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Quantum-mechanical treatment of the electronic structure and geometry of hydrogen cyanide dimer
J. theor. Biol. (1972) 35, 247-257
Quantum-mechanical Treatment of the Electronic Structure and Geometry of Hydrogen Cyanide Dimer CYNTHIA J. JAMESON AND WILLIAM
YANG
Department of Chemistry, University of Illinois at Chicago Circle, Box 4340 Chicago, Ill. 60680, U.S.A. (Received 17 August 1971) Experiments used to develop theories of chemical evolution se-emto indicate that hydrogen cyanide, HCN, was an important molecule in prebiotic synthesis.In particular, polymerization products of hydrogen cyanide have beenfound to yield polypeptidesupon hydrolysis. The proposedkey intermediatein prebiotic synthesisis the aminocyanocarbene isomerof the dimer,eitherasa I,3 biradicalor asa dipolar singletstructure. Sincethis moleculehasnever beensuccessfullyisolatedand characterized, a quantum mechanicalstudy of various structuresof the dimer is carried out using the INDO method. The resultsindicate that the lowest energy isomer is the iminoacetonitrile, with the aminocyanocarbenebeing next lowest. The triplet and singletenergy surfacesof the aminocyanocarbene intersect, so that for somegeometriesthe singletis lower in energy than the triplet, for others the reverse is true. The minima of both surfaces correspond to the linear configuration, with slightly different bond lengths.The triplet stateminimumis 8.8 kcal/mol lower in energythan the singlet minimum. The calculatedspin density distribution for the ground state of the carbenecan be qualitatively describedas a 1,3 biradical, in agreementwith the early proposal of Kliss & Matthews. The charge distribution of the singlet at its minimum energy geometry was also calculated.Wefound the chargeseparationto belessthan that proposedfor the dipolar structure of Moser ei al. Thesecalculationsindicate that while the lowestenergyisomeris the iminoacetonitrile,the aminocyanocarbene, the lowest-energytriplet, doeshave the appropriate spindistribution in its ground state for the biradical polymerization proposedin the theory of chemical evolution of Kliss & Matthews. Experimentsare suggestedto determinethe nature of the HCN polymerization mechanism,especially in the gasphase.By application of standardtechniquesusedin polymer science,the nature of the gasphasepolymerization of HCN can be determined, and the role of suchreactionsin chemicalevolution can be better understood. 247
248
C.
I.
JAMESON
1. Introduction
AND
W.
YANG
and Methods
The hypothesis that life originated by a process of slow chemical evolution has been the basis of many attempts to synthesize biochemical molecules under simulated primitive earth conditions. From these experiments it appears to be well established that cl-amino acids could have been synthesized readily in the primitive earth atmosphere presumed to consist of hydrides of carbon, nitrogen and oxygen. These experiments seemed to indicate that HCN is a reaction intermediate in the formation of simple amino acids via the familiar Strecker synthesis. From the reaction between HCN and aqueous NH,, various workers (Oro & Kamat, 1961; Lowe, Rees & Markham, 1963; Abelson, 1966) detected purines, and a-amino acids. Since black HCN polymers were also produced, it was suggested (Oro, 1963) that the a-amino acids were formed by hydrolysis of HCN oligomers such as the tetramer (which has recently been well characterized as 1,2-diaminomaleonitrile). Matthews & Moser (1966, 1967) showed that when the products of the polymerization of hydrogen cyanide (whether in acqueous solution or by electrical discharge in the gas-phase) are hydrolyzed, the products of hydrolysis were polypeptides which further hydrolyzed to amino acids of which at least 14 were identified. This seems to support the possibility that prebiotic synthesis of polypeptides and proteins arose directly from polymerization of HCN, as had been proposed earlier by Kliss & Matthews (1962) rather than from condensation of free amino-acids which had arisen from simple inorganic gases. The proposed key step in the polymerization is the dimerization of HCN (Kliss 8z Matthews, 1962). As yet, there has been no unequivocal experimental evidence which supports any particular structure for HCN dimer. Among the possible structures are shown in Figs 1 and 3 : the cis and trans conformations of the iminoacetonitrile isomer (numbered I and II), the cis (IV), truns (III), and linear (V) conformations of the vinylidene di-imine isomer, and the various planar and non-planar conformations of the aminocyanocarbene isomer (VII, VI), the angle 01indicated in Figs 1 and 3 being unknown. In the absence of experimental evidence, it had been widely assumed (Volker, 1960 and references cited therein) that HCN dimer is iminoacetonitrile (I or II). Moser, Fritzch, Westman, Kliss & Matthews (1967) attempted to synthesize VII by decomposition of the Na or Li salt of 1-cyanoformamide p-toluenesulfonylhydrazone, a precursor of VII:
H,C
S02N-N
= h4
c
PN ‘NH?
