Atomic and Molecular Dimensions

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1 1 Atomic and Molecular Dimensions Equilibrium Interatomic Distances When two atoms approach each other, their positively charged nuclei and negatively charged electronic clouds interact. The total interaction is the sum of attraction (plus minus) and repulsion (plus plus; minus minus). If the curve of the total energy has a minimum, the minimum occurs for a certain interatomic distance r0. Once two atoms approached each other at the distance r0 and some energy was released, the two atoms will stay together until they receive this energy back.

2 If the amount of energy is very significant, the two atoms will stay together for a long time. These atoms are defined as bonded, and the attraction relation is called chemical bond.

2 2 If the amount of energy is very significant, the two atoms will stay together for a long time. These atoms are defined as bonded, and the attraction relation is called chemical bond. If the amount of energy is not very significant, the two atoms may stay together for a moment and fly apart, or may stay longer due to some external restrictions. These atoms are regarded as interacting weakly. There is the whole spectrum of interatomic interactions: the strongest is the chemical bond (covalent, ionic, etc), the weakest is a so called van der Waals interaction. Two hydrogen atoms can form a covalent bond at a distance of r0 = 0.74 Å (bond energy is 432 kj/mol) or van der Waals contact at a distance of r'0 = 2.32 Å (energy is <0.1 kj/mol) The equilibrium interatomic distances can be predicted for various combinations of two atoms through the concept of atomic, ionic, and van der Waals radii.

3 3 Atomic Radii The equilibrium bond length can be partitioned into contributions from each atom involved in the bond. The contribution of an atom to a covalent bond is called effective atomic radius (DeKock) or covalent radius of the element (Shriver). The covalent radius can be defined as one half the internuclear distance between neighboring atoms of the same element in a molecule. Two atoms A with covalent radius ra and van der Waals radius rvdw form the A2 molecule. The A A bond distance is equal to raa = 2rA; the "length" of the molecule is (2rvdW + 2rA); the "thickness" of the molecule is 2rvdW.

4 4 For example, the separation of two protons in the H2 molecule is 0.74 Å. Therefore the covalent radius of H is 0.37 Å. The covalent radius of another atom rb can be determined as the A B bond distance in the AB molecule rab minus ra As a rule, covalent radii: decrease from left to right along a given period; increase as we go down a given group (not always for transition metals and f-elements) Can you explain these trends? (For explanations of these effects read DeKock 2-2 or Shriver 1,9a.) Can you explain why the greatest changes are between H and Li and between Li and Be (see next page)?

5 5 (from DeKock) Also, it is evident that, for the same element, covalent radius will depend on the order of the bond, for example: Bond single aromatic double triple rc, Å

6 6 (from Li) Metallic Radii The metallic radius of a metallic element is defined as half the experimentally determined distance between the centers of nearest-neighbor atoms in the solid (crystalline) metal (Shriver, 1.9a).

7 Metal Li Na K Rb Cs Cov. rad., Å 1.34 1.54 1.96 2.16 Met. rad., Å 1.57 1.91 2.35 2.50 2.72 Can you explain why metallic radius is greater than the covalent radius of the same element?

7 7 Metal Li Na K Rb Cs Cov. rad., Å Met. rad., Å Can you explain why metallic radius is greater than the covalent radius of the same element? Ionic Radii By analogy with atomic radius, the ionic radius of an ion is the contribution of this ion to the ionic bond. The ionic radius is related to the distance between the centers of neighboring cations and anions in an ionic (crystalline) solid. The system of ionic radii depends on an arbitrary decision on how to apportion the cation anion distance between the two ions. One common scheme is based on assumption that the radius of O 2 is 1.40 Å.

