Computational roles

Egelman DM, Person C, Montague PR (1998) A computational role for DA delivery in human decision-making. J Cogn Neurosci 70 623-630. 

There are basically two numerical approaches to obtain approximate solutions to the Schrodinger equation variational and perturbational. In calculations, we usually apply variational methods, while perturbational methods are often applied to estimate some small physical effects. The result is that most concepts (practically all the ones we know of) characterizing the reaction of a molecule to an external field come from the perturbational approach. This leads to such quantities (see Chapter 12) as dipole moment, polarizability, and hyperpolarizability. The computational role of perturbational theories may, in this ctmtext, be seen as being of the second otder. 

After the passage quoted near the beginning of this chapter, Dennett (2001) goes on to explain that the level of detail in functional descriptions relevant to the mind - especially consciousness - is the level of detail that makes a difference in computational role. He sees the failure of AI-oriented research about the mind as one of thinking one could get away with too little of the functionalized detail, since functionalized neuroscience is required. 

Of course, it is no recent discovery that has shown that what the molecules that make up neurons do is important to the causal role played by the neurons. What Dennett means is that what has been discovered is that neuromodulators are important to the functional or computational roles played by neurons. Computational roles are a species of causal roles that play a role in a specific kind of causal process, a computation. Thus the phosphors in an old-fashioned screen make it possible for us to see the output of the computer, but our seeing the output is not part of the computation itself It can scarcely be thought that it is a new idea that neurotransmitters contribute to computational roles. The first discovery of a neurotransmitter was in 1921, and I don t think that those who have thought of the mind as computational would ever have denied that neurotransmitters are part of the implementation of those roles. 

What was wrong with AI approaches to consciousness is invisible from the point of view of the Canberra Plan with its excessive focus on ontology at the expense of metaphysics. The flaw in traditional AI was metaphysical. It was not that the Al-ers failed to notice that neurotransmitters have important causal or computational roles. They had the mistaken view that the metaphysical problem of mind could be solved at a level of description that paid no attention to details of neuroscience. Now that mistake can be corrected in one of two ways ... 

It should be emphasized that isomerization is by no means the only process involving chemical reactions in which spectroscopy plays a key role as an experimental probe. A very exciting topic of recent interest is the observation and computation [73, 74] of the spectral properties of the transition state [6]—catching a molecule in the act as it passes the point of no return from reactants to products. Furthennore, it has been discovered from spectroscopic observation [75] that molecules can have motions that are stable for long times even above the barrier to reaction. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

In this section we present several numerical teclmiques that are conmronly used to solve the Sclirodinger equation for scattering processes. Because the potential energy fiinctions used in many chemical physics problems are complicated (but known to reasonable precision), new numerical methods have played an important role in extending the domain of application of scattering theory. Indeed, although much of the fomial development of the previous sections was known 30 years ago, the numerical methods (and computers) needed to put this fomialism to work have only been developed since then. 

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

If computing time does not play the major role that it did in the early 1980s, the [12-6] Lennard-Jones potential is substituted by a variety of alternatives meant to represent the real situation much better. MM3 and MM4 use a so-called Buckingham potential (Eq. (28)), where the repulsive part is substituted by an exponential function ... 

In summary, a wealtli of experimental data as well as a number of sophisticated computer simulations univocally indicate that two important effects underlie the acceleration of Diels-Alder reactions in aqueous media hydrogen bonding and enforced hydrophobic interactionsIn terms of transition state theory hydrophobic hydration raises the initial state more tlian tlie transition state and hydrogen bonding interactions stabilise ftie transition state more than the initial state. The highly polarisable activated complex plays a key role in both of these effects. 

This discussion may well leave one wondering what role reality plays in computation chemistry. Only some things are known exactly. For example, the quantum mechanical description of the hydrogen atom matches the observed spectrum as accurately as any experiment ever done. If an approximation is used, one must ask how accurate an answer should be. Computations of the energetics of molecules and reactions often attempt to attain what is called chemical accuracy, meaning an error of less than about 1 kcal/mol. This is suf-hcient to describe van der Waals interactions, the weakest interaction considered to affect most chemistry. Most chemists have no use for answers more accurate than this. 

Several VTST techniques exist. Canonical variational theory (CVT), improved canonical variational theory (ICVT), and microcanonical variational theory (pVT) are the most frequently used. The microcanonical theory tends to be the most accurate, and canonical theory the least accurate. All these techniques tend to lose accuracy at higher temperatures. At higher temperatures, excited states, which are more difficult to compute accurately, play an increasingly important role, as do trajectories far from the transition structure. For very small molecules, errors at room temperature are often less than 10%. At high temperatures, computed reaction rates could be in error by an order of magnitude. 

Molecular modeling has evolved as a synthesis of techniques from a number of disciplines—organic chemistry, medicinal chemistry, physical chemistry, chemical physics, computer science, mathematics, and statistics. With the development of quantum mechanics (1,2) ia the early 1900s, the laws of physics necessary to relate molecular electronic stmcture to observable properties were defined. In a confluence of related developments, engineering and the national defense both played roles ia the development of computing machinery itself ia the United States (3). This evolution had a direct impact on computing ia chemistry, as the newly developed devices could be appHed to problems ia chemistry, permitting solutions to problems previously considered intractable. 

To gain a proper perspective of the role of computed physical properties, the relationship between estimated and computed properties needs to be understood. A thorough reading of Horvath (25) permits formulation of the following definitions of estimating or computing properties. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

Computer-aided process synthesis systems do not mean completely automated design systems (57). Process synthesis should be carried out by interactive systems, in which the engineer s role is to carry out synthesis and the machine s role is to analy2e the performance of synthesized systems. Computet apphcations in the future will probably deal with the knowledge-based system in appHed artificial intelligence. Consequendy, research on computer-aided process synthesis should be directed toward the realization of such systems with the collaboration of experienced process engineers. 

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