Test in medicinal chemistry. Ticket questions on computer molecular modeling and QSAR methods.

General information

The abbreviation QSAR is an abbreviation for the English Quantitative Structure Activity Relationships, which translated into Russian means Quantitative Structure Activity Relationship (therefore, sometimes in Russian-language literature the abbreviation KSSA is used).

One of the most important tasks of modern chemical science is to establish relationships between the structure and properties of substances. The number of newly synthesized new organic compounds is constantly increasing, so the most pressing task is the quantitative prediction of specific properties for new, not yet synthesized substances based on certain physicochemical parameters of individual compounds.

Historically, it all began with attempts by scientists to find a quantitative relationship between the structures of substances and their properties and express this relationship in quantitative form, for example, in the form of a mathematical equation. This equation must reflect the dependence of one set of numbers (representing properties) on another set of numbers (representing structures). Expressing a property in numerical form is quite simple - the physiological activity of a series of substances can be measured quantitatively. It is much more difficult to express the structures of chemical compounds numerically. For this expression, QSAR currently uses so-called chemical structure descriptors.

A descriptor is a parameter that characterizes the structure of an organic compound in such a way that certain specific features of this structure are noted. In principle, a descriptor can be any number that can be calculated from the structural formula of a chemical compound - molecular weight, number of atoms of a certain type (hybridization), bonds or groups, molecular volume, partial charges on atoms, etc.

To predict physiological activity in QSAR, descriptors are usually used, calculated on the basis of steric, topological structural features, electronic effects, and lipophilicity. So-called topological descriptors play a significant role in QSAR. Structural descriptors play an important role in assessing the strength of binding of a test compound to a biotarget molecule; electronic effect descriptors describe the ionization or polarity of compounds. Lipophilicity descriptors make it possible to assess the ability to dissolve in fats, that is, it characterizes the ability of a drug to overcome cell membranes and various kinds of biological barriers.

In the QSAR method, the structural formula is presented in the form of a mathematical representation - a graph and is operated using a specialized mathematical apparatus - graph theory. A graph is a mathematical object defined by a set of vertices and a set of ordered or unordered pairs of vertices (edges). Graph theory allows you to calculate the so-called graph invariants, which are considered as descriptors. Complex fragment descriptors are also used, which evaluate the contribution of different parts of the molecule to the overall property. They make it much easier for researchers to reverse engineer unknown compounds with potentially high activity. Thus, the QSAR model is a mathematical equation (model) that can be used to describe both physiological activity (a special case) and any property in general, and in this case it is more correct to talk about QSPR - the quantitative relationship between structure and property.

The QSAR methodology works as follows. First, a group of compounds with a known structure and known physiological activity values ​​(obtained from experiment) is divided into two parts: a training set and a test set. In these sets, numbers characterizing activity are already correlated with a specific structure. Next, descriptors are selected (many hundreds of descriptors have been invented at present, but a fairly limited number are actually useful; there are different approaches to selecting the most optimal descriptors). At the next stage, a mathematical dependence is built (a mathematical equation is selected) of the activity on the selected descriptors for compounds from the training (training) set and, as a result, the so-called QSAR equation is obtained,

The correctness of the constructed QSAR equation is checked on a test set of structures. First, descriptors are calculated for each structure from the test sample set, then they are substituted into the QSAR equation, activity values ​​are calculated and compared with already known experimental values. If a good agreement between the calculated and experimental values ​​is observed for the test set, then this QSAR equation can be used to predict the properties of new, not yet synthesized structures. The QSAR method allows, having at its disposal a very small number of chemical compounds with known activity, to predict the required structure (or indicate directions for modification) and thereby sharply limit the range of searches.

In developed countries, work in the field of QSAR is carried out at an ever-increasing pace - the use of QSAR methods when creating new compounds with specified properties allows one to significantly reduce time and resources and carry out a more targeted synthesis of compounds that have the required set of properties.

Question No. 3. The concept of molecular graphs and their invariants. Types of molecular structure descriptor. The concept of topological indices. Wiener, Randić, Keira-Hall indices and other topological indices. QSAR using topological indices.

Molecular graph- a connected undirected graph that is in one-to-one correspondence with the structural formula of a chemical compound in such a way that the vertices of the graph correspond to the atoms of the molecule, and the edges of the graph correspond to chemical bonds between these atoms. The concept of “molecular graph” is basic for computer chemistry and chemoinformatics. Like a structural formula, a molecular graph is a model of a molecule, and like any model, it does not reflect all the properties of the prototype. Unlike a structural formula, which always indicates which chemical element a given atom belongs to, the vertices of a molecular graph can be unlabeled - in this case, the molecular graph will reflect only the structure, but not the composition of the molecule. Similarly, the edges of a molecular graph can be unlabeled, in which case no distinction will be made between single and multiple chemical bonds. In some cases, a molecular graph may be used that reflects only the carbon skeleton of an organic compound molecule. This level of abstraction is convenient for computationally solving a wide range of chemical problems.

A natural extension of the molecular graph is the reaction graph, whose edges correspond to the formation, breaking, and reordering of bonds between atoms.

“We emphasize that it was in the theory of R. Bader that the empirical idea of ​​additivity was first substantiated; it was this theory that made it possible to give a strict physical meaning to a number of concepts of the classical theory of chemical structure, in particular, the “valence stroke” (bonding path) and the structural chemical formula (molecular graph)."

Topological index- invariant (invariant is a term meaning something unchangeable) of a molecular graph in computer chemistry problems. EThis is some (usually numerical) value (or set of values) characterizing the structure of the molecule. Typically, topological indices do not reflect the multiplicity of chemical bonds and types of atoms (C, N, O, etc.), hydrogen atoms are not taken into account. The most famous topological indices include the Hosoi index, Wiener index, Randić index, Balaban index and others.

Global and local indexes

The Hosoi index and the Wiener index are examples of global (or integral) topological indices that reflect the structure of a given molecule. Bonchev and Polyansky proposed a local (differential) index for each atom in the molecule. Another example of local indexes is the modification of the Hosoi index.

Discrimination power and superindices

The values ​​of the same topological index for several different molecular graphs can be the same. The fewer such matches, the higher the so-called discriminating ability of the index. This ability is the most important characteristic of the index. To improve it, several topological indices can be combined into one superindex.

Computational complexity

Computational complexity is another important characteristic of a topological index. Many indices, such as the Wiener index, the Randić index and the Balaban index are calculated using fast algorithms, unlike, for example, the Hosoi index and its modifications, for which only time exponential algorithms are known.

