A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.     

Ab initio polypeptide structure prediction

The biological activity of a polypeptide strongly depends on its 3D structure. Ab initio prediction of the native structure from the sequence of amino acids has long motivated the development of an optimum energy model such that interactions present in the native conformation are stronger than those present in nonnative conformations and of algorithms capable of finding the basin of lowest free energy among an astronomically large number of possible conformations. Despite recent progress in our understanding of the factors responsible for both polypeptide stability and formation, computer simulations of polypeptide models are still far from being practical software tools for biologists. In this work, state-of-the-art computer simulations aimed at ab initio structure prediction in aqueous solution are reviewed and their strengths and weaknesses are highlighted. Received: 23 June 1999 / Accepted: 20 September 1999 / Published online: 15 December 1999     

Modeling the cluster formation during infrared and ultraviolet matrix-assisted laser desorption ionization of oligonucleotides in succinic acid matrix with molecular mechanics

A large succinic acid (HOOC(CH₂)₂COOH) matrix containing 7 × 7 × 7 unit cells with guest oligonucleotide AGCAGCT was modeled with molecular dynamics simulation for infrared matrix-assisted laser desorption ionization. We simulated the laser heating of the succinic acid (this data is still missing from the literature) with λ=2.94 μm infrared laser pulses and compared it to ultraviolet excitation. We did this in order to elucidate the cluster formation of succinic acid in the gas phase in itself and around the analyte. At this wavelength, the laser energy is coupled into the matrix through the OH vibrations of the carboxyl groups. The most pronounced difference we observed at 1,500 K simulation is that infrared heating generates about 10–15 more succinic acid molecules bound to the analyte in noncovalent complex form than the ultraviolet mode, which generates about 2 molecules thus bound. We report energy redistribution within the matrix between the host and guest species as well as other dynamical properties. The parameter and topology data for succinic acid that we used are reported and ready for use in CHARMM computer code environment for simulation. Revised: 12 October 2001 / Accepted: 27 February 2002 / Published online: 13 June 2002     

Global optimization of atomic and molecular clusters using the space-fixed modified genetic algorithm method

A modified genetic algorithm approach has been applied to atomic Ar clusters and molecular water clusters up to (H₂O)₁₃. Several genetic operators are discussed which are suitable for real-valued space-fixed atomic coordinates and Euler angles. The performance of these operators has been systematically investigated. For atomic systems, it is found that a mix of operators containing a coordinate-averaging operator is optimal. For angular coordinates, the situation is less clear. It appears that inversion and two-point crossover operators are the best choice. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1233–1244     

Structures and stability of N7+ and N7− clusters

Ab initio molecular orbital theory and density functional theory have been used to study nine isomers of N₇ ionic clusters with low spin at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, and B3LYP/6-311(+)G* levels of theory. All stationary points are examined with harmonic vibrational frequency analyses. Four N₇ ⁺ isomers and five N₇ ⁻ isomers are determined to be local minima or very close to the minima on their potential-energy hypersurfaces, respectively. For N₇ ⁺ and N₇ ⁻, the energetically low lying isomers are open-chain structures (C _{2 v} and C _{2 v} or C₂). The results are very similar to those of other known odd-number nitrogen ions, such as N₅ ⁺, N₉ ⁺, and N₉ ⁻, for which the open-chain structures are also the global minima. This research suggests that the N₇ ionic clusters are likely to be stable and to be potential high-energy-density materials if they could be synthesized. Received: 16 July 2001 / Accepted: 8 October 2001 / Published online: 21 January 2002     

Theoretical study of the structural character of weakly bonding silicon carbonyl complexes

