2000

S. Zhang, T.N. Truong.
**“Direct ab initio Dynamics Studies of N+H2NH+H Reaction,”** In *Journal of Chemical Physics*, Vol. 113, No. 15, pp. 6149--6153. 2000.

DOI: 10.1063/1.1308544

Kinetics of the N+H_{2}↔NH+Hreaction have been studied using a direct ab initio dynamics method. Potential energy surface for low electronic states have been explored at the QCISD/cc-pVDZ level of theory. We found the ground-statereaction is N(^{4}S)+H_{2}→NH(^{3}Σ^{−})+H. Thermal rate constants for this reaction were calculated using the microcanonical variational transition state theory.Reaction path information was calculated at the QCISD/cc-pVDZ level of theory. Energies along the minimum energy path (MEP) were then refined at the QCISD(TQ)/cc-pVTZ level of theory. The forward and reverse barriers of the ground-statereaction are predicted to be 29.60 and 0.53 kcal/mol, respectively. The calculated rate constants for both forward and reverse reactions are in good agreement with available experimental data. They can be expressed as k(T)=2.33×10^{14} exp(-30.83 (kcal/mol)/RT) cm^{3 }mol^{−1} s^{−1} for the forward reaction and k(T)=5.55×10^{8}T^{1.44} exp(−0.78(kcal/mol)/RT) cm^{3} mol^{−1} s^{−1} for the reverse reaction in the temperature range 400–2500 K.

S. Zhang, T.N. Truong.
**“Thermal Rate Constants of the NO2 fission reaction of Gas Phase a-HMX: A Direct Ab Initio Dynamics Study,”** In *Journal of Physical Chemistry, A*, Vol. 104, pp. 7304--7307. 2000.

DOI: 10.1021/jp001419e

The NO_{2} fission reaction of gas phase α-HMX has been studied using a direct ab initio method within the framework of microcanonical variational transition state theory (μVT). The potential energy calculations were calculated using the hybrid nonlocal B3LYP density functional theory with the cc-pVDZ basis set. The calculated results show that the potential energy of breaking the axial NO_{2} groups is lower than that of breaking the equatorial NO_{2} groups. No traditional transition state was found along the reaction path. Microcanonical rate constants calculation shows the variational transition state varies from 2.0 to 3.5 Å of the breaking N−N bond length as a function of the excess energy. The μVT method was used for thermal rate constants calculation over a temperature range from 250 to 2000 K. The fitted Arrhenius expression from the calculated data is *k*(*T*) = 1.66 × 10^{15} exp(−18748K/*T*) s^{-1}, which is in good agreement with the experimental data at low temperatures.

1999

O.G. Byutner, G.D. Smith.
**“Conformational Properties of Poly(vinylidene fluoride). A Quantum Chemistry Study of Model Compounds,”** In *Macromolecules*, Vol. 32, No. 25, pp. 8376--8382. 1999.

DOI: 10.1021/ma9902605

The molecular geometries and conformational energies of model molecules of poly(vinylidene fluoride) (PVDF) have been determined from high-level quantum chemistry calculations and have been used in parametrization of a six-state rotational isomeric state (RIS) model for PVDF. The model molecules investigated were 1,1,1,3,3-pentafluorobutane, 1,1,1,3,3,5,5,5-octofluoropentane, 2,2,4,4-tetrafluoropentane, and 2,2,4,4,6,6-hexafluoroheptane (HFH). Analysis of the conformations of these molecules revealed split trans minima (t_{+} = 195°, t- = 165°), as was seen in previous studies of perfluoroalkanes. In contrast, the gauche minima, which split in perfluoroalkanes, did not do so in the PVDF model compounds. The lowest energy conformer of HFH, g^{+}g^{+}g^{+}g^{+}, was found to be at least 0.4 kcal/mol lower in energy per backbone dihedral than any of the conformers of HFH resembling crystalline polymorphs of PVDF, indicating that intermolecular interactions are important in stabilizing conformations of PVDF in the crystalline phases. A six-state RIS model was able to accurately reproduce the conformer energies of the PVDF model compounds. The RIS analysis revealed that, as in n-alkanes and perfluoroalkanes, the trans conformation of the backbone dihedral is intrinsically lower in energy than the gauche conformation in the PVDF model compounds. However, very large unfavorable second-order interactions between fluorine atoms occur in −CH_{2}− centered t_{+}t_{+} sequences and, to a lesser extent, t_{+}g^{+} and t_{+}g^{-} sequences. The quantum chemistry based RIS model yielded a characteristic ratio for PVDF in good agreement with experiment, but with significantly different conformer populations than predicted by earlier RIS models, including a much higher gauche probability. The high gauche probability of 65% for unperturbed PVDF chains (at 463 K), greater than that for poly(ethylene) and much greater than that for poly(tetrafluoroethylene), is a consequence of the unfavorable second-order interactions occurring in −CH_{2}− centered sequences containing trans conformations.

