Calculation Of Frequency-dependent Polarizabilities Research Articles

Calculation of frequency-dependent polarizabilities using the approximate coupled-cluster triples model CC3

The calculation of frequency-dependent polarizabilities is discussed for the iterative approximate coupled-cluster singles, doubles and triples model CC3. A new implementation of the linear response functions is reported, which has the same computational O(N7) scaling as CC3 ground state calculations and uses an explicitly spin-coupled excitation space. Sample calculations are presented for the static and frequency-dependent polarizabilities of Ne and ethylene, as well as for the static polarizabilities of HF. The largest calculation employs the t-aug-cc-pVTZ basis set for ethylene giving a total of 328 basis functions. The results obtained agree well with the experimental data.

Calculation of Frequency-Dependent Polarizabilities of Quasi-One-Dimensional Systems

Calculations of frequency-dependent polarizabilities of quasi-one-dimensional systems are reported using the coupled Hartree-Fock method recently developed for polymers. Computations have been performed for infinite model chains of hydrogen and water molecules, respectively. The frequency dispersions applying different basis sets agree very well with theoretical results in the literature both for the chain and the respective molecule. In addition the dynamic polarizabilities of the conjugated periodic systems polyacetylene, polycarbonitrile and polyaziridine have been investigated.

Calculation of frequency-dependent polarizabilities and hyperpolarizabilities by the second-order Møller-Plesset perturbation theory

The QED-MP2 model based on the quasi-energy derivative method in the second-order Møller-Plesset perturbation theory is formulated, and frequency-dependent (dynamic) polarizabilities [α(−ω;ω)] for H 2O and NH 3 are calculated. Dynamic polarizabilities obtained for H 2O agree with experimental values. First hyperpolarizabilities for the electro-optic Pockels effect [β(−ω;ω, 0)] and second hyperpolarizabilities for the electro-optic Kerr effect [γ(−ω;ω, 0, 0)] are also calculated as the numerical derivatives of α(−ω; ω).

Calculation of frequency-dependent polarizabilities using coupled-cluster response theory

Coupled-cluster singles and doubles linear response (CCLR) calculations have been presented for frequency-dependent dipole polarizabilities and the results compared with the results from a CI-like approach to the equation of motion (EOMCC). The frequency-dependent polarizabilities are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-extensive polarizabilities, whereas the EOMCC approach does not. EOMCC calculations can therefore give unphysical polarizabilities, e.g. EOMCC calculations on a sequence of non-interacting LiH systems gave a negative polarizability for 20 or more non-interacting LiH systems. The CCLR approach is shown to be an attractive “black box” approach for the calculation of accurate frequency-dependent polarizabilities.

The calculation of frequency-dependent polarizabilities as pseudo-energy derivatives

The definition of frequency-dependent polarizabilities α(−ω;ω), β(−2ω;ω,ω), β(−ω;ω,0), and β(0;ω,−ω) is discussed, and it is argued that the most convenient definitions are as energy derivatives, a pseudo-energy being defined as the expectation value of [H−i(∂/∂t)]. This definition outlines a straightforward procedure for obtaining frequency-dependent polarizabilities for all quantum chemistry methods including those which account for the effects of electron correlation. It is demonstrated at the self-consistent field level of theory that αλμ(−ω;ω) cos ωt may be considered as the derivative of the static dipole moment μλ with respect to the strength Eωμ of a frequency-dependent field Eωμ cos ωt (as is usual), or as the derivative of an appropriately defined frequency-dependent dipole moment μμ cos ωt with respect to a static field E0λ. In this way, polarizabilities may be determined from finite static field calculations on lower-order tensors. Therefore, α(−ω;ω) cos ωt is defined within second-order Mo/ller–Plesset perturbation theory (MP2) as the second derivative of the MP2 energy with respect to one static and one frequency-dependent field. An analytic expression is given for αλμ(−ω;ω) at the MP2 level of theory. An MP2 frequency-dependent dipole expression is also defined, which if finite static field calculations are applied, gives the same values for αλμ(−ω;ω). MP2 values are reported for α(−ω;ω) of formaldehyde and ammonia for a range of frequency ω=0.01–0.1 a.u. From comparison of the self-consistent field (SCF) and MP2 values of the frequency-dependent contribution to ᾱ(−ω;ω), it is concluded that it is appropriate to use an SCF frequency-dependent correction in conjunction with a static polarizability determined at a higher level of theory in order to obtain an accurate value for ᾱ(−ω;ω) of H2CO in this frequency range. For ammonia, the frequency-dependent contribution to ᾱ(−ω;ω) is more sensitive to electron correlation. Nevertheless, compared to the total polarizability ᾱ(−ω;ω), the error in the frequency-dependent contribution determined using the SCF method is small (∼2% at ω=0.1 a.u.)

Calculation of frequency-dependent polarizabilities with application to photodetachment threshold shift in a strong laser field.

Calculation of frequency-dependent polarizabilities with application to photodetachment threshold shift in a strong laser field.

Calculation of frequency-dependent polarizabilities by means of SCF perturbation theory

The SCF perturbative method developed for the calculation of static polarizabilities is extended to the frequency-dependent case. Calculations are reported for helium and methane. The helium results are compared with those of other workers.