Table of Contents
Introduction
Research Proposal for Origin of Life
Vibrational Dephasing of Methyl Iodide in Sol Gels
A Layman's Discussion of the Research and Its Justification
Application of Zwanzig-Mori Theory to Raman Spectroscopy


Nanopore Origin of Life

Richard E. Wilde

Professor Emeritus, Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas
Contact: Additional Research    email: Richard.Wilde@ttu.edu


I. Introduction

      The question as to the origin of life has never been answered, although it is a very old question, which can be traced back through the Christian antagonist Celsus to the Greek philosopher Epicurus in the third century BCE. It is the intent here to propose an experiment that may reveal the origin of life. All theories of the origin of life suffer from two major deficiencies—they do not propose any experiment that will confirm or reject the theories, and they do not answer the important question of how early life chemistry was protected from the environment. Both questions are answered by the experiment to be described in Sec. II.

      The rationale for the experiment has been found in spectroscopic work on silica sol gels. This work has explored the vibrational relaxation of molecules in confined spaces such as nanopores. The spectroscopic work is detailed in Sec. III in a paper entitled “Vibrational Dephasing of Methyl Iodide in Sol Gels.” Section IV is a layman’s discussion of the research proposal and its justification. Finally, Sec. V discusses Zwanzig-Mori theory and its application to Raman spectroscopy. Scientists should feel free to download the research proposal and use it in grant applications. I am retired from the Department of Chemistry and Biochemistry at Texas Tech University, and I have no resources to carry out the experiments in the proposal. I am making the proposal available, because I believe that it stands a high probability of success and because I want to see the origin of life problem solved.



II. Research Proposal for Origin of Life

I. Introduction

      Theories of the origins of life go back to the ancient Greek philosophers. These philosophers advocated the spontaneous generation of life. That is, life forms arose spontaneously from both organic and inorganic sources. Observations, such as maggots coming from putrid meat, lent support to this theory. The theory of spontaneous generation was overthrown in 1862 by Louis Pasteur. Up to the time of Pasteur, the interest in the origin of life was restricted to present-day life forms such as bacteria, insects, and mice. With the publication of Darwin’s The Origin of Species in 1859, interest shifted to the real origin of all species. As Oparin notes in his Origin of Life, two early theories of the origin of life were the theories of cosmozoa and panspermia. Regarding cosmozoa, Helmholtz wrote in 1874, “If every attempt to create organisms from inanimate matter has failed us, it is entirely within the domain of scientific discussion to inquire whether life had ever been created, whether it is not just as old as matter itself and, finally, whether germs are not carried from one celestial body to another, taking root and developing wherever they find favorable soil.” The theory of panspermia, advocated by Arrhenius in 1903, says that microorganismal spores, which are carried into the upper atmosphere of planets, can be accelerated by solar pressure into outer space, where they travel until they find another planet to populate. These theories are closely related, but no evidence has been presented to show that bacterial spores can survive transport between solar systems or that bacterial spores are present in meteorites on Earth.

     A major step towards understanding the origin of life was made by Oparin in his book, Origin of Life, published in 1936. Although many of Oparin’s conclusions now appear to be simplistic, he was one of the first scientists to propose that life originated through basic chemistry and to outline the chemical steps that may have preceded life. Many of Oparin’s ideas were brought to fruition by Urey and Miller in 1953. The Miller-Urey experiment, which produced amino acids by sparking a mixture of water, methane, ammonia, and hydrogen, gave emphasis to Haldane’s 1929 prebiotic soup theory of biogenesis. Scientists jumped on the prebiotic soup bandwagon in the 1960s and began synthesizing amino acids, sugars, and RNA bases in a prebiotic soup. John Oró at University of Houston found that a concentrated hydrogen-cyanide solution produced adenine when heated. Concentrated solutions of formaldehyde easily produced sugars. However, scientists soon realized that life needed more than random reactions in a chemical soup. It was also becoming apparent that the early atmosphere was not as reducing as Urey and Miller had supposed.

     In the 1980s, a catalytic RNA molecule, called a ribozyme, was discovered by Thomas Cech and Sidney Altman. This discovery gave rise to the theory of the RNA World. According to this theory, the catalytic activity of the ribozyme replaces the protein catalysts that provide the metabolism of all cells. It is well known that protein catalysts are necessary to synthesize DNA and RNA. This was a stumbling block for those scientists who proposed RNA as the earliest cell replicator, since it was unknown which came first, RNA or proteins. The RNA or DNA is necessary to make proteins, but proteins are necessary to make RNA and DNA. With the discovery of ribozymes, it is possible to use RNA as a catalyst for the production of RNA. The RNA World proposes that the first life form was a self-replicating strand of RNA enclosed in some type of lipid membrane. The lipid membrane is necessary to derive free energy by a redox reaction on the surface of the membrane, which sets up an EMF across the membrane. This EMF in turn allows for hydrogen-ion and electron transport through the membrane. In addition, it is known that RNA is susceptible to alkaline hydrolysis, so that it must be protected by a membrane.

      There are many problems with the “RNA World” theory. The formation of a membrane is essential for this theory. It has been suggested that glycerides in the early primordial soup could have formed micelles. These micelles could have trapped simple chemicals such as formaldehyde and amino acids. One problem with any theory that proposes the formation of a vesicle is showing that such vesicles would indeed form under the conditions of a primitive Earth and that, once formed, they would be stable to wave motion and UV radiation. Another problem is finding a mechanism for chemiosmosis across the membrane in order for metabolism to take place. It is not a trivial matter to synthesize a ribozyme inside a vesicle. Many investigators have tackled these problems, but no one has succeeded in producing a membrane enclosing a ribozyme from conditions existing on the primitive Earth.

     An alternative to a vesicle is a surface. Beginning in 1966, A. G. Cairns-Smith speculated that the first life originated on the surface of clays. Clays are layered aluminum silicates with many stacking possibilities. The tubes and vesicles formed in the clays can protect the adsorbed molecules from a hostile environment. It is proposed that the stacking sequence in a crystallized clay can act like DNA in holding information. The clay structure, itself, dictates the growth of the organic molecules adsorbed on its surface. Moreover, the clays would be exposed to all the organic chemicals present in the primitive oceans and ponds. It has also been suggested that surface catalysis of organic reactions can explain the dominance of right-handed D-sugars and left-handed L-amino acids in life forms. To date, no early life forms have been found on clays.

     A break-through in origin of life studies was made in 1977 with the discovery of deep-sea hydrothermal vents. Günter Wächtershäuser seized on the discovery of “black smokers” at hydrothermal vents to formulate his elegant Iron-Sulfur World. This theory revives the surface-catalysis theory of Cairns-Smith, but it substitutes a pyrite surface for a clay surface. Demonstrating a phenomenal knowledge of organic chemistry for a patent attorney, Wächtershäuser published in 1988 a detailed analysis of the origin of life on a surface and its metamorphosis into three-dimensional cells. The energy for the Iron-Sulfur World comes from the pyrite reaction at the hydrothermal vents:

FeS + H2S   →   FeS2 + H2 + energy

The energy is utilized by hydrogen in order to reduce carbon dioxide in seawater:

energy + H2 + CO2   →   HCOOH

The formic acid and associated molecules such as formaldehyde, ketones, alcohols, as well as other acids and their phosphorylated derivatives, attach themselves to the positively charged pyrite surface. Wächtershäuser then sketches the complex chemistry that can occur on the surface, leading to a complete metabolism. The temperatures at the black smokers can be as high as 300°C and the pressures as high as 300 atm. However, within the pyrite the temperatures are expected to be lower, possibly about 150°C. Being surface adsorbed,the molecules are protected from the external heat and ocean currents.

     Not everyone supports Wächtershäuse’s flat life. No one has been able to experimentally verify Wächtershäuser’s model, although parts of it have been subjected to experiment. It is not clear how the metabolism proceeds on an actively forming pyrite surface. In fact, Wächtershäuser admits that “the proposed carbon fixation by pyrite formation is thermodynamically possible but mechanistically obscure.” Our feeling is that the formation of flat life on an actively forming black smoker is tenuous at best, although many of Wächtershäuser’s mechanisms may well be occurring at hydrothermal vents.


II. A New Approach

     The problem, as we see it, is to protect the emerging chemistry of life and its resulting metabolism from the elements of the early Earth—the asteroids, comets, UV radiation, and earthquakes. The best place for this is at the sea bottom. The next problem is an energy source. The hydrothermal vents at the sea bottom provide the energy necessary for chemical reactions through the pyrite reaction. These are the conditions that Wächtershäuser used for his Iron-Sulfur World. However, it seems to us that an actively forming black smoker is an unstable environment for the establishment of life.

