Chemistry 125: Lecture 4 Sept. 10, 2010 Coping with Earnshaw, Smallness and Scanning Probe Microscopy Despite Earnshaw’s Theorem, might there actually be shared-electron bonds? Is it possible to confirm their reality by seeing or feeling them? The spectacle of “clairvoyant” charlatans from the beginning of the 20th Century, who claimed to “see” details of atomic and molecular structure, contrasts with proper bases for scientific understanding. The molecular scale is not inconceivably small; indeed Newton and Franklin could perform simple experiments capable of measuring nanometer-scale distances. In the last 25 years various manifestations of Scanning Probe Microscopy have enabled chemists to “feel” individual molecules and atoms, but not bonds. For copyright notice see final page of this file PRELIMINARY

Motivation for the Trajectory of Coulomb’s Work with his Torsion Balance: Devises an improved suspension for a compass needle. Studies wire torsion “in order to determine the laws of cohesion and elasticity in metals and in all solid bodies.” (Engineering; Newton’s “Business of Experimental Philosophy”) Confirms Hooke’s Law for torsion Determines 1/r 2 Laws for E&M.

Some Resonance Structures for H, C, N, O Isomers For quantum-calculated local-minimum-energy (valley) atomic arrangements

H, C, N, O isomers C in middle H C N O : : : H C N O : : : H C N O : : : + _ H C N O : : : + _ bad charge separation (most “electronegative” atom bears + charge) charge separation H C N O : + _ : : bad charge separation

H C N O : : : : H C N O : : : + _ : H C N O : : + _ + _ H C N O : : : : + _ H C N O : : : bad charge sestet bad charge H, C, N, O isomers N in middle H C N O : : : + _ : better charge sestet

H C N O : : : : + _ H C N O : : : : _ + H C N O : : : : _ + H C N O : : : : + _ bad charge sestet H, C, N, O isomers O in middle

Ring Open H C N O : : : H C N O : : + : _ H C N O : : : : sestet bad charge H, C, N, O isomers cyclic H C N O : : : + _ sestet H C N O : : : + _ : bad charge Unlike O 3, lowest energy form can’t even be calculated. (smoothly downhill to open the ring)

HNCO isomers H C N O : : : H C N O : : : H C N O : : : H C N O : : : : H C NO : : : + _ H C N O : : : : + _ H C N O : : : : _ + H C N O : : + : _

kcal/mole H C N O H C N O H C N O H C N O H C N O H C N O H C N O H C N O E calc “I once poured 6 drams of concentrated sulfuric acid upon 50 grains of mercury fulminate. An explosion nearly at the instant of contact was effected; I was wounded severely, and most of my apparatus was destroyed. … I must confess that I shall feel more disposed to prosecute other chemical subjects. Edward Howard (1800). … I must confess that I shall feel more disposed to prosecute other chemical subjects.

References: Most of these structures and energies were calculated at a very high level of theory as reported in Journal of Chemical Physics, 120, (2004). The much less stable structures with O in the middle were calculated using the highest level of theory available in the Spartan 04 package of quantum programs. This program could not find an energy minimum for the cyclic structure with H on oxygen.

Coping with Earnshaw

J.J. Thomson ( ) Electron (1897) Plum-Pudding Atom © Cavendish Laboratpry, Cambridge University

"[We can] solve the special case where the corpuscles are confined to a plane." Thomson's Model of Electron Configuration "consider the problem as to how 1…2…3…n corpuscles would arrange themselves if placed in a sphere filled with positive electricity of uniform density…" “distributed in the way most amenable to mathematical calculation” in Thomson, Corpuscular Theory of Matter (1907)

    Vortex Lattice Models (Greg Blonder  

"[We can] solve the special case where the corpuscles are confined to a plane." Thomson's Model of Electron Configuration "consider the problem as to how 1…2…3…n corpuscles would arrange themselves if placed in a sphere filled with positive electricity of uniform density…" "the equilibrium of eight corpuscles at the corners of a cube is unstable." in

“I have ever since regarded [the cubic octet] as representing essentially the arrangement of electrons in the atom” G. N. Lewis (1923) Was Lewis ignorant of Earnshaw's Theorem? “Electric forces between particles which are very close together do not obey the simple law of inverse squares which holds at greater distances.” G. N. Lewis (1916)

The Electron in Chemistry J. J. Thomson (1923) “… if [electron-nuclear attraction] were to vary strictly as the inverse square of the distance we know by Earnshaw's theorem than no stable configuration in which the electrons are at rest or oscillating about positions of equilibrium is possible... Couloumb r c r c … then a number of electrons can be in equilibrium about a positive charge without necessarily describing orbits around it.” I shall assume that the law of force between a positive charge and an electron is expressed by the equation F =F = Ee r2r2 1 atomic length scale (for distances r smaller than c, the force changes sign.)

Quantum Mechanics (1926) Kinetic energy is reformulated to explain electron clouds and produce an "inverted" plum-pudding atom. Cubic octets and the ad hoc electrostatic force law soon disappeared from conventional Chemistry and Physics But shared-pairs and lone-pairs remained useful tools for discussing structure and bonding. Coulomb’s Law is just fine.

Earnshaw: No structure of minimum energy for point charges Classical

Despite Earnshaw, might there still be shared-pair bonds and lone pairs?

How do you know? By Seeing? Feeling?

Problem: Inconceivably Small ?

