Correlation energy intermolecular

The scope of this work is to deal with the possible treatments of electron correlation in a localized representation. Several methods will be discussed in detail elaborated by present authors. Special attention will be payed to the analysis of the transferability of certain correlation energy contributions. The use of their transferability will be discussed for extended systems series of hydrocarbons and polyenes will be investigated. The transferable properties of the contributions to the correlation energy, furthermore, turned out to be useful in the study of weakly interacting intermolecular systems. A detailed description of this procedure will be given in the present work. 

The parametrization procedure that we have opted for in the most recent works is as follows (1) Compute the intermolecular dynamic correlation energy for the ground state with a second-order Mpller-Plesset (MP2) expression that only contains the intermolecular part and which uses monomer orbitals. Fit the dispersion parameters to this potential. To aid in the distribution of the parameters, a version of the exchange-hole method by Becke and Johnson is sometimes used [154,155], Becke and Johnson show that the molecular dispersion coefficient can be obtained fairly well by a relation that involves the static polarizability and the exchange-hole dipole moment ... 

For systems which interact so weakly, one would not expect the correlation energy within a subsystem to vary significantly with intermolecular separ-... 

The quantum mechanical approach cannot be used for the calculation of complete lattice energies of organic crystals, because of intrinsic limitations in the treatment of correlation energies. The classical approach is widely applicable, but is entirely parametric and does not adequately represent the implied physics. An intermediate approach, which allows a breakdown of the total intermolecular cohesion energy into recognizable coulombic, polarization, dispersion and repulsion contributions, and is based on numerical integrations over molecular electron densities, is called semi-dassical density sums (SCDS) or more briefly Pixel method. [12-14]... 

Hydrogen-bonding.—The results of ab initio calculations on the hydrogen bond in (HF)2 show that there is a relatively small net effect of the total correlation energy on the interaction energy, on the F(H)F distance, and on the intermolecular vibration. N.m.r. studies ( H and F) of HFj in a single crystal of KHFj have confirmed that the proton in this linear anion is centred, to within 0.025 A. The mean H—F bond length is 1.168 0.002 A the F—F distance was... 

Electron correlation effects are known to be impx>rtant in systems with weak interactions. Studies of van der Waals interetctions have established the importance of using methods which scale linearly with the number of electrons[28] [29]. Of these methods, low-order many-body perturbation theory, in particular, second order theory, oflfers computational tractability combined with the ability to recover a significant firaction of the electron correlation energy. In the present work, second order many-body perturbation theory is used to account for correlation effects. Low order many-body perturbation theory has been used in accurate studies of intermolecular hydrogen bonding (see, for example, the work of Xantheas and Dunning[30]). 

In a (rather crude) summary, it might be said that DFT does not rigorously solve the problem of correlation energy, but displaces the problem to a well defined location, the Sex(p), where a parametric ambush can be set for its solution. The method, whose computational demand is similar or sometimes more modest than those of MO methods, has been very successful in applications to isolated molecules, where the introduction of electron correlation corrections has been seen to improve, for example, calculated optimized molecular geometries, but has not yet proved completely satisfactory for the calculation of intermolecular interaction energies in systems where coulombic contributions are not overwhelmingly dominant. Molecular crystals are a typical example. 

Several other methods for quantum chemical calculations that approach the correlation energy problem have been proposed, but their detailed examination would be out of place in this book [17]. They all require a substantial increase in computational effort with respect to HF and to MPn or DFT. Even these more refined methods stumble upon the fundamental physical obstacle represented by the fact that these intermolecular interaction energies are often very small (see Chapter 4). For inter-molecular selectivity, sometimes the decision has to be made at the level of less than... 

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