Oscillations electron correlation

The HF level as usual overestimates the polarity, in this case leading to an incorrect direction of the dipole moment. The MP perturbation series oscillates, and it is clear that the MP4 result is far from converged. The CCSD(T) method apparently recovers the most important part of the electron correlation, as compared to the full CCSDT result. However, even with the aug-cc-pV5Z basis sets, there is still a discrepancy of 0.01 D relative to the experimental value. 

If we find the structural factor from some independent experimental data, say, from those concerning the scattering of neutrons, relation (3.25) will enable us to find the loss function also. Since the structural factor is determined by the density-density electron correlation function, relation (3.25) implies that the excitation of plasmon oscillations is determined by the correlation in electron motion. 

Abstract. We have calculated the scalar and tensor dipole polarizabilities (/3) and hyperpolarizabilities (7) of excited ls2p Po, ls2p P2- states of helium. Our theory includes fine structure of triplet sublevels. Semiempirical and accurate electron-correlated wave functions have been used to determine the static values of j3 and 7. Numerical calculations are carried out using sums of oscillator strengths and, alternatively, with the Green function for the excited valence electron. Specifically, we present results for the integral over the continuum, for second- and fourth-order matrix elements. The corresponding estimations indicate that these corrections are of the order of 23% for the scalar part of polarizability and only of the order of 3% for the tensor part... 

On the other hand, by emphasizing the state-specific calculation of the wavefunctions of initial and final states and by taking into account orbital NON, it is possible to understand semiquantitatively multiple electron excitations in atoms even at the SCF level. Such one-photon excitations may reach doubly, triply, or even quadruply excited unstable states. Given the existing high-energy photon sources, in atoms these are measurable. Two examples of transitions whose oscillator strengths are finite and reasonable even without the inclusion of electron correlation, are as follows ... 

In metals and highly conjugated dye molecules many electrons correlate at once and behave as an electron gas with collective screening and oscillation effects. ... 

Instead, Nicolaides and Beck [37b, p. 506] considered the exactly solvable problems of the harmonic oscillator and of hydrogen and found that in fact, a single function can diagonalize H(rd ). This is the rotated function of the unrotated solution, i.e., [H(rd ) — e ] (rd ) = 0, for each state n > and real e . (The proof is straight-forward). In fact, we stated two "theorems" that are basic to the development of the practical implementation of the CESE-SSA [37b, p. 505], since, in practice, they allow the difficult electron correlation calculations to be done only once on the real axis, and then continue the computation in the complex energy plane where the Gamow orbitals are optimized until the complex energy is stabilized. 

In the late 1980s, this three-electron excitation was cited by other researchers as a heuristic case to argue that, "as far as we can tell, a multiply excited state such as 3p is virtually inaccessible by single-photon absorption." Yet, small-size (for reasons of economy) SSA calculations show that the state-specific HF result, which is of course obtained from an independent electron model with no electron correlation, produces nonzero values for the probabilities of the three transitions. Furthermore, the order of magnitude of the HF transition probabilities is the same as that from computations that include some part of electron correlation. Specifically, the results of the SSA calculations for the oscillator strengths, using only approximate wavefunctions for the oS, are ... 

For these molecular metals, we still observe electronic correlations, whose presence is detected by an enhanced Pauli paramagnetism, and the analysis of the oscillator strength... 

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