M.A. Johnson, T.N. Truong.
**“High Level Ab Initio and Density Functional Theory Evaluation of Combustion Reaction Energetics: NO2 and HONO Elimination from Dimethylnitramine,”** In *Journal of Physical Chemistry, A*, Vol. 103, No. 44, pp. 8840--8846. October, 1999.

DOI: 10.1021/jp9925029

Dimethylnitramine (DMNA) is used as a model system for investigating accurate and efficient electronic structure methods for nitramines. Critical points on the potential energy surfaces of DMNA, CH_{3}NCH_{3}, CH_{3}NCH_{2}, NO_{2}, HONO, and the transition state to HONO elimination were located through geometry optimizations using the B1LYP, B3LYP, MPW1PW91, and BH&HLYP density functional methods, in addition to MP2, G2(MP2), and QCISD ab initio theories using the cc-pVDZ basis set. For cost-effective determination of nitramine reaction energetics, highly correlated single-point calculations at DFT geometries are recommended. Our best estimated reaction enthalpies for N-N bond scission and HONO elimination are 41.6 and −0.9 kcal/mol, respectively, determined at the QCISD(T)//QCISD level of theory. These numbers can be reproduced to within 1.3 kcal/mol for the N-N bond and to within 0.5 kcal/mol for the HONO reaction by calculating QCISD(T) energies at B1LYP geometries, thus saving considerable computational cost without sacrificing accuracy. Using the same strategy, the transition state energy for HONO elimination can be modeled to within 0.1 kcal/mol of the QCISD(T)//QCISD result.

M.A. Johnson, T.N. Truong.
**“Importance of Polarization in Simulations of Condensed Phased Energetic Materials,”** In *Journal of Physical Chemistry, B*, Vol. 103, No. 44, pp. 9392--9393. October, 1999.

DOI: 10.1021/jp992514u

An embedded cluster model is used to estimate the molecular dipole moment of crystalline dimethylnitramine (DMNA). The electrostatic potential due to the crystal is included in the calculation via the SCREEP (surface charge representation of the electrostatic embedding potential) approach. The resulting dipole moment for DMNA in the crystalline environment is 6.69 D. This number is more than 40% greater than the gas-phase value and 15% greater than the estimated dipole moment in the liquid phase, thus providing evidence of a strong polarization effect in condensed phases of DMNA.

C.R. Johnson, S.G. Parker, C.D. Hansen, G.L. Kindlmann, Y. Livnat.
**“Interactive Simulation and Visualization,”** In *IEEE Computer*, Vol. 32, No. 12, pp. 59--65. Dec, 1999.

D. Maity, W.T. Duncan, T.N. Truong.
**“Direct Ab Initio Dynamics Studies of the Hydrogen Abstraction Reactions of Hydrogen Atom with Fluoromethanes,”** In *Journal of Physical Chemistry, A*, Vol. 103, No. 13, pp. 2152--2159. March, 1999.

DOI: 10.1021/jp984281x

A direct ab initio dynamics study on the gas-phase reactions of atomic hydrogen with different fluoromethanes has been carried out. The thermal rate constants were calculated using canonical variational transition state (CVT) theory augmented by multidimensional semiclassical zero and small curvature tunneling approximations. The potential energy surfaces for the reactions were calculated using hybrid density functional theory, namely, Becke's half-and-half (BH) nonlocal exchange and the Lee−Yang−Parr (LYP) nonlocal correlation functionals using the cc-pVDZ basis set. The reaction energies and barrier heights were improved by single-point energy calculations along the minimum energy path (MEP) at the spin-projected fourth order Moller−Plesset perturbation theory (PMP4) using the cc-pVTZ basis set. The calculated forward and reverse thermal rate constants are in the good agreement with the experimental data. The electronic effects of fluorine substitution on the rate of this class of reactions are examined.

