7/31/2019 Atomic Structures of Molecules

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Atomic Structures of Molecules Basedon Additivity of Atomic and/or Ionic Radii

Raji Heyrovska* and Saraswathi Narayan#

ABSTRACTBond lengths as sums of atomic and or ionic radii: Work in recent years [1] has shown for the first time

that the lengths of the chemical bonds, whether completely or partially covalent or ionic,are sums of the radii of the adjacent atoms and/or ions. Many examples are provided, wherethe experimental bond lengths agree with the radii sums. The examples here includeinorganic compounds like alkali halides and graphene, organic like methane and benzene andbiological like nucleic acids, amino acids, vitamin B2 & its reduced form and caffeine relatedmolecules. This has enabled presenting the structures at the atomic level of these moleculesfor the first time. The ATOMIC STRUCTURES and the radii used are shown in Figs. 1 7.

INTRODUCTION1) THE COVALENT [2a] OR BONDING ATOMIC RADIUS [2b], d(A) and the covalent bond length, d(AB):

d(A) = d(AA)/2 and d(AB) = d(A) + d(B) (for examples: see Figs. 3-7 here) (1a,b)

2) GOLDEN RATIO BASED ANIONIC AND CATIONIC RADII, [1a]: The Golden ratio ( = 1.618), also knownas The Divine ratio, appears in the geometry of a variety of Natures creations [3]. It wasshown [1a,b] that, in fact, arises right in the core of the H-atom due to the two oppositecharges of the proton and electron, p+ and e-, respectively. The ionization potential, IH as thesum of Ip (= e/ ap) and Ie (= -e/ ae), where aB = ap + ae is he ground state Bohr radius, gives:

IH = e/ aB = Ip + Ie = (e/ )[(1/ap) (1/ae)]; (1/aB) = (1/ap) (1/ae); aB = ap + ae (2a-c)

Eqs. 2b,c, give ae/ap = = (1 + 51/2)/2 = 1.618.. and ap = (aB/

2) < ae = (aB/ ), the Golden sections ofaB.

The covalent bond length, d(HH) = 2d(H) (= 0.74 ) is the diagonal of a square with aB as a side.

d(HH) = 2d(H) = 21/2aB = 21/2( ap + ap) = d(HH)/

2 + d(HH)/ = d(H+) + d(H-) (3)

where the ionic radii, d(H+) = d(HH)/ 2 (= 0.28 ) and d(H-) = d(HH)/ (= 0.46 ). The empirical radius(= 0.28 ) for H suggested [2a] in the partially ionic bonds in hydrogen halides (HX), is thusactually d(H+).Also, note that H+, H- are the resonance forms [2a] of H in the H2 molecule.

3) PARTIALLY AND COMPLETELY IONIC BONDS: On subtracting d(H+

) = 0.28 , from the bond lengthsd(HX)expt and d(MH)expt one obtains [1a,b] the successive Eqs. (4a-c):

d(HX)expt - d(H+) = d(XX)expt/2 = d(X); (for HX, hydrogen halides) (4a)

d(MH)expt - d(H+) = d(MM)expt/

2 = d(M+); (for MH, alkali hydrides) (4b)

d(MX)expt - d(M+) = d(XX)expt/ = d(X

-); (for MX, alkali halides, see Fig. 1) (4c)

4) IN GENERAL,

d(AA) = 2d(A) = d(AA)/ 2 + d(AA)/ = d(A+) + d(A-); (for any atom A) (5)

5) ADDITIVITY OF RADII IN AQUEOUS SOLUTIONS AND THE HYDROGEN BONDS [1b,4] (see Fig. 3):

d(--H) = md(H) + nd(H+) (where n = 1 or 2 and m = 0, 1, 2 or 3; see p.349 below from [4b]) (6)

Fig. 3. COMPLETELY COVALENT BONDS:Atomic structures of MOLECULES IN DNA(17 : 20 section)

All bond lengths = sums of the covalent radii of adjacent atoms, [1c]. In the 17 section, there are 5P atoms.This is half the 34 : 20 section per turn of the helix with ten P atoms, and each P atom is 10 from the centralaxis: Franklin R.E., Gosling R.G., [5]. Note: RNA has U and ribose in place of T and deoxyribose, [1c]. Lengths ofthe NHO and NHN hydrogen bonds in the AT and CG pairs: see [4b] and p. 349 in the box below: RH: CPL, 2006.

Fig. 7. COMPLETELY COVALENT BONDS Atomic structuresof CAFFEINE AND RELATED MOLECULES

All bond lengths = sums of covalent radii of adjacent atoms, [9].

