What is hybridization of NO2 +

The chemical bond in beginner lessons - an open model

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Overview

The following terms describe a path from the atomic structure to the covalent bond (electron pair bond, atomic bond). The goal is an open model that represents a real subset of a comprehensive description. Such a “correct” model (vulgo: the truth) can be expanded further and further through additions without having to withdraw individual aspects. The focus - in line with the current state of computational chemistry - is the octet rule, which is consistently applied, and the energy of the atomic orbitals involved. The VSEPR model, which allows octet exceeding, is severely curtailed.

The building blocks in detail:

After an atomic term was derived from the stoichiometric laws (Atoms as the smallest particles with mass chemical elements), line spectra show the need to represent the energy of electrons in terms of quantum numbers.

Bohr's atomic model shows the principle: with 1 quantum number, the Principal quantum numberto translate the Balmer series into a scheme of electronic energies (later: orbital energies).

Multi-electron atoms require a total of 4 quantum numbers, the main quantum number being the Minor quantum number and the Orientation quantum number are linked by a hierarchical order.

A given combination of these three quantum numbers defines a Orbital, in which up to two electrons with different spin quantum numbers filled can be.

Taking into account the energetic sequence of the orbitals, the Construction principle derive the periodic table of the elements.

The orbitals correspond three-dimensional standing waveswhose properties can be derived from low-dimensional analogues: the nodal planes from one-dimensional standing waves (violin string), and the behavior during superposition ("orbital overlap") from the behavior of two-dimensional progressing waves (wave pattern on water).

A simple case like the valence shell of neon indicates the principle of increase Node planes with increasing energy (decreasing stability).

The meaning of Valence shell itself results from the Orbital energieswith measurable quantities like the Ionization energies, the Electron affinity and the Electronegativity connected is. Also the Octet rule arises at this point.

The Covalent bond is introduced by the superposition of atomic orbitals.

Lewis formulasthat adhere to the octet rule are an adequate means of describing a molecule.

Molecular orbitals and localized bonds are equivalent descriptions of the binding state of a molecule.

The methane molecule shows that the equal participation of s and p orbitals in the bonding state of the molecule also emerges from an MO consideration; also the sp3-Hybridization of the carbon atom can be derived from an MO treatment.

Conclusion: while an MO treatment for school-relevant molecules is best for O2 and for aromatics, numerous details can be derived for main group element atoms from a consideration of the s and p orbitals of the valence shell including their characteristic orbital energies: the structure of the periodic table, the octet rule, atomic properties (ionization energy, electron affinity, electronegativity), the structure numerous molecules through spin pairing between singly occupied atomic orbitals. Since the quantitative treatment of main group elements does not lead to any significant d orbital participation, the octet rule applies here strictly. An octet overrun with molecules like SO2 or H2SO4 should be avoided in favor of partially ionic formulations. The VSEPR model with its careless handling of exceeding octets (with complete hybridization at the same time) has weaknesses here: it says the structure of a CIF3 quite well ahead, but assumes the existence of a ClH3 = H3Cl close. While the recipe “pair the electrons of the atoms in their ground state to form molecules”, for example in the case of S8-Molecule which describes the p-p bonds very well and assigns the s orbital to a lone pair of electrons, the important molecules are NH3, H2O and many organic molecules characterized by the complete involvement of the s orbital in the bond; spn-Hybrids are adequate to describe this.

Working materials

The following pages are excerpts from the basic chemistry lecture at LMU Munich in the winter semester 2008/2009. The complete lecture is available as an internet script.

3 atoms

Atoms are made up of nucleons (protons, neutrons) and electrons. While the occurrence of isotopes can be understood from the structure of the atomic nucleus, the chemical properties result from the electronic structure. The focus of the consideration is the description of electronic states through the four quantum numbers n, l, ml and ms. Of these, the principal quantum number becomes first n introduced, with the help of which the position of the emission lines in the hydrogen spectrum can be interpreted. Then the electronic lounges, the orbitals, are examined in detail. The assignment of electron configurations to the basic states of the atoms leads to the Periodic Table of the Elements (PSE). Conversely, atomic properties such as ionization energy or electron affinity show a characteristic course in the PSE.

Mortimer: 2, 6
Binnewies: 2, 3
Riedel: 1.2, 1.4

Elementary particles

The smallest particles of a chemical element, the atoms, are made up of the elementary particles Electrons, Protons and Neutrons which differ in mass and electrical charge. The atomic nucleus is formed by positively charged protons with a relative mass of 1.007277 and a charge of + e as well as electrically neutral neutrons with a mass of 1.008665. Compared to the core particles, the nucleons, electrons are almost massless (approx. 1/2000), they carry the charge −e. 1 e is the Elemental charge, the smallest electrical charge; all charges occurring are integral multiples of this elementary charge. Your amount is:

1 e = 1.6022 × 10−19 C.

The radii of the atomic nuclei are of the order of 10−2 until 10−3 pm (1 pm = 10−12 m; compare, for example, the radius of a copper atom of 128 pm, see Rutherford's experiment). The atomic nucleus, which is very small compared to the entire atom, contains almost the entire mass of the atom. The number of protons determines the size of the positive charge on the nucleus, the atomic number, which is equal to the number of protons. The total number of protons and neutrons determines the mass of the nucleus and approximates that of the atom, so it becomes Mass number called. A chemical element consists of atoms with the same number of protons (atomic number), but the number of neutrons can be different. The proton number characteristic of the element will also be Atomic number called.

An atomic type characterized by atomic number and neutron number is called nuclide. Nuclides with the same number of protons but different numbers of neutrons are called Isotopes. Examples are the isotopes of hydrogen (note the usual notation, note the mass number at the top left and the atomic number at the bottom left of the element symbol): 21H, (= D, deuterium), 31H (= T, tritium).

Since the information about the atomic number is already given by the atom symbol, nuclides are often only described by the mass number, for example for the various carbon isotopes:

12C, 13C,14C.

or for the isotopes of nitrogen:

14N, 15N

Most elements are mixed elements, which consist of several isotopes, often with very different frequencies. The isotopes of hydrogen, carbon and nitrogen are found with the following frequencies: 1H (99.985%), 2H (0.015%); 12C (98.89%), 13C (1.11%); 14N (99.63%), 15N (0.36%).

Some elements are pure elements that consist of only one type of nuclide in their natural occurrence (for example fluorine only 19F, sodium only 23N / A). Nuclides with the same mass number but different atomic numbers are called isobars (for example 14C, 14N).

Electrons as particles: Bohr's model of the atom

The investigation of emission spectra shows an essential property of the electrons - the quantization of the energy states. Atoms in an excited electronic state can be generated by supplying thermal or electrical energy. When returning to the basic electronic state, the energy difference to the excited state is often emitted in the form of light energy. The spectral decomposition of the generated radiation results in line spectra as an indication of discrete energy states that can be assumed by the electrons.

Experiment 6-1: Li, Na, B flame staining

Experiment 6-2: Plücker tube (hydrogen and nitrogen) • High voltage is applied to a glass tube. The tube is filled with hydrogen and then evacuated. When a sufficient vacuum is reached, the tube begins to glow blue-violet. The luminous phenomenon is the mixed color of the spectral lines shown in the following figure.

The first five lines in the Balmer series. The wavelength in nm is given below the emission spectrum, and above the spectrum n2, the principal quantum number of the excited state. The lower energy state is included with the Balmer series n1 = 2.

