Electron correlations, nonlinear

Establishing a hierarchy of rapidly converging, generally applicable, systematic approximations of exact electronic wave functions is the holy grail of electronic structure theory [1]. The basis of these approximations is the Hartree-Fock (HF) method, which defines a simple noncorrelated reference wave function consisting of a single Slater determinant (an antisymmetrized product of orbitals). To introduce electron correlation into the description, the wave function is expanded as a combination of the reference and excited Slater determinants obtained by promotion of one, two, or more electrons into vacant virtual orbitals. The approximate wave functions thus defined are characterized by the manner of the expansion (linear, nonlinear), the maximum excitation rank, and by the size of one-electron basis used to represent the orbitals. 

Electron correlation effects are expected to play an important role in determining optical nonlinearities. Both the configuration interaction and Moeller-Plesset perturbation correction approaches have been used to incorporate electron-correlation effects (26,27) ... 

In the past few years, a great effort has been devoted to the extensions of solvation models to QM techniques of increasing accuracy. All these computational extensions have been based on a reformulation of the various QM theories describing electron correlation so as to include in a proper way the effects of the nonlinearity of the solvation model by assuming the free-energy functional as the basic energetic quantity. 

Continuing advances in the theoretical treatment of metallocenes and substituted derivatives can be anticipated. Despite the historical difficulties with molecular orbital calculations on ferrocene, the problems are now recognized to stem from failure to account for electron correlation effects. New approaches to addressing this issue, coupled with inevitable increases in computing power, should make more metallocenes with substituted groups systems amenable to accurate calculation. More realistic predictions of donor ability, and thus better estimates of their effects in nonlinear optical (NLO) systems, will be possible. 

A later work continued the investigation of extended chains of water molecules, incorporating the effects of electron correlation. As in the oligomers of HF, the length of the H-bond contracts as the chain enlarges. The small nonlinearity present in the dimer vanishes as well. Crystal orbital techniques were employed to consider infinitely extended chains. Some of the more interesting features of the infinite chain are listed in Table 5.11... 

Molecular polarizabilities and hyperpolarizabilities are now routinely calculated in many computational packages and reported in publications that are not primarily concerned with these properties. Very often the calculated values are not likely to be of quantitative accuracy when compared with experimental data. One difficulty is that, except in the case of very small molecules, gas phase data is unobtainable and some allowance has to be made for the effect of the molecular environment in a condensed phase. Another is that the accurate determination of the nonlinear response functions requires that electron correlation should be treated accurately and this is not easy to achieve for the molecules that are of greatest interest. Very often the higher-level calculation is confined to zero frequency and the results scaled by using a less complete theory for the frequency dependence. Typically, ab initio studies use coupled-cluster methods for the static values scaled to frequencies where the effects are observable with time-dependent Hartree-Fock theory. Density functional methods require the introduction of specialized functions before they can cope with the hyperpolarizabilities and higher order magnetic effects. 

The TT-electron states are true many-body states because electron correlations due to natural repulsive Coulomb interactions tend to localize the otherwise delocalized electrons. Electron correlations play an important role in the nonlinear optical responses of conjugated organic structures (1-3,16,17,26), and their description of 3 and Y i l differs markedly from inde-... 

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). 

C. Adant, M. Dupuis, and J. L. Bredas, Int.J. Quantum Chem., Quantum Chem. Symp., 29, 497 (1995). Ab Initio Study of the Nonlinear Optical Properties of Urea Electron Correlation and Dispersion Effects. 

The quantum chemical calculations of optical and nonlinear optic molecular parameters are an important step in designing new materials. However, adequate description of molecular optical parameters presents a challenge for contemporary quantum chemistry. The main problem in such calculations is the necessity of accounting for a significant part of the electron correlation effects. In the last decade the density functional theory (DFT) has been used for (hyperjpolarizability calculations (see for instance [45]). It allows the consideration of systems with extended sizes. However, the DFT calculations are known to produce significant errors in the evaluation of the optical properties of a -conjugated systems [8, 26, 83]. 

An alternative approach for predicting optical properties of larger molecular systems is to employ semiempirical methods which can be used to calculate large polymeric systems. As mentioned above, the description of the nonlinear molecular optical parameters strongly depends on the level of accounting for the electron correlation effects. Thus, the semiempirical wave function has to include these effects in... 

Figs. 3.6 and 3.7). Therefore the HF and MP2 methods are not suitable for describing the optical nonlinear properties for systems with strong electron correlation. 

Heflin, J. R., Wong, K. Y, Zamani-khamiri, O., and Garito, A. F, Symmetry-controlled electron correlation mechanism for third order nonlinear optical properties of conjugated linear chains. Mol. Cryst. Uq. Cryst., 160, 37-51 (1988). 

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