Equilibrium atomization energies calculations

Benchmark calculations of the equilibrium atomization energies (AEs) of the small molecules CH2, H2O, HF, N2, CO and F2 are presented in Table II. The CCSD(T) calculations are performed in systematically increasing correlation-... 

By contrast, the nonrelativistic equilibrium atomization energy Dg calculated theoretically represents the difference between the nonrelativistic atomic ground-state term energy and... 

Our final statistical sample for the atomization energy thus consists of the 16 molecules ticked in Table 15.1. These molecules should be well suited for testing the performance of the standard electronic-structure models for the four molecules omitted from the statistical analysis, the calculations presented here should serve as accurate predictions of the equilibrium atomization energies. 

From the experimental atomization energy of Do = 3.42 eV and the vibrational and relativistic corrections, calculate the experimental equilibrium atomization energy De in Eh and kJ/mol units. 

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

To be consistent, the minimum energies from the LMTO-program were used even though this underestimated the lattice constant. Murnaghan s equation of state was used to determine bulk moduli and equilibrium volumes. The energy calculations were converged within 1 mRy/atom. 

With such calculations one can approach Hartree-Fock accuracy for a particular cluster of atoms. These calculations yield total energies, and so atomic positions can be varied and equilibrium positions determined for both ground and excited states. There are, however, drawbacks. First, Hartree-Fock accuracy may be insufficient, as correlation effects beyond Hartree-Fock may be of physical importance. Second, the cluster of atoms used in the calculation may be too small to yield an accurate representation of the defect. And third, the exact evaluation of exchange integrals is so demanding on computer resources that it is not practical to carry out such calculations for very large clusters or to extensively vary the atomic positions from calculation to calculation. Typically the clusters are too small for a supercell approach to be used. 

Figure 4 Heterocycles for which the tautomeric equilibrium in aqueous solution has been studied using free energy calculations including explicit solvent. Tautomerism occurs by exchanging a proton between the labeled atoms.

Figure 10. Lowest energy equilibrium geometries and calculated adsorption energies of CO molecules on neutral Au clusters with 5

In this way there is obtained an interaction-energy curve (the lower full curve in Figure 1-7) that shows a pronounced minimum, corresponding to the formation of a stable molecule. The energy of formation of the molecule from separated atoms as calculated by Heitler, London, and Sugiura is about 67 percent of the experimental value of 102.6 kcal/mole, and the calculated equilibrium distance between the nuclei is 0.05 A larger than the observed value 0.74 A. 

The CH(F)=XH2 series has planar equilibrium structures for X = C and Si, while for X = Ge, Si and Pb the optimized fraws-bent geometry is more stable (Table 2). The planar forms for the last three X atoms are calculated to be 0.3, 2.3 and 5.4 kcalmol-1 higher in energy than the respective fraws-bent forms. DFT/CEP-5ZP calculations using the B3LYP functional do not show stationary states in the planar geometry for the Sn and Pb compounds, while, as noted above, at the ab initio CAS(4,4)/CEP-DZP level... 

Fig. 1.12. Two-dimensional polar plots of the potential energy surfaces (denoted below by Vx, Va, and Ve) of the three lowest electronic states of H2O. One of the O-H bonds is frozen at its equilibrium in the electronic ground state. The contours represent the potential energy as the other H atom swings around the O atom. Energies and distances are given in eV and A, respectively. The energy is normalized such that H + OH(2II, re) and H + OH(2E, re), respectively, correspond to E — 0. Vx is the empirical fit of Sorbie and Murrell (1975) whereas Va and Vb have been calculated by Staemmler and Palma (1985) and by Theodorakopoulos, Petsalakis, and Buenker (1985), respectively. The heavy arrows illustrate the main dissociation paths in the excited states.

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