The structures, properties and the bonding character for sub-carbonyl Si, SiCO and Si(CO)₂, in singlet and triplet states have been investigated using complete-active-space self-consistent field (CASSCF), density functional theory and second-order M?ller–Plesset methods with a 6-311+G* basis set. The results indicate that the SiCO species possesses a ³∑⁻ ground state, and the singlet ¹Δ excited state is higher in energy than the ³∑⁻ state by 17.3 kcalmol⁻¹ at the CASSCF–MP2/6-311+G* level and by 16.4 kcalmol⁻¹ at the CCSD(T)/6-311+G* level. The SiCO ground state may be classified as silene (carbonylsilene), and its CO^δ− moiety possesses CO⁻ property. The formation of SiCO causes the weakening of CO bonds. The Si–C bond consists of a weak σ bond and two weak π bonds. Although the Si–C bond length is similar to that of typical Si–C bonds, the bond strength is weaker than the Si–C bonds in Si-containing alkanes; the calculated dissociation energy is 26.2 kcalmol⁻¹ at the CCSD(T)/6-311+G* level. The corresponding bending potential-energy surface is flat; therefore, the SiCO molecule is facile. For the bicarbonyl Si systems, Si(CO)₂, there exist two V-type structures for both states. The stablest state is the singlet state (¹A₁), and may be referred to the ground state. The triplet state (³B₁) is energetically higher in energy than the ¹A₁ state by about 40 kcalmol⁻¹ at the CCSD(T)/6-311 + G* level. The bond lengths in the ¹A₁ state are very close to those of the SiCO species, but the SiCO moieties are bent by about 10°, and the CSiC angles are only about 78°. The corresponding ³B₁ state has a CSiC angle of about 54° and a SiCO angle of about 165°, but its Si–C and C–O bonds are longer than those in the ¹A₁ state by about 0.07 and 0.03 ?, respectively. This Si(CO)₂ (¹A₁) has essentially silene character and should be referred to as a bicarbonyl silene. Comparison of the CO dissociation energies of SiCO and Si(CO)₂ in their ground states indicates that the first CO dissociation energy of Si(CO)₂ is smaller by about 7 kcalmol⁻¹ than that of SiCO; the average one over both CO groups is also smaller than that of SiCO. A detailed bonding analysis shows that the possibility is small for the existence of polycarbonyl Si with more than three CO. This prediction may also be true for similar carbonyl complexes containing other nonmetal and non-transition-metal atoms or clusters. Received: 17 April 2002 / Accepted: 11 August 2002 / Published online: 4 November 2002 Acknowledgements. This work was supported by the National Natural Science Foundation of China (29973022) and the Foundation for Key Teachers in University of the State Ministry of Education of China. Correspondence to: Y. Bu e-mail: byx@sdu.edu.ch     

A theoretical investigation of the mechanism for the reaction between a quebrachitol derivative and N3−

The reaction between a mesylated compound and sodium azide was previously studied experimentally at a temperature of 140 °C using dimethylformamide as a solvent. The product was assigned on the basis of the analysis of the NMR spectra. In this work semiempirical (AM1 and PM3), ab initio (Hartree–Fock and MP2) and density functional theory (BLYP functional) quantum mechanical calculations, using continuum models for describing the solvent effect, were carried out for this process to better understand the reaction mechanism. Three distinct mechanisms involving a carbocation and epoxide intermediates, and a transition-state structure for direct attack of the N₃ ⁻ species to the reactant were investigated. The theoretically calculated preferred reaction pathway passing through an epoxide intermediate agrees nicely with the experimental proposal, providing a good example of where theoretical calculations can be of great help to definitively elucidate the reaction mechanism. Received: 10 July 2001 / Accepted: 20 December 2001 / Published online: 8 April 2002     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

A variationally stable quasi-relativistic method: low-order approximation to the normalized elimination of the small component using an effective potential

A simple and variationally stable quasi-relativistic method based on a modified low-order (LO) approximation to the normalized elimination of the small component (NESC) method is presented. The modification of the original LO-NESC scheme implies the use of an energy-independent factor in the relativistic correction to the potential energy. This factor cuts off the potential energy at short distances from the nucleus and in this way restores the variational stability of LO-NESC. The new method, dubbed LO-NESC-effective potential (EP) was tested in calculations on one-, two- and many-electron atoms. The LO-NESC-EP can be easily implemented into the existing nonrelativistic quantum-chemical program codes because its Hamiltonian matrix can be expressed entirely in terms of the integrals appearing in a nonrelativistic calculation. Received: 1 April 2002 / Accepted: 23 June 2002 / Published online: 30 August 2002     

