Electronic and molecular structures of HCNn polymers: (HCN)3n

European Polymer Journal Vol. 17, pp. 913 to 917, 1981

0014-3057/81/080913-05502.00/0 Crpyright © 1981 Pergamon Press Ltd

Printed in Great Britain. All rights reserved

ELECTRONIC A N D MOLECULAR STRUCTURES OF

-(-HCN--)~. POLYMERS:-~HCN)3--~n M . O H S A K U . 1 , T. SASAKI 1, H . M U R A T A 1 and A. IMAMURA 2 ~Department of Chemistry, Faculty of Science, Hiroshima University, Higashisenda-machi, Hiroshima 730 and 2Department of Chemistry, Shiga University of Medical Science, Setatsukinowa-cho, Otsu, Shiga 520-21, Japan

(Received 18 November 1980)

Abstract--The CNDO/2 method using the tight-binding approximation for polymers was applied to several forms of-[-(HCN)3-~ polymers. From these calculations, we conclude that the polymer exists in the helical form rather than the planar trans zigzag, TTT, form. It was found that, from comparison of the TTT form with the polyglycine II type (Gly-II) form, the intrasegment energy of the TTT form is lower than for the Gly-II type form while the intersegment energy of the Gly-II form is lower than for the TTT form. It was also revealed that, in the typical or-helix type structures, hydrogen bonding between the central and the fourth nearest neighbour segments may play an important stabilizing role.

Table 1. Geometries of --[---(HCN)3--~,

INTRODUCTION

The mechanisms of synthesis of polypeptide from H C N gas have been extensively examined by Matthews et al. [1-6] ; their proposed mechanisms are shown in Fig. 1. The H C N pentamer and precursor to adenine have also been discussed [7]. For the H C N dimer (HCN)2, the semi-empirical [8, 9] and ab initio [10] calculations were applied, giving useful information on the electronic structures of the molecule. Very recently, the C N D O / 2 method [11] using the tight-binding approximation [12] for polymers was applied to --[-(HCN)2-]~n polymers 1 [13]. For this kind of polymer constituent 1, an ab initio crystal study has also been carried out [14]. Matthews et al. have concluded that poly(hydrogen cyanide) may become polyglycine type molecules with helical structures at the end of these mechanisms [4, 15]. The polypeptide, in general, exists in the helical form as

[NH (HCN)~ I HCN

,

[NH CN ;n

LNH

R"

Jn

4H ]H -COz

[OR

Jn

II

I

OR*

l

Jn

Fig. 1. Mechanisms of protein syntheses from HCN-gas proposed by Matthews et al. [1-6].

r(~N), A r(N--C), A r(C~N), A, r(C--C),/~ r(N--H), A r(C--H),/~ q~(C--C N ) ~b(H--N~-----C) q~(N=C--C) O~(N=C--N) ~(C--C--H) ~(C--C--C) th(C--C--N) ~b(C--N--H) tp(C--N--C)

1.206 1.462 1.158 1.530 1.00 1.05 180° 120° 120° 120'~ 109.47122" 109.47122° 109.47122° 120° 120~

Ref. 1-18] Ref. [19] Ref. [20] Ref. [21] Ref. [21] Ref. [22] Ref. [20] * * * * * * * *

* Assumed. the most stable form. However in polymer 1, only the planar form can be acceptable although several forms can be considered; in our previous paper [13] we concluded that the HH1 form (trans zigzag) is the most stable form. It is very interesting to know at which point the polymer takes the helical structure in place of the planar form in the mechanisms shown in Fig. 1. This is one of the main purposes of the present work. We have attempted to discover which of the planar trans zigzag and the helical forms is more stable, assuming several molecular conformations. The numerical calculations were made according to the previous papers [16, 17]. Geometries used for the calculations are summarized in Table 1 [18-22]. Schematic structures, with atom and segment numberings, are shown in Fig. 2. RESULTS AND DISCUSSION

* To whom all correspondence should be addressed. Present address (February 1981-January 1982): Organischchemisches Institut, Universit~it Heidelberg, Im Neuenheimer Feld 270, 6900 Heidelberg, West Germany. 913

The skeletal conformations of the present polymer 2 can be described by three internal rotation angles (~, 4~, ¢o) as shown in Fig. 2. For the conformation of

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M. OHSAKU et al.