Application

Topological indices are used in computational chemistry to solve a wide range of general and special problems. These tasks include: search for substances with predetermined properties (search for dependencies such as “structure-property”, “structure-pharmacological activity”), primary filtering of structural information for repeated generation of molecular graphs of a given type, preliminary comparison of molecular graphs when testing them for isomorphism and a number of others. The topological index depends only on the structure of the molecule, but not on its composition, therefore molecules of the same structure (at the level of structural formulas), but different compositions, for example, furan and thiophene will have equal indices. To overcome this difficulty, a number of indices have been proposed, for example, electronegativity indices.

In a vector description, a chemical structure is associated with a vector of molecular descriptors, each of which represents an invariant of the molecular graph.

Molecular descriptors. Types of molecular descriptors.

Existing sets of molecular descriptors can be divided into the following categories:

1. Fragment Descriptors exist in two main versions - binary And integer. Binary fragment descriptors indicate whether a given fragment (substructure) is contained in a structural formula, that is, whether a given subgraph is contained in the molecular graph describing a given chemical compound, while integer fragment descriptors indicate how many times a given fragment (substructure) is contained in a structural formula. That is, how many times a given subgraph is contained in the molecular graph describing a given chemical compound. The unique role of fragment descriptors is that they form the basis of the descriptor space, that is, any molecular descriptor (and any molecular property) that is an invariant of the molecular graph can be uniquely decomposed into this basis. In addition to modeling the properties of organic compounds, binary fragment descriptors in the form of molecular keys (screens) and molecular fingerprints are used when working with databases to speed up substructural search and organize similarity searches.

2. Topological indices.(for information on them, see above)

3. Physico-chemical descriptors- these are numerical characteristics obtained as a result of modeling the physicochemical properties of chemical compounds, or values ​​that have a clear physicochemical interpretation. The most commonly used descriptors are: lipophilicity (LogP), molar refraction (MR), molecular weight (MW), hydrogen bond descriptors, molecular volumes, and surface areas.

4. Quantum chemical descriptors- these are numerical quantities obtained as a result of quantum chemical calculations. The most commonly used descriptors are: energies of frontier molecular orbitals (HOMO and LUMO), partial charges on atoms and partial bond orders, Fukui reactivity indices (free valency index, nucleophilic and electrophilic superdelocalizability), energies of cationic, anionic and radical localization, dipole and higher multipole moments of the electrostatic potential distribution.

5. Molecular field descriptors- these are numerical quantities that approximate the values ​​of molecular fields by calculating the energy of interaction of a test atom placed at a lattice site with a current molecule. 3D-QSAR methods, the most famous of which is CoMFA, are based on constructing correlations between the values ​​of molecular field descriptors and the numerical value of biological activity using the partial least squares (PLS) method.

6. Substituent constants were first introduced by L.P. Hammett in the framework of the equation that received his name, which connects reaction rate constants with equilibrium constants for certain classes of organic reactions. Substituent constants entered QSAR practice with the advent of the Hancza-Fujita equation, which relates biological activity to substituent constants and lipophilicity values. Currently, several dozen substituent constants are known.

7. Pharmacophore descriptors show whether the simplest pharmacophores, consisting of pairs or triplets of pharmacophore centers with a specified distance between them, can be contained within the analyzed molecule.

8. Molecular similarity descriptors indicate a measure of similarity (molecular similarity) to compounds from the training set.

Wiener index(English Wiener index), also known as Wiener number, is a topological index of an undirected graph, defined as the sum of the shortest paths (English) d(vi,vj) between the vertices of the graph:

Randić index ( English Randić index), also known as connectivity index of an undirected graph, is the sum of the contributions along the edges, where v i And v j- vertices forming an edge, d(vk) - vertex degree vk:

The Randić index is characterized by good differentiating ability, but is not a complete invariant. For the pairs of graphs below, it is the same, although the graphs are not isomorphic.

