Information Theory molecular systems

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

Atextbook describing the theory associated with calculations of the electronic structure of molecular systems. While the book focuses on ab initio calculations, much of the information is also relevant to semi-empirical methods. The sections on the Hartree-Fock and Configuration Interactions methods, in particular, apply to HyperChem. The self-paced exercises are useful for the beginning computational chemist. 

An analogous role has been played by other scientists in strengthening the ties between quantum chemistry of type I (and type II) with the area corresponding to biochemistry (or complex molecular systems in general), a task made more difficult by the explosive growth of structural and functional information about biomolecular systems. It is worth to remark here that such a fruitful use of quantum chemical concepts in biology has requested the extension of the methods to approaches different from quantum molecular theory in the strict sense introduced before. We shall comeA back to this remark later. 

Nalewajski, R. F. 2006a. Information Theory of Molecular Systems. Amsterdam Elsevier. 

Density functional theory (DFT) uses the electron density p(r) as the basic source of information of an atomic or molecular system instead of the many-electron wave function T [1-7]. The theory is based on the Hohenberg-Kohn theorems, which establish the one-to-one correspondence between the ground state electron density of the system and the external potential v(r) (for an isolated system, this is the potential due to the nuclei) [6]. The electron density uniquely determines the number of electrons N of the system [6]. These theorems also provide a variational principle, stating that the exact ground state electron density minimizes the exact energy functional F[p(r)]. 

The vast majority of quantum chemical studies focus on equilibrium properties. However, a detailed understanding of chemical reactions requires a description of their chemical dynamics, which in turn requires information about the change in potential energy as bonds are broken or formed. Even though modem electronic structure theory can provide near-spectroscopic accuracy for small molecular systems near their equilibrium geometries, the general description of potential energy surfaces away from equilibrium remains very much a frontier area of research. 

It should be stressed that the most widely accepted models of the origin and evolution of life are based on the concept of self-assembling molecular systems. The models rooted in information theory involve [17] ... 

Maximizing the information entropy of a distribution gives in some sense the smoothest distribution consistent with our available information65 on this distribution. We have tested the information theory prediction of from for two different systems the Stockmayer and modified Stockmayer simulations of CO. We have already seen that these two systems represent two extreme forms of molecular rotational motion. In the Stockmayer simulation the molecules rotate essentially freely whereas in the modified Stockmayer simulation there is evidence for strongly hindered rotational motion. from the... 

Chemical systems may store information either in an analog fashion, in the structural features (size, shape, nature and disposition of interaction sites, etc. [1.27]) of a molecule or a supermolecule, or in a digital fashion, in the various states or connectivities of a chemical entity. Information theory has been applied to the description of the features of molecular machines [10.2]. The evaluation of the information content of a recognition process based on structural sensing in receptor-substrate pairs... 

The general theory for the absorption of light and its extension to photodissociation is outlined in Chapter 2. Chapters 3-5 summarize the basic theoretical tools, namely the time-independent and the time-dependent quantum mechanical theories as well as the classical trajectory picture of photodissociation. The two fundamental types of photofragmentation — direct and indirect photodissociation — will be elucidated in Chapters 6 and 7, and in Chapter 8 I will focus attention on some intermediate cases, which are neither truly direct nor indirect. Chapters 9-11 consider in detail the internal quantum state distributions of the fragment molecules which contain a wealth of information on the dissociation dynamics. Some related and more advanced topics such as the dissociation of van der Waals molecules, dissociation of vibrationally excited molecules, emission during dissociation, and nonadiabatic effects are discussed in Chapters 12-15. Finally, we consider briefly in Chapter 16 the most recent class of experiments, i.e., the photodissociation with laser pulses in the femtosecond range, which allows the study of the evolution of the molecular system in real time. 

Solvent effects can significantly influence the function and reactivity of organic molecules.1 Because of the complexity and size of the molecular system, it presents a great challenge in theoretical chemistry to accurately calculate the rates for complex reactions in solution. Although continuum solvation models that treat the solvent as a structureless medium with a characteristic dielectric constant have been successfully used for studying solvent effects,2,3 these methods do not provide detailed information on specific intermolecular interactions. An alternative approach is to use statistical mechanical Monte Carlo and molecular dynamics simulation to model solute-solvent interactions explicitly.4 8 In this article, we review a combined quantum mechanical and molecular mechanical (QM/MM) method that couples molecular orbital and valence bond theories, called the MOVB method, to determine the free energy reaction profiles, or potentials of mean force (PMF), for chemical reactions in solution. We apply the combined QM-MOVB/MM method to... 

A second interesting new theoretical development of a quite different kind has been the application of an information theory approach to the classification of experimental results [478-488]. The outcome of collisions, for example, the distribution of product translational or vibrational energies, is compared with the statistically predicted result for a closed system and the difference between the two is recorded as the surprisal. The surprisal is defined by an expression of the type found in information theory for example, if the probability of a reaction producing a molecular product in a final vibrational state v, corresponding to a fractional energy yield/,., is P fv.) and the corresponding statistical expression for a closed system is P°(fV ), then the surprisal is given by... 

A system of fundamental theoretical importance in many-body theory is the uniform-density electron gas. After decades of effort, exchange-correlation effects in this special though certainly not trivial system are by now well understood. In particular, sophisticated Monte Carlo simulations have provided very useful information (5) and have been conveniently parametrized by several authors (6). If the exchange-correlation hole function at a given reference point r in an atomic or molecular system is approximated by the hole function of a uniform electron gas with spin-densities given by the local values of p (r) and Pp(C obtain an... 

The unique features of our system enable us to use three different theoretical tools — a molecular dynamics simulation, models which focus on the repulsion between atoms and a statistical approach, based on an information theory analysis. What enables us to use a thermodynamic-like language under the seemingly extreme nonequilibrium conditions are the high density, very high energy density and the hard sphere character of the atom-atom collisions, that contribute to an unusually rapid thermalization. These conditions lead to short-range repulsive interactions and therefore enable us to use the kinematic point of view in a useful way. 

The success of the maximum entropy procedure to predict the shattering of clusters encourages us to use it in more complicated systems, where very little is known about the potential energy surface. In the next section the results from both molecular dynamics simulations and information theory analysis for clusters made up of N2 and O2 molecules are presented. 

The linear response function [3], R(r, r ) = (hp(r)/hv(r ))N, is used to study the effect of varying v(r) at constant N. If the system is acted upon by a weak electric field, polarizability (a) may be used as a measure of the corresponding response. A minimum polarizability principle [17] may be stated as, the natural direction of evolution of any system is towards a state of minimum polarizability. Another important principle is that of maximum entropy [18] which states that, the most probable distribution is associated with the maximum value of the Shannon entropy of the information theory. Attempts have been made to provide formal proofs of these principles [19-21], The application of these concepts and related principles vis-a-vis their validity has been studied in the contexts of molecular vibrations and internal rotations [22], chemical reactions [23], hydrogen bonded complexes [24], electronic excitations [25], ion-atom collision [26], atom-field interaction [27], chaotic ionization [28], conservation of orbital symmetry [29], atomic shell structure [30], solvent effects [31], confined systems [32], electric field effects [33], and toxicity [34], In the present chapter, will restrict ourselves to mostly the work done by us. For an elegant review which showcases the contributions from active researchers in the field, see [4], Atomic units are used throughout this chapter unless otherwise specified. 

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