N7

N

y

II 3

18

2H/Nj

H9

g~ H

C

~,

"

If

I

H/N

H

N

Fig. 2. Schematic structures, and atom and segment numberings of-[-{HCNh--~ 2. Table 2. Torsional angles (deg) for some regular structures of-(--(HCN)3--~ Conformations/ structures TTT Gly-II* GGG GTT GGT G'G'T TGT fl-I fl-ll

~ 180 150 - 60 -60 - 60 60 180 113 135

~b

~0

Descriptions

180 180 - 80 180 - 60 - 60 180 180 - 60 180 60 180 -60 180 - 119 180 - 1 3 9 - 178

Planar trans zigzag Left-handed helix Left-handed helix Left-handed helix Right-handed ~-helix Left-handed ~-helix left-handed helix Parallel-chain pleated sheet Antiparallel-chain pleated sheet

* Polyglycine II. Table 3. Total energy (eV) of-[--(HCN)3--~ Energy Total Total intrasegment Total one centre Total two centre Total intersegment Total two centre

TTT(L)

GGG(L)

GTT(L)

GGT(L)

G'G'T(L)

-1557.56 -1305.71 -251.85 -28.85 14.41 -0.01

-1586.46 -1556.99 -1305.79 -251.20 -29.47 - 14.72 -0.01

-1586.09 -1557.86 -1306.17 -251.69 -28.23 - 14.09 -0.02

-1586.32 -1557.61 -1305.87 -251.74 -28.71 - 14.34 -0.01

-1586.45 -1556.27 -1305.92 -250.35 -30.19 - 14.48 -0.01 -0.04 - 0.56

-1586.71 -1555.80 -1305.73 -250.07 -30.91 - 14.42 -0.01 -0.03 - 1.00

TGT(L)

rid(L)

fl-II(L)

TTT(D)

Gly-II(D)

GGG(D)

-1586.36 - 1557.47 - 1305.83 -251.64 - 28.89 - 14.42 -0.01 - 0.01

- 1585.38 - 1554.76 -1305.55 -249.21 - 30.62 - 15.30 -0.01

- 1586.04 -1555.63 -1305.64 -249.99 - 30.41 - 15.19 -0.01

-1586.41 -1557.56 -1305.71 -251.85 - 28.85 - 14.41 -0.01

-1586.25 -1557.72 -1305.82 -251.90 - 28.54 - 14.26 -0.01

-1586.09 - 1557.98 - 1306.15 -251.84 - 28.11 - 14.04 -0.01

-1586.41

0-1" 0-2 0-3 0-4

Energy Total Total intrasegment Total one centre Total two centre Total intersegment Total two centre

Gly-II(L)

0-1" 0-2 0-3

* For simplicity, 0-1 (segments) means the central and the first nearest neighbour segments and 0-2, 0-3 . . . . , to the central and the second, third . . . . , nearest neighbour segments. In the present article, up to 0-4 segments were considered for all polymers under study. Energy term: absolute values less than 0.01 eV are not catalogued. Energies are calculated from Eqns (1)-(4) of Ref. 1-17]. H2, t h e r e c a n be t w o a c c e p t a b l e forms, i.e. t h e g r o u p C 4 - - - C 3 - - N 1 - - H 2 is t r a n s for o n e f o r m a n d cis for a n o t h e r . First, t h e c a l c u l a t i o n s were c a r r i e d o u t a s s u m i n g two c o n f o r m a t i o n s for several forms, t h e n it w a s f o u n d t h a t t h e c a l c u l a t e d total e n e r g y is s m a l l e r w h e n t h e C4 C 3 - - N 1 - - H 2 g r o u p is trans. All s u b s e q u e n t c a l c u l a t i o n s were carried o u t a s s u m i n g t h a t this g r o u p is in the t r a n s c o n f o r m a t i o n . T h e r e a r e very m a n y c o n f o r m a t i o n s w h i c h c a n be

a c c e p t a b l e for p o l y m e r 2. In t h e p r e s e n t paper, h o w ever, the c a l c u l a t i o n s were carried o u t a s s u m i n g o n l y t h e typical forms. T h e e x a m i n e d m o l e c u l a r c o n f o r m a t i o n s a n d their i n t e r n a l r o t a t i o n a n g l e s are s u m m a rized in T a b l e 2. T h e n o t a t i o n s for t h e i n t e r n a l r o t a tion a n g l e s follow I U P A C r e c o m m e n d a t i o n [15]. T h e total energies c a l c u l a t e d are s u m m a r i z e d in T a b l e 3. T h e relative stability c a l c u l a t e d f r o m t h e o b t a i n e d total energies is as follows:

G ' G ' T > G l y - I I > G G T > T T T > T G T > G T T > G G G > fl-II > fl-I, 0.25 0.01 0.04 0.05 0.03 0.24 0.05 0.66

Electronic and molecular structures of-(-HCN-)~, polymers:-[-(HCN)3-]-~

915

Table 4. The difference in the two centre interaction energy (eV) in the central segment between TTT and Gly-II forms* N1 Resonance term H27 C3 C6 N7 N8 H9 Exchange term H2 N7 Electrostatic term H2 H9 Total

C3

C4

H5

C6

Total 0.51

0.16 - 0.07 0.18

-0.08 0.15

-0.07 0.19

0.14 -0.11

0.07 -0.05

-0.14 0.12 0.20

0.11 0.10 - 0.06 0.05 - 0.06 0.65

* Digits show the energy difference: Gly-ll - TTT. Energy terms: absolute values less than 0.05 eV are not catalogued. See eqn (3) of Ref. [17] for details. t Atom numberings are shown Fig. 2. with differences in eV. Generally, therefore, the stabilities are as follows: helical > trans zigzag (TTT) > fl-structures.