VARIABILITY DIVERSITY OF STRUCTURES AND FORMS AND FORMS OF MOLECULES OF ORGANIC COMPOUND OF ORGANIC COMPOUNDS MOLECULES L. P. OLEKHNOVICH g. and. ygTspzyZau KUTU‚TNLI „UTY‰‡ TЪ‚VMM˚I YML‚V TLIV, KUTU‚-M‡-SUMY The question of genesis and the variety of the types ZZTSSZATS of mirror configurational isomerism of organic com- Chemistry of carbon - organic chemistry - stands out for its variety of structure and extreme pounds are discussed with the numerous individual connections the application of some. The total number of known organic compounds - elements of graph theory. tions (over ten million) is annually replenished with tens of thousands of new substances synthesized in laboratories. Organic chemistry surprises the analysis of molecular with the variety of classes of molecules, in the structure of which, at first glance, no logic is visible. The main reason for the emergence of a set of organizations that cannot be easily enumerated (>107) of organizations are enlightened. Different compounds are the unique properties of ferences of achiral and central element – ​​carbon. chiral compounds are The world of carbon compounds is an inexhaustible combinatorics of options and methods for constructing classified. molecules of n C atoms, m O atoms, k–N, l–S, h–P, etc. k‡TTPUЪ VM˚ ‚UF UT˚ schgTseZnkh ntsikaa YkDoyZ F ULTıUK‰VMLfl PMU„U-Z abyEkDZaip eigTsdmg U· ‡BLfl ‚L‰U‚ BV N‡O¸- Similar to physicists use economical In the ˆLUMMUI, but capacious language of mathematical formulas and calculations, chemists use a special language for recording the structure of compounds. This language is especially not used in organic chemistry to organize ideas about the numerous subclasses of “SCHU”. d ‡ЪNU UT‚В˘В- a gigantic variety of molecules. In order to spend less time and space when depicting structural formulas, organic chemists often do not bother themselves with the designations of atoms. This technique M‡ UTMU‚V F V‰ТЪ‡‚OV- is especially convenient when one considers not any properties of a particular compound, but the general patterns of the structure and shape of the series of mo- b LL, BUT‡TTLSHLˆL U‚‡- lecules. So, instead of drawing the letter M˚ UTU·VMMUTL TJUV- designations of carbon and hydrogen atoms in all structural isomers, for example, limit- © ІOVıMU‚L˜ g.i. , 1997 MLfl TLPPV L˜M˚ı L th hydrocarbon hexane – C6H14, depicted by ‡TLPPV L˜M˚ı TUV‰LMV-graphs (Scheme 1) MLI, ‰‡MU UV V‰WOWMLV NL ‡O¸MUI TLPPV Kommersant LL. Scheme 1 44 lykyljZldav jEkDbjZDnTsg'zhv LmkzDg, No. 2, 1997 The vertices of the graphs (points) are carbon atoms, compounds, also depict complex transformations, and the lines (edges) connecting them are C–C bonds. molecules (reactions) and understand each other. Since carbon is tetravalent, and hydrogen is monovalent, it is clear that at the terminal (free) vertices of the graph there should be three H atoms, with graphs . In this theory, a graph G of order n is determined by the average vertices of the type - two each, and is tertiary as a non-empty set of vertices V1, V2, ..., Vn. hydrogen atoms at quaternary vertices calling different vertices. The theory of graphs began with the famous arguments of L. Euler. The above graphs, therefore, are not (1736) about the Königsberg bridges, where the formulas were complete, but they are sufficient to represent the criteria for traversing all the edges of the graph without cross-structural isomers of hydrocarbons. Below are greetings, as well as his other works related to Madena graphs of unsaturated hydrocarbon molecules with thematic puzzles and entertainment. double (C=C) and triple (C≡C) bonds, as well as graphs of some cyclic and frame carbons by G. Kirchhoff (1847) and W. Hamilton (Table . 1). (1859). A. Cayley (1857, 1874–1875) was the first to generalize the trigonal graph (Scheme 2) to use graph representations (enumerations of the figures of very different molecules. graph “trees”) in connection with counting the number of isomers of the first terms a number of saturated hydrocarbons. Thus, graphical (graphic) forms of alkanes. Indeed, only with the help of la connection is an economical representation of the important apparatus of graph theory (Pólya’s theorem, 1937) of its possible particular and most general patterns but to solve the problem of enumeration (enumeration) of all structures and forms. For chemists, similar structural isomers of molecules CnH2n + 2, CnH2n, graphs are enough so that, without using long names CnH2n - 2, CnH2n - 4, etc. (see graphs of hexane isomers), Table 1 Z,E-isomers of butene-2 ​​Z E H3C CH CH CH3 .R . R,L-isomers of 1,3-dimethyl-3-cumulene L. Z. . E. Z,E-isomers of 1,4-dimethyl-4-cumulene. . . . . . Dimethylacetylene 1,4-dimethylbiacetylene Xylenes Benzene Toluene ortho-meta-para- Cyclic saturated hydrocarbons Cyclopropane Cyclobutane Cyclopentane Cyclohexane and so on Framework hydrocarbons Tetrahedran Prizman Kuban ygTspzyZau g.i. ezyYYYEKDBATS lnkyTszaa oike eigTsdmg ykYDzauTsldap lyTSSazTszav 45 O 2− O − CH2 + F B C N C = F F O O O O H2C CH2 Trifluoride Anion of acidic residue Trimethylenemethane boron cation carbonic nitric acid acid Scheme 2 as well as isomers of derivatives (substituted) of carbon eeTsnka a DlaeeTsnka eygTsdmg, hydrogens, when “manually”, for large n, this takes a lot of time. Currently, the theory Let us now turn to another feature of our graphs that naturally enters many consciousnesses - attention. When we consider branches of modern mathematics, such as topology of some of the surrounding objects (including logic and combinatorics, linear algebra and molecular graph theory), then often realizu- groups, probability theory and numerical analysis. There are also consciously uncontrolled operations. It is successfully used in physics, chemistry, genetics, which note the correspondence of parts of an object to each other. Ancient Greeks in computer science, architecture, sociology and linguistics. the term “commensurable” (σιеёετροσ) was used to designate. It is necessary to keep in mind the features of the “language” such features of mutual arrangement, relational graphs: parts of an object, which determine its symmetrical appearance, shape - strict symmetry; molecular graphs formalize the connections of buildings, crystals minerals, two-sided symmetry, including, as a rule, several (two and geometry of plant leaves, rotational symmetry more) varieties of atoms-vertices; flowers, etc. if the general theory of graphs allows the production of Objects are symmetrical, if the proportionality and free number of edges emanating from one ver- the relative arrangement of their parts allow such buses (including isolated vertices during the operation of rotations, internal reflections, complete absence of edges), then the vertices chemical versions (combination of rotations and reflections), the graph must have exactly as many edges (the connection of which leaves them (objects) unchanged), what is the valence (coordination number) of the graphs, transforms them into themselves. The structure of a symmetry-given atom in a chemical compound; ric objects is such that it is characterized by the presence of at least one of the following elements of the vertex of the chemical graph along with symmetry: the directions of the edges must be clearly oriented, the planes of mirror reflection σ (S1) - because they represent the relative position of the speed of symmetry, having it objects consist of atoms in molecules, as well as the angles between the bonds of identical, mirror-identical halves of atoms: for a tetrahedral carbon atom these (see. graphs in diagrams 1, 2 and in table. 1); the angles are usually equal to 109.5°, for trigonal planar - 120°, for digonal, acetylene - symmetry axes Cn, n = 2, 3, 4, ..., - parts of the object - 180°, but there may be exceptions ( see the graphs of the map are combined, like the object as a whole, with its pokasal hydrocarbons in Table 1), and three-dimensional (turned around at angles 2π / n (see Table 1 and Scheme 2); large) graph projections are necessary for the pre-mirror-rotational axis Sn, S2 = i is the center of arrangement of molecular configurations. inversion - is a combination of C2 + S1, S4 = com- Experimental chemists design, combinations of C4 + S1 (see E-isomers of butene-2, even like engineers, graphs of new, previously unknown cumulenes, tetrahedron and cubane in Table. 