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Quantum Numbers/Electron Configurations Quantum Numbers/Electron Configurations The Schrodinger equation, which was shown in class, is a wave function and the solutions to this function provide information about the probability of finding electrons in a particular space. Each electron in an atom can be uniquely described using four quantum numbers: Principle quantum number (n): This number describes the most probable distance from the nucleus and thus the size of the orbital. Because electrons farther from the nucleus also have higher energy, this number describes the overall energy of an electron. Each value of n (integers 1,2,…) refers to a shell of electrons. Angular momentum quantum number (l): This number describes the shape of an orbital and the value ranges from 0,1,…(n-1). These are referred to as subshells. l value Subshell Number of Orbitals 0 s 1 1 p 3 2 d 5 3 f 7 Magnetic quantum number (ml): This number describes the orientation of an orbital in space. It ranges from –l to l. For s orbitals, a sphere only has one orientation, but for p orbitals, there are three orbitals and they have three orientations px, py, pz which are oriented along the 3 perpendicular axes. Spin quantum number (ms): It represents the spin of an electron and can only take one of two values: up or down. Valence Electrons/Octets/Bonding You’ve learned how to assign electrons to the different subshells to obtain the atomic configuration for a particular atom. We are particularly interested in the electrons contained in the outermost shell. These outermost electrons are called valence electrons and they are the only electrons that participate in bonding. Examples: Element Configuration Valence Electrons Lithium 1s22s1 1 Magnesium 1s22s22p63s2 2 Carbon 1s22s22p2 4 Silicon 1s22s22p63s23p2 4 Nitrogen 1s22s22p3 5 Oxygen 1s22s22p4 6 Sulfur 1s22s22p63s23p4 6 Fluorine 1s22s22p5 7 You can notice from the table below that for main group elements (groups 1,2, 13-18) the number of valence electrons corresponds to the group (column number or (column number – 10) for columns 13-18) on the periodic table. Transition metals are harder to predict so often you must actually write out the electron configuration. Since valence electrons are the only electrons involved in bonding, they are largely responsible for the different properties of atoms and thus you can use the columns of the periodic table to predict properties. Elements tend to form bonds in order to form a closed shell, meaning all orbitals in that particular shell have the maximum two electrons. So for main group elements, this corresponds to achieving s2p6 in the outermost shell. This is often called the octet rule because the bonded atoms prefer to have eight valence electrons either through sharing or giving/taking. Group 1 and Group 2 metals have only one or two valence electrons respectively, thus they are most likely to lose electrons and form cations. Na Na+ e- Mg Mg2+ 2e- Group 7 elements have seven valence electrons and thus only need one to fill their octet. They can gain this electron either through removing it from another atom to form an ionic bond or through sharing with another atom to form covalent bonds. F e- F- F H H F Lewis Structures/Formal Charge The number of valence electrons tells you the number of bonds an atom prefers to form. For example, carbon has 4 valence electrons and will form 4 bonds while nitrogen has 5 valence electrons and prefers to form 3 bonds. This does not mean that nitrogen cannot form more than three bonds, but if it does, it will be charged. When nitrogen has four bonds, it has 8 valence electrons which is good, but it is sharing all eight in bonds, so it really only has four to itself. Since it normally has 5, it is one electron short and thus has a positive charge. This can be calculated through finding the formal charge which is basically finding the difference between the expected number of valence electrons in an isolated atom and the number of electrons it actually has when it is within a compound either through lone pairs or covalent bonds. Each covalent bond contains two shared electrons, but for formal charge calculations, an atom is considered to have “possession” of one per bond. Examples + - H2O H O HO 3 H o H H o H H o H + - NH3 NH NH 4 2 H H N H N H N H H H H H Formal charge = #valence electrons – (number of lone pair electrons + #bonds Electronegativity Above, we have been considering bonding as either purely ionic (electrons lost or gained) or purely covalent (electrons shared), but in reality bonding falls on a spectrum with many bonds having unequal sharing of electrons. This is due to differences in electronegativity which can be thought of as a measure of the atom’s ability to pull electrons towards it. When one atom in a bond is much more electronegative than the other, it can pull the electrons closer to its nucleus, thus concentrating a bit more of the negative charge on itself. These bonds are considered polar and they result in one atom having a partial negative charge and the other (the less electronegative) having a partial positive charge (indicated by a δ- or δ+. Bonding Spectrum Ionic Polar Covalent Nonpolar Covalent + δ- Na+ F- δH F F F Electronegativity 0.9 4.0 2.1 4.0 4.0 4.0 Values Molecular Orbital Theory When two atoms come together to form a bond, the orbitals containing the electrons involved in bonding must begin to overlap to form an orbital that is shared by both atoms. This combined orbital is called a molecular orbital because it belongs to the entire molecule rather than a specific atom and just like an atomic orbital, it describes the volume of space where an electron is likely to be found. Bonding must be energetically favorable, otherwise it would not occur. Thus bonding molecular orbitals are lower in energy than the individual atomic orbitals that form them. Intuitively this makes sense as when two atoms are far apart there is no interaction between their nuclei, but as they approach, the positively charged nuclei attract the negatively charged electrons of the other atom. At some distance though, the repulsion of the nuclei of the two atoms will begin to outweigh the attraction to the electrons and moving the nuclei any closer together is energetically unfavorable. This is what determines the atomic distances in bond length. The diagram below shows this effect. Remember that electrons behave like a standing wave (see image of sinusoidal wave), so atomic orbitals have phases and nodes. For each shell, there is a single s orbital which is spherical in shape. Shells with number two and above have three identical p orbitals oriented at 90 angles to each other. With a standing wave, you have both upward and downward displacement which are the two phases. The the region with no displacement is called the node. Atomic orbitals also have phases and nodes and it is easiest to visualize this with p orbitals. In the image above, the colors represent the two phases and there is a nodal plane between the two lobes where there is zero probability of finding an electron. When two waves combine, they can combine in a constructive, additive manner or a destructive manner and atomic orbitals are the same way. When two atomic orbitals overlap to form a bond, you get two separate molecular orbitals because the atomic orbitals combine either in an additive or destructive manner. If they combine such that the in-phase ends overlap (additive), this generates a bonding molecular orbital. If they combine in the opposite way (destructive), you get an antibonding molecular orbital. The following diagram demonstrates this with two p orbitals. Orbitals can overlap to form two different types of bonds: sigma and pi Sigma Bonds Sigma bonds are cylindrically symmetrical which just means that electrons are symmetrically distributed around the bond, or around an imaginary line connecting the centers of the two atoms. The overlap of two s orbitals always results in a sigma bond while two p orbitals can give sigma bonds when they overlap end-to-end (as shown in the figure above). As was mentioned above, you always generate two molecular orbitals when you combine two atomic orbitals which in this case are denoted as σ and σ*. • The σ orbital is the bonding molecular orbital and is lower in energy than either of the p or s orbitals that combined to form it. • The σ* is the antibonding orbital and it is higher in energy than either of the atomic orbitals. The σ* orbital has a node between the two nuclei meaning the electrons are more likely to be found somewhere other than between the two nuclei. This means that the two nuclei can repel each other because the positive nuclear charge isn’t mediated by the negative charge of the electrons. This repulsion explains why this is a higher energy orbital. Much like with atomic orbitals, you always fill the lowest energy molecular orbital first which in this case is always σ. Any electrons in the σ* orbital actually detract from bonding because they are in a higher energy state than they would be if they were in the original s or p atomic orbital. The diagram below just shows the molecular orbital diagram for bonding two H atoms. The two s orbitals from H overlap to give a σ and σ* where the σ is lower in energy and σ* is higher.
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