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 )ii 2 + ZZe 2 /r - i Ze 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 ! ...)