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A theoretical study of the asymmetric adsorption of alanine on the (1010) face of quartz
Surface Science 165 (1986) L53-L58 North-Holland, Amsterdam
L53
SURFACE SCIENCE LETTERS A T H E O R E T I C A L STUDY O F T H E ASYMMETRIC A D S O R P T I O N O F ALANINE ON T H E (1010) FACE O F QUARTZ A. JULG, A. FAVIER and Y. OZIAS Laboratoire de Chimie Thborique, Universitb de Provence, Place Victor Hugo, F-13331 Marseille-3, France
Received 28 June 1985; accepted for publication 30 September 1985
The adsorption of L- and D-alanine on the (1010) face of quartz is studied by means of the self-consistent field method, the actual crystal being replaced by a finite number of point charges. The dispersion-repulsion terms arising from the finite size of the atoms of the substrate are calculated by means of a pair potential. The positive ion is more easily adsorbed than the neutral molecule and the Zwitterion. The Van der Waals terms are proving negligible with respect to the electrostatic contribution. On /-quartz, L-ion is preferentially adsorbed, the difference between the adsorption energies of the L- and D-forms is about 0.07 kcal/mol. These results agree with experiment.
Among all the numerous hypotheses which have been proposed to explain the dominance of L-amino acids in the living organisms [1], the asymmetric synthesis on minerals which present chirality [2], and the difference in energy between the enantiomeric forms (i.e. symmetrical with respect to a m i r r o r - fig. 1) arising from the neutral currents which result from the weak interactions [3], seem to be the most probable. Valid for mineral structures, such as quartz or layer alumino-silicates, the latter explanation nevertheless seems difficult to be accepted for amino acids. Indeed, if in the isolated state L-alanine is effectively more stable than D-alanine under the effect of the weak interactions, the energy difference between both forms is extremely weak: 6 x 10-19 e V , i.e. ca. 6 X 10 -17 kcal/mol [1,4], whereas the difference between the adsorption energies of L- and D-forms an /-quartz (which is slightly more abundant than d-quartz - ca. 1% [5]) (fig. 2) is about 10 -3 kcal/mol (a value calculated from the experimental ratio D / L of the adsorbed molecules given in ref. [6]), the adsorption of the L-form being preponderant. Moreover, amino acid chains can be synthesized in vitro on clays [7]. At last, it is well known that after death, the amino acids of organisms racemize [8], i.e. are transformed into an L - D equimolecular mixture. All these facts which lead us to think that the asymmetric synthesis on chiral minerals is the most probable cause of the chirality observed in the living 0039-6028/86/$03.50 © Elsevier Science Publishers B.V.
A. Julg et al, / Asymmetric adsorption of alanine on (1010) quartz
L54
I I
.c
.. co, H', Hqc
I~C ""
c.
,
"C I"%
I I
Fig. 1. Structure of both inverse forms (L and D) of an amino acid (Fischer's notation).
organisms emphasize the necessity of systematic investigations on the asymmetric adsorption, more especially as negative results have been also announced for reactions on quartz [9]. Of course, the mechanisms proposed to explain the evolution towards the more stable form in the case of weak interactions [1,10] (autocatalytic reaction sequence with a metastabte racemic output) are a f o r t i o r i valid for asymmetric syntheses for which the differences in energy are considerably greater. In this outlook, as a first example, we propose a theoretical study of the adsorption of alanine on quartz, for which we dispose of significant experimental results [6]. In the general case, the theoretical study of adsorption is a very difficult problem which necessitates the determination of the Gibbs energy of the whole
^~ 1 I I t
4"
O,
*o,
Z ,i-
Fig. 2. Position of oxygens atoms on an m(1010) face of /-quartz. The arrows indicate the two orientations envisaged for the molecule (CO2H ---, NH2). See fig. 3.
A. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
L55
system (substrate + molecule + solvent). Nevertheless, in the case we consider, the problem can be considerably simplified given that only the terms which differentiate the isomers have to be considered. In particular, all the terms corresponding to the solvent-substrate and solvent-molecule interactions do not intervene. Likewise, for the entropic terms which arise essentially from the vibrations of the molecule. Consequently, the difference in behavior of both enantiomers results from the difference between the molecule-substrate interaction energies only. In order to calculate the interaction energies, we will proceed as follows [11]. We will replace the actual substrate by a finite number of point charges located at the sites of Si and O atoms of the crystal so that the cluster is neutral and possesses the symmetries of quartz (this latter condition being very important [12]). The interaction energy between the molecule and this cluster will be calculated by means of the ab initio self-consistent field method (SCF) [13] which introduces all the electrons of the molecule. Successively, we will calculate the energy of the isolated molecule and that of the molecule within the electrostatic field created by the point charges of the cluster. The difference A SCF corresponds to the electrostatic interaction and to the polarization of the molecule under the effect of the crystal field. In order to take the finite size and the polarizability of the atoms of the substrate into account, we will introduce a dispersion-repulsion term. For polar systems, as those we consider, this latter contribution is small with respect to the former term Asc F (about 1/10). Therefore, we can be content with an evaluation from a pair potential: - A r - 6 + Br -12 [11], where A and B are constants deduced from atomic data. Given the fact that in alanine the dissymmetry arises from the CH3 group which exchanges with the H atom, we will only introduce the contribution of these groups (H and CH3) in our calculation. Such a procedure is equivalent to a configuration interaction calculation given that in this latter the dispersion is included [14]. Quartz occurs as prismatic crystals with well-developed lateral faces rn (1010). On the molecular scale, the crystal is constituted by - O - S i - O - helices whose axes are parallel to the lateral faces, each Si atom belonging to two helices [15]. In the laevorotatory form (i.e. which provokes a rotation of the polarization plane to the left to one looking in the direction of the ray), the helices are right-handed (space group P312 ) [16]. The lateral faces m constituting the most important part of the total surface of the natural crystals, we will consider the adsorption on these faces only. On these latter, the oxygen atoms are grouped in pairs [17] (fig. 2), the distance between the oxygens of a pair (4.95 ,~) being of the same order of magnitude as that of the two functional groups of alanine [18]. Given that adsorption of a polar compound on an ionic crystal is essentially governed by the electrostatic interactions [19], these O - O pairs constitute preferential adsorption sites f o r
L56
A. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
alanine. Moreover, hydrogen bonds can stabilize the system if the polarities of the terminal groups are suitable. More precisely, with the neutral molecule or the positive ion H O C O - C H ( C H 3 ) - N H ~ , two H bonds can be formed, O - H and N - H bonds pointing respectively towards the oxygens. With the Zwitterion C O 2 - C H ( C H 3 ) - N H ~ - , only one H bond is possible (-NH~- - - - O I - ) ) . Given the repulsion between the group CO~ and the surface, this ion will be perpendicular to the surface above one oxygen and the adsorption energy weaker than that corresponding to the adsorption on an oxygen pair. Given that the energy of a H bond is much greater between charged partners than between neutral molecules, the adsorption of the positive ion is a priori easier. Moreover, if we neglect the asymmetry of the molecule, the optimal stabilization must be obtained when the plane O C O C N is perpendicular to the surface of the crystal and passes by the oxygen pair. A preliminary calculation performed on the system 0 2 . . . H O H having shown us that the charge transfer between the two partners is weak, in order to obtain the difference between the adsorption energies, we have kept the model of the molecule within the field created by the point charges, without introducing a delocalization between the adsorbed entity and the surface ions, but using the actual H bond lengths for O . . . H O and N H . - - O distances. The two orientations, N H 2 or NH;- linked to 02 and to O1 (cases I and II, respectively), will be considered (fig. 3). The calculations have been performed by means of G A U S S I A N - 7 0 (STO-6 G) program [20], modified to take exterior point charges into account. In order to simulate the crystal, we have used a cluster of 24 Si atoms and 48 O atoms. The net charges of these atoms have been assumed equal to + 3 and - 1 . 5 , respectively [21]. At last, we have assumed that the adsorbed molecules keep the same geometry as in the isolated state [18]. Indeed, in order to obtain appreciable modifications in the geometry (ca. 0.01 ,~) for the bond lengths, very strong electric fields (of about 10 ~° V / m ) are necessary [22]. Such fields are much more important that those existing near the faces of a crystal. Table 1 gives the SCF contributions for the orientations I and II. The reader will notice that the symbols L and D refer to the structural conformation, regardless of the sign of rotation. L-alanine, indeed, is dextrorotatory, and D-alanine, laevorotatory. Moreover, using the values listed in ref. [11], we have Clt~ ,),4
H -
-
q
\H .......
