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Molecular Orbital Theory 16 February, 2016 Dr. Emőke Bódis The Wave Mechanical Model of the Atom Some small history 1859: Black body radiation (a problem by Kirchoff) 1877: Boltzmann suggested that the energy states of a physical system can be discrete 1887: Problem of photoelectric effect 1900: Quanrum hypothesis by Max Planck: Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" (or energy elements) precisely matched the observed patterns of black-body radiation. E = hf 1905: Einstein offered a quantum-based theory to explain the photoelectric effect Rutherford Atomic Model (Sir E. Rutherford, 1911): Gold foil experiment: he shot a thin film of gold atoms high velocity alpha particles (helium nuclei). As expected, most alpha particles went right through the gold foil but to his amazement a few alpha particles rebounded almost directly backwards. He developed the planetary model of the atom. Bohr Atomic Model (Nils Bohr, 1913): 1. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. 2. An electron may jump spontaneously from one orbit to the other orbit, ∆E = E2-E1 = hv 3. The motion of an electron in a circular orbit is restricted in such a manner that its angular momentum is an integral multiple of h/2π, Thus mvr = nh/2π. The Wave Mechanical Model of the Atom Planck Boltzmann Heisenberg Einstein Schrödinger de Broglie The Wave Mechanical Model of the Atom Heisenberg's Uncertainty Principle One of the biggest problems with quantum experiments is the seemingly unavoidable tendency of humans to influence the situation. To know the velocity of a particle we must measure it, and to measure it, we are forced to affect it. The same goes for observing an object's position. The Wave Mechanical Model of the Atom Wave-Particle Duality The Wave Mechanical Model of the Atom Matter Waves In 1924 a French graduate student, Louis de Broglie (was impressed with Einstein's 1905 discovery and the dual nature of light) he suggested in his graduate thesis that since nature is often symmetric, matter which is mostly particle should also have wave properties. These waves were not electromagnetic but a new kind of wave, matter waves. In 1927, the American physicists Clinton J. Davisson and Lester H. Germer verified de Broglie's hypothesis experimentally. They were able to diffract a beam of electrons in a crystal of nickel and only waves can be diffracted. Therefore, if an electron that is particle can be diffracted, it must have wave properties. De Broglie was right matter has wave properties. The Wave Mechanical Model of the Atom Standing Waves In 1926 Erwin Schrödinger proposed the electron was a 3-D waveform waveform circling the nucleus in a whole number of wavelengths allowing the waveform to repeat itself as a stable standing wave representing the energy levels of the Bohr model. • a whole number of waves • does not transfer energy • it can absorb energy from a nearby source which is oscillating at a proper frequency • the energy needed to change from one standing wave to another must be quantized in order to maintain a whole number of wavelengths and avoid collapsing The Wave Mechanical Model of the Atom Newtonian world: Everything appears to have a definite position, a definite momentum, a definite energy, and a definite time of occurrence. Quantum world: The state of a system at a given time is described by a complex wave function (also referred to as state vector in a complex vector space) Quantum mechanics does not assign definite values, instead an abstract mathematical object allows for the calculation of probabilities of outcomes) Probability clouds The Schrödinger equation describes how wave functions change in time, playing a role similar to Newton’s II. law. (The Schrödinger equation predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. ) „Itt láthatják a táblán a nevezetes Schrödinger-féle hullámegyenletet. Ezt az egyenletet Önök persze nem értik. Én sem értem. Schrödinger úr sem értette, de ez ne zavarja Önöket. Én ezt majd minden óra elején felírom a táblára, és elmagyarázom, mire lehet használni. Önök pedig majd lassan hozzászoknak.” Marx György, egyetemi tanár egyik előadásának kezdete Firefly Experiment • Suppose a male firefly is in a dark room with an open vial of female sex-attractant hormones. If we set up a camera to take pictures every time the firefly flashes and records the firefly’s location in the room we will find that most of it’s time is around the female, however, sometimes he flies farther away and