GEOMETRY
OF
HCN
DIMER
249
where M is either Na or Li. Indirect evidence for formation of V is the appearance of the p-toluenesulfinate and N,, as well as a yellow color trapped in a frozen glass, which species readily eliminates HCN. The formation of the well-characterized HCN tetramer (diaminomaleonitrile) was strong indirect evidence that VII was the trapped species, but no direct, positive evidence could be obtained of its structure since it was short-lived. Thus, there is no direct experimental evidence for either the structure of the HCN dimer which is a possible intermediate in the observed base-catalyzed polymerization of HCN, or the structure of the HCN dimer which is a possible reactive intermediate in proposed gas-phase prebiotic synthesis. Also, if indeed the dimer is an intermediate in the base-catalyzed polymerization (and/or the gas-phase prebiotic polymerization), it remains to be seen whether it is the lowest energy isomer or some reactive excited configuration which is involved. Thus, the relative energies and electronic structures of the various configurations and conformations possible for HCN dimer are of considerable interest. Of special interest is the electronic structure of aminocyanocarbene (VII) which is the key intermediate in the proposed theory of prebiotic synthesis of Kliss & Matthews (1962). Thus, we have undertaken to characterize by semi-empirical quantum-mechanical calculations, the different structures for HCN dimer. The structures I to IV involve only the usual formal bonds and the bond lengths and angles assumed are those obtained from the X-ray diffraction or microwave data for analogous bonding situations. On the other hand, structures VI and VII cannot be characterized with bond lengths for lack of similar data on carbenes. Thus, for VI and VII we have calculated energies and electron distributions as a function of geometry. Since both the singlet and triplet electronic states of VII are of interest, both singlet and triplet potential surfaces were calculated. The method which was used is the intermediate neglect of differential overlap (INDO) method of Pople which has been shown to be quite successful in predicting relative energies as a function of geometry. For a complete discussion of the method, see Pople & Beveridge (1970). INDO avoids complete neglect of electron repulsion terms. Although most of the electron repulsion integrals are ignored, the important ones are included. Of the available semi-empirical methods of molecular quantum mechanics, INDO was chosen since we are interested in charge distribution and spin densities as well as geometry. Extended Htickel theory (EHT) gives poor prediction of bond angles especially for molecules containing atosm of widely different electronegativities. EHT does better than CNDO/2 (complete neglect of differential overlap) or INDO in predicting conformations
250
C.
J.
JAMESON
AND
W.
YANG
around single bonds, but this is of no particular interest in this study. Charge distributions by EHT are grossly exaggerated and unsatisfactory for molecules containing atoms with large differences in electronegativity. CND0/2 or INDO gives much better charge distributions. Also, application of EHT to unsaturated molecules must be undertaken with caution since in some cases the order of the virtual orbital levels seem to indicate that the n: electron system is not treated correctly by the method. INDO has the added advantage that both closed shell (singlet) and open-shell states can be characterized with ease, without having to resort to non-self-consistent open-shell states made up from self-consistent closed shell state molecular orbitals. INDO has been found to give spin densities which are sufficiently accurate for reasonable predictions of hypertine coupling constants (Pople & Beveridge, 1970). This means that the calculated unpaired spin distribution in triplet states will be reliable. Since there has been some question as to the multiplicity (singlet or triplet) of the ground state of structure VII, the reliability of the relative ordering of energies of singlet-triplet states of the same geometry for compounds of this type were checked by calculations on both the singlet and triplet states of cyanomethylene, H-C-C-N, known to be both linear and triplet in the ground state (Bernheim, Kempf, Humer & Skell, 1964; Bernheim, Kempf, Gramas & Skell, 1965). 2. Results Calculations were carried out on two slightly different geometries for each of I-IV, using bond lengths and angles from X-ray diffraction or microwave data on compounds with analogous bonding situations. The bond lengths and angles shown in Fig. 1 are those of the lower-energy geometry. Seven different geometries were used for VI, with various angles a. Other than these seven points no further attempt was made to explore the potential surface of VI. All energy values obtained for VI were higher in energy than any of the corresponding points (identical N-C, C-C bond lengths) in the VII potential surface. Exploratory calculations on VII singlet and triplet were done first, using bond lengths and angles found in X-ray diffraction and microwave data on compounds with bonding situations which were close to VII. The exploratory variations in lengths and angles were done by the method of steepest descent. The triplet was found consistently higher in energy than the singlet for configurations away from the minimum energy. Out-of-plane bent structures were slightly higher in energy than in-plane bent structures. Then, for both the singlet and triplet, a was varied in steps of 15” from 90” to 180” and the
GEOMETRY
Hloo6NmlC
K!6c
OF
HCN
N131
121 ~;lcfxH 0995
P
H
251
DIIviER
li
\
; ! il 109”
c 130
C125N
L/’ (I = IOB” m
FIG. 1. Geometries of lowest energy found for various configurations of HCN dimer: I, truns-iminoacetonitrile; II, cis-iminoacetonitrile; III, kurzknylidenediimine; IV, cisvinylidenediimine; V, linear vinylidenediimine; VI, aminocyanocarbene (with tetrahedral NH2 group).