OCCULT CHEMISTRY A SERIES OF Clairvoyant Observations on the Chemical Elements BY ANNIE BESANT, P.T.S. AND CHARLES W. LEADBEATER Reprinted from the Theosophist. T HEOSOPHIST O FFICE, A DYAR, M ADRAS, S. T HEOSOPHICAL P UBLISHING S OCIETY, L ONDON AND B ENARES C ITY (105 pp.) 1919 (123 pp.) 1951 (400 pp.)

Mrs. Annie BESANT P.T.S. ( ) Curuppumullage JINARAJADASA P.T.S. (~ ) "Bishop" Charles Webster LEADBEATER ( ) The Occult Chemists ( )

H O N (1895) Hydrogen Oxygen “Anu” Atom Model in Charles Jencks’s Garden of Cosmic Speculation (1994) constructed “with several scientists”

Helium 72 Lithium 127 Iron 1008 Neon 360 Occult Atoms

Neon 360 4f orbital e-density Occult Atoms Bases for Scientific Belief: 1) Experimental Evidence "cross-examine an assertion" 3) Taste matures with experience Why should you believe the professor/text? 2) Logic

Sodium 418 Occult Atoms

Na 2 CO 3 (1924) "note that this trian- gular arrangement of O 3 has just been deduced by Bragg from his X-ray analysis of Calcite" O O O C Na

Benzene (1924) "each of the three valencies of each Carbon are satisfied by Hydrogen, and the fourth valency, which some have postulated as going to the interior of the molecule, does actually do so." Cf. Question 6

Benzene “Resonance” H H H H H H C C C C C C H H H H H H C C C C C C H H H H H H C C C C C C (1889)

Clean Slates April, 1923 Giuseppe Bruni (Bologna) G. N. Lewis Honor Roll of (mostly) dead chemists Dedication:

discovered Thallium developed Cathode Ray Tube invented Crookes Radiometer Sir William Crookes FRS, FTS ( ) Supplied Li, Cr, Se, Ti, V, B, Be to Leadbeater and Besant (1907) and The Society for Psychical Research "[Telepathic research] does not yet enlist the interest of the majority of my scientific brethren." President of the Royal Society President British Assn. for the Advancement of Science

6/18  molecules molecules / cm 1 cm 3 of water, 1/18 mole Are Molecules Unobservably Small for “Vulgar Eyes”? ~ 3Å / H 2 O molecule

10 5 Lecture Room ~10 m Hair ~100  m Nucleus ~10 fm Molecule ~1 nm (small atom ~ 0.1 nm = 1 Å) (again)

3/8   2.54 cm/inch ≈ cm = 10 nm = 30 "waters" ! Newton Opticks (1717) p. 369

flat to flat 62 mm convex to flat Newton’s Rings ~1 mm gap at rim 1 mm

p. 175 Newton Opticks (1717)  = cos -1 (0.29"/(12"  51')) = ° air gap 0.29" = (12  51)(1-sin  ) = 7  inch = 1.8  m  51'

Simpler Measurement of Smaller Distance 1774

Benjamin Franklin Philosophical Transactions of the Royal Society 1774 Portrait by Paulze Lavoisier

Benj. Franklin to Wm. Brownrigg (1773) …I had, when a youth, read and smiled at Pliny's account of a practice among the seamen of his time, to still the waves in a storm by pouring oil into the sea; as well as the use made of oil by the divers... I think that it has been of late too much the mode to slight the learning of the ancients. The learned, too, are apt to slight too much the knowledge of the vulgar.

In 1757, being at sea in a fleet of ninety-six sail bound against Louisbourg, I observed the wakes of two of the ships to be remarkably smooth, while all the others were ruffled by the wind, which blew fresh. Being puzzled with the differing appearance, I at last pointed it out to our captain and asked him the meaning of it. "The cooks," said he, "have I suppose been just emptying their greasy water through the scuppers, which has greased the sides of those ships a little." … Benj. Franklin to Wm. Brownrigg (1773) recollecting what I had formerly read in Pliny, I resolved to make some experiment of the effect of oil on water when I should have the opportunity.

Franklin's Experiment London, 1762 Clapham Common

for I had applied it first on the leeward side of the pond where the waves were greatest; and the wind drove my oil back upon the shore. I then went to the windward side where they began to form; and there the oil, though not more than a teaspoonful, produced an instant calm over a space several yards square which spread amazingly and extended itself gradually till it reached the lee side, making all that quarter of the pond, perhaps half an acre, as smooth as a looking glass. Benj. Franklin to Wm. Brownrigg (1773) At length being at Clapham, where there is on the common a large pond which I observed one day to be very rough with the wind, I fetched out a cruet of oil and dropped a little of it on the water. I saw it spread itself with surprising swiftness upon the surface; but the effect of smoothing the waves was not produced; 1 tsp ≈ 5 cm acre ≈ 2000 m 2 = 2 x 10 7 cm 2 layer thickness ≈ 5 cm 3 / 2 x 10 7 cm 2 = 2.5 x cm = 2.5 nm = 25 Å

Benj. Franklin to Wm. Brownrigg (1773) When put on water it spreads instantly many feet round, becoming so thin as to produce the prismatic colours for a considerable space, and beyond them so much thinner as to be invisible except in its effect of smoothing the waves at a much greater distance. It seems as if a mutual repulsion between its particles took place as soon as it touched the water

Are there Electron Pairs? Scanning Probe Microscopy for Feeling Individual Molecules, Atoms, Bonds?

Scanning Tunneling Microscopy (1981) Heinrich Rohrer Gerd Binnig Nobel Prize (1986) © IBY by permission

End of Lecture 4 Sept 10, 2010 Copyright © J. M. McBride Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0