Even before an explanatory model was recognized, it was possible to establish a simple relationship that describes the position of the lines in the "Balmer series" shown: For n ≥ 3 applies namely (frequency ν, wavelength λ):

ν = c λ−1 = 3,289 × 1015 × (1/4 − 1/n2) sec−1

The search for further series in the invisible areas of the electromagnetic spectrum led to the general relationship:

ν = 3.289 × 1015 × (1/n12 − 1/n22) sec−1

For n2n1. It is particularly revealing for the series with n1 = 1 - the Lyman series observable in the UV range - over the lines observed for n2 = 2, 3, 4, ... on n2 = To extrapolate ∞. The energy obtained is the equivalent of 13.6 eV. This amount corresponds to Ionization energy of the hydrogen atom, this is the energy required for the process

H → H+ + e

must be applied (this amount of energy is also called Rydberg's constant; you can find it tabulated in textbooks in other energy units). N. Bohr succeeded in interpreting these observations using a shell model of the hydrogen atom. In this model, the electrons can only assume discrete energy states, the lowest-energy, most stable state of which is 13.6 eV below the ionization limit, which is set at 0 eV (see figure, together with the Balmer series also as a pdf).

Orbital energy scheme of the hydrogen atom. The energy of a state only depends on the principal quantum number n from, the "shell" in Bohr's atomic model. The ionization limit is at the ordinate value 0. The blue arrows indicate the electron jumps that cause the Balmer series.

The permitted states appear in ever closer succession the closer the ionization limit gets. The energy values ​​follow in sequence

E. = 13.6 eV With n = 1, 2, 3, …
n2

n is a "quantum number" with which an electron energy is uniquely described; in Bohr's model n interpreted as the number of the “shell” on which the electron circles the nucleus. Note that Bohr's atomic model treats the electron as a particle. So becomes the Rydberg constant R.H derived in this model as (reduced mass μ, Charge Z, Vacuum dielectric constant ε0):

R.H = μ Z2 e4
8 ε02H2

The reduced mass occurs μ on; for the hydrogen nuclide 1H applies: 1 /μ = 1/mproton + 1/melectron. The treatment of the electron as a rotating mass is obvious.

Quantum numbers

The wave-mechanical treatment of the electronic structure followed the Bohr model of the atom. A mathematical elaboration is not given at this point. In lectures on quantum mechanics you will deduce that the “shell” of Bohr's atomic model is only one of four quantum numbers that uniquely define the state of an electron. The first three quantum numbers follow a hierarchical scheme, at the starting point of which the main quantum number n stands:

The Principal quantum number can the values n = 1, 2, 3, ... assume.

Possible values ​​for the Minor quantum numberl are l = 0, 1, 2, … (n - 1); For l so there is n possible values.

Possible values ​​for the magnetic or Orientation quantum numberml are ml = −l, …, 0, …, +l; ml so depends on l off, there are 2 l + 1 possible values.

Independent of n, l and ml is the (magnetic) Spin quantum numbermswhich can take the values ​​+ ½ and −½.

Note that the principal quantum number n the possible values ​​for the minor quantum number l and this defines the possible values ​​for the orientation quantum number ml. In addition to the designation by numbers, quantum numbers are also described by letters; the following symbols apply:

nl
0 s
1 K p
2 L. d
3 M. f

According to this, a “2p electron” is to be understood as an electron with the main quantum number 2 and the secondary quantum number 1; "Electrons of the L-shell" are electrons of the main quantum number 2. This applies to the occupation of the energy levels Pauli ban: All four quantum numbers of electrons in an atom never match. The principal quantum number 1 can therefore apply to at most two electrons (n = 1; l = 0; ml = 0; ms = + ½ or −½) and the principal quantum number 2 for at most eight electrons (n = 2; l = 0, 1; ml = 0 for l = 0, ml = −1, 0, +1 for l = 1; ms = + ½ or −½). In general, 2 n2 Electrons have the same principal quantum number ("being in the same shell"), while the following maximum electron numbers result for a given principal and secondary quantum number:

2 electrons in state ns, 6 at np, 10 at nd and 14 at nf.

The energies of each level depend on n and l from; their sequence is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, ...

Note that there is no law of nature behind the donkey bridge shown in many textbooks, which derives this sequence from a checkerboard pattern.

In an atom in the ground state, the electrons occupy the permitted energy levels with the lowest energy, whereby the Hund's rule Note: states of the same energy are initially occupied by one electron each.

The periodic table of the elements

In the periodic table of the elements, the elements are arranged in the order of their number of electrons (= atomic numbers = atomic numbers). A clear allocation results from the Moseley law, which will be discussed further below.

The usual long-period system arises when blocks are formed according to the secondary quantum numbers, i.e. when all s-elements are arranged one below the other, all p-elements one below the other, and so on; Elements whose electrons with the highest energy have the same principal quantum number are written in one line (period):

ns blockd blockp block
12312131415161718
11H2Hey
23Li4Be5B.6C.7N8O9F.10No
311N / A12Mg13Al14Si15P16S.17Cl18Ar
419K20Approx21Sc 30Zn 31Ga32Ge33As34Se35Br36Kr

In this way, elements with the same electron arrangement come to stand one below the other in the outermost shell; this same arrangement of the electrons of the incompletely filled shell, the Valence electrons conditionally similar chemical properties of such elements of a group of the periodic table (note a deviation from the rule: helium, He, despite its two electrons in the 1s state is not above beryllium, Be, but in accordance with its chemical properties in the group of noble gases) .

The elements of the s-block and the p-block are called Main group elements designated; in these, the period number corresponds to the main quantum number of the electrons, which are filled into their corresponding level in the course of the period; According to the old counting, the group number corresponds to the number of valence electrons; with the new counting method, a p-block element shows the group number i just i - 10 valence electrons. The group number 18 corresponds to a complete filling of the s and p levels of a shell (exception: for n = 1 the shell is filled with two electrons). this is the Noble gas configuration, the particularly stable electron arrangement of the noble gases.

With the elements of the d-block, the Subgroup elements, electrons become the main quantum number n - 1 filled in, although electrons already have the principal quantum number n available. The elements of the first nine subgroups, in which the d-level is not completely filled, are also referred to as transition elements or transition metals. Finally, in the elements of the f-block, electrons become the main quantum number n - 2 filled up.

Orbitals

The 10 electrons of the noble gas neon form the electron configuration 1s2 2s2 2p6. The energetic sequence reflects the high atomic number of neon compared to hydrogen. The valence electron concept becomes clear when the special stability of the 1s level is considered (figure also as pdf):

The five occupied atomic orbitals of neon. Each orbital is occupied by a spin-coupled electron pair. Note the strong contraction and high stability of the 1s orbital.

In the figure, a shape is given for the individual orbitals. In the particle model, the orbital is linked to the electron's living space. For the interpretation of the chemical bond in the next chapter it is more useful to refer to n, l and ml characterized orbitals to be viewed as three-dimensional standing waves. In the wave model, sign information is added to the contour of the orbital, which corresponds to the wave crest and valley in the case of a two-dimensional wave. In the figure, the different signs are distinguished by the colors red and gray.

Experiment 6-3: One-dimensional standing waves

The 1s orbital is spherically symmetrical, the associated wave function has a positive sign at every location in space. The same seems to apply to the 2s orbital, but a section through the orbital would show a change in sign near the core. Due to the closeness to the core of the sign change, this does not play a role for the following bond considerations, since the interactions between the orbitals of two atoms are dominated by the outer contour.

The 2p orbital shows a change in sign in the outer contour. The orbital has a nodal plane running through the nucleus in which the probability of encountering the electron is zero. Note that this statement is incompatible with a particle concept. The three energetic, "degenerate" (eng. degenerate) p-orbitals differ in their orientation in space. The three values ​​for ml correspond to three orbital orientations along the three basis vectors of a Cartesian coordinate system. To differentiate the three p orbitals are used alternatively to ml = −1, 0 or 1 the designations px, py and pz.

Note an important property of the neon orbitals shown below: If any two orbitals are superimposed on each other, the common space in which the same sign meet and the waves reinforce each other (constructive interference) is just as large as the space in which the wave functions have different signs and cancel each other out (destructive interference) - the net overlap is 0, the orbitals are orthogonal.

