Có 200+ tài liệu thuộc chủ đề "nghiên cứu hóa học"
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The next term already takes into account that the induced moment also interacts with the electric field (eq. (12.19. α qq E q E q (12.39) where the component qq of the polarizability is equal to. n (12.40). The hydrogen atom in an electric field – perturbational approach. An atom or molecule, when located in electric field undergoes a deformation....
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The Molecule in an Electric or Magnetic Field. (12.49). μ 3ω q cos(3ωt) (12.50) where the amplitudes μ corresponding to the coordinate q ∈ x y z and to the particular resulting frequencies 0 ω 2ω 3ω have the following form 46. ω ω ω), is accom- panied (in parenthesis) by the frequencies ω corresponding to the three directions x...
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μ· ˆ H, where μ ˆ is the magnetic moment operator of the corresponding particle.. Why do we not have together with H ˆ SH + ˆ H IH in H ˆ 1 the term H ˆ LH , i.e. the interaction of the electron orbital magnetic moment with the field? It would be so nice to have the full...
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where the shielding constant σ C characterizes the vicinity of the nucleus. The energy levels of the carbon magnetic spin result from the magnetic field and from the m I H ’s of the protons according to eq. (12.83), Fig. 12.14. The resonance of the 13 C nucleus means a transition between energy levels that correspond to m I C....
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The Molecule in an Electric or Magnetic Field. There is an arbitrariness in the choice of A and φ.. In order to calculate the energy states of a system of nuclei (detectable in NMR spec- troscopy) we have to use the Hamiltonian H ˆ given above, supplemented by the inter- action of all magnetic moments related to the orbital and...
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The interacting objects are two isolated water molecules and the interaction energy is equal to about − 5 kcal/mol (attraction). 0 and − q, and one of the charges is ascribed to one, and the other to the second molecule. The value of q may be chosen in such a way as to produce the interaction energy of the new...
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A perturbation of the wave function is a small correction.. This tiny deformation is the target of the expansion in the basis set {ψ (0) n. In other words, the perturbation theory involves just a cosmetic ad- justment of the ψ (0) 0 : add a small hump here (Fig. 13.5), subtract a small function there, etc. Therefore, the presence...
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Table 13.1.. 13.6 Interaction energy E int (i). Here μ = (0 0 ±a) for electrons i = 1 2 according to definition (13.17), and μ ≡ a in a.u. Note, that the probabilities should be dif- ferent only because of the electron correlation. Well, but how to calculate them? 15 We may suspect that for the ground state (we...
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Now we are ready to use formula (13.28) with n = 1:. ˆ A ϕ After inserting ψ 0 (1) into the iterative scheme (13.29) with n = 2 we obtain the second-iteration energy. (13.33) These equations are identical to the corresponding corrections in perturbation the- ories derived by Murrell and Shaw 27 and by Musher and Amos 28 (MS–MA).....
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The apparent garbage produced by the perturbational series represented for the Padé approximants precise information that the absurd perturbational corrections pertain the energy of the 2pσ u state of the hydrogen atom in the electric field of the proton. How come? Low-order perturbational corrections, even if absolutely crazy, somehow carry information about the physics of the problem. The convergence properties...
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E disp (ABC) (13.55) where the first term represents the induction energy:. The second term in (13.55) represents the dispersion energy (this will be con- sidered later on, see p. For the time being let us consider the induction energy E ind (ABC). Writing V as the sum of the Coulomb interactions of the pairs of molecules we have. 1...
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13.12.2 DISTINGUISHED ROLE OF THE ELECTROSTATIC INTERACTION AND THE VALENCE REPULSION. This is because only the electrostatics may change the sign of the energy contribution when the molecules reorient, thus playing the pivotal role in the interaction energy.. 13.12.3 HYDROGEN BOND. Most often the hydrogen bond X–H. The hydrogen bond features are unique, because of the extraordinary properties of the...
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On the other side of the connector there is a plate with six spikes pro- truding from it as well as six long, kinked “legs” made of several different protein molecules. First, an enzyme belonging to the monster makes a hole in the cell wall of the bacterium. Then the 144 protein molecules contract probably at the expense of energy...
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14.1 HYPERSURFACE OF THE POTENTIAL ENERGY FOR NUCLEAR MOTION. Theoretical chemistry is still in a stage which experts in the field characterized as. 2 The majority of the systems studied so far are three-atomic systems. The reactants as well as the products may be quite large systems and the many- dimensional ground-state potential energy hypersurface E 0 0 (R) may...
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(b) The Euler angles show the mutual orientation of the two Cartesian coordinate systems. sin β ij cos β ij r j R j (14.7) tan β ij. When a chemical reaction proceeds, the role of the atoms changes and using the same Jacobi coordinate system all the time leads to technical problems. not to favour any of the three...
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Simply, the valley bottom profile results from the fact that the molecule hardly holds together when moving along the reaction coordinate s, a chemical bond breaks, while other bonds remain strong and it is not so easy to stretch their strings. After such vibrational aver- aging the only information that remains about the oscillations are the vibrational quantum levels for...
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Let us consider several versions of the reaction that differ by assuming various vibrational states of the reactants. (14.29), for each set of the vibra- tional quantum numbers we obtain the vibrationally adiabatic potential V adiab as a function of s (Fig. 14.10).. The adiabatic potential corresponding to the vibrational ground state (v OH v HH. Excitation of the OH...
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Kenichi Fukui Japanese chemist, profes- sor at the Kyoto University.. One of the first scholars who stressed the importance of the IRC, and introduced what is called the frontier orbitals (mainly HOMO and LUMO), which govern practically all chemical processes. Now instead of 0 let us take two doubly excited configurations of the to- tal system: 58. (14.44) 3d =...
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14.5.6 NUCLEOPHILIC ATTACK H. Maybe the acceptor–donor theory described above pertains only to the H. Let us consider a nucleophilic attack of the H − ion on the ethylene molecule (Fig. 14.17), perpen- dicular to the ethylene plane towards the position of one of the carbon atoms. The arriving ion binds to the carbon atom forming the CH bond, while...
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14.20.d) oriented towards the other ethylene molecule. 14.20.b). The lowest energy corresponds, of course, to SS (because the newly formed σ chemical bonds correspond to the bonding combination and the lateral overlap of the hybrids is also of the bonding character), the next in energy however is the AS (because of the bonding interactions in the newly formed σ bonds,...