bond lengths by 0.05A around the low-energy points found. The results for the singlet are shown in Table 1. The singlet and triplet surfaces of VII intersect. One such crossing point is shown in Fig. 2. The lowest calculated energy point on the 0.05A grid was the same for both triplet and singlet states. The minimum energy occurs for angle M = 180”. (The surface is symmetrical with respect to angles on either side of 180”.) The actual minimum point was obtained by differentiation of Newton’s interpolation formula (Margenau & Murphy, 1957) for energy vs. distances r, -c, r, -c and rc --N respectively, leading to a value of r, -c = 1.313 A, k -c = 1.302 and r, --N = 1.237 for the singlet. A final INDO calculation was made with these values. The minimum point on the triplet surface was obtained in the same way. The geometries of lowest energy in the singlet and triplet surfaces of VII are shown in Fig. 3. As is to be expected, the bond lengths are all slightly different in the triplet state from that in the singlet. The triplet was found to be lower in energy by about 0.014 atomic units or O-38 eV. From these results, we see that the ground state of VII is a triplet with the singlet only 0.38 eV or 8.8 kcal/mol higher in energy. In order to check the reliability of the relative ordering of singlet and triplet energies of a particular molecule by the INDO method, calculations were performed on cyanomethylene, H-C-C-N, known to be both linear and triplet in the ground
1.25 1.28 1.30
1.25 1.30 1.35 140 1.45
(A) 1.23 1.28 1.33 1.38
roq-&1*20
ho(A)
rNec
1
36.981979 37WOOO8 37.002419 36.992395
- 36.995821 - 37GOOOO8 - 36.994097
- 36.991812 - 37.OOOOO8 - 36.997120
-
180
36.981223 36.999476 37GO2078 36.992220
- 36.996025 - 36.999476 - 36.993558
- 36.989815 - 36.994760 - 36.997955
-
165”
rN-c
= 1.30 and
1.25A
1JY
- 36.943120
36.958357 36.982635 36.994409 36.996195 36.989659
- 36.912027
-
- 36.986402 - 36.982635
= 1.30A
36-973270 36.991878 36.999472 36.996531
- 36.960780 - 36.982635 - 36.988414
120”
- 36.993291 - 36.991808
-
rC-N = l.ZS?i
- 36.971644 - 36.991878 - 36.996127
rC-N =
= 1.28 and rc-c
36.984032 36.997314 36.999290 36.992298
- 36.995810 - 36.997314 - 36.990320
-
= 1.28 and
- 36.978332 - 36.997314 - 37GOO547
rNec
rcec
150”
Energies (in atomic units) for various configurations of aminocyanocarbene
TABLE
- 36.930369
- 36.974718 - 36.969389
- 36.940098 - 36.969389 - 36.985088
- 36.945432 - 36.969388 - 36.977043
105” -
(VZZ) singlet
- 36.856205
- 36.957878 - 36.953653
- 36.921365 - 36.953653 - 36.972053
- 36.925937 - 36.953653 - 36.964620
90”
GEOMETRY
OF HCN
253
DIMER
I - ] -36
97
- -36 99
I 1 -3699
J -37
2
00
;-T
\
\
\
\
\
\
37.01
\
0.
.T
FICL 2. Some traces on the singlet and triplet potential surfaces of aminocyanocarbene (VII) showing one of the crossing points between singlet and triplet surfaces.
state (Bernheim et al., 1964, 1965). Our calculations show that in all of the various points scanned on the potential surfaces near the minimum, the triplet was consistently lower in energy than the singlet, the lowest energy triplet geometry being that with rc -c = 1*237A and rCeN = 1*315A, and the singlet-triplet separation being 0462 atomic unit or le69eV. These calculations show that on a compound of the same type as VII, the INDO
H
t-l
XD
singlet
PIT
triplet
FIG. 3. Geometry of lowest energy in the singlet and triplet surfaces of aminocyanocarbene (VII).
254
C. J. JAMESON
AND
W.
YANG
method is indeed sufficiently reliable for determination of the relative ordering of singlet and triplet energies. Of particular interest with respect to the theory of Kliss & Matthews are the charge distribution and bond orders of the VII singlet and triplet and the spin distribution of VII triplet. Kliss and Matthews (1962) had postulated that aminocyanocarbene exists as a 1,l biradical and as a 1,3 biradical. The 1,3 biradical (presumably the lower energy of the two forms) is assumed to polymerize head-to-tail to yield a polymer with a -C-C-Nbackbone. This postulated reaction is dependent upon the spin distribution being such as to have close to unit a-spin on both carbon and nitrogen atoms and small spin densities elsewhere. In addition the charge distribution and bondorders of the singlet structure have been suggested (Moser et al., 1967) to be that qualitatively described by the following: s-
Ei+ “‘C”CeN “ZN
The calculated spin densities, charge densities and bond orders in the triplet are given in Fig. 4. The charge densities and bond orders in the singlet are likewise in Fig. 4. The charge separation in the singlet state is not nearly as 0 0363 $00897
to
1211 00800
-0.0461
t 0 1098
-0 5553 t +00475
-0 2333
N-C-C-N /
0 9577
14412 + -01762
N-C-C-N
I536
1.665
H
2 198
/
1200
2.045
1708
H
SLU
singlet
‘XII
triplet
FIG. 4. Molecular indices of the singlet and triplet states of aminocyanocarbene (VII). Bond orders are shown between atoms. Atomic charge densities are shown next to the symbol for that atom. Spin densites are indicated at the ends of arrows in the triplet structure.
large as that proposed by Moser et al., corresponding
to a dipole moment
of 5.75 Debye and a simplified structure somewhat like H,N-C--t’-&. Matthews’ dipolar structure would correspond to a much greater dipole moment. The spin distribution in the triplet state is, as predicted by Kliss & Matthews, very nearly that of the following structure: H,N-C=C=N. The linear configuration found for the ground state of aminocyanocarbene prompted us to consider the linear form of vinylidenediimine: H-N=C==C=N-H (V).
GEOMETRY
OF HCN
255
DIMER
The symmetry of the linear diimine is such as to suggest the possibility of a degenerate highest occupied molecular orbital, which would make the triplet state of the linear vinylidenediimine lower in energy than its singlet state, possibly lower in energy than the cis or frans forms and possibly even lower than the triplet state of aminocyanocarbene (VII). However, as it turned out, the linear conformation is higher in energy than either cis or trans. The lowest energies found for each of I to VII are shown in Table 2 for singlet and triplet states. These correspond to the geometries shown in TABLE
2
Lowest energies (in atomic units) found for each of structures I to VII correspondingto geometriesshownin Figs I and 3. Structure
Energy (a.u.) triplet singlet
Relative energy, (kcal/mole) singlet triplet
I Puns-iminoacetonitrile II Cis-iminoacetonitrile
- 37.100810 - 37.107328
- 36.972176 - 36.970887
4.1 0.0
84.7 85.5
III Truns-vinylidenediimine IV Cis-vinylidenediimine V Linear vinylidenediimine
- 37.006146 - 37004637 - 36.948062
- 36.941069 - 36.942768 - 36.975070
63 94 64.4 99.9
104.3 103.2 82.9
VI Aminocyanocarbene (tetrahedral N) VII Aminocyanocarbene (linear)
- 36.982501
- 36.999414
78.2
67.6
- 37.003447
- 37.017427
65.1
56.4
Also shown are the energies (in kcal/mol) of the various structures relative to the lowest energy isomer, cis-aminoacetonitrile. One atomic unit of energy is 27.20 eV or 627 kcal/ mol.
