Polarizability electron correlation effect

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

The remainder of this section will be devoted largely to a summary of recent results from our group on the polarizabilities of LIF and (L1F)2- These represent, respectively, the first calculation of an alkali halide polarizability In which electron correlation effects have been included and the first calculation of a polarizability of an alkali halide dimer. The section concludes with a summary of recent theoretical results for the Ionization potentials for (LlF)jj, n 1-4. 

Walker, S. and Straw, H. (1966) Spectroscopy, paperback edn, Chapman Hall, London. Werner, H.-J. and Meyer, W. (1976) PNO-CI and PNO-CEPA studies of electron correlation effects V. Static dipole polarizabilities of small molecules. Mol. Phys., 31, 855-872. 

The situation is somewhat different for the convergence with the wavefunction model, i.e. the treatment of electron correlation. As an anisotropic and nonlinear property the first dipole hyperpolarizability is considerably more sensitive to the correlation treatment than linear dipole polarizabilities. Uncorrelated methods like HF-SCF or CCS yield for /3 results which are for small molecules at most qualitatively correct. Also CC2 is for higher-order properties not accurate enough to allow for detailed quantitative studies. Thus the CCSD model is the lowest level which provides a consistent and accurate treatment of dynamic electron correlation effects for frequency-dependent properties. With the CC3 model which also includes the effects of connected triples the electronic structure problem for j8 seems to be solved with an accuracy that surpasses that of the latest experiments (vide infra). 

Using the extrapolated ciystal packing ratios for one-dimensional arrays of MNA, the global packing ratios were calculated within the multiplicative scheme and then used to evaluate the effective dipole moment, polarizability and first hypetpolarizability of the MNA dimer in the crystal. Finally, the correspon g macroscopic quantities were evaluated. Although electron correlation effects have been indirectly accounted for, our estimates still underestimate the available x experimental values. On the other hand, the... 

An adequate account of the electron correlation effects requires the use of basis sets of considerable sizes which include polarization and diffuse functions. The ab initio CC calculations with such basis sets are expensive. Thus more exact CC calculations of molecular optical parameters can be carried out only for relatively small molecules. In the calculations of polarizabilities and hyperpolarizabilities for larger a -systems more approximate methods need to be used. Such calculations still remain a difficult problem in quantum chemistry. 

As noted in the Sect. 3.3.2, the polyacenes are characterized by a more complex structure of the wave function, and therefore, to adequately describe this structure a higher level of theory is needed. It is expected that for the polycyclic aromatic hydrocarbons discussed in this section the selection of an appropriate correlation radius is a very important aspect of the calculation. To study the effect of the level of accounting for the electron correlation effects for polyacenes, we have calculated the polarizability and 2nd hyperpolarizabUity values for different levels of the cue-CCSD theory. In Figs. 3.14 and 3.15 the dependencies of the specific values of these properties on the number of the r-electrons are shown. 

The second noteworthy feature is the difference in the accuracy of the description of (a) and (y) in the HF and MP2 methods. In general, these methods are satisfactory in describing the values of the polarizabilities (except the case of linear polyacenes). At the same time, for the 2nd hyperpolarizabilities, there are significant deviations from the results obtained from the cue-CCSD calculations (especially for Y)benzene)-Therefore, a rough accounting for the electron correlation effects cannot guarantee a similarly accurate description of every optical property. As it will be shown below, this conclusion remains true for optical properties proportional to odd powers of the strength of the applied field. 

Costa et al. present results of many-body perturbation theory, coupled cluster and quadratic Cl methods apphed to the calculation of the polarizability and first hyperpolarizability of NaH. It is shown that the nuclear relaxation contribution is substantial for this molecule and that it is appreciably affected by electron correlation effects. 

Electron Correlation Effects. -PITZER has suggested that London, or van der Waals, dispersion forces between atoms or groups in the same molecule may lead to an appreciable stabilization of the molecule. Such London forces are large when both groups are highly polarizable. It seems plausible to generalize and state that additional stability due to London forces will always exist in a complex formed between a polarizable acid and a polarizable base. In this way the affinity of soft acids for soft bases can be accounted for. 

Thierfelder C, AssadoUahzadeh B, Schweidtfeger P et al (2008) Relativistic and electron correlation effects in static dipole polarizabilities for the Group 14 elements from ctirbon to element Z = 114 theory and experiment. Phys Rev A 78 052506... 

SA(A)1011]. Static dipole polarizabilities were computed up to the MP4(SDQ) level [94MP557]. A study of the electronic structure of the 2 and 3 states of 192 showed that inclusion of dynamic electron correlation effects is very important [98JPC(A)8021]. The multiplicity of the 13.5-triazine dication is predicted to be a high-spin triplet while the trication is most likely a doublet. In hexahydro-... 

The static longitudinal and transverse polarizabilities of polyyne chains have been calculated at the CCSD(T)/cc-pVTZ level of theory in order to address their scaling with chain length (L) . For n = 1-9, the transverse component of the polarizability evolves linearly with L whereas the longitudinal component scales as This exponent is smaller than for the free electron in a box, which has been attributed to electron-electron repulsions in contrast to electron correlation effects. 

The static dipole polarizabilities for the Pq ground state of the neutral group-14 elements C, Si, Ge, Sn, Pb, and element Z = 114 have been determined from all-electron relativistic coupled cluster theory. It is shown that the isotropic and anisotropic components of the polarizability increase monotonically with the nuclear charge, except for the spin-orbit coupled /=0 states, which start to decrease from Sn to Pb and even further to element 114. So, spin-orbit coupling leads to a significant reduction of the polarizability of element 114, i.e., from 47.9 a.u. at the scalar-relativistic Douglas-Kroll level to 31.5 a.u. at the Dirac-Coulomb level of theory, which is below the value of Si. The calculations further demonstrate that relativistic and electron correlation effects are nonadditive. The measured dipole polarizabilities of Sn (42.4 11 a.u.) and Pb (47.1 7) are in reasonable agreement with the theoretical values, 52.9 a.u. and 47.3 a.u., respectively. 

Compounding the difficulty of accounting for electron correlation effects properly, accurate computations of noncovalent interactions also require very large basis sets. This is not surprising because London dispersion interactions can be expressed in terms of the polarizabilities of the weakly interacting molecules, and polarizability computations are known to have large basis set requirements. In many weakly bound complexes, the dispersion terms can be the dominant ones. 

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