Gillespie method examples. Predicting the Geometric Shape of Molecules

A simple and convenient method for predicting the geometry of molecules is the model of repulsion of localized electron pairs or the Gillespie method, which is based on the BC method. The initial data for this method are the number of other atoms associated with the central atom, the valence capabilities of all associated atoms, and the number of electrons on the outer layer of the central atom. The main provisions of the Gillespie method are as follows.

1. Each electron pair, both forming a bond and unshared, occupies a certain place in space (localized electron pair). The cloud of double and triple bonds is considered as a single one. Of course, electron pairs (electron clouds) repel.

2. Depending on the number of localized electron pairs (electron clouds), they are located in space as follows:

2 – linear configuration,

3 – regular triangle,

4 – tetrahedron,

5 – regular trigonal bipyramid,

The procedure for working according to the Gillespie method is approximately as follows. Let us denote the central atom by the letter A, any other atom connected to it by the letter B, and the lone electron pair by the letter E. Let the total number of chemical bond partners of the central atom be n, and the number of lone electron pairs it has is m. Then the molecule in question in a peculiar folded form relative to the central atom will be written AB n E m . Of course, the most multivalent atom is chosen as the central atom. Complex, bulky molecules are considered in parts within the Gillespie method. As a result of summing n and m using the method proposed above, the initial model of the geometry of the molecule or ion is determined, and then, after a kind of discarding of lone electron pairs, the actual geometry of the particle is determined.

Possible additions to the Gillespie method:

a) the double bond cloud occupies a larger space in space than the single bond cloud;

b) the triple bond cloud occupies a larger space in space than the double bond cloud and, even more so, than the single bond cloud;

c) in the case of a polar covalent bond, the electron cloud is concentrated to a greater extent near the more electronegative atom;

d) the cloud of a lone electron pair occupies a larger space in space than the cloud of a single bond.

These additions allow refinements to the geometry of molecules and deviations from the bond angles predicted by the main procedure.

Let us demonstrate the capabilities of Gillespie's method using the example of several molecules. Let's start with the water and ammonia molecules discussed above.

H 2 O; AB 2 E 2; ; the initial model is a tetrahedron; the molecule is angular, the H–O–H angle is 109 o 28".

NH3; AB 3 E 1; ; the initial model is a tetrahedron; molecule is a trigonal pyramid, angle H–N–H 109 o 28". Note that the tetrahedron, which is a regular trigonal pyramid, is a more senior figure (central atom and four chemical bond partners) than the trigonal pyramid proper (central atom and three chemical bonding partner).

A few more examples.

SnCl2; AB 2 E 1; ; the original model is a regular triangle; the molecule is a corner molecule, the Cl–Sn–Cl angle is 120 o or less due to the fact that the free electron pair occupies a larger space in space than the bonding pair.

CO 2; AB 2 E 0; ; linear molecule.

Anions of acids are easiest to consider in the same way as the molecules of the acids themselves: H 2 SO 4 and SO 4 2– AB 4 E 0; H 3 PO 4 and PO 4 3– AB 4 E 0 ; H 2 CO 3 and CO 3 2 – AB 3 E 0, etc.

In some cases, several models of particle structure are possible within the Gillespie method, and the energetically more favorable one is selected. For example, XeF 2; AB 2 E 3; the initial model is a trigonal pyramid, the following options are possible:

The first option is energetically more favorable: electron pairs are maximally separated, fluorine atoms having identical effective charges are also maximally removed. Conclusion: the XeF 2 molecule is straight.

Concepts about the direction of bonds and the theory of hybridization of electronic orbitals make it possible to explain the geometric shape of molecules of substances with covalent bonds, but cannot predict it. Theoretical calculation of the geometric configuration of a particle using quantum mechanical methods is a very complex problem that does not always have a unique solution. However, there is a fairly simple technique that allows one to qualitatively estimate the geometry of molecules with fairly high reliability. This technique was developed by R. Gillespie and was called: the method of repulsion of electron pairs of the valence shell. The method relates the shape of a particle to the repulsive forces acting between electron pairs formed during the formation of the corresponding molecule. Gillespie's method is especially effective for molecules formed by s- and p-elements.

