Strange states, molecular

Such quantum-mechanical molecular states, with respect to which a given nucleus has an ambiguous position, will be referred to here as strange states. This is done to stress the fact that such states are neither predicted by nor admissible in traditional chemistry. In the latter only different mesomeric forms of a given molecule are admitted, and it is not assumed that the molecule is in different mesomeric forms at the same time. In traditional chemistry, the nuclei of a molecule always have an unambiguous position in space and hence the molecule has a nuclear structure. 

It should be emphasized that it is not our aim here to investigate some particular pure state (wave functions), such as the ground state, of a molecular species. The issue at stake is rather which pure states actually arise in a thermal situation Are these pure states strange or do they admit a nuclear structure What are the respective probabilities of finding strange states in a vessel containing 10 ° molecules at a given temperature and pressure ... 

The symmetry-adapted eigenstates in Eq. (8) correspond to the states and of ammonia. They do not fit into the molecular structure scheme of traditional chemistry and are therefore considered as strange states from a chemical point of view. Neither chemical structures nor chemical bonds exist any more. 

We stress again that different decompositions of a molecular thermal state can refer to entirely different physical situations If all possible decompositions are considered as being equivalent, one cannot infer from the thermal state alone whether the molecule under discussion has a nuclear structure or not. Also, one cannot infer from the thermal state alone if the molecule admits strange states and so on. 

The theory discussed here gives a special role to the stationary states of the molecular hamiltonian. In particular, there are stationary electronic states, not a set of electrons. For example, the hydrogen atom cannot be seen as formed by one proton plus one electron. It is the electronic spectra which define it, not the model we use to calculate the energy levels and wave functions. This may sound strange but consider a thermal neutron. This system decomposes into one proton plus an electron and a neutrino. One cannot say that a neutron is made of such particles. Matter may exist in different kinds of stationary states processes can be seen as changes among them. 

Strange to state, the methylated uric acids, when reduced, do yield purons which (excepting tetramethylpuron) can be molecularly rearranged into isomeric isopurons, but the corresponding hydrated uric acids are not produced (Tafel2). 

In the Car and Parrinello (1985) scheme, ion dynamics is combined with a fictitious classical electron dynamics, with nuclei assigned real masses and the electron wave functions arbitrary fictitious masses. One starts the molecular-dynamics simulation at high temperature and cools progressively to zero temperature to find the ground state of both electrons and ions simultaneously. Although this approach at first seems strange and unphysical, it has yielded excellent results for amorphous Si (Car and Parrinello, 1988) and recently for SiOj (Allan and Teter, 1987) and S clusters (Hohl et al., 1988) and will probably play an important role in the future development of the field. 

Most molecular species can be expected to possess a nuclear structure, although for some, e.g., hydrogen bonded species or ammonia, the issue is not so obvious. The ammonia-maser transition, for example, is thought to be a transition between strange molecular (pure) states that do not admit a nuclear structure. 

Ammonia typifies a molecule without a chemical structure. Its ground state, in particular, does not admit a nuclear molecular framework. Moreover, for all molecules with at least two possible isomeric structures, the same strange conclusions could be drawn. 

Homomolecular O2 exchange is very slow on ZnO at 298 K in the dark. However, cooling to 77 K produces a sudden increase in rate. There is debate over the active intermediate for this strange, non-photocatalytic reaction. Tanaka et al. and Hirota et al. favour O4 and 4 species, respectively, whereas Russian workers conclude that these cannot be involved. Tanaka et al. published e.s.r. studies using " 02 in support of neutral O4 species, but Gundrizer et al. state that such species in liquid O2 are inactive in exchange and, therefore, that it is more likely for the intermediate on ZnO to be a non-radical , molecularly adsorbed species. It is not clear in their paper what exactly is meant by this nor how such species can function as intermediates. 

The majority of this kind of FCS studies treat intermolecular interactions such as molecular association to clarify the function of biomolecules in the target. In addition to the concentration of molecules, the binding constants of the two interacting molecules are easily obtained by FCS. A number of researchers have found it convenient to obtain a cellular map indicating where the objective molecular interaction occurs. This approach requires only qualitative values of D from FCS to distinguish the on-off of the molecular interaction. Therefore, only a small number of studies have stated the existence of anomalous diffusion in cells [35-37] or discussed the strangeness of the absolute values of D obtained from intracellular FCS measurements [38]. 

Organic chemistry provided the arena in which this renaissance flowered. It required the reconciliation of two strange bedfellows, thermodynamics and structural theory— the first supposedly independent of any hypotheses about the structure of matter, the second inescapably committed to the atomic-molecular hypothesis. Their meeting ground would be transition-state theory. 

Following the works by Gaiduk and Crothers [23, 31] and by Gaiduk and Kutuza [65], an attempt was undertaken in Section V to apply for ice Ih the model, originally elaborated for calculation of water spectra. At first sight, this idea is seemingly strange due to difference of phase states of these fluids and because in the known molecular dynamics simulations, quite different approaches are used for water and ice. However, two facts can serve as foundation for such an attempt evident similarity of structures of these fluids and of their far-IR spectra. 

At present, a newcomer to solid-state chemistry might therefore believe that this science must have been a key proponent in challenging quantum mechanics (and quantum chemistry, too) for the solution of solid-state chemical problems. Strangely, this is not at all the case. Let us remind ourselves that the puzzle of chemical bonding was ingeniously clarified in 1927, not for a crystalline solid but for the hydrogen molecule. The rapidly emerging scientific discipline, quantum chemistry, also focused on the molecular parts of chemistry both because of technical and "political" reasons first, the most important quantum-chemical workhorse (Hartree-Fock theory) has been particularly resistant to adaptation to the solid state (see Section 2.11.3) and, second, we surely must be aware of the fact that the solid-state chemical commimity is limited in size such that the number of "customers" for quantum chemists is relatively small. As a sad consequence, the solid-state chemists have been left alone for some... 

The phase space representation of trajectories computed numerically, as described above, has been introduced in another chapter of this volume. TTie systems considered there are Hamiltonian systems which arise in chemistry in the context of molecular dynamics problems, for example. The difference between Hamiltonian systems and the dissipative ones we are considering in this chapter is that, in the former, a constant of the motion (namely the energy) characterizes the system. A dissipative system, in contrast, is characterized by processes that dissipate rather than conserve energy, pulling the trajectory in toward an attractor (where in refers to the direction in phase space toward the center of the attractor). We have already seen two examples of attractors, the steady state attractor and the limit cycle attractor. These attractors, as well as the strange attractors that arise in the study of chaotic systems, are most easily defined in the context of the phase space in which they exist. 

Fig. 6.20. A strange situation An election is unable to follow the motion of the nuclei (we are beyond the adiabatic approximation, a non-adiabatic case), ia) Some molecular dipoles with a sufficiently large dipole moment may bind an extra electron (a cloud on the right), which in such a case is far from the dipole and is attracted by its pole. The positive pole plays a role of a pseudonucleus for the extra electron, (b) When the dipole starts to rotate (a state with a nonzero angular momentum), the electron follows the motion of the pole. This is, however, difficult for high angular momenta (the electron has not enough time to adapt its position right toward the pole), and it is even harder because the centrifugal force pushes the extra electron farther away.

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