Comparison between L- with D-configurations Brief discussion is given on the L- and D-peptide structures. In the TTT form, there is no difference in total energy between the L- and D-configurations. For the G G G form, the total energy obtained is nearly equal in the L- and D-configurations, although difference appeared in the partitioned energy terms. With the Gly-II form, from the total energy obtained, the D-configuration is less stable than the L-one. For the Gly-II form according to the partitioning of the total energy, the total intrasegment energy is smaller in the D-configuration, but with the total intersegment term, the L-configuration is much smaller in energy than the D. As a result, it can be said that the stabilities of the L-configuration and the D-configuration are governed by a balance of several energy terms.

Comparison of planar zigzag (TTT) with Gly-ll structures In order to compare the planar zigzag and helical forms, we considered two typical conformations, viz. T T T and Gly-II forms. Consider first the intrasegment energy. The total intrasegment energy is smaller in the T T T form than in the Gly-II form. The one centre energy is smaller in the Gly-II form than in the T T T form but the two centre energy is much smaller in the TTT form. Using Table 4, the situation will be discussed in some detail. The element with plus sign shows that the TTT form is stabilized more than the Gly-II form, while the element with minus sign shows that the Gly-II form is stabilized more than the TTT form. The elements to stabilize the T T T form are found in the resonance and exchange terms. Among the elements, (H2, N1), (H9, N1), (C6, C3), (N8, C3), (H9, H5) and (N7, C6) stabilize the T T T form more than the Gly-II form, while the elements (H9, C3),

(C6, H5) and (N8, H5) stabilize more the Gly-lI form than the T T T form. We now discuss the intersegment energy term. Most of the energy difference between the two forms appeared in the 0-1 term. According to this term, the Gly-II form is stabilized more than the T I T form, moreover most appeared in the resonance term. Among them, the element (°C6, 1H2) is the largest element governing the energy difference. F r o m the electrostatic term, the T T T form is stabilized more than the Gly-II form, and the element with the largest contribution is, (°C6, 1H2). F r o m this discussion, we can recognize again that the T I T form is stabilized in the intrasegment, while the Gly-II form is stabilized in the intersegment, especially in the 0-1 term. As a result, it was found that the Gly-II form is slightly more stable than the TTT form. Therefore the helical structure is more stable than the trans zigzag form. This reveals that this polymer 2 may exist in the helical form rather than the other forms. This is one of the important findings in the present contribution. Moreover it is shown that the elements (H2, N1), (H9, N1), (C6, C3), (N8, C3), (H9, H5), (N7, C6) and (°C6, 1H2) govern dominantly the energy difference between the two forms.

Analysis of the GGT and G'G'T forms We now discuss the typical :t-helical structures, G G T and G'G'T. With these two forms, fairly small energies appeared in the intersegment 0-3 and 0 ~ terms. As to these two forms, G G T and G'G'T, these two intersegment terms are the dominant stabilizing terms. In Tables 6 and 7, the large elements which appeared in the ~ 4 segments in the G G T and G ' G ' T forms are summarized. From these tables, it is easily recognized that the element (°H9,4N1) in the resonance term is dominant in stabilizing the G G T form. For the G ' G ' T form, in addition to the element (°H9, 4N1), the element (°C6, 4N1) is also important for stabilization. In these forms, G G T and G'G'T, there are pairs of atoms with short contacts. The short contacts below 2.5A between the central and

M. OHSAKUet al.

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Table 5. The difference in the two centre interaction energy (eV) in the 0-1 segments between TTT and Gly-II forms* IN1 Resonance term OH5-I°C6 °N7 ON8 OH9

1H2

1C3

1C6

-0.41 -0.05 -0.05 0.06

-0.44 0.05 -0.05

Exchange term Electrostatic term °N1 °C3 °C6 Total

Total

- 0.05 0.16 0.04 -0.04 0.12 -0.31

* Digists show the energy difference: GI-II - TTT. Energy terms: absolute values less than 0.04eV are not catalogued. See Eqn (4) of Ref. [17] for details. t See footnote t of Table 4. :~For example, (°H5, 1N1) refers to the interaction element between the H5 hydrogen atom in the central segment and the N1 nitrogen atom in the first nearest neighbour segment. the fourth nearest neighbour segments are shown in Table 8. Here the distance of ( ° H 9 . . . 4 N 1 ) is the order of usual hydrogen bonding 1-27]. As a result, the interactions between these short contacts may be important in stabilizing these typical ~-helical structures. Analogous stabilization has been proposed for the poly(L-alanine) [16], although the situation is quite different.

not be compensated by the destabilization due to the intrasegment term in the fl-structures. As a result, the fl-structures become less stable structures. From these discussions, the polymer 2 in general exists in the helical structure. Therefore, after polymer 2 is formed from polymer 1 in the mechanisms shown in Fig. 1, the structure of the polypeptide prepared from the polymer 2 is decided.