Figs 1 and 3. As the table shows, the lowest energy isomer is the iminoacetonitrile, with the cis conformer (II) being insignificantly lower than the trans one. The ground state of aminocyanocarbene (VII) is found to be about 56 kcal/mol higher in energy than the lowest energy isomer. Of all the structural isomers studied, only the aminocyanocarbene had a triplet ground state, and was the lowest energy triplet among all the structures considered. 3. Conclusions We have found that the lowest energy configurations are the iminoacetonitriles (I and II) with the linear aminocyanocarbene being next lowest. The 7.R. 17
256
C.
J.
JAMESON
AND
W.
YANG
triplet and singlet states of the aminocyanocarbene intersect, so that for some geometries, the singlet is lower in energy than the triplet, for others the reverse is true. Near the minimum, the triplet surface lies below the singlet. At the minimum, the triplet is about Oa38eV or 8.8 kcal/mol below the singlet. The relative ordering of singlet and triplet energies for the same configuration by the INDO method was checked by calculations on cyanomethylene. These support the reliability of the method for H-C-C-N, and presumably it is just as reliable for H,N-C-C-N. The spin and charge distributions and the bond orders in aminocyanocarbene agree with the earlier qualitative description of its electronic structure, except that the charge separation in the proposed dipolar singlet structure was much greater than that found here. Our calculations indicate that the ground state of aminocarbene (VII) is a triplet whereas the ground states of the other isomers are singlets. Furthermore, if INDO calculations are to be believed, the difference in energy between the singlet and the triplet states of the lower energy isomer is greater than that between the ground states of the different isomers. That is, the lowest energy triplet state is that of VII. This brings up the point of the nature of the polymerization reaction in hydrogen cyanide. The original proposed theory by Kliss & Matthews involved a radical polymerization. The possibility of an ionic polymerization was considered upon failure to observe any EPR (electron paramagnetic resonance) signal expected of a ground triplet state in the trapped species in the attempted synthesis of VII by Moser et al. (1967). However, the interaction between the spins of the two unpaired electrons in VII triplet may have broadened the EPR signal sufficiently to prevent its detection. Since the trapped species was never fully characterized, neither the identity nor the multiplicity (singlet or triplet) of the trapped species had been conclusively verified. Our calculations show that the lowest energy triplet state is that of the linear aminocyanocarbene. If the polymerization of hydrogen cyanide in prebiotic synthesis occurred by a radical polymerization involving a triplet dimer intermediate, then linear aminocyanocarbene (VII) ground state triplet is its most likely form. The most obvious experiment which is suggested by our results is the determination of the type (ionic or radical) of polymerization in HCN in the gas phase. This is easily done by attempting to initiate the reaction with some radical and seeing whether it can be radical initiated and still produce the same results. Also, attempts could be made to trap the radical intermediate in the simulation of prebiotic polymerization of HCN by standard methods used by polymer chemists in studying radical polymerizations. Ionic polymerizations can likewise be characterized by standard techniques. By application of standard techniques used in polymer science,
GEOMETRY
OF
HCN
DIMER
257
the nature of the gas phase polymerization of HCN can be determined, and the role of such reactions in chemical evolution can be better understood. Note added in proof: While this paper was in pressa paper by G. H. Loew, “Conformation of Hydrogen Cyanide Dimer and its Role in ChemicalEvolution” appearedin J. theor. Biof. (1971) 33, 121-130.Loew’s EHT calculations on the aminocyanocarbenewere for singlepoints chosenon eachof the potential surfaces and thus would not give any indication of the relative energy ordering of the different conformations unlesseach of the points happenedto be chosenfortuitously at the minimum of each surface.This is of specialinterest here sincethe calculatedsurfaceswerefound to cross.
REFERENCES ABELSON, P. H. (1966). Proc. natn. Acud. Sci. U.S.A. 55, 1365. BERNHEIM, R. A., KEMPF, R. J., GRAMAS, J. V. & SKELL, P. S. (1965). J. them. Phys. 43, 196.
BERNHEIM, R. A., KEMPF, R. J., HUMER, P. W. & SKELL, P. S. (1964). J. them. Phys. 41, 1156. Kuss, R. M. & MATHEWS, C. N. (1962). Proc. natn. Acad. Sci. U.S.A. 48, 1300. LOWE, C. U., REES, M. W. & MARKHAM, R. (1963. Nature, Land. 199, 219. MARGENAU, H. & MURPHY, G. M. (1957). The Mathematics of Physics and Chemistry.
New York: D. Van Nostrand.
MAITHEWS, C. N. & MOSER, R. E. (1966). Proc. natn. Acud. Sci. U.S.A. 56, 1087. MATHEWS, C. N. & MOSER, R. E. (1967). Nature, Land. 215, 1230. MOSER, R. E., FRITZCH, J. M., WESTMAN, T. L., KLISS, R. M. & MATTHEWS, C. N. (1967). J. Am. them. Sot. 89, 5673. ORO, J. (1963). Ann. New York Acad Sci.. 108, 464. ORO, J. & KAMAT, J. S. (1961). Nature, Land. 190, 442. POPLE, J. A. & BEVERIDGE,D. L. (1970. Approximate Molecular Orbital Theory. New York:
McGraw-Hill.