Orbital energies

In the following discussions of the chemical properties of atoms and molecules, the orbital energy in the area of ​​the valence electrons will play an important role. Orbital energy diagrams show trends in PSE, for example in the ionization energy of atoms or their electron affinity.

The 1. Ionization energy ("1st ionization potential") I.1 of an atom is the minimum energy required to completely remove an electron from the atom. A single positively charged ion arises from the atom:

X → X+ + e

The 1st ionization energy largely corresponds to the orbital energy of the most energetic electron. The removal of the second electron requires the energy I.2, the third I.3, and so on. Ionization energies are a measure of the strength with which electrons are bound in the atom. I.1 grows from left to right within a period; That means that the removal of an electron becomes more difficult, the smaller an atom is, the closer the considered electron is to the attractive nucleus - see the previous figure. For a given element, the ionization potentials grow in sequence I.1, I.2, I.3, ... quickly, as the removal of electrons from an atom with an increasingly higher positive charge requires more and more energy. The removal of an electron from a noble gas shell causes a noticeable jump in the sequence of the ionization potentials (figure also as pdf).

Orbital energies for Mg, Mg+ and Mg2+. The ionization energy is needed to remove the most energetic electron. Note the jump in the omission of the valence shell (technical note: orbital energies with hf / 6-31g (d, p), mean values ​​for α- and β-spin for Mg+).

The Electron affinity (EA) of an atom is the energy that is released or required when an atom attaches an electron. A neutral atom becomes an anion:

X + e → X

The close relation to the ionization energy becomes clear when the reverse process is considered:

X → X + e

The amount of the electron affinity now appears as the ionization energy of the anion; it therefore largely corresponds to the orbital energy of the highest occupied orbital of the X anion. The following figure (pdf) shows I.1 and EA in the orbital scheme of fluorine:

The highest EA values ​​are found for the halogens, which, by absorbing an electron, achieve the electron configuration of the noble gas following in the periodic table. I.1 and EA of an atom are taken up again below in order to define the important term "electronegativity" when dealing with the chemical bond.

4 The covalent bond

The constructive interference of singly occupied atomic orbitals leads to binding molecular orbitals. In addition, non-bonding and antibonding combinations of atomic orbitals must be taken into account when the valence electrons of two atoms interact in order to establish σ and π bonds. The covalent 2e-2z bond, which can be represented by a Lewis formula, is the focus of the valence bond method (“VB method”), which can be derived from the more general molecular orbital method (“MO method”).

Mortimer: 2, 6
Binnewies: 2, 3
Riedel: 1.2, 1.4

The H2-Molecule

Hydrogen comes in the form of H.2Molecules. Two H atoms are connected to one another by a covalent bond (atomic bond). The formation of the bond can be interpreted if, as in the case of the occupation of atomic orbitals in the previous chapter, the question is asked about molecular orbitals in which electrons now interact with more than one atomic nucleus. A conceptually obvious method for the construction of such molecular orbitals (MOs) is hidden behind the abbreviation LCAO (linear ccombination of atomic Orbitals, Linear combination of atomic orbitals). Here, atomic orbitals are assumed and their interaction with one another is investigated. The standing wave image helps to identify a strengthening or weakening of the wave (constructive or destructive interference). The principle is shown in the following figure.

MO diagram for H2. (The position of the antibonding orbital is the energy of the lowest unoccupied MO of the stable 1σ20-Basic state drawn.)
Technical note: H.2-Energies with hf / aug-cc-pv5z at 73.37 pm core distance.

This lies in two spatially separated H atoms a Electron in the spherically symmetric 1s state. If the two atoms approach each other, there are two possibilities of interaction: the waves reinforce each other (same sign of the wave function) or they cancel each other out (different sign). The first possibility leads to a localization of the electrons between the positively charged nuclei and thus to a bond. Electrons that are in this MO are stabilized against the free atom due to their interaction with two instead of one nucleus, they lie on the energy axis below the atomic orbital energy - which is MO binding. The opposite is true when the two waves are combined with different signs: an MO is created that has a nodal plane on the core connecting line. Is this antibonding Orbital occupied by electrons, electrons are localized beyond the proton-proton axis, which corresponds to an unstable state. Note an important rule: n Atomic orbitals (here 2) occur n Molecular orbitals together.

The final step in constructing an MO scheme is "filling in" the electrons that are present. Analogous to the construction principle, these are distributed to the most stable states possible, taking into account the Pauli principle and Hund's rule. At the H2Molecule, the binding MO is filled with a spin-coupled pair of electrons while the antibonding MO remains empty - it is a Covalent bond (Electron pair bond, atomic bond) emerged. The binding MO is rotationally symmetrical, there is one σ bond before (compare the symmetry properties of a s-Orbitals). The two orbitals of the scheme are denoted by 1σ and 2σ, σ and σ * (pronounced “sigma star”) are also common, with the * marking the orbital as antibonding. The notation of the electron configuration corresponds exactly to that used for atoms; for the basic state of the H2Molecule 1σ20.

Another important term is the Binding order. To do this, add the number of electrons in bonding molecular orbitals (those without a nodal plane perpendicular to the core-core axis), then subtract the number of electrons in antibonding MOs (those with a nodal plane perpendicular to the core-core axis) and divide by two. At H2:

BO = (2 - 0) / 2 = 1

The two hydrogen atoms are replaced by one Single bond held together.

The HCl molecule

In the following chapter we will discuss the reaction of hydrogen with chlorine, Cl2, examine. The two gases react exothermically to form hydrogen chloride (hydrogen chloride), which is also gaseous, and which is used to clarify the principle of non-binding interaction.

In contrast to the hydrogen atom, the chlorine atom has 1s due to the electron configuration2 2s2 2p6 3s2 3p5 also pay attention to p orbitals. Opposite the H2-Case now two new aspects arise: (1) What interaction occurs between the H (1s) and the Cl (3p) orbitals? (2) What is the interaction between the H (1s) and the Cl (3s) orbital, which are quite far apart on the energy axis. The following figure shows the answer:

MO scheme for HCl, electrons in atomic orbitals omitted (technical note: rmp2 / 6-31g (d, p), averaged over α and β spins for Cl, charge on Cl according to Mulliken population analysis: −0.17 e)

Of the three 3p orbitals of chlorine, only one combines with the H (1s) orbital to form a bonding (2σ) and an antibonding (3σ) MO. It is precisely the one that is rotationally symmetrical to the H-Cl bond axis (the interaction is “symmetry allowed”). If the H-Cl bond axis is chosen as the z-axis in a Cartesian coordination system, then it is the 3pz-Orbital.

If the interaction between the H (1s) orbital and the 3px- or 3py-Orbital of chlorine considered, each constructively interfering area is compensated by an equally large destructively interfering area. The orbitals are orthogonal, the interaction is not binding or "symmetry forbidden". The two nonbonding p orbitals appear energetically unchanged in the scheme (which is not mandatory, see below for HF) and without interaction with the H (1s) orbital.

The H (1s) -Cl (3s) interaction is treated in a similar way in the diagram. The 1σ orbital appears at almost the same energy as the Cl (3s) orbital, and the H (1s) orbital seems to contribute little to the shape of 1σ - the originally spherically symmetrical Cl (3s) orbital is in the 1σ orbital can still be seen clearly, but it is "bulged" in the direction of the H atom. In a very rough approximation, the orbital can be classified as non-binding and assigned to the chlorine atom. This is a quantitative determination, because in principle the symmetry-permitted interaction leads to a binding-antibonding combination and not to a strictly non-binding, symmetry-forbidden interaction - we will come back to this in a moment.

