9.8: Theory of orbital molecules (2023)

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    learning goals

    Make sure you fully understand the essential ideas below.

    • How is the molecular orbital model fundamentally different from the other chemical bonding models described in these lessons?
    • Explain how bonding and antibonding orbitals arise from atomic orbitals and how they differ physically.
    • Describe the main difference between aSigmait is apiMolekul Orbitals.
    • Definemandatory order, and give its meaning.
    • Construct a "molecular orbital diagram" of the type shown in this lesson for a simple diatomic molecule and indicate whether the molecule or its positive and negative ions need to be stable.

    The molecular orbital model is by far the most productive of the various chemical bonding models and serves as the basis for most quantitative calculations, including those that lead to many of the computer-generated images of these entities that you've seen elsewhere. In its full development, molecular orbital theory involves a lot of complicated math, but the basic ideas behind it are quite easy to understand, and that's all we're trying to achieve in this lesson.

    This is a big departure from the simpleLuisjVSEPRModels based on the orbitals of a center of individual atoms. the more sophisticatedhybridizationModell recognized that these orbitals are modified by their interaction with other atoms. but all thesevalence bondModels, as they are commonly called, are very limited in their applicability and predictive power because they fail to recognize that the distribution of clustered valence electrons is governed by the set of positive centers.

    molecular orbitals

    Chemical bonding occurs when the net attractive forces between an electron and two nuclei exceed the electrostatic repulsion between the two nuclei. To do this, the electron must be in a region of space that we callbinding region. Conversely, if the electron is on one side, on aanti-binding region, actually contributes to the repulsion between the two nuclei and helps to separate them.

    9.8: Theory of orbital molecules (2)

    The easiest way to imagine a molecular orbital is to first imagine two isolated atoms, each of which would have separate electron orbitals. These are just the orbitals of each atom that we already understand. Next, we'll try to predict how these atomic orbitals will interact as we gradually bring the two atoms closer together. Eventually, we will reach a point where the distance between the nuclei matches that of the molecule we are studying. The corresponding orbitals will then bemolecular orbitalsour new molecule.

    The ion of the hydrogen molecule: the simplest molecule

    To see how this works, let's consider the simplest possible molecule \(\ce{H2^{+}}\). This is the ion of the hydrogen molecule, which consists of two nuclei with a +1 charge and a single electron shared between them.

    9.8: Theory of orbital molecules (3)

    If two H nuclei move towards each other, the 1SThe atomic orbitals of the isolated atoms gradually merge into a new molecular orbital where the highest electron density is between the two nuclei. Since this is precisely the place where the electrons can simultaneously exert the greatest attraction on the two nuclei, this arrangement represents abonding molecular orbital. If we look at it as a three-dimensional region of space, we see that it is symmetric about the centerline between the nuclei; In keeping with our usual nomenclature, we refer to this as aOrbital σ (Sigma).

    Bonding and antibonding molecular orbitals

    There is a small difficulty: we start with two orbitals (1Satomic orbitals) and ended up with just one orbital. Well, by the rules of quantum mechanics, orbitals can't just pop in and out of existence at will. On the one hand, this would raise the question: What nuclear spacing are we suddenly changing from two orbitals to just one? It turns out that when the orbitals interact, they are free to change shape, but there must always be the same number. This is just another way of saying that there must always be the same number of possible allowable sets of electron quantum numbers.

    How can we find the missing orbital? To answer this question, we must return to the wave character of orbitals, which we developed in our earlier treatment of the hydrogen atom. You probably know that wave phenomena such as sound waves, light waves or even ocean waves can combine or interact with each other in two ways: they can reinforce each other, resulting in a stronger wave, or they can interfere and partially destroy each other. . Something more or less similar occurs when the "matter waves" correspond to the two separated hydrogenSorbitals interact; Both in-phase and out-of-phase combinations are possible, and both occur. The phased reinforcement interaction creates thebond orbitalthat we just saw. The other, corresponding to the out-of-phase combination of the two orbitals, results in a molecular orbital that has its highest probability of electrons in the clearly antibonding region of space. Therefore, this second orbital is calledanti bondorbital.

