General Physical Chemistry II Lecture 13 Aleksey Kocherzhenko October 16, 2014"
Last time "
The Hückel method" Ø Used to study π systems of conjugated molecules" Ø π orbitals are treated separately from σ orbitals " (AOs contributing to σ and π MOs have a different symmetry)" Erich Hückel " Ø Consider σ bonds to be fixed and try to find energies of π bonding and antibonding orbitals " Ø Construct MOs as LCAOs using only orbitals that contribute to the π system" Ø Introduce MOs into TISE and reduce it to a system of secular equations for the coefficients in the LCAO expansion" Ø Solve the secular equations to find Hamiltonian eigenvalues (MO energies) and the relation between coefficients in the LCAO expansion of each MO" Ø Use normalization conditions to establish the final values for these coefficients"
How do molecules interact with each other?" Hi!"
Van der Waals interactions" Johannes van der Waals" Ø Attractive and repulsive interactions involving partial electric charges, electron clouds of polar and nonpolar molecules. " Ø Repulsive interactions due to exclusion of electrons from regions of space where the orbitals overlap (closed-shell species) "
Electric dipole moments" Electric dipole moment:" µ Q +Q Units:" 1D=3.335 10 30 C m Ø Polar molecules: permanent dipole moment" Ozone" Carbon dioxide" R µ = QR Dipole moments of some molecules" Ø Nonpolar molecules: no permanent dipole moment" The electric dipole moment of a molecule can be estimated by adding dipole moments of atomic groups that make up the molecule" Example: dichlorobenzene isomers" Add two C6H5Cl dipole moments (1.57 D) "
Calculating dipole moments of molecules" Adding dipole moments:" ~µ 1 ~µ 1 + ~µ 2 = ~µ 1 + ~µ 2 ~µ 2 Ozone" ~µ 1 2 + ~µ 2 2 +2 ~µ 1 ~µ 2 cos 1 2 Carbon dioxide" Know position and magnitude of partial charges à calculate dipole moment: " ~µ = ~e x µ x + ~e y µ y + ~e z µ z q µ = ~µ = µ 2 x + µ 2 y + µ 2 z µ x = X n Q n x n µ y = X n Q n y n µ z = X n Q n z n
Interactions between dipoles"
Dipole-dipole interactions in macroscopic systems" Ø The potential energy of dipole near another dipole depends on relative orientation " Ø In a macroscopic system the dipoles assume all possible orientations" on average, interaction is attractive" hv i = 2 3(4 " 0 ) 2 µ2 1µ 2 2 k B Tr 6 inversely proportional to temperature" interaction falls off quickly with distance " hv i/ 1 Ø Characteristically for van der Waals interactions, " r 6 Ø Increase in thermal motion overcomes mutual orientating effects of dipoles "
Induced dipole moment" Nonpolar molecule (no permanent dipole moment)" Interacts with external electric field (e.g., of charges in other molecules)" µ = E Electric field" Polarizability" Polarizability volume:" 0 = 4 " 0 correlates with HOMO-LUMO separation in atoms and molecules:" Ø LUMO close to HOMO à electron distribution easy to distort, large α " Ø LUMO high above HOMO à electron distribution difficult to distort, low α " charge redistribution, appearance of electric dipole" inversely proportional to ionization energy " anisotropic: depends on the orientation of the molecule with respect to the electric field "
Dipole induced dipole interactions" Ø A polar molecule with µ 1 can induce dipole moment in a polarizable molecule (polar or nonpolar) with α 2 " Ø The induced dipole is attracted to the permanent dipole of the first molecule" V = 1 µ2 1 2 " 0 r 6 V / 1 r 6 (Another example of van der Waals interactions)"
Induced dipole induced dipole interactions" London dispersion interaction:" Ø Interaction between nonpolar molecules due to transient dipoles that occur because of fluctuations in the instantaneous positions of electrons" (an instantaneous dipole on one molecule induces a dipole on another molecule, and the two dipoles then interact to lower the energy)" V = 2 3 0 1 0 2 r 6 I 1 I 2 I 1 + I 2 The potential energy of interaction increases with decreasing ionization energies" (Why?)" 1 / I 1 1, 2 / I 1 2
Hydrogen bonding" Coulomb interaction of partial positive charge on H (that is covalently bound to a strongly electronegative atom: N, O, or F) with a partial negative charge on a strongly electronegative atom in a different molecule:" A H + B ±12 " 19.6 kj/mol "
MO theory: Description of hydrogen bonding" A H + B Orbital for H-bond:" H bond = c 1 A + c 2 H + c 3 B Orbital on A that forms a bond with H" 1s orbital of H" Orbital on B that is occupied by a lone pair" Only the two lower orbitals are occupied à net lowering of energy compared to separate AH and B species (if A and B are N, O, or F)" If H bond is present, it dominates the other intermolecular interactions (~20 kj/mol) "
Lennard-Jones potential" To account for both attractive and repulsive forces that act between electron clouds and nuclei, Lennard-Jones proposed the following interaction potential (for non-ionic systems):" apple 12 6 V =4" r repulsive part" r attractive part" (only an approximation)" Sir John Lennard-Jones"
Summary of interactions"