But first the result in the overview: The greater the energy difference between two orbitals, the smaller the energetic split of the MOs. The electron pair is spatially localized on the atom that contributes the atomic orbital with almost the same energy. When calculating the bond order, non-bond orbitals are not counted. Five atomic orbitals (1 of H, 4 of Cl) result in 1 bonding, 1 fairly nonbonding, 2 strictly nonbonding and 1 antibonding, a total of 5 MOs, the more stable 4 of which each contain 2 electrons. The following applies:

BO = {2 (in 2σ) - 0 (in 3σ)} / 2 = 1

A quantitative statement on the H (1s) -Cl (3s) interaction is not very clear in the MO formalism. In the next but one section, the example of Cl2Molecule presented a method that combines the MO theory with the valence bond method presented first.

Lewis formulas

Lewis formulas allow the brief formulation of electron pair bonds. The electrons of the valence shell are shown, a line symbolizes a spin-coupled electron pair, a point an unpaired electron. The electron configurations of the atoms H (1s1), N (2s2 2p3 = 2s2 2px1 2py1 2pz1), O (2s2 2p4 = 2s2 2px2 2py1 2pz1), F (2s2 2p5 = 2s2 2px2 2py2 2pz1) and Cl (3s2 3p5 = 3s2 3px2 3py2 3pz1) in the basic state is represented as:

Bonds are created by spin coupling of unpaired electrons to form electron pairs:

Lewis formulas are often adequately suited to the result of the Valence bond method (engl. valence bond method, VB method). While in the molecular orbital method, molecular orbitals extending over the entire molecule (mostly according to the LCAO method) are determined in order to then fill in the existing electrons according to the construction principle, in the VB method, electron pairs are on an atom (lone electron pairs) or between two atoms (bonding electron pairs) localized. (A delocalization over several atoms can often be described by "mesomeric boundary structures", which will be discussed below.)

At H2 and HCl, the method summarized in the orbital diagrams, which essentially corresponds to the MO method, leads to a result that is very close to a VB treatment due to the only one valence orbital on each H atom. So it is obvious that the 1σ orbital of the H2Molecule as the binding electron pair of the Lewis formula. In the case of the HCl molecule, the MO scheme with three chlorine orbitals (1 π and 1σ) shows a very similar situation to the Lewis formula with 3 lone electron pairs. lone pairs). The bonding pair of electrons in the Lewis formula is essentially found as 2σ in the MO scheme.

In order to show the closer relationship between the MO and VB methods, we now consider the chlorine molecule.

Localization of molecular orbitals: the Cl2-Molecule

On the chlorine molecule, Cl2, to show that there is a connection between MO and VB treatment. First the VB method. The starting point is two chlorine atoms and their 3s23p5-Valence configuration. According to the VB method, a σ-single bond is created by the interaction of the singly occupied pz-Orbitals to be expected:

Expressed as a Lewis formula:

The MO method also starts from the atomic orbitals and combines them to form bonding and antibonding MOs:

As with H2 and HCl σ-interactions occur - both binding through 3s-3s- and 3pz-3pz-Overlap as well as an antibonding 3s-3s interaction. In addition, there is a side overlap of type 3px-3px and 3py-3py a further interaction is added, namely binding and antibonding π molecular orbitalswhich, in contrast to the σ orbitals, are not rotationally symmetrical about the bond axis, but rather have a nodal plane in the bond axis.

In the following scheme, all molecular orbitals of the energy diagram are shown on the left.In addition, the result of a calculation method is shown with which a VB-typical view can be derived from an MO analysis whenever the valence electrons of the molecule in question can be divided into normal covalent bonds and lone pairs of electrons. For this purpose, MOs (which were previously calculated from AOs by linear combination) among themselves linearly combined. For the Cl2-Molecule, the result is particularly clear:

The result of this Localization of MOs A comparison with the Lewis formula reveals itself immediately: if both a bonding MO and the corresponding antibonding MO are occupied in a molecule (left side of the diagram), the linear combination of the pair leads to a free electron pair on each atom (right side of the diagram) ). Since this condition applies to all orbitals except the 3σ-MO, this is the only one that remains assigned to two chlorine atoms. In the Lewis formula, it would correspond to the binding electron pair, while the remaining six electron pairs can be equated with the lone pairs of electrons in the Lewis formula.

A particularly useful result of the method consists in a quantitative statement of the extent to which the bond - mainly caused by the 3pz-3pz-Interaction occurs - parts of the type 3s-3pz contains. (As a preliminary exercise, make sure that the orbital marked ≈3σ on the right-hand side arises from the 3σ-MO if 1σ is subtracted to a small extent). For Cl2 the result confirms the impression that the bond is mainly 3pz-3pz-Character in that each 3s atomic orbital contributes less than 10% to the bond.

The proportion is higher for the HCl molecule. The "bump" in the 1σ orbital that is visible in the MO scheme of HCl corresponds to a proportion of the H (1s) -Cl (3s) interaction of approx. 15%, which we had neglected approximately. The joint contribution of s and p orbitals to a bond is dealt with in the VB model under the heading “hybridization”. We carry out this concept using the example of the N2Molecule, since the s-p interaction is much stronger there.

The N2-Molecule

Nitrogen is the main constituent of air, which is inert. Like hydrogen, chlorine and oxygen, nitrogen is made up of diatomic molecules. The electron configuration of the N atom is 1s2 2s2 2p3. In a VB treatment, the three unpaired p electrons of each nitrogen atom would be spin-coupled to form electron pair bonds:

Spin coupling the two pz-Electrons are created as with Cl2Molecule has a σ bond. The two remaining unpaired electrons of each N atom can be coupled to form two π bonds. Overall bond order 3 results. The spin-coupled electron pair in the ground state of the N atom (2s2) appears in the molecule as a lone pair of electrons at each of the two N atoms. Represented with Lewis formulas:

Even with this only diatomic particle, the MO treatment is still close to the VB consideration: in the search for symmetry-permitted interactions, the same considerations lead to those for Cl2 to two groups of atomic orbitals (the bond axis is also here the z-axis): a total of four 2s- and 2pz-Orbitals can be combined in a symmetry-permissible way and also four 2px- and 2py-Orbitals exist in non-binding interactions with the orbitals of the first group. The two 2px- and the two 2py-Orbitals are combined into two π interactions: MOs to be bound with a nodal plane in the molecular axis (1π) and antibonding MOs with a nodal plane in the molecular axis and a nodal plane perpendicular to the core connecting line (2π). Only the π interaction in the plane of the drawing is shown in the figure (πy with the coordinate system of the VB consideration), but not the perpendicular πx-Orbital.

MO diagram for N2 (pdf). It's just each time a 1π and 2π orbital shown. (Technical note: the 2s orbital is shown at the mean value of α and β spin.)

The bond order is obtained by summing the 8 MOs formed from 2 × 4 atomic orbitals:

BO = {2 (1σ) - 2 (2σ) + 2 (3σ) + 4 (1π) - 0 (2π) - 0 (4σ)} / 2 = 3

In contrast to Cl2 the σ-interactions now show a noticeable intermingling of 2s- and 2p-components. You will discover these even if you only analyze the MO scheme at first.

