Molecular bonding

Molecular Bonding and Spectra

• The Coulomb force is the only one to bind atoms.
• The combination of attractive and repulsive forces creates a stable molecular structure.

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• Force is related to potential energy F = −dV / dr, where r is the distance separation.

it is useful to look at molecular binding using potential energy V

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• Negative slope (dV / dr < 0) with repulsive force
• Positive slope (dV / dr > 0) with attractive force

Molecular Bonding and Spectra

• An approximation of the potential of one atom in the vicinity of another atom is

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where A and B are positive constants.

• Because of the complicated shielding effects of the various electron shells, n and m are not equal to 1.

• Eq. 10.1 provides a stable equilibrium for total energy E < 0. The shape of the curve depends on the parameters A, B, n, and m. �Also n > m.

Molecular Bonding and Spectra

• Vibrations are excited thermally, so the exact level of E depends on temperature.

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• Once a pair of atoms is joined, then:

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• One would have to supply energy to raise the total energy of the system to zero in order to separate the molecule into two neutral atoms.

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• The corresponding value of r at the minimum value is an equilibrium separation. The amount of energy to separate the two atoms completely is the binding energy which is roughly equal to the depth of the potential well.

Molecular Bonds

Ionic bonds:

• The simplest bonding mechanisms.
• Ex: Sodium (1s²2s²2p⁶3s¹) readily gives up its 3s electron to become Na⁺, while chlorine (1s²2s²2p⁶3s²3p⁵) readily gains an electron to become Cl⁻. That forms the NaCl molecule.

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Covalent bonds:

• The atoms are not as easily ionized.
• Ex: Diatomic molecules (H₂, N₂, O₂) formed by the combination of two identical atoms tend to be covalent. These are referred to as homopolar molecules.
• Larger molecules are formed with covalent bonds.

Molecular Bonds

Van der Waals bond:

• Weak bond found mostly in liquids and solids at low temperature
• Ex: In graphite, the van der Waals bond holds together adjacent sheets of carbon atoms. As a result, one layer of atoms slides over the next layer with little friction. The graphite in a pencil slides easily over paper.

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Hydrogen bond:

• Holds many organic molecules together

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Metallic bond:

• Free valence electrons may be shared by a number of atoms.

Ionic bonding NaCl

Potential energy of and

Covalent Bonding or homopolar bonding

Responsible for formation of stable diatomic molecules

Plots of wave function and of two electrons when they are apart

1. Spins anti-parallel

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• Spins parallel

Total potential energy versus r for two hydrogen atoms

Exchange energy and the Pauli exclusion principle

Four covalent bond of molecule: the hybrid (mixed) orbitals are represented by

Each C----H bond consists of an overlapping 1s orbital from hydrogen and an sp3 hybrid orbital from carbon. Theses orbitals have two lobes and only the longer ones are depicted.

Or other combinations by subtracting rather than adding the mixture of one 2s and three 2p orbitals to give four hybrids

Hybrid covalent bonds

Probability density

Van der Waals bonds

Dipole-dipole force

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Dipole-induced force

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Dispersion force

All types fall off with 1/r^6

The van der Waals forces for bonding arises when an electrically neutral

molecule has centers of positive and negative charge which do not coincide

Hydrogen bond

The two negative fluorine ions are bound by the positively charged proton between them

Very weak = bond energy 0.1 eV

A hydrogen atom attached to a relatively

electronegative atom is a hydrogen bond donor.

Hydrogen bond

The hydrogen bond (5 to 30 kJ/mole) is stronger than a van der Waals interaction, but weaker than covalent or ionic bonds.

This type of bond occurs in both inorganic molecules such as water and organic molecules like DNA and proteins.

(a) And (b): Formation of a sigma bond in from the overlap of the orbitals on adjacent N atoms. (c) Formation of a pi bond by overlap of the orbitals on adjacent N atoms. A similar bond is formed by overlap of the orbitals.

Bonding in complex molecules

Fermions versus bosons

Symmetry of Boson wave function

Requirements or symmetric and antisymmetric wavefunctions

Show that the wavefunction satisfies being symmetric and antismmetric

Bose-Einstein condensation in gases

Two horizontal axes represent velocity components in x and y

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Vertical axis represents number of atoms having those having velocities

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Field of view 200um by 270um

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2001 Nobel Prize

Wieman

Cornell

Ketterle

The transitions from a broad velocity distribution to an extremely narrow one signifies Bose-Einstein condensation

Rb, Na atoms

Bose-Einstein Condensation in Gases

• By the strong Coulomb interactions among gas particles it was difficult to obtain the low temperatures and high densities needed to produce the condensate. Finally success was achieved in 1995.
• First, they used laser cooling to cool their gas of ⁸⁷Rb atoms to about 1 mK. Then they used a magnetic trap to cool the gas to about 20 nK. In their magnetic trap they drove away atoms with higher speeds and further from the center. What remained was an extremely cold, dense cloud at about 170 nK.

Is Bose-Einstein condensation possible with stored ions in an RF -trap

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