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vis a vis
Rudolph A. Marcus's
Theory of electron transfer reactions in chemical
systems
| Following are several excerpts from Understanding the Integral Universe (1992), in which I discussed in every day terms the substance of Rudolph Marcus's Nobel Prize winning work in Chemistry. I also address correlations it has with the "plural entropies" model of complexity I have theorized as 'Integrity Dynamics'. |
" ... In separate and simplisticly organized systems (where the "bounds" are highly specific and ordered...such as a gas existing in a rigidly formed container), entropy exists very much the way it has been traditionally conceived. But, when the "bounds" are less "ordered" and are more actively participant in the ƒfunctional behaviors of what is at hand... that is, are equally and mutually responsive to all the energetics going on and all the transiting partial differential components encountered, in this situational environment, there is an interactivity of several entropies. And the small-field entropy of some components create, drive and determine the negentropic ordering of larger spatio-temporally bounded co-extants.
I was thrilled in October of 1992 when I read that Dr Rudolph Marcus of Caltech was awarded the Nobel Prize in Chemistry for his work describing definable differences in the transfer rates of electrons from one atom to another, and from one molecule to another. This covers inorganic and organic reactions. I called and spoke with him briefly in October of 1993, telling him that I felt his work was applicable to chaos and complexity theories. He modestly deferred, indicating that he wasn't knowledgeably familiar enough with those efforts, however, he would be more than happy enough to forward a copy of his Nobel presentation1 to me. I will elaborate on his extraordinary achievement later on in this paper.
Needless to say, Dr. Marcus's explanation of variable electron dynamics details something which the Integrity Paradigm hints at in its overview and understanding of systems dynamics in general, especially concerning EM fields - their interactions and the arising of complex systems through the sheer localized entropy of electrons. I will be so bold as to say that, even though Dr.Marcus might not yet personally recognize the importance of these connections as seen from the perspective of the ideas presented in my work, his understanding and description of electron behavior is the defining explanation of what produces the subtle entropy and negentropy gradients in EM fields around molecules .... and what drives the continual creation of negentropic complexity and life.
It is far and away superior to the concepts and methodology being proposed by the current group of Chaos and Complexity theorists, who have had to introduce a host of new and subjectively debatable concepts at principle metabolic junctures, in order to achieve a rationale path for the functional complexity of living systems. For example, in a situation where 2 stable energy-minima states exist on either side of a saddle-point transition plateau, Marcus recognizes the bi-directionality of reversible mechanisms and shows that several factors produce a very distinct preference differential (thus giving a gradient when placed within a sequence chain of reactions), yet still noting that on either side of the saddle-point, the reactants will arrange themselves toward the 2 distinct minima. The Chaos theorists, looking at such "behaviors" without linking them to any specific mechanism, say that the molecular configurations are "drawn toward" 2 separate "attractors". It is eminently possible to define, describe and model such behaviors using chaos mathematics. That does not mean that fundamentally simpler traditional ƒfunctions could not produce them or are not a superior way of understanding them.
Shortly, I will get to how this translates into mathematical terms, and examine some crucial paradigm shifts that will clarify older accepted formulations, as well as open the door to creating new ones. If you will bear with me though, I want to elaborate more fully on language, symbols and conceptual experiencing. It will be difficult to appreciate or accept the changes I want to make in mathematical symbolism unless you can objectively perceive it as just another language whose symbolic meanings are open to refinement and change. ..."
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[The discussion returned to comparing
specific text by Dr. Marcus with Integrity concepts] :
"... Several things are accomplished with this broad holistic Integrity Paradigm perspective. The principle one being that we don't have to postulate any additional extraordinary "force" such as an amorphous extraneous "attractor" (ala complexity mathematics).
Dynamic stability - as a concept - becomes more broadly pertinent as a constantly open variable process rather than a fixed steady state of thermodynamic balance. "Steady-state", in fact, becomes only one mechanism of "stability". It is my perception that we should appreciate "stability" in the broader sense, and attempt to define systems in terms of self-relevant maintenance ... seen as the ability to function within limits of energy transfer. That is, ƒunctioning within a latitude of internally and externally oriented energy flows.
That is why I find the work of Dr. Rudolph Marcus, the Nobel winner at Caltech, intriguing, and particularly pertinent here. One of the cogent aspects of the Integrity Paradigm says that successful self-maintenance Integrity survival rests as much upon the rates of transfer of energy and information, as it does on the quantity. That is, a system's innate construction determines not only how much information it can process, but also how fast it can proces, before the construction of the system is over-stressed. These are just the conditions of molecular bonding which Rudlph Marcus' work details.
