Origin-Independent Decomposition of the Static Polarizability

Abstract

Real-space analysis tools afford additive and transferable contributions of atoms to molecular properties. In the case of the molecular (hyper)polarizabilities, the atomic contributions that have been derived so far include a charge-transfer term that is origin-dependent. In this letter, we present the first genuinely origin-independent energy-based (OIEB) methodology for the decomposition of the static (hyper)polarizabilities that benefits from real-space molecular energy decomposition schemes, focusing on the static polarizability and showing that extension to static hyperpolarizabilities is straightforward. The numerical realization of the OIEB method shows the expected origin independence, atomic additivity, and transferability of atomic and functional group polarizability tensors. Furthermore, the OIEB atomic (fragment) polarizability tensors are symmetric by definition.

Decomposition of Molecular Integrals into Atomic Contributions via Becke Partitioning Scheme: a Caveat

“…In the context of density functions, the quantum theory of atoms in molecules (QTAIM) has played a fundamental role, [5] see for example the atomic partitioning of polarizabilities [6] and magnetizabilities [7] presented by the Bader group. More recently, Hirshfeldbased partitioning scheme for the intrinsic polarizability density [8] and origin-independent decomposition of the static polarizability [9] have been presented.…”

Origin-Independent Densities of Static and Dynamic Molecular Polarizabilities

“… 35 − 37 Recently, an origin-independent decomposition of static polarizability based on AIM has been put forward by Montilla and co-workers. 21 Alparone reported calculated polarizabilities and hyperpolarizabilities obtained integrating origin-dependent perturbed electron densities, at first and second order, respectively, employing a Coulomb-attenuating Density Functional Theory (DFT) method. 38 …”

“…35−37 Recently, an origin-independent decomposition of static polarizability based on AIM has been put forward by Montilla and co-workers. 21 Alparone reported calculated polarizabilities and hyperpolarizabilities obtained integrating origin-dependent perturbed electron densities, at first and second order, respectively, employing a Coulombattenuating Density Functional Theory (DFT) method. 38 A Hirshfeld-based scheme for resolving the intrinsic polarizability densities has been proposed by Otero and coworkers, 39 and a partition into fluctuating charge and induced atomic dipole contributions has been put forward by Mei et al 40 An extension to consider also hyperpolarizability density has been advanced and applied by Nakano et al, 41 Yamada et al, 42 and Alparone.…”

“…In order to understand mechanisms and causes that come into play to bring about polarization of the electron cloud and to understand the role of different substituents and moieties entering a given molecular substrate, and related push–pull effects, attempts have been made to define reliable resolutions of the electric dipole polarizability into contributions arising from various molecular domains, with the aim that they be movable from molecule to molecule. Accordingly, partitions into transferable additive terms have been defined allowing for various criteria. − A simple scheme for separating molecular polarizability into atomic and bond contributions has been obtained by employing the electric dipole acceleration gauge. , …”

“…Frequency-dependent distributed polarizabilities have been computed by time-dependent Hartree–Fock (TDHF) calculations by Hättig et al, within Bader’s theory of atoms in molecules (AIM). − Recently, an origin-independent decomposition of static polarizability based on AIM has been put forward by Montilla and co-workers . Alparone reported calculated polarizabilities and hyperpolarizabilities obtained integrating origin-dependent perturbed electron densities, at first and second order, respectively, employing a Coulomb-attenuating Density Functional Theory (DFT) method …”