     Deep-sea hydrothermal vents occur at mid-ocean ridges. Mid-ocean ridges form when magma emerges onto the ocean floor near rifts along the ridge axes. The crystallized magma forms a new crust of basalt. Black smokers form where mineral-rich sea water flows out through the magma. The formation of black smokers is described by Van Dover [C. L. Van Dover, The Ecology of Deep-Sea Hydrothermal Vents, Princeton University Press, Princeton, N.J., 2000, Sec. 2.5.2]. The first stage in the formation of a black smoker is the precipitation of an anhydrite (CaSO4) tube around the vent fluids. Horizontal flux of iron, copper, and zinc sulfides through the porous anhydrite results in the deposition of these sulfides. As the outer walls cool below 150°C, the anhydrite dissolves, leaving the metal sulfide deposits and a complex system of pores and tunnels.

     It has been assumed by Cairns-Smith and Wächtershäuser that the surface of the crystalline material hosting the organic chemicals is essential for catalytic activity and for directing polymer growth into D- and L-forms. We argue, on the other hand, that life is so ubiquitous and arose so early in geologic time that it was not necessary to have a specific crystalline site. The necessity for such a site would have greatly restricted the probability for the emergence of life. Rather, we argue that it was not the particular crystalline site that was of importance, but rather it was the presence of porous rock that was important, whether this rock was quartz, basalt, anhydrite, or pyrite. It is known that these crystals tend to be porous in the vicinity of deep-sea hydrothermal vents. The pores need not be large. Indeed, we believe that mesoporous (20-200 Å) material may be ideal for the synthesis of early-Earth chemicals. For the small molecules present in the Archean oceans, the confinement effects present in the pores would have had a major influence on the type of chemistry occurring in the pores, and these effects could have selected the chirality of the molecules. In small pores, the polar water molecules tend to form a structured lattice, much as in ice, with molecular relaxation times orders of magnitude slower than for bulk water [C. H. Cho, M. Chung, J. Lee, T. Nguyen, S. Singh. M. Vedamuthu, S. Yao, J.-B. Zhu and G. Wilse Robinson, J. Phys. Chem. 99, 7806 (1995)]. This would have had a major effect on the formation and growth of the early metabolic chemicals. As the molecules grew, they would have migrated to larger pores. Indeed, the distribution of pore shapes and sizes would have been utilized in dictating the type of metabolism taking place in the crystals. In this scenario, there is no need for a membrane, since the pore structure itself provides protection from the elements, while allowing access to nutrients.

     Besides the pyrite reaction, Shock et al. [E. L. Shock, T. McCollom, and M. D. Schulte, Origin of Life 25, 141 (1995)] argue for the energy-favorable reactions

H2S   →   S + H2

S + 4H2O   →   SO42- + 2H+ + 3H2

The energy released in these reactions can appear as vibrational excitations, which then immediately result in a chemical reaction or a transfer of energy to another type of molecule, which itself undergoes reaction. An example was given above where H2 reacts with CO2 to produce HCOOH. These reactions must take place at their energy source near hydrothermal vents. This requires that the pores be situated fairly close to the vents, probably on an off-axis ridge flank, where the temperature is about 150°C. We note that the situation described here would have existed throughout the early oceans, so that there would have been numerous sites experiencing the same conditions and generating the same chemistry. Thus, the early chemicals, which were the precursors of life, would have formed simultaneously over the entire planet.

     We can only speculate on what these precursor chemicals might have been. Most scientists believe that either amino acids and/or nucleotides were formed at an early stage in life’s origin. Wächtershäuser  [G. Wächtershäuser, Microbiology Review 52, 469-480 (1988)] has addressed this in his 1988 paper. He discusses the surface formation of tribonucleic acid (TNA), ribonucleotides, early translation, formation of RNA and DNA, and finally the formation of proteins. Wächtershäuser shows how all-purine TNA structures could have formed. He posits that the TNA structure may be more stable than DNA, since its covalent backbone does not depend on phosphodiester bridge groups, which are sensitive to hydrolysis, and reactive hydroxyl groups are absent. “With the formation of these purine bases, an entirely new functional and structural feature emerges. It is the base pairing between the purine bases of two strands of TNA and the base stacking between the purine base pairs.” Furthermore, “the conditions of surface banding, base pairing, and stacking have the effect of forcing an isotactic regularity. This is the origin of optical asymmetry.” Wächtershäuser further states, “The double-stranded surface-bonded TNA structure has the character of a ribbon crystal. It accumulates as a surface-metabolic end product in massive amounts and with very high molecular weights.”

     The formation of surface-bonded ribonucleotides (RNs) is postulated next by Wächtershäuser, followed by an autocatalytic translation pathway, whereby the TNA and RNs promote the synthesis of their bases. “TNA cannot replicate by modular template copying, since it is not composed of nucleotides which can exist as stable monomers. TNA grows by terminal extensions, and it changes its sequence by purine modifications.” Wächtershäuser  then envisions TNA-TNA ribbon structures being replaced by TNA-RNA structures. The RNA resists hydrolysis by being bonded to the stable TNA. The RNA can leave the surface and fold. Once folding occurs, the advent of RNA-dependent translation cannot be far behind. This is followed by the formation of DNA. Finally, amino acid pathways in surface-metabolic representation are discussed. The transition from a surface metabolism to a cellular metabolism can explain the appearance of folded proteins.

     Hennet et al. [R. J. C. Hennet, N. G. Holm, and M. H. Engel, Naturwiss. 79, 361 (1992)] showed the abiotic synthesis of amino acids under simulated hydrothermal conditions at 150°C and 10 atm. Starting from a gas-phase mixture of CO2 and H2, an aqueous phase of KCN (0.19 M), NH4Cl (0.23 M), CH2O (0.18 M), and HCl (0.08 M), and a mineral phase consisting of pyrite, pyrrhotite, and magnetite, the reaction produced aspartic acid, serine, glutamic acid, glycine, alanine, and isoleucine. A criticism of this reaction is that the starting chemicals are more concentrated than would have been the case for the early hydrothermal vents. Also, the pressure is less than observed on the sea floor. It is noteworthy that, when the mineral illite was substituted for pyrite, pyrrhotite, and magnetite, the amino acids were all L-enantiomers.

     Yanagawa and Kobayashi [H. Yanagawa and K. Kobayashi, Origins Life Evol. Biosphere 22, 147 (1992)] prepared amino acids from simulated deep-sea hydrothermal-vent water containing dilute concentrations of Fe(NH4)2(SO4)2, MnCl2, ZnCl2, CuCl2, CaCl2, BaCl2, and NH4Cl. This solution was heated with a gaseous CH4-N2 mixture in an autoclave at 325°C for 1.5-12 hr at ambient pressure. The major amino acids produced were glycine, alanine, and sarcosine. When the metal ions were removed from the reaction mixture, the yield of amino acids fell precipitously.

     It is generally agreed that ammonia is essential for the formation of amino acids. However, it is thought by geochemists that the Archean atmosphere contained only traces of ammonia. To circumvent this problem, it was shown by Jay Brandes et al. [J. A. Brandes, N. Z. Boctor, G. D. Cody, B. A. Cooper, R. M. Hazen, and H. S. Yoder, Jr., Nature 395, 365 (1998)] that hydrothermal vents could have produced ammonia by abiotic nitrogen reduction. This reduction would have occurred at high pressure and at temperatures ≤ 800°C in the Earth’s basalt mantle above the magma. Brandes’ experiments make a good case for NH3 being present in the early hydrothermal vents.

     Sugars are considered necessary for early metabolic processes. No empirical prebiotic synthesis of sugars has been shown, but the formose reaction is favored for giving rise to sugars by continuous addition of formaldehyde:

2CH2O → CH2(OH)CHO → CH2(OH)-CHOH-CHO →

It is known that anaerobic chemosynthesis takes place in magma when seawater hits it:

2CO2 + 6H2 → CH2O + CH4 + 3H2O

producing both formaldehyde and methane.

     A possible prebiotic route to nucleic-acid bases has been described by Oró [J. Oro, Biochem. Bioph. Res. Commun. 2, 407 (1960)] and Oró and Kimball [J. Oro and A. P. Kimball, Arch. Biochem. Biophys. 94, 221 (1961); 96, 293 (1962)]. These reactions require HCN, which seems to be ubiquitous, having been found in the Murchinson and other meteorites. Zahnle [K. J. Zahnle, J. Geophys. Res. 91, 2819 (1986)] has suggested that HCN could have been formed on Earth photochemically in a weakly reducing atmosphere containing small amounts of methane. The problem with proposing the formation of nucleic-acid bases in the ocean from hydrogen cyanide is that hydrogen cyanide is easily hydrated to formic acid and ammonia. For this reason, we believe (along with Wächtershäuser) that nucleic-acid bases formed late in the development of the first cell.