A correlation-consistent basis set for Fe

 A series of correlation-consistent basis sets are developed for Fe. Our best computed ⁵F–⁵D separation in the Fe atom is in excellent agreement with experiment. Our best estimate for the FeCO D ₀ value is in good agreement with experiment. The ⁵Σ⁻–³Σ⁻ separation in FeCO has an error of 3.6 kcal/mol; while the origin of this error is not clear, it is probably not due to the basis set. Received: 5 March 2001 / Accepted: 2 May 2001 / Published online: 9 August 2001     

Computational structural determination and energy landscape analysis of the hepatic carcinogen 2-(acetylamino)fluorene

 2-(Acetylamino)fluorene (AAF), a potent mutagen and a prototypical example of the mutagenic aromatic amines, forms covalent adducts to DNA after metabolic activation in the liver. A benchmark study of AAF is presented using a number of the most widely used molecular mechanics and semiempirical computational methods and models. The results are compared to higher-level quantum calculations and to experimentally obtained crystal structures. Hydrogen bonding between AAF molecules in the crystal phase complicates the direct comparison of gas-phase theoretical calculations with experiment, so Hartree–Fock (HF) and Becke–Perdew (BP) density functional theory (DFT) calculations are used as benchmarks for the semiempirical and molecular mechanics results. Systematic conformer searches and dihedral energy landscapes were carried out for AAF using the SYBYL and MMFF94 molecular mechanics force fields; the AM1, PM3 and MNDO semiempirical quantum mechanics methods; HF using the 3-21G*and 6-31G* basis sets; and DFT using the nonlocal BP functional and double numerical polarization basis sets. MMFF94, AM1, HF and DFT calculations all predict the same planar structures, whereas SYBYL, MNDO and PM3 all predict various nonplanar geometries. The AM1 energy landscape is in substantial agreement with HF and DFT predictions; MMFF94 is qualitatively similar to HF and DFT; and the MNDO, PM3 and SYBYL results are qualitatively different from the HF and DFT results and from each other. These results are attributed to deficiencies in MNDO, PM3 and SYBYL. The MNDO, PM3 and SYBYL models may be unreliable for compounds in which an amide group is immediately adjacent to an aromatic ring. Received: 26 May 2002 / Accepted: 12 December 2002 / Published online: 14 February 2003     

A priori rate constants for kinetic modeling

The advent of computer-aided methods for constructing detailed kinetic models of multicomponent reacting systems provides fresh motivation for the development of efficient and accurate methods for estimating rate constants. There is now the real likelihood that a priori rate estimates, formerly of primarily academic interest, could directly impact major public policy and business decisions. This opportunity brings many challenges. The process of building a computer model for a real-world system can require hundreds of thousands of rate estimates, making most existing rate calculation techniques impractical. Also, the demands for tight error bars on model predictions used to make major decisions often imply levels of accuracy unachievable with existing rate calculation techniques. Past and recent progress towards developing fast and accurate rate estimates is selectively reviewed, and our methodology is outlined. New rate estimates for several types of reactions involving O and HO₂ are presented. Several technical issues requiring further work by the theoretical chemistry community are highlighted. Electronic supplementary material to this paper can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00214-002-0368-4. Received: 6 February 2002 / Accepted: 2 June 2002 / Published online: 2 October 2002 Acknowledgements. This work was partially supported by the National Computational Science Alliance under Grant CTS010006 N and utilized the Origin 2000 High-performance Computing and UniTree Mass Storage systems. We are grateful for financial support from the EPA Center for Airborne Organics, the NSF CAREER program, Alstom Power, Dow Chemical, and the Office of Basic Energy Science, U.S. Department of Energy through grant DE-FG02-98ER14914. The authors acknowledge the contribution of Hans-Heinrich Carstensen in the initial stages of this work. Correspondence to: W.H. Green Jr. e-mail: whgreen@mit.edu Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00214-002-0368-4     

