AC/DC Analysis: Broad and Comprehensive Approach to Analyze Infrared Intensities at the Atomic Level

Abstract

We present a complete theoretical protocol to partition infrared intensities into terms owing to individual atoms by two different but related approaches: the atomic contributions (ACs) show how the entire molecular vibrational motion affects the electronic structure of a single atom and the total infrared intensity. On the other hand, the dynamic contributions (DCs) show how the displacement of a single atom alters the electronic structure of the entire molecule and the total intensity. The two analyses are complementary ways of partitioning the same total intensity and conserve most of the features of the total intensity itself. Combined, they are called the AC/DC analysis. These can be further partitioned following the CCTDP (or CCT) models according to the population analysis chosen by the researcher. The main conceptual features of the equations are highlighted, and representative numerical results are shown to support the interpretation of the equations. The results are invariant to rotation and translation and can readily be extended to molecules of any size, shape, or symmetry. Although the AC/DC analysis requires the choice of a charge model, all charge models that correctly reproduce the total molecular dipole moment can be used. A fully automated protocol managed by the Placzek program is made available, free of charge and with input examples.

Are “GAPT Charges” Really Just Charges?

“…Similar to CT, the DP tensor concerns the modifications of the intraatomic dipoles that are also caused by displacements. A more detailed derivation of the above equations is presented in a recent report from our group, 27 specifically within equations 15−30.…”

“…The protocol, however, is not restricted to Gaussian since these tasks can be performed by a number of codes, some of them being open-source. The C, CT, and DP components from GAPT were calculated by the Placzek program using the equilibrium and additional 6N (for an N-atom molecule) distorted geometries (±0.01 Å on each Cartesian direction) by means of a well-known protocol described in detail elsewhere. ,, Hirshfeld atomic charges and dipoles, as well as CHELPG charges, were obtained by Gaussian’s default routines, with additional constraint for CHELPG to reproduce the correct molecular dipole moment given by the wavefunction (pop = (hirshfeld, chelpg, dipole)); this constraint applies only to CHELPG as Hirshfeld charges and atomic dipoles combined will naturally reproduce the dipole moment. CHELPG charges with additional intraatomic dipoles were obtained by means of the (pop = (chelpg, dipole, atomdip)) setup.…”

Symmetry-Constrained Properties Behave Differently for 2D or 3D Structures under the Same Point Group

“…A comprehensive, detailed, and commented derivation from eqs 1 and 2 toward eqs 3 and 4, respectively, can be found elsewhere. 8,18 In 1989, Dinur and Hagler explored both these situations 23 and first noticed that if we are dealing with the out-of-plane bending vibration of a planar molecule (i.e., displacements along the normal coordinate that are perpendicular to the molecular plane), the symmetry of the normal coordinate requires the second derivative in the RHS (the CT one) to vanish, regardless of the charge model being used. This result was used by some authors in the 1990s to pursue the so-called "IR charges", supposedly derived directly from experiment.…”

“…The property under investigation here is the dipole moment derivative or, more precisely, the derivative of the molecular dipole moment with respect to the normal coordinate of vibration; if the molecular dipole moment is written p⃗ and the k th normal coordinate (concerning the k th molecular vibration) is written Q k , this derivative will then be true( ∂ p⃗ ∂ Q k true) . , When squared and multiplied by the appropriate constants, this derivative yields the IR intensity ( A k ) of that vibration, which is also a real, quantitative, and measurable property, and is also easily calculated by most of the standard quantum chemical packages.…”

“…These terms are interpreted straightforwardly: the charge term regards the effect of the static charges (from the equilibrium geometry) vibrating along the normal coordinate, whereas the charge transfer and dipolar polarization terms concern the changes in the charges and the changes in the atomic dipoles that necessarily occur when the molecular structure departs from the equilibrium arrangement. A comprehensive, detailed, and commented derivation from eqs and toward eqs and , respectively, can be found elsewhere. , …”