     We are not suggesting that pore metabolism would follow necessarily along the lines suggested by Wächtershäuser or the other researchers mentioned above. Since no experiments have been done under deep-sea hydrothermal-vent conditions, it is impossible to know what type of chemistry would occur in pores at 150-200°C and 300 atm.


III. Proposed Research

A. Chemicals and equipment necessary for the research

     The object of the proposed research is to duplicate what we believe to be the conditions at the hydrothermal vents of the early Earth in order to study the chemistry of these vents. The chemicals believed to be present are listed in Table I below [H. Elderfield and A. Schultz, Ann. Rev. Earth Planet. Sci. 24, 191 (1996), Table 14]. The porous material will be a silica sol gel. We have had experience in the preparation and study of silica sol gels using Raman spectroscopy and BET adsorption analysis to determine pore sizes [T. R. Bryans, R. E. Wilde, M. W. Holtz, and E. L. Quitevis, Chem. Phys. Lett. 314, 459 (1999)]. Hence, we consider a silica sol gel to be an ideal material for the study of the chemistry occurring in pores at deep-sea hydrothermal vents. The pore-size distribution can be determined, and the optical nature of the silica sol gel enables the pore material to be studied by Raman spectroscopy. In addition, the surface of the sol gel can be modified to test for surface effects. Other materials that may be studied include porous basalt, Wyoming Bentonite, Iceland Nontronite (all three samples provided by Prof. Necip Guven), and illite.

Table I. Chemicals thought to have been part of the early deep-sea hydrothermal vents.

Element/Compound

Form

Conc. (mmol/kg)

Conc. (g/kg); press. (torr/L)

H2S

Gas

12,200

225 torr

H2

Gas

1000

18.4 torr

CO2

Dry Ice

16,700

0.735 g

CH4

Gas

100

1.84 torr

Mn

MnCl2

1140

1.44 x 10-2 g

Fe

FeCl2.4H2O

6470

1.29 g

Be

BeCl2.4H2O

0.0385

5.85 x 10-6 g

Zn

ZnBr2

106

2.39 x 10-2 g

Cu

CuCl2.2H2O

44

7.48 x 10-3 g

Ag

AgNO3

0.038

6.46 x 10-6 g

Pb

PbCl2

0.359

9.98 x 10-5 g

Co

CoCl2.6H2O

0.227

5.40 x 10-5 g

Si

Silica sol gel

22,000

 

Al

AlCl3.6H2O

20

4.82 x 10-3 g

Ba

BaCl2.2H2O

43

1.05 x 10-2 g

Cs

CsBr

0.202

4.30 x 10-5 g

Li

LiCl

1322

5.55 x 10-2 g

Rb

RbCl

33

3.99 x 10-3 g

Ca

CaCl2

55,000

6.11 g

Sr

SrCl2.6H2O

87

2.32 x 10-2 g

B

B2O3

565

1.97 x 10-2 g

As

As2O5

0.452

5.20 x 10 –5 g

Se

SeCl4

0.072

1.59 x 10-5 g

P

P2O5

0.5

3.55 x 10-5 g

SO4

Na2SO4

600

8.52 x 10-2 g

*N2

Gas

17.9

0.328 torr

*Na

NaCl

457,000

26.7 g

*F

NaF

68.4

2.87 x 10-3 g

*Cl

NaCl

542,000

31.7 g

*Br

NaBr

812

8.36 x 10-2 g

*I

NaI

0.472

7.08 x 10-5 g

CH2O

Solid

100

3.00 x 10-3 g

                            *Concentration in seawater.    Same as CH4 concentration.

     A high-pressure batch reactor will be purchased for this research, since the batch reactors in our Chemistry Department are not available for extended periods of use. The requirements for a batch reactor are the following:

      1.  The volume must be 1 L.
      2.  The reactor must accept solid, aqueous and gaseous phases, the mixture being pressurized up to 300 atm.
      3.  Provision must be made to extract liquid samples of 40 mL under pressure.
      4.  The temperature range is room temperature to 200°C.
      5.  The reactor lining must be inert.

Suitable reactors are available from Autoclave Engineers, Erie, PA, and from CTP Corporation, Northport, NY.


B. Preparation of deep-sea environment

     A standard aqueous solution representing the chemicals thought to be in the early deep-sea hydrothermal vents, taken from Table I, will be prepared in a 5-L batch (excluding the gases). Those chemicals present in less than 1.0 μmol/kg will be excluded. The silica sol gel will be prepared utilizing a two-step base-catalyzed hydrolysis of tetraethyl orthosilicate (TEOS):

      1.  Stir 208 g TEOS, 216 g H2O, 92 g EtOH, and 1 g 1N HCl for 40 min at 40°C giving a mol ratio H2O:EtOH:TEOS:HCl = 120:20:10:0.1.
      2.  Transfer this mixture to an ice bath, add 216 g H2O and 5 mL-25mL of 1N NH4OH and stir until mixed.
      3.  Pour this mixture into a container and cover tightly.
      4.  After gelation, age at 54°C for 2-4 weeks. Uncover the sample until the gel shrinks and hardens.
      5.  Heat in a muffle furnace at 0.5°C/min to 800°C for 24 hr.


C. Preparation of the batch reactor

      1.  The silica sol gel (or mineral) will be placed in the glass-lined reactor. The reactor will be evacuated, sealed, and heated overnight at 240°C.
      2.  800 mL of the deep-sea aqueous solution will be added to the reactor through a charging port.
      3.  Gases will be added through a gas-inlet port to bring the pressure to atmospheric.
      4.  The reactor will be pressurized with ultra-pure water to 300 atm.
      5.  The reactor will be heated to 150°C.


D. Analysis of batch reactor solution

      Periodically, 40-mL samples will be withdrawn for analysis using LCMS and GCMS instruments. These analyses will be compared with a standard obtained from an identical experiment without the silica sol gel or mineral phase. The length of time between samples and the total time of the experiment will depend on the results of the analyses. Because the system is closed, it will be necessary to periodically cool and drain the aqueous solution and add fresh solution and gases and reheat. It is anticipated that the experiment could run for several months before enough product is collected in the mineral phase for analysis.


E. Analysis of the mineral phase

      There are two methods for analyzing the mineral phase. If the mineral is silica sol gel, a special sol gel pellet will be prepared that will fit into a Raman spectrophotometer, so that the pores can be studied in situ. Another method involves flushing the mineral with water to extract the contents of the pores and then analyzing the liberated chemicals by LCMS. The mineral phase can be studied also by means of surfaced enhanced Raman spectroscopy using a Raman microscope spectrometer.


IV. Results To Be Expected

      Although not part of Table I, ammonia will be added to the chemicals in increasing concentrations in order to produce amino acids. Cyanide has not been added to the chemicals of Table I, because cyanide undergoes hydrolysis in water, and for this reason would not have been present in the Archean ocean. Hence, cyanide could not have been available for the formation of amino acids through the Strecker synthesis. Also the formation of the nucleoside pyrimidine and purine bases could not have been formed via the HCN pathway.

      We will be looking for simple sugars via the formose reaction. Thioesters may be present also and may, in turn, form amino acid multimers via reactions such as

CH2(NH2)COOH + RSH + energy   →   CH2(NH2)COSR + H2O

CH2(NH2)COSR + CH2(NH2)COOH   →   CH2(NH2)CONHCH2COOH + RSH

      The phosphate in Table I will be present as H3PO4, but its concentration at hydrothermal vents is too small to be effective in providing the phosphate necessary for nucleotides or for phospholipid membranes. Besides, the addition of monophosphate to simple sugars would not have been energetically favorable. For these reasons, phosphate will be left out of our hydrothermal-vent chemicals.


V. Experiments Put in Perspective

      The research described in Sec. III is aimed at elucidating the chemistry at the deep-sea hydrothermal vents. We believe that the chemistry leading to life will occur in our silica sol gel pores. However, only so much chemistry can be done under hydrothermal-vent conditions; the formation of nucleotides, polypeptides, proteins, and phospholipid membranes came later under different conditions. To see how this happened, we must look at early Earth and at how geothermal events affected the origin of life.

      We note that the early earth was molten when formed 4.5 billion years ago. The first indication that we have of a solidified Earth is the Eoarchean Era of the Archean Eon. The Eoarchean Era lasted from 3.8 billion years ago to 3.6 billion years ago. The most plausible model of crustal formation [Kent C. Condie, Plate Tectonics & Crustal Evolution, Pergamon Press, New York, 1982] predicts linear continental growth beginning 4.1 billion years ago, with 10% of the present continents having been formed by 3.6 billion years ago. The Earth cooled enough for oceans to form before 3.8 billion years ago. It has been speculated [T. E. Zegers, M. J. de Wit, J. Dann and S. H. White, Terra Nova 10, 250 (1998)] that the first super-continent, Vaalbara, appeared in the Eoarchean Era about 3.6 billion years ago and broke up completely around 2.8 billion years ago in the Mesoarchean Era. The oldest rock formation on earth, the Isua greenstone belt, appeared during the Eoarchean Era around 3.8 billion years ago. Hence, we have little information about plate tectonics before the Mesoarchean Era. We assume that hydrothermal vents appeared about 3.8 billion years ago, giving rise to primitive chemistry. There were 200 million years for this primitive chemistry to occur and establish itself in basalt pores. As the volcanic ridges spread, these pores would have been covered up and isolated from further exposure to the external conditions.