A molecule can encounter just so much external energy before valence bonds are broken and the energy restructured. The important part of the dynamics is not so much at what energy values the de-composition may occur, but that those values represent a limit, beneath which there persists a wide range of normal continuous behaviors and interactions, and the bond is maintained.
As there are acknowledged variations in electron transfer rates, per Dr. Marcus' work (derived as they are from aspects of electron shell variances not dissimilar to the subtle van der Waals forces), this only adds support to how the Integrity paradigm models these regions of information transfer.
I have been writing for over 20 years that at some point in the future, I would like to see bio-metabolic pathway molecules evaluated for the EM fields they present to other metabolic molecules. EM fields will vary around such molecules according to the dips and folds and bulges of where atoms - and their electronclouds - are realtive to one another in space. By mapping these field intensities and inter-relations - as the field makes a textured global face of varying positive and negative charges and so on around the molecule, then DNA, RNA, and other protein structure binding sites will be more clearly understood. Stereo configurations only give us an instantaneous snapshot rather than a dynamic pattern for how the binding sites work. Metabolic pathways - described as a flow-chart of compatible EM region-site states is far superior. Oxidation and reduction are site-specific for each molecule, by form and by EM values. As "processes" they establish relative gradients for electron transfers through the molecular soup/environment. A gradient which follows strong quantum nodal values co-organizes under local entropies.
It is interesting that Virtual Reality studies are now being done to realize these phenomena. The studies and equipment cyberneticly link human interactive experience with the EM fields and individual molecular interactions by interfacing pressure sensitive gloves with VR visuals so that researchers can literally "feel" the intensity and locations of electromagnetic forces as they exist around given molecules. It is 'real time' exposure to felt-forces, which gives a sense of how and why molecules congruently lock-and-key recognize each other, how they template each other. The technique skips over specific schematic value-mapping, even though those are the number-values that they are really manipulating (that data being generated and stored inside the computers doing the modeling). Hopefully, someone is going to coordinate that data some day in a readable metabolic map, in just the same manner as the earth is mapped for local variations in the strength of gravity, from place to place.
The "information" being shared with the people wearing the Virtual Reality interfaces are the "sensations" of what the interacting molecules must supposedly "feel" as their EM fields encounter each other....a complex version of what an EM field feels like if you bring two North or two South poles of bar magnets together...the sensation is almost of a rubbery, fluid, organic energy-presence keeping the bars apart. In this case, researchers are directly "feeling" the blended force values of attraction and repulsion, as they build up a physiological appreciation for how these molecules interact. But only on a one by one reaction basis.
Additionally however, there is research proceeding in another area of Chemistry which can be brought to bear here. The new field of Computational Chemistry is using the power of the current generation of computers to do all the quantum calculations necessary to literally "build" new and different molecular configurations that nature and traditional linear sequence chemistry have not. This is an off-shoot extension of the Virtual Reality work, but is more specific. Carbon atoms configured in 18 atom loops, or bi-level graphite, or Buckyballs and Fullerene chains of arbitrary length bounded by complex caps are just some of the examples to date. (They refer to trad- itional chemistry as zero-dimensional...building specific linear orientations one at a time, whereas Computational Chemistry is taking into account several quantum-determined degrees of freedom at the same time.)
These physical effects and research accomplishments show the penultimate importance of Rudolph Marcus's work. I will refer to, quote from and comment on that work ({ } brackets) as presented in the English edition of "Angewandte Chemie" vol32no8, 1993: Nobel Lectures "Electron Transfer Reactions in Chemistry: Theory and Experiment".
