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Molecular structure nuclear wave function

Confining and asymptotic GED states A hint at molecular structure. The change from a configuration space where the nuclear wave function is defined to a special role as the positive source (nuclear) configuration space Q in eq. (7), is achieved by an isometry mapping the distances are invariant but the ideology is changed. [Pg.186]

Transient vibrational dynamics. Perturbation theory yields an intuitive picture of adsorbate relaxation the loss of a vibrational quantum and associated nodal structure in the nuclear wave function is coupled to an irreversible transfer of momentum to the metallic electrons (see Fig. 2). To obtain time-resolved information about the dynamical processes at work, it is nonetheless necessary to go beyond this simple model. In the past decades, classical molecular dynamics has been hugely successful at shedding light on the transient vibrational evolution in a variety of adsorbate-surface systems (see, e.g., ref. 54-56). The methods of choice for including non-adiabatic effects on the dynamics can be divided in two main families friction-lype... [Pg.95]

Very recently, Singleton has suggested a new way of calculating isotope effects illustrated by the bromonium ion [61]. This method could possibly also be used for tautomeric systems. Another new approach is the multicomponent molecular orbital method for direct treatment of nuclear quantum effects [62]. The basic idea is to incorporate the nuclear wave function and in particular the proton wave function directly into the electronic structure calculation. This approach has great potential but has so far been tested only for secondary isotope effects on chemical shifts [63]. The geometric isotope effect has also been looked into based on Pauling valence-bond orders [20]. [Pg.166]

One is purely formal, it concerns the departure from symmetry of an approximate solution of the Schrodinger equation for the electrons (ie within the Bom-Oppenheimer approximation). The most famous case is the symmetry-breaking of the solutions of the Hartree-Fock equations [1-4]. The other symmetry-breaking concerns the appearance of non symmetrical conformations of minimum potential energy. This phenomenon of deviation of the molecular structure from symmetry is so familiar, confirmed by a huge amount of physical evidences, of which chirality (i.e. the existence of optical isomers) was the oldest one, that it is well accepted. However, there are many problems where the Hartree-Fock symmetry breaking of the wave function for a symmetrical nuclear conformation and the deformation of the nuclear skeleton are internally related, obeying the same laws. And it is one purpose of the present review to stress on that internal link. [Pg.103]

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... [Pg.76]

Solutions to the Schrodinger equation Hcj) = E(f> are the molecular wave functions 0, that describe the entangled motion of the three particles such that (j) 4> represents the density of protons and electron as a joint probability without any suggestion of structure. Any other molecular problem, irrespective of complexity can also be developed to this point. No further progress is possible unless electronic and nuclear variables are separated via the adiabatic simplification. In the case of Hj that means clamping the nuclei at a distance R apart to generate a Schrodinger equation for electronic motion only, in atomic units,... [Pg.364]

Background Philosophy. Within the framework of the Born-Oppenheimer approximation (JJ ), the solutions of the Schroedin-ger equation, Hf = Ef, introduce the concept of molecular structure and, thereby, the total energy hyperspace provided that the electronic wave function varies only slowly with the nuclear coordinates, electronic energies can be calculated for sets of fixed nuclear positions. The total energies i.e. the sums of electronic energy and the energy due to the electrostatic re-... [Pg.141]

Using the Born-Oppenheimer approximation, electronic structure calculations are performed at a fixed set of nuclear coordinates, from which the electronic wave functions and energies at that geometry can be obtained. The first and second derivatives of the electronic energies at a series of molecular geometries can be computed and used to find energy minima and to locate TSs on a PES. [Pg.967]

The quantum theory of molecular structure developed here and the standard BO approach rely on the separability between electronic and nuclear configurational degrees of freedom. However, the way this is achieved differs radically between the approaches. In the treatment described here, the nuclei are seen to be trapped by an attractor generated by the stationary electronic wave function (nuclei follow the electronic states ) the electronic wave function does not depend upon the instantaneous positions of the nuclei as early proposed by this author [4] a change of electronic state, characterizing a chemical reaction with reactants and products in their ground electronic states, is described as a Franck-Condon like process. [Pg.24]

An alternative strategy is to synthesize a molecular wave function, on chemical intuition, and progressively modify this function until it solves the molecular wave equation. However, chemical intuition fails to generate molecular wave functions of the required spherical symmetry, as molecules are assumed to have non-spherical three-dimensional structures. The impasse is broken by invoking the Born-Oppenheimer assumption that separates the motion of electrons and nuclei. At this point the strategy ceases to be ab initio and reduces to semi-empirical quantum-mechanical simulation. The assumed three-dimensional nuclear framework is no longer quantum-mechanically defined. The advantage of this model over molecular mechanics is that the electron distribution is defined quantum-mechanically. It has been used to simulate the H2 molecule. [Pg.122]

As we have discussed many times elsewhere, the magnetic and electric nuclear hyperfine constants provide information about the electronic structure of the molecule. The latter was outlined and summarised briefly in (8.391), where the unpaired electron is placed in a 7r-type molecular orbital, which may be regarded as a linear combination of the N and O atomic 2p orbitals. Dousmanis [ 140] was among to first to show the relationships between the dipolar hyperfine constants and the electronic wave function. The orbital hyperfine constant, a, which in NO is found to have the value 84.20378 MHz, is given by the expression... [Pg.537]


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See also in sourсe #XX -- [ Pg.276 ]

See also in sourсe #XX -- [ Pg.276 ]




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