      There was tectonic-plate activity 3.6 billion years ago, leading to uplift of the ocean floor to form the first super-continent of Vaalbara, probably at the North Pole. The formation of Vaalbara would have exposed the former deep-sea basalt to shallow seas, tide pools, and crucial phosphate compounds. Being protected by the pores, the early chemicals were exposed to pyrophosphate and to what Herric Baltscheffsky [H. Baltscheffsky, J. Theor. Biol. 187, 495 (1997)] has called the “Pyrophosphate World.” It is believed that pyrophosphate was a primordial energy-rich molecule, which preceded ATP as a source of energy for primordial life. In the shallow seas and tide pools of Vaalbara, the heating and drying of phosphate solutions would have produced pyrophosphate. A problem with the Pyrophosphate World is the limited amount of phosphate in the ocean and consequently the limited amount of pyrophosphate that could be produced. However, the phosphate compounds could have entered the basaltic pores and established phosphorous chemistry in the pores. Because of the small concentration of phosphorous available to the pores, a long time would have been required for enough phosphorous to accumulate to produce phospholipid membranes. It is believed that stromatolites, which are fossilized microbial mats, appeared 3.5 billion years ago. This gives about 100 million years for the phosphate concentration to build up in the pores to form membranes, which then moved outside the pores, where the chemistry was driven by sunlight. It is significant that the cell chemistry that led to the formation of nucleotides and proteins within the membranes and that was driven by both sunlight and pyrophosphate, occurred at the North Pole, where the sunlight was weak enough not to destroy the developing life. It appears, once membranes moved outside the pores, that prokaryotes developed rapidly.

      Future experiments to test the influence of phosphate require that the research of Sec. III be modified by increasing the concentrations of phosphate and pyrophosphate substantially at ambient temperature and pressure and in the presence of simulated sunlight. If phospholipids are found in this research, experiments would have to be devised to check for phospholipid vesicles and for the chemicals within them. These chemicals would be those of a true life form.



III. Vibrational Dephasing of Methyl Iodide in Sol Gels

Vibrational Dephasing of Methyl Iodide in Sol Gels

Richard E. Wilde and Edward L. Quitevis
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409


Abstract

      The ν3 vibrational band of methyl iodide adsorbed in silica sol gel pores has been recorded using Raman spectroscopy. Pore sizes between 51 Å and 20 Å have been studied. The isotropic band has been Fourier transformed to give the vibrational autocorrelation and memory functions. Autoregressive time-series analyses of the memory functions associated with the pores have provided the homogeneous and inhomogeneous spectral second moments. The results of this study suggest that the vibrational relaxation in the pores is mainly through resonant vibrational energy transfer. There is evidence that some pores promote direct vibrational depopulation through Coriolis coupling between the ν3 and ν6 modes.


Introduction

      There have been several studies of the dynamics of molecules in confined spaces [1-12]. There are two reasons for these studies. One is to understand the behavior of molecules confined in mesopores, which are pores with diameters equal to or greater than 20 Å. The other is to understand the nature of the mesopores. Techniques used to probe the molecular dynamics include NMR [1-3], Raman scattering [4-9], and optical Kerr effect (OKE) spectroscopy [10-12]. These studies have concentrated on molecular behavior in nanoporous silica glasses. Silica glasses have been chosen because it is possible to produce a range of pore sizes down to 12 Å, and the clear glasses allow for optical studies. Efforts are usually made to correlate the results of these studies with the nature of the sol gels as determined by BET adsorption isotherms. It is routine to determine experimental BET isotherms. The problem is the explanation of the isotherms. Models to explain adsorption isotherms usually assume a simple pore structure within the sol gel. Complex models take into account differing pore sizes, branching pores, and bottlenecks within pores. Within any sol gel, surface tension effects will affect the behavior of the adsorbent. Surface tension forces will cause a compacting of the adsorbed molecules in the pores and will align the molecules at the pore surface. These effects must appear in the vibrational relaxation of the adsorbed molecules. If surface effects are important, one would expect to see a difference in relaxation between the molecules in the bulk liquid of the pore and the molecules at the surface of the pore.

      Methyl iodide has been used to study molecular behavior in silica sol gels by Lee et al. [6], by Bryans et al. [9], and by Loughnane and Fourkas [12]. Methyl iodide is an ideal liquid for the study of vibrational relaxation. Its Raman spectrum is relatively free of overlapping bands in the regions of the n2 and n3 vibrational modes. The vibrational relaxation of neat liquid methyl iodide has been well characterized [see Ref. 15 and references therein]. Methyl iodide, being a polar but non-wetting liquid, should interact only weakly with the surface of the silica sol gel.

      Lee et al. [6] used the Raman scattering effect to study the confinement of methyl iodide in silica sol gels. These investigators recorded the polarized Raman spectra of the ν2 methyl deformation band of methyl iodide in pores ranging from 24 to 140 Å diameter. Band-center frequencies and bandwidths were measured for both neat and isotopically diluted methyl iodide. The findings of Lee et al. showed that (1) the band centers (both neat and isotopically diluted) shifted to higher frequencies with decrease in pore size, (2) the bandwidths decreased in the isotopically diluted solutions compared to the neat liquid in all pores, and (3) the bandwidths increased (for both neat and isotopically diluted solutions) with decrease in pore size. According to these authors, the shift of the polarized band center with pore size is a non-coincidence effect arising from resonant vibrational energy transfer (resonant V-V transfer), as suggested by Logan [13]. The resonant V-V transfer is measured as the difference between the bandwidth in the neat liquid and the bandwidth in the isotopically dilute solution. It was found that the resonant V-V transfer was less in the sol gel pores relative to the liquid outside the pores. In other words, the vibrational relaxation tends to slow when the liquid is confined to the pores. The final conclusions of Lee et al. are “that the liquid methyl iodide confined to very small pores has a higher reorientational order and slower resonant energy transfer relaxation rates.”

      Bryans et al. [9] recorded the Raman scattering by the ν2 band of methyl iodide in a 50-Å diameter silica sol-gel pore. This study utilized an autoregressive analysis to find the homogeneous and inhomogeneous contributions to vibrational dephasing. The analysis showed an increase in the inhomogeneous second moment of the confined molecules by a factor of 2.6 over the bulk liquid and an increase of the homogeneous second moment of the confined molecules by a factor of 1.4 over the bulk liquid. The large increase of the inhomogeneous second moment of the confined liquid was attributed to the non-uniform nature of the silica pore surface. This study also emphasized the importance of inhomogeneous relaxation, which had been ignored by Lee et al.

      Loughnane and Fourkas [12] used the optical Kerr effect to measure the orientational time correlation function of methyl iodide in silica sol gels in pores of 24-, 42-, and 83-Å diameter. For methyl iodide, the orientational motion represents the tumbling of the molecule. The neat liquid gave a single exponential decay with a relaxation time of 2.1 ps at 291 K. The sol gels showed a biexponential decay. In addition to the bulk relaxation, the pore-confined liquid gave decay times of 6.4 ps for the 83-Å pore, 7.2 ps for the 42-Å pore, and 8.5 ps for the 24-Å pore. These times increase significantly for lower temperatures. The biexponential decay was interpreted as representing molecules in the bulk liquid and molecules on the surface of the pores, the surface molecules relaxing slower than the bulk molecules. It was estimated that the percentage of molecules on the surface are <10% for the 83-Å pore, ~10% for the 42-Å pore, and ~30% for the 24-Å pore. These authors favor the model of Korb et al. [3], which has the reorientation perpendicular to the pore surface. Supposedly, in this model, the iodine atom would be on the surface, and the methyl group would be in the bulk liquid.

      In this paper, we extend our study of the Raman scattering of methyl iodide to the ν3 band and investigate several pore sizes. The advantages of studying the ν3 symmetric methyl-iodine stretch include a stronger band, allowing smaller pore sizes and dilution studies, and the ability to draw on our extensive study of the Raman scattering of the ν3 band, neat and diluted [14] and at high pressure [15].


Experimental Techniques

      The recording of the Raman spectra has been discussed previously [14] and will not be repeated here. Pore sizes were determined by using the Brunauer-Emmet-Teller (BET) method on a NOVA 1000 surface adsorption instrument.


