### Journal: The Journal of chemical physics

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##### Perspective: Stochastic algorithms for chemical kinetics

- The Journal of chemical physics
- Published over 6 years ago
- Discuss

We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.

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##### Long-range interactions in the ozone molecule: Spectroscopic and dynamical points of view

- The Journal of chemical physics
- Published almost 7 years ago
- Discuss

Using the multipolar expansion of the electrostatic energy, we characterized the asymptotic interactions between an oxygen atom O((3)P) and an oxygen molecule O(2)((3)Σ(g) (-)), both in their electronic ground state. We calculated the interaction energy induced by the permanent electric quadrupoles of O and O(2) and the van der Waals energy. On one hand, we determined the 27 electronic potential energy surfaces including spin-orbit connected to the O((3)P) + O(2)((3)Σ(g) (-)) dissociation limit of the O-O(2) complex. On the other hand, we computed the potential energy curves characterizing the interaction between O((3)P) and a rotating O(2)((3)Σ(g) (-)) molecule in its lowest vibrational level. Such curves are found adiabatic to a good approximation, namely, they are only weakly coupled to each other. These results represent a first step for modeling the spectroscopy of ozone bound levels close to the dissociation limit, as well as the low energy collisions between O and O(2) thus complementing the knowledge relevant for the ozone formation mechanism.

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##### Quasi-diabatic representations of adiabatic potential energy surfaces coupled by conical intersections including bond breaking: A more general construction procedure and an analysis of the diabatic representation

- The Journal of chemical physics
- Published almost 7 years ago
- Discuss

The analytic representation of adiabatic potential energy surfaces and their nonadiabatic interactions is a key component of accurate, fully quantum mechanical descriptions of nonadiabatic dynamics. In this work, we describe extensions of a promising method for representing the nuclear coordinate dependence of the energies, energy gradients, and derivative couplings of N(state) adiabatic electronic states coupled by conical intersections. The description is based on a vibronic coupling model and can describe multichannel dissociation. An important feature of this approach is that it incorporates information about the geometry dependent interstate derivative couplings into the fitting procedure so that the resulting representation is quantifiably quasi diabatic and quasi diabatic in a least squares sense. The reported extensions improve both the rate of convergence and the converged results and will permit the optimization of nonlinear parameters including those parameters that govern the placement of the functions used to describe multichannel dissociation. Numerical results for a coupled quasi-diabatic state representation of the photodissociation process NH(3)+hv → NH(2)+H illustrate the potential of the improved algorithm. A second focus in this numerical example is the quasi-diabatic character of the representation which is described and analyzed. Special attention is paid to the immediate vicinity of the conical intersection seam.

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##### Rabi and Larmor nuclear quadrupole double resonance of spin-1 nuclei

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

We demonstrate the creation of two novel double-resonance conditions between spin-1 and spin-½ nuclei in a crystalline solid. Using a magnetic field oscillating at the spin-½ Larmor frequency, the nuclear quadrupole resonance (NQR) frequency is matched to the Rabi or Rabi plus Larmor frequency, as opposed to the Larmor frequency as is conventionally done. We derive expressions for the cross-polarization rate for all three conditions in terms of the relevant secular dipolar Hamiltonian, and demonstrate with these expressions how to measure the strength of the heterogenous dipolar coupling using only low magnetic fields. In addition, the combination of different resonance conditions permits the measurement of the spin-½ angular momentum vector using spin-1 NQR, opening up an alternate modality for the monitoring of low-field nuclear magnetic resonance. We use ammonium nitrate to explore these resonance conditions, and furthermore use the oscillating field to increase the signal-to-noise ratio per time by a factor of 3.5 for NQR detection of this substance.

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##### Chaotic dynamics in multidimensional transition states

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if the invariant hyper-sphere is normally hyperbolic, i.e., the dynamics within the transition state is not too strongly chaotic. We study the dynamics within the transition state for the hydrogen exchange reaction in three degrees of freedom. As the energy increases, the dynamics within the transition state becomes increasingly chaotic. We find that the transition state first looses and then, surprisingly, regains its normal hyperbolicity. The important phase space structures of transition state theory will, therefore, exist at most energies above the threshold.