J.A. Nairn.
**“Fracture Mechanics of Composites with Residual Stresses, Traction-Loaded Cracks, and Imperfect Interfaces,”** In *European Structural Integrity Society: Fracture of Polymers, Composites and Adhesives*, Vol. 27, pp. 111--121. 1999.

DOI: 10.1016/S1566-1369(00)80012-6

By partitioning the total stresses in a damaged composite into either mechanical and residual stresses or into initial and pertubation stresses, it was possible to derive several exact results for the energy release rate due to crack growth. These general results automatically include the effects of residual stresses, traction-loaded cracks, and imperfect interfaces. By considering approximate solutions based on admissible stress states and admissible strain states, it was possible to derive rigorous upper and lower bounds to the energy release rate for crack growth. Two examples of using these equations are mode I fracture in adhesive double cantilever beam specimens and analysis of microcracking in composite laminates.

**Keywords:** Fracture Mechanics, Energy Release Rate, Residual Stresses, Adhesive Fracture, Matrix Microcracking

S.G. Parker, M. Parker, Y. Livnat, P.P. Sloan, C.D. Hansen, P. Shirley.
**“Interactive Ray Tracing for Volume Visualization,”** In *IEEE Transactions on Visualization and Computer Graphics*, Vol. 5, No. 3, pp. 238--250. July-September, 1999.

J.D. Peterson, S. Vyazovkin, C.A. Wight.
**“Kinetic Study of Stabilizing Effect of Oxygen on Thermal Degradation of Poly(methyl methacrylate),”** In *Journal of Physical Chemistry, B*, Vol. 103, No. 38, pp. 8087--8092. August, 1999.

DOI: 10.1021/jp991582d

The thermal degradation of poly(methyl methacrylate) (PMMA) has been studied in both pure nitrogen and oxygen-containing atmospheres. The presence of oxygen increases the initial decomposition temperature by 70 °C. The stabilizing effect of oxygen may be explained by forming thermally stable radical species that suppress unzipping of the polymer. This assumption is supported by the experimental fact that introduction of NO into gaseous atmosphere increases the initial decomposition temperature by more than 100 °C. The model-free isoconversional method has been used to determine the dependence of the effective activation energy on the extent of degradation. The initial stages of the process show a dramatic difference in the activation energies that were found to be 60 and 220 kJ mol^{-1} for respective degradations in nitrogen and air.

J.D. Peterson, S. Vyazovkin, C.A. Wight.
**“Stabilizing Effect of Oxygen on Thermal Degradation of Poly(methyl methacrylate),”** In *Macromolecular Rapid Communications*, Vol. 20, No. 9, pp. 480--483. September, 1999.

DOI: 10.1002/(SICI)1521-3927(19990901)20:93.0.CO;2-7

The thermal degradation of poly(methyl methacrylate) has been studied under nitrogen and air. The presence of oxygen increases the initial decomposition temperature by 70 degrees C. The stabilizing effect of oxygen is explained by the formation of thermally stable radical species that suppress unzipping of the polymer. This assumption is supported by the experimental fact that introduction of NO into the gaseous atmosphere increases the initial decomposition temperature by more than 100 degrees C.

G.D. Smith, R. Bharadwaj.
**“Quantum Chemistry Based Force Field for Simulations of HMX,”** In *Journal of Physical Chemistry, B*, Vol. 103, No. 18, pp. 3570--3575. April, 1999.

DOI: 10.1021/jp984599p

The molecular geometries and conformational energies of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and 1,3-dimethyl-1,3-dinitro methyldiamine (DDMD) and have been determined from high-level quantum chemistry calculations and have been used in parametrizing a classical potential function for simulations of HMX. Geometry optimizations for HMX and DDMD and rotational energy barrier searches for DDMD were performed at the B3LYP/6-311G** level, with subsequent single-point energy calculations at the MP2/6-311G** level. Four unique low-energy conformers were found for HMX, two whose conformational geometries correspond closely to those found in HMX polymorphs from crystallographic studies and two additional, lower energy conformers that are not seen in the crystalline phases. For DDMD, three unique low-energy conformers, and the rotational energy barriers between them, were located. In parametrizing the classical potential function for HMX, nonbonded repulsion/dispersion parameters, valence parameters, and parameters describing nitro group rotation and out-of-plane distortion at the amine nitrogen were taken from our previous studies of dimethylnitramine. Polar effects in HMX and DDMD were represented by sets of partial atomic charges that reproduce the electrostatic potential and dipole moments for the low-energy conformers of these molecules as determined from the quantum chemistry wave functions. Parameters describing conformational energetics for the C−N−C−N dihedrals were determined by fitting the classical potential function to reproduce relative conformational energies in HMX as found from quantum chemistry. The resulting potential was found to give a good representation of the conformer geometries and relative conformer energies in HMX and a reasonable description of the low-energy conformers and rotational energy barriers in DDMD.

