College 2

σ- and π-molecular orbitals Fig (a) the constructive interference leading to the formation of a 2p  -bonding orbital and (b) the corresponding antibonding MO. Fig (a) The interference of 2p x - or 2p y - AO’s leading to the formation of a 2p  -bonding orbital and (b) the corresponding antibonding orbital. Note that for the  -orbitals the contribution to the binding energy of a molecule is relatively small

Hybridization and the Structure of Polyatomic Molecules Waarom hebben moleculen bepaalde vormen? H 2 O driehoek, NH 3 pyramide CH 4 tetrahedral, CO 2 linear? H 2 O O elektron configuratie: Dus een basis set van met 4 elektronen te verdelen over deze bindingen overlap elke H1s met een O2p, resulterend in 2 σ-bonds, met elk 2 e, dus: Maar: hoek van 90 o, in werkelijkheid 104 o …

Drie belangrijke soorten hybride orbitalen

Molecular orbital theory Molecules with extensive π-bonding systems, like benzene or for instance the photosynthetic pigments chlorophyll a, b-carotene, are not described very well by valence bond theory, because the π-electrons are often not localized in a single bond, but instead are delocalized over the whole molecule. Fig Bonding in ethylene. (a) In the plane of the nuclei: the formation of a  bond between the carbon atoms 1 and 2 using sp 2 hybrid orbitals and  -bonds between the 4 H 1s electrons and the remaining sp 2 orbitals on each C-atom. (b) Perpendicular to the plane of the 6 nuclei: formation of a  -bond between the two 2p- orbitals (that were not involved in the sp 2 - hybrids. Voorbeeld ethyleen Π Electronen houden het molekuul vlak!

Huckel theorie π electrons do not interact with one another, and so the many-electron wavefunction is just a product of one-electron molecular orbitals. Furthermore it assumes that the structure of the molecule is given by the σ-framework, plus some simplifications gives…. Fig Hückel molecular orbitals for ethylene. The carbon nuclei are represented by dots, and the nodal planes for the MO’s are represented by the dashed lines. Excitation energy is 2β (resonance integral) Highest occupied molecular orbital is called HOMO, the lowest unoccupied molecular orbital is called LUMO

Huckel voor 1,3 butadiene CH2=CHCH=CH2 C atomen: 3 sp 2 hybidide orbitalen h1, h2, h3 2 e - in 1s 3 e - in h1, h2, h3 1 e- over voor π orbitaal Voor alle 4 C atomen, dus 4e Fig Hückel molecular orbitals for 1.3-butadiene. The orbitals are viewed perpendicular to the plane of the molecule. The carbon nuclei are represented by dots, and the nodal planes for the MO’s are represented by the dashed lines. With each carbon atom contributing one electron the 1  and 2  orbitals are filled.

Vergelijk ethyleen met butadieen Als butadieen = 2 x ethyleen Dan bindingsenergie is 4α+4β, Maar door delocalisatie: 2(α β) + 2(α β)= 4 α β Verschil: β

Nog groter: benzeen In plaats van

Thymine electron configuration..

DNA base pairing A with T: adenine (A) always pairs with thymine (T) C with G: cytosine (C) always pairs guanine (G) This is consistent with there not being enough space (20 Å) for two purines to fit within the helix and too much space for two pyrimidines to get close enough to each other to form hydrogen bonds between them. But why not A with C and G with T? The answer: only with A & T and with C & G are there opportunities to establish hydrogen bonds (shown here as dotted lines) between them (two between A & T; three between C & G).hydrogen bonds These relationships are often called the rules of Watson-Crick base pairing, named after the two scientists who discovered their structural basis. The rules of base pairing tell us that if we can "read" the sequence of nucleotides on one strand of DNA, we can immediately deduce the complementary sequence on the other strand.

H-Bonds

Non-Covalent Interactions that determine 3-D structures of proteins, membranes… Fig The energy of interaction of two N 2 -molecules as a function of distance according to the Lennard-Jones potential. Note that the ordinate is in kelvins; the interaction energy has been divided by the Boltzmann constant. When two neutral molecules come close to one another (even when they are non-polar)….. Attraction ~ k B T

Charge-Charge and dipole-dipole interactions Molecules with charges, come close → interaction energy is given by Coulombs law, 1/r ‘long range interaction’ Potential energy (at 1 by 2) In water Coulomb interactions are reduced by a factor, which is the dielectric constant of water. (water molecules have a large permanent dipole which effectively screens the charges). In a protein environment, ion pairs with opposite charges may contribute significantly to the stabilization of a biomolecular structure. Of course on an atomic scale the concept of the dielectric constant becomes meaningless and one would have to calculate explicitly all the interactions between the charges.