1). connections, think through and implement methods for them. The object is asymmetrical if its internal synthesis. Theoretical chemists compare the structure and the external form; it is impossible to characterize the characteristic analysis in quantum chemical calculations with any of the listed elements sym- sometimes very different structures in order to reveal the properties (see the 2nd and 4th isomers of hexane in Scheme 1, limits of changes in interatomic distances and ras-alanine in Scheme 3). For such objects there is a common distribution of electrons in ions and molecules, the previous trivial symmetry operation is C1. put in one graph (see diagram 2). Graphic- Rotating C1 by 360° (2π) combines the asymmetrical formulas that have become commonplace little more than the object with itself. Of course, the action of the operation - 100 years ago, and the graph communication language of chemistry C1 are combined with themselves and everything is symmetrically - continuously improved. ny objects, since this rotation is trivial. 46 lykyl Zldav yEkDbjZDnTsgzhv LmkzDg, ‹2, 1997 3 3 H H H H H COOH H3C COOH HOOC CH3 C 2 C C C 2 C 1 4 4 1 H H H2N H H2N H H2N H H NH2 Methane Methylamine Glycine l-alanine r-alanine Scheme 3 Spheres, balls - examples objects that have an asymmetric molecule (alanine) have a mirror - infinite sets of all symmetry elements - a double - a double (see diagram 3). S1(σ), Cn , Sn . The ball is aligned with itself at any rotation, any orientation of the mirror In the 60–70s of our century, scientists of stereoplanes and axes of rotation passing through it, chemists R. Kahn, K. Ingold and V. Prelog developed a center. Therefore, the correct convex polyhedral general rules for assigning duplicate components (tetrahedron, cube, octahedron, dodecahedron, icosahedron - similar types to left (l) and right (r) forms: ideal Platonic solids), into which substituents are inscribed (atoms) associated with the asymmetry of the sphere, although they have finite sets of elemental carbon or other atomic centers of symmetry, but their number and diversity are always sorted according to their hierarchy, and the oldest (but larger in comparison with others polyhedra. measure 1) is the one that has the largest It has long been noted that if the asymmetric atomic mass: in alanine (Scheme 3) 14N is older than 12C, and this figure is reflected in a mirror plane, located among the carbon atoms of the methyl and carboxyl groups is older than the latter : it is connected with heavy 16O placed outside this object, then a figure is obtained, while the first one is with light 1H; accuracy similar to the original one, but incompatible with the first one for any shifts and rotations. The follower-observer is oriented (of course, mentally, all asymmetric objects can be salted) towards the molecule, or the molecule is oriented towards placing mirror-like twins. It is commonplace for an observer to see that carbon examples of this are our shoes and gloves, the left center is “overshadowed” by the youngest substituent (N), and the right pairs of figures of which fit correspondingly, and if at the same time the trajectory of the successive song left and right are mirrored -doublet finite transition from the oldest to the youngest (unobscured by our generally planar-symmetrical) substituents (that is, from the first number to the figures. Crystallographers several centuries ago to the next) is similar to the movement of clock hands, noted the prevalence of mirror-like then the configuration is absolutely right (r), if the two enantiomorphic forms in the inorganic world are the mouth, then it is absolutely left (l). left and right crystals of quartz, tourmaline, calcite (Iceland spar). Having introduced ideas about absolutely left and right configurations, we must warn about Mirror isomerism, enantiomerism, in the organic relativity of this absoluteness. Zerce chemical operations are a very common phenomenon. cal reflection corresponds to P – inversion of the co- The priority of its discovery in the middle of the past table- ordinates of all atomic and subatomic parts of the object. tion belongs to the outstanding Frenchman Louis Pas- However, since the internal structure of Theur, who drew attention to the mirror similarity of atomic (electrons) and subatomic (quarks, gluoforms of crystals of potassium-ammonium tartaric salts) particles, is unknown, the operation P of physics is complemented by phoric acids. The name of Pasteur is associated with the formation of a small operation of charge conjugation C - stereochemistry, based on the problems of sim- change to opposite signs of charges and all the geometry and asymmetry of molecules, their structure (shape) and other antipodeal quantum characteristics of the atom - in three-dimensional space. An important milestone in the development of (protons, neutrons, electrons) and subatomic stereochemistry was the proposed in 1874 particles (quarks, gluons), as well as the operation of Ya. Van't Hoff and J. Le Bel tetrahedral inversion of the directions of motion (momentum and model of the carbon atom. If in the simplest carbonament of momentum) of all components of the object, corode, the figure of which is similar to the high-symto- ry corresponds to the reversal of time T. Poetometric tetrahedron, - methane hydrogen atoms, the actual limiting inversion is to successively replace (replace) with other atoms - a combined CPT operation. From this it follows, between atomic groups and groups, that the symmetry that is the absolute antipode of the original one, for example, of the resulting molecules quickly decreases. After the r-molecule there must be its l-partner, but consisting of three such procedures, four different substituents are already connected to the tetrahedral carbon of the antimatter and the center moving in time, and in reverse. Ideas for combining P-, C- and T-operators ygTspzyZau g.i. ezyYyyEkDbaTs lnkyTsza a oike eigTsdmg ykYDzauTsldap lyTSSazTszav 47 symmetries belong to G. Lüders and W. Pauli to unite to an infinitely symmetric sphere, then everything (1954–1955). the symmetry elements of the original object are degraded due to the gigantic possibilities vary completely, that is, the asymmetric “adding” of atoms and atomic groups capable of bonding transforms a perfectly symmetrical (singlet) with carbon, an infinitely realizable in principle object into the class of enantiomeric doublets. However, one should not assume that enantiomerism of molecules with asymmetric carbon centers is impossible among symmetrical figures (molecules). mi. Let us note their fundamental feature: let us remember a simple regularity: whether a mirror asymmetric carbon or another atom, configurational isomerism, a truly impossible center can be placed as a substituent in the rows of objects (molecules) that have at each of the vertices of a highly symmetrical object (on - the quality of internal elements of symmetry plane - for example, tetrahedron, cuban; Table 1) and even specular reflection suction σ (S1) and/or mirror reflection - Table 2 C2 C2 R L . . (CH 2) n (CH 2) n R, L-trans-cyclooctenes R, L-trans-cycloethylenes C2 C2 C2 C2 C2 C2 Twistan R L Z Z -biphenyls of symmetry C2 Z Z R L -triphenylmethanes of symmetry C3 L R C2 R Hexagelicene L Spirals, springs, screws, screws, nuts, bolts 48 lykylZldav jEkDbyZDnTsgzhv LmkzDg, ‹2, 1997 rotary axes i (S2, 3, 4, ...). When such d are reflected, they are topologically chiral molecules (their shapes by the outer mirror plane are nans, nodes in Scheme 4). copy objects identical to the original ones (see graph However, the convention of partitioning is obvious in the light of diagrams 1, 2 and Table 1). On the contrary, if the structure developed by R. Kahn, K. Ingold and V. Prelonie objects (molecules) is characterized by the absence of rules for assigning enantiomeric configurations (σ, i), supplemented by their successors internal mirror symmetry elements Sn, but they are symmetrical relative to rotations of molecules to R- or L-rows, these are circular, spi- Cn (n = 2, 3, 4, ...), then such figures are always R, L-dual (chiral) movements along (R) or against flying. The simplest example is 1,3-dimethyl-3-cumu-(L) clock hands with sequential distribution (Table 1) and all its homologues with an odd number depending on the “seniority” (weight) of substituents, carbon ra- atoms in linear circuit. In table 2 shown (scheme 3) around the atomic center - we have some R, L-doublets from a large set of a, selected plane - b (trans-cycloethylenes, molecules symmetric with respect to rotations. Table 2), when going around the contours of the propellers - c , vin- Note that they do not have asymmetries at all - r, nodes - d in the table. 