The concept of repulsion of electron pairs of the valence shell can be reduced to the following basic principles:

1. The geometric shape of the molecule is determined by the number of electron pairs in the valence shell (VES), which does not include electron pairs forming p-bonds.

2. The electron pairs of the valence shell are oriented so that the repulsion between them is minimal.

3. Lone electron pairs occupy a larger volume of perinuclear space than bonding ones. A consequence of the nonequivalence of lone and bonding electron pairs is a distortion of bond angles.

To determine the EPVO number, you need to add the number of valence electrons of a given atom with the number of electrons provided by the attached atoms, and then subtract the number of electrons forming p-bonds from the resulting sum and divide the result by two. Thus, for a CO 2 molecule having two s- and two p-bonds, each oxygen atom provides two electrons to form bonds with a carbon atom, and the carbon atom provides two electrons to form bonds with each oxygen atom. Accordingly, the number of EPVO for a carbon atom is 2:

The number of bonding EPVOs is equal to the number of s-bonds formed by the central atom (N s); the difference is equal to the number of lone electron pairs: N np = N EPVO - N s.

Ideal geometric shapes corresponding to different values ​​of the number of EPVOs and lone electron pairs are given in Table. 6, the atom for which the type of hybridization is determined is indicated in parentheses.

If the valence shell of an atom in a molecule includes two electron pairs, two point charges of the same name, once on the surface of the sphere, will be located at the ends of the diameter of the large circle. Accordingly, two EPVOs should occupy orbitals that provide a bond angle of 180°, which, according to the valence bond method, corresponds to sp-hybridization of atomic orbitals. The maximum distance and minimum repulsion of the three EPVOs will correspond to the orientation of the orbitals from the center to the vertices of an equilateral triangle (sp 2 hybridization). Four EPVOs correspond to a tetrahedral configuration (sp 3 hybridization). In the case of five EPVOs, the most favorable distribution of electron pairs is in the directions towards the vertices of the trigonal bipyramid (sp 3 d-hybridization); six EPVOs correspond to an octahedral configuration (sp 3 d 2 -hybridization).

In the presence of lone electron pairs, the geometry of the molecule changes depending on their number. As can be seen from table. 6, in the case of three EPVO molecules can be angular (N np = 1) and linear (N np = 2). The presence of four electron pairs in the valence shell allows the formation of trigonal-pyramidal molecules at N np = 1, angular molecules at N np = 2, and linear (N np = 3) molecules.

If the number of EPVOs is five and all pairs are bonding, the molecule has the shape of a trigonal bipyramid. If there are lone electron pairs, it is necessary to know which orbitals, axial or equatorial, will be occupied by them. Calculation shows that the equatorial position is more advantageous. Indeed, lone pairs occupying an equatorial position have only two nearest neighbors at an angle of 90°, whereas in an axial position there would be three such neighbors, which would lead to stronger repulsion. As a result, a molecule with one lone pair has the shape of a bisphenoid (distorted tetrahedron), with two - a T-shape, and three lone pairs correspond to linear molecules.

Table 6.

Geometry of molecules of s- and p-elements

N EPVO	Hybridization type	Number of lone pairs
	sp	linear BeF 2 (Be)	linear AlF (Al)
	sp 2	triangle BF 3 (B)	angular SnCl 2 (Sn)	linear NH(N)
	sp 3	tetrahedron CF 4 (C)	trigonal pyramid NH 3 (N)	angular H 2 O (O)	linear IF(I)
	sp 3 d	trigonal bipyramid PF 5 (P)	bisphenoid SF 4 (S)	T-form IF 3 (I)	Linear XeF 2 (Xe)
	sp 3 d 2	octahedron SF 6 (S)	tetragonal pyramid BrI 5 (Br)	square XeF 4 (Xe)	T-shape - (Xe)

In the case of six EPVOs, the lone pairs occupy a trans position relative to each other in the octahedron. Because of this, for six EPVOs the following molecular shapes are realized: octahedron (N np = 0), tetragonal pyramid (N np = 1), square (N np = 2), etc.