    9.8: Theory of orbital molecules (4)

    When the two 1SWave functions combine out of phase, regions with a high probability of electrons do not merge. In fact, the orbitals behave as if they are repelling each other. In particular, note that there is a region of space exactly equidistant between the nuclei where the probability of finding the electron is zero. This region is callednot superficial, and is characteristic of antibonding orbitals. It should be clear that no electrons in an antibonding orbital are likely to contribute to bond formation; In fact, they will actively resist it.

    So we see that whenever two orbitals, originally on separate atoms, start to interact, as we push the two nuclei towards each other, those two atomic orbitals gradually merge into a pair of molecular orbitals, one of which has character. Link while the other will be Anti-Link. In a more advanced treatment, it would be quite easy to show that this result follows naturally from the wave nature of the combined orbitals.

    What is the difference between these two types of orbitals in terms of their potential energies? More specifically, what kind of orbital would allow an electron to have a lower potential energy? Potential energy clearly decreases as the electron moves into a range that allows it to "see" the maximum amount of positive charge. In a simple diatomic molecule, it is in the region between the nuclei that the electron can be in the vicinity of two nuclei at the same time. Therefore, the bonding orbital has the lowest potential energy.

    (Video) 9.8 Bonding inPeriod 2 Diatomic Orbitals - Part 1

    molecular orbital diagrams

    This scheme of bonding and antibonding orbitals is usually represented by a molecular orbital diagram like the one shown here.Diwasserstoffion H2+. Atomic valence electrons (shown in boxes on the left and right) fill lower-energy molecular orbitals before higher-energy ones, just like atomic orbitals. Therefore, in this simplest of all molecules, the single electron enters the bonding orbital, leaving the antibonding orbital empty.

    9.8: Theory of orbital molecules (5)

    Since each orbital can hold a maximum of two electrons, the bonding orbital in H2+it's only half full. However, that single electron is enough to reduce the potential energy of a mole of hydrogen nuclei pairs by 270 kJ, enough for them to stick together and behave as a separate molecular species. although H2+Stable in this energetic sense, it turns out to be an extremely reactive molecule, so much so that it even reacts with itself, so these ions are not common in everyday chemistry.


    If one electron in the bonding orbital leads to bonding, could two electrons be even better? We can fix this by combining two hydrogen atoms, two nuclei and two electrons. Both electrons enter the bonding orbital as shown in the figure.

    9.8: Theory of orbital molecules (6)

    Recall that one electron reduced the potential energy of the two nuclei by 270 kJ/mol, so we can expect two electrons to produce twice as much stabilization, or 540 kJ/mol.

    (Video) 9.8-LCAO Antibonding Orbitals

    9.8: Theory of orbital molecules (7)

    mandatory orderIt is defined as the difference between the number of pairs of electrons occupying bonding and non-bonding orbitals in the molecule. A unit connection order corresponds to a conventional "single connection".

    Experimentally, it has been found that only 452 kJ are needed to split one mole of hydrogen molecules. The reason why the potential energy was not completely reduced is that the presence of two electrons in the same orbital causes repulsion, which counteracts the stabilization. This is exactly the same effect we saw when comparing the ionization energies of hydrogen and helium atoms.


    We're still ahead with two electrons, so let's try three. The positive dihelium ion is a three-electron molecule. We can imagine that it contains two helium nuclei and three electrons. This molecule is stable, but not as stable as dihydrogen; the energy needed to break He2+ is 301 kJ/mol. The reason for this should be obvious; two electrons are placed in the bonding orbital, but the third electron has to go to the next higher slot, which is the sigma antibonding orbital. As we have seen, the presence of an electron in this orbital results in a repulsive component that neutralizes and partially cancels the attractive effect of the filled ligand orbital.

