1. For copyright notice see final page of this file
Chemistry 125: Lecture 4 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

2. J.J. Thomson (1856-1940) Electron (1897) Plum-Pudding Atom
© Cavendish Laboratpry, Cambridge University
Electron (1897)
Plum-Pudding Atom

3. 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…" in
“distributed in the way most amenable to mathematical calculation”
“In default of exact knowledge of the nature of the way in which positive electricity occurs in the atom, we shall consider a case in which the positive electricity is distributed in the way most amenable to mathematical calculation, i.e., when it s=occurs as a sphere of uniform density, throughout which the corpuscles are distributed.” 1907 JJT
"[We can] solve the special case where the corpuscles are confined to a plane."
Thomson, Corpuscular Theory of Matter (1907)

4. Vortex Lattice Models (Greg Blonder www.genuineideas.com)
 









    






JJT went up to 100 particles (7 shells) p. 110 of “The Corpuscular Theory of Matter” Among these first 20 he had instead 9 =1 8 ; 13 = 3 10 ; 16 = 5 11 ; 19 = ; and 20 =

5. Thomson's Model of Electron Configuration
"[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…" in
"the equilibrium of eight corpuscles at the corners of a cube is unstable."

6. Was Lewis ignorant of Earnshaw's Theorem?
“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)
GNL, “Valence and the Structure of Atoms and Molecules”, 1923, p. 29
GNL, “The Atom and the Molecule”, JACS, 38, (1916), p. 768

7. 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 ...
… 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 = Ee r2 1
atomic length scale
(for distances r smaller than c, the force changes sign.)
Couloumb r c r c

8. Quantum Mechanics (1926) Coulomb’s Law is just fine.
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.

9. Earnshaw: No structure of minimum energy for point charges
Classical

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

11. How do you know?
By Seeing? Feeling?

12. Problem: ?
Inconceivably Small

13. 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. THEOSOPHIST OFFICE, ADYAR, MADRAS, S. THEOSOPHICAL PUBLISHING SOCIETY, LONDON AND BENARES CITY.
1909 (105 pp.)
1919 (123 pp.)
1951 (400 pp.)

14. The Occult Chemists (1895-1932)
"Bishop"
Charles Webster
LEADBEATER
( )
Mrs. Annie
BESANT
P.T.S.
( )
Curuppumullage
JINARAJADASA
P.T.S.
(~ )

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

16. Occult Atoms
Iron
1008
Lithium
127
Neon
360
Helium 72

17. Bases for Scientific Belief:
Occult Atoms 4f
orbital
e-density
Neon
360
Bases for Scientific Belief:
Evidence
"cross-examine an assertion"
2) Logic
Doubting Thomas was a scientist. John 20:24-29
3) Taste
matures with experience
Why should you believe the professor/text?

18. Occult Atoms
Sodium
418

19. C Na
Na2CO3 (1924) O
"note that this trian-gular arrangement of O3 has just been deduced by Bragg from his X-ray analysis of Calcite"

20. 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

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

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

23. Sir William Crookes FRS, FTS (1832-1919)
Supplied Li, Cr, Se, Ti, V, B, Be
to Leadbeater and Besant (1907)
discovered Thallium
developed Cathode Ray Tube
invented Crookes Radiometer
President of the Royal Society
President
British Assn. for the Advancement of Science
and
The Society for Psychical Research
"[Telepathic research] does not yet
enlist the interest of the majority
of my scientific brethren."
Cartoon from “Vanity Fair” by "Spy" Sir Leslie Ward ( )

24. Are Molecules Unobservably Small for “Vulgar Eyes”?
1 cm3 of water, 1/18 mole
6/18  molecules
molecules / cm
~ 3Å / H2O molecule

25. 105 Lecture Room ~10 m Hair ~100 mm 101 10-4 10-9 Molecule ~1 nm 10-14
(again)
Lecture Room ~10 m
Hair ~100 mm
101
10-4
105
10-9
105
Molecule ~1 nm
(small atom ~ 0.1 nm = 1 Å)
Cf.Lecture 2:` magnetism, electrostatics, strong force on atomic scale
10-14
105
Nucleus ~10 fm