2, in the diagram 4. there are many carbon centers. In technology, the molecules of biphenyls and triphenylmethyls are similar to the shapes of fan blades, propellers, and turbine rotors; The figures of helicene molecules are similar to spirals, springs, screws, left and right threading of screws. For a brief description of the phenomenon under discussion at the turn of the 19th and 20th centuries, Lord Kelvin Trefoil knot (CH2)m, with oriented and non-minimum m = 66, proposed the term “chirality” (from the Greek χειρ - hand). identical rings In Russian, two variants of pronunciation and spelling of this term are used: chirality and Scheme 4 chirality. The author, together with physicists, gives preference to the first. Conjugated by the operation of mirror reflection (coordinate inversion P) mo- Therefore, strictly speaking, there are no molecules - components of enantiomeric doublets - qualitatively different types of molecular chirality. differ only in one property - pro- For example, called topological chiralty opposite signs +(R) and −(L) of the rotation angle d in diagram 4 is just a reflection of that structure of the plane of polarization of light. Similar features of the depicted molecules are that antipodal (+, −) relationships are also characteristic of their individual parts are held together not by chemical- for the poles of magnets, charges and other quantum bonds, but by the topology of the structure of the chains (characteristics of atomic and subatomic particles. Such tenans), closed spirals and knots; their chiral relationship is called by physicists the chiral sym- (R, L) form is quite similar to the propellemetric form. ditch – in and spirals – g. Therefore, all of the above types of chirality of molecules are quantitatively, thanks to the efforts of synthetic chemists, uniformly: the sign (+, −) and quantified by the problems of stereostructure, over the last rank of the angle of rotation of the plane of polarization for decades have become known and available at a very wide variety of wavelengths of light. numerous, including exotic, types of ki- However, it is also known that at polyral molecules (see Table 2 and Scheme 4). It is accepted that the condensation of centrally chiral (r or l) ami- consider that the diversity of chiral chemical acids, ribonucleotides, the total chirality of rest compounds is divided into five types in the corresponding polymer (protein, DNA) cannot be assessed with symmetrical structural features : by trivial summation of individual chia – molecules with a chiral center do not have unit ralities: Σrn(ln) . This sum “volume- no symmetry elements, except for the element letsya” spiral (helical) chirality identity C1 (examples - amino acids (ala- macromolecules, which have their own sign (+R h, −Lh) and nin in Scheme 3), sugars-carbohydrates ); absolute value, b – planar-chiral molecules of symmetry Nr (l) ∑ l (r) ⊂ R (L). h h C1 and/or C2 (the selected structural element is the plane n n (1) bone, examples are trans-cycloethylenes in Table 2); The fact that regular ortho-condensation of Akiva - axially chiral molecules from symmetrical benzene rings also leads to spirium Cn (have the shape of propellers or swastikas, ral helicenes (Table 2), only confirmed examples - twistane , biphenyl, triphenylmethane in gives a general rule: and circular association of Table 2, etc.); achiral monomers of a suitable structure, and d – helical-chiral molecules of symmetry linear polycondensation of chiral (only r C2 (characteristic shape is a helix, examples are hexa- or only l) units automatically lead to spigelicene in Table 2, proteins, DNA) ; ral form of the polymer. It can be assumed that in ygTspzyZau g.i. In 49 rows of such macromolecules, a certain symmetry of chiralities is realized, which corresponds to the configuration Sn, configurationally unambiguous (singlet), hierarchy of levels of stereostructure. For example, per- since their internal structure is P-even. Objective, secondary, tertiary and quaternary levels of the structure of hemoglobin, which do not have internal P-parity of structure, are obviously character- (not having symmetry elements Sn), are always inter- terized by the sequences “nested-figurationally two-valued (doublet, left + chiralities” type (1) sum of individual chiralities). In order to obtain from a P-even object its co-amino acids into the helical chirality of polypeppia, one Pσ(i)-operation is sufficient, but in order to copy these two into the “globular” chirality of a P-odd object, two tertiary levels are needed, finally, these three - into “super-sequential P-operations: lecular” chirality of a quartet (tetrahedron) of united globules. From here, by the way, it follows that the stereochemistry of polymers and their associates should take into account in addition to those listed. Note, however, that not everyone around us also has the “globular” - e and “supramolecular” us in living and inanimate nature P-odd” – types of chirality. It is the following objects that you can easily find the left or right primary (structural) upper configurations of twin partners, for example, the selected tree levels of organization of macromolecules play in the forest or a stone from a pile of rubble. Let us further note that the decisive role in their functioning in the body is that chiral symmetry is absolutely (100%) important. Thus, biochemical reactions with the participation of P-odd molecules of organic enzymes are effectively carried out only in compounds that are part of all living organ- cases when previously realized com- isms on our planet. If these are amino acids, breeding, that is, “recognition,” selection of those molecules is only left (l); if sugars are carbohydrates, then only a cool of reagents and substrates, features config-right (r); if these are biopolymers, then they are spirals of which (“figures” of which) are ideally but twisted only to the right (proteins, DNA). This is consistent with the contours and shapes of a corresponding pattern called chiral asymmetric cavities in enzyme globules. The everyday anarias of the biosphere were also the first to draw attention to the log of such complementation by D. Koshland, who proposed L. Pasteur. lived to consider the correspondence of the key and the lock. ganTskDnmkD dakDguzD DlaeeTsnka 1. General organic chemistry: Trans. from English M.: Chemistry, Let us summarize the above. This article is pre- 1981–1986. T. 1–12. the goal should be to show that in the boundless on the per- 2. Zhdanov Yu.A. Carbon and life. Rostov n/d: Publishing house view on the material of organic chemistry easier than the Russian State University, 1968. 131 p. to navigate if you master the principles of graph- 3. Tatt U. Graph theory. M.: Mir, 1988. images of the most general characteristics of the structure of molecules, as well as principles for assessing them 4. Sokolov V.I. Introduction to theoretical stereo-configurations – shapes in three-dimensional spatial chemistry. M.: Nauka, 1982; Chemistry progress. 1973. T. 42. ve - based on the ideas of symmetry and asymmetry. Po- pp. 1037–1051. the latter include ideas about the main 5. Nogradi M. Stereochemistry. M.: Mir, 1984. symmetry speakers: planes, axes and mirror- 6. Hargittai I., Hargittai M. Symmetry through the eyes of rotary axes used in identifying those chemists. M.: Mir, 1989. internal features of the structure of molecules, which 7. Filippovich I.V., Sorokina N.I. // Let's make progress. These determine their appearance, shape and ultimately biology. 1983. T. 95. pp. 163–178. their most important properties. When “sorting” molecules into symmetric and * * * asymmetric, a special role belongs to the mirror reflection operator – coordinate inversion Lev Petrovich Olekhnovich, Doctor of Chemical Sciences R. Operator Pσ coordinates of all parts (atouk, professor, head of department chemistry of natural and mov) object located to the left of the selected high-molecular compounds of the Rostov go-plane, puts it in unambiguous correspondence of the cooperative university, head. laboratory of the dinata of the inverted (reflected) object of the internal dynamics of molecules of the Faculty of Chemistry and the Research Institute of Phy- to the right of this plane. The operator Pi carries out the sic and organic chemistry of the Russian State University, the corresponding term is a similar coordinate inversion of the relative-pondent of the Russian Academy of Natural Sciences. but a point chosen outside the object (it’s easy to figure out Area of ​​scientific interests: organic synthesis, and check that under the action of the Pi operator, also the kinetics and mechanisms of molecular rearrangements, a mirror double of the object is obtained, but verified, stereochemistry and stereodynamics. Co-author 180°). Objects (molecules), two monographs and author of more than 370 scientific articles. 50 likes Zldav yEkDbyZDnTsg'zkhv LmkzDg, No. 2, 1997