Treatment of Data

      Sol gels are new territory for us compared with neat liquids, and there are many points to be considered when analyzing Raman data from sol gels. It cannot be taken for granted that the system is isotropic. If the system is anisotropic, an isotropic intensity cannot be obtained from the polarized and depolarized components. Anisotropy may be indicated by extraordinarily large or small depolarization ratios or by a failure to model the experimental vibrational correlation function within experimental error. In order to get an isotropic band, the polarized and depolarized spectra must be recorded and smoothed in order to determine the truncation points on the wings of the bands. The polarized and depolarized spectra then must be separated carefully from the background Rayleigh scattering. The isotropic band is calculated from the polarized and depolarized intensities, Ipol and Idep, by use of the relation Iiso = Ipol – (4/3) Idep. This calculation may not give a smoothly varying isotropic band, in which case further smoothing must be done in such a manner as not to distort the band. This whole process requires time-consuming and careful work if errors are not to be introduced into the isotropic band and into the resulting vibrational autocorrelation function. The isotropic bands are Fourier transformed to give the vibrational autocorrelation functions. The vibrational autocorrelation functions are checked by fitting the correlation functions within experimental error (±0.010) by the method of Cohen and Wilde [16; see below]. Failure to fit the correlation functions indicates errors in the construction of the isotropic band; the band is then either corrected or discarded.

      A further check on the isotropic band is the autoregressive time series analysis of the memory function, to be described below. This analysis should severely restrict the order and lag time, and the three lowest frequencies should give a consistent M2inh value. Any problem at this stage may indicate errors in recording the band or an inherent problem with the sol-gel environment, such as the presence of both bulk and surface methyl iodide molecules or anisotropy. Only those spectra that have survived the checks up to this point are reported in this paper.


Analysis Techniques

      The studies of previous workers [4-8] focused on the measurements of bandwidths to obtain vibrational relaxation times and on the frequencies at the band center to obtain frequency shifts. They assumed Lorentzian band shapes; this assumption ignores the wings of the bands and automatically puts the molecules into the fast modulation regime. We measure the entire band, both polarized and depolarized components, to obtain the isotropic band, from which the vibrational autocorrelation function can be calculated. Measuring the entire band, rather than just the center of the band, puts added responsibility on the analyst, as discussed above. This procedure requires that the experimental spectra be accurately recorded, that the truncation points of the bands be determined within 10 cm-1 by comparing the spectra with baseline spectra, that the smoothing of the data not distort the bands, and that anomalies arising in the application of Iiso = Ipol – (4/3) Idep be minimized. A mistake anywhere in this procedure will render the resulting vibrational autocorrelation function useless. Fortunately, we have built-in checks along the way in our analyses to test the reliability of our spectral measurements and our subsequent calculations.

      Wilde and Zyung [14] have described our experimental equipment and techniques, including the treatment of hot bands, and have described in detail the methods of analysis. Consequently, our discussion can be kept short. In the fast modulation regime, an isotropic Raman intensity can be obtained from a normalized intensity Iiso (ω) at each frequency ω: Iiso (ω) = Ipol (ω) – (4/3) Idep (ω), where Ipol is the polarized intensity and Idep is the depolarized intensity. Fourier transformation of Iiso (ω) gives the vibrational autocorrelation function, C(t). The vibrational autocorrelation function is related to memory functions Ki(t) via a set of coupled Volterra equations:


EqnSet1.jpg


The memory functions represent autocorrelation functions in a Hilbert space of dynamical variables, where C(t) is in the “slow” space, and the Ki(t) are in a succeeding set of faster subspaces [17]. It is possible to model the experimental correlation function beginning with a Gaussian autocorrelation function, which represents the static lattice that the molecule sees at very short times (<< 1 ps):

C0(t) = exp(-M2 t2/2)                 (2)

Kn(t) = κn Kn0(t) exp(-t/τ)         (3)

where κn = Kn(0)/Kn0(0). Using the Volterra equations in reverse order, it is possible to calculate a real C(t), which can then be compared with the experimental C(t). The experimental and real vibrational autocorrelation functions should agree within experimental error (0.010). If the standard deviation is much greater than this, it is an indication that the experimental autocorrelation function is in error or else the memory-function procedure has not been taken far enough. This can happen if the procedure is stopped at n = 2. Going to n = 3 should give a good correlation function. This procedure is not sensitive to n > 3. We notice that the Poisson modulation given by Equation (3) renders Kn+1 a delta function, which represents a Markovian process. Thus, it is necessary to take the procedure far enough to get Markovian behavior.

     We have found it necessary to go through this memory function calculation and compare the calculated with the experimental autocorrelation function C(t) for each pore size studied. This procedure certifies that the isotropic band is correct and that the autocorrelation function is a valid function. A typical comparison is shown in Figure 1, and the corresponding experimental memory function is shown in Figure 2.


Figure1.jpg

Figure 1. The experimental (♦) and calculated (■) vibrational autocorrelation functions for the 25-Å pore silica sol gel.



Figure2.jpg

Figure 2. The memory function for the 25-Å pore silica sol gel.



      At very short times, the vibrational autocorrelation function is Gaussian, reflecting the static distribution of the inhomogeneous environments. Then, as pure dephasing takes over in the fast modulation limit, the correlation function becomes exponential, the surrounding environment becomes homogeneous, and the spectral band narrows into a Lorentzian shape near the band center. The wings of the band are Gaussian, corresponding to the short-time Gaussian behavior of the autocorrelation function. Beginning in 1980, attempts were made to separate the homogeneous and inhomogeneous components of the autocorrelation function [18]. These attempts were not successful. In 1984, Wilde [19] suggested separating the homogeneous and inhomogeneous processes at the memory function level, where the effects are additive. It turns out that the memory functions cannot be completely separated, but it is possible to separate the second spectral moments into homogeneous and inhomogeneous components [20]. This method utilizes that fact that any autocorrelation function can be represented by a time series. The time series, in turn, can be determined by an autoregressive analysis [21]. The memory function, being an autocorrelation function of the fast-subspace variable, can be expressed as a sum of damped cosine terms:

K(t) = Σ bi exp(- ηit) cos(Ωit+θi)

The values of the parameters bi, ηi, Ωi, and θi are chosen by an autoregressive parsimonious analysis to fit the memory function. The principle of parsimony dictates that a minimum number of parameters are to be used. The model itself dictates that the values of these parameters be severely restricted. The only one of these parameters that has physical significance is the frequency term Ωi (rad/ps). It turns out that the three lowest frequencies represent the static inhomogeneity. The higher frequencies are homogeneous and represent the frequencies of the power spectrum of the force autocorrelation function for the intermolecular forces. There must be a clear time and frequency separation between the homogeneous and inhomogeneous processes. Failure to get a clear time separation shows up in three inhomogeneous second moments that differ from one another by more than the experimental uncertainty. As shown in Ref. 20 (Fig. 2), the three lowest frequencies are associated with the same inhomogeneous second moment. Failure to get the same inhomogeneous second moment can also occur if more than one type of oscillator is present, reflecting different environments for the oscillators.

      The inhomogeneous process is a Gaussian process that gives directly an inhomogeneous second moment M2inh. The homogeneous contribution to the isotropic second moment M2iso is obtained as a difference: M2hom = M2iso - M2inh. Thus, instead of separating the memory functions into homogeneous and inhomogeneous parts, it is the second spectral moment that separates. The result of a typical autoregressive time-series analysis is shown in Table I .

Table I. Result of the autoregressive time-series analysis for the 25-Å pore silica sol gel.

Term

1

2

3

4

5

6

7

8

9

10

11

12

b

0.10

0.10

0.08

0.08

0.07

0.08

0.09

0.09

0.09

0.09

0.07

0.07

h

0.39

0.43

0.48

0.50

0.57

0.59

0.62

0.59

0.52

0.48

0.43

0.42

W

0.36

1.08

1.72

2.47

3.11

3.77

4.38

4.93

5.58

6.25

6.92

7.72

q

0.01

0.08

-0.15

0.16

0.09

0.17

0.13

-0.18

-0.14

-0.15

-0.23

0.08

 

Results

      The results of analyses of the n3 band of methyl iodide in sol gels of various diameters are listed in Table II. Also listed are the results of analyses of 0.3 and 0.6 mole-fraction solutions of methyl iodide in n-pentane. The isotropic second moments are accurate to 15 %. We do not report the measurement of the band centers, since our instrument has a backlash in the drive screw that limits the wave number precision to ±0.5 cm-1.

Table II. Results of the vibrational dephasing studies of methyl iodide in silica sol gels.

Pore Diam.

      Å

FWHM

   cm-1

Vib. Relax.

