Multireference perturbation CI III. Fast evaluation of the one-particle density matrix

Within the frame of multireference perturbation configuration interaction we have developed a fast algorithm, based on diagrammatic techniques, for the calculation of the first-order correction to the one-particle density matrix. As an example of an application we have chosen the evaluation of the dipole moment of the CO molecule, where utilization of the first-order density is shown to corroborate the variational calculation. Received: 4 August 1998 / Accepted: 21 September 1998 / Published online: 16 November 1998     

Estimation of detection limits in inductively coupled plasma mass spectrometry

The theoretical estimation of the detection limits in inductively coupled plasma mass spectrometry has been investigated. This calculation includes significant parameters of the ICP source and mass spectrometer. The calculated values show generally good agreement with experimental results. The development of a mathematical relationship may be useful for evaluation of instrumental parameters and sample introduction techniques. Received: 30 January 1998 / Revised: 9 June 1998 / Accepted: 16 June 1998     

Assessment of limits of detection and quantitation using calculation of uncertainty in a new method for water determination

 An approach to the assessment of the limit of detection and the limit of quantitation using uncertainty calculation is discussed. The approach is based on the known evaluation of the limits of detection and quantitation as concentrations of the analyte equal to three and ten standard deviations of the blank response, respectively. It is shown that these values can be calculated as the analyte concentrations, for which relative expanded uncertainty achieves 66% and 20% of possible results of the analyte determination, correspondingly. For example, the calculation is performed for the validation of a new method for water determination in the presence of ene-diols or thiols, developed for analysis of chemical products, drugs or other materials which are unsuitable for direct Karl Fischer titration. A good conformity between calculated values and experimental validation data is observed. Received: 27 July 1998 · Accepted: 29 November 1998     

Towards an order-N DFT method

One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (the “Fock” matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential. Received: 30 March 1998 / Accepted: 6 July 1998 / Published online: 15 September 1998     

Efficient boundary basis functions for time-independent quantum scattering calculations

Novel parametrically energy-dependent boundary functions, F, combined with a finite L ² basis set, permit accurate and efficient calculation of scattering wavefunctions for many energies. Both accuracy and efficiency are achieved simultaneously because all the necessary integrals are energy-independent and also certain functionals, (H−E)|F>, in the Schr?dinger equation are allowed to satisfy desirable boundary conditions. In addition, slight modification of the Schr?dinger equation in the boundary region is shown to be useful for improving the numerical accuracy when a cutoff-radius-truncated basis set is used. The advantages of the present approaches are demonstrated for the one-dimensional Eckart barrier problem. Received: 17 June 1998 / Accepted: 13 July 1998 / Published online: 18 September 1998     

Fast summation boundary element method for calculating solvation free energies of macromolecules

We present a boundary element method (BEM) for calculating the reaction field energy of a macromolecule embedded in a high-dielectric medium such as water. In a BEM calculation, the key computational task is the calculation of the induced surface charge distribution at the dielectric boundary. This is obtained by solving a system of linear equations whose dimension can run into the tens of thousands for a macromolecule. In this work, we use a fast summation hierarchical multipole method to solve for the induced surface charge densities. By careful analysis of the levels of approximation required for the various terms in the calculation, we avoid the unnecessary computation of terms that contribute negligibly to the final outcome and, consequently, achieve high computational efficiency. For a protein such as BPTI with 890 atoms, the calculation of the induced surface charge density distribution and the reaction field energy was completed in 7.9 s on an SGI workstation with an R10000 CPU. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1494–1504, 1998     

Transition-state structures for describing the enzyme-catalyzed mechanisms of rubisco

The carboxylation and oxygenation processes of a model substrate, 3,4-dihydroxy-2-pentanone, have been theoreticaly characterized as a set of steps, mimicking the corresponding reactions of D-ribulose-1,5-bisphosphate catalyzed by rubisco. A theoretical characterization is carried out of transition-state structures and possible molecular intermediates represented as saddle points of index 1 and minimum energy structures, respectively. The quantum chemical characterization, at the HF/3-21G calculation level, of these stationary points is used to rationalize and to discuss both catalyzed sequences. The reported set of these stationary points maps out most experimental aspects of the reaction pathways for the real system. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

Variational solution of the single-particle Dirac equation in the field of two nuclei using relativistically adapted Slater basis functions