    9.8: Theory of orbital molecules (8)

    If we take our construction process one step further, we can see the possibilities of joining helium atoms together to form dihelium. Now you should be able to predict that He2it cannot be a stable molecule; The reason, of course, is that we now have four electrons: two in the bonding orbital and two in the antibonding orbital. The orbital almost exactly cancels the effect of the other. Experimentally, the binding energy of dihelium is only 0.084 kJ/mol; This is insufficient to hold the two atoms together in the presence of random thermal motion at normal temperatures, so dihelium dissociates as quickly as it forms and is therefore not a chemical species in its own right.

    Diatomic molecules containing second-tier atoms

    The four simplest molecules we've studied so far involve molecular orbitals made up of two 1Satomic orbitals. If we want to extend our model to larger atoms, we also have to deal with larger atomic orbitals. A very simplifying principle is that only thevalence shellOrbitals must be considered. Inner atomic orbitals like 1Sthey are at the bottom of the atom and well shielded from the electric field of a neighboring nucleus, so these orbitals largely retain their atomic character when forming bonds.


    For example, in the case of lithium, whose configuration is 1S22S1merges with itself to form Li2, 1 we can forgetSatomic orbitals and consider only bonding and antibonding σ orbitals. Since there are not enough electrons to fill the antibonding orbital, the attractive forces win out and we have a stable molecule.

    9.8: Theory of orbital molecules (9)

    The binding energy of dilithium is 110 kJ/mol; Note that this value is less than half the binding energy of 270 kJ in dihydrogen, which also has two electrons in a bonding orbital. The reason is, of course, the 2SLi's orbital is much farther from its nucleus than 1SH orbital, and this applies equally to the corresponding molecular orbitals. Therefore, it is generally true that the larger the starting atom, the less stable the corresponding diatomic molecule is.

    lithium hydride

    All the molecules we have considered so far arehomonuclear; They consist of one type of atom. As an example ofheteronuclearLet's look at a very simple example: lithium hydride. Lithium hydride is a stable, although very reactive, molecule. The diagram shows how the molecular orbitals of lithium hydride can be related to the atomic orbitals of the parent atoms. One thing that makes this diagram different from the ones we've seen before is that the main atomic orbitals have very different energies; increasing the nuclear charge of lithium reduces the energy of its 1stSorbital to a value well below 1Shydrogen orbitals.

    9.8: Theory of orbital molecules (10)

    The lithium atom has two occupied atomic orbitals, while the hydrogen atom has only one. Which of the lithium orbitals does hydrogen 1 behave with?Sorbital interaction? lithium 1SOrbital is the lowest energy orbital on the graph. Because this orbital is so small and holds its electrons so tightly, it does not contribute to bonding; we only need the 2SLithium orbital combined with 1SHydrogen orbital to form the usual pair of bonding and antibonding sigma orbitals. Of the four electrons in lithium and hydrogen, two are retained in lithium 1Sorbital, and the remaining two are in the σ orbital that forms the Li-H covalent bond.

    The resulting molecule is 243 kJ/mol more stable than the original atoms. As expected, the binding energy of the heteronuclear molecule is very close to the average of the energies of the corresponding homonuclear molecules. In fact, the correct way to make this comparison is to use the geometric mean rather than the arithmetic mean of the two binding energies. The geometric mean is simply the square root of the product of the two energies.

    9.8: Theory of orbital molecules (11)

    The geometric mean of the H2doctor2The binding energy is 213 kJ/mol, so the lithium hydride molecule appears to be 30 kJ/mol more stable than was "thought". This is attributed to the fact that the electrons in the 2σ bonding orbital are not evenly distributed between the two nuclei; The orbital is slightly crooked, so the electrons are pulled a little closer to the hydrogen atom. Oconnect polarity, which we considered in detail at the beginning of our study of covalent bonds, stems from the greater electron-withdrawing power of hydrogen, a consequence of the very small size of this atom. Electrons can have a lower potential energy if they are slightly closer to the hydrogen end of the lithium hydride molecule. However, it is worth noting that the electrons are also closer to the lithium nucleus on average than in the 2ndSLithium atom orbital isolated. So it seems that here everyone wins and no one loses!