G.D. Smith, W. Paul, M. Monkenbusch, L. Willner, D. Richter, X.H. Qiu, M.D. Ediger.
**“Molecular Dynamics of a 1,4-Polybutadiene Melt. Comparison of Experiment and Simulation,”** In *Macromolecules*, Vol. 32, No. 26, pp. 8857--8865. November, 1999.

DOI: 10.1021/ma991130z

We have made detailed comparison of the local and chain dynamics of a melt of 1,4-polybutadiene (PBD) as determined from experiment and molecular dynamics simulation at 353 K. The PBD was found to have a random microstructure consisting of 40% cis, 50% trans, and 10% 1,2-vinyl units with a number-average degree of polymerization 〈*X** _{n}*〉 = 25.4. Local (conformational) dynamics were studied via measurements of the

T.N. Truong, W.T. Duncan, M. Tirtowidjojo.
**“A Reaction Class Approach for Modeling Gas Phase Reaction Rates,”** In *Physical Chemistry Chemical Physics*, Vol. 1, No. 6, pp. 1061-1065. 1999.

DOI: 10.1039/A808438F

We present a series of new tunneling models based on a reaction class approach. Reaction class consists of all reactions that have the same reactive moiety. One can expect that reactions in the same class share similarities in the shape of the potential energy surfaces along the reaction path. By exploring such similarities, we propose to use reaction path information from the parent (smallest) reaction in calculations of tunneling contributions of larger reactions in the class. This significantly reduces the computational cost while maintaining the accuracy of the model.

T.N. Truong, T.-T.T. Truong.
**“A Reaction Class Approach with the Integrated Molecular Orbital + Molecular Orbital (IMOMO) Methodology,”** In *Chemical Physics Letters*, Vol. 314, No. 5-6, pp. 529--533. 1999.

DOI: 10.1016/S0009-2614(99)01188-4

We investigate the use of the reaction-class approach within the integrated molecular + molecular orbital (IMOMO) methodology for improving energetic information of chemical reactions. We have tested this approach using two classes of hydrogen abstraction reactions. One is abstraction from saturated hydrocarbons and the other from unsaturated hydrocarbons. For saturated hydrocarbon systems, this approach yields average unsign errors of the order of 1 kcal/mol in the reaction energy and about 0.2 kcal/mol in the barrier height. The errors are larger in the unsaturated hydrocarbon systems and are of the order of 2 kcal/mol. Analysis of the performance shows that this approach provides a practical and cost-effective tool for studying reactions involving large molecules.

S. Vyazovkin, C.A. Wight.
**“Kinetics of Thermal Decomposition of Cubic Ammonium Perchlorate,”** In *Chemistry of Materials*, Vol. 11, No. 11, pp. 3386--3393. October, 1999.

DOI: 10.1021/cm9904382

The methods of thermogravimetric analysis (TGA) and differential scanning calorimettry (DSC) have been used to study the thermal decomposition of ammonium perchlorate (AP). TGA curves obtained under both isothermal and nonisothermal conditions show a characteristic slowdown at the extents of conversion, α = 0.30-0.35. DSC demonstrates that in this region the process changes from an exothermic to an endothermic regime. The latter is ascribed to dissociative sublimation of AP. A new computational technique (advanced isoconversional method) has been used to determine the dependence of the effective activation energy (Eα) on α for isothermal and nonisothermal TGA data. At α > 0.1, the Eα dependencies obtained from isothermal and nonisothermal data are similar. By the completion of decomposition (α → 1) the activation energy for the isothermal and nonisothermal decomposition respectively rises to ∼110 and ∼130 kJ mol^{-1}, which are assigned to the activation energy of sublimation. The initial decomposition (α → 0) shows the activation energy of 90 kJ mol^{-1} for the isothermal decomposition and 130 kJ mol^{-1} for the nonisothermal decomposition. The difference is explained by different rate-limiting steps, which are nucleation and nuclei growth for isothermal and nonisothermal decompositions, respectively.