0~ . . . .
Fig. 3. Position of the L-alanine ion on the m-face of/-quartz (case I). Case II corresponds to the inverse disposition (N above O1, and COaH above O2).
A. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
L57
Table 1 SCF contribution to the adsorption energy(in kcal/mol) of L- and D-alanine and the corresponding positiveions on /-quartz (face m); negativevalues correspond to a repulsion Alanine
Positive ion
Form
L
D
I~ Orientation II)
- 23 to - 24
L
D
73.003 68.490
72.934 68.556
ve,~fied that the dispersion-repulsion terms bring a negligible contribution ( < 0.001 kcal/mol) to the difference of t h e adsorption energies (ca. 0.07 kcal/mol). In passing, we will notice that the difference of the dispersion-repulsion terms is approximately equal to 10 -3 times the Van der Waals interaction (a few kcal/mol); this is consistent with results obtained from more sophisticated calculations [23]. It results from table 1 that: (i) a neutral molecule is not adsorbed; (ii) the orientation I is the more favorable; (iii) for this orientation (I), the adsorption energy of the L-positive ion is slightly greater than that of the D-ion (0.069 kcal/mol). In other words, we find the experimental conclusion again [6]: L-(alanine) + is preferentially adsorbed by /-quartz, and, consequently, D-(alanine)- by d-quartz. In dimethyl formamide, indeed, the alanine chlorhydrate gives the positive ion. Given that the solvent does not intervene in the differentiation of both isomers, our result is more general and is applicable to any acidic medium containing the positive ion (e.g., the prebiotic medium saturated with CO 2). According to Boltzmann's law, the adsorption percentage of L-form minus that of D-form would be about 4% at 170°C. This value is slightly greater than the experimental value at the same temperature (about 1% to 2% [6]). Given the simplifying hypotheses introduced in our calculation, in particular the replacing of the actual crystal by a finite number of point charges, our result has, nevertheless, to be considered as very satisfying. Besides, we must notice that experiment [6] has been performed with quartz powder which presents faces other than m, in a weaker but non-negligible proportion. In conclusion, we see that the electrostatic interaction plays the dominant role in the adsorption of amino acids on polar substrates, and that this latter must be able to explain the dominance of L-amino acids in the living organisms by an asymmetric synthesis process on a chiral mineral.
The authors thank Professor R. Kern (University of Marseille) for valuable bibliographic information.
