Ideas of Quantum Chemistry P102 ppt

... getting ˜ L 1 . K. DIAGONALIZATION OF A MATRIX In quantum chemistry we often encounter the following mathematical problem. We have a Hermitian 1 matrix A (of dimension n), i.e. A † =A, and are ... orthogonalization”) admix- ture of the old vectors, i.e. the contribution of u and v in u  isthesameasthatofv and u in v  . The new vectors are obtained by correcting the directions of...

Ngày tải lên: 06/07/2014, 09:20

... abyss of the sea without a bottom. 22 The presence of the Dirac sea makes the Dirac the- ory, in fact, a theory of an infinite number of particles, whereas formally it was only a theory of a single ... CALCULATION OF THE GROUND STATE OF THE HYDROGEN-LIKE ATOM WITHIN DIRAC THEORY Matrix form of the Dirac equation We will use the Dirac equation (3.59). First, the basis set compos...

Ngày tải lên: 06/07/2014, 09:20

... disposal all the necessary solutions of eq. (5.16). The eigenfunctions of the ˆ H (0) operator appeared as a consequence of using them as the complete set of functions (e.g., in expanding ψ (1) k ). ... ψ k (λ) are analytical functions of λ (p. 205). In this mathematical aspect of the physical problem we may treat λ as a complex number. Then the radius of convergence ρ of the...

Ngày tải lên: 06/07/2014, 09:20

... describe future vibrations of the molecule (changes of R) as well as its rotations (changes of the direction of R). A simple analogy Let us stop for a while to catch the sense of the adiabatic approximation. To ... PES, for the motion of the nuclei, rep- resents one of the most important ideas in chemistry. This concept makes possible contact with what chemists call the spati...

Ngày tải lên: 06/07/2014, 09:20

... has to be convex as a function of the positions of the nuclei. 6. Please choose the wrong answer. As a result of the rotational excitation J → (J +1) of a molecule of length R: a) the angular momentum ... func- tion in the form of a product of an electronic function and a function describing the motion of the nuclei; c) leads to the notion of the potential energy curve for t...

Ngày tải lên: 06/07/2014, 09:20

... a function of the configuration of the nuclei. Our motivation is as follows: • economy of computation: ab initio calculations of the electronic energy for larger molecules would have been many orders of ... oligopeptide the num- ber of conformations is of the order 36 of 10 20 , and for a hundred amino acids – 35 Wijnand Schepens, PhD thesis, University of Gand, 2000. 36 The...

Ngày tải lên: 06/07/2014, 09:20

... bond One of the molecules is a donor, the other is an acceptor of a proton, Fig. 7.10.a. A local minimum of smaller stability appears when one of the water molecules serves as a donor of two protons, ... 7.10.a): • stretchingofthehydrogenbondO–H O(thevibrationoftwowatermolecules treated as entities): 183 cm −1 • bendingofthehydrogenbondO–H Ointheplaneofthefigure:345cm −1 • bendingoft...

Ngày tải lên: 06/07/2014, 09:20