Shock-Driven Decomposition of Polymers and Polymeric Foams.

Polymers and foams are pervasive in everyday life, as well as in specialized contexts such as space exploration, industry, and defense. They are frequently subject to shock loading in the latter cases, and will chemically decompose to small molecule gases and carbon (soot) under loads of sufficient strength. We review a body of work-most of it performed at Los Alamos National Laboratory-on polymers and foams under extreme conditions. To provide some context, we begin with a brief review of basic concepts in shockwave physics, including features particular to transitions (chemical reaction or phase transition) entailing an abrupt reduction in volume. We then discuss chemical formulations and synthesis, as well as experimental platforms used to interrogate polymers under shock loading. A high-level summary of equations of state for polymers and their decomposition products is provided, and their application illustrated. We then present results including temperatures and product compositions, thresholds for reaction, wave profiles, and some peculiarities of traditional modeling approaches. We close with some thoughts regarding future work.

Shockwave compression and dissociation of ammonia gas.

We performed a series of plate impact experiments on NH3 gas initially at room temperature and at a pressure of ∼100 psi. Shocked states were determined by optical velocimetry and the temperatures by optical pyrometry, yielding compression ratios of ∼5-10 and second shock temperatures in excess of 7500 K. A first-principles statistical mechanical (thermochemical) approach that included chemical dissociation yielded reasonable agreement with experimental results on the principal Hugoniot, even with interparticle interactions neglected. Theoretical analysis of reshocked states, which predicts a significant degree of chemical dissociation, showed reasonable agreement with experimental data for higher temperature shots; however, reshock calculations required the use of interaction potentials. We rationalize the very different shock temperatures obtained, relative to previous results for argon, in terms of atomic versus molecular heat capacities.

Reactive Monte Carlo sampling with an ab initio potential.

We present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH3 to those of ab initio molecular dynamics (AIMD). We find that there are regions of state space for which RxMC sampling is much more efficient than AIMD due to the "rare-event" character of chemical reactions.

Intermolecular stabilization of 3,3'-diamino-4,4'-azoxyfurazan (DAAF) compressed to 20 GPa.

The room temperature stability of 3,3'-diamino-4,4'-azoxyfurazan (DAAF) has been investigated using synchrotron far-infrared, mid-infrared, Raman spectroscopy, and synchrotron X-ray diffraction (XRD) up to 20 GPa. The as-loaded DAAF samples exhibited subtle pressure-induced ordering phenomena (associated with positional disorder of the azoxy "O" atom) resulting in doubling of the a-axis, to form a superlattice similar to the low-temperature polymorph. Neither high pressure synchrotron XRD, nor high pressure infrared or Raman spectroscopies indicated the presence of structural phase transitions up to 20 GPa. Compression was accommodated in the unit cell by a reduction of the c-axis between the planar DAAF layers, distortion of the ß-angle of the monoclinic lattice, and an increase in intermolecular hydrogen bonding. Changes in the ring and -NH2 deformation modes and increased intermolecular hydrogen bonding interactions with compression suggest molecular reorganizations and electronic transitions at ∼ 5 GPa and ∼ 10 GPa that are accompanied by a shifting of the absorption band edge into the visible. A fourth-order Birch-Murnaghan fit to the room temperature isotherm afforded an estimate of the zero-pressure isothermal bulk modulus, K0 = 12.4 ± 0.6 GPa and its pressure derivative K0' = 7.7 ± 0.3.

An efficient approach to ab initio Monte Carlo simulation.

We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature ß(0)), which was otherwise unconstrained. Local density approximation results are presented for shocked states of argon at pressures from 4 to 60 GPa, where-depending on the quality of the reference system potential-acceptance probabilities were enhanced by factors of 1.2-28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.

Nested Markov chain Monte Carlo sampling of a density functional theory potential: equilibrium thermodynamics of dense fluid nitrogen.