    (Video) 9.8 Lecture Video Second Row Diatomic Molecules

    Orbitais \(\Sigma\) e \(\pi\)

    The molecules considered so far consist of atoms that each have no more than four electrons; our molecular orbitals were therefore derivedSJust enter atomic orbitals. If we want to apply our model to molecules with larger atoms, we need to look carefully at howPage- Type orbitals also interact. although two atomsPageIf orbitals are expected to split into bonding and antibonding orbitals as before, the extent of that splitting, and therefore the relative energies of the resulting molecular orbitals, turns out to depend largely on the nature of the particular particle.Pageorbital involved.

    You will remember that there are three optionsPageOrbitals for each value of the principal quantum number. You have to think about it tooPageOrbitals are not sphericalSorbitals, but they are elongated and therefore have specific directional properties. ThreePageOrbitals correspond to the three directions of Cartesian space and are often referred to asPagex,Pj, jPagezto specify the axis along which the orbital is oriented. Of course, in the free atom, where no coordinate system is defined, all directions are equivalent, as are directions.PageOrbitals However, when the atom is close to another atom, the electric field acts as a reference point, due to that other atom, which defines a set of directions. The line of centers between the two nuclei is usually taken asxAxle. If this direction is plotted horizontally on a piece of paper, then thejThe axis is in the vertical direction and thezthe axis would be normal to the side.

    9.8: Theory of orbital molecules (12)

    These directional differences lead to the formation of two different classes of molecular orbitals. The figure above shows how twoPagexatomic orbitals interact. In many ways, the resulting molecular orbitals are similar to what we got back then.Scombined atomic orbitals; The bonding orbital has a high electron density in the region between the two nuclei and therefore corresponds to the lowest potential energy. In combination with phase shift, most of the electron density is outside the core region, and yet there is an area right in the middle between the nuclei that corresponds to zero electron density. This is clearly aOrbital antienlace—again in general, similar to what we've seen with hydrogen and similar molecules. as derivatives ofS-atomic orbitals, these molecular orbitals are σ (Sigma) Orbital.

    Sigmaorbitals are cylindrically symmetric about the centerline of nuclei; This means that if you could look down this line of centers, the electron density would be the same in all directions.

    9.8: Theory of orbital molecules (13)

    Orbitals, we get the expected bonding and antibonding pairs, but the resulting molecular orbitals have a different symmetry: instead of being rotationally symmetric about the center line, these orbitals extend in both directions perpendicular to that center line. Orbitals with this more complicated symmetry are called π (pi) orbitals. There are two of them, πjsim pzthey differ only in orientation, but are completely equivalent.

    (Video) 9.8 Bonding in Period 2 Diatomic Molecules - Part 2

    The different geometric properties of the π and σ orbitals cause the latter orbitals to share more than the π orbitals, so the antibonding σ* orbital always has the highest energy. The σ bonding orbital can be larger or smaller than the π bonding orbitals, depending on the atom.

    Second-line diatoms

    If we combine the distribution schemes for the 2Se 2PageOrbitals allow us to predict the bond order in all diatomic molecules and ions composed of elements from the first complete row of the periodic table. just remembervalenzorbitalof atoms are taken into account; As we saw in the case of lithium and dilithium hydride, the inner orbitals remain tightly bound and retain their localized atomic character.


    Carbon has four electrons in the outer shell, two 2Sand two 2Page. With two carbon atoms we have a total of eight electrons that can be placed in the first four molecular orbitals. The two lowest are the 2.Sbonding and antibonding pair derived so that the "first" four electrons do not contribute to bonding. The other four electrons go to the pair ofpibonding orbitals, and there are no more electrons for the antibonding orbitals, so we would expect the dicarbon molecule to be stable, which it is. (But since it is extremely reactive, it is only known in the gas phase.)

