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In fact, it can generally be a complex number with both a "real" part that's an ordinary number and an "imaginary" part that's multiplied by the square root of one.

IIRC, the author wanted the square root of negative one. After seeing the credit for the image, the following appears to be the title & abstract: High-Resolution Molecular Orbital Imaging Using a p-Wave STM Tip

Leo Gross, Nikolaj Moll, Fabian Mohn, Alessandro Curioni, Gerhard Meyer, Felix Hanke, and Mats Persson

Phys. Rev. Lett. 107, 086101 (2011) – Published August 15, 2011

Abstract

Individual pentacene and naphthalocyanine molecules adsorbed on a bilayer of NaCl grown on Cu(111) were investigated by means of scanning tunneling microscopy using CO-functionalized tips. The images of the frontier molecular orbitals show an increased lateral resolution compared with those of the bare tip and reflect the modulus squared of the lateral gradient of the wave functions. The contrast is explained by tunneling through the p-wave orbitals of the CO molecule. Comparison with calculations using a Tersoff-Hamann approach, including s- and p-wave tip states, demonstrates the significant contribution of p-wave tip states.

"Sometimes quantum calculations are not correct, and sometimes you see things you don't expect," he says. The researchers themselves hope the technique will lead to engineering designer orbitals for molecule-sized machinery.

That's why better methods have been devised:

BlackLight has formed a wholly-owned subsidiary company, Millsian, Inc., dedicated to developing the molecular modeling applications of classical physics (CP), solving atomic and molecular structures based on applying the classical laws of physics, (Newton's and Maxwell's Laws) to the atomic scale. The set of individual bonds between two atoms apiece of a molecule are known as the functional groups. The functional groups (Table 1) of essentially all major classes of chemical bonding including those involved in most organic molecules have been solved in analytical form. By using these functional groups as building blocks, or independent units, a potentially infinite number of molecules can be solved. As a result, Millsian software can visualize the exact three-dimensional physical structure, calculate physical characteristics of a boundless number of molecules of any length and complexity, and facilitate the engineering of new pharmaceuticals and materials at the molecular level. The results obtained in real-time match the experimental values typically to the limit of measurement."

See MILLSIAN 2.0: A molecular modeling software for structures, charge distributions, and energetics of biomolecules in Phys. Essays 24, 200 (2011); doi:10.4006/1.3567145 (13 pages)

mark

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