Potential-energy surfaces Repulsive

Here, the first term is the kinetic energy of the electrons only. The second term is the attraction of electrons to nuclei. The third term is the repulsion between electrons. The repulsion between nuclei is added onto the energy at the end of the calculation. The motion of nuclei can be described by considering this entire formulation to be a potential energy surface on which nuclei move. 

After solving the electronic Schrodinger equation (equation 4), to calculate a potential energy surface, you must add back nuclear-nuclear repulsions (equation 5). 

Figure 1. Schematic of the radial cuts of the ground- and excited-state potential energy surfaces at the linear and T-shaped orientations. Transitions of the ground-state, T-shaped complexes access the lowest lying, bound intermolecular level in the excited-state potential also with a rigid T-shaped geometry. Transitions of the linear conformer were previously believed to access the purely repulsive region of the excited-state potential and would thus give rise to a continuum signal. The results reviewed here indicate that transitions of the linear conformer can access bound excited-state levels with intermolecular vibrational excitation.

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

Figure 7. Two-dimensional cut of the ground- and excited-state adiabatic potential energy surfaces of Li + H2 in the vicinity of the conical intersection. The Li-EL distance is fixed at 2.8 bohr, and the ground and excited states correspond to Li(2,v) + H2 and Lit2/j ) + H2, where the p orbital in the latter is aligned parallel to the H2 molecular axis, y is the angle between the H-H intemuclear distance, r, and the Li-to-H2 center-of-mass distance. Note the sloped nature of the intersection as a function of the H-H distance, r, which occurs because the intersection is located on the repulsive wall. (Figure adapted from Ref. 140.)...

Fig. 8. Potential energy surfaces for ligand addition. Case (c) weakly repulsive potential energy surface for approach of the incoming ligand to the high-spin metal fragment.

Database/3 and the other data used in this paper consist entirely of zero-point-exclusive data, which allows for direct comparisons with calculated Bom-Oppenheimer potential energy surfaces, i.e., the sum of the electronic energies and nuclear repulsion. Although the G3X and CBS families of methods have standard geometry and frequency calculations associated with them, in this paper only the potential energy surfaces are required to compare with Database/3. The geometries used are optimized QCISD/MG3 geometries for all calculations in this paper. 

AMI. While MNDO was widely accepted and extensively used, there were still some deficiencies in the model. In particular, excessive repulsions were observed in MNDO potential energy surfaces just outside chemical bonding distances. This deficiency manifested itself (5,7) in the inability of MNDO to model hydrogen bonding, as well as in large positive errors in the AHf of sterically crowded molecules and in heats of activation. Again Dewar set off to correct this deficiency. 

Fig. 5. The pseudo-Jahn-Teller effect in ammonia (NH3). (a) CCSD(T) ground state potential energy curve breakdown of energy into expectation value of electronic Hamiltonian (He), and nuclear-nuclear repulsion VNN. (b) CASSCF frequency analysis of pseudo-Jahn-Teller effect showing the effect of including CSFs of B2 symmetry is to couple the ground and 1(ncr ) states to give a negative curvature to the adiabatic ground state potential energy surface for the inversion mode.

A potential energy of repulsion may extend appreciable distances from surfaces, but its range is compressed (i.e., reduced) by increasing the electrolyte content of the system. 

That these different compounds produce the same effect at so nearly the same concentration argues that the principal cause of the effect is electrostatic. Use the average of these concentrations to calculate (a) the value of k at which this system coagulates, (b) the force of repulsion (Equation (82)), and (c) the potential energy of repulsion (Equation (86)) when two planar surfaces are separated by a distance of 10 nm. For the purpose of calculation in parts (b) and (c), i/ o may be taken as 100 mV. Comment on the applicability of these equations to the physical system under consideration. 

Auerbach et al. (101) used a variant of the TST model of diffusion to characterize the motion of benzene in NaY zeolite. The computational efficiency of this method, as already discussed for the diffusion of Xe in NaY zeolite (72), means that long-time-scale motions such as intercage jumps can be investigated. Auerbach et al. used a zeolite-hydrocarbon potential energy surface that they recently developed themselves. A Si/Al ratio of 3.0 was assumed and the potential parameters were fitted to reproduce crystallographic and thermodynamic data for the benzene-NaY zeolite system. The functional form of the potential was similar to all others, including a Lennard-Jones function to describe the short-range interactions and a Coulombic repulsion term calculated by Ewald summation. 

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