"In transition state theory, a quasi-equilibrium ... is then calculated with equilibrium statistical mechanics." In 1938, Eugene Wigner "used a classical mechanical description of the reacting system in the many-dimensional space (of coordinates and momenta). Wigner pointed out that the quasi-equilibrium would follow as a dynamical consequence"...depending on limited recrossing of the transition state. {JNR: This is a partial component of gradients that get established.}
"In practice, transition state theory is generalized to include as many coordinates as are needed to describe the reacting system. Further, when the system can tunnel quantum mechanically through the potential energy barrier (the pass) separating the two valleys {stability energies}, ... the method of treating the passage across the transition state region needs, and has received, refinement. (The principle problem encountered here has been the lack of "dynamical separability" of the various motions in the transition state region.)" {JNR: In other words, transition state regions are loosely specified localizable bounds ... with a latitude of energy values that fluctuate in regard to multiple variables that can affect it. Besides the flux relative to center-of-mass separation between atoms, electron cloud responsiveness towards the molecule it initially resides in, etc., the wave-state of an electron that permits tunneling, et al, means that there are several paths ... and energy states of those paths ... through which electron transfer occurs. Each with its own particular relative-entropies gradients.}
However, " a somewhat different picture of the reaction is needed." After studying a 1952 symposium paper by Libby where Libby indicated that a particular reaction studied produced unexpected results because the "environment" was not one congenial to the reaction at hand because there was not enough time for the molecules to re-orient out of the way, Marcus continues: "I realized that fluctuations had to occur in the various nuclear coordinates {JNR: therefore, presenting a different EM "face"}, such as in the orientation coordinates of the individual solvent molecules and indeed in any other coordinates... . With such fluctuations, values of the coordinates could be reached which satisfy both Franck-Condon and energy conservation conditions...".
{JNR: The reactants are simultaneously "participant", "environment" & "boundary".}"The theory proceeded as follows. The potential energy Ur of the entire system, reactants plus solvent, is a function of the many hundreds of relevant coordinates of the system .... which include ... the position and orientation of the individual solvent molecules (and hence their dipole moments, for example), and the vibrational coordinates...particularly those in any inner coordination shell of the reacting ions. ... No longer were there just the two or so important coordinates that were dominant in a reaction." {JNR: Though an atom or molecule is ostensibly spatially designated by the predominant expression of the outer location of the electron cloud/shell, the behavior of an atom or molecule ... every "boundary definable" system ... is affected by information and energy transferences and transcriptions both internal to that bound and external to that bound.}
"Similarly, after the electron transfer, the reacting molecules have the ionic charges appropriate to the reaction products... . These two potential energy surfaces will intersect if the electronic coupling which leads to electron transfer is neglected. For a system with N coordinates this intersection occurs on an (N-1) {JNR : ! } dimensional surface, which then constitutes in our approximation the transition state of the reaction." {JNR: We currently discuss the universe as n-dimensional, whereas according to my premise to include a zero-th dimension (ƒluence), the universe ƒunctions as n+1. I arrived at this conclusion via logic-reasonings regarding topology and information theory as a single geometry. It is a direct corollary of Marcus's statement.}
"...electronic coupling, electronic motion, nuclear motion" added in ... require "a rather different approach..."
"...what was then needed was a method of calculating the electrostatic free energy G of this system and its still unknown polarization function Pu(r). I obtained this free energy G by finding a reversible path for reaching this state of the system. ... I was able to find Pu(r) ... and ... G for the transition state. ... and the reaction rate calculated." {JNR: Marcus was able to specify a process rate and a process direction, based upon the differentials of existing quantum and ion values. This included "vibrational" components, , and center-to-center separation distances.} There is a component , "where is the charge transferred ... and is the activation overpotential, namely, potential difference ... relative to the value it would have if the rate constants for the forward and reverse reactions were equal." .... "When | |< , most electrons go into or out of quantum states ... that are near the Fermi level." {JNR: There are variations which occur because of high exothermic activity.}
Marcus then applied a linkage : "a linear response approximation in which any hypothetical change in charge of the reactants produces a proportional change in the dielectric polarization of the solvent." He has now applied a central limit theorem that gives a better approximation than simple perturbation theory.
The result were geometric quadratic functions displayable as parabolic free energy plots. Very distinct for each reaction. "It was important to use the free energy curves, instead of oversimplified potential energy profiles, because of the large entropy changes {!!!} which occur in many electron transfer cross-reactions..." {It is clear from this that it is reasonable, accurate and requisite to treat electrons thermodynamically (in terms of 'entropy'), not just quantum mechanically.}
Several subtleties became apparent from Marcus's work. One is "cross-relation" which defines fine rate distinctions around equilibrium. Another is that the activation free energy component G* can be either positive or negative as it pivots around - . And likewise produces an "inverted region" when - G0 > . The net effect is that the free energy barrier G* is decreased. {JNR: Such "free energy barriers" are therefore not fixed and firm. There is a variable latitude of energy levels which still constitute a path region .... but the region is very flexible and dependent upon the EM configurations that are presented by environmental molecules. The propensities for electron transfer are dictated by the internal-oriented configurations relative to external-oriented presentations. All effecting entropy changes and transferences...in local regions...and in the overall, creating transaction paths describable as "entropy gradients".}
Marcus continues: "...there are now detailed experimental and theoretical studies in photosynthetic and other protein systems."!!!! He continues with remarks about the nonpolar nature of protein environments, the forward reactions, the participation of inverted regions, long-range transfer, comparations of back-transfer which give direction impetus to chained transfers, and small step stability nodes.