An optimized variant of the nested Markov chain Monte Carlo [n(MC)(2)] method [J. Chem. Phys. 130, 164104 (2009)] is applied to fluid N(2). In this implementation of n(MC)(2), isothermal-isobaric (NPT) ensemble sampling on the basis of a pair potential (the "reference" system) is used to enhance the efficiency of sampling based on Perdew-Burke-Ernzerhof density functional theory with a 6-31G(*) basis set (PBE6-31G(*), the "full" system). A long sequence of Monte Carlo steps taken in the reference system is converted into a trial step taken in the full system; for a good choice of reference potential, these trial steps have a high probability of acceptance. Using decorrelated samples drawn from the reference distribution, the pressure and temperature of the full system are varied such that its distribution overlaps maximally with that of the reference system. Optimized pressures and temperatures then serve as input parameters for n(MC)(2) sampling of dense fluid N(2) over a wide range of thermodynamic conditions. The simulation results are combined to construct the Hugoniot of nitrogen fluid, yielding predictions in excellent agreement with experiment.

Optimal sampling efficiency in Monte Carlo simulation with an approximate potential.

Building on the work of Iftimie et al. [J. Chem. Phys. 113, 4852 (2000)] and Gelb [J. Chem. Phys. 118, 7747 (2003)], Boltzmann sampling of an approximate potential (the "reference" system) is used to build a Markov chain in the isothermal-isobaric ensemble. At the end points of the chain, the energy is evaluated at a more accurate level (the "full" system) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. For reference system chains of sufficient length, consecutive full energies are statistically decorrelated and thus far fewer are required to build ensemble averages with a given variance. Without modifying the original algorithm, however, the maximum reference chain length is too short to decorrelate full configurations without dramatically lowering the acceptance probability of the composite move. This difficulty stems from the fact that the reference and full potentials sample different statistical distributions. By manipulating the thermodynamic variables characterizing the reference system (pressure and temperature, in this case), we maximize the average acceptance probability of composite moves, lengthening significantly the random walk between consecutive full energy evaluations. In this manner, the number of full energy evaluations needed to precisely characterize equilibrium properties is dramatically reduced. The method is applied to a model fluid, but implications for sampling high-dimensional systems with ab initio or density functional theory potentials are discussed.

An "optimal" spawning algorithm for adaptive basis set expansion in nonadiabatic dynamics.

The full multiple spawning (FMS) method has been developed to simulate quantum dynamics in the multistate electronic problem. In FMS, the nuclear wave function is represented in a basis of coupled, frozen Gaussians, and a "spawning" procedure prescribes a means of adaptively increasing the size of this basis in order to capture population transfer between electronic states. Herein we detail a new algorithm for specifying the initial conditions of newly spawned basis functions that minimizes the number of spawned basis functions needed for convergence. "Optimally" spawned basis functions are placed to maximize the coupling between parent and child trajectories at the point of spawning. The method is tested with a two-state, one-mode avoided crossing model and a two-state, two-mode conical intersection model.

On the extent and connectivity of conical intersection seams and the effects of three-state intersections.

We discuss the connectivity of intersection spaces and the role of minimal energy points within these intersection spaces (minimal energy conical intersections or MECIs) in promoting nonadiabatic transitions. We focus on malonaldeyde as a specific example, where there is a low-lying three-state conical intersection. This three-state intersection is the global minimum on the bright excited electronic state, but it plays a limited role in population transfer in our ab initio multiple spawning (AIMS) simulations because the molecule must traverse a series of two-state conical intersections to reach the three-state intersection. Due to the differences in seam space dimensionality separating conventional (two-state) and three-state intersections, we suggest that dynamical effects arising directly from a three-state intersection may prove difficult to observe in general. We also use a newly developed method for intersection optimization with geometric constraints to demonstrate the connectivity of all the stationary points in the intersection spaces for malonaldehyde. This supports the conjecture that all intersection spaces are connected, and that three-state intersections play a key role in extending this connectivity to all pairs of states, e.g. the S1/S0 and S2/S1 intersection spaces.