Author: Chemical Encyclopedia I.L. Knunyants

GRAPH THEORY in chemistry, the branch of finite mathematics that studies discrete structures is called graphs; used to solve various theoretical problems. and applied problems.

Some basic concepts. A graph is a collection of points (vertices) and a collection of pairs of these points (not necessarily all), connected by lines (Fig. 1,k). If the lines in the graph are oriented (that is, the arrows indicate the direction of connection of the vertices), they are called arcs, or branches; if unoriented, - edges. Resp. a graph containing only arcs is called a directed or digraph; only edge-unoriented; arcs and ribs mixed. A graph having multiple edges is called a multigraph; a graph containing only edges belonging to two of its disjoint subsets (parts) - bipartite; arcs (edges) and (or) vertices, to-Crimea correspond to certain weights or numerical values ​​of k.-l. parameters - weighted. A path in a graph is an alternating sequence of vertices and arcs in which none of the vertices is repeated (for example, a, b in Fig. 1,a); contour - a closed path in which the first and last vertices coincide (for example, f, h); a loop-arc (edge) that begins and ends at the same vertex. A graph path is a sequence of edges in which none of the vertices are repeated (for example, c, d, e); cycle is a closed chain in which its initial and final vertices coincide. A graph is called connected if any pair of its vertices is connected by a chain or path; otherwise, the graph is said to be disconnected.

A tree-connected undirected graph that does not contain cycles or contours (Fig. 1, b). The spanning subgraph of a graph is a subset of it that contains all the vertices and only certain edges. The spanning tree of a graph is its spanning subgraph, which is a tree. Graphs are called isomorphic if there is a one-to-one correspondence between the sets of their vertices and edges (arcs).

To solve problems of GRAPHS THEORY and its applications, graphs are represented using matrices (adjacency, incidence, two-row, etc.), as well as special ones. numerical characteristics. For example, in the adjacency matrix (Fig. 1c), the rows and columns correspond to the numbers of the vertices of the graph, and its elements take the values ​​0 and 1 (respectively, the absence and presence of an arc between a given pair of vertices); in the incidence matrix (Fig. 1d), the rows correspond to the numbers of the vertices, the columns correspond to the numbers of the arcs, and the elements take the values ​​0, + 1 and - 1 (respectively, the absence or presence of an arc entering and leaving the vertex). the most common numerical characteristics: number of vertices (m), number of arcs or edges (n), cyclomatic. number, or rank of the graph (n - m + k, where k is the number of connected subgraphs in a disconnected graph; for example, for the graph in Fig. 1,b, the rank will be: 10-6+ 1 =5).

The application of GRAPH THEORY is based on the construction and analysis of various classes of chemical and chemical-technological graphs, which are also called topology, models, i.e. models that take into account only the nature of the connections between the vertices. The arcs (edges) and vertices of these graphs display chemical and chemical-technol. concepts, phenomena, processes or objects and, accordingly, qualities. and quantitative relationships or specific relationships between them.

Rice. 1. Illustration of some basic concepts: a-mixed graph; b-tree (solid arcs a, h, d, f, h) and some subgraph (dotted arcs c, c, d, k, I) of the digraph; c, r-matrices, respectively, of the adjacency and incidence of the digraph.

Theoretical problems. Chemical graphs make it possible to predict chemical transformations, explain the essence and systematize some basic concepts of chemistry: structure, configuration, conformations, quantum mechanical and statistical-mechanical interactions of molecules, isomerism, etc. Chemical graphs include molecular, bipartite and signal graphs of kinetic reaction equations.

Molecular graphs, used in stereochemistry and structural topology, chemistry of clusters, polymers, etc., are undirected graphs that display the structure of molecules (Fig. 2). The vertices and edges of these graphs correspond, respectively, to atoms and chemical bonds between them.

Rice. 2. Molecular graphs and trees: a, b - multigraphs of ethylene and formaldehyde, respectively; they say pentane isomers (trees 4, 5 are isomorphic to tree 2).

In stereochemistry, organic substances are most often used. trees - core trees pier. graphs that contain only all vertices corresponding to atoms C (Fig. 2, a and b). Compiling sets of piers. trees and the establishment of their isomorphism make it possible to determine that they say. structure and find the total number of isomers of alkanes, alkenes and alkynes (Fig. 2, c).

Mol. graphs make it possible to reduce tasks related to coding, nomenclature and structural features (branching, cyclicity, etc.) of molecules of various compounds to the analysis and comparison of pure mathematics. signs and properties they say. graphs and their trees, as well as their corresponding matrices. To identify quantitative correlations between the structure of molecules and the physical-chemical (including pharmacological) properties of a compound, more than 20 so-called topological studies have been developed. indices of molecules (Wiener, Balaban, Hosoya, Plat, Randic, etc.), which are determined using matrices and numerical characteristics of the mol. trees. For example, the Wiener index W = (m 3 + m)/6, where m is the number of vertices corresponding to C atoms, correlates with the mol. volumes and refractions, enthalpies of formation, viscosity, surface tension, chromatographic. connection constants, octane numbers of hydrocarbons and even physiol. activity of lek. drugs.

Important parameters say. graphs used to determine the tautomeric forms of a given substance and their reactivity, as well as for the classification of amino acids, nucleic acids, carbohydrates and other complex natural compounds, are late and complete (H) information. containers. The parameter is calculated using the Shannon information entropy formula: , where p t is the probability of vertex membership m of the graph to the i-th species, or equivalence class, k; i =, Parameter (see also Entropy). Studying the pier structures such as inorganic clusters or Möbius strips comes down to establishing the isomorphism of the corresponding molecules. graphs by placing them (embedding) into complex polyhedra (for example, polyhedra in the case of clusters) or special ones. multidimensional surfaces (for example, Riemann surfaces). Analysis mol. graphs of polymers, the vertices of which correspond to monomer units, and the edges correspond to chemical bonds between them, make it possible to explain, for example, the effects of excluded volume leading to qualities. changes in the predicted properties of polymers.