A variational method for solving the time-independent single-particle Dirac equation in the Coulomb field of two nuclei is described. A minimax variational principle and basis functions that have the proper analytic behavior, i.e. behave like r ^γ,γ non-integer, in the neighborhood of a nucleus, are used. A momentum space integration scheme for computing the necessary two-center integrals is described. Results are given for a standard test problem on two nuclei with Z=90 with an internuclear separation of 2.0/Z. The results confirm those of a previous calculation [F.A. Parpia and A.K. Mohanty, Chem Phys Lett 238: 209 (1995)]. Received: 13 May 1998 / Accepted: 22 June 1998 / Published online: 28 August 1998     

Atomic radii: Incorporation of solvation effects

Atomic radii used to define the solute cavity in continuum-based methods are determined by reproducing the solvent-accessible surface defined as the loci of minima in a potential (solvent interaction potential) between the solute and a probe. This potential includes electrostatic interaction (ion–dipole, ion–quadrupole, and ion-induced dipole) terms as well as a Lennard–Jones energy term. The method alleviates the need to distinguish solute atoms in different chemical environments. These radii, when used in the calculation of solvation free energies, are shown to be superior to fixed atom-specific radii or to radii obtained from the electron isodensity surface from quantum-mechanical calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1482–1493, 1998     

Molecular fragment approach to the study of pyrrole oligomers and polypyrrole

A molecular fragment approach is used to compute ionization potentials, transition energies and electron affinities of pyrrole oligomers. The calculations of these quantities include correlation energy contributions evaluated by integrating a functional of the two-particle Hartree-Fock density matrix. Pyrrole oligomers with chains of up to 16 rings are explicitly treated and the calculated quantities extrapolated to the limit of an infinitely long chain, to predict polymer properties. The theoretical results compare favorably with data on gas-phase ionization potentials deduced from experimental oxidation potentials, and with optical absorption peaks recorded in solution or on solid films. The large discrepancy between electron affinities obtained from the eigenvalues of an independent-particle frozen-orbital calculation and those obtained from separate, correlated calculations on the neutral system and the negative ion in shown. Received: 24 March 1998 / Accepted: 2 September 1998 / Published online: 7 December 1998     

Reference program for molecular calculations with Slater-type orbitals

A program for computing all the integrals appearing in molecular calculation with Slater-type orbitals is reported. The program is mainly intended as a reference for testing and comparing other algorithms and techniques. An analysis of the performance of the program is presented, paying special attention to the computational cost and the accuracy of the results. Results are also compared with others obtained with Gaussian basis sets of similar quality. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1284–1293, 1998     

Electrostatic model for infrared intensities in a spectroscopically determined molecular mechanics force field

A new electrostatic model for the calculation of infrared intensities in molecular mechanics and molecular dynamics is presented. The model is based on atomic charges, atomic charge fluxes, and internal coordinate dipoles and their fluxes. The internal coordinate dipoles are used instead of atomic dipoles, thus simplifying the derivation of parameters. The model is designed to reproduce ab initio dipole derivatives, and the parameters can be obtained by (iterative) transformations from these, or by linear least squares fitting to them. A first application to linear alkanes has been made. For these molecules, the intensities can be predicted with an average accuracy of 30–40%. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 754–768, 1998     

Improved convergence in dual-topology free energy calculations through use of harmonic restraints

When calculating free energy differences between two molecular systems by means of molecular dynamics simulation, accessory potential functions can help eliminate uninteresting configurational entropy contributions, improve convergence, and facilitate reversibility. In this work, we demonstrate that the use of a harmonic potential function to restrain key portions of a molecular system in a free energy perturbation dual-topology molecular dynamics approach dramatically improves convergence and precision of the calculation. Limitations of this technique are illustrated, and its use in conjunction with a fixed bond-length constraint is developed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1278–1283, 1998     

Construction of ternary phase diagrams in nonsolvent/solvent/PMMA systems

In this work, the ternary phase diagrams in three nonsolvent/solvent/PMMA systems (n-hexane/n-butyl acetate/PMMA, water/acetone/PMMA, and n-hexane/acetone/PMMA) were constructed by theoretical calculation and experimental measurement. Binodal curves were calculated by using the Flory–Huggins theory for three-component systems and measured by titrating the PMMA solution with nonsolvent until the onset of turbidity. By using concentration-dependent nonsolvent/solvent and solvent/PMMA interaction parameters and constant nonsolvent/PMMA interaction parameters, good agreement has been obtained between the calculation and the measurement. The values of nonsolvent/solvent interaction parameters were taken from the literature sources, and the values of solvent/PMMA and nonsolvent/PMMA interaction parameters were measured by vapor sorption and swelling equilibrium, respectively. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 607–615, 1998     

Convergence of the density functional one-centre expansion for the molecular continuum: N2 and (CH3)3N