In the VB method, the s-p interaction is regarded as a property of the atomic orbitals. In practice, the MOs are localized for this purpose. The two π bonds are retained as such, since in contrast to Cl2 no occupied antibonding π orbitals are available for the linear combination of the MOs. In the case of the σ orbitals, it is to be expected that the 1σ-2σ pair can be combined to form two lone pairs of electrons. The calculation gives the following picture (left the MOs, right the localized orbitals; under both orbital groups there is an N for orientation2-Hull drawn):

Neither the σ bond orbital nor the two lone pairs of electrons (in the picture: lp1 and lp2) have the shape that is to be expected for an interaction between pure s or p orbitals. Accordingly, the calculation results in the s and p components shown in the figure. A clear formalism is now introduced in the VB method: the s-p-mixture becomes in front the linear combination is made into bonds by adding s and p atomic orbitals to Hybrid orbitals can be combined linearly. For example, a bond with 35% s and 65% p character is created through the interaction of two hybrid orbitals with precisely these s and p components:

Note that the sum of the s and p components must correspond to the total number of orbitals: for the N2-Molecule therefore add 1/3 s-part of the σ-bond and 2/3 s-part of the lone pair of electrons to 1. The same applies to the pz-Orbital. The actual extent of the s-p mixing is a characteristic variable in the chemistry of the main group elements. Part B of the lecture deals with trends in the periodic table.

Lewis formulas vs. MO diagrams

The description of the chemical bond by the Lewis formalism is the simplest tool to represent a molecule. If the only question is basic information on molecular structure and properties (is the molecule angled or linear? Does it have a dipole moment or not?), Lewis formulas are often sufficient.

As a minimum requirement for the representability of a molecule by a Lewis formula, it should be required that - if necessary through the formulation of the "mesomeric boundary structures" discussed in detail later - (1) the bond order and (2) the spin state (number of unpaired electrons) is played back correctly. Of the molecules discussed, this applies to H2, HCl, Cl2 and N2 to. Even with the most important air component for life, oxygen, the Lewis formulation comes to a false conclusion.

The O2-Molecule

O2 is paramagnetic in its ground state. This property shows that in the O2-Molecule unpaired electrons are present. Quantitative treatment shows that there are two unpaired spins per molecule. This is not to be expected from the simple formulation of a Lewis formula:

However, a closer look at the underlying atomic orbital interactions shows that difficulties can be expected. While in N2 freely giving two equivalent π bonds from four equivalent p orbitals shows the same view for O2 a problem:

Although geometrically equivalent, the px- and py-Orbitals now occupied differently - one with a single electron, the other with a pair of electrons.

The MO calculation produces a diagram that is very similar to that of the nitrogen molecule. However, because of the two larger number of valence electrons, the one at N2 empty 2π-state occupied by two electrons and, because of Hund's rule, each with 1 electron - O2 is paramagnetic. The description of the spin state is commonly used as “multiplicity”. For this purpose, the msValues ​​for a total spin S. added, then the multiplicity is calculated as 2S. +1 formed (for the oxygen molecule with S. = 2 × ½ = 1: 2 × 1 + 1 = 3). Particles with a multiplicity of 1, 2, 3 are in the singlet, doublet, triplet state. The stable form of O2 so is the Triplet oxygen.

MO diagram for O2.
Technical note: O2-Energies and atomic distance with ump2 / aug-cc-pvqz, 121.9 pm atomic distance.

While the spin state cannot be represented by a Lewis formula, there is agreement in the bond order. The figure also shows a for the MO treatment Double bond:

BO = {2 (1σ) - 2 (2σ) + 2 (3σ) + 4 (1π) - 2 (2π)} / 2 = 2

Oxygen, a “diradical”, is one of the few molecules that are stable without having 0 in the ground state for the sum of the (magnetic) spin quantum numbers, without all electrons being spin-paired. Numerous chemical reactions only take place unchecked (mostly those in which no transition metals are present) if the sum of the unpaired spins remains the same. If oxygen is produced in such a reaction, it is not released in the triplet ground state, but as an unstable and extremely reactive one Singlet oxygen (which one could describe with the Lewis formula shown).

Experiment 9.2: Singlet oxygen • During the reaction

H2O2 + Cl2 + 2 OH1O2 + 2 cl + 2 H.2O

singlet oxygen is formed. When returning to the 3O2-Ground state, red light with wavelengths 633 and 760 nm is emitted (190 = 2 × 95 and 158 kJ mol−1 corresponding to an emission of two singlet oxygen forms), on this Holleman-Wiberg: "... the conversion of hypochlorite with hydrogen peroxide is accompanied by an emission that can be perceived as a red shimmer with the dark-adapted eye."

Comparison of the binding models: methane, CH4

The MO model showed the O2-Molecule its performance. Nevertheless, the basic idea of ​​this consideration - delocalizing orbitals over the entire molecule - naturally hardly comes to the fore when dealing with diatomic molecules, since not much can be delocalized over just two atoms. The differences between the MO and VB methods become much clearer when polyatomic molecules are considered. A prime example is methane, CH4.

Methane has a tetrahedral structure, i.e. the H atoms form the corners of a tetrahedron with the carbon atom in the center of gravity:

Schematic (explanation of the notation):

In the MO method, the atomic orbitals of the four H atoms and the C atom are combined to form 5z-2e bonds - each molecular orbital therefore extends over all atoms. Starting from the atomic orbitals of carbon, each of the four carbon valence orbitals is linearly combined with a set of four H-position orbital combinations so that four bonding MOs result. In the case of the unoccupied antibonding MOs, the signs of the wave functions are reversed (either for C or for H.4-Part):

Schematic:

Note that each of the four equivalent C – H contacts is made up of four components. Since each bonding MO includes all four C – H contacts, the bond order for the single C – H bond is 4 × ¼ = 1.

Because of the high symmetry, the localization in 2z-2e bonds is clear: for practice, superimpose all four MOs of the illustrated scheme with a positive sign. The result is a 2e bond, to which only the 1s orbital of the H atom at the top right contributes, as well as a hybrid orbital on the carbon atom that has ¼ s and ¾ p character. This applies to all bonds in this highly symmetrical molecule. Because of the three times higher weight of the p orbitals at the four similar bonds, these “sp3-Hybrid orbitals "called. (It is an instructive exercise to make it clear to yourself graphically that two mutually perpendicular p orbitals lose their orthogonality due to a 25% s admixture. This is restored if, by increasing the angle between the orbitals, their mutual overlap is reduced in the reinforced area and increased in the weakened area. At the "tetrahedral angle" of 109.5 , orthogonality is achieved again.)

If, as is usual in textbooks, the VB orbitals are not derived from MOs by localization, the formulation of the formula begins with a problem. A carbon atom in the ground state appears with its valence electron configuration 2s2 2p2 not having four singly occupied orbitals. The first step is therefore a more energetic 2s1 2p3-Condition formulated. The required number of unpaired electrons is now available. By linear combination, the 2s1 2p3Configuration to a (sp3)4-Configuration hybridized. The four equivalent hybrid orbitals now point to the corners of a tetrahedron.

The VSEPR model

All four bonds in the methane molecule are equivalent. In the sense of the VB model, all four electron pairs are hybridized in the same way. A fundamentally simpler approach than the VB and MO method results when this peculiarity of methane is transferred to all conceivable molecules - i.e. when we use the Cl2Understand the molecule in such a way that the binding electron pair as well as the free electron pairs sp3Represent hybrid orbitals. Since we will only see a few molecules for which this simplification is allowed, we will use this VSEPR model (valence shell electron pair repulsion, Valence electron pair repulsion) do not pay too much attention (we will come to the more serious disadvantage of not observing the important octet rule). Examples of molecules to which this model can be successfully applied are NH3 and H2O. The VSEPR model is therefore presented in the “Polar Molecules” chapter.

What now?

In the lecture we will use the attachment model that is sufficiently - but not unnecessarily - complex to adequately answer the question of interest. Often the Lewis formula will suffice to describe a molecule. The MO method is particularly suitable for multi-center bonds, but mesomeric limit formulas are also discussed here, if only because they are widely used in textbooks.

The example of methane shows particularly clearly in which case the MO method can generally hardly be dispensed with, namely when it comes to orbital energies. If methane is investigated with spectroscopic methods similar to those discussed above for the H atom, occupied orbitals are shown in the ground state at two Orbital energies and not - as the VB consideration with four equivalent hybrid orbitals suggests - only one! When do we need a model that represents energies correctly? One example is the discussion of semiconductors that cannot be meaningfully described on a VB basis. Another example is the relationship between the color of a substance and its electronic structure (why is hemoglobin red? What can we conclude if it changes color when it interacts with CO or NO?).

