1
Atomic Structures of Molecules Based on Additivity of Atomic and/or Ionic Radii Raji Heyrovska * and Saraswathi Narayan # ABSTRACT Bond 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, where the experimental bond lengths agree with the radii sums. The examples here include inorganic compounds like alkali halides and graphene, organic like methane and benzene and biological like nucleic acids, amino acids, vitamin B2 & its reduced form and caffeine related molecules. This has enabled presenting the structures at the “atomic level” of these molecules for the first time. The ATOMIC STRUCTURES and the radii used are shown in Figs. 1 – 7. INTRODUCTION 1) 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 (φ = 1.618), also known as The Divine ratio, appears in the geometry of a variety of Nature’s creations [3]. It was shown [1a,b] that, in fact, “φ arises right in the core of the H-atom” due to the two opposite charges of the proton and electron, p + and e - , respectively. The ionization potential, I H as the sum of I p (= e/κa p ) and I e (= -e/κa e ), where a B = a p + a e is he ground state Bohr radius, gives: I H = e/κa B = I p + I e = (e/κ)[(1/a p ) – (1/a e )]; (1/a B ) = (1/a p ) – (1/a e ); a B = a p + a e (2a-c) Eqs. 2b,c, give a e /a p = φ = (1 + 5 1/2 )/2 = 1.618.. and a p = (a B /φ 2 )<a e = (a B /φ), the Golden sections of a B . The covalent bond length, d(HH) = 2d(H) (= 0.74 Å) is the diagonal of a square with a B as a side. d(HH) = 2d(H) = 2 1/2 a B = 2 1/2 (a p + a p ) = d(HH)/φ 2 + d(HH)/φ = d(H + ) + d(H - ) (3) where the ionic radii, d(H + ) = d(HH)/φ 2 (= 0.28 Å) and d(H - ) = d(HH)/φ (= 0.46 Å). The empirical radius (= 0.28 Å) for H suggested [2a] in the partially ionic bonds in hydrogen halides (HX), is thus actually d(H + ). Also, note that H + , H - are the resonance forms [2a] of H in the H 2 molecule. 3) PARTIALLY AND COMPLETELY IONIC BONDS: On subtracting d(H + ) = 0.28 Å , from the bond lengths d(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 /φ 2 = d(M + ); (for MH, alkali hydrides) (4b) d(MX) expt - d(M + ) = d(XX) expt /φ = d(X - ); (for MX, alkali halides, see Fig. 1) (4c) 4) IN GENERAL, d(AA) = 2d(A) = d(AA)/φ 2 + d(AA)/φ = 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 Å section) All bond lengths = sums of the covalent radii of adjacent atoms, [1c] . In the 17 Å section, there are 5P atoms. This is half the 34 : 20 Å section per turn of the helix with ten P atoms, and each P atom is 10 Å from the central axis: Franklin R.E., Gosling R.G., [5]. Note: RNA has U and ribose in place of T and deoxyribose, [1c]. Lengths of the NH…O and NH…N 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 structures” of “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 and AV0Z50040702 grants of the Academy of Sciences of the Czech Republic (ASCR) and thanks ASCR and the Organizers of ICWIP2008 for the financial support to participate in this conference. S. N. thanks Stevenson University, for the partial financial support 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: 600-605 and 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 Å aspect ratio in DNA: Nature, 1953; 171: 740-741; see for full texts of this and other papers: 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 Å d(M + X - ) = R(M + ) + R(X - ); R(M + ) = d(MM)/φ 2 and R(X - ) = d(XX)/φ 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 (R cov ) of “the 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 structures of “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 Å Fig. 4. Atomic structures of “20 AMINO ACIDS”: COMPLETELY COVALENT BONDS: All bond lengths = sums of covalent radii of adjacent atoms, [6] (see the box above from Fig. 2). “Conventional formulae” of 20 essential amino acids: Fig. 5. “RIBOFLAVIN (VITAMIN B2) & ITS REDUCED FORM”: COMPLETELY COVALENT BONDS, [7] Conventional Structures Fig. 6. “METHANE, BENZENE, GRAPHENE”: All Bond lengths = sum of the radii of the adjacent atoms, [8] C s.b. C g.b. C d.b. N s.b. N d.b. H s.b. O s.b. O d.b. P S s.b. 0.77 0.71 0.67 0.70 0.62 0.37 0.67 0.60 0.92 1.04 Å *Institute of Biophysics, Academy of Sciences of the Czech Republic, Czech Republic; Email: * [email protected] #Stevenson University, Stevenson, MD 21153; Email: # [email protected] 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. C s.b. C g.b. C d.b. N s.b. N d.b. H s.b. O s.b. O d.b. P S s.b. Nature Precedings : doi:10.1038/npre.2009.3292.1 : Posted 28 May 2009