VOLKER, T. (1960). Angew. Chem. 72, 379.
Quantum-mechanical Treatment of the Electronic Structure and Geometry of Hydrogen Cyanide Dimer CYNTHIA J. JAMESON AND WILLIAM
YANG
Department of Chemistry, University of Illinois at Chicago Circle, Box 4340 Chicago, Ill. 60680, U.S.A. (Received 17 August 1971) Experiments used to develop theories of chemical evolution se-emto indicate that hydrogen cyanide, HCN, was an important molecule in prebiotic synthesis.In particular, polymerization products of hydrogen cyanide have beenfound to yield polypeptidesupon hydrolysis. The proposedkey intermediatein prebiotic synthesisis the aminocyanocarbene isomerof the dimer,eitherasa I,3 biradicalor asa dipolar singletstructure. Sincethis moleculehasnever beensuccessfullyisolatedand characterized, a quantum mechanicalstudy of various structuresof the dimer is carried out using the INDO method. The resultsindicate that the lowest energy isomer is the iminoacetonitrile, with the aminocyanocarbenebeing next lowest. The triplet and singletenergy surfacesof the aminocyanocarbene intersect, so that for somegeometriesthe singletis lower in energy than the triplet, for others the reverse is true. The minima of both surfaces correspond to the linear configuration, with slightly different bond lengths.The triplet stateminimumis 8.8 kcal/mol lower in energythan the singlet minimum. The calculatedspin density distribution for the ground state of the carbenecan be qualitatively describedas a 1,3 biradical, in agreementwith the early proposal of Kliss & Matthews. The charge distribution of the singlet at its minimum energy geometry was also calculated.Wefound the chargeseparationto belessthan that proposedfor the dipolar structure of Moser ei al. Thesecalculationsindicate that while the lowestenergyisomeris the iminoacetonitrile,the aminocyanocarbene, the lowest-energytriplet, doeshave the appropriate spindistribution in its ground state for the biradical polymerization proposedin the theory of chemical evolution of Kliss & Matthews. Experimentsare suggestedto determinethe nature of the HCN polymerization mechanism,especially in the gasphase.By application of standardtechniquesusedin polymer science,the nature of the gasphasepolymerization of HCN can be determined, and the role of suchreactionsin chemicalevolution can be better understood. 247
248
C.
I.
JAMESON
1. Introduction
AND
W.
YANG
and Methods
The hypothesis that life originated by a process of slow chemical evolution has been the basis of many attempts to synthesize biochemical molecules under simulated primitive earth conditions. From these experiments it appears to be well established that cl-amino acids could have been synthesized readily in the primitive earth atmosphere presumed to consist of hydrides of carbon, nitrogen and oxygen. These experiments seemed to indicate that HCN is a reaction intermediate in the formation of simple amino acids via the familiar Strecker synthesis. From the reaction between HCN and aqueous NH,, various workers (Oro & Kamat, 1961; Lowe, Rees & Markham, 1963; Abelson, 1966) detected purines, and a-amino acids. Since black HCN polymers were also produced, it was suggested (Oro, 1963) that the a-amino acids were formed by hydrolysis of HCN oligomers such as the tetramer (which has recently been well characterized as 1,2-diaminomaleonitrile). Matthews & Moser (1966, 1967) showed that when the products of the polymerization of hydrogen cyanide (whether in acqueous solution or by electrical discharge in the gas-phase) are hydrolyzed, the products of hydrolysis were polypeptides which further hydrolyzed to amino acids of which at least 14 were identified. This seems to support the possibility that prebiotic synthesis of polypeptides and proteins arose directly from polymerization of HCN, as had been proposed earlier by Kliss & Matthews (1962) rather than from condensation of free amino-acids which had arisen from simple inorganic gases. The proposed key step in the polymerization is the dimerization of HCN (Kliss 8z Matthews, 1962). As yet, there has been no unequivocal experimental evidence which supports any particular structure for HCN dimer. Among the possible structures are shown in Figs 1 and 3 : the cis and trans conformations of the iminoacetonitrile isomer (numbered I and II), the cis (IV), truns (III), and linear (V) conformations of the vinylidene di-imine isomer, and the various planar and non-planar conformations of the aminocyanocarbene isomer (VII, VI), the angle 01indicated in Figs 1 and 3 being unknown. In the absence of experimental evidence, it had been widely assumed (Volker, 1960 and references cited therein) that HCN dimer is iminoacetonitrile (I or II). Moser, Fritzch, Westman, Kliss & Matthews (1967) attempted to synthesize VII by decomposition of the Na or Li salt of 1-cyanoformamide p-toluenesulfonylhydrazone, a precursor of VII:
H,C
S02N-N
= h4
c
PN ‘NH?