Charge-Charge and dipole-dipole interactions Molecules with no net charges, also attract each other, when they have an asymmetric charge distribution, resulting in a dipole μ. μ1 μ2 interaction affects potential energy Fig (a) Attractive dipole-dipole interaction between two molecules. (b) repulsive counterpart of (a). If molecules are randomly oriented the average interaction energy is zero. But: attractive orientations are energetically more favorable

Charge-Charge and dipole-dipole interactions includes a weighting factor in the averaging that is equal to the probability that the molecules (dipoles) will adapt a certain orientation. This probability is given by the Boltzmann factor, with E interpreted as the potential energy of interaction of the two dipoles in that orientation. This implies that for every orientation f we have: with Als V<< KT, dan kunnen we dit ontwikkelen leidende tot turns out to be 2/3

Charge-Charge and dipole-dipole interactions Belangrijk: R 6, 1/T (greater thermal motion overcomes the mutual orientating effects of the dipoles at higher temperatures) Averaging only for ‘freely moving’ solvents In proteins a typical electrostatic calculation puts partial charges on all of the atoms (or groups of atoms) and simply solves the Poisson equation numerically

Van der Waals krachten non-charged, non-ionic molecules permanent dipole–permanent dipole forces √ permanent dipole–induced dipole forces instantaneous induced dipole-induced dipole

Van der Waals krachten non-charged, non-ionic molecules permanent dipole–induced dipole forces If molecule A has a dipole moment this creates an electric field which polarizes the charge distribution on molecule B → induced dipole moment μB = α = polarizability of molecule B. μ B is always oriented in the direction of the electric field created by μA and consequently the interaction is always attractive. A calculation of this interaction yields:

Van der Waals krachten non-charged, non-ionic molecules How do non-polar molecules form condensed phase??? For example, hydrogen or argon condensate to a liquid at low temperatures and benzene is a liquid at normal temperatures permanent dipole–permanent dipole forces √ permanent dipole–induced dipole forces √ instantaneous induced dipole-induced dipole

Van der Waals krachten non-charged, non-ionic molecules permanent dipole–permanent dipole forces √ permanent dipole–induced dipole forces √ instantaneous induced dipole-induced dipole Also in proteins Van der Waals forces and specifically the dispersion force, plays a major role in the formation of their stable and active conformation, in particular in stabilizing the hydrophobic core. Coupling of instantaneous fluctuations in the charge distribution on one molecule that gives it a dipole briefly; that dipole may induce another dipole in a neighbouring molecule, and these two dipoles will interact favorably.

The intermolecular potential energy At small distances the molecules repel strongly, (we try to push the electrons of one molecule into the non-bonding orbitals of the other, the bonding orbitals are occupied by electron pairs), ~R -n Fig Typical form of the Lennard Jones potential. The distance at which the minimum occurs would be two times the van der Waals radius of the molecules involved.

The hydrogen bond Fig A hydrogen bond between two water molecules. The strength of the interaction is maximal when the O-H covalent bond points directly along a lone-pair electron cloud of the oxygen atom to which its hydrogen bonded. In het algemeen: D—H · · · ·A The large electronegativity difference between H and O confers a 33% ionic character on the OH-bond as reflected by water’s dipole of 1.85 debye units. → highly polar molecule The electrostatic interactions between the dipoles of two water molecules tend to orient them such that the O-H bond on one molecule points towards a lone pair electron cloud on the oxygen atom of the other water molecule H-bond distances 0.5 Å shorter than van der Waals distance! Energy of the hydrogen bond, about 20kJmol -1 in H 2 O, is small compared to covalent bond energies (for instance 460 kJmol -1 for an O-H covalent bond)

The hydrophobic interaction Because these cage structures are more ordered than the surrounding water, their formation increases the free energy. This free energy cost is minimized, however, if the hydrophobic (or hydrophobic parts of amphipathic molecules) cluster together so that the smallest number of water molecules is affected.

The hydrophobic interaction in membranes

The hydrophobic interaction in proteins