around the room. • If we plot the firefly’s location we would see a picture like the one here • The area most often occupied is darkest in the picture and is the center where the hormones are found. • Now suppose you see the firefly flash in the center of the room, where will you see it flash next? Is there any way to know? Is the path of the firefly predictable? • NO, we cannot predict the location, but we can find the probability of its location. Thus the picture on the right is a sort of probability map. Atomic orbital An atomic orbital is a mathematical function (wave function) that describes the wave-like behavior of e.g. an electron in an atom. This wave function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. Orbitals and orbits When a planet moves around the sun, its definite path, called an orbit, can be plotted. A drastically simplified view of the atom looks similar, in which the electrons orbit around the nucleus. The truth is different; electrons, in fact, inhabit regions of space known as orbitals. Orbits and orbitals sound similar, but they have quite different meanings. It is essential to understand the difference between them. Molecular Orbital Theory LCAO: Lineare Combination of Atomic Orbitals ( F. Hund, R. Mulliken, E. Hückel, 1927-29) • Atomic and Molecular Orbitals are wave functions. • Molecular orbitals are the lineare combination of atomic orbitals • Atomic orbitals approach each other and form new orbitals, the molecular orbitals. Remember The Valence Bond Theory - that considers the overlapping of orbitals to create bonds. - is only limited in its use because it does not explain the molecular geometry of molecules very well. The atomic orbitals Interaction of the waves (Interference) Additive Remember: Subtractive How do the wave functions behave during the interaction? in Atom: s,p, d, f in Moleculs: σ, π, δ, φ Example: H2 s s σ (1sσ) constructive Interference, bonding effect s σ★ s destructive Interference, antibonding effect „node” where there is zero chanche of finding electrons The wave function in Atom: s,p, d, f in Molecule: σ, π, δ, φ Example: H2 s s σ (1sσ) constructive Interference, bonding effect s σ★ s destructive Interference, antibonding effect Node ΣAO = ΣMO Energy of Hydrogen σ★ (1sσ★) E 1s 1s A B σ (1sσ) Energy of Hydrogen Energy taker σ★ (1sσ★) E 1s 1s A B σ (1sσ) Energy giver: stabiler, bevorzugter Zustand Energy of Hydrogen Energy taker σ★ (1sσ★) E Jump between bondings: energy is needed, eg light Energie 1s 1s A B σ (1sσ) Energy giver: stabiler, bevorzugte Zustand Energy of Hydrogen antibonding MO σ★ E 1s 1s A B σ bonding MO Bond Order Bond order is the number of chemical bonds between a pair of atoms and indicates the stability of a bond: 1: Single bond 2: double bond 3: triple bond Example 1: H2 BO = (2-0) / 2 = 1 σ★ E Singel bond 1s A B 1s H-H σ Bindungselektronpaare Example 2: He2 σ★ E 1s A B 1s σ BO = (2-2) / 2 = 0 Unknown molecule Example 2: N2 N2 E BO = (10 – 4) / 2 = 3 Dreifachebindung Example 2: N2 N2 BO = (10 – 4) / 2 = 3 Tripple bond verantwortlich für Bindung HOMO (Highest Occupied Molecular Orbital,) LUMO (Lowest Unoccupied Molecular Orbital) Formaldehyd As the electronegativity differences increases the interacting orbitals will be at different energies. The „Aufbau” Principle: the order of filling orbitals (Aufbau is a German word meaning building up or construction.) Notice that the s orbital always has a slightly lower energy than the p orbitals at the same energy level, so the s orbital always fills with electrons before the corresponding p orbitals do. The oddity is the position of the 3d orbitals. They are at a slightly higher level than the 4s, so the 4s orbital fills first, followed by all the 3d orbitals and then the 4p orbitals. Types of bonding 1s 2s 3 x 2p σ+σ★ σ+σ★ π + π★ Atoms from the 2. Periode Rotational symmetry - σ- Symmetry - σ- MO - σ - Bond p Orbitals - the electron density is not distributed in a spherically symmetric fashion as in an sorbital - electron density is concentrated on two sides of the nucleus, separated by a node at the nucleus - this orbital has two lobes - there are three 2p orbitals: px, py,and pz orbitals 3*2p 1. Overlap of p-AO’s : 2*px same phase opposite phase Node 3*2p 1. Overlap of p-AO’s : 2*px σ-rotational symmetry σ – Bond σ(2pσ) σ★(2pσ★) 3*2p 2. Parallel p-AO’s: 2*py Same Phase Opposite Phase 3*2p 2. Parallel ausgerichtete p-AO’s π NO rotational symmerty π★ - π- Symmetrie - π- MO - π - Bindung 2 x 2s σ + σ★ 2 x 2px σ + σ★ 2 x 2py π + π★ 2 x 2pz π + π★ Thank you!