Theory of chemical structure. Educational program. Part 1

For connections (edges) this is the multiplicity k (order), is a valid set of bond orders between atoms of a particular element(s). Rarely goes above 3

For atoms (vertices) this is the valency V (coordination number), there is a certain set of acceptable valences for each element. For hydrogen it is 1, for oxygen 2, for carbon 4, for nitrogen 3-4.

As knowledge about the structure of the atom and the nature of chemical bonds accumulated, this theory received a fundamental justification and a number of additions; the integrity of the bond order, as usual, ceased to be a prerequisite, but the basis remained unchanged. We will not touch on the theoretical justification of TCS; for now we will consider it purely empirical.

Formaldehyde molecule. Atomic valences are in red, bond orders are in black.

The main condition that determines the order of connection of atoms into a molecule is the condition

V = Σk

that is, the sum of the bond orders coming into an atom is equal to its valency. In principle, this is sufficient information to draw basic conclusions regarding the structure of molecules. The first conclusion is that the structure of a molecule can be unambiguously and accurately described, for example, the structure of a molecule of n atoms, like any graph, can be described by an n*n matrix. Or a list of structures of the form (atom A, atom B, bond order). The second conclusion is that one set of atoms can correspond to several molecules of different structures. Such molecules are called isomers. It is important to understand that TCS does not say anything about the spatial arrangement of atoms in a molecule – only about their connectivity. Therefore, one structure can correspond to several stereoisomers – the most stable geometric configurations of this structure in three-dimensional space.

The structure of a molecule can be depicted in the form of a 2D projection, for example, with a drawing on paper – a structural formula known to everyone from school. There are different ways to project a molecule onto a plane, with their own mapping rules. In addition to the classical projection, Fisher (mainly for biochemistry) and Newman (for stereochemistry and conformational analysis) projections are used, as well as specific methods for depicting individual elements, such as cyclohexane (chair-bath). The rules for depicting structural formulas make it possible to preserve stereochemical information, so an experienced organic specialist can easily build a 3D model of a not too large molecule from a picture in his imagination. To make it easier to depict and understand structural formulas, hydrogen atoms are not designated (since their valence is always 1, and, therefore, the order of bonding with them is also 1), and instead of carbon atoms, simply vertices are drawn.

After simplifying the image, the propene molecule began to look much more compact and neat.

Moving from interatomic connectivity to spatial structure, we must take into account that the structural elements, bonds and atoms have a geometric size in three-dimensional space. You must understand that the nucleus of an atom is a very small thing, so the real size of the structural elements of a molecule is determined by the size of their electron clouds. Since electrons are completely quantum objects, the size of their clouds is not a strict parameter, but a certain region of space, but for our purposes it is enough to approximate them by enclosing (non-strictly, say, 95% of the electron density) geometric bodies: atoms – balls, and bonds – sticks or cylinders (Ball and stick model). This model already gives a completely adequate idea of the spatial structure of the molecule. You also need to understand that these objects, being close to each other, repel. I will not consider in detail the nature and nature of the forces of interatomic and intermolecular interaction, I will only say that, unlike macroscopic objects of the scale we are accustomed to, the closer these objects are, the stronger they repel. IN Lennard-Johnson potential and we won’t dig deeper, but from this we can already draw a logical conclusion – the bonds (as well as lone electron pairs) emanating from one atom will repel each other, and will eventually take the position of greatest mutual distance from each other.

From this postulate grows the legs of the theory of OEPVO – repulsion of electron pairs of the valence shell. It is accepted that electron pairs (no matter bonded or lone) around an atom repel each other equally, and therefore the task of determining the spatial relative position of n substituents and lone pairs of a particular atom under consideration is determined by the correct n-vertex polyhedron, because it is in it that the vertices are most distant from each other from each other at equal distances from the center. For n = 2 it is a segment, for n = 3 it is a flat triangle, for n = 4 it is a tetrahedron, and so on. The corresponding polyhedra up to n = 6 are depicted in the figure below, provided with examples of specific molecules. Why up to n = 6? Because OEPVO works only for non-transition elements, and they have more than 6 pairs in the valence shell – a rarity.

A visual illustration of the theory of OEPVO, wandering from textbook to textbook

The figure clearly shows why methane is tetrahedral, ammonia is pyramidal, and water has the shape of an obtuse angle. In all three molecules, the central atom (carbon, nitrogen and oxygen, respectively) has a tetrahedral configuration with angles of ~109 °, but carbon has all four vertices occupied by substituents, ammonia has three, and water has only two. For transition elements (periods 3 to 12 in the long representation), as well as for some heavy atoms, OEPVO does not work; they use TCT – crystal field theory, and more complex theories, which we will not touch on. In a situation where the immediate environment of the atom is anisotropic, that is, the substituents have different actual volumes and repel differently, or there is geometric stress (for example, in cyclopropane), the configuration corresponds to a distorted tetrahedron, but in most cases the distortions are not so great. On a circle, the theory of OEPVO gives us very important information – the angles between bonds at each atom.

We have angles, but what about interatomic distances? And with them everything is simple. For each pair of elements (A, B) and bond order k, the length of this bond is in a fairly narrow range of a couple of percentage points wide. And deviations from this are usually due to the fact that the real order of communication differs from the integer order. Therefore, all bond lengths were tabulated a long time ago and are reference information. For, let's say, popular bonds, for example C-C, a set of values is often given for different types of chemical environments. There are multi-volume reference books and Internet resources where a huge amount of data on the lengths of chemical bonds in various compounds is indexed.

A small table of bond lengths. There is still energy there, but more about that another time.

So, we know the connectivity of atoms, we know the angles, we know the bond lengths. And this, in general, is almost the entire gentleman’s set necessary for understanding the structure of the molecule. All that remains is the phenomenon of stereoisomerism, but I don’t have enough strength for it today, and I will allow myself to separate it into a separate post. As for the rest, the information presented today is quite enough to imagine the structure of the molecule of an organic compound, which will allow us to continue discussing the NMR method and its capabilities in application to organic compounds. For those who want to feel the structure of molecules live, I can recommend a free drawing tool MolView, in which you can draw flat structural formulas (it adds hydrogens automatically, just like the consciousness of an organic chemist), and by pressing the “2D to 3D” button, transform this into a three-dimensional rotating structure, which, by the way, is generated on the basis of OEPVO and tabular bond lengths. We, of course, use other tools in our work, for example ChemDraw for drawing and Gaussian for calculations and visualization, but they are very, very paid, and MolView is frivolous and online)

I hope that in the future I will (not) have more free time to finish the series on NMR and start something equally interesting about instruments and research methods in chemistry.