The Integrity Paradigm began initially by examining broad systems behaviors. It deduced that local entropy dynamics could be used to re-interpret the motivation and direction for those behaviors. It even intimated negentropic complexity formation as a consequence of regional localized entropy. It was a noble and well thought out deduction. Marcus has given it a "presence". Right where it counts, on the atomic level. Right where I always felt it could best be "proved". Its applications elsewhere should be more than obvious now.
Rudolph Marcus's work shows that the universe is indeed an elegant place. Extraordinarily vast in subtlety and interconnectedness and complexity. And, comprehensible with the understandings at hand. 'Autocatalysis' 2, 3 is not required.
Autotrophic behaviors, however, are a way of evaluating and understanding complexity dynamics. In the case of botanical phototrophic responses, auxins are produced on the side of the high energy interaction ... the side where photons are arriving from. Plants in general use light as part of the photosynthetic process of food formation. In this instance, the light is not limited to excessive food production only in the cells closest to the light source. The light helps produce the auxin growth-retardants on that side. The net affect being that comparative growth on the far-side of the light source is higher, and the plant - as a holistic organism - moves or grows "toward" the light ... where the overall plant structure has better access to the light source.
What I am trying to indicate by this reference is that "photosynthetic-predominated" analysis alone would imply greater growth strictly on the near-light-source side. The growth impetus is not the result of a singular dynamic, and therefore runs counter to simple intuitive observation.
This is directly analogous to negentropic complexity development. The Complexity Dynamic is not the result of a singular function. It is the net-result of an opposite gradient ... entropy ... which expresses itself on the next higher level of organization. ... "
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"... The next thing for researchers to quantitatively approach is to translate "stored energy" into "information". The kinds and quantities of "information" can be clearly distinguished for each level of ƒfunction. -Apollonian holographic transcription of information means that energy encounters will retain data and react to data beyond the local Integrity structure. For example, a Marcus envisioned molecule now incorporates a range of behavioral flexibility. That flexibility is "information" retained in the qualities and abilities of the molecular structure to "respond" to a wide variety of molecular EM presentations from the environment. Consciousness crosses the threshold from "stimulus-response" to "controlled behavior". Very pertinent, very specific, for each molecule or grouping of gradient interlinked molecules.
Massive crosslinked pathways begin to accumulate extraordinary information quantae. And the extent of "conscious behavior" depends on the fitness, vigor and magnitude of integral feedback loops. It is a process of Synergy. Simple components combining to make responsive-entities which are so much more than the simple sum of their parts. Old style reductionist thinking would say that this makes Life only a conglomeration of mundane mechanistic operations. Quite the contrary. The way we or any life forms experience "living" is exactly what our perceptions tell us it is. We are not randomly quivering blobs of protoplasm. We are thoughtful, conscious, spiritual, emotional, energetic, goal-oriented, striving sentient creatures. We seek to endure. We grow biologically and mentally. We do not need to consciously control every biochemical reaction that we are made of ... an antigen/antibody binding site does not need to fixate the location of every electron or nuclear particle within its whole molecular matrix - only work with the level of information it is capable of - the corresponding molecules it shares its space with. Ceptual models, languages, societies, physical health, economic welfare, art, creativity, hopes desires and dreams - these and more are Real for us. In analog. In fact. Qualities that are equally as real and extant - existing as Potential - in each and every atom and sub-atomic particle."
- "Understanding the Integral Universe" (1992)
References:
1.
Rudolph Marcus. Nobel Lectures "Electron Transfer Reactions in
Chemistry: Theory and Experiment". Angewandte
Chemie. v.32, n.8, 1993.
2. Stuart Kauffman. "Origins of
Order". Oxford University Press, Oxford, New York, 1993.
3. . (Critique of Chaotic
Autocatalysis) - Oct '97. I/CI Bulletin NUC-002.
ceptualinstitute.com/nuc/nuc_com002.htm
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