GEOMETRY
OF
HCN
DIMER
249
where M is either Na or Li. Indirect evidence for formation of V is the appearance of the p-toluenesulfinate and N,, as well as a yellow color trapped in a frozen glass, which species readily eliminates HCN. The formation of the well-characterized HCN tetramer (diaminomaleonitrile) was strong indirect evidence that VII was the trapped species, but no direct, positive evidence could be obtained of its structure since it was short-lived. Thus, there is no direct experimental evidence for either the structure of the HCN dimer which is a possible intermediate in the observed base-catalyzed polymerization of HCN, or the structure of the HCN dimer which is a possible reactive intermediate in proposed gas-phase prebiotic synthesis. Also, if indeed the dimer is an intermediate in the base-catalyzed polymerization (and/or the gas-phase prebiotic polymerization), it remains to be seen whether it is the lowest energy isomer or some reactive excited configuration which is involved. Thus, the relative energies and electronic structures of the various configurations and conformations possible for HCN dimer are of considerable interest. Of special interest is the electronic structure of aminocyanocarbene (VII) which is the key intermediate in the proposed theory of prebiotic synthesis of Kliss & Matthews (1962). Thus, we have undertaken to characterize by semi-empirical quantum-mechanical calculations, the different structures for HCN dimer. The structures I to IV involve only the usual formal bonds and the bond lengths and angles assumed are those obtained from the X-ray diffraction or microwave data for analogous bonding situations. On the other hand, structures VI and VII cannot be characterized with bond lengths for lack of similar data on carbenes. Thus, for VI and VII we have calculated energies and electron distributions as a function of geometry. Since both the singlet and triplet electronic states of VII are of interest, both singlet and triplet potential surfaces were calculated. The method which was used is the intermediate neglect of differential overlap (INDO) method of Pople which has been shown to be quite successful in predicting relative energies as a function of geometry. For a complete discussion of the method, see Pople & Beveridge (1970). INDO avoids complete neglect of electron repulsion terms. Although most of the electron repulsion integrals are ignored, the important ones are included. Of the available semi-empirical methods of molecular quantum mechanics, INDO was chosen since we are interested in charge distribution and spin densities as well as geometry. Extended Htickel theory (EHT) gives poor prediction of bond angles especially for molecules containing atosm of widely different electronegativities. EHT does better than CNDO/2 (complete neglect of differential overlap) or INDO in predicting conformations
250
C.
J.
JAMESON
AND
W.
YANG
around single bonds, but this is of no particular interest in this study. Charge distributions by EHT are grossly exaggerated and unsatisfactory for molecules containing atoms with large differences in electronegativity. CND0/2 or INDO gives much better charge distributions. Also, application of EHT to unsaturated molecules must be undertaken with caution since in some cases the order of the virtual orbital levels seem to indicate that the n: electron system is not treated correctly by the method. INDO has the added advantage that both closed shell (singlet) and open-shell states can be characterized with ease, without having to resort to non-self-consistent open-shell states made up from self-consistent closed shell state molecular orbitals. INDO has been found to give spin densities which are sufficiently accurate for reasonable predictions of hypertine coupling constants (Pople & Beveridge, 1970). This means that the calculated unpaired spin distribution in triplet states will be reliable. Since there has been some question as to the multiplicity (singlet or triplet) of the ground state of structure VII, the reliability of the relative ordering of energies of singlet-triplet states of the same geometry for compounds of this type were checked by calculations on both the singlet and triplet states of cyanomethylene, H-C-C-N, known to be both linear and triplet in the ground state (Bernheim, Kempf, Humer & Skell, 1964; Bernheim, Kempf, Gramas & Skell, 1965). 2. Results Calculations were carried out on two slightly different geometries for each of I-IV, using bond lengths and angles from X-ray diffraction or microwave data on compounds with analogous bonding situations. The bond lengths and angles shown in Fig. 1 are those of the lower-energy geometry. Seven different geometries were used for VI, with various angles a. Other than these seven points no further attempt was made to explore the potential surface of VI. All energy values obtained for VI were higher in energy than any of the corresponding points (identical N-C, C-C bond lengths) in the VII potential surface. Exploratory calculations on VII singlet and triplet were done first, using bond lengths and angles found in X-ray diffraction and microwave data on compounds with bonding situations which were close to VII. The exploratory variations in lengths and angles were done by the method of steepest descent. The triplet was found consistently higher in energy than the singlet for configurations away from the minimum energy. Out-of-plane bent structures were slightly higher in energy than in-plane bent structures. Then, for both the singlet and triplet, a was varied in steps of 15” from 90” to 180” and the
GEOMETRY
Hloo6NmlC
K!6c
OF
HCN
N131
121 ~;lcfxH 0995
P
H
251
DIIviER
li
\
; ! il 109”
c 130
C125N
L/’ (I = IOB” m
FIG. 1. Geometries of lowest energy found for various configurations of HCN dimer: I, truns-iminoacetonitrile; II, cis-iminoacetonitrile; III, kurzknylidenediimine; IV, cisvinylidenediimine; V, linear vinylidenediimine; VI, aminocyanocarbene (with tetrahedral NH2 group).
