coupling terms which arise from the orbital angular momentum operator in the coupled differential equations in the body-fixed axis system. The second approximation is to treat the remaining coupling terms, which arise from the interaction potential, using a unitary perturbation approximation. The CDEDW method is applied to the calculation of total and partial rotationally inelastic cross sections in the ArN₂ system, and detailed comparisons are made with exact and several other types of approximate calculations. Agreement with exact calculations is good and often comparable with the coupled states and p-helicity decoupled approximations. The CDEDW method requires a similar amount of computational effort to the infinite order sudden (IOS) approximation, and we show that for the present system the CDEDW method gives more reliable results.     

Relaxed core projector-augmented-wave method

We extend the full-potential projector-augmented-wave method beyond the frozen core approximation, i.e., include the self-consistent optimization of the core charge density, in such a manner that the valence wave functions remain orthogonal to the core. The method consists of an on-the-fly repseudization of the all-electron problem, solving for the self-consistent core charge density within a spherical approximation. The key ideas in our procedure are to keep the projector functions fixed throughout the electronic minimization and to derive the new pseudopartial waves from these original projector functions, at each step of the electronic minimization procedure. Results of relaxed core calculations for atomic interconfigurational energies, structural energy differences between bulk phases of Fe, atomization energies of a subset of Pople's G2-1 set, and the Rh 3d surface core level shifts for the (log3 x log3)-Rh(111) surface at 1/3 CO coverage are presented.     

Light-scattering form factors of asymmetric particle dimers from heteroaggregation experiments

Measurements of form factors of asymmetric particle dimers composed of oppositely charged polystyrene latex particles are presented. These measurements are based on time-resolved static and dynamic light scattering on dilute aggregating aqueous suspensions. The experimental form factors are compared with independent calculations based on the superposition T-matrix method and Rayleigh-Debye-Gans (RDG) approximation. While the RDG approximation is found to be reliable only up to particle diameters of about 250 nm, the superposition T-matrix method is very accurate for all types of dimers investigated. The present results show clearly the appropriateness of the superposition T-matrix method to estimate the optical properties of colloidal particles in the micrometer range reliably.     

Representation of molecules by atomic charges: A new population analysis

For the calculation of atomic charges in molecules, a new fast procedure based on extended Mulliken population analysis is presented. The reliability of the new population analysis is tested within the AM1 approximation and the results are compared in detail with those obtained by different methods reported in the literature.     

A mathematical model for stress-driven diffusion in polymers

A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.     

Solvatons. II. Aqueous dissociation of hydrides in the MINDOS approximation

A simple electrostatic model of solvation is presented which allows the interaction with solvent to be included systematically within semiempirical SCF calculations. Solvent effects are incorporated into the Hamiltonian for a solute molecule through a series of imaginary particles, solvatons, which represent the oriented solvent distribution around the solute.The proposed model is based on an algorithm for approximating the enthalpy of solvation of each atomic center from its charge in the molecular system and the experimental hydration enthalpies of its various ions. The calculated atomic solvation energy of one center is then modified to include the interaction with other charged atomic centers in the molecule. The method, developed here for the MINDO/3 approximation, has been applied to the calculation of the aqueous dissociation of a series of hydrides. In general, it leads to fairly accurate solvation enthalpies andpK _a values when applied to systems with fixed molecular geometries. A general discussion of the problems associated with the development of a solvation model within a semiempirical framework is also presented.