Atomic radii

For most elements an “atomic radius” is given in the textbooks. The non-metallic elements are usually the covalent single bond radius. This is defined as half the distance between atoms in a homonuclear single bond. Examples: the atomic distances in H2 and Cl2 are 74 and 198 pm. The covalent radii are then 37 and 99 pm. With the help of these radii, expected values ​​for heteronuclear bonds can be calculated. For HCl this results in 136 pm (exp. 127 pm).

6 polar molecules

The concept of electronegativity is helpful for describing polar atomic bonds. Scales such as those by Pauling or Mulliken allow the bond polarization to be recorded quantitatively. Polar covalent bonds are the prerequisite for hydrogen bonds, which shape the state diagram of water.

Mortimer: 8, 9.11
Binnewies: 5
Riedel: still missing

Electronegativity

HCl is formed in a clearly exothermic reaction during the chlorine oxyhydrogen reaction. In this clear implementation, in which 1 molecule of H2 and 1 molecule of Cl2 If 2 molecules of HCl arise, the energy released is equal to the difference between the bond dissociation energy of HCl and the mean value of the dissociation energies of hydrogen and chlorine molecules (see below). Why is the H – Cl bond unexpectedly strong? Obviously the same can be observed with water.

The properties of H2O and HCl, as well as those of its light analogue HF, cannot be interpreted by a simple atomic bond alone. For example, HCl has an extremely strong tendency to produce an H on other molecules+-Ion and thereby a ClIon (see below in the chapter "Acid-base reactions"). Furthermore, hydrogen fluoride, HF, is not a gas down to low temperatures, as would be expected due to its small molecular mass, but its boiling point is 19.5 ° C. This behavior becomes more plausible if one for the HF and HCl molecules polarization the atomic bond is assumed if the center of gravity of the binding electron pair would be shifted towards the fluorine or chlorine side. A common formulation for this issue uses the symbols δ + and δ− above the atomic symbol to indicate a charge that is a fraction of the elementary charge. But how big are δ + and δ−? Pauling introduced the first scale with values ​​for Electronegativity of atoms, in which the ability of an atom to attract the bonding pair of electrons of a covalent bond was expressed in numbers. Pauling had noticed one because of this polar bond has a higher bond dissociation energy between two atoms than expected (D.HCl = 428 kJ mol−1, ½ D.H2 + ½ D.Cl2 = 336 kJ mol−1). In the formulation

If the bond is stabilized by the electrostatic interaction between the partial charges, the greater the value of δ, the more so. The wording below describes the same state of affairs by two mesomeric limit formulaswhich - with different weights - contribute to the observed electron distribution.

From the stabilization of covalent bonds through dipole formation, Pauling derived an electronegativity scale that was originally normalized to 4.0 for the most electronegative element fluorine. In addition to the Pauling scale, other scales are in use, for example the Allred-Rochow scale, which is based on the charge density of the atomic core. Notice the trends in the periodic table.

Electronegativity (χ) of some elements according to Pauling (P) and Allred-Rochow (AR):

χ (P) χ (AR)
H 2,20 2,20
 
Li 0,98 0,97
Be 1,57 1,47
B. 2,04 2,01
C. 2,55 2,50
N 3,04 3,07
O 3,44 3,50
F. 3,98 4,10
No 4,84
 
N / A 0,93 1,01
Mg 1,31 1,23
Al 1,61 1,47
Si 1,90 1,74
P 2,19 2,06
S. 2,58 2,44
Cl 3,16 2,83
Ar 3,20
 
Br 2,96 2,74
I. 2,66 2,21

To estimate the polarity of a bond, consider the difference of χ of the two connected atoms. The center of gravity of the charge is shifted towards the more electronegative element in a polar bond. On the Pauling scale, an electronegativity difference of 2 corresponds to about 50% charge separation, that is, in the formula above

δ is about 0.5; Expressed using mesomeric limit formulas, a Δχ of 2 would correspond to an equal weighting of the two formulas below, the covalent and the ionic.

Since electronegativity is supposed to be a measure of the endeavor of an atom to withdraw electron density from a binding partner, that of Mulliken in particular appears to be immediately obvious among the widespread electronegativity scales. He defines EN values ​​as the mean value of 1st ionization energy I.1 and electron affinity EA, i.e. as the mean value of two energy values ​​that reflect the addition and removal of an electron.

Mulliken electronegativity, illustrated with the I.1- and EA-Values ​​of the atoms in the ground state (see text).

The figure relates to the orbital diagrams used above, but only shows the principle of the procedure. If the Mulliken electronegativity is to be used for the analysis of the bonding situation of a specific molecule, the χ is drawnMulliken-Values ​​for the individual atoms in their valence state (s / p-parts of the bonds), which often results in very different values ​​for one and the same element (that means for us at the moment only: do not overinterpret small differences in electronegativity!).

The dipole molecule water

The concept of the polar atomic bond describes HF as a dipole molecule (dipole moment = charge × distance between the charges). While the forces between non-polar molecules like H2, N2 and O2 are only small and these substances are gases with an extremely low boiling point, dipole molecules attract each other electrostatically after they have adopted the most favorable orientation to one another. Water is even more than HF the Dipole molecule par excellence. Like HF, water is also created in a strongly exothermic reaction from gaseous elements. The astonishingly high boiling point of 100 ° C for such a small molecule indicates that considerable intermolecular (intermolecular) forces exist between the H2O molecules have to act.

The water molecule shows itself to be angled in the methods of structure determination. With an electronegativity difference of approx. 1.3, each of the two H-O bonds is clearly polar. The two binding dipole moments add vectorially to the total moment.

Experiment 13-4: Water dipoles in an electric field

The angled structure of the water molecule can be seen directly from the Lewis formula, but not with the numerical value of 105 °. In the case of a bond of two hydrogen atoms via the two half-occupied p orbitals of an oxygen atom, a 90 ° angle should rather be expected. This leads to a more correct - semi-quantitative - statement VSEPR model (valence shell electron pair repulsion, Valence electron pair repulsion). In this simple model, all valence electron pairs are treated as equivalent, so no distinction is made between s and p orbitals. Expressed in terms of the VB model: complete hybridization of the valence orbitals is assumed, in this case sp3Hybridization.

A structure prediction is now made using a few simple rules. The most important: The electron pairs repelling each other move as far apart as possible in space. The four valence electron pairs on the oxygen atom should point to the corners of a tetrahedron. With this structure, the H-O-H angle initially results in a value of 109.5 °. The structural model is refined by a second rule: Lone electron pairs require more space than binding electron pairs. Thus the prediction for the H-O-H angle is 109.5 ° - x obtained, whereby the found 105 ° angle is not poorly approximated.

The structure of ice-IH

The ice IH-Structure shows tetrahedral environment around each oxygen atom. The structural analysis shows disordered hydrogen atoms along the O-O connecting lines, which reflect a spatially and / or temporally averaged situation:

The structure of ice1h (drawn in the space group P 63/mmc). The hydrogen atoms are “disordered”, which means that the probability of finding them on the bond to one of the four nearest O atoms is ½; note 4 × ½ = 2 corresponding to the 2 H atoms per O atom in water.

A real hydrogen atom distribution could look like the following picture (here the same as a moving picture):

The structure of ice1h. A “snapshot” of the real H atom distribution in the middle plane of the previous figure could look like this. By changing places along the "hydrogen bonds" marked in yellow, the H atoms are mobile.