L58
~t. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
References [1] S.F. Mason, Intern. Rev. Phys. Chem. 3 (1983) 217. [2] A.G. Cairns-Smith, Genetic Takeover and the Mineral Origins of Life (Cambridge, 1982). [3] S. Weinberg, Phys. Rev. Letters 19 (1967) 1264; A. Salam, in: Proc. 8th Nobel Symp.: Elementary Particle Theory (Almqvist and Wiksell, Stockholm, 1968). [4] S.F. Mason and G.E. Tranter, Chem. Phys. Letters 94 (1983) 34; Chem. Commun. (1983) 117. [5] C. Palache, N. Berman and C. Frondel, Dana's System of Mineralogy, Vol. III, 7th ed. (Wiley, New York, 1962) p. 16. [6] W.A. Bonner, P.R. Kavasmaneck, F.S. Martin and J.J. Flores, Science 186 (1974) 186. [7] S.E. Luria, Life: The Unfinished Experiment (Scribner, New York, 1973). [8] J.L. Bada, Earth Planet. Sci. Letters 15 (1972) 223. [9] G.M. Schwab and L. Rudolph, Naturwissenschaften 20 (1932) 363; R. Tsuchida, A. Nakamura and M. Kobayashi, J. Chem. Soc. Japan 56 (1935) 1335; G. Karagonnis, Helv. Chim. Acta 32 (1949) 1840; A. Nakahara and R. Tsuchida, J. Am. Chem. Soc. 76 (1954) 3103; A. Amariglio, H. Amariglio and X. Duval, Helv. Chim. Acta 51 (1968) 2110. [10] C. Fajszi and J. Czrgr, Origins of Life 11 (1981) 143. [11] B. Deprick and A. Julg, Chem. Phys. Letters 110 (1984) 150. [12] A. Julg and D. Lrtoquart, Phil. Mag. 33 (1976) 721. [13] C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [14] P. Claverie, in: Intermolecular Interaction from Diatomics to Biopolymers, Ed. B. Pullman (Wiley, New York, 1978). [15] A.F. Wells, Structural Inorganic Chemistry (Clarendon, Oxford, 1952); R.W.G. Wyckoff, Crystal Structures, Vol. II (Wiley, New York, 1963). [16] A. de Vries, Nature 181 (1958) 1193. [17] P. Hartman, Bull. Mineral. 101 (1978) 195. [18] Tables of Interatomic Distances (Chem. Soc., 1958). [19] A. Julg and B. Deprick, Croat. Claim. Acta 57 (1984) 85. [20] W.J. Hehre, W.A. Lathan, R. Dichtfield, M.D. Newton and J.A. Pople, Quantum Chemistry Program Exchange (Bloomington, 1973). [21] A. Julg, Crystals as Giant Molecules (Springer, Berlin, 1978); A. Julg, A. Pellegatti and F. Marinelli, Nouv. J. Chim. 6 (1982) 31. [22] H. Nakatsuji, T. Hayakawa and T. Yonezawa, J. Am. Chem. Soc. 103 (1981) 7426. [23] C. Girardet and L. Vega, Surface Sci. 151 (1985) 447.
L53
SURFACE SCIENCE LETTERS A T H E O R E T I C A L STUDY O F T H E ASYMMETRIC A D S O R P T I O N O F ALANINE ON T H E (1010) FACE O F QUARTZ A. JULG, A. FAVIER and Y. OZIAS Laboratoire de Chimie Thborique, Universitb de Provence, Place Victor Hugo, F-13331 Marseille-3, France
Received 28 June 1985; accepted for publication 30 September 1985
The adsorption of L- and D-alanine on the (1010) face of quartz is studied by means of the self-consistent field method, the actual crystal being replaced by a finite number of point charges. The dispersion-repulsion terms arising from the finite size of the atoms of the substrate are calculated by means of a pair potential. The positive ion is more easily adsorbed than the neutral molecule and the Zwitterion. The Van der Waals terms are proving negligible with respect to the electrostatic contribution. On /-quartz, L-ion is preferentially adsorbed, the difference between the adsorption energies of the L- and D-forms is about 0.07 kcal/mol. These results agree with experiment.
Among all the numerous hypotheses which have been proposed to explain the dominance of L-amino acids in the living organisms [1], the asymmetric synthesis on minerals which present chirality [2], and the difference in energy between the enantiomeric forms (i.e. symmetrical with respect to a m i r r o r - fig. 1) arising from the neutral currents which result from the weak interactions [3], seem to be the most probable. Valid for mineral structures, such as quartz or layer alumino-silicates, the latter explanation nevertheless seems difficult to be accepted for amino acids. Indeed, if in the isolated state L-alanine is effectively more stable than D-alanine under the effect of the weak interactions, the energy difference between both forms is extremely weak: 6 x 10-19 e V , i.e. ca. 6 X 10 -17 kcal/mol [1,4], whereas the difference between the adsorption energies of L- and D-forms an /-quartz (which is slightly more abundant than d-quartz - ca. 1% [5]) (fig. 2) is about 10 -3 kcal/mol (a value calculated from the experimental ratio D / L of the adsorbed molecules given in ref. [6]), the adsorption of the L-form being preponderant. Moreover, amino acid chains can be synthesized in vitro on clays [7]. At last, it is well known that after death, the amino acids of organisms racemize [8], i.e. are transformed into an L - D equimolecular mixture. All these facts which lead us to think that the asymmetric synthesis on chiral minerals is the most probable cause of the chirality observed in the living 0039-6028/86/$03.50 © Elsevier Science Publishers B.V.
