Roger G. Gymerl Fort Lewis College Durongo, Colorodo 81301
Fluid-Flow Simulation of Molecular Orbitals
A
dynamic method for showing the formation and final charge cloud pattern of simple molecular orbitals would he useful for lecture demonstrations or as an undergraduate laboratory exercise. Here a simple device, the fluid mapper, used long ago to visually depict potential fields, has been adapted to the simulation of molecular orbitals. The features of symmetry, overlap of atomic orbitals, and the nodal characteristics of bonding and antibonding molecular orbitals for homonuclear diatomics are clearly shown. The construction and operation of fluid-flow mappers for depicting potential fields has been previously de~ c r i h e d . ~A simpler method of construction, however, is sufficient for the simulation of molecular orbitals. Basically, the fluid mapper consists of a pair of flat horizontal plates separated by a small distance. The top plate is transparent. The two plates and the region betweeu them are completely immersed in water. The bottom plate contains holes which are conuected by tubes to one or more reservoirs of colored solution. Solution is admitted to the space between the plates by raising the reservoir so that the fluid level in the reservoir is above that in a shallow pan in which the plates are immersed. Alternatively, solution may be added to the reservoir to generate an outgoing flow without raising the reservoir. I n either case, the holes function as sources of the dyed liquid which spreads out radially from each hole until it interacts with the flow from adjacent sources. Colored solution may be removed from between the plates by lowering the reservoirs or by applying suction. The holes then act as sinks. The results shown here were obtained with Acrylite bottom plates with various hole configurations. The underside of this plate was painted white for increased contrast and the plate was supported by four rubber stoppers. The '/,-in. source holes were connected to 'Present address: Advisory Council on College Chemistry, Department of Chemistry, Stanford Universit,~, St,anford, California 94305. ' Moonz, A. I)., "Flrdd Mapper INanual," The University of Michigan, Ann Arbor, 1961, quoted by STONG, C. L., Scientific American, 217, 119 (1967).
the single reservoir with in. 0.d. Tygon or rubber tubing. A drying tower was used as the reservoir. Metal washers about 1.5 mm thick served as spacers between the top and bottom plates. The top plate was 6 X 10 in. clear glass. The weight of glass helps counteract the slight buoyancy of the lower plastic plate. The connecting tubes were filled with water from the pan and the colored solution was then poured into the drying tower reservoir until it covered the bottom outlet and began to flow through the tubes to the mapper. The flow rate may be controlled by closing off the top of the reservoir. Different flow rates to various holes may be obtained by using tubing of smaller or greater inside diameter or by otherwise constricting thc tubes leading to t,he holes from which a smaller flow is desired. Antibonding molecular orbitals are formed when colored water emerges from the source holes into the interplanar region. The lobes forming at each hole do not merge and a node is formed betweeu the lobes. Bonding orbitals are simulated when a colored waterethanol solution containing at least 50% alcohol is used. I n this case, the solution emerging from the holes mixes on contact with that emerging from nearby holes. Nodes may be preserved, even with alcohol solutions, by judicious placing of holes in the lower plate so that mixing takes place between certain lobes before it can occur wi'ih others. The antibonding orbitals formed with colored water are reversible. That is. after the orbital is formed. the colored solution may be pulled back into the reservoir by suction and allowed to re-emerge to again form the orbital. These re-formed orbitals are often better than the original ones. The bonding orbitals generated with alcohol solutions are not as re-formable because the solution soon becomes diluted with water from the pan when it is withdrawn into the reservoir. The als and the c*ls orbitals shown in Figures 1 and 2, respectively, were formed from two source holes
Figure 3. o2p, orbital. internuclear aiir.
Figure 1 .
c l r orbital.
Figure 2.
m*lr orbitol.
Figure 4.
The x axis i s the
o*2p, orbital.
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spaced 2 in. apart in the lower plate. Both tubes were connected to the same reservoir. I t is only in this case that the positions of the source holes correspond to the positions of the nuclei. Figure 3 shows the o2p, orbital and Figure 4 shows the n*2p,. Both were formed with a plate having four holes spaced along the internuclear axis, the x axis. The two center holes were ll/,in. apart while the end holes were separated from the nearest center hole by 2 in. This spacing permits merger of the two center lobes for bonding orbital formation before any merger of the end and adjacent lobes can occur. I n the bonding orbital the two end tubes were constricted to reduce the flow rate into the end holes so that the end lobes were smaller. In the anti-bonding orbital the two center tubes were constricted. All four tubes were connected to the same reservoir with two outlet tubes and two Y connectors. The source holes for the a2p, orbital, Figure 5, and the a*2p, orbital, Figure 6, are located a t the corners of a rectangle 25 mm wide and 42 mm deep, the longer side (y axis) being perpendicular to the internuclear axis. Again, all four tubes were connected to a single reservoir and all were, in this case, of equal inside diameter.
Figure 5. s 2 p , orbitol. They oxis is perpendicular to the internuclear .xi..
Figwe 6.
r*2p. orbital.
These simulated two-center molecular orbital charge clouds agree closely with the contour diagrams commonly found in the literature and in textbooks. The figures here do not fully show the decrease in intensity of color toward the periphery of the lobes but the effect is evident, especially in the antibonding orbitals, when the experiment is performed. Certainly these simulated orbitals show the nodal pattern and the basic symmetry of the charge clouds. best attention he paid details in the construction and operation of the simple fluid mapper. If only one reservoir is used, all tubes leading
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from the reservoir must be of equal length, especially if all tubes have the same bore. The tubes must be inserted into the holes in the lower plate so their end surfaces are flush with, or below, the upper surface of this plate. Burrs or other irregularities on the ends of the tubes may cause uneven flow away from the holes and lead to striations in the pattern, particularly in the case of the antihonding orbitals. Air bubbles in the tubes have the effectof decreasing the bore and result in unequal flow rates. Sometimes this is the desired effect, as in the o2p, and ZZp, orbitals, but then the amount of con~trict~ion should he controlled by using smaller bore tubing or by inserting a short length of glass tubing inside the tube. Unequal upward or downward bends in the tubing also change the flow rate and lead to too early or too late flow from some holes. The extension to the simulation of more complex molecular orbitals such as multicenter orbitals is a matter of using more source holes, more tubes, and perhaps more than one reservoir. The more tubes, however, the more the problems associated with unequal flow in different tubes will be encountered, leading to lopsided orbitals. The use of two or more reservoirs, containing different colors or even different liquids, would produce interesting and colorful patterns. Two or more operators can handle the manipulation of several reservoirs and the flow rate can be controlled by reservoir height. The fluid mapper described cannot handle the problem of phase differences in combining atomic orbitals. Thus the non-overlapping effect of an s and a p, orbital on different atoms cannot be shown. Simple representations of one member of a set of hybrid atomic orbitals can be made through use of the unequal flow method but the course of formation is rather far from reality, only the final form of the hybrid orbital being of any use. This simulation of molecular orbitals has generated much interest in students since they see, in addition to the final charge cloud shape, the growth of the lobes representing the individual stomi: orbitals and their subsequent merger or repulsion. The generation of these simple orbitals using the fluid mapper can he uqed as a lecture demonstration for small classes or as a laboratory exercise. For large classes, a motion picture of the simulation process has been found u ~ e f u l . ~
A fiveminute Super-8 color motion picture of the formation of the orhita.1~ &scribed above is available at cost from Dr. Rod O'connor, A C ~Film Clearinghouse, Department of Chemistry, University of Arizona, Tucson, Arizona 85721.