Time (ps)

Mem. Fcn Relax

     Time (ps)

Isotropic M2

      cm-2

Inhomo. M2

      cm-2

Homo. M2

      cm-2

      51

   6.9

     1.9

         0.26

       70

       17

       53

 51 (0.3 mf)

   5.9

     2.5

         0.74

       23

         9

       14

      31

   6.6

     2.2

         0.82

       17

         0

       17

 31 (0.6 mf)

   6.2

     2.4

         1.04

       13

         0

       13

      30

   6.3

     2.0

         0.41

       41

         0

       41

      25

   6.6

     1.8

         0.28

       72

       11

       61

      20

   7.1

     1.6

         0.26

       98

       15

       83


      In order to understand the significance of Table II, it is necessary to put the results into perspective. The Raman spectra of the n3 band of neat liquid methyl iodide has FWHM = 5.3 cm-1, a vibrational relaxation time of 2.6 ps, a memory function relaxation time of 0.30 ps, M2iso = 36 cm-2, M2inh = 14 cm-2, and M2hom = 22 cm-2. In a 0.24 mf solution of n-pentane, the band is narrowed significantly, the vibrational relaxation time increasing accordingly, M2iso decreases significantly, but M2inh remains unchanged, leading to a marked decrease in M­2hom. The conclusion to be drawn is that the n-pentane solution eliminates most of the resonant V-V transfer and most of the long-range, slowly varying dipolar interaction, which contribute to the homogeneous broadening.

      The results of Table II can now be understood. The 53 cm-2 for the homogeneous second moment in the 51-Å pore sample reflect mainly the increased resonant V-V transfer in the sol gel pores. The inhomogeneous second moment is essentially unchanged from the neat liquid. The autoregressive analysis gives no indication of surface adsorbed methyl iodide. The homogeneous second moment of the methyl iodide/n-pentane solution decreases to 14 cm-2 in the sol gel, suggesting that most of the resonant V-V transfer is removed in the n-pentane solution.

      The 30-Å and 31-Å pore samples are near the borderline between mesoporosity and microporosity. In these samples, the inhomogeneous broadening vanishes, leaving only homogeneous effects to dictate the band shape. The situation does not change for the methyl iodide/n-pentane solution in the 31-Å pore sample. The complete vanishing of inhomogeneity is very unusual. A possible explanation has been suggested by Laubereau et al. [22] and Velsko and Oxtoby [23]. The explanation involves rotationally induced vibrational depopulation. The theory has been worked out by Velsko and Oxtoby, who “show that the direct dynamic coupling of vibrations by the rotational angular momentum must be considered when the rotations are strongly coupled to the bath, as in the case of liquids.” This interaction is known as Coriolis coupling, and for methyl iodide, Jahn’s rule allows the n3 CH3-I stretch at 525 cm-1 to couple with the n6 CH3 rocking mode at 880 cm-1. In order for this to happen, the rotation must be strongly coupled to the bath. To understand what is meant by a strong coupling to the bath, we must briefly consider the Zwanzig-Mori formalism.

      Our approach to vibrational relaxation is based on the Zwanzig-Mori formalism as discussed by one of us [24]. This formalism utilizes a Hilbert space of dynamical variables. The variables are assigned to a particular space depending on the speed of relaxation. The slow variables occupy the primary space. For our purposes, the slow variables are the n3 normal mode and any dynamical variables that relax on the same time scale (1-20 ps) as the normal mode. The tumbling of the methyl iodide figure axis is usually a slow variable and, for ethane and methyl iodide, has been identified as being responsible for the necessity of a third-order memory function procedure to fit the observed vibrational autocorrelation functions. The spinning motion is a fast variable that relaxes on the time scale of the memory function (0.1-0.5 ps) and is responsible for the so-called pure dephasing. The fast subspace constitutes the bath in the Zwanzig-Mori formalism. Processes that relax on a time scale longer than 20 ps such as long-range, slowly varying dipolar forces are so slow that they do not introduce frequency dependence into the memory function. These slowly varying forces are essentially static forces as far as the normal mode is concerned, and as a result, these forces contribute to the inhomogeneous broadening.

      Loughnane and Fourkas [12] used the optical Kerr effect to study the orientational dynamics of methyl iodide neat and in silica sol gels. These investigators observed two reorientational relaxation times in the sol gels. They observed a bulk decay time for the neat liquid of 2.5 ps at 291 K. In the sol gels, they observed this bulk decay time and a second decay time of 6.4 ps (83 Å diameter), 7.2 ps (42 Å diameter), and 8.5 ps (24 Å diameter) at 291 K. The second decay time was attributed to surface adsorbed methyl iodide. If this model is correct, then we should see two types of methyl iodide molecules, and our autoregressive analysis would not yield a single value for the inhomogeneous second moment. However, we have seen no indication of surface adsorbed molecules.

      It is clear that there are two rotational relaxation times for methyl iodide in silica sol gels. Loughnane and Fourkas “ascribed the slower relaxation process to hindered reorientation of methyl iodide molecules on or near the surfaces of the pores.” Our results suggest that there are two reorientation relaxation processes—a short-time relaxation involving small-angle orientational diffusion and a long-time relaxation involving large-angle orientational diffusion. We suggest that the reorientational diffusion time of the neat liquid splits into the short-time and long-time components in the pores. The smaller the pore, the larger is the separation of decay times. The conditions within the sol gel dictate what these relaxation times will be. If the small-angle diffusion moves into the fast subspace in the Zwanzig-Mori formalism, then there will indeed be a strong coupling with the bath. The longer relaxation times (0.41 and 0.82 ps) for the memory function in the 30-31-Å pores suggest that a slower dynamical variable has moved into the fast subspace. According to the theory of Velsko and Oxtoby, this is the situation necessary for Coriolis coupling and vibrational depopulation. We have no idea what features of the sol gel would promote Coriolis coupling, but our results for the 30-31-Å pores strongly suggest such a coupling.

      The 20- and 25-Å pores show the expected behavior of a large homogeneous second moment and an inhomogeneous second moment in the usual range of 10-15 cm-2. The large homogeneous second moment reflects the influence of confinement and increased resonant V-V coupling. It may be wondered why the smallest pores do not show Coriolis coupling. We have no answer for this. We note that the silica sol gels are complex structures and that the average pore size is only one characteristic of the sol gel. The average pore size gives no information about the branching and irregular structures within the sol gel.

Conclusions

      This study has shown the advantage of going beyond the reporting of only the band origin and bandwidth. The reporting of the homogeneous and inhomogeneous second spectral moments has given insight into the mechanisms of vibrational relaxation within the pores of the silica sol gels. The homogeneous broadening, due mainly to resonant V-V transfer, is accentuated in the pores. In this respect, the confinement in the pores acts much like an increase in pressure on the neat liquid. There is no evidence for surface adsorbed methyl iodide molecules in the pores. This may not be particularly surprising, since methyl iodide is a non-wetting liquid.

      We suggest that the bimodal relaxation observed in the OKE study is a separation of the rotational diffusion into small-angle and large-angle rotations. It is further suggested that this separation can move the small-angle diffusion into the fast Hilbert subspace of Zwanzig-Mori formalism. This results in a purely homogeneous vibrational depopulation via Coriolis coupling.

References

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IV. A Layman’s Discussion of the Research Proposal and Its Justification

      There are three critical components for the development of life—water, amino acids, and nucleic acids. In addition, it is necessary that these components be combined in a cell membrane. Since life is thought to have originated shortly after the formation of Earth, it must be shown how life survived the conditions on the early Earth, which included meteor bombardment, volcanic eruptions, earthquakes, continental uplift, ultraviolet radiation, and ocean currents. The first serious effort at an explanation was the 1953 Urey-Miller experiment, wherein amino acids were produced by sparking a mixture of water, methane, ammonia, and hydrogen. In this scenario, life is assumed to have arisen from shallow ponds containing a prebiotic soup of amino acids, sugars, and nucleic acids. The energy for the chemical reactions in this soup comes from sunlight. There are several reasons why this scenario is unrealistic, including the random processes by which chemicals would have to form and the chemical destroying ultraviolet radiation that was present.

      A more realistic picture of life formation is the clay theory advanced by Cairns-Smith in 1966. It is suggested that the clay minerals that existed on the early Earth provided a template on which organic molecules could grow. Cairns-Smith envisioned the crystal structure of the clay as acting as a type of DNA that was able to pass on genetic information to the growing organic molecules. Such surface growth may also account for the left-handed amino acids and right-handed sugars that dominate life today. Although an intriguing theory, no life forms have ever been obtained from experiments on clay surfaces.