Atomic Structures of Molecules Based on Additivity of ... · Atomic Structures of Molecules Based on Additivity of Atomic and/or Ionic Radii Raji Heyrovska* and Saraswathi Narayan#

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Page 1: Atomic Structures of Molecules Based on Additivity of ... · Atomic Structures of Molecules Based on Additivity of Atomic and/or Ionic Radii Raji Heyrovska* and Saraswathi Narayan#

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, where the experimental bond lengths agree with the radii sums. The examples here include inorganic compounds like alkali halides and graphene, organic like methane and benzene and biological like nucleic acids, amino acids, vitamin B2 & its reduced form and caffeine related molecules. This has enabled presenting the structures at the “atomic level” of these molecules for 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 (φ = 1.618), also known as The Divine ratio, appears in the geometry of a variety of Nature’s creations [3]. It was shown [1a,b] that, in fact, “φ arises right in the core of the H-atom” due to the two opposite charges of the proton and electron, p+ and e-, respectively. The ionization potential, IH as the sum of Ip (= e/κap) and Ie (= -e/κae), where aB = ap + ae is he ground state Bohr radius, gives:

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

Eqs. 2b,c, give ae/ap = φ = (1 + 51/2)/2 = 1.618.. and ap = (aB/φ2) < ae = (aB/φ), the Golden sections of aB.

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

d(HH) = 2d(H) = 21/2aB = 21/2( ap + ap) = d(HH)/φ2 + d(HH)/φ = d(H+) + d(H-) (3)

where the ionic radii, d(H+) = d(HH)/φ2 (= 0.28 Å) and d(H-) = d(HH)/φ (= 0.46 Å). The empirical radius (= 0.28 Å) for H suggested [2a] in the partially ionic bonds in hydrogen halides (HX), is thus actually 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 Å, from the bond lengths d(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/φ2 = d(M+); (for MH, alkali hydrides) (4b)

d(MX)expt - d(M+) = d(XX)expt/φ = d(X-); (for MX, alkali halides, see Fig. 1) (4c)

4) IN GENERAL,

d(AA) = 2d(A) = d(AA)/φ2 + d(AA)/φ = 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 Å section)

All bond lengths = sums of the covalent radii of adjacent atoms, [1c]. In the 17 Å section, there are 5P atoms. This is half the 34 : 20 Å section per turn of the helix with ten P atoms, and each P atom is 10 Å from the central axis: Franklin R.E., Gosling R.G., [5]. Note: RNA has U and ribose in place of T and deoxyribose, [1c]. Lengths of the NH…O and NH…N 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 structures” of “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 and AV0Z50040702 grants of the Academy of Sciences of the Czech Republic (ASCR) and thanks ASCR and the Organizers of ICWIP2008 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: 600-605 and 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 Å aspect ratio in DNA: Nature, 1953; 171: 740-741; see for full texts of this and other papers: 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 Å

d(M+X-) = R(M+) + R(X-); R(M+) = d(MM)/φ2 and R(X-) = d(XX)/φ

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) of “the 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 structures of “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 Å

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

“Conventional formulae” of 20 essential amino acids:

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

Conventional Structures

Fig. 6. “METHANE, BENZENE, GRAPHENE”: All Bond lengths = 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 Å

*Institute of Biophysics, Academy of Sciences of the Czech Republic, Czech Republic; Email: * [email protected]#Stevenson University, Stevenson, MD 21153; Email: # [email protected]

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.

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