Correlation energy, second order

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

An extensive quantum-mechanical study that included correlation by second-order Meller-Plesset perturbation and quadratic configuration-interaction methods showed that the cluster species (NH4)2 is bound with respect to 2 NH4 by 7.5 to 9.7 kcal/mol, but unstable with respect to 2 NH3 + H2 by 86 to 89 kcal/mol. The bonding results from the interaction of the 3sai Rydberg orbitals of NH4. A minimum-energy structure of C2h symmetry was predicted. 

The dispersion is purely quantum mechanical in origin and is the only term at second order in A that describes intermonomer electron correlation. The second-order dispersion energy is long ranged, always negative, and exists between all types of molecules. 

Specifies the calculation ofelectron correlation energy using the Mwllcr-i lessct second order perturbation theory (Ml 2). This option can only be applied Lo Single Point calculations. 

HyperChem supports MP2 (second order Mdllcr-l Icsset) correlation energy calcu latiou s u sin g any available basis set. lu order to save main memory and disk space, the HyperChem MP2 electron correlation calculation normally uses a so called frozen-core approximation, i.e. th e in n er sh el I (core) orbitals are omitted. A sett in g in CHHM.IX I allows excitation s from th e core orbitals to be include if necessary (melted core). Only the single poin t calcula-tion is available for this option. 

Petersson and coworkers have extended this two-electron formulation of asymptotic convergence to many-electron atoms. They note that the second-order MoUer-Plesset correlation energy for a many-electron system may be written as a sum of pair energies, each describing the energetic effect of the electron correlation between that pair of electrons ... 

CBS model chemistries make the correction resulting from these extrapolations to the second-order (MP2) correlation energy ... 

A more balanced description requires MCSCF based methods where the orbitals are optimized for each particular state, or optimized for a suitable average of the desired states (state averaged MCSCF). It should be noted that such excited state MCSCF solutions correspond to saddle points in the parameter space for the wave function, and second-order optimization techniques are therefore almost mandatory. In order to obtain accurate excitation energies it is normally necessarily to also include dynamical Correlation, for example by using the CASPT2 method. 

Thomas and Long488 also measured the rate coefficients for detritiation of [l-3H]-cycl[3,2,2]azine in acetic acid and in water and since the rates relative to detritiation of azulene were similar in each case, a Bronsted correlation must similarly hold. The activation energy for the reaction with hydronium ion (dilute aqueous hydrochloric acid, = 0.1) was determined as 16.5 with AS = —11.3 (from second-order rate coefficients (102At2) of 0.66, 1.81, 4.80, and 11.8 at 5.02, 14.98, 24.97, and 34.76 °C, respectively). This is very close to the values of 16.0 and —10.1 obtained for detritiation of azulene under the same condition499 (below) and suggests the same reaction mechanism, general acid catalysis, for each. 

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