To determine the geometric shape of a molecule using Gillespie's method, it is necessary to know the electronic configurations of atoms, the order of connection of these atoms in the molecule, the number of s- and p-bonds in the resulting particle, and take into account the effects leading to distortion of bond angles. Let's consider several examples.

Example 1. For a COCl 2 molecule, in which the oxygen atom forms a double bond with carbon, and the chlorine atoms form single bonds (Fig. 20a), the numbers of EPVOs and lone pairs are:

N EPVO (C) = ; N np (C) = 3 - 3 = 0

Therefore, the COCl 2 molecule must have the shape of an equilateral triangle with bond angles equal to 120°. In reality, this molecule has the shape of an isosceles triangle (d C = O = 117 pm, d C - Cl = 175 pm, Ð ClCO = 124 °, Ð C lCCl = 111 °). Since multiple bonds occupy more volume at the central atom, which leads to compression of bond angles.

Example 2. For the CHCl 3 molecule, the number of EPVO and bonding pairs is the same (N EPVO = 4, N np = 0), however, the chloroform molecule does not have the shape of a regular tetrahedron (d C - Cl = 176 pm, d C - H = 110 pm, ÐClCCl = 111 .3°, ÐHCCl = 107.5°). This is due to the inequality of the attached atoms: the hydrogen atom and chlorine atoms have different radii and form bonds with the carbon atom of different lengths.

Example 3. Let us determine the shape of the xenon oxofluoride molecule XeO 2 F 2 , in which the central xenon atom forms four s- and two p-bonds (Fig. 20b).

The numbers of EPVO and lone pairs of the xenon valence shell are:

N EPVO (Xe) = ; N np (Xe) = 5 - 4 = 1

In accordance with table. 10, the resulting molecule has the form of a bisphenoid, in which the oxygen atoms form bonds due to equatorial orbitals, which provide these atoms with the maximum distance from the orbital occupied by a lone pair, and the fluorine atoms, which have three lone pairs, are in the trans position. It can be expected that the length of the Xe=O double bonds will be less than the length of the Xe-F single bonds, and the angles OXeO and FXeF due to the presence of a lone pair in the equatorial orbital will be less than 120° and 180°, respectively. These assumptions are in good agreement with the results of experimental determination of the shape of the particle in question: the XeO 2 F 2 molecule actually has the shape of a slightly distorted bisphenoid (d Xe = O = 171 pm, d Xe - F = 190 pm, ÐOXeO = 105.7 °, ÐFXeF = 174 ,7°).

Example 4. Let us determine the geometry of gaseous sodium metaborate (Fig. 20c).

When determining the geometry of complex molecules containing chains of four or more atoms, it is rational to break the molecule into fragments and determine the geometry of each of them separately. For sodium metaborate, the shape of the O=B-O and B-O-Na fragments should be determined separately. For a boron atom:

N EPVO (V) = N np (B) = 2 - 2 = 0;

those. the O=B-O fragment has a linear shape.

N EPVO (O) = N np (O) = 4 - 2 = 2

Thus, the B-O-Na fragment has an angular shape, with a bond angle close to 109.5°. The NaBO2 molecule is indeed a combination of linear and angular fragments with bond angles of 180° and 109° (Fig. 20c).

Rice. 20. Structural formulas of molecules COCl 2 (a), XeOF 2 (b), NaBO 2 (c).

Example 5. Let's determine the geometry of the IO 2 F 2 - ion.