A. Julg et al, / Asymmetric adsorption of alanine on (1010) quartz
L54
I I
.c
.. co, H', Hqc
I~C ""
c.
,
"C I"%
I I
Fig. 1. Structure of both inverse forms (L and D) of an amino acid (Fischer's notation).
organisms emphasize the necessity of systematic investigations on the asymmetric adsorption, more especially as negative results have been also announced for reactions on quartz [9]. Of course, the mechanisms proposed to explain the evolution towards the more stable form in the case of weak interactions [1,10] (autocatalytic reaction sequence with a metastabte racemic output) are a f o r t i o r i valid for asymmetric syntheses for which the differences in energy are considerably greater. In this outlook, as a first example, we propose a theoretical study of the adsorption of alanine on quartz, for which we dispose of significant experimental results [6]. In the general case, the theoretical study of adsorption is a very difficult problem which necessitates the determination of the Gibbs energy of the whole
^~ 1 I I t
4"
O,
*o,
Z ,i-
Fig. 2. Position of oxygens atoms on an m(1010) face of /-quartz. The arrows indicate the two orientations envisaged for the molecule (CO2H ---, NH2). See fig. 3.
A. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
L55
system (substrate + molecule + solvent). Nevertheless, in the case we consider, the problem can be considerably simplified given that only the terms which differentiate the isomers have to be considered. In particular, all the terms corresponding to the solvent-substrate and solvent-molecule interactions do not intervene. Likewise, for the entropic terms which arise essentially from the vibrations of the molecule. Consequently, the difference in behavior of both enantiomers results from the difference between the molecule-substrate interaction energies only. In order to calculate the interaction energies, we will proceed as follows [11]. We will replace the actual substrate by a finite number of point charges located at the sites of Si and O atoms of the crystal so that the cluster is neutral and possesses the symmetries of quartz (this latter condition being very important [12]). The interaction energy between the molecule and this cluster will be calculated by means of the ab initio self-consistent field method (SCF) [13] which introduces all the electrons of the molecule. Successively, we will calculate the energy of the isolated molecule and that of the molecule within the electrostatic field created by the point charges of the cluster. The difference A SCF corresponds to the electrostatic interaction and to the polarization of the molecule under the effect of the crystal field. In order to take the finite size and the polarizability of the atoms of the substrate into account, we will introduce a dispersion-repulsion term. For polar systems, as those we consider, this latter contribution is small with respect to the former term Asc F (about 1/10). Therefore, we can be content with an evaluation from a pair potential: - A r - 6 + Br -12 [11], where A and B are constants deduced from atomic data. Given the fact that in alanine the dissymmetry arises from the CH3 group which exchanges with the H atom, we will only introduce the contribution of these groups (H and CH3) in our calculation. Such a procedure is equivalent to a configuration interaction calculation given that in this latter the dispersion is included [14]. Quartz occurs as prismatic crystals with well-developed lateral faces rn (1010). On the molecular scale, the crystal is constituted by - O - S i - O - helices whose axes are parallel to the lateral faces, each Si atom belonging to two helices [15]. In the laevorotatory form (i.e. which provokes a rotation of the polarization plane to the left to one looking in the direction of the ray), the helices are right-handed (space group P312 ) [16]. The lateral faces m constituting the most important part of the total surface of the natural crystals, we will consider the adsorption on these faces only. On these latter, the oxygen atoms are grouped in pairs [17] (fig. 2), the distance between the oxygens of a pair (4.95 ,~) being of the same order of magnitude as that of the two functional groups of alanine [18]. Given that adsorption of a polar compound on an ionic crystal is essentially governed by the electrostatic interactions [19], these O - O pairs constitute preferential adsorption sites f o r
L56
A. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