      An approach somewhat similar to that of Cairns-Smith is the Iron-Sulfur World of Günter Wächtershäuser, who suggested in 1988 that hydrothermal vents on the floor of the ocean would have provided pyrite surfaces on which the chemicals of life could have emerged. The heat from the vents would have provided the energy to drive the chemical reactions. Wächtershäuser has sketched out a complete chemical scheme by which the flat life forms that emerged from surface-catalyzed beginnings left the pyrite surface and joined the three-dimensional world above the surface. Eventually, the life-forming chemicals found a refuge in cell membranes. The major problem with the theory of Wächtershäuser is the lack of a complete experimental synthesis of life from pyrite surfaces at hydrothermal vents. There have been experiments to test parts of Wächtershäuser’s theory, but there has been no complete experiment that demonstrates chemical movement from a flat surface to three-dimensional forms in cell membranes.

      The theories discussed so far stress the formation of amino acids as the first step in the synthesis of life. A different approach has been taken by scientists who work with DNA and nucleic acids. These scientists maintain that the formation of nucleic acids preceded the synthesis of amino acids and proteins. A major breakthrough in this approach was made by Sidney Altman and Thomas Cech in the early 1980s and for which these scientists received the Nobel Prize. These researchers showed that a catalytic RNA molecule, called a ribozyme, can replace the protein catalysts that provide the metabolism of all cells. This discovery ushered in the so-called RNA World. The RNA World proposes that the first life form was a self-replicating strand of RNA enclosed in some type of cell membrane. The Achilles heel of the RNA World is the necessity to have a cell membrane inside of which the ribozyme can work its wonders. No one has succeeded in synthesizing such a system.

      This brings us to the proposal discussed in Sec. II, above and its justification discussed in Sec. III. We begin with the justification. It has long been known that small objects such as capillary tubes produce surface effects when in contact with liquids. These effects are attributed to surface tension forces, which either draw the liquids up the capillary or force the liquid down the capillary and below the surface of the liquid. The effect depends on whether the liquid wets the capillary surface. Surface effects were an important consideration in the early 1990s, when scientists began studies of liquids in confined spaces for a better understanding of lubrication and oil recovery. Studies at the molecular level were mainly spectroscopic and involved studies of laser light scattered from porous silica sol gels. The phenomenon of light scattered by transparent materials was first explained by C. V. Raman in 1921 and is known as the Raman effect. With the discovery of lasers (Light Amplification by Stimulated Emission of Radiation), spectorscopists had a bright light source for a detailed study of the Raman effect.

      The earliest studies of the Raman effect of liquids in the 1970s centered on the behavior of the liquid molecules when they were hit by a pulse of laser light. It was found that some of the energy absorbed by the molecules from the laser light was sent into the rotational motions of the molecules, while the rest of the energy went into the vibrational motions of the atoms comprising the molecules. It was also found that the rotational and vibrational energies quickly left the molecules as they interacted with each other and their surroundings. The rotational and vibrational energies were dissipated as heat.

      Scientists were soon studying the Raman spectra of molecules in order to understand exactly how the energy leaked out of the molecules. These studies involved detailed analyses of the shapes of the spectral bands that characterized the molecular vibrations. It became possible to correlate the rate at which molecules lost energy to the rotational and vibrational motions of the molecules and to do this as a function of time as the molecules were losing energy. This dynamical information is exceedingly important for understanding how molecules interact with their environment and with each other. Scientists began to ask if molecules behave differently in confined spaces than they do in the bulk liquid phase. It was at this time that I and Ed Quitevis at Texas Tech University looked at methyl iodide confined to small pores in silica sol gels. We found that the molecules behaved entirely differently in the sol gel pores than they did in the bulk liquid. The dynamics of energy loss were completely different in the sol gels. It immediately became apparent that, if the dynamics of energy loss were completely different in small confined spaces, the chemical reactions that molecules undergo in confined spaces could also be very different from that in the bulk phase. No experiments have been done to confirm or refute this hypothesis.

      Upon finishing the study of methyl iodide in silica sol gel pores, I realized that all the problems that beset investigators seeking the origin of life could be solved if life began inside porous rock such as basalt rather than in shallow pools or on surfaces. Hydrothermal vents are surrounded by basalt from the lava flows that created the vents. The pores in the basalt would have been ideal places for unusual chemistry to occur, and this chemistry would have been protected from events occurring outside the basalt. The chemistry that could have taken place in the basalt is unknown, since the experiments have not been done, but it may have been similar to that espoused by Wächtershäuser. Since basalt and hydrothermal vents were ubiquitous on the early Earth, unusual pore chemistry would have been occurring over the entire Earth as early as 3.8 billion years ago. It is possible that this chemistry had 200 million years to form the earliest life-producing chemicals—amino acids and primitive sugars. Then continental uplift began about 3.6 billion years ago, forming shallow seas and tidal pools. These conditions allowed the formation of phosphate compounds in and around the basalt. This led to what Herric Baltscheffsky has called the Pyrophosphate World. Since the earliest forms of life are stromatolites, which appeared 3.5 billion years ago, we have about 100 million years for the phosphate concentration to build up in the basalt pores to form phospholipid cell membranes, which then moved outside the pores, where nucleic acid chemistry could be driven by sunlight. Once membranes moved outside the pores, it was possible for prokaryotes to develop rapidly.

      The beauty of this scenario for the origin of life, is that it can be tested experimentally. If the test should prove negative for the origin of life, at least we will have learned something about the chemistry of hydrothermal vents as it occurs in confined spaces. If it proves positive for the origin of life, the scientists who do the research can pick up their Nobel Prizes.


V. Application of Zwanzig-Mori Theory to Raman Spectroscopy

 Introduction

      The 1950s witnessed a revolution in the treatment of non-equilibrium dynamics of molecular systems. This revolution was led in large part by Ryogo Kubo, who proposed a statistical mechanical theory of linear response. Linear response states that, for systems close to equilibrium, the rate at which the system moves toward equilibrium is linearly dependent on the generalized forces acting on the system. Kubo showed in 1962 how his linear response theory could be applied to the study of spectroscopic line shapes and how the line shapes are related to relaxation of the systems back to equilibrium. Kubo's paper lays out the process of Fourier transforming a band shape to get a response correlation function and how the correlation function can be interpreted.

      Roy Gordon, who was at Harvard, published a paper in 1965 that put Kubo's somewhat abstract discussion into a form useful to spectroscopists. He showed how spectral line widths could be Fourier transformed to provide dipole autocorrelation functions for infrared and Raman spectra. Gordon focused on the rotational correlation functions.

      In the meantime, Hazime Mori at Kyoto University was investigating time correlation functions for transport in fluids for properties such as viscosity, thermal conductivity, and diffusion, and Bob Zwanzig at the Bureau of Standards was using projection operators to break an irreversible process into a relevant part and an irrelevant bath. Zwanzig derived an equation for the time development of the statistical distribution function for the relevant part by projecting the entire distribution function onto the relevant and irrelevant bath parts. Then, in studying vibrational relaxation in liquids, Zwanzig introduced the force autocorrelation function of the bath. In 1965, Mori developed a generalized Langevin equation (GLE) along the projection operator lines that Zwanzig had used. The Zwanzig-Mori formalism untilizes a Hilbert space of dynamical variables A. The axes are labeled A1, A2, A3, etc. for the Hilbert spaces. The space A1 contains the slow variables or the relevant part, which is to be directly studied. The variables in A2 are the fast variables that modulate the slow variables. This is a hierarchy of spaces in which the A3 are even faster variables that modulate the fast variables. As we will see later, it is sometimes necessary to go to a third-order memory function procedure or to A4. The basis vectors in the Hilbert space are |Ai>. A general vector |B> can be projected onto the A1 axis by the operation: |A1><A1|B>. This gives a vector of length <A1|B>  lying along |A1>. We can also project out the A2 component of |B>  as |A2><A2|B>.    

Figure1.jpg

 

      The mathematics are somewhat involved, but Mori's generalized Langevin equation can be written

∂A(t)/∂t  =  Ω A(t) - ∫K(τ) A(t-τ) dτ + F(t)

for a time dependent slow variable A(t), where

K(τ)  =  <F(τ) F(0)>

is called the memory function, F(t) is vector in the fast subspace orthogonal to A, and W is a frequency term that can be ignored for spectroscopic problems. The memory function is an autocorrelation function for the fast variables that modulate the slow variables. Correlation functions, in general, represent the knowledge of the system at time t, given complete knowledge at time t = 0.

