Molecular orbitals visualization

The JME Editor is a Java program which allows one to draw, edit, and display molecules and reactions directly within a web page and may also be used as an application in a stand-alone mode. The editor was originally developed for use in an in-house web-based chemoinformatics system but because of many requests it was released to the public. The JME currently is probably the most popular molecule entry system written in Java. Internet sites that use the JME applet include several structure databases, property prediction services, various chemoinformatics tools (such as for generation of 3D structures or molecular orbital visualization), and interactive sites focused on chemistry education [209]. 

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

Besides molecular orbitals, other molecular properties, such as electrostatic potentials or spin density, can be represented by isovalue surfaces. Normally, these scalar properties are mapped onto different surfaces see above). This type of high-dimensional visualization permits fast and easy identification of the relevant molecular regions. 

For many reasons, including the Woodward-IIoffm an rules that describe the likelihood of reaction based on arguments about the shapes of orbitals, it is desirable to be able to visualize molecular orbitals. 

Wave functions can be visualized as the total electron density, orbital densities, electrostatic potential, atomic densities, or the Laplacian of the electron density. The program computes the data from the basis functions and molecular orbital coefficients. Thus, it does not need a large amount of disk space to store data, but the computation can be time-consuming. Molden can also compute electrostatic charges from the wave function. Several visualization modes are available, including contour plots, three-dimensional isosurfaces, and data slices. 

Two successful and widespread appHcations of visualization techniques in the field of chemistry are the visualization of molecular orbitals and the visualization of molecules in molecular mechanics studies. 

It is now possible to "see" the spatial nature of molecular orbitals (10). This information has always been available in the voluminous output from quantum mechanics programs, but it can be discerned much more rapidly when presented in visual form. Chemical reactivity is often governed by the nature of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Spectroscopic phenomena usually depend on the HOMO and higher energy unoccupied states, all of which can be displayed and examined in detail. 

When discassing molecular orbitals, three dimensional visualization software mar be very instructive. 

For molecular systems with up to thirty valence electrons, an amplitude of =t0.1 a.u. was chosen for the contour level. For systems with more than thirty valence electrons it was necessary to reduce this value to 0.08 a.u. to maintain the orbital size at a comfortable visual level. The molecular orbitals were normalized to an occupancy... 

One can visualize the effects of covalence on magnetic properties using a simple molecular orbital scheme. In the usual notation the orbitals considered for the transition metal M and the ligand X are ... 

The trigonal bond orbitals in the ten valence electron system as well as the two sets of trigonal lone pair orbitals in the 14 valence electron system are superpositions of it orbitals and o orbitals. The formation of such trigonally symmetric molecular orbitals from a-type and w-type molecular orbitals is entirely analogous in character to the formation of the three (sp2) hybrid atomic orbitals from one (s) and two ip) atomic orbitals which was discussed in the preceding section. This can be visualized by looking at the diatomic molecule... 

Practitioners of quantum chemistry employed both the visual imagery of nineteenth-century theoretical chemists like Kekule and Crum Brown and the abstract symbolism of twentieth-century mathematical physicists like Dirac and Schrodinger. Pauling s Nature of the Chemical Bond abounded in pictures of hexagons, tetrahedrons, spheres, and dumbbells. Mulliken s 1948 memoir on the theory of molecular orbitals included a list of 120 entries for symbols and words having exact definitions and usages in the new mathematical language of quantum chemistry. 

The effects of Lewis acids on the stereoselectivities can also be understood in terms of orbital interactions. The variation in charge at the respective basic centre gives rise to a change in the magnitude of the orbital coefficients of the entire interacting molecular orbital. These effects are visualized by the HOMO and LUMO representations of the Lewis acid-base complex of acrolein and trifluoroborane (Figure 3), and in an even more extreme case by the HOMO and LUMO representations of one of the simplest dienophile-Lewis acid complexes protonated acrolein92,93. 

The free-electron model is a simplified representation of metallic bonding. While it is helpful for visualizing metals at the atomic level, this model cannot sufficiently explain the properties of all metals. Quantum mechanics offers a more comprehensive model for metallic bonding. Go to the web site above, and click on Web Links. This will launch you into the world of molecular orbitals and band theory. Use a graphic organizer or write a brief report that compares the free-electron and band-theory models of metallic bonding. 

Roald Hoffmann, a former coworker of R.B. Woodward and Nobel Prize as well for his contribution to the frontier orbital theory (the famous Woodward-Hoffmann rules concerning the conservation of molecular orbital symmetry), has also emphasised the artistic aspects of organic synthesis "The making of molecules puts chemistry very close to the arts. We create the objects that we or others then study or appreciate. That s exactly what writers, visual artists and composers do" [15a]. Nevertheless, Hoffmann also recognises the logic content of synthesis that "has inspired people to write computer programs to emulate the mind of a synthetic chemist, to suggest new syntheses". 

Orbital symmetry arguments or the Woodward-Hoffmann rules, as they are now commonly referred to are, however, not easily extended beyond planar tz systems. In great part, this is due to the difficulty of constructing and sketching by hand and visualizing molecular orbitals of three-dimensional systems, a situation which modem computer graphics has now completely altered. 

However, thermodynamic and quantum mechanical calculations indicate that the stability of nitrosyldioxyl radical will be greatly increased by hydrogen bonding with water (Beckman and Koppenol, 1992). TTie reason for this increased stability can be readily visualized in Fig. 7. Nitrosyldioxyl radical is most stable when bent into the cis (or C-shaped) conformation (Boehm and Lohr, 1989). In this conformation, the lobes of the highest occupied molecular orbital from... 

It needs to be stressed that this simple molecular orbital picture is not appropriate for all purposes, but it is convenient for visualizing the changes brought about by light absorption in organic molecules, and as a qualitative basis for describing the mechanisms of organic photochemical reactions. 

In the valence bond theory, hybridization of orbitals is an integral part of bond formation. As we shall see, the concept need not be explicitly considered in molecular orbital theory but may be helpful in visualizing the process of bond formation. 

There is no unequivocal answer to the question as to which is the better method. Calculations by the VB method are likely to be more reliable than those by the MO method, but in practice are much more difficult to carry out. For many-electron molecules the MO procedure is simpler to visualize because we combine atomic orbitals into molecular orbitals and then populate the lower-energy orbitals with electrons. In the VB method, atomic orbitals are occupied, but the electrons of different atoms are paired to form bonds, a process that requires explicit consideration of many-electron wave functions. To put it another way, it is easier to visualize a system of molecular orbitals containing N electrons than it is to visualize a hybrid wave function of N electrons. 

The valence bond model of covalent bonding is easy to visualize and leads to a satisfactory description for most molecules. It does, however, have some problems. Perhaps the most serious flaw in the valence bond model is that it sometimes leads to an incorrect electronic description. For this reason, another bonding description called molecular orbital (MO) theory is often used. The molecular orbital model is more complex than the valence bond model, particularly for larger molecules, but sometimes gives a more satisfactory accounting of chemical and physical properties. 

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