bond lengths by 0.05A around the low-energy points found. The results for the singlet are shown in Table 1. The singlet and triplet surfaces of VII intersect. One such crossing point is shown in Fig. 2. The lowest calculated energy point on the 0.05A grid was the same for both triplet and singlet states. The minimum energy occurs for angle M = 180”. (The surface is symmetrical with respect to angles on either side of 180”.) The actual minimum point was obtained by differentiation of Newton’s interpolation formula (Margenau & Murphy, 1957) for energy vs. distances r, -c, r, -c and rc --N respectively, leading to a value of r, -c = 1.313 A, k -c = 1.302 and r, --N = 1.237 for the singlet. A final INDO calculation was made with these values. The minimum point on the triplet surface was obtained in the same way. The geometries of lowest energy in the singlet and triplet surfaces of VII are shown in Fig. 3. As is to be expected, the bond lengths are all slightly different in the triplet state from that in the singlet. The triplet was found to be lower in energy by about 0.014 atomic units or O-38 eV. From these results, we see that the ground state of VII is a triplet with the singlet only 0.38 eV or 8.8 kcal/mol higher in energy. In order to check the reliability of the relative ordering of singlet and triplet energies of a particular molecule by the INDO method, calculations were performed on cyanomethylene, H-C-C-N, known to be both linear and triplet in the ground
1.25 1.28 1.30
1.25 1.30 1.35 140 1.45
(A) 1.23 1.28 1.33 1.38
roq-&1*20
ho(A)
rNec
1
36.981979 37WOOO8 37.002419 36.992395
- 36.995821 - 37GOOOO8 - 36.994097
- 36.991812 - 37.OOOOO8 - 36.997120
-
180
36.981223 36.999476 37GO2078 36.992220
- 36.996025 - 36.999476 - 36.993558
- 36.989815 - 36.994760 - 36.997955
-
165”
rN-c
= 1.30 and
1.25A
1JY
- 36.943120
36.958357 36.982635 36.994409 36.996195 36.989659
- 36.912027
-
- 36.986402 - 36.982635
= 1.30A
36-973270 36.991878 36.999472 36.996531
- 36.960780 - 36.982635 - 36.988414
120”
- 36.993291 - 36.991808
-
rC-N = l.ZS?i
- 36.971644 - 36.991878 - 36.996127
rC-N =
= 1.28 and rc-c
36.984032 36.997314 36.999290 36.992298
- 36.995810 - 36.997314 - 36.990320
-
= 1.28 and
- 36.978332 - 36.997314 - 37GOO547
rNec
rcec
150”
Energies (in atomic units) for various configurations of aminocyanocarbene
TABLE
- 36.930369
- 36.974718 - 36.969389
- 36.940098 - 36.969389 - 36.985088
- 36.945432 - 36.969388 - 36.977043
105” -
(VZZ) singlet
- 36.856205
- 36.957878 - 36.953653
- 36.921365 - 36.953653 - 36.972053
- 36.925937 - 36.953653 - 36.964620
90”
GEOMETRY
OF HCN
253
DIMER
I - ] -36
97
- -36 99
I 1 -3699
J -37
2
00
;-T
\
\
\
\
\
\
37.01
\
0.
.T
FICL 2. Some traces on the singlet and triplet potential surfaces of aminocyanocarbene (VII) showing one of the crossing points between singlet and triplet surfaces.
state (Bernheim et al., 1964, 1965). Our calculations show that in all of the various points scanned on the potential surfaces near the minimum, the triplet was consistently lower in energy than the singlet, the lowest energy triplet geometry being that with rc -c = 1*237A and rCeN = 1*315A, and the singlet-triplet separation being 0462 atomic unit or le69eV. These calculations show that on a compound of the same type as VII, the INDO
H
t-l
XD
singlet
PIT
triplet
FIG. 3. Geometry of lowest energy in the singlet and triplet surfaces of aminocyanocarbene (VII).
254
C. J. JAMESON
AND
W.
YANG
method is indeed sufficiently reliable for determination of the relative ordering of singlet and triplet energies. Of particular interest with respect to the theory of Kliss & Matthews are the charge distribution and bond orders of the VII singlet and triplet and the spin distribution of VII triplet. Kliss and Matthews (1962) had postulated that aminocyanocarbene exists as a 1,l biradical and as a 1,3 biradical. The 1,3 biradical (presumably the lower energy of the two forms) is assumed to polymerize head-to-tail to yield a polymer with a -C-C-Nbackbone. This postulated reaction is dependent upon the spin distribution being such as to have close to unit a-spin on both carbon and nitrogen atoms and small spin densities elsewhere. In addition the charge distribution and bondorders of the singlet structure have been suggested (Moser et al., 1967) to be that qualitatively described by the following: s-
Ei+ “‘C”CeN “ZN
The calculated spin densities, charge densities and bond orders in the triplet are given in Fig. 4. The charge densities and bond orders in the singlet are likewise in Fig. 4. The charge separation in the singlet state is not nearly as 0 0363 $00897
to
1211 00800
-0.0461
t 0 1098
-0 5553 t +00475
-0 2333
N-C-C-N /
0 9577
14412 + -01762
N-C-C-N
I536
1.665
H
2 198
/
1200
2.045
1708
H
SLU
singlet
‘XII
triplet
FIG. 4. Molecular indices of the singlet and triplet states of aminocyanocarbene (VII). Bond orders are shown between atoms. Atomic charge densities are shown next to the symbol for that atom. Spin densites are indicated at the ends of arrows in the triplet structure.
large as that proposed by Moser et al., corresponding
to a dipole moment
of 5.75 Debye and a simplified structure somewhat like H,N-C--t’-&. Matthews’ dipolar structure would correspond to a much greater dipole moment. The spin distribution in the triplet state is, as predicted by Kliss & Matthews, very nearly that of the following structure: H,N-C=C=N. The linear configuration found for the ground state of aminocyanocarbene prompted us to consider the linear form of vinylidenediimine: H-N=C==C=N-H (V).
GEOMETRY
OF HCN
255
DIMER
The symmetry of the linear diimine is such as to suggest the possibility of a degenerate highest occupied molecular orbital, which would make the triplet state of the linear vinylidenediimine lower in energy than its singlet state, possibly lower in energy than the cis or frans forms and possibly even lower than the triplet state of aminocyanocarbene (VII). However, as it turned out, the linear conformation is higher in energy than either cis or trans. The lowest energies found for each of I to VII are shown in Table 2 for singlet and triplet states. These correspond to the geometries shown in TABLE
2
Lowest energies (in atomic units) found for each of structures I to VII correspondingto geometriesshownin Figs I and 3. Structure
Energy (a.u.) triplet singlet
Relative energy, (kcal/mole) singlet triplet
I Puns-iminoacetonitrile II Cis-iminoacetonitrile
- 37.100810 - 37.107328
- 36.972176 - 36.970887
4.1 0.0
84.7 85.5
III Truns-vinylidenediimine IV Cis-vinylidenediimine V Linear vinylidenediimine
- 37.006146 - 37004637 - 36.948062
- 36.941069 - 36.942768 - 36.975070
63 94 64.4 99.9
104.3 103.2 82.9
VI Aminocyanocarbene (tetrahedral N) VII Aminocyanocarbene (linear)
- 36.982501
- 36.999414
78.2
67.6
- 37.003447
- 37.017427
65.1
56.4
Also shown are the energies (in kcal/mol) of the various structures relative to the lowest energy isomer, cis-aminoacetonitrile. One atomic unit of energy is 27.20 eV or 627 kcal/ mol.
