Có 220+ tài liệu thuộc chủ đề "nghiên cứu hóa học"
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despite the multidimensionality of the problem, eq. This is connected to the width of the low-energy basin associated with the entropy 86 and to the free energy. In statistical thermodynamics we introduce the idea of the potential of the mean force, related to the free energy. The example just considered of the electron transfer reaction: Fe 2. The intersection point...
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Shaik “What Happens to Molecules as They React? Valence Bond Approach to Re- activity”, Journal of the American Chemical Society . b) the steepest descent path in the Cartesian space of the nuclear coordinates;. c) the steepest descent path from a saddle point in the Cartesian space of the mass- weighted nuclear coordinates;. d) a straight line in the Cartesian...
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Information Processing – the Mission of Chemistry. A model of the immune system. (b) The attacking factor I (the irregular body shown) is best recognized and bound by one of the hexamers. The defence is highly specific and at the same time highly flexible (adjustable).. All possi- ble complexes are present in the solution, none of the complexes dominates.. The...
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Information Processing – the Mission of Chemistry. Wacław Sierpi ´nski Polish mathematician, from 1910 professor at the Jan Casimir University in Lwów, and from 1918 at the Univer- sity of Warsaw. One of the founders of the famous Pol- ish school of mathematics.. On the other hand, it is striking that fractals of fantastic complexity and shape may be constructed...
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Information Processing – the Mission of Chemistry Claude Elwood Shannon. It was said that Shannon used to under- stand problems ‘ in zero time. where p stands for the probability of the event the information reports. How much information is contained in the news that in a single trial coin came down tails? Well, it is I. Claude Shannon introduced...
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Information Processing – the Mission of Chemistry c) is independent of external conditions;. A molecular library composed of the associates of the molecules A and B represents:. a) a mixture of the complexes AB. b) a mixture of all possible complexes of the A and B species. In the iterative solution of the logistic equation x n + 1 =...
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This example is important in the context of this book. A set of vectors is called a set of linearly independent vec- tors if no vector of the set can be expressed as a linear combination of the other vectors of the set. The number of linearly independent vectors in a vector space is called the dimension of the space.....
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This means that the displacement in space of function f (r) is simply equivalent to leaving the function intact, but instead inversing the displacement of the coordi- nate system. Operators R ˆ rotate functions without their deformation, therefore they pre- serve the scalar products in the Hilbert space and are unitary. They form a group isomorphic with the group of...
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Reducible representation, block form and irreducible representation. In the first row the ma- trices ( R ˆ i ) are displayed which form a reducible representation (each matrix corresponds to the symme- try operation R ˆ i. The central row shows a representation equivalent to the first, i.e. The last row shows an equivalent representation that corresponds to the smallest...
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Some operations will lead to the same (new) orbital, sometimes with the opposite sign. Then we apply the symmetry operations to the third or- bital, etc. All the results of the application of operation R ˆ i on the orbitals ϕ i are collected in a transformation matrix R i. The matrices R i , i = 1 2 g,...
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perpendicular to the ring of the molecule.. pendicularly to the N–N line. This means that the allowed states are now of the B 2u type.. Thus for polarization parallel to the NN axis of the molecule, absorption may occur from the ground state to any state of the B 1u type (and vice versa).. We will not get any information...
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the molecule is isolated,. elements are represented by the same isotope,. the molecule is in a stationary state,. the electromagnetic field interacts with the molecule only through the electric field-molecule interaction,. in the interaction of the molecule with the electromagnetic field only what are called the dipole transitions are involved. However, in practice the molecule is never isolated. In particular,...
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is the total momentum operator (see Chapter 1). This relation corresponds to the opposite rotation (i.e. 58) of the coordinate system:. Now instead of the large rotation angle α, let us consider first an infinitesimally small rotation by angle ε = α/N , where N is a huge natural number. 1 A positive value of the rotation angle means an...
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How do we understand the arbitrariness of the vector potential A? Figs. Such A therefore determines H directed perpendic- ularly to the page and oriented towards the reader. By the way, note that any shift of the potential obtained should give the same magnetic field perpendicular to the drawing, Fig. const The transformation is only one of the possibilities. which...
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It is seen that once again we have reached a situation allowing us to separate the motion of the centre of mass in the Schrödinger equation. This time, however, the form of the operator H ˆ is different (e.g., xyz has only formally the same form as. Then, R CM almost shows the position of the nucleus, and x y...
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SLATER–CONDON RULES. The Slater determinants represent something like the daily bread of quantum chemists. Our goal is to learn how to use the Slater determinants when they are involved in the calculation of the mean values or the matrix elements of some im- portant operators. We will need this in the Hartree–Fock method, as well as in other important methods...
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On the left side we see pictorial representations of matrix elements of the total Hamiltonian H. LAGRANGE MULTIPLIERS METHOD. The constraints cause the number of independent variables to be n.. where the derivatives are calculated at the point of the extremum. From (N.2) we cannot draw the conclusion that the ( ∂x ∂E. Let us try to exploit this. To...
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To obtain the total spin vector, we there- fore have to add the x components of the spins of the particles, similarly for the y and z components, and to construct the total vector from them. Then we might be interested in the corresponding spin operators. For any stationary state the wave function is an eigenfunction of the square of...
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charges plications and serve to provide information on how much of the electronic den- sity ρ is concentrated on atom A. Such a quantity is of interest because it may be directly linked to the reactivity of atom A, often identified with its ability to be attacked by nucleophilic or electrophilic agents. The first term represents the contributions q ¯...
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i h(i) ˆ is the sum of the one-electron operators 7 h(i) ˆ acting on functions of the coordinates of electron i.. The I Slater–Condon rule says (see Appendix M), that for the Slater determi- nant ψ built of the spinorbitals φ i , the matrix element ψ| ˆ Fψ. In the second quantization. Interestingly, the summation extends to infinity,...