About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
The Journal of Chemical Physics
Paper
The calculation of frequency-dependent polarizabilities as pseudo-energy derivatives
Abstract
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 μ λ 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 E 0λ. 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 Møller-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 α(- ω;ω) of H 2CO in this frequency range. For ammonia, the frequency-dependent contribution to ā(- 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.) © 1991 American Institute of Physics.