Rice. 3. Reaction graphs: a-bipartite; b-signal kinetics equations; r 1, g 2 reactions; a 1 -a 6 -reagents; k-rate constants p-tsny; s-complexity of the Laplace transform variable.

Using GRAPHS THEORY and the principles of artificial intelligence, software for information retrieval systems in chemistry, as well as automated ones, has been developed. identification systems mol. structures and rational planning organic. synthesis. For the practical implementation on a computer of operations for selecting rational paths of chemical transformations based on retrosynthetics. (see Retrosynthetic analysis) and syntonic principles use multi-level branched graphs for searching for solution options, the vertices of which correspond to the pier. graphs of reactants and products, and arcs depict transformations of substances.

Rice. 4. Single-circuit chemical-technological system and corresponding graphs: a-structural diagram; b, c-material flow graphs, respectively, for total mass flow rates and the flow rate of component A; r - thermal flow graph; d-fragment of the system of equations (f 1 - f 6) of the material balance, obtained from the analysis of the graphs in Fig. 4, b and c; e-bipartite information digraph; g-information graph, I-mixer; II-reactor; III-distillation column; IV-refrigerator; I 1 -I 8 -technol. streams; q-mass flow; H is the enthalpy of the flow; i. s and i*, s* are respectively real and fictitious sources and sinks of material and heat flows; c-concentration of the reagent; V is the volume of the reactor.

Matrix representations say. graphs of various compounds are equivalent (after transforming the corresponding matrix elements) to the matrix methods of quantum chemistry. Therefore, GRAPH THEORY is used when performing complex quantum chemical calculations: to determine the number, properties and energies of mol. orbitals, for example in complex compounds, predicting the reactivity of conjugated alternant and non-alternant polyenes, identifying aromatic and anti-aromatic properties of substances, etc.

To study disturbances in systems consisting of a large number of particles in chemical physics, so-called Feynman diagrams are used - graphs, the vertices of which correspond to the elementary interactions of physical particles, the edges of which correspond to their paths after collisions. In particular, these graphs make it possible to study the mechanisms of oscillatory reactions and determine the stability of reaction systems.

To select rational paths for the transformation of reagent molecules for a given set of known interactions, bipartite reaction graphs are used (vertices correspond to molecules and these reactions, arcs correspond to the interaction of molecules in a reaction; Fig. 3,a). Such graphs make it possible to develop interactive algorithms for selecting optimal solutions. paths of chemical transformations that require naim. number of intermediate reactions, min. the number of reagents from the list of acceptable ones or the highest yield of products is achieved.

Signal graphs of reaction kinetics equations display systems of kinetic equations presented in algebraic operator form (Fig. 3b). The vertices of the graphs correspond to the so-called information. variables, or signals, in the form of concentrations of reagents, arc-signal relationships, and the weights of the arcs are determined by kinetic constants. Such graphs are used in studying the mechanisms and kinetics of complex catalytic reactions, complex phase equilibria in the formation of complex compounds, as well as for calculating the parameters of the additive properties of solutions.

Applied problems. To solve multidimensional problems of analysis and optimization of chemical technology. systems (XTS) use the following chemical technology. graphs (Fig. 4): flow, information flow, signal and reliability graphs. Flow graphs, which are weighted digraphs, include parametric, material in terms of the total mass flow rates of physical flows and the mass flow rates of some chemical components or elements, as well as thermal graphs. The listed graphs correspond to the physical and chemical transformations of substances and energy in a given chemical system.

Parametric flow graphs display the transformation of parameters (mass flow rates, etc.) of physical flows by CTS elements; the vertices of the graphs correspond to mat. models of devices, as well as sources and sinks of the specified flows, and arcs - the flows themselves, and the weights of the arcs are equal to the number of parameters of the corresponding flow. Parametric graphs are used to develop algorithms for analyzing technology. modes of multi-circuit CTS. Such algorithms establish the sequence of calculation of systems of mathematical equations. models of individual devices system to determine the parameters of its output streams with known values ​​of variable input streams.

Material flow graphs display changes in the consumption of substances in chemical substances. The vertices of the graphs correspond to devices in which the total mass flow rates of physical flows and the mass flow rates of some chemical components or elements are transformed, as well as sources and sinks of substances of flows or these components; accordingly, the arcs of the graphs correspond to physical flows or physical and fictitious (chemical transformations of matter in apparatuses) sources and sinks of s.-l. components, and the weights of the arcs are equal to the mass flow rates of both types. Thermal flow graphs display heat balances in CTS; the vertices of the graphs correspond to devices in which the heat consumption of physical flows changes, and, in addition, to the sources and sinks of thermal energy of the system; arcs correspond to physical and fictitious (physical-chemical energy transformations in devices) heat flows, and the weights of the arcs are equal to the enthalpies of the flows. Material and thermal graphs are used to create automation programs. development of algorithms for solving systems of equations of material and heat balances of complex chemical systems.

Information-stock graphs display logical information. structure of systems of mathematical equations. XTS models; are used to compile optimal algorithms for calculating these systems. Bipartite information graph (Fig. 4, e) is an undirected or oriented graph, the vertices of which correspond, respectively, to the equations f l - f 6 and the variables q 1 - V, and the branches reflect their relationship. Information graph (Fig. 4, g) - a digraph depicting the order of solving equations; the vertices of the graph correspond to these equations, sources and receivers of XTS information, and branches of information. variables.

Signal graphs correspond to linear systems of mathematical equations. models of chemical technology. processes and systems. The vertices of the graphs correspond to signals (for example, temperature), branch connections between them. Such graphs are used to analyze static data. and dynamic multi-parameter modes processes and chemical resistance, as well as indicators of a number of their most important properties (stability, sensitivity, controllability).

Reliability graphs are used to calculate various indicators of the reliability of chemical systems. Among the numerous groups of these graphs (for example, parametric, logical-functional), the so-called fault trees are especially important. Each such tree is a weighted digraph that displays the interrelationship of many simple failures of individual processes and CTS devices, which lead to many secondary failures and the resulting failure of the system as a whole (see also Reliability).