    9.8: Theory of orbital molecules (14)

    You will recall that a shared pair of electrons between two atoms constitutes a "unique" chemical bond; this is the original Lewis definition of the covalent bond. Inc.2there are two pairs of electrons in the π bond orbitals, so here we have a double bond; in other words, the bond order in the dicarbon is two.


    The electronic configuration of oxygen is 1.S22S22Page4. I am2Therefore, we need to insert twelve valence electrons (six from each oxygen atom) into molecular orbitals. As you can see in the diagram, this places two electrons in antibonding orbitals. Each of these electrons occupies a separate π* orbital, as this leads to less electron-electron repulsion (Hund's rule).

    The binding energy of molecular oxygen is 498 kJ/mol. This is less than the 945 kJ binding energy of N2— not surprising, considering that oxygen has two electrons in an antibonding orbital compared to one for nitrogen.

    9.8: Theory of orbital molecules (15)

    The two unpaired electrons in the dioxygen molecule give this substance an unusual and distinctive property: O2esparamagnetismoC. The paramagnetism of oxygen is easily demonstrated by pouring liquid into it.2between the poles of a strong permanent magnet; The liquid flow is trapped by the field and fills the space between the poles.

    Since molecular oxygen contains two electrons in an antibonding orbital, it may be possible to make the molecule more stable by removing one of these electrons, thereby increasing the binding ratio to antibonding electrons in the molecule. As expected and according to our model,2+has higher binding energy than neutral dioxygen; Removing an electron actually gives us a more stable molecule. This is a very good test of our model of bonding and antibonding orbitals. Likewise, an electron is added to O2leads to a weakening of the bond, as shown by the lower binding energy of O2. The binding energy in this ion is not known, but the bond length is longer and this indicates a lower binding energy. By the way, these two dioxygen ions are very reactive and can only be observed in the gaseous phase.

    (Video) 9.7 Molecular Orbital Theory


    How many electrons can each molecular orbital contain maximum of ___? ›

    This means that each molecular orbital can accommodate a maximum of two electrons with opposite spins.

    What does viable molecule mean? ›

    According to the molecular orbital theory, a molecular is viable of its bond order is more than or equal to one. The bond order is defined as number of bond between to two atoms of that molecule. It is calculated as the difference of electrons in bonding molecules and anti-bonding molecules whole divided by two.

    How do you fill molecular orbital theory? ›

    1. Find the valence electron configuration of each atom in the molecule. ...
    2. Decide if the molecule is homonuclear of heteronuclear. ...
    3. Fill molecular orbitals using energy and bonding properties of the overlapping atomic orbitals. ...
    4. Use the diagram to predict properties of the molecule.
    Jun 5, 2019

    How many pi bonds are in a B2 molecule? ›

    B2 has 1π bond, according to M.O.T.

    What is the maximum number of electrons which can orbit in any shell? ›

    No known element has more than 32 electrons in any one shell. This is because the subshells are filled according to the Aufbau principle. The first elements to have more than 32 electrons in one shell would belong to the g-block of period 8 of the periodic table.

    What is the maximum number of orbital? ›

    Maximum number of orbitals identified by the given quantum no. is only one i.e 3pz. Q.

    How do you know if a molecular orbital is stable? ›

    You need to mix the orbitals, populate them with the electrons and see if you have net bonding. Eg: H + H two 1s orbitals mix to form sigma and sigma*. Two electrons total, both occupy the sigma orbital, two more electrons in bonding than antibonding orbitals, the compound is stable.

    Which is not a viable molecule? ›

    Zero bond order indicates not a viable molecule. Bond order of H2-2=Nb-Na2=2-22=0. Hence, H2-2 does not exist, due to zero bond order.