8 8 Compare ionic and covalent radii (see p.5). What conclusions can you make? Van der Waals Radii Van der Waals radius of an element is defined as a half distance between two approaching identical atoms of the element when their van der Waals interaction is minimal. H Li Na K Van der Waals Radii vs Covalent Radii (Å) Be B Al C Si N P O S F Cl Br I He 1.4 Ne 1.5 Ar 1.8 Kr 2.0 Xe 2.2

9 9 Explain the trends in the rows and groups. Why the two sets of radii reveal similar trends? What interatomic distance do you expect in liquid and solid Xe? What interatomic distances do you expect to see between two I atoms in I 2 molecule and between two contacting I atoms of neighboring I 2 molecules? Type of interaction covalent bond (molecule) ionic bond (solid) metallic bond (solid) van der Waals interaction Summary on Atomic Size Measures Contribution of the atom to the interatomic distance (radius type) effective atomic radius covalent radius ionic radius metallic radius van der Waals radius Main factor responsible for variations the order of the bond coordination number coordination number various It is expected that the length of the A B interaction is approximately the sum of the corresponding radii for elements A and B

10 10 Molecular Dimensions For the purpose of modeling, the molecule is considered as a shape formed by spherical atoms with the corresponding van der Waals radii. Some molecules are rigid and so their shape and dimensions are constant. Other molecules are flexible and can adopt two or more conformations. Molecular diameter is defined as the diameter of the molecule assuming it to be spherical: h = 1/3(hx + hy + hz) where h is the mean molecular diameter and the hi are the dimensions of the molecule in three perpendicular directions. The molecular (maximal) size hmax is the maximal linear dimension of the molecular shape (max of hi). Ellipsoid approximation is the most straightforward way to roughly describe the size and shape of a molecule. Find the maximal linear dimension of the molecule (hx = hmax). Than find a minimal dimension in the plane to the x axis (hz). The last dimension is in the direction to both x and z (hy). Ellipsoid approximation may not be adequate for irregular geometries such as a concave shape.

11 Working example: molecular dimensions of para-dichlorobenzene h max = h x = 2r vdw (Cl) + 2r C + 2r Cl +2r C-C(ar) = 3.8 + 1.54 + 1.98 + 2.78 10 Å!!! Useful notes: h y 6.6 Å h z = 3.8 Å h 6.

11 11 Working example: molecular dimensions of para-dichlorobenzene h max = h x = 2r vdw (Cl) + 2r C + 2r Cl +2r C-C(ar) = Å!!! Useful notes: h y 6.6 Å h z = 3.8 Å h 6.8 Å The methyl group is usually in fast rotation and can be approximated by a ball. Since it is known experimentally that the attached Cl creates similar volume as CH 3, the methyl group has approximate radius of 2Å. In molecular size calculations, it is helpful to use the cosine formula: c 2 = a 2 + b 2 2ab cos γ The translation length in a stretched normal hydrocarbon is about 2.5Å (two 1.53Å bonds at the angle of o ). For example, the translational period in crystalline polyethylene is 2.54Å. The distance between two C atoms in the peptide backbone is ~3.8Å. The contribution of one nucleotide unit to the length of DNA is 3.3Å. For big molecules the contribution of van der Waals radii to the overall size becomes small.

12 Relative size of some molecules: water, ethanol, glycine (the simplest amino acid) and fullerene (C 60 ). The size of the bar is 1 nm How Can We See the Molecule?

12 12 Relative size of some molecules: water, ethanol, glycine (the simplest amino acid) and fullerene (C 60 ). The size of the bar is 1 nm How Can We See the Molecule? There are various methods to measure the bond lengths and overall size of the molecules. There are techniques making it possible to literally "see" a molecule. Most experimental data on bond lengths and molecular geometries come from spectroscopy measurements (especially rotational/vibrational spectroscopy) and crystal diffraction experiments (especially single-crystal X-ray diffraction). Spectroscopy techniques work best for gaseous samples, while the diffraction analysis requires crystals or at least crystalline materials. Discuss the strengths and weaknesses of the two methods and how they can complement each other.

