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Polycyclic aromatic hydrocarbons (PAHs) constitute an essential family of compounds in interstellar (ISM) and circumstellar (CSM) media. Recently, formation routes for the corresponding polycyclic aromatic phosphorus heterocycles (PAPHs) in astrophysical environments have been proposed. In order to contribute to a better understanding of the phosphorus chemistry in the ISM, infrared (IR) spectra and selected properties of PAPHs were computed at the density functional theory level for neutral, cationic, and anionic species. Our results reveal that several protonated PAPHs do not have planar backbones, and all species have permanent dipole moments between 2D and 4D. Closed-shell PAPHs have similar ionization potentials compared to the parent PAHs, below the Lyman threshold limit. In addition, all PAPHs show positive electron affinities higher than those of PAHs. Protonation preferably occurs on the heteroatom but with lower proton affinities than those of the corresponding nitrogen analogues (polycyclic aromatic nitrogen heterocycles). In general, neutral species have similar IR spectra profile with the most intense bands around 800 cm−1 (12.5 μ m) related to C−H wagging. Charge and protonation affect the IR spectra mainly by decreasing the intensities of these modes and increasing the ones between 1000 (10.0 μ m) and 1800 cm−1 (5.6 μ m). The P−H stretching appears in a different spectral region, between 2300 (4.3 μ m) and 2700 cm−1 (3.7 μ m). Our results are discussed in the context of distinct sources where PAHs and phosphorus are detected. PAPHs, in particular the coronene derivatives, can contribute to the unidentified infrared emission band at 6.2 μ m. [ABSTRACT FROM AUTHOR]

Transition paths characterize chemical reaction mechanisms. In this paper, we present a new method to find mean reaction paths based on the free energy. A nudged elastic band (NEB) is optimized using gradients and Hessians of the free energy, which are obtained from umbrella integration. The transition state can be refined by a Newton-Raphson search starting from the highest point of the NEB path. All optimizations are done using Cartesian coordinates. Independent molecular dynamics (MD) runs are performed at each image used to discretize the path. This makes the method intrinsically parallel. In contrast to other free energy methods, the algorithm does not become more expensive when including more degrees of freedom in the active space. The method is applied to the alanine-dipeptide as a test case and compared to pathways that have been derived from metadynamics and forward flux sampling. [ABSTRACT FROM AUTHOR]

We investigated the behavior of H2, the main constituent of the gas phase in dense clouds, after collision with amorphous solid water (ASW) surfaces, one of the most abundant chemical species of interstellar ices. We developed a general framework to study the adsorption dynamics of light species on interstellar ices. We provide binding energies and their distribution, sticking probabilities for incident energies between 1 meV and 60 meV, and thermal sticking coefficients between 10 and 300 K for surface temperatures from 10 to 110 K. We found that the sticking probability depends strongly on the adsorbate kinetic energy and the surface temperature, but hardly on the angle of incidence. We observed finite sticking probabilities above the thermal desorption temperature. Adsorption and thermal desorption should be considered as separate events with separate time scales. Laboratory results for these species have shown a gap in the trends attributed to the differently utilized experimental techniques. Our results complement observations and extend them, increasing the range of gas temperatures under consideration. We plan to use our method to study a variety of adsorbates, including radicals and charged species. [ABSTRACT FROM AUTHOR]

Umbrella integration is a method to analyze umbrella sampling simulations. It calculates free-energy changes from distributions obtained from molecular dynamics. While it can be formulated on the full sampled distributions, they are generally approximated by normal distributions. This is equivalent to the truncation of a power series of the free energy with respect to the reaction coordinate after the quadratic term or by a truncation of a cumulant expansion. Here, expressions for additional terms in the power series are derived. They can be calculated from the central moments of the distributions. This extension allows to test the approximations in applications. [ABSTRACT FROM AUTHOR]