26. 3/8  10-6  2.54 cm/inch ≈ 10-6 cm = 10 nm = 30 "waters" !
Newton Opticks (1717)
p. 369
3/8  10-6  2.54 cm/inch
≈ 10-6 cm = 10 nm
= 30 "waters" !
The length of a side of a cube containing 1 molecule of liquid water is about 1/3 nm
10^-6 cm is10 nm = 30 waters

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

28. Newton Opticks (1717) air gap
51'
Newton Opticks (1717)
p. 175
pp.
 = cos-1(0.29"/(12"51')) = °
0.29"
air gap
= (1251)(1-sin ) = 7  10-5 inch = 1.8 mm

29. Simpler Measurement of Smaller Distance 1774

30. Philosophical Transactions of the Royal Society 1774
Benjamin
Franklin
Portrait of Benjamin Franklin (private collection)
In receiving this painting on October , Benjamin Franklin wrote to Madame Lavoisier the following: “I have long time been disabled from writing to my dear friend, by a severe fit of the gout, or I should have return’d my thanks for her kind present of the portrait, which she has herself done me the honour to make of me. It is allow’d by those who have seen it to have great merit as a picture in every respect; but what particularly endears it to me, is the hand who drew it.” Of this portrait Madame Lavoisier made two copies. One, the present, which was sent to Benjamin Franklin, the other which was retained by Madame Lavoisier and passed over Lavoisier's heirs. The latter was probably sold during the 1950s by Nelly de Chazelles and no photographic reproduction is known.
(halfway down the page)
Portrait by Paulze Lavoisier 1783

31. 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.

32. Benj. Franklin to Wm. Brownrigg (1773)
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." …
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.

33. Franklin's Experiment London, 1762
Clapham Common
Franklin's Experiment London, 1762

34. 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;
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.
1 tsp ≈ 5 cm3
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.
layer thickness ≈ 5 cm3 / 2 x 107 cm2
= 2.5 x 10-7 cm = 2.5 nm = 25 Å
0.5 acre ≈ 2000 m2 = 2 x 107 cm2

35. 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

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

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

38. Atomic Force Microscopy
Gold coated Si Chip
Only one of these five cantilevers is used in any one experiment. They differ in stiffness and ability to twist.
1.4 mm
Hair
The smallest scale
division is 20 mm

39. Scanning Electron Micrographs of
AFM Cantilever
Tip
1m
Radius of curvature ~20 nm
©The IN-VSEE Project; Arizona State University 1999

40. Cantilever/Chip Holder
Tips
Cantilever/Chip Holder

41. Cantilever/Chip Holder
Sensitive to
< 1 molecule
change in
height !

42. fast Ledge Dissolution Rate slow
slower
Ledge
Dissolution
Rate
AFM traces at 1 min intervals of part of the surface of a benzoin crystal dissolving in
95% water /
5% n-propanol.
The larger pit
is 5.1 nm deep.
Each ledge
is one “unit cell”
(1.7 nm) high.
5 m
(~600 molecules)

43. Scanning Tunneling Microscopy (1999)
Graphite
Br(CH2)11COOH
on graphite O Br
Geo. Flynn
D. Yablon
(Columbia Univ)

44. Permission limited by IBM
Quantum corral
STM
Image
of Fe
atoms
on Cu
(1993)
Permission limited by IBM
Click to link to copyright webpage
Reprint Courtesy of International Business Machines Corporation, copyright 1993 © International Business Machines Corporation

45. SNOM Scanning Near-Field Optical Microscope Scanning Near-Field
Sample (scanned)
Light
Glass Fiber
Aluminum Coating
100 nm Aperture
Lens
Emitted Light
Detector

46. SNOM image of nanofabricated materialmm
scale
red wavelength
W. Brocklesby by permission

47. Scanning Probe Microscopies (AFM, STM, SNOM)
are really powerful. Sharp points can resolve individual molecules and even atoms
but not bonds

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

49. H, C, N, O isomers C in middle
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 separation
(most “electronegative”
atom bears + charge)
charge separation

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

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

52. H, C, N, O isomers cyclic H C N O : + _ bad charge bad charge H C N O
sestet
sestet
Lowest energy form can’t even be calculated.
(downhill to open the ring)

53. HNCO isomers H C N O : _ + H C N O : + _ H C N O : + _ H C N O : H C N

54. 150
100 50
200
HNCO isomers H C N O
kcal/mole
Ecalc

55. 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.

56. End of Lecture 4 Sept 9, 2009
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