A large-scale one-centre expansion with a radial B-spline basis set is implemented for bound and continuum states. A Kohn-Sham hamiltonian is employed with Hartree and exchange-correlation potentials calculated from the SCF electron density taken from a previous LCAO calculation. An inverse iteration method is used to obtain the continuum wavefunction, from which the cross section and asymmetry parameter are calculated. The convergence with respect to angular momentum and cut-off radius is analysed for N₂. The relevance of multipolar contributions even at large distances is shown and suggestions for further improvements are given. In order to show that the present method is suitable to treat systems of moderate size, the (CH₃)₃N molecule has also been calculated and the results are compared with experiment. Received: 19 May 1998 / Accepted: 20 August 1998 / Published online: 7 December 1998     

Parallel implementation of divide-and-conquer semiempirical quantum chemistry calculations

We have implemented a parallel divide-and-conquer method for semiempirical quantum mechanical calculations. The standard message passing library, the message passing interface (MPI), was used. In this parallel version, the memory needed to store the Fock and density matrix elements is distributed among the processors. This memory distribution solves the problem of demanding requirement of memory for very large molecules. While the parallel calculation for construction of matrix elements is straightforward, the parallel calculation of Fock matrix diagonalization is achieved via the divide-and-conquer method. Geometry optimization is also implemented with parallel gradient calculations. The code has been tested on a Cray T3E parallel computer, and impressive speedup of calculations has been achieved. Our results indicate that the divide-and-conquer method is efficient for parallel implementation. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1101–1109, 1998     

Accurate and rapid estimation on spectral interferences in routine analysis by ICP-AES: use of mutual interference coefficients

A practical method to estimate spectral interferences and to select optimum analytical lines in ICP-AES is suggested. Depending on the matrix composition and the amounts of the analyte, the analytical lines suffering from little interferences and the limit of determination can be determined from calculation using spectral interference coefficients. For this calculation, the spectral interference coefficients, which are defined as apparent mass of the analyte equivalent to the spectral interference from unit mass of the interferent, are obtained experimentally for 639 emission lines of 68 elements. There is a good correlation between the coefficients obtained on two spectrometers having different resolutions. Received: 24 June 1997 / Revised: 4 December 1997 / Accepted: 24 January 1998     

On the rapid evaluation of cofactors in the calculation of nonorthogonal matrix elements

The calculation of matrix elements involving nonorthogonal orbitals is speeded up by recognizing the orthogonalities between orbitals, leading to generalized Slater rules. The block structure present in the overlap matrix makes an efficient evaluation of its cofactors possible. These cofactors are calculated per subblock, each with its own parity sign. An adjustment parity sign has to be evaluated, which is added to the combined local signs, to give the correct total sign for the matrix element. An algorithm for the evaluation of this adjustment sign has been developed, making an easy and correct evaluation possible. The current scheme is shown to be very efficient, but possibilities for further improvement remain. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 77–83, 1998     

Ion channels of biological membranes: prediction of single channel conductance

The Poisson-Boltzmann equation was solved numerically for models of the pore regions of the Shaker K⁺ channel and of two glycoporins (LamB and ScrY) to yield electrostatic potential profiles along the pore axes. From these potential profiles, single-channel current-voltage (I–V) relations were calculated. The importance of a proper treatment of the ionisation state of two rings of aspartate sidechains at the mouth of the K⁺ channel pore emerged from such calculations. The calculated most likely state, in which only two of the eight aspartate sidechains were deprotonated, yielded better agreement with experimental conductance data. An approximate calculation of single-channel conductances based simply on pore geometry yielded very similar conductance values for the two glycoporins. This differed from an␣experimentally determined conductance ratio of ScrY:LamB=10:1. Preliminary electrostatics calculations appeared to reproduce the observed difference in conductance between the two glycoporins, confirming that single-channel conductance is determined by electrostatic as well as geometric considerations. Received: 25 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Effect of inclusion of electron correlation in MM3 studies of cyclic conjugated compounds

Electron correlation at the Møller–Plesset second-order level was incorporated into the π-system portion of MM3 calculations for several conformers of [10]annulene, [18]annulene, bicyclo[5.3.1]undecapentaene, and bicyclo[4.4.1]undecapentaene. The conformers with “localized” C(SINGLE BOND)C π bonds (strongly alternating bond lengths) were found to be of lower energy than their counterparts with “delocalized” C(SINGLE BOND)C π bonds (similar bond lengths) before correlation energy was included. Correlation always lowered the energies of the delocalized conformation more than it did that of the localized conformation, such that often the latter was found to be more stable after correlation energy was included in the calculation. When a delocalized structure was not at a stationary point on the MM3 energy surface, such comparison could not be made. An example is the porphin molecule. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 475–487, 1998