A new look at the reduced-gradient-following path

 The mathematical structure of the reduced-gradient-following (RGF) path introduced by Quapp et al. (1988 J. Comput. Chem. 19:1087) is reviewed and analyzed. We report two new algorithms to evaluate the RGF path. The RGF path is also compared mathematically and computationally with the gradient extremals path. An example of the evaluation of the RGF path is also reported. Received: 21 May 2001 / Accepted: 27 September 2001 / Published online: 9 January 2002     

Internal rotation in squaramide and related compounds. A theoretical ab initio study

The structural and energetic changes associated with C–N bond rotation in a squaric acid derivative as well as in formamide, 3-aminoacrolein and vinylamine have been studied theoretically using ab initio molecular orbital methods. Geometry optimizations at the MP2(full)/6-31+G* level confirmed an increase in the C–N bond length and a smaller decrease in the C=O length on going from the equilibrium geometry to the twisted transition state. Other geometrical changes are also discussed. Energies calculated at the QCISD(T)/6-311+G** level, including zero-point-energy correction, show barrier heights decreasing in the order formamide, squaric acid derivative, 3-aminoacrolein and vinylamine. The origin of the barriers were examined using the atoms-in-molecules approach of Bader and the natural bond orbital population analysis. The calculations agree with Pauling's resonance model, and the main contributing factor of the barrier is assigned to the loss of conjugation on rotating the C–N bond. Finally, molecular interaction potential calculations were used to study the changes in the nucleophilicity of N and O (carbonyl) atoms upon C–N rotation, and to obtain a picture of the abilities of the molecules to act in nonbonded interactions, in particular hydrogen bonds. The molecular interaction potential results confirm the suitability of squaramide units for acting as binding units in host–guest chemistry. Received: 13 March 2002 / Accepted: 23 June 2002 / Published online: 21 August 2002     

Accuracy assessment of semiempirical molecular electrostatic potential of proteins

 Accurate electrostatic maps of proteins are of great importance in research of protein interaction with ligands, solvent media, drugs, and other biomolecules. The large size of real-life proteins imposes severe limitations on computational methods one can use for obtaining the electrostatic map. Well-known accurate second-order M?ller–Plesset and density functional theory methods are not routinely applicable to systems larger than several hundred atoms. Conventional semiempirical tools, as less resource demanding ones, could be an attractive solution but they do not yield sufficiently accurate calculation results with reference to protein systems, as our analysis demonstrates. The present work performs a thorough analysis of the accuracy issues of the modified neglect of differential overlap type semiempirical Hamiltonians AM1 and PM3 on example of the calculation of the molecular electrostatic potential and the dipole moment of natural amino acids. Real capabilities and limitations of these methods with application to protein modeling are discussed. Received: 26 April 2002 / Accepted: 19 September 2002 / Published online: 14 February 2003     

A density functional theory study of a concerted mechanism for proton exchange between amino acid side chains and water

 A concerted mechanism for proton exchange between water and the amino acid side chains of cysteine, serine, arginine and glutamic acid has been investigated with hybrid density functional theory. The models used include, besides the amino acid side chain, a number of water molecules ranging from one to five in some cases. The modeling of the amino acids without their backbones is shown to be an excellent approximation. Long-range polarization effects were incorporated through a dielectric cavity method allowing a better comparison to existing measurements for free amino acids in water. The barriers converge rather fast with the number of water molecules for all the present amino acids and the converged values are in reasonable agreement with experiments with discrepancies in the range 2–6 kcal/mol. The dielectric effects were found to be small for all systems except cysteine, where there is a lowering of the barrier by 3–5 kcal/mol. The transition states for these concerted pathways form rings in which the separated charges can be stabilized. Received: 25 October 1999 / Accepted: 5 April 2000 / Published online: 21 June 2000     

A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I)

 A relativistic pseudopotential of the energy-consistent variety simulating the Tl²¹⁺ (1s– 4f) core has been generated by adjustment to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. Valence ab initio calculations using this pseudopotential have been performed for atomic excitation energies and for spectroscopic constants of the X0⁺ and A0⁺ states of TlX (X = F, Cl, Br, I). Comparison is made to experiment and to four-component density functional results. Received: 22 June 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999