H.F. Walker.
**“An Adaptation of Krylov Subspace Methods to Path Following Problems,”** In *SIAM journal on scientific computing*, Vol. 21, No. 3, pp. 1191--1198. 1999.

DOI: 10.1137/S1064827597315376

A procedure is outlined for adapting Krylov subspace methods to solving approximately the underdetermined linear systems that arise in path following (continuation, homotopy) methods. This procedure, in addition to preserving the usual desirable features of Krylov subspace methods, has the advantages of satisfying orthogonality constraints exactly and of not introducing ill-conditioning through poor scaling.

1998

M. Sosonkina, L.T. Watson, R.K. Kapania, H.F. Walker.
**“A new adaptive GMRES algorithm for achieving high accuracy,”** In *Numerical Linear Algebra and Applications*, Vol. 5, No. 4, pp. 275--297. 1998.

DOI: 10.1002/(SICI)1099-1506(199807/08)5:43.0.CO;2-B

GMRES(*k*) is widely used for solving non-symmetric linear systems. However, it is inadequate either when it converges only for *k* close to the problem size or when numerical error in the modified Gram–Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES(*k*) which tunes the restart value *k* based on criteria estimating the GMRES convergence rate for the given problem is proposed here. This adaptive GMRES(*k*) procedure outperforms standard GMRES(*k*), several other GMRES-like methods, and QMR on actual large scale sparse structural mechanics postbuckling and analog circuit simulation problems. There are some applications, such as homotopy methods for high Reynolds number viscous flows, solid mechanics postbuckling analysis, and analog circuit simulation, where very high accuracy in the linear system solutions is essential. In this context, the modified Gram–Schmidt process in GMRES, can fail causing the entire GMRES iteration to fail. It is shown that the adaptive GMRES(*k*) with the orthogonalization performed by Householder transformations succeeds whenever GMRES(*k*) with the orthogonalization performed by the modified Gram–Schmidt process fails, and the extra cost of computing Householder transformations is justified for these applications.

M.D. Tocci, C.T. Kelley, C.T. Miller, C.E. Kees.
**“Inexact Newton Methods and the Method of Lines for Solving Richards' Equation in Two Space Dimensions,”** In *Computational Geosciences*, Vol. 2, No. 4, pp. 291--309. 1998.

DOI: 10.1023/A:1011562522244

Richards' equation (RE) is often used to model flow in unsaturated porous media. This model captures physical effects, such as sharp fronts in fluid pressures and saturations, which are present in more complex models of multiphase flow. The numerical solution of RE is difficult not only because of these physical effects but also because of the mathematical problems that arise in dealing with the nonlinearities. The method of lines has been shown to be very effective for solving RE in one space dimension. When solving RE in two space dimensions, direct methods for solving the linearized problem for the Newton step are impractical. In this work, we show how the method of lines and Newton-iterative methods, which solve linear equations with iterative methods, can be applied to RE in two space dimensions. We present theoretical results on convergence and use that theory to design an adaptive method for computation of the linear tolerance. Numerical results show the method to be effective and robust compared with an existing approach.

S. Vyazovkin, C.A. Wight.
**“Isothermal and non-isothermal kinetics of thermally stimulated reactions of solids,”** In *International Reviews in Physical Chemistry*, Vol. 17, No. 3, pp. 407--433. 1998.

DOI: 10.1080/014423598230108

This review covers both the history and present state of the kinetics of thermally stimulated reactions in solids. The traditional methodology of kinetic analysis, which is based on fitting data to reaction models, dates back to the very first isothermal studies. The model fitting approach suffers from an inability to determine the reaction model uniquely,and this does not allow reliable mechanistic conclusions to be drawn even from isothermal data. In non-isothermal kinetics, the use of the traditional methodology results in highly uncertain values of Arrhenius parameters that cannot be compared meaningfully with isothermal values. An alternative model-free methodology is based on the isoconversional method. The use of this model-free approach in both isothermal and non-isothermal kinetics helps to avoid the problems that originate from the ambiguous evaluation of the reaction model. The model-free methodology allows the dependence of the activation energy on the extent of conversion to be determined. This, in turn, permits reliable reaction rate predictions to be made and mechanistic conclusions to be drawn.