If the particle is an ion, then when calculating the EPVO number, the charge of the ion should be subtracted from the number of valence electrons. For the iodine atom, which is central and forms four s- and two p-bonds:

N EPVO (I) = N np (I) = 5 - 4 = 1

The ion in question must be in the form of a bisphenoid, which has been confirmed experimentally.

A simple and convenient method for predicting the geometry of molecules is the model of repulsion of localized electron pairs or the R. D. Gillespie method, which is based on the VS method. The initial data for this method are: the number of other atoms associated with the central atom; valence possibilities of all bonded atoms; the number of electrons in the outer layer of the central atom.

The main provisions of the Gillespie method are as follows.

Each electron pair, whether forming a bond or unshared, occupies a specific location in space (localized electron pair). Electron pairs, due to repulsion, are arranged in such a way as to be as far apart from each other as possible, with lone electron pairs occupying a larger volume than shared ones. Double and triple bonds are treated as single bonds, although they occupy a larger volume.

The procedure for working according to the Gillespie method is approximately as follows. Let us denote the atom of the structure as A, any other atom associated with it as B, etc.; lone electron pair - E, the total number of partners of the central atom in a chemical bond - P, and the number of lone electron pairs is T. Then the molecule considered in the simplest case relative to the central atom will have the form AB w E ;// . Typically the most polyvalent atom is chosen as the central atom. Complex, bulky molecules are considered in parts within the Gillespie method. As a result of the summation P And T According to the method proposed above, the initial model of the geometry of the molecule or ion is determined, and then the actual geometry of the particle.

The spatial configuration of molecules depending on the number of electron pairs is given in Table. 3.1.

Table 3.1

Configuration of molecules using Gillespie's method

End of table. 3.1

Number of electron pairs	Location electronic	molecules	Geometry molecules
	Tetrahedral		Tetrahedron
			Trigonal
			pyramid
		aw 2 e 2
	Trigonal-		Trigonal
	bipyramidal-		bipyramid
		aw 4 e,	Disphenoid
			T-shaped
			Linear
	Octahedral
			Square
			pyramid
	Pentagonal-	aw 7	Pentagonal
	bipirami-		bipyramid
		av 6 e,	One-cap
			octahedron

Let us demonstrate the capabilities of Gillespie's method using the example of several molecules.

Ammonia (NH 3): central atom is nitrogen, t =(5 - 3*1)/2 = = 1; hence the type of molecule is AB 3 E t, the initial model is a tetrahedron, the molecule is a trigonal pyramid, the angle between the H - N - H bonds is less than tetrahedral (109°28") due to the lone pair of electrons occupying a larger volume and is about 107 ,3°.

Water (H 2 0): the central atom is oxygen, t = (6 --2 - 1) / 2 = 2; hence the type of molecule follows - AB 9 E 9, the initial model of which is a tetrahedron, the molecule is angular, the bond angle between the chemical bonds H - O - H is even smaller due to the presence of two lone pairs of electrons on the oxygen atom and is equal to 104.5°.

Tin chloride (SnCl 9): central atom is tin, T= = (4-2 -1) / 2 = 1; type of molecule - AB 2 E G the original model is a regular triangle, the molecule is angular, the bond angle between the chemical bonds Cl - Sn - Cl is 120°.

Carbon monoxide (1U) (C0 9): the central atom is carbon, t =(4 - 2 2) / 2 = 0; the type of molecule is AB 2, the molecule is linear, the angle between the bonds O = C = O is 180°.

It should be noted that Gillespie's method has significant limitations. Its main disadvantages:

• not applicable to most compounds d- and 5-elements;
• inapplicability to compounds with significant ionicity of the chemical bond. Thus, the Li 2 0 molecule is linear, but, as belonging to the AB 2 E 2 type, it must be angular;
• impossibility of predicting the “inertness” (lack of directionality, stereoactivity) of a lone electron pair. Thus, the Pblg^SbBr^" and TeBr 6 2_ ions belong to the AB 6 Ej type, but in reality turn out to be regular octahedral structures. This distribution of the electron pair is characteristic of ions and molecules of complex compounds formed by a complexing cation with a large radius and ligands with a relatively low electronegativity.

