量子化学与群论基础1ppt课件

1、Quantum Chemistry and Group theory Dr. Ce HaoRoom 228, Department of ChemistryPhone: 4708901Cell phone:-mail: haoceelongURL: /class/501141pchem/jiangyi/aboutus/haoce.htm0 Introduction ThermodynamicsQuantum mechanicsBulk properties(p,V,T,)Macroscopic(N1024)Properties of i

2、ndividual particleMicroscopic(N=1)statistical mechanicsThermodynamic methodQuantum mechanic methodStatistical mechanic method0.1 Quantum chemistrythe branch of Physical chemistrythe application of quantum mechanics to chemical problems, emerged as a new branch of chemistry. 0.2 The structure of scie

3、nceLaw a summary of experienceHypothesis a tentative explanation that accounts for a set of facts and can be tested by further investigation.Theory a system of assumptions, accepted principles, and rules of procedure devised to analyze, predict, or explain the nature or behavior of phenomenon.Model

4、a simplified version of the system that focuses on the essentials of the problem.0.3 The methods of Quantum chemistryAtomsmoleculesE HE0.2.1 Wave-function methodsPople0.3 Density methodsKohndensity functional theoryChemistry is not only test tubes and chemicals. In quantum chemistry, quantum mechani

5、cs is used to compute the properties of molecules and their interaction to study molecules and chemical processes.0.4 applications of Quantum chemistryThe three-dimensional structure of molecules can be accurately determined using quantum-chemical methods. One application of this is the development

6、of new catalysts to generate very specific products such as drugs and plastics. Applications in organic chemistryApplications in biochemistryBy selecting a limited number of atoms (20-60) from the active site of an enzyme, bonding and reaction mechanisms can be studied with quantum-chemcial methods.

7、 The surrounding protein is described with simpler methods. The model below shows a possible mechanism of how myoglobin in muscles protects itself agains carbon monoxide poisoning. Using hydrogen bonding to one of the amino acids in the protein, oxygen can overcome the competition from the dangerous

8、 carbon monoxide. BibliographyI.N. Levine, Quantum Chemistry. Prentice Hall, Englewood Cliffs, NJ, 4th edition, 1991(有中译本，宁世光译）2. John W. Norbury, QUANTUM MECHANICS,go1.163/zorkov/qm.rar3. ID: qchemPass word:123454. Peter R. Taylor Group Theory and its Applications go1.163/zorkov/group.rar 5

9、. 量子化学中文网 go1.163/zorkov/6. Physics 2000physics2000index803e.html7.曹阳，量子化学引论8.唐敖庆， 量子化学1. Quantum Theory1.1 The Motivation for Quantum Mechanics1.1.1 The Ultraviolet CatastropheRayleighPlanck (1900)Planck (1900)E n hn0,1,2,) “quanta”1.1.2 The Photoelectric EffectAccording to the classica

10、l wave theory of light, the intensity of the light determines the amplitude of the wave, and so a greater light intensity should cause the electrons on the metal to oscillate more violently and to be ejected with a greater kinetic energy. In contrast, the experiment showed that the kinetic energy of

11、 the ejected electrons depends on the frequency of the light. The light intensity affects only the number of ejected electrons and not their kinetic energies. 1.1.3 Quantization of Electronic Angular MomentumRutherford (1901) proposed that electrons orbit about the nucleus of an atom.Bohr assumed st

12、able electronic orbits with the electronic angular momentum quantized as l=mr=nh/2 E=h7.2 Wave-Particle Duality7.2.1 Nature of LightThe argument in 17th centuryGeometrical optics Huygens(1690) the wave theoryHuygens(1690) the wave theory1221ccnnNewton(1680) the particle theory2121ccnnInterference an

13、d Diffraction “ether”Thomas Young(1803)ElectromagnetismMaxwell(1864)The Theory of Photons（iPhotons: the particlelike aspect of light；（iiEnergy of a photon,h （iii） Mass of a photon, m = hc2（iv） Momentum of a photon, P mc hc hWave-Particle Duality of light hP hPlanck-Einstein equationEinstein(1905)1.2

14、.1 The Wave Character of Particlesde Broglie reasoned in 1924 that matter also can exhibit this wave-particle duality. He further reasoned that matter would obey the same equation as light Eh P h Planck-Eistain- de Broglie relationsDavisson and Germer(1925)“lucky accident”Thomson1.3 The Uncertainty

15、Principle(1) x0，Px； Px0，x。It is impossible to specify simultaneously the precise position and momentum of any particle.(2) Classical mechanics trajectory Quantum mechanics probabilityHeisenberg(1927)， x Pxh/ 41.5 WavefunctionThe Uncertainty Principle xPxh/ 4The state descriptionThermodynamics: Bulk

16、properties(p,V,T,)Classical mechanics:Pzyxr),(de Broglie Hypothesis1. Matter could also behave as waves. 2. Matter would obey the same equation as light Eh P h 3. The states of matter can be described by wavefunction. The 1-dimensional free particle:)(1cos).(EtPxAtx1.5.1 Interpretation of the wavefu

17、nctionWhat is this wavefunction? What does it mean?Born(1926) suggested that wavefunction was that the square at a given point in space was proportional to the probability of finding the particle at that point in space. The square is called the probability density while we can call the wavefunction

18、is probability amplitude.Classical particles(e.g. bullet)A single electronxPxh/ 4A swarm of electrons d*dkP dd*PkProbability densitynmP(A)ProbabilityStatistical definition:nnPnAlimdef(A)Calculation of probabilityProperties of probability1(A)0 PProbability deals with measuring or determining the like

19、lihood that an event will have a particular outcome.P(A)=0 impossible eventP(A)=1 inevitable evente.g. , throw a coin , dice1d*dkPd*dkP 2121d*1kAANormalization constantFor the case of a single particle1.6 The dynamics of microscopic systemsWave MechanicsSchrdinger (1925) developed Broglies idea into

20、 the differential equations capable of dealing with a number of physical phenomena and with problems that could not be handled by classical physics.Matrix MechanicsHeisenberg (1925)chose to pursue the Matrix pathway and started to associate matrices with the properties of matter.Relativistic Quantum TheoryA synthesis of quan