      It is possible to obtain an equation for the autocorrelation function of the slow variables by multiplying the GLE for the bra vector <A(t)| on the right by |A(0)>:

∂<A(t) A(0)>/∂t  =  Ω<A(t) A(0)> - ∫ K(τ) <A(t-τ) A(0)> dτ + <F(t) A(0)>

or
∂C(t)/∂t  =  Ω C(t) - ∫ K(t) C(t-τ) dτ


Application of the Generalized Langevin Equation to Raman spectra

      Following the lead of Gordon, it is possible to separate the vibrational from the rotational motions in Raman spectra by measuring the polarized and depolarized components of a Raman band and then subtracting the depolarized from the polarized components:

Iiso(ω)  =  Ipol(ω) – (4/3) Idep(ω)

A Fourier transform of the isotropic intensity of the Raman band then takes us from frequency space to time space for the normal mode Q of the molecular vibration:

<Q(t) Q(0)> ≡  C(t)  =  ∫ Iiso(ω) e-iωt dω

      At first, investigators focused on rotational reorientation, because there were models of free and hindered molecular rotation that could be used to interpret the rotational correlation functions. Thus, there were free rotor models (Gaussian band shape), Debye diffusion model (delta function memory, exponential correlation, Lorentzian band shape), and intermediate J- and M-diffusion models (part Gaussian and part Lorentzian band shapes). No models existed for vibrational dephasing represented by the vibrational correlation function. The correlation function measures the loss of phase coherence among the molecules in time. The relaxation time of the oscillator is that time at which C(t) has a value of 1/e. What is meant by dephasing here is the loss of phase coherence among an ensemble of oscillators; at t = 0 we have complete knowledge of the phases of the oscillators, but with time the interactions with the bath destroys our knowledge of these phases, until at long times we lose all knowledge of the phases. This loss of phase coherence is reflected in the isotropic band shape. In a pulsed laser experiment we could ideally see a sharp line at t = 0, and then the line would broaden into a broad band with time. The Raman experiment is done with a continuous wave laser, so that the entire broadened band is revealed.

      With no models for vibrational dephasing, it was difficult to understand the vibrational autocorrelation function. In the 1970s there were attempts at formulating ad hoc statistical equations to model the correlation functions. One of the most successful of these was used by Walter Rothschild of the Ford Motor Company to handle both slow and fast modulation processes. The slow modulation process produced a Gaussian band shape, while fast modulation leads to motional narrowing of the band and to a Lorentzian band shape. Rothschild's equation could not explain the memory function.


A Memory-Functions Approach to Vibrational Dephasing

      In 1978, Simon Cohen and I published a paper showing how it is possible to model the vibrational autocorrelation function within experimental error. Ignoring the vibrational frequency-shift term in the GLE, we wrote a series of coupled Volterra equations for the Hilbert space of the vibrational normal coordinates:


EqnSet2.jpg

Similar to the rigid rotor reference system for rotational relaxation, we proposed a rigid-lattice reference system that began with a Gaussian correlation function:  C0(t) = exp(-M2t2/2), where M2 is the spectral second moment, M2 = ∫ω2I(ω) dω. The Volterra equations are then solved for the memory functions, the rigid lattice allowed to move at the "link" step, and the Volterra equations solved backward to arrive at the modeled correlation function C(t):


EqnSet3.JPG

Contact with the real world is made through the "link" term. We assumed that the "link" is a simple stochastic process whose interactions followed a Poisson distribution:

Kn(t)  =  κn Kn0(t) exp(-t/τ)

where κn= Kn(0)/Kn0(0) and is related to the various moments of the band, and τ is an adjustable parameter that is related to the relaxation time of the Poisson distribution of random forces or is simply a correction for neglect of higher-order memory functions.

      Another way of viewing this is to realize that the first-order procedure is for only one slow variable (the normal mode) and that the real first-order memory function is non-Markovian (i.e., it has wiggles at long time) indicating interaction among slow variables. This interaction is in the perturbing molecular Hamiltonian, which contains intramolecular vibration, rotation, vibration-rotation interactions, as well as intermolecular vibrational interactions. Thus, by including all the relevant slow variables in n steps, it is possible to introduce Markovian behavior in the n+1 memory function. At the “link” step, the system is perturbed through the Poission modulation, thus allowing the correlation function to exhibit its fast modulation and deviation from Gaussian behavior.

      It was readily determined that a first-order memory function procedure did not reproduce C(t) within experimental error. In some cases, a second-order memory function procedure was satisfactory, while in other cases the procedure had to be carried to third order. A second-order fit is interpreted to mean that there is an additional slow variable such as the tumbling of the molecule if the spinning is in the fast subspace. A third-order fit means that there are at least two slow processes influencing the dephasing such as V-V transfer and tumbling of the molecule. It is important to realize that the coupled slow processes can be mechanically coupled as in the case of V-V transfer or statistically coupled as in the case of tumbling. I do not wish to pursue this line of study in detail, but I want to point out that this memory-function procedure can be used to assure that the spectra have been accurately measured. In those cases where the band shape was distorted because of experimental problems with the laser or the electronics or the smoothing was in error, it was impossible to fit the band within experimental error.

Separation of homogeneous and inhomogeneous dephasing

      We wish to study the loss of vibrational phase coherence by the molecules with time. The term “phase coherence” comes from NMR studies. Vibrational dephasing is not the same, since the Raman spectroscopic experiment does not put the molecules into the same vibrational phase. Rather, if we know the phase of a molecule (or ensemble of molecules) at t=0, then with time the interaction with the environment will change the phase until we lose all knowledge of the phase. This is, of course, a broadening of the vibrational energy level.

      In 1980, Chuck Harris at Berkeley suggested that the vibrational correlation function could be expressed as a product of a homogeneous function, Chom(t), and an inhomogeneous function, Cinh(t). The homogeneous part was determined from stimulated Raman scattering. David Oxtoby at Chicago questioned whether it is possible to separate the dephasing process into homogeneous and inhomogeneous parts, because dephasing can be due to processes intermediate between homogeneous and inhomogeneous. To understand the problem here, it is necessary to discuss the vibrational-relaxation band shape. The typical band shape is composed of a narrow Lorentzian center with broad Gaussian wings. Early studies restricted themselves to obtaining the vibrational relaxation time from the FWHM = (pc tv)-1, thus giving more weight to the Lorentzian component of the vibrational band. When dephasing analyses were restricted to simply measuring the FWHM, little attention was paid to the Gaussian wings. However, when experimental correlation functions were experimentally determined, it became possible to see the relaxation effects of both the short-time and the long-time or the fast-modulating and the slow-modulating processes in the bath. As Oxtoby pointed out, it was now necessary to consider the time scales involved in the modulation of the vibrational frequency. It was also necessary to define "homogeneous dephasing" and "inhomogeneous dephasing." A Gaussian modulating process arises from a slowly varying, long-range intermolecular force field that the molecule sees as it undergoes a random walk. In this case, the dephasing process is said to be inhomogeneous and the band shape is Gaussian. If the molecular motion speeds up, say through rotation, the intermolecular force field begins to blur, there is motional narrowing of the band into a Lorentzian shape, and the dephasing process becomes homogeneous. It is possible to have both homogeneous and inhomogeneous processes taking place simultaneously. The problem is how to unravel these processes that occur in the Raman spectra.

      In the early 1980s there was talk of separating homogeneous and inhomogeneous processes by combining pulsed laser techniques (stimulated Raman scattering) with spontaneous Raman measurements in an effort to get homogeneous and inhomogeneous correlation functions as suggested by Harris. There were problems with the rise time in the pulsed technique and with a clear separation of time scales in the analysis of the data. In 1984, I suggested the use of the memory function to separate the homogeneous and inhomogeneous processes. It was hoped that the memory function, in the realm of overall fast modulation, would break up into a sum of memory functions instead of a product of correlation functions. That would make the separation of the processes much easier. It didn't quite work out this way. In all the spectra we considered, the molecules were small and the so-called "pure dephasing" occurred through the rotations of the molecules, leading to motional narrowing of the bands.

      My method was based on time series analysis, since any autocorrelation function can be represented by a time series. The time series can be determined by an autoregressive analysis, which is too detailed to go into here. Suffice it to say that the memory function can be expressed as a sum of damped cosine terms:


K(t) =  Σ  bi exp(-ηit) cos(Ωit + θi)

The values of the parameters bi, ηi, Ωi, and θi are chosen by an autoregressive parsimonious analysis to fit the memory function. The principle of parsimony dictates that a minimum number of parameters are to be used. The model itself dictates that the values of these parameters be severely restricted. The only one of these parameters that has physical significance is the frequency term Ωi. It turns out that the three lowest frequencies represent the static inhomogeneity [see Fig. 2, R. E. Wilde, Mol. Phys. 57, 675 (1986)]. The higher frequencies are homogeneous and represent the frequencies of the power spectrum of the force autocorrelation function for the intermolecular forces. There must be a clear time and frequency separation between the homogeneous and inhomogeneous processes. Failure to get a clear time separation shows up in three inhomogeous second moments that differ from one another by more than the experimental uncertainty. This could also occur if more than one type of oscillator is present reflecting different environments for the oscillators.

      The inhomogeneous process is a Gaussian process that gives directly an inhomogeneous second moment M2inh. The homogeneous contribution to the isotropic second moment M2iso is obtained as a difference: M2hom = M2iso - M2inh. Thus, instead of separating the memory functions into homogeneous and inhomogeneous parts, it is the second spectral moment that separates.