Hydrogen bonds

The one in the ice-IH-Structure shown in yellow are hydrogen bonds. The tetrahedral environment of the oxygen atoms is a consequence of these bonds:

Hydrogen bonds are characterized by the following features: The positively polarized H atom of a Hydrogen bond donors (in the following picture: "hb donor") shows an interaction with a lone pair of electrons Hydrogen bond acceptors ("Hb-acceptor"). The resulting hydrogen bond is spatially directed like a covalent bond, but has a much smaller bond dissociation energy than this. Above all, the amount of energy depends on the environment. If the bond is isolated, the dissociation energy is smaller, if the bond is part of a system in series or cyclically connected O-H vectors, if the energy is greater, the hydrogen bond is then part of a system cooperative hydrogen bond system.

Due to the spatial alignment of the bonds, a rather small coordination number is realized in the ice structure; the structure is “airy” compared to tightly packed salt and metal structures. This has important consequences for the properties of ice and liquid water, which also determine the appearance of the phase diagram.

Experiment 13-1: density anomaly

Experiment 13-3: Pressure dependence of the melting point of ice

The density anomaly of the water in the pressure-temperature diagram. The triple point is 0.01 ° C and 0.006 × 105 Pa (normal pressure: 1.013 × 105 Pa), the critical point at 374 ° C and 220 × 105 Pa.

When ice melts, a liquid is created in which the gaps in the crystal structure are reduced on average. Despite this contraction, however, the structure of the ice remains a good model for the structure of liquid water. Above all, the principle of building a hydrogen bond system leads to the formulation of a Cluster model of water, in which larger groups of molecules (“clusters”) are organized according to the same rules as sections of the ice structure. An example of a component that is organized cooperatively is the shown four-part "homodrome" (in the same direction) cycle:

Strong hydrogen bonds

Especially when the hb acceptor and the hb donor without a hydrogen atom (soon: the conjugate base of the hb donor) are the same, strong hydrogen bonds are often found in which the distance between the donor and acceptor atom is smaller than usual . In the case of particularly strong bonds, the hydrogen atom is arranged symmetrically, so that no distinction between donor and acceptor is possible. In this case, the bond can be described by mesomeric boundary structures; one example is the HF2-Ion:

Compare a normal and a symmetrical, strong hydrogen bond: Instead of a donor-acceptor distance of 283 pm in Eis-IH is the F ··· F distance in the HF2 less than 230 pm.

A borderline situation arises when the hb acceptor has a higher binding capacity for the hydrogen atom than the hb donor. A proton then transfers to the acceptor, whereby the reaction product can be stable as a hydrogen-bonded pair:

The chapter “Acid-Base Reactions” is devoted to this situation.

The H2O molecule in the MO and VB models

In the case of the water molecule, the simple description with the help of the VSEPR model is successful: we assume four equivalent electron pairs which, in the language of the VB theory, have four sp3-Hybrid orbitals mean. The tetrahedral environment of the water molecule in the ice is quite informal.

How do further bonding theories see the water molecule? Because of the importance of the H2O-molecule we use this as an exercise object in order to apply the essential bonding models again. First the MO theory, in which 2e-3z bonds result for the triatomic water molecule in addition to a nonbonding interaction:

MO scheme for H2O; Charge on O according to Mulliken population analysis: −0.60 e (technical note: rmp2 / aug-cc-pvqz, averaged over α and β spins at O)

All occupied MOs contribute to the bond between O and H atoms except for the most energetic one, which is in a nonbonding arrangement to the H (1s) orbitals. The interaction between the two remaining oxygen p and the H (1s) orbitals leads to the bond, to which the O (2s) orbital obviously also contributes (note its stabilization and the deviation from the spherical shape that it would without H. Participation).

The MO energies are a bit irritating. Why is the nonbonding orbital more unstable than in the atom? To explain this, combine two results obtained so far: (1) Fluorine valence orbitals become significantly more unstable when the atom accepts an electron and becomes the fluoride ion, the F-Ion, will; (2) in the polar H.2O molecule, the O atom carries approximately the charge −½e.

If the s-p mixture is expressed as hybridization in the sense of the VB model, the calculation results in O-H bonds, to which the oxygen atom contributes two orbitals with a ¼ s portion. This numerical value corresponds to a sp3-Hybridization, if it is formulated with equivalent free electron pairs (2 × ¼ s-part in the bonds leave ½ s-part for both free e-pairs, so ¼ for each e-pair with equal distribution; an alternative view of the free e -Pairs will be at H2S discussed in Part B). It becomes clear that whenever the quantitative treatment leads to bonds with approx. 25% s character, the VSEPR model is in good shape, assuming complete s-p mixing (see also part B).

7 The ionic bond

The limit case of the polar atomic bond with a high electronegativity difference is the ionic bond. With the transfer of the binding electron pair to the more electronegative element, the spatial alignment of the bond is lost. Salt structures therefore show different construction principles than structures that result from covalent links or hydrogen bridges.

Mortimer: 7, 20
Binnewies: 4, 7
Riedel: still missing

The NaCl structure is a prototypical ion structure. The dense packing of the crystal building blocks stands out as a structural principle, in which each type of ion is octahedral surrounded by counterions:

The bond between the ions is largely electrostatic. The energetic situation is revealed through a particularly informative tool, a "circular process". Above all, the observation that ions with a noble gas configuration are formed when a salt is formed is shown in the right light.

Experiment 12-2: Synthesis of sodium chloride from the elements

Born-Haberscher cycle process

The formation of an ion crystal from the elements, which for the example NaCl with the energy balance

Na (s) + ½ Cl2(g) → NaCl (s) ΔHf0 = −411 kJ mol−1

expires, is broken down into sub-steps for the formulation of a cycle process. The following steps with the corresponding energies result for NaCl:

(a) The formation of individual Na atoms from solid sodium, the sublimation energy ΔHS.0,

(b) the formation of single Cl atoms from Cl2, the bond dissociation energy D.,

(c) the formation of a Na+-Ions by ionizing a Na atom, the 1st ionization energy, I.1,

(d) the formation of a Cl-Ions by adding an electron to a Cl atom, the electron affinity EA,

(e) in the last step, the formation of the ion crystal from Na+- and Cl-Ions that come together from infinite distance in the gas space to form a crystal. This process sets the lattice energy UG free.

The standard enthalpy of formation Δ given aboveHf0 is the sum of these individual steps:

ΔHf0 = ΔHS.0(Na) + ½ D.(Cl2) + I.1(Na) + EA(Cl) + UG

The numerical values ​​for NaCl (in kJ mol−1):

−411 = + 108 + 121 + 496 − 356 − 780

The energy balance shows that the formation of the noble gas configurations only requires energy: the process

Na (g) + Cl (g) → Na+(g) + Cl(G)

is namely the sum of the partial steps:

Na (g) → Na+(g) + e

and

Cl (g) + e → Cl(G)

The following results for the entire process:

ΔH0 = I.1 + EA = +496 + (−356) = +140 kJ mol−1

The formation of Na+- and ClIons from Na and Cl atoms are therefore endothermic. An important conclusion is that when the bond dissociation energy is supplied to NaCl, the ionic bond is split just like the covalent bond with the formation of atoms - the two important basic types of chemical bond behave the same when the bond dissociation energy is supplied, both will homolytic split.

The grid energy

The largest single amount in the cycle is the release of the lattice energy, i.e. the energy that is released when ions come together from an infinite distance to form an ion lattice. The lattice energy usually makes the greatest contribution to the strongly exothermic course of many formation reactions of ionically structured substances from the elements.