Analysis of the fl-structures

Table 7. Large elements in the 0 ~ segments in the G'G'T form*

There is now a brief discussion of the fl-structures. With the fl-structures, we have considered two typical forms. The total energy calculated for the T T T form is, for example, compared with that for the fl-I form. The total intrasegment energy is smaller in the TTT form, while the total intersegment energy is smaller in the fl-I form. The fl-structures are stabilized largely in the intersegment term. However in the intrasegment term, the fl-structures are greatly destabilized, Therefore the stabilization by the intersegment terms canTable 6. Large elements in the 0-4 segments in the GGT form* Resonance term't" (°H5, 4N1) (°N8, 4N1) (°H9, 4N1) (°H9, 4C3) (°H9, 4C6) Total Exchange termt (°H9, 4N1) Total

-0.05 0.17 -0.66 -0.06 -0.10 -0.81

Electrostatic term:~ (°N1, 4N1) 0.12 (°C3, 4N1) -0.14 (°N8, '*N1) 0.27 (°N8, 4C3) -0.14 (°H9, '*C3) 0.12 (°N8, 4N8) 0.11 Total 0.35

-0.05 - 0.10

* Energy in eV. t Energy terms: absolute values less than 0.05 eV are not catalogued. :~Energy terms: absolute values less than 0.10 eV are not catalogued.

Resonance term'[" (°C6, 4N1) (°N7, 4N1) (°N8, 4N1) (°H9, 4N1) (°C6, 4H2) (°H9, 4C3) Total

-0.72 0.11 0.19 -0.66 -0.05 -0.07 - 1.26

Exchange term'[" (°H9, 4N1) Total

-0.05 - 0.16

Electrostatic term:~ (°N1, 4N1) 0.11 (°C3, 4NI) - 0.14 (°N7, 4N1) 0.12 (°N8, 4N1) 0.26 (°N8, 4C3) -0.14 (°H9, 4C3) 0.12 (°N8, 4N8) 0.11 Total 0.42

* Energy in eV. 1", :~See footnotes "[', ~ of Table 6. Table 8. Short contacts between the 0 ~ segments below 2.5 A in the GGT and G'G'T forms GGT form GGT form (°H5... 4N1) (°N8... '~N1) (°H9... 4N1) (°H5... 4H2) (°H9... 4H2) (°H9... 4C3) (°H9... 4C6)

G'G'T form 2.27 2.25 1.67 2.45 2.24 2.41 2.41

G'G'T form (°C6... 4N1) (°N8... 4N1) (°H9... 4NI) (°C6... 4H2) (°N8... 4H2) (°H9... 4H2) (°H9... 4C3) (°H9... 4H5)

2.26 2.25 1.67 2.50 2.48 2.24 2.41 2.45

Electronic and molecular structures of-(--HCN--)~,polymers:--[--(HCN)3-]~. CONCLUSION The conformational stability of the polymer, -[--(HCN)a--]~,, is accounted for by the C N D O / 2 method using the tight-binding approximation. The stability of polymer 2 has been estimated to be in the following order: helical > trans zigzag > fl-structure. F r o m comparison of the energy for the typical forms, T I T and Gly-II, it was found that the intrasegment energy stabilizes the T T T form to a greater extent while the intersegment energy tends to stabilize the Gly-II form. The result of the partitioning of the total energy reveals which atoms or atom pairs stabilize the form. F r o m the typical s-helical forms, G G T and G'G'T, it was found that one of the dominant terms stabilizing these forms corresponds to the intersegment hydrogen bonding between the central and the fourth nearest neighbour segments. With the fl-structures, the intersegment energy is fairly small, but these forms are greatly destabilized by the intrasegment two centre term. This term is a large part of the total energy for the fl-structures of the polymer 2. The//-structures of the peptide is unlikely to come from polymer 2. Acknowledgements--This work was supported in part by a

Grant-in-Aid for Scientific Research from the Ministry of Education, for which the authors express their gratitude. We are also grateful to the Information Processing Center of Hiroshima University, the Data Processing Center of Kyoto University, and the Computer Center of Institute for Molecular Science, for generous permission to use HITAC M-180H, FACOM M-200, and HITAC M-180H and M-200H Computers, respectively.

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