ACKNOWLEDGEMENTS: R. H. is grateful to the IBP for support by institutional research plans Nos. AV0Z50040507 andAV0Z50040702 grants of the Academy of Sciences of the Czech Republic (ASCR) and thanks ASCR and the Organizers ofICWIP2008 for the financial support to participate in this conference. S. N. thanks Stevenson University, for the partial financialsupport to attend this conference.

REFERENCES[1] Heyrovska R., a) Golden ratio, Bohr radius, ionic radii, additivity of radii in bond lengths etc: Mol. Phys. 2005; 103: 877,and the literature therein, b) Golden ratio, ionic radii, aqueous solutions, etc: Chapter 12 in Innovations in Chemical Biology,ed: B. Sener, Springer, October 2008 c)Atomic structures of nucleic acids etc: Open Structural Biology J., 2 (2008) 1 7.[2] a) Pauling L., The Nature of the Chemical Bond(Cornell Univ. Press, NY, 1960) and b)http://wps.prenhall.com/wps/media/objects/3311/3390919/blb0702.html[3] The Golden ratio: http://www.goldennumber.net/(and the literature therein).[4] Heyrovska R., a) Golden ratio and additivity of radii in ionic and hydration distances Chem. Phys. Lett. 2006; 429: 600-605and b) Golden ratio and additivity of radii in the lengths of hydrogen bonds Chem. Phys. Lett. 2006; 432: 348-351.[5]: Franklin R.E., Gosling R.G., 34:21 aspect ratio in DNA: Nature, 1953; 171: 740-741; see for full texts of this and otherpapers: http://www.nature.com/nature/dna50/archive.html[6]: Heyrovska R., The 20 essential amino acids: http://arxiv.org/ftp/arxiv/papers/0804/0804.2488.pdf[7]: Heyrovska R., Riboflavin and its reduced form: http://arxiv.org/ftp/arxiv/papers/0806/0806.3462.pdf[8]: Heyrovska R., Methane, Benzene and graphene: http://arxiv.org/ftp/arxiv/papers/0804/0804.4086.pdf[9]: Heyrovska R. and Narayan S., Caffeine and related molecules: http://arxiv.org/ftp/arxiv/papers/0801/0801.4261.pdf

Na+

Cl-All alkali halides Example:

SODIUM CHLORIDE(shown below: an fcc plane)

d(Na+Cl-) = R(Na+) + R(Cl-)2.83 = 1.61 + 1.22

d(M+X-) = R(M+) + R(X-); R(M+) = d(MM)/ 2 and R(X-) = d(XX)/

Li+ Na+ K+ Rb+ Cs+

R(M+): 1.33 1.61 1.96 2.09 2.31

R(X-): F- Cl- Br- I-

0.88 1.22 1.37 1.58

Fig. 2. The radii (Rcov) ofthe six atoms, C, N, H, O, P and S, that build the molecules of life.

C (quadrivalent), N (trivalent), H (monovalent), O (divalent), P (pentavalent) & S (hexa/bivalent), which constitute the atomic structuresof THE LIFE GIVING MOLECULES[1c, 6, 7, 9]. [Subscripts: s.b: single bond, g.b. : graphite/graphene bond, d.b: double bond.]

0.77 0.71 0.67 0.70 0.62 0.37 0.67 0.60 0.92 1.04

Fig. 4. Atomic structures of 20 AMINO ACIDS: COMPLETELYCOVALENT BONDS:All bond lengths = sums of covalent radii of adjacentatoms, [6] (see the box above from Fig. 2).

Conventional formulae of20 essential amino acids:

Fig. 5. RIBOFLAVIN (VITAMIN B2) & ITS REDUCED FORM:COMPLETELY COVALENT BONDS, [7]

Conventional Structures

Fig. 6. METHANE, BENZENE, GRAPHENE:All Bondlengths = sum of the radii of the adjacent atoms, [8]

Cs.b. Cg.b. Cd.b. Ns.b. Nd.b. Hs.b. Os.b. Od.b. P Ss.b.

0.77 0.71 0.67 0.70 0.62 0.37 0.67 0.60 0.92 1.04

*Institute of Biophysics, Academy of Sciences of the Czech Republic, Czech Republic; Email: * rheyrovs@hotmail.com#Stevenson University, Stevenson, MD 21153; Email: # f-naraya@stevenson.edu

The 3rd IUPAP International Conference on Women in Physics 2008, Seoul, KOREA

Fig. 1. Completely ionic bonds: Alkali halides, [1]: Heyrovska R., a) Mol. Phys. 2005; 103: 877-882.

Cs.b. Cg.b. Cd.b. Ns.b. Nd.b. Hs.b. Os.b. Od.b. P Ss.b.