Electronic energies computation

The quaniity, (R). the sum of the electronic energy computed 111 a wave funciion calculation and the nuclear-nuclear coulomb interaciion .(R.R), constitutes a potential energy surface having 15X independent variables (the coordinates R j. The independent variables are the coordinates of the nuclei but having made the Born-Oppenheimer approximation, we can think of them as the coordinates of the atoms in a molecule. 

This last equation is the nuclear Schrodinger equation describing the motion of nuclei. The electronic energy computed from solving the electronic Schrodinger equation (3) on page 163 plus the nuclear-nuclear interactions Vjjjj(R,R) provide a potential for nuclear motion, a Potential Energy Surface (PES). 

Table 3 Unique Many-Body Electronic Energies Computed at the RHF/aug-cc-pVDZ Level...

Wang C S and Callaway J 1978 BNDPKG. A package of programs for the calculation of electronic energy bands by the LCGO method Comput. Phys. Commun. 14 327... 

B. A. Hess and C. M. Marian, Relativistic Effects in the Calculation of the Electronic Energy, in Computational Molecular Spectroscopy, P. Jensen and P. Bunker, eds., John Wiley Sc Sons, Inc., Chichester, UK, 2000, pp. 169-220. 

Determination of the paiameters entering the model Hamiltonian for handling the R-T effect (quadratic force constant for the mean potential and the Renner paiameters) was carried out by fitting special forms of the functions [Eqs. (75) and (77)], as described above, and using not more than 10 electronic energies for each of the X H component states, computed at cis- and toans-planai geometries. This procedure led to the above mentioned six parameters... 

All m oleciilar orbitals are com biiiations of the same set of atom ic orbitals they differ only by their LCAO expansion coefficients. HyperC hem computes these coefficients, C p. and the molecular orbital energies by requiring that the ground-state electronic energy beat a minimum. That is, any change in the computed coefficients can only increase the energy. 

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

Simply doing electronic structure computations at the M, K, X, and T points in the Brillouin zone is not necessarily sufficient to yield a band gap. This is because the minimum and maximum energies reached by any given energy band sometimes fall between these points. Such limited calculations are sometimes done when the computational method is very CPU-intensive. For example, this type of spot check might be done at a high level of theory to determine whether complete calculations are necessary at that level. 

The value of k was fixed at 0-5 and the n electron energy when the orbital representing the attacking reagent was positioned near to a particular position in the aromatic nucleus was computed, using values of h var3nng from — 3 to +3. 

How is electronic potential energy computed Electrons, which are more than three orders of magnitude lighter than nuclei, are too small for classical mechanics calculations. Electronic energy must... 

DFT methods compute electron correlation via general functionals of the electron density (see Appendix A for details). DFT functionals partition the electronic energy into several components which are computed separately the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and an exchange-correlation term accounting for the remainder of the electron-electron interaction (which is itself... 

CBS-4 does very well for the atomization energy and electron affinity computations and fairly well for the other two calculations. ... 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

In Table II the state of the ion and the recombination energies in electron volts (computed from (65)) are given. Some very uncertain information is included in the right hand column as to the relative abundances of the metastable states of the ions when produced by electron impact with 100-e.v. electrons from the indicated compounds. 

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