GILLESPIE THEORY

a system of postulates and rules for explaining and predicting geoms. molecular configurations based on the Pauli principle and the model of repulsion of electron pairs of valence orbitals. According to G. t., the spatial orientation of chemistry. The bonds of a polyvalent atom in a molecule depend primarily on the total number of electrons in its valence shell. Electronic clouds of electron pairs connecting atoms and electrons in non-bonding orbitals (i.e., lone pairs of the valence shell of atoms) are roughly represented as hard spheres, respectively. smaller and larger diameters. The atomic skeleton, including the nucleus and internal electron shells are also considered spherical (with certain exceptions). Spherical clouds of electron pairs surround the core so that their mutual repulsion is minimal, i.e. they are as far apart as possible. This model allows evaluation in molecules. The ideal configurations and values ​​of bond angles for molecules with the number of pspheres of the same diameter are given in the table.

TYPES OF MOLECULE CONFIGURATIONS

When decl. diameters of the spheres (bonding and lone pairs of electrons), distorted configurations are formed with bond angles that differ from their ideal values. For example, in the molecules CH 4, NH 3 and H 2 O, there are four electron pairs in the valence shells of the C, N and O atoms, but for CH 4 they are all bonding, and the nitrogen and oxygen atoms have corresponding pairs. one and two lone electron pairs. Therefore, an ideal tetrahedral. only CH 4 has a configuration; in NH 3 and H 2 O molecules the bond angles are less than tetrahedral. Estimating the radii of electronic spheres and atomic cores using the values ​​of the covalent and ionic radii of atoms, as well as the postulates of geometric theory concerning multiple and polar bonds, etc., makes it possible to judge the lengths of bonds in molecules. G. t. gives results of qualities. or semi-quantities. character and applies Ch. arr. in chemistry inorg. and coordination connections. The theory is also useful when considering fragments of chain, layered and bulk crystalline particles. structures.

Basic the provisions of the theory were formulated by R. Nyholm and R. Gillespie in 1957.

Lit.: Gillespie R., Geometry of Molecules, trans. from English, M., 1975; Minkin V.I., Simkin B.Ya., Minyaev R.M., Theory of the structure of molecules, M., 1979. Yu. A. Pentin.

Chemical encyclopedia. - M.: Soviet Encyclopedia. Ed. I. L. Knunyants. 1988 .

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Based on electrostatic concepts Gillespie proposed a more general theory of the spatial structure of molecules. Key points:

• 1. The geometry of a molecule or ion is determined only by the number of electron pairs at the valence level of the central atom.
• 2. Electron pairs occupy such an arrangement on the valence shell of an atom when they are maximally distant from each other, that is, electron pairs behave as if they were mutually repelling.
• 3. The region of space occupied by a nonbonding (lone) pair of electrons has big sizes than the region occupied by the bonding electron pair.
• 4. The size of the region of space occupied by a bonding pair of electrons decreases with increasing electronegativity of the ligand and with decreasing electronegativity of the central atom.
• 5. Two electron pairs of a double bond occupy a larger area of ​​space than one electron pair of a single bond.

Notations used to describe the geometric configuration of molecules: A - multivalent atom; X - atoms associated with atom A;

n is the number of atoms X; E - lone pair of electrons; m is the number of lone electron pairs.

Then the formula of the molecule according to Gillespie is written as follows: AX n E m.

The geometry of the molecule depends on the sum (n + m). The number n, which determines the number of X atoms directly attached to the A atom, coincides with its coordination number. Each electron pair is taken to be a point charge. The central atom A is placed at the center of a sphere of a certain radius, which for similar attached atoms X is equal to the length of the A-X bond. Point electron pairs are located on the surface of the sphere.

