Describing potential energy surfaces

Structures with a cyclic character (70° a 110°) are less solvated than open cation structures (a < 70° a > 110°) due to a larger charge delocalization in the former. Thus, the alterations of the potential energy surface described above are plausible. There are two possible structures for activated complexes in solution. They... 

Classical trajectory calculations, performed on the PES1 and PESl(Br) potential energy surfaces described above, have provided a detailed picture of the microscopic dynamics of the Cl- + CH3Clb and Cl" + CH3Br SN2 nucleophilic substitution reactions.6,8,35-38 In the sections below, different aspects of these trajectory studies and their relation to experimental results and statistical theories are reviewed. 

The outer part of the potential energy surface describes the motion of the molecule far from the surface. The motion along z is a smooth translation, while the motion along r is just the vibration of the free molecule. 

The inner part of the potential energy surface describes the motion of the chemisorbed molecule. 

The great speed and known properties of RHF calculations are not sufficient justification for a limitation to RHF methods when they are inherently inappropriate. It is worth remarking that most potential-energy surfaces describing reactions, and many describing dissociations are inappropriate for RHF methods. Restricted Hartree-Fock methods are also of limited validity in many situations where two or more surfaces are at nearly the same energy. 

Fig. 10 The three-dimensional potential energy surface describing the motion of protons between N6(A) and 04(T) and between N3(T) and N1(A) shows two critical points in the ground state. The deeper minimum corresponds to the amine/keto structure of AT and a shallow one to the imine/enol structure (A T ). Upon absorption of a UV photon the initaly delocalized excitonic states (1) undergo a rapid localization on f 10 ps timescale for single bases and 100 ps timescale for stacked base pairs to form a charge transfer (CT) states. The subsequent CT states passing through a conical intersection are carried back to the ground state.

Usually one assumes that the electrons stay in their ground state. The ground-state energy of the electronic Hamiltonian as a function of the nuclear coordinates then represents the potential energy surface describing the interaction of a molecule with a substrate. Of course all electronic transitions are neglected in this ansatz. Often this is a reasonable assumption although its validity is hard to prove. Still, there is an important class of dynamical processes on surfaces which involve electronic transitions. I will also briefly discuss such processes later in this review. 

Figure 3 A contour plot of the potential energy surface described in the text, as a function of z and Zu the distance of the incident and target atoms, respectively, above the surface plane. The distance between the atoms parallel to the surface is held fixed at the gas-phase H-H bond length. The marked contours are in eV, with a contour spacing of 0.2 eV. Taken from Ref. [83].

A particular effort has been addressed to the study of the dynamics within the dimer and to the characterization of fhe low lying rovibrational states in view of pofenfial inferesf for fhe analysis of spectral features in atmospheric research. Calculations of fhe bound rovibrational states of the dimers have been performed for rofafional sfafes having fofal angular momentum / < 6 by solving the secular problem over the exact Hamiltonian. We have calculated the rovibrational levels for the potential energy surfaces described above of the dimers N2-N2, N2-O2 and for all fhree surfaces (singlet, triplet and quintet) [4,5] of O2-O2. A summary of resulfs and fheir discussion follows. Full accounf of all available data has been given in [5,6,8-10]. 

The empty, monoclinic MFI structure is calculated to be 37.0 kj/mol more stable than empty MEL. Both the monoclinic and the orthorhombic MFI structures are minima on the potential energy surface described by the force field and, in agreement with the experimental data, the monoclinic MFI structure has... 

NaCn represents a molecule of vibrationally excited sodium chloride, while Na is an electronically excited, P, sodium atom which emits the resonance radiation. It will be remembered that these studies made very significant contributions to fundamental theories of reaction kinetics, especially with regard to the understanding of the potential energy surface describing reactions, activated complex and products. 

The paper is organized as follows. In section 2, we provide the relevant background information about the MMCC formalism and overview the CR-CC methods employed in this study. In section 3, we examine the performance of various CC and CR-CC methods in calculations for the three cuts of the water potential energy surface described above and compare the results with those obtained with MRCI(Q) and the ES potential function. Finally, in section 4, we provide the concluding remarks. 

Zou, S.L. Bowman, J.M. A new ab initio potential energy surface describing acetylene/vinylidene isomerization. Chem. Phys. Lett. 2003, 368, 421-424. 

For the purposes of simplification, we now assume that the jump rates are independent of position, which amounts to assuming that the potential energy surface describing the atomic motions is symmetrically disposed and that there are no applied fields. This assumption tells us that all of the jump rates may be replaced by T/2, where the factor of 2 derives from the fact that F is the total jump rate (i.e. the total number of atoms leaving a given site per unit time). If we now expand the concentrations c(x =t a, f) as... 

Consideration of the nature of the LMCT transitions, redox energetics, and photoredox behaviour of transition-metal ammine complexes has allowed Endicott and co-workers18 to propose new models for the potential energy surfaces describing their photoredox reactions. These models have been used to discuss the differences in photoreactivity of [Co(NH3)5Br]2+ and [Co(NH3)5-N03]2+.21 These differences are ascribed to (i) more Co-radical bonding in the... 

In order to demonstrate the accuracy of the potential energy surface described by GAP outside the harmonic regime, we calculated the temperature dependence of the optical phonon mode of the T point in diamond. In fact, the low temperature variation of this quantity has been calculated using Density Functional Perturbation Theory by Lang et al. [9]. The ab initio calculations show excellent agreement... 

In 19, four years after the breakthrough of the Heitler-London quantum treatment of the H + H problem, Eyring and Polanyi provided the first potential energy surface describing the motion of three atoms (Fig. 2) ... 

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