13 13 Relative size of the molecule of oxygen (2 atoms) and oxy-hemoglobin (crystal structure data: one half of oxy-hemoglobin in vivo that contains >9000 atoms; H-atoms omitted). The size of the bar is 1 nm Relative size of the molecule of ethanol and alcohol dehydrogenase (crystal structure data). The size of the bar is 10 nm

14 14 Dynamic Light Scattering and Nanoparticle Tracking Analysis help to determine the overall size of particles down to 1 nm (DLS) or 10 nm (NTA). Both methods analyze the Brownian motion of nanoparticles suspended in a fluid and give size distribution of the particles in a sample. Scanning Tunneling Microscopy and Atomic Force Microscopy are the two most common techniques used to study individual molecular-size objects at atomic resolution. In both techniques the signal comes from a tip that moves over and in very close proximity to a surface (2D scan). STM records the differences in electric current between the tip and the surface as the tip moves. AFM records the changes in the mechanical force ("contact force") as the tip moves across the surface. Probing surface with an Au and CO-modified tips (Gross) "2ML" means "two monolayers"

15 15 STM and AFM images of pentacene. (A) Ball-and-stick model. (B) STM image. (C),(D) AFM images obtained with a CO-modified tip (Gross) STM images: "Atom", iron atoms on Cu(111); "CO Man", CO molecules on Pt(111). From

16 16 Typical Bond Lengths (Data from the International Tables for Crystallography and DeKock, Å) Bond Range Average Bond Range Average C sp3 C sp (2) C F C sp3 C sp (2) C Cl C sp3 C aryl (1) C Br C sp3 C sp (1) C I C sp2 C sp (1) C P C sp2 C aryl (2) C S C sp3 C sp (1) C = S C aryl C aryl (1) C aryl C sp (1) C H C sp1 C sp (1) N H C aryl C aryl (1) O H C sp2 = C sp (2) C sp1 C sp (1) N N N N C sp3 N N = N C sp2 N N N* 1.10 in N 3 C aryl N C aryl N N O C sp2 = N N = O C sp1 N N S C sp3 O O O C sp2 O a O = O 1.21 in O 2 C aryl O O S C sp2 = O O = S O P b

17 17 Bond Range Bond Range H F 0.92 in HF Li Li 2.67 in Li 2 H Cl 1.27 in HCl Na Na 3.08 in Na 2 H Br 1.41 in HBr K K 3.92 in K 2 H I 1.61 in HI M H c F F 1.42 in F 2 M CO Cl Cl 1.99 in Cl 2 M CH Br Br 2.28 in Br 2 M NCR I I 2.67 in I 2 M NO I I 2.92 in I 3 M N d S Te M N e Cl Te 2.52 M N f I Te 2.93 M N g Si Si 2.36 M NH a Only one oxygen in the molecule. b Phosphorus with four or three bonds. c In terminal metal hydrides. M is a transition metal. d In porphinates. e In phthalocyanines. f In pyrazole complexes. g In pyridine complexes.

18 18!!! Some numbers to remember: H-H 0.74 Å the shortest bond C-H, N-H, O-H ~1 Å C-C ~1.5 Å C-C-C ~2.5 Å (in hydrocarbons) C=C, C=N ~1.3 Å C C, C N ~1.2 Å C C, C N, N N ~1.4 Å (aromatics) M-N, M-O ~2 Å (metal complexes) Additional literature/data used: L Gross et al, Science 2009, 325, International Tables for Crystallography, 5th Ed (T Hahn, ed.), IUCr, Springer, 2005, Volume C. Protein Data Bank; W-K Li et al, Advanced Structural Inorganic Chemistry, IUCr, Oxford University Press, Reading: DeKock: 2-2, 2-5, 7-3 (pp 430-4); Tables 4-5, 4-9, 4-10 Shriver: 1.9a, 2.13, 3.7, 3.10a Atkins: 17.6; Tables 10.2, 19.3.

Chemistry 101 Chapter 9 CHEMICAL BONDING. Chemical bonds are strong attractive force that exists between the atoms of a substance

Chemistry 101 Chapter 9 CHEMICAL BONDING. Chemical bonds are strong attractive force that exists between the atoms of a substance CHEMICAL BONDING Chemical bonds are strong attractive force that exists between the atoms of a substance Chemical Bonds are commonly classified into 3 types: 1. IONIC BONDING Ionic bonds usually form between