alanine. Moreover, hydrogen bonds can stabilize the system if the polarities of the terminal groups are suitable. More precisely, with the neutral molecule or the positive ion H O C O - C H ( C H 3 ) - N H ~ , two H bonds can be formed, O - H and N - H bonds pointing respectively towards the oxygens. With the Zwitterion C O 2 - C H ( C H 3 ) - N H ~ - , only one H bond is possible (-NH~- - - - O I - ) ) . Given the repulsion between the group CO~ and the surface, this ion will be perpendicular to the surface above one oxygen and the adsorption energy weaker than that corresponding to the adsorption on an oxygen pair. Given that the energy of a H bond is much greater between charged partners than between neutral molecules, the adsorption of the positive ion is a priori easier. Moreover, if we neglect the asymmetry of the molecule, the optimal stabilization must be obtained when the plane O C O C N is perpendicular to the surface of the crystal and passes by the oxygen pair. A preliminary calculation performed on the system 0 2 . . . H O H having shown us that the charge transfer between the two partners is weak, in order to obtain the difference between the adsorption energies, we have kept the model of the molecule within the field created by the point charges, without introducing a delocalization between the adsorbed entity and the surface ions, but using the actual H bond lengths for O . . . H O and N H . - - O distances. The two orientations, N H 2 or NH;- linked to 02 and to O1 (cases I and II, respectively), will be considered (fig. 3). The calculations have been performed by means of G A U S S I A N - 7 0 (STO-6 G) program [20], modified to take exterior point charges into account. In order to simulate the crystal, we have used a cluster of 24 Si atoms and 48 O atoms. The net charges of these atoms have been assumed equal to + 3 and - 1 . 5 , respectively [21]. At last, we have assumed that the adsorbed molecules keep the same geometry as in the isolated state [18]. Indeed, in order to obtain appreciable modifications in the geometry (ca. 0.01 ,~) for the bond lengths, very strong electric fields (of about 10 ~° V / m ) are necessary [22]. Such fields are much more important that those existing near the faces of a crystal. Table 1 gives the SCF contributions for the orientations I and II. The reader will notice that the symbols L and D refer to the structural conformation, regardless of the sign of rotation. L-alanine, indeed, is dextrorotatory, and D-alanine, laevorotatory. Moreover, using the values listed in ref. [11], we have Clt~ ,),4
H -
-
q
\H .......
0~ . . . .
Fig. 3. Position of the L-alanine ion on the m-face of/-quartz (case I). Case II corresponds to the inverse disposition (N above O1, and COaH above O2).
A. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
L57
Table 1 SCF contribution to the adsorption energy(in kcal/mol) of L- and D-alanine and the corresponding positiveions on /-quartz (face m); negativevalues correspond to a repulsion Alanine
Positive ion
Form
L
D
I~ Orientation II)
- 23 to - 24
L
D
73.003 68.490
72.934 68.556
ve,~fied that the dispersion-repulsion terms bring a negligible contribution ( < 0.001 kcal/mol) to the difference of t h e adsorption energies (ca. 0.07 kcal/mol). In passing, we will notice that the difference of the dispersion-repulsion terms is approximately equal to 10 -3 times the Van der Waals interaction (a few kcal/mol); this is consistent with results obtained from more sophisticated calculations [23]. It results from table 1 that: (i) a neutral molecule is not adsorbed; (ii) the orientation I is the more favorable; (iii) for this orientation (I), the adsorption energy of the L-positive ion is slightly greater than that of the D-ion (0.069 kcal/mol). In other words, we find the experimental conclusion again [6]: L-(alanine) + is preferentially adsorbed by /-quartz, and, consequently, D-(alanine)- by d-quartz. In dimethyl formamide, indeed, the alanine chlorhydrate gives the positive ion. Given that the solvent does not intervene in the differentiation of both isomers, our result is more general and is applicable to any acidic medium containing the positive ion (e.g., the prebiotic medium saturated with CO 2). According to Boltzmann's law, the adsorption percentage of L-form minus that of D-form would be about 4% at 170°C. This value is slightly greater than the experimental value at the same temperature (about 1% to 2% [6]). Given the simplifying hypotheses introduced in our calculation, in particular the replacing of the actual crystal by a finite number of point charges, our result has, nevertheless, to be considered as very satisfying. Besides, we must notice that experiment [6] has been performed with quartz powder which presents faces other than m, in a weaker but non-negligible proportion. In conclusion, we see that the electrostatic interaction plays the dominant role in the adsorption of amino acids on polar substrates, and that this latter must be able to explain the dominance of L-amino acids in the living organisms by an asymmetric synthesis process on a chiral mineral.
