Condensed phase chemical systems

VER occurs as a result of fluctuating forces exerted by the bath on the system at the system s oscillation frequency (22). We will use the upper-case to denote the system s vibrational frequency and lower-case co to denote other vibrations. It may also be useful to look at fluctuating forces exerted on a particular chemical bond (23). Fluctuating forces are characterized by a force-force correlation function. The Fourier transform of this force correlation function at Q, denoted rj(Q), characterizes the quantum mechanical frequency-dependent friction exerted on the system by the bath (19,22). This friction, especially at higher (i.e., vibrational) frequencies, plays an essential role in condensed phase chemical reaction dynamics (24,25). 

Another way to define ionic charges consists in partitioning space into elementary volumes associated to each atom. One method has been proposed by Bader [240,241]. Bader noted that, although the concept of atoms seems to lose significance when one considers the total electron density in a molecule or in a condensed phase, chemical intuition still relies on the notion that a molecule or a solid is a collection of atoms linked by a network of bonds. Consequently, Bader proposes to define an atom in molecule as a closed system, which can be described by a Schrodinger equation, and whose volume is defined in such a way that no electron flux passes through its surface. The mathematical condition which defines the partitioning of space into atomic bassins is thus ... 

In a second example the discrete time-reversible propagation scheme for mixed quantum-classical dynamics is applied to simulate the photoexcitation process of I2 immersed in a solid Ar matrix initiated by a femtosecond laser puls. This system serves as a prototypical model in experiment and theory for the understanding of photoinduced condensed phase chemical reactions and the accompanied phenomena like the cage effect and vibrational energy relaxation. It turns out that the energy transfer between the quantum manifolds as well as the transfer from the quantum system to the classical one (and back) can be very well described within the mixed mode frame outlined above. 

The third part of this text focuses on several important dynamical processes in condensed phase molecular systems. These are vibrational relaxation (Chapter 13), Chemical reactions in the barrier controlled and diffusion controlled regimes (Chapter 14), solvation dynamics in dielectric environments (Chapter 15), electron transfer in bulk (Chapter 16), and interfacial (Chapter 17) systems and spectroscopy (Chapter 18). These subjects pertain to theoretical and experimental developments of the last half century some such as single molecule spectroscopy and molecular conduction—of the last decade. 

This approach is able to model a variety of condensed phase chemical reactions with essentially experimental accuracy [16]. We did And, however, one specific experimental system for which this methodology was not able to reproduce experimental results, and that is proton transfer in benzoic acid crystals. In developing a physical understanding of this system, we first identified the concept of the promoting vibration. 

To directly simulate the condensed-phase chemical reactivity of HMX, we use the SCC-DFTB method to determine the interatomic forces and simulate the decomposition at constant-volume and temperature conditions. The initial condition of the simulation included six HMX molecules in a cell, corresponding to the unit cell of the S phase of HMX (Fig. 10) with a total of 168 atoms. It is well known [76] that HMX undergoes a phase transition at 436 K from the P phase (two molecules per unit cell with a chair molecular conformation, density = 1.89 g/cm ) to the 6 phase (with boat molecular conformation, density=1.50 g/cm ). We thus chose the 8 phase as the initial starting structure so as to include all the relevant physical attributes of the system prior to chemical decomposition. The calculation started with the experimental unit cell parameters and atomic positions of 8 HMX. The atomic positions were then relaxed in an energy minimization procedure. The resulting atomic positions were verified to be close to the experimental positions. 

Since a portion of this chapter is devoted to the derivation of rate laws and various microscopic expressions for the rate coefficients of condensed-phase chemical reactions, it is useful to first write down the phenomenological rate law we expect to obtain, to define the various rate coefficients and relaxation times, and to present the different points of view that we shall adopt in describing the system. 

Similar considerations apply to the study of quantum reaction rates. In most instances one is interested in a rate process involving a subset of the DOF of the system characterized by some reaction coordinate operator (or set of reaction coordinate operators) This is the case, for example, for electron and proton transfers from a reactant state A to a product state B taking place in a condensed phase chemical or biochemical system. The free energy W along a reaction coordinate often has the typical double-well form shown in... 

One of the goals of a theory of condensed-phase chemical reactions is the calculation of the rate coefficient. The apparatus of linear response theory can be brought to bear on this problem for reactions taking place close to chemical equilibrium, and formal correlation function expressions for the rate coefficient can be derived. Of course, the dynamics of a liquid-state reacting mixture are not simple and these expressions are difficult to evaluate however, molecular dynamics simulations for simple systems are now possible and provide insight into the details of the reactive event and how it couples to solvent motions, as well as numerical estimates of the rate coefficient. Theoretical treatments necessarily model the full many-particle dynamics by stochastic equations of motion, and it is in the development and utilization of such models that most progress has been made in the theory of condensed-phase reaction rates. 

Cong, E and J. D. Simon (eds.) (1994). Introduction to Ultrafast Laser Spectroscopic Techniques Used in the Investigation of Condensed Phase Chemical Reactivity. Ultrafast Dynamics of Chemical Systems. Dordrecht, Kluwer. 

Condensed-phase Electronic Systems Path Integral Simulations Monte Carlo Quantum Methods for Electronic Structure Rates of Chemical Reactions Wave Packets. 

The physical forces described above aptly account for most molecular interactions in the gas phase. We now direct our discussion toward the condensed phases. Sohds and liquids form when the net attractive intermolecular forces are stronger than the thermal energy in the system and, consequently, hold the molecules together. While the force of attraction can sometimes be attributed to the electrostatic and van der Waals interactions described above, chemical forces also frequently play a role in condensed phases. Chemical forces are based on the nature of covalent electrons, the concept of the chemical bond, and the formation of new chemical species. The main difference between chemical and physical forces is that chemical forces saturate whereas physical forces do not, since chemical interactions are specific to the electronic wavefunc-tions of the chemical species involved. Indeed, a complete quantitative description of chemical interactions involves solution of the Schrodinger equation to describe the overlap of the molecular orbitals involved. We will consider chemical interactions only qualitatively. The goal of this discussion is to realize that there may be other important forces that govern the behavior of solids and liquids and to get a flavor of what these forces might be. 

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