Optimizing conical intersections without derivative coupling vectors: application to multistate multireference second-order perturbation theory (MS-CASPT2).

We introduce a new method for optimizing minimal energy conical intersections (MECIs), based on a sequential penalty constrained optimization in conjunction with a smoothing function. The method is applied to optimize MECI geometries using the multistate formulation of second-order multireference perturbation theory (MS-CASPT2). Resulting geometries and energetics for conjugated molecules including ethylene, butadiene, stilbene, and the green fluorescent protein chromophore are compared with state-averaged complete active space self-consistent field (SA-CASSCF) and, where possible, benchmark multireference single- and double-excitation configuration interaction (MRSDCI) optimizations. Finally, we introduce the idea of "minimal distance conical intersections", which are points on the intersection seam that lie closest to some specified geometry such as the Franck-Condon point or a local minimum on the excited state.

Ab initio molecular dynamics of excited-state intramolecular proton transfer using multireference perturbation theory.

We present the first calculations of excited-state dynamics using ab initio molecular dynamics with a multireference perturbation theory description of the electronic structure. The new AIMS-CASPT2 method is applied to a paradigmatic excited-state intramolecular proton-transfer reaction in methyl salicylate, and the results are compared with previous ultrafast spectroscopic experiments. Agreement of AIMS-CASPT2 and experimental results is quantitative. The results demonstrate that the lack of an observed isotope effect in the reaction is due to multidimensionality of the reaction coordinate, which largely involves heavy-atom bond alternation instead of proton transfer. Using the dynamics results as a guide, we also characterize relevant minima on the ground and first singlet excited state using CASPT2 electronic structure theory. We further locate an S1/S0 minimal energy conical intersection, whose presence explains experimental observations of a sharp decrease in fluorescence quantum yield at excitation energies more than 1,300 cm-1 above the excited-state origin.

Ab initio molecular dynamics of excited-state intramolecular proton transfer around a three-state conical intersection in malonaldehyde.

Excited-state potential energy surface (PES) characterization is carried out at the CASSCF and MRSDCI levels, followed by ab initio dynamics simulation of excited-state intramolecular proton transfer (ESIPT) on the S2(pipi*) state in malonaldehyde. The proton-transfer transition state lies close to an S2/S1 conical intersection, leading to substantial coupling of proton transfer with electronic relaxation. Proton exchange proceeds freely on S2, but its duration is limited by competition with twisting out of the molecular plane. This rotamerization pathway leads to an intersection of the three lowest singlet states, providing the first detailed report of ab initio dynamics around a three-state intersection (3SI). There is a significant energy barrier to ESIPT on S1, and further pyramidalization of the twisted structure leads to the minimal energy S1/S0 intersection and energetic terminal point of excited-state dynamics. Kinetics and additional mechanistic details of these pathways are discussed. Significant depletion of the spectroscopic state and recovery of the ground state is seen within the first 250 fs after photoexcitation.

Competitive decay at two- and three-state conical intersections in excited-state intramolecular proton transfer.

We demonstrate the existence of a simultaneous degeneracy (not required by symmetry) of three electronic states in malonaldehyde. This is one of the first reports of such a triple degeneracy involving S0, S1, and S2 in a molecule with a closed-shell ground state. We further report on a two-state S2/S1 conical intersection which is higher in energy than the three-state intersection, but closer to the Franck-Condon point. First-principles quantum dynamics calculations of the photochemistry after excitation to S2 show that there is a competition between these intersections, with more than half of the population decaying to S1 through the higher energy S2/S1 intersection. Surprisingly, much of the population which makes it to the triple degeneracy point is not funneled directly to S0, but rather remains trapped on S1. We attribute this to the large dimensionality of the branching plane at a three-state intersection (the degeneracy is lifted along at least five distinct molecular displacements).