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##### Note: Excited state studies of ozone using state-specific multireference coupled cluster methods

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

Vertical excitation energies obtained with state-specific multi-reference coupled cluster (MRCC) methods are reported for the low-lying singlet and triplet excited of the ozone molecule. The MRCC results are also compared with those obtained with high-order equation-of-motion coupled cluster methods.

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##### Stability of molecular dynamics simulations of classical systems

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

The existence of a shadow Hamiltonian H̃ for discrete classical dynamics, obtained by an asymptotic expansion for a discrete symplectic algorithm, is employed to determine the limit of stability for molecular dynamics (MD) simulations with respect to the time-increment h of the discrete dynamics. The investigation is based on the stability of the shadow energy, obtained by including the first term in the asymptotic expansion, and on the exact solution of discrete dynamics for a single harmonic mode. The exact solution of discrete dynamics for a harmonic potential with frequency ω gives a criterion for the limit of stability h ≤ 2∕ω. Simulations of the Lennard-Jones system and the viscous Kob-Andersen system show that one can use the limit of stability of the shadow energy or the stability criterion for a harmonic mode on the spectrum of instantaneous frequencies to determine the limit of stability of MD. The method is also used to investigate higher-order central difference algorithms, which are symplectic and also have shadow Hamiltonians, and for which one can also determine the exact criteria for the limit of stability of a single harmonic mode. A fourth-order central difference algorithm gives an improved stability with a factor of 3, but the overhead of computer time is a factor of at least two. The conclusion is that the second-order “Verlet”-algorithm, most commonly used in MD, is superior. It gives the exact dynamics within the limit of the asymptotic expansion and this limit can be estimated either from the conserved shadow energy or from the instantaneous spectrum of harmonic modes.

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##### A hierarchical exact accelerated stochastic simulation algorithm

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

A new algorithm, “HiER-leap” (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled “blocks” and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms.

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##### Quantitative determination of the lateral density and intermolecular correlation between proteins anchored on the membrane surfaces using grazing incidence small-angle X-ray scattering and grazing incidence X-ray fluorescence.

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

As a physical model of the surface of cells coated with densely packed, non-crystalline proteins coupled to lipid anchors, we functionalized the surface of phospholipid membranes by coupling of neutravidin to biotinylated lipid anchors. After the characterization of fine structures perpendicular to the plane of membrane using specular X-ray reflectivity, the same membrane was characterized by grazing incidence small angle X-ray scattering (GISAXS). Within the framework of distorted wave Born approximation and two-dimensional Percus-Yevick function, we can analyze the form and structure factors of the non-crystalline, membrane-anchored proteins for the first time. As a new experimental technique to quantify the surface density of proteins on the membrane surface, we utilized grazing incidence X-ray fluorescence (GIXF). Here, the mean intermolecular distance between proteins from the sulfur peak intensities can be calculated by applying Abelé’s matrix formalism. The characteristic correlation distance between non-crystalline neutravidin obtained by the GISAXS analysis agrees well with the intermolecular distance calculated by GIXF, suggesting a large potential of the combination of GISAXS and GIXF in probing the lateral density and correlation of non-crystalline proteins displayed on the membrane surface.

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##### Plasmon resonances in linear noble-metal chains.

- The Journal of chemical physics
- Published about 7 years ago
- Discuss

The electronic excitations of three noble-metall chains-copper, silver, and gold-have been investigated at the time-dependent density functional theory level. The reduced single-electron density matrix is propagated according to the Liouville-von Neumann equation in the real-time domain after an impulse excitation. The propagation in the real-time domain enables us to investigate the formation and size evolution of electronic excitations in these metallic chains with different number of atoms, up to a total of 26 atoms. The longitudinal oscillations at lower excitation energies are dominated by s → p transitions in these chains and have collective or central resonances, while the first peak involving d → p transitions in the longitudinal mode appears at a higher excitation energy and shows collective resonances. In the transverse oscillations, there are in most cases d → p transitions in each resonance, which can be attributed to either central or end resonances. Convergence of the oscillations, in particular those involving the collective and central resonances in the three noble-metal chains can only be observed for chains with 18 atoms or more. Different spectroscopic characteristics among these three metallic chains can be attributed to their different electronic structures, in particular the relativistic effects in the gold chains have a dramatic effect on their electronic structures and excitations.