Có 160+ tài liệu thuộc chủ đề "nghiên cứu hóa học"
tailieu.vn Xem trực tuyến Tải xuống
for the harmonic oscillator. The corresponding wave functions also resemble those for the harmonic oscillator. Higher-energy vibrational levels are getting closer and closer, as for the Morse potential. This is a consequence of the anharmonicity of the potential – we are just approaching the dissociation limit where the U k (R) curves differ qualitatively from the harmonic potential.. What would...
tailieu.vn Xem trực tuyến Tải xuống
Therefore, the middle part of the above formula for kinetic energy represents an analogue of mv 2 2 and the last part is an analogue of 2m p 2. The reason is that, in the above expression, we have curvilinear coordinates (because of the rotation from BFCS to RMCS 40. How do we write an operator expressed in some curvilinear...
tailieu.vn Xem trực tuyến Tải xuống
V ii (R) (6.44) The crossing of the energy curves at a given R means that E. E − may occur only when, for some reason, e.g., because of the symmetry, the coupling constant is automatically equal to zero. 12 = 0 due to the orthogonality of both eigenfunctions of H ˆ 0 (R 0. The Hamiltonian represents a fully...
tailieu.vn Xem trực tuyến Tải xuống
The molecule is excited from its ground state at the nuclear configuration P to the excited state (point FC) at the same nuclear configuration (according to the Franck–Condon rule). The point FC representing the system is usually located on a slope of the potential energy (corresponding to the excited state) and this is why it slides downhill towards the energy...
tailieu.vn Xem trực tuyến Tải xuống
Anisotropy of the potential V. Application of the Ritz method. As shown in Chapter 6, the solution of the Schrödinger equation in the adiabatic approx- imation can be divided into two tasks: the problem of electronic motion in the field of the clamped nuclei (this will be the subject of the next chapters) and the problem of nuclear motion in...
tailieu.vn Xem trực tuyến Tải xuống
equation (6.8) for every configuration R of the nuclei and take the eigenvalue [i.e.. V (R) would be obtained about its minimum, if any chemical bond between atoms X and Y had a certain characteristic reference length r 0 that would depend on the chemical species of the atoms X and Y . If the bond length were changed (shortened...
tailieu.vn Xem trực tuyến Tải xuống
where x = R − R 0 is the vector with the displacements of the atomic positions from their equilibria (x i = X i − X i 0 for i = 1 3N. In R 0 all the first derivatives vanish. According to the harmonic approximation, the higher order terms denoted as. 1 2 x T V x, where...
tailieu.vn Xem trực tuyến Tải xuống
Therefore the new po- sitions and the new velocities are easy to calculate. The computer simulation makes the system evolve from the initial state to the final one. The position R in 3N-dimensional space becomes a function of time and therefore R(t) represents the trajectory of the system in the configurational space.. Knowing the trajectory means that we know the...
tailieu.vn Xem trực tuyến Tải xuống
A scheme showing why the acceleration ψ ¨ i of the spinorbital ψ i has to be of the same sign as that of − ˆ Fψ i . It is seen that the velocity of the change is not constant and the corresponding acceleration is equal to 1. In such a situation we may easily foresee the sign of...
tailieu.vn Xem trực tuyến Tải xuống
Electronic Motion in the Mean Field: Atoms and Molecules. It can be expressed in the following way.. The motion of the cars proves to be very complex (as it does for the electrons) and therefore the problem is extremely difficult. In the mean field approximation method we focus on the motion of one car only considering its motion in such...
tailieu.vn Xem trực tuyến Tải xuống
Variation is an analogue of the differential (the differential is just the linear part of the function’s change). Substituting φ ∗ i → φ ∗ i + δφ ∗ i in (8.6) (and retaining only linear terms in δφ ∗ i to be inserted into (8.9)) the variation takes the form (the symbols δi ∗ and δj ∗ mean δφ...
tailieu.vn Xem trực tuyến Tải xuống
(8.7)) is the sum of the kinetic energy operator of electron 1 and the operator of the interaction of this electron with the nuclei in the molecule, the next two terms, i.e. Coulombic J ˆ and exchange K ˆ operators, are connected with the potential energy of the interaction of electron 1 with all electrons in the system, and they...
tailieu.vn Xem trực tuyến Tải xuống
If a tiny admixture of the 3d x 2 −y 2 function is added to the spherically symmetric 1s orbital (a football ball, both orbitals with 0.5 orbital exponent). We will get shrinking in one direction, and elongation in the other (the dimension in the third direction is unchanged), i.e. If the admixture were of the 2p type, the ball...
tailieu.vn Xem trực tuyến Tải xuống
Electronic Motion in the Mean Field: Atoms and Molecules. The Hartree–Fock–Roothaan matrix equation is solved iteratively:. often in the zero-th iteration we put P = 0, as if there were no electron repulsion),. c) we solve the Hartree–Fock–Roothaan equation (see Appendix L, p. d) we obtain a new c matrix, and then a new P, etc., e) we go back...
tailieu.vn Xem trực tuyến Tải xuống
Electronic Motion in the Mean Field: Atoms and Molecules. Thus a small di- versification of the orbital functions leads to some triplet (second term) and singlet (third term) admixtures to the original singlet function N + N − ψ RHF (called triplet contamination). The former is proportional to δ and the latter to δ 2 . Now the total wave...
tailieu.vn Xem trực tuyến Tải xuống
Electronic Motion in the Mean Field: Atoms and Molecules. Let us first consider the electron density described by the ϕ orbital: ϕ S. Let us note that the density can be divided into the part close to nucleus a, that close to nucleus b, and that concentrated in the bonding region 95. of the electron cloud from the a atom...
tailieu.vn Xem trực tuyến Tải xuống
their amplitudes are significant for all atoms in the molecule.. Yet the canonical MOs of the inner shells are usually very well localized. The picture which agrees with intuition may be obtained after the localization of the MOs.. The localization is based on making new orbitals as linear combinations of the canonical MOs, a fully legal procedure (see p. 338,...
tailieu.vn Xem trực tuyến Tải xuống
The dimensions of the electron pairs, i.e. a “Core” means the 1s orbital of the atom indicated. similar to the compounds of oxygen with hydrogen, because sulphur and oxygen have analogous electronic configuration of the valence electrons (i.e. those of the highest energies), and they differ only in the inner shells (O: [He]2s 2 2p 4 as com- pared to...
tailieu.vn Xem trực tuyến Tải xuống
The figure shows the all im- portant (proteins) example of the peptide bond. Usually in chemistry, knowing the geometry, we make a conjecture pertain- ing to the hybridization of particular atoms. This leads to the electron count for each atom: the electrons left are supposed to participate in bonds with other atoms.. In the example shown, the sp 2 hybridization...
tailieu.vn Xem trực tuyến Tải xuống
Electronic Motion in the Mean Field: Atoms and Molecules ers. Hartree–Fock computations result in the molecular orbital model: the molecular orbitals and the orbital energies scheme (“minimal model. A set of the very interesting articles by the leading quantum chemists.. b) in a form of one Slater determinant, that depends on all coordinates of N electrons and which is an...