《中级物理化学 Intermediate Physical Chemistry》课程教学资源（PPT讲稿）

Intermediate Physical chemistry Driving force of chemical reactions Boltzmann's distribution Link between quantum mechanics thermodynamics

Intermediate Physical Chemistry Driving force of chemical reactions Boltzmann’s distribution Link between quantum mechanics & thermodynamics

Intermediate Physical Chemistry Contents Distribution of molecular states Partition function Perfect Gas Fundamental relations Diatomic molecular gas

Intermediate Physical Chemistry Contents: Distribution of Molecular States Partition Function Perfect Gas Fundamental Relations Diatomic Molecular Gas

Beginning of computational chemistry In 1929, Dirac declared, "The underlying physical laws necessary for the mathematical theory of. the whole of chemistry are thus completely know, and the dificulty is only that the exact application of these laws leads to equations much too complicated to be soluble Dirac

In 1929, Dirac declared, “The underlying physical laws necessary for the mathematical theory of ...the whole of chemistry are thus completely know, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.” Beginning of Computational Chemistry Dirac

Schrodinger equation HV=EY Wavefunction Hamiltonian H=∑a(-h2maa2-(h2/2m。)∑v2 +∑62a4pera8-2aze/ EI nergy +∑∑:e2

H y = E y SchrÖdinger Equation Hamiltonian H =  (-h 2 /2m ) 2 - (h 2 /2me )ii 2 +  ZZe 2 /r - i  Ze 2 /ri + i j e 2 /rij Wavefunction Energy

Principle of equal a priori probabilities All possibilities for the distribution of energy are equally probable provided the number of molecules and the total energy are kept the same Democracy among microscopic states! ! a prior. as far as one knows

Principle of equal a priori probabilities: All possibilities for the distribution of energy are equally probable provided the number of molecules and the total energy are kept the same Democracy among microscopic states !!! a priori: as far as one knows

For instance. four molecules in a three-level system: the following two conformations have the same probability 画mm 2 l--2 8 8 ======= a demon

For instance, four molecules in a three-level system: the following two conformations have the same probability. ---------l-l-------- 2 ---------l--------- 2 ---------l----------  ---------1-1-1----  ---------l---------- 0 ------------------- 0 a demon

THE DISTRIBUTION OF MOLECULAR STATES Consider a system composed of n molecules and its total energy e is a constant. These molecules are independent, i. e no interactions exist among the molecules

THE DISTRIBUTION OF MOLECULAR STATES Consider a system composed of N molecules, and its total energy E is a constant. These molecules are independent, i.e. no interactions exist among the molecules

Population of a state: the average number of molecules occupying a state. Denote the energy of the state 8 The Question: How to determine the population

Population of a state: the average number of molecules occupying a state. Denote the energy of the state i The Question: How to determine the Population ?

Configurations and Weights Imagine that there are total N molecules among which no molecules with energy co, n, with energy 81) n, with energy a,, and so on, where 8o <8,<8,<... are the energies of different states. The specific distribution of molecules is called configuration of the system, denoted as i no, nis

Configurations and Weights Imagine that there are total N molecules among which n0 molecules with energy 0 , n1 with energy 1 , n2 with energy 2 , and so on, where 0 < 1 < 2 < .... are the energies of different states. The specific distribution of molecules is called configuration of the system, denoted as { n0 , n1 , n2 , ......}

N,D,0,……} corresponds that every molecule is in the ground state, there is only one way to achieve this configuration; N-2, 2, 0,.o.3 corresponds that two molecule is in the first excited state and the rest in the ground state and can be achieved in N(N-1)/2 ways A configuration (no, nu, n 2,…… can be achieved in w different ways, where w is called the weight of the configuration And w can be evaluated as follows W=M!/(mnln1n2…)

{N, 0, 0, ......} corresponds that every molecule is in the ground state, there is only one way to achieve this configuration; {N-2, 2, 0, ......} corresponds that two molecule is in the first excited state, and the rest in the ground state, and can be achieved in N(N-1)/2 ways. A configuration { n0 , n1 , n2 , ......} can be achieved in W different ways, where W is called the weight of the configuration. And W can be evaluated as follows, W = N! / (n0 ! n1 ! n2 ! ...)