To create automated program complexes. synthesis optimal. highly reliable production (including resource-saving) along with the principles of the arts. intelligence, they use oriented semantic, or semantic, graphs of CTS solution options. These graphs, which in a particular case are trees, depict procedures for generating a set of rational alternative CTS schemes (for example, 14 possible when separating a five-component mixture of target products by rectification) and procedures for the ordered selection among them of a scheme that is optimal according to some criterion of system efficiency (see. Optimization). GRAPH THEORY is also used to develop algorithms for optimizing time schedules for the operation of equipment in multi-product flexible production, optimization algorithms. placement of equipment and routing of pipeline systems, optimal algorithms. management of chemical technology processes and production, during network planning of their work, etc.

Lit.. Zykov A. A., Theory of finite graphs, [in. 1], Novosibirsk, 1969; Yatsimirsky K. B., Application of graph theory in chemistry, Kyiv, 1973; Kafarov V.V., Perov V.L., Meshalkin V.P., Principles of mathematical modeling of chemical technological systems, M., 1974; Christofides N., Graph theory. Algorithmic approach, trans. from English, M., 1978; Kafarov V.V., Perov V.L., Meshalkin V.P., Mathematical foundations of computer-aided design of chemical production, M., 1979; Chemical applications of topology and graph theory, ed. R. King, trans. from English, M., 1987; Chemical Applications of Graph Theory, Balaban A.T. (Ed.), N.Y.-L., 1976. V.V. Kafarov, V.P. Meshalkin.

Chemical encyclopedia. Volume 1 >>

Molecular graphs and types of molecular structures

from "Application of Graph Theory in Chemistry"

Chemistry is one of those areas of science that are difficult to formalize. Therefore, the informal use of mathematical methods in chemical research is mainly associated with those areas in which it is possible to construct meaningful mathematical models of chemical phenomena.
Another way of graphs' introduction into theoretical chemistry is associated with quantum chemical methods for calculating the electronic structure of molecules.
The main section discusses methods for analyzing molecular structures in terms of graphs, which are then used to construct topological indices and based on structure-property correlations, and also outlines the elements of molecular design.
As you know, a substance can be in a solid, liquid or gaseous state. The stability of each of these phases is determined by the condition of minimum free energy and depends on temperature and pressure. Every substance consists of atoms or ions, which under certain conditions can form stable subsystems. The elemental composition and relative arrangement of atoms (short-range order) in such a subsystem are preserved for quite a long time, although its shape and size may change. As the temperature decreases or the pressure increases, the mobility of these subsystems decreases, but the motion of the nuclei (zero-point oscillations) does not stop at absolute zero temperature. Such stable coherent formations, consisting of a small number of molecules, can exist in a liquid, in a bunk or in a solid and are called molecular systems.
The MG in a perspective projection reflects the main features of the geometry of the molecule and gives a visual representation of its structure. Let us discuss some types of molecular structures in MG terms. Let us consider molecules for which it is convenient to use planar graph implementations to describe their structure. The simplest systems of this type correspond to tree-like MGs.
In the case of molecules of the ethylene series, MGs contain only vertices of degree three (carbon) and degree one (hydrogen). The general formula for such compounds is CH,g+2. CH+2 molecules in the ground state are usually flat. Each carbon atom is characterized by a trigonal environment. In this case, the existence of cis- and trans-type isomers is possible. In the case of tg 1, the structure of the isomers can be quite complex.
Let us now consider some molecular systems containing cyclic fragments. As in the case of paraffin hydrocarbons, there are molecules whose structures can be described in terms of graphs having only vertices of degree four and one. The simplest example of such a system is cyclohexane (see Fig. 1.3,6). Typically, the structure of cyclohexane is described as MG in a perspective image, while omitting the vertices of degree one. For cyclohexape, the existence of three rotary isomers is possible (Fig. 1.7).

Often chemical bonds are formed by electrons located in different atomic orbitals (for example,s - And R– orbitals). Despite this, the bonds turn out to be equivalent and located symmetrically, which is ensured by the hybridization of atomic orbitals.

Orbital hybridization is a change in the shape of some orbitals during the formation of a covalent bond to achieve more efficient orbital overlap.

As a result of hybridization, new hybrid orbitals, which are oriented in space in such a way that after their overlap with the orbitals of other atoms, the resulting electron pairs are as far apart as possible. This minimizes the repulsion energy between electrons in the molecule.

Hybridization is not a real process. This concept was introduced to describe the geometric structure of a molecule. The shape of particles resulting from the formation of covalent bonds involving hybrid atomic orbitals depends on the number and type of these orbitals. In this case, σ-bonds create a rigid “skeleton” of the particle:

Orbitals involved in hybridization	Hybridization type	Spatial shape of the molecule	Examples
s, p	sp – hybridization	Linear	BeCl2 CO2 C2H2 ZnCl2 BeH 2 Twosp - orbitals can form two σ - bonds ( BeH 2 , ZnCl 2 ). Two morep- connections can be formed if two p - orbitals not involved in hybridization contain electrons (acetylene C 2 H 2 ).
s, p, p	sp 2 – hybridization	Triangular (flat trigonal)	BH 3 BF 3 C2H4 AlCl3 If a bond is formed by overlapping orbitals along a line connecting the atomic nuclei, it called σ - bond. If the orbitals overlap outside the line connecting the nuclei, then a π bond is formed. Three sp 2 - orbitals can form three σ - bonds ( B.F. 3 , AlCl 3 ). Another bond (π - bond) can be formed if p- the orbital not participating in hybridization contains an electron (ethylene C 2 H 4 ).
s, p, p, p	sp 3 – hybridization	Tetrahedral	C H 4 NH4+ PO 4 3- BF 4 -

In practice, the geometric structure of the molecule is first established experimentally, after which the type and shape of the atomic orbitals involved in its formation are described. For example, the spatial structure of ammonia and water molecules is close to tetrahedral, but the angle between bonds in a water molecule is 104.5˚, and in a water molecule NH 3 – 107.3˚.

How can this be explained?

Ammonia NH 3

The ammonia molecule has the shape trigonal pyramid with a nitrogen atom at the apex . The nitrogen atom is in sp 3 - hybrid state; Of the four hybrid orbitals of nitrogen, three are involved in the formation of single N–H bonds, and the fourth sp 3 - the hybrid orbital is occupied by a lone electron pair, it can form a donor-acceptor bond with a hydrogen ion, forming an ammonium ion NH 4 +, and also causes a deviation from the tetrahedral angle in the structure

Water H2O

A water molecule has angular structure: is an isosceles triangle with an apex angle of 104.5°. The oxygen atom is in sp 3 - hybrid state; Of the four hybrid orbitals of oxygen, two are involved in the formation of single O–H bonds, and the other two sp 3 - hybrid orbitals are occupied by lone electron pairs, their action causes the angle to decrease from 109.28˚ to 104.5°.