The authors thank Professor R. Kern (University of Marseille) for valuable bibliographic information.
L58
~t. Julg et al. / Asymmetric adsorption of alanine on (1010) quartz
References [1] S.F. Mason, Intern. Rev. Phys. Chem. 3 (1983) 217. [2] A.G. Cairns-Smith, Genetic Takeover and the Mineral Origins of Life (Cambridge, 1982). [3] S. Weinberg, Phys. Rev. Letters 19 (1967) 1264; A. Salam, in: Proc. 8th Nobel Symp.: Elementary Particle Theory (Almqvist and Wiksell, Stockholm, 1968). [4] S.F. Mason and G.E. Tranter, Chem. Phys. Letters 94 (1983) 34; Chem. Commun. (1983) 117. [5] C. Palache, N. Berman and C. Frondel, Dana's System of Mineralogy, Vol. III, 7th ed. (Wiley, New York, 1962) p. 16. [6] W.A. Bonner, P.R. Kavasmaneck, F.S. Martin and J.J. Flores, Science 186 (1974) 186. [7] S.E. Luria, Life: The Unfinished Experiment (Scribner, New York, 1973). [8] J.L. Bada, Earth Planet. Sci. Letters 15 (1972) 223. [9] G.M. Schwab and L. Rudolph, Naturwissenschaften 20 (1932) 363; R. Tsuchida, A. Nakamura and M. Kobayashi, J. Chem. Soc. Japan 56 (1935) 1335; G. Karagonnis, Helv. Chim. Acta 32 (1949) 1840; A. Nakahara and R. Tsuchida, J. Am. Chem. Soc. 76 (1954) 3103; A. Amariglio, H. Amariglio and X. Duval, Helv. Chim. Acta 51 (1968) 2110. [10] C. Fajszi and J. Czrgr, Origins of Life 11 (1981) 143. [11] B. Deprick and A. Julg, Chem. Phys. Letters 110 (1984) 150. [12] A. Julg and D. Lrtoquart, Phil. Mag. 33 (1976) 721. [13] C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [14] P. Claverie, in: Intermolecular Interaction from Diatomics to Biopolymers, Ed. B. Pullman (Wiley, New York, 1978). [15] A.F. Wells, Structural Inorganic Chemistry (Clarendon, Oxford, 1952); R.W.G. Wyckoff, Crystal Structures, Vol. II (Wiley, New York, 1963). [16] A. de Vries, Nature 181 (1958) 1193. [17] P. Hartman, Bull. Mineral. 101 (1978) 195. [18] Tables of Interatomic Distances (Chem. Soc., 1958). [19] A. Julg and B. Deprick, Croat. Claim. Acta 57 (1984) 85. [20] W.J. Hehre, W.A. Lathan, R. Dichtfield, M.D. Newton and J.A. Pople, Quantum Chemistry Program Exchange (Bloomington, 1973). [21] A. Julg, Crystals as Giant Molecules (Springer, Berlin, 1978); A. Julg, A. Pellegatti and F. Marinelli, Nouv. J. Chim. 6 (1982) 31. [22] H. Nakatsuji, T. Hayakawa and T. Yonezawa, J. Am. Chem. Soc. 103 (1981) 7426. [23] C. Girardet and L. Vega, Surface Sci. 151 (1985) 447.