Figs 1 and 3. As the table shows, the lowest energy isomer is the iminoacetonitrile, with the cis conformer (II) being insignificantly lower than the trans one. The ground state of aminocyanocarbene (VII) is found to be about 56 kcal/mol higher in energy than the lowest energy isomer. Of all the structural isomers studied, only the aminocyanocarbene had a triplet ground state, and was the lowest energy triplet among all the structures considered. 3. Conclusions We have found that the lowest energy configurations are the iminoacetonitriles (I and II) with the linear aminocyanocarbene being next lowest. The 7.R. 17
256
C.
J.
JAMESON
AND
W.
YANG
triplet and singlet states of the aminocyanocarbene intersect, so that for some geometries, the singlet is lower in energy than the triplet, for others the reverse is true. Near the minimum, the triplet surface lies below the singlet. At the minimum, the triplet is about Oa38eV or 8.8 kcal/mol below the singlet. The relative ordering of singlet and triplet energies for the same configuration by the INDO method was checked by calculations on cyanomethylene. These support the reliability of the method for H-C-C-N, and presumably it is just as reliable for H,N-C-C-N. The spin and charge distributions and the bond orders in aminocyanocarbene agree with the earlier qualitative description of its electronic structure, except that the charge separation in the proposed dipolar singlet structure was much greater than that found here. Our calculations indicate that the ground state of aminocarbene (VII) is a triplet whereas the ground states of the other isomers are singlets. Furthermore, if INDO calculations are to be believed, the difference in energy between the singlet and the triplet states of the lower energy isomer is greater than that between the ground states of the different isomers. That is, the lowest energy triplet state is that of VII. This brings up the point of the nature of the polymerization reaction in hydrogen cyanide. The original proposed theory by Kliss & Matthews involved a radical polymerization. The possibility of an ionic polymerization was considered upon failure to observe any EPR (electron paramagnetic resonance) signal expected of a ground triplet state in the trapped species in the attempted synthesis of VII by Moser et al. (1967). However, the interaction between the spins of the two unpaired electrons in VII triplet may have broadened the EPR signal sufficiently to prevent its detection. Since the trapped species was never fully characterized, neither the identity nor the multiplicity (singlet or triplet) of the trapped species had been conclusively verified. Our calculations show that the lowest energy triplet state is that of the linear aminocyanocarbene. If the polymerization of hydrogen cyanide in prebiotic synthesis occurred by a radical polymerization involving a triplet dimer intermediate, then linear aminocyanocarbene (VII) ground state triplet is its most likely form. The most obvious experiment which is suggested by our results is the determination of the type (ionic or radical) of polymerization in HCN in the gas phase. This is easily done by attempting to initiate the reaction with some radical and seeing whether it can be radical initiated and still produce the same results. Also, attempts could be made to trap the radical intermediate in the simulation of prebiotic polymerization of HCN by standard methods used by polymer chemists in studying radical polymerizations. Ionic polymerizations can likewise be characterized by standard techniques. By application of standard techniques used in polymer science,
GEOMETRY
OF
HCN
DIMER
257
the nature of the gas phase polymerization of HCN can be determined, and the role of such reactions in chemical evolution can be better understood. Note added in proof: While this paper was in pressa paper by G. H. Loew, “Conformation of Hydrogen Cyanide Dimer and its Role in ChemicalEvolution” appearedin J. theor. Biof. (1971) 33, 121-130.Loew’s EHT calculations on the aminocyanocarbenewere for singlepoints chosenon eachof the potential surfaces and thus would not give any indication of the relative energy ordering of the different conformations unlesseach of the points happenedto be chosenfortuitously at the minimum of each surface.This is of specialinterest here sincethe calculatedsurfaceswerefound to cross.
REFERENCES ABELSON, P. H. (1966). Proc. natn. Acud. Sci. U.S.A. 55, 1365. BERNHEIM, R. A., KEMPF, R. J., GRAMAS, J. V. & SKELL, P. S. (1965). J. them. Phys. 43, 196.
BERNHEIM, R. A., KEMPF, R. J., HUMER, P. W. & SKELL, P. S. (1964). J. them. Phys. 41, 1156. Kuss, R. M. & MATHEWS, C. N. (1962). Proc. natn. Acad. Sci. U.S.A. 48, 1300. LOWE, C. U., REES, M. W. & MARKHAM, R. (1963. Nature, Land. 199, 219. MARGENAU, H. & MURPHY, G. M. (1957). The Mathematics of Physics and Chemistry.
New York: D. Van Nostrand.
MAITHEWS, C. N. & MOSER, R. E. (1966). Proc. natn. Acud. Sci. U.S.A. 56, 1087. MATHEWS, C. N. & MOSER, R. E. (1967). Nature, Land. 215, 1230. MOSER, R. E., FRITZCH, J. M., WESTMAN, T. L., KLISS, R. M. & MATTHEWS, C. N. (1967). J. Am. them. Sot. 89, 5673. ORO, J. (1963). Ann. New York Acad Sci.. 108, 464. ORO, J. & KAMAT, J. S. (1961). Nature, Land. 190, 442. POPLE, J. A. & BEVERIDGE,D. L. (1970. Approximate Molecular Orbital Theory. New York:
McGraw-Hill.
VOLKER, T. (1960). Angew. Chem. 72, 379.