Potential topology

Abstract In the present study, the effect of the potential energy surface representation on the infrared spectra features of the and Df clusters is investigated. For the spectral simulations, we adopted a recently proposed (Sanz-Sanz et al. in Phys Rev A 84 060502-1-4, 2011) two-dimensional adiabatic quantum model to describe the proton-transfer motion between the two H2 or D2 units. The reported calculations make use of a reliable on the fly DFT-based potential surface and the corresponding new dipole moment surface. The results of the vibrational predissociation dynamics are compared with earlier and recent experimental data available from mass-selected photodissociation spectroscopy, as well as with previous theoretical calculations based on an analytical ab initio parameterized surfaces. The role of the potential topology on the spectral features is studied, and general trends are discussed. 

At the CCSD(T)/aug-cc-pVTZ level, our theory gives the ground-state splitting as Ao(theor.) = 0.53 cm , which almost perfectly reproduces the experimental value Ao(exp.) = 0.54 cm (see Table 7.4). In this table also shown are the three factors B = Bexp[—5i], So, and when we write Aq = B exp(—So/ti — Si) [see, for instance. Equation (6.100) and (6.117), where = 2Wos and 5i = 21Vis]. As one can see, the difference in Aq between the two methods comes mainly from the principal exponent So and the other two factors are fairly close to each other. This also confirms the above surmise about the similarity in the potential topology for different ab initio methods. On the other hand, the principal exponent So is mainly affected by the height of the potential barrier, which in the case of CCSD(T)/aug-cc-pVTZ reduces to 1770 cm Note that there is almost 200 cm difference from the estimate made by Tanaka et al. [149], which is probably due to the drawback of their one-dimensional model. 

As mentioned in the introduction, the simplest way of approximately accounting for the geomehic or topological effects of a conical intersection incorporates a phase factor in the nuclear wave function. In this section, we shall consider some specific situations where this approach is used and furthermore give the vector potential that can be derived from the phase factor. 

Similarides Between Potential Ruid Dynamics and Quantum Mechanics Electrons in the Dirac Theory The Nearly Nonrelativistic Limit The Lagrangean-Density Correction Term Topological Phase for Dirac Electrons What Have We Learned About Spinor Phases ... 

In Section III.D, we shall investigate when this happens. For the moment, imagine that we are at a point of degeneracy. To find out the topology of the adiabatic PES around this point, the diabatic potential matrix elements can be expressed by a hrst order Taylor expansion. 

A. The Necessary Conditions for Obtaining Single-Valued Diabatic Potentials and the Introduction of the Topological Matrix... 

An index with extremely low degeneracy (i.e., where no degenerate structures have been observed yet) [6], the Charge-related Topological Index (CTI), has been proposed by one of the authors (l.B.) (Figure 6-1). It has a potential-like form (Eq. (4)). 

For current consoHdation, the basic circuits, used at each of the multiple power take-off points, are stacked into a Christmas tree topology to form a single power take-off terminal pair. Scale-up of these devices to commercial sizes is not expected to be a problem, as standard electrical components are available for all sizes considered. A different type of consoHdation scheme developed (117), uses dc to ac converters to connect the individual electrodes to the consoHdation point. The current from each electrode can be individually controUed by the converter, which can either absorb energy from or deHver energy to the path between the electrode and the consoHdation point. This scheme offers the potential capabiHty of controlling the current level of each electrode pair. 

The need for simple descriptions of complicated organic ligands has led to the evolution of some trivial nomenclature systems, such as those for crown ethers (e.g. 76) 72AG(E)16) and cryptands 73MI10200), which have become quite elaborate 8OMII0200). These systems are intended primarily to indicate topology, and the positions of potential donor atoms, and are not particularly appropriate for general use. 

OM Becker, M Karplus. The topology of multidimensional potential energy surfaces Theory and application to peptide stiaicture and kinetics. I Chem Phys 106 1495-1517, 1997. 

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