By applying the rule of maximum distance of electron pairs on a sphere from each other, it is possible to derive the geometry of the simplest molecules and ions, gradually increasing the sum of shared and lone pairs (Fig. 4 and Table 1). valence hybridization polarity covalent

It makes no sense to consider the AX molecule, since it will always be linear, regardless of the number of lone electron pairs in atom A.

The AX 2 molecule is also always linear, since the maximum repulsion of two electron pairs will place them at the ends of the diameter of a conventional sphere.

Three bonding electron pairs, furthest apart from each other, form a regular triangle (molecule AX 3). In this case, the angle X-A-X is 120°. BF 3 and AlF 3 molecules have this structure. If one of the bonding electron pairs is replaced by a lone pair of electrons, then the molecule will be described by the formula AX 2 E and have an angular structure, and, according to Gillespie’s third rule, the angle X-A-X will become less than 120 o. An example of such a geometry is the SnF 2 molecule.

Rice. 4.

The four bonding pairs of electrons will form a tetrahedron in space. According to Gillespie's theory, this is a type of molecule called AX 4. The angle X-A-X will be 109 about 28?. Typical representatives of this type of molecules are molecules CH 4, CCl 4, SnF 4. By successively reducing the number of bonding electron pairs and increasing the number of lone electron pairs, for molecules of the AX 3 E type we obtain a trigonal-pyramidal structure (ammonia molecule NH 3), and for molecules of the AX 2 E 2 type - an angular structure (water molecule H 2 O).

The coordination number "five" is realized in molecules of the AX 5 type. Examples of such molecules are phosphorus pentafluoride or pentachloride (PF 5 , PCl 5 ). Five halogen atoms in space occupy the vertices of a trigonal bipyramid. Three atoms are located in the equatorial plane, forming an isosceles triangle, and two are located above and below this plane, respectively. The distance A-X from the center of the molecule to one of the vertices of the pyramid, called axial, is greater than the similar equatorial one.

The bond angle between bonds lying in the equatorial plane is 120°, and the bond angle between bonds lying in the axial plane is 180°. For molecules derived from a trigonal bipyramid, two alternative arrangement possibilities arise for the lone electron pairs. When positioned axially, it experiences repulsion from three nearby atoms, and in an equatorial position, from two. Therefore, the first lone pairs of electrons always occupy the equatorial position as the most energetically favorable. An example is the sulfur tetrafluoride molecule SF 4, which has the shape of a seesaw or disphenoid. In molecules of the AX 3 E 2 type, such as ClF 3 or ICl 3, the second lone electron pair is also located in the equatorial plane. Therefore, all four atoms are in the same plane, resembling the letter T in shape. Due to the fact that a lone pair of electrons occupies a region in space more size, the corresponding bond angles are distorted towards their decrease. The third lone pair of electrons, also occupying a position in the equatorial plane, turns the T-shaped molecule into a linear one. A representative of molecules of the AX 2 E 3 type is the xenon difluoride molecule XeF 2.

The most favorable arrangement of six X atoms around a central A atom is octahedral. Molecules of the AX 6 type, for example SF 6, have the shape of an octahedron. The first lone pair of electrons will occupy any of the vertices of the octahedron, turning it into a square pyramid. An example of a molecule of the AX 5 E type is IF 5. There are two possible locations for the second lone electron pair: adjacent to the first (cis position) and opposite it (trans position). Maximum repulsion of electron pairs forces the trans position to take place. As a result, molecules of the AX 4 E 2 type have a square shape, for example, XeF 4.

Table 1.

Number of electron pairs	Coordination			Molecule Type	Molecule shape
	Linear				Linear
	Tetrahedron				Tetrahedron Trigonal bipyramid
	Trigonal bipyramid				Trigonal bipyramid Disphenoid T-shaped Linear
					Square bipyramid Flat square