The instanton method allows to accurately calculate tunneling rates down to very low temperature. However, with lowering the temperature, the computational effort steeply increases as many more discretization points are required. This is caused in practical applications by the majority of the discretization points accumulating at a very small region in configuration space. Here, we describe a method to flexibly discretize the instanton path adapted to the temperature. Chosen appropriately, the discretization leads to a much more uniform distribution of the images (control points) along the path which reduces the number of required images by about a factor of two. Combined with a modified Newton-Raphson optimizer and successive updates of the Hessians, the proposed method provides converged reaction rates at computational costs reduced by more than an order of magnitude. We show the success of the method on analytic test potentials and on molecules with energies directly obtained from density functional theory calculations. [ABSTRACT FROM AUTHOR]

Umbrella integration is a method to analyze umbrella sampling simulations by calculating and integrating the mean force. Here, the method is extended to multidimensional reaction coordinates. Approximation of the probability distribution obtained from sampling by a multivariate normal distribution allows to calculate the mean force from the average and the covariance matrix of the reaction coordinate. Integration schemes of the free-energy gradient field are discussed. Integration on a real-space grid is compared to expansion of the gradient in a series of analytic functions (such as a Fourier analysis), which can be integrated, and the expansion of the gradient only at the window means in a series of analytic functions. The Fourier analysis was found particularly useful for periodic reaction coordinates, such as torsion angles. An expression is provided to calculate the Hessian of the free energy with respect to the reaction coordinates from sampling data. The utility of the method is demonstrated at the example of the free-energy surface of the alanine dipeptide in vacuum calculated with respect to the backbone torsion angles [uppercase_phi_synonym] and Ψ. Relevance of the Jacobian term for non-Cartesian reaction coordinates is discussed. [ABSTRACT FROM AUTHOR]

Algorithmic improvements of the dimer method [G. Henkelman and H. Jónsson, J. Chem. Phys. 111, 7010 (1999)] are described in this paper. Using the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimizer for the dimer translation greatly improves the convergence compared to the previously used conjugate gradient algorithm. It also saves one energy and gradient calculation per dimer iteration. Extrapolation of the gradient during repeated dimer rotations reduces the computational cost to one gradient calculation per dimer rotation. The L-BFGS algorithm also improves convergence of the rotation. Thus, three to four energy and gradient evaluations are needed per iteration at the beginning of a transition state search, while only two are required close to convergence. Moreover, we apply the dimer method in internal coordinates to reduce coupling between the degrees of freedom. Weighting the coordinates can be used to apply chemical knowledge about the system and restrict the transition state search to only part of the system while minimizing the remainder. These improvements led to an efficient method for the location of transition states without the need to calculate the Hessian. Thus, it is especially useful in large systems with expensive gradient evaluations. [ABSTRACT FROM AUTHOR]

Umbrella sampling simulations, or biased molecular dynamics, can be used to calculate the free-energy change of a chemical reaction. We investigate the sources of different sampling errors and derive approximate expressions for the statistical errors when using harmonic restraints and umbrella integration analysis. This leads to generally applicable rules for the choice of the bias potential and the sampling parameters. Numerical results for simulations on an analytical model potential are presented for validation. While the derivations are based on umbrella integration analysis, the final error estimate is evaluated from the raw simulation data, and it may therefore be generally applicable as indicated by tests using the weighted histogram analysis method. [ABSTRACT FROM AUTHOR]

We present a method to analyze biased molecular-dynamics and Monte Carlo simulations, also known as umbrella sampling. In the limiting case of a strong bias, this method is equivalent to thermodynamic integration. It employs only quantities with easily controllable equilibration and greatly reduces the statistical errors compared to the standard weighted histogram analysis method. We show the success of our approach for two examples, one analytic function, and one biological system. [ABSTRACT FROM AUTHOR]

The protonation of N2 bound to the active center of nitrogenase has been investigated using state-of-the-art density-functional theory calculations. Dinitrogen in the bridging mode is activated by forming two bonds to Fe sites, which results in a reduction of the energy for the first hydrogen transfer by 123 kJ/mol. The axial binding mode with open sulfur bridge is less reactive by 30 kJ/mol and the energetic ordering of the axial and bridged binding modes is reversed in favor of the bridging dinitrogen during the first protonation. Protonation of the central ligand is thermodynamically favorable but kinetically hindered. If the central ligand is protonated, the proton is transferred to dinitrogen following the second protonation. Protonation of dinitrogen at the Mo site does not lead to low-energy intermediates. [ABSTRACT FROM AUTHOR]