    What does most viable solution mean? ›

    1. [more viable; most viable] a : capable of being done or used : workable. a viable solution to the problem.

    Which molecular orbital theory is the most stable? ›

    Energy-Level Diagrams

    A bonding molecular orbital is always lower in energy (more stable) than the component atomic orbitals, whereas an antibonding molecular orbital is always higher in energy (less stable).

    What is the orbital filling rule? ›

    Remember that we have three rules that determine how electrons fill atomic orbitals. The Aufbau Principle: Electrons fill the lowest energy orbitals first. Hund's Rule: Atomic orbitals maximize the number of electrons with the same spin. The Pauli Exclusion Principle: Electrons will pair with opposite spins.

    How many electrons are required to fill a molecular orbital? ›

    It takes four-electron to fill the molecular orbital, two from each 2p atomic orbital. It takes two electrons to form a sigma anti-bonding molecular orbital. It takes 4 electrons to form the molecular orbital from the combination of the two 2s atomic orbitals.

    Why does C2 not exist? ›

    We have 4 electrons in bonding and 0 in antibonding for C2So putting in formula-B. O. =(4−0)/2=2As the bond order is 2, the molecule cannot exist.

    Is C2 exist? ›

    Diatomic carbon (systematically named dicarbon and 1λ2,2λ2-ethene), is a green, gaseous inorganic chemical with the chemical formula C=C (also written [C2] or C2). It is kinetically unstable at ambient temperature and pressure, being removed through autopolymerisation.

    Can a molecule have 3 pi bonds? ›

    Each of these atomic orbitals has an electron density of zero at a shared nodal plane that passes through the two bonded nuclei. This plane also is a nodal plane for the molecular orbital of the pi bond. Pi bonds can form in double and triple bonds but do not form in single bonds in most cases.

    What is the 2 8 8 18 rule in chemistry? ›

    It is an arrangement of electrons in various shells, sub-shells and orbitals in an atom. It is written as 2, 8, 8, 18, 18, 32. It is written as nlx ( where n indicates the principal quantum number), l indicates the azimuthal quantum number or sub-shell, and x is the number of electrons.

    Why are there only 8 electrons in the outer shell? ›

    In general, atoms are most stable, least reactive, when their outermost electron shell is full. Most of the elements important in biology need eight electrons in their outermost shell in order to be stable, and this rule of thumb is known as the octet rule.

    Why does the third shell have 8 electrons? ›

    The third period contains only eight elements even though the electron capacity of the third shell is 18 because when the other shells get filled and the resultant number of electrons becomes eighteen, it gets added up and settles in the third electron shell and three shells are acquired by the fourth period.

    What can molecular orbitals contain a maximum of? ›

    Each molecular orbital can accommodate a maximum of two electrons with opposite spins.

    What is the maximum number of electrons in an orbital quizlet? ›

    Each electron shell or orbit can hold a certain number of electrons. The first shell from the nucleus can have a maximum of 2 electrons. The second shell can hold up to eight electrons, whereas the third shell can have a maximum of 18 electrons.

    Can maximum of two electrons occupy each orbital? ›

    Pauli exclusion principle – states that a maximum of two electrons can occupy a single atomic orbital but only if the electrons have opposite spins.

    What is the maximum number of electrons that can be in an atomic orbital quizlet? ›

    How many electrons can each orbital hold? Each orbital is capable of holding a maximum of 2 electrons. Orbitals can be divided into s, p, d, and f types.


    1. Ch 9 and Ch 12 MOT overview pt.1 (9.7-9.8)
    2. Orbital Overlap Diagram for CH2O (methanal, formaldehyde)
    3. 9.7 Molecular Orbitals
    (Chemistry - Ohio State - Loza)
    4. Ch 9 Molecular Orbital Theory
    5. Chapter 9 - Molecular Geometry and Bonding Theories
    (Pablo Gonzalez)
    6. Module 6 Overview of Polyatomic States
    (John Frederick)


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