The first step in building an ion crystal is the formation of an ion pair Na+Cl. The energetic contribution of this first step to the grid energy can be calculated. When Na+- and Cl-Ions

• it sinks too r−1 proportional coulomb potential

UC, ion pair = z+ze2
4 π ε0r

gradually (dashed blue in the picture),

• a repulsive potential increases rapidly (shown in green in the picture; with NaCl it is proportional to approx. r−8), if the distance between the ions falls below a limit value below which the electron shells of the ions would penetrate each other to a greater extent:

The numerical value of the potential energy in the equilibrium distance (UG in the picture) is approximately determined by the Coulomb term alone (UC. in the picture). For Na+Cl (Nuclear distance in the ion pair = 238 pm) such a consideration gives −584 kJ mol−1. Compared to the lattice energy of −780 kJ mol−1 shows that the formation of the ion pair Na+Cl causes this amount to a large extent. The calculation explains the behavior of salts when evaporating or when dissolving in poorly solvating solvents - here there are no individual ions, but ion pairs or higher associations.

In a similar way to the Coulomb fraction UC. To be able to calculate the lattice energy, the environment of the ions has to be considered. For a na+-Ion in NaCl, this environment consists of:

6 cl at a distance d,

12 Well+ at a distance of √2 d,

8 cl at a distance of √3 d,

6 Well+ at a distance of √4 d = 2 d,

24 cl at a distance of √5 d, etc.

The Coulomb energy of the NaCl structure is the sum of the individual contributions, whereby the frequency of the distances must be taken into account; For r the corresponding distances are expressed as multiples of d inserted, the found distance between the ions (in the NaCl crystal 283 pm); z+ and z, the amounts of the ion charges (= 1 for NaCl) are given, since the relationship also applies to other compounds with this structure type; attractive energy contributions are used with a negative sign, repulsive ones positively. The following applies to 1 mol of salt:

UC. = − NA.z+ze2 (6 − 12/√2 + 8/√3 − 6/√4 + 24/√5 …)
4 π ε0r

The expression in brackets, the limit for an infinite number of summands, is the Madelung constantA.which only depends on the structure of the structure. The numerical value for the NaCl structure type is 1.7476. It indicates the factor by which the ion crystal is more stable than an imaginary ion pair in which the ion spacing is the same as in the crystal. The equation for UC. thus simplifies to:

UC. = − NA.A.z+ze2
4 π ε0r

The neglected repulsion term contributes about 10% to the lattice energy UC. estimated values ​​are too high in terms of amount. In the course of time, various approximation methods have been described in order to UG to be able to calculate more precisely. The Born-Landé formula is widespread:

UC. = − NA.A.z+ze2 (1 − 1/n)
4 π ε0r

A correction term 1 /n used, which depends on the electron configuration of the ions involved. It can have the following numerical values:

configuration example n
[Hey] H, Li+5
[Ne] O2−, F, N / A+, Mg2+7
[Ar], 3d10Cl, K+, Cu+9
[Kr], 4d10Br, Sr2+, Cd2+10
[Xe], 5d10I., Cs+, Ba2+12

For NaCl, the Born-Landé approximation results in with NA. = 6,022 ×1023 mol−1, A. = 1.7476 for NaCl, e = 1,602 × 10−19 C, n = 8 as the mean of 7 and 9, ε0 = 8,854 ×10−12 F m−1 = 8,854 ×10−12 C.2 J−1 m−1, 2.83 x 10−10 m ion distance in NaCl:

UBorn = − 6,022 ×1023 mol−1 × 1,7476 × (1,602 × 10−19 C)2 × (1 − 1/8) = 751 kJ mol−1
4 π 8.854 × 10−12 C.2 J−1 m−1 X 2.83 x 10−10 m

Lattice energies cannot be measured directly, but can be determined indirectly as state variables. The equation used in the cycle can be traced, for example UG dissolve; all other terms can be determined experimentally. Compare the value of −780 kJ mol obtained in this way−1 with the value of −751 kJ mol−1 according to the Born-Landé formula.

If different compounds of the same structure are considered, the consideration of the Coulomb component results in an increase in the lattice energy at

• an increase in the charge of the ions; compare well+Cl and Ba2+O2−:

NaCl (d = 283 pm), z+ = z = 1: UG = −780 kJ mol−1,

BaO (d = 276 pm), z+ = z = 2: UG = −3128 kJ mol−1,

It follows: UG(BaO) ≈ 4 UG(NaCl).

• a reduction in the distance between the ions; compare the lattice energy of BaO (d = 276 pm) with the value for MgO (d = 212 pm) of −3936 kJ mol−1.

Lattice energies are a measure of the strength of the bond in an ion crystal, therefore they are, for example, in the series NaCl, BaO, MgO with other physical properties such as the melting point (800, 1925, 2642 ° C) and the hardness (scratch hardness according to Mohs: 2.5; 3.3; 6) connected.

Dissociation in water

Experiment 12-3: NaCl solution conducts the current

The cryoscopic experiment had shown the dissociation of NaCl in water. The environment of the ions in the crystal is a model for the very similar environment in solution. When the salt dissolves, the ions are rearranged by water molecules in the same way as they had counterions as neighbors in the crystal. This is how NaCl works6-Fragment of the crystal into a [Na (H.2O)6]+-Ion in solution over. The sodium ion will hydrated (generally: solvated), it imagines Aqua complex, here the hexaaquasodium ion. The chloride counter-ions have been replaced by water dipoles, which attach themselves to the cations with their negative end and to the anions with their opposite side.

The strong analogy between ion crystal and solution is particularly noticeable in the energy balance. The one defined analogously to the lattice energy Enthalpy of hydration (the energy released during the hydration of 1 mol of ions) has approximately the same amount as the lattice energy. For NaCl (lattice energy −780 kJ mol−1) is the difference between the lattice energy and the enthalpy of hydration, the Enthalpy of solution, only 3.6 kJ mol−1.

Experiment 3-11: NH4NO3 dissolves endothermically

Experiment 12-8: CaCl2 dissolves exothermically, the hexahydrate endothermically

In the case of a salt such as sodium chloride that dissolves endothermically, the lattice energy is greater than the enthalpy of solvation. The question naturally arises here, why does NaCl even dissolve in water?

Entropy and free enthalpy

The approximation used so far: "Exothermic reactions take place voluntarily (at the latest after activation), endothermic reactions must be forced by constant supply of energy", only applies to reactions with strong warming (compare the standard enthalpy of formation of NaCl of −411 kJ mol−1 with the enthalpy of solution of +3.6 kJ mol−1!). However, the enthalpy of reaction is not decisive for the voluntary course of a chemical reaction, in this case the dissolution process. Rather, a chemical reaction takes place voluntarily (at the latest after activation) when the disorder of the universe (as the sum of the disorder of the system under consideration and the disorder of the environment) increases.

The Gibbs-Helmholtz relationship is used for a quantitative description:

ΔG = ΔHT ΔS.

ΔG is the change in another variable of the state of the system under consideration, the free enthalpy G. ΔG is linked to the change in disorder in space. An increase in the total entropy, the condition for a voluntary reaction, is accompanied by:

ΔG < 0

The Gibbs-Helmholtz relationship divides the entire change in entropy into two parts: the change in entropy in the environment, denoted by ΔH is linked (see above) and the change in entropy in the system under consideration, ΔS..

NaCl dissolves in water in spite of the endothermic course of the reaction, since due to a positive T ΔS.-Terms ΔG becomes negative. T ΔS. is positive if ΔS. is positive, i.e. when the entropy of the system increases. This is understandable for the dissolution of NaCl, since the ordered crystal lattice is destroyed and ions that move freely in the solution are generated.

ΔG, ΔH and T ΔS. have the following values ​​for some salts (in kJ mol−1):

ΔHT ΔS.ΔG
NaCl +3,6 +12,8 −9,2
AgF −20,3 −5,8 −14,5
NH4Cl +15,1 +21,8 −6,7
MgCl2−155,0 −29,0 −126,0

For silver fluoride, AgF, and magnesium chloride, MgCl2, result in negative T ΔS.