Field‐induced fluctuation correlations and the effects of van der Waals interactions on molecular polarizabilities

Origin-Independent Dynamic Polarizability Density from Coupled Cluster Response Theory

The calculation of the origin-independent density of the dynamic electric dipole polarizability, previously presented for uncorrelated and density functional theory (DFT)-based methods, has been developed and implemented at the coupled cluster singles and doubles (CCSD) level of theory. A pointwise analysis of polarizability densities calculated for a number of molecules at Hartree-Fock (HF) and CCSD clearly shows that the electron correlation effect is much larger than one would argue considering the integrated dipole electric polarizability alone. Large error compensations occur during the integration process, which hide fairly large deviations mainly located in the internuclear regions. The same is observed when calculated CCSD and B3LYP polarizability densities are compared, with the remarkable feature that positive/negative deviations between CCSD and HF reverse sign, becoming negative/positive when comparing CCSD to B3LYP.

Electronic current densities and origin-independent property densities induced by optical fields

The interaction of a molecule with optical fields is customarily interpreted by means of induced time-dependent electric polarizabilities, magnetizabilities and mixed electric-magnetic polarizabilities. In general, these properties can be rationalized by integrals of density functions formulated in terms of induced charge and current densities. In this perspective, we focus on what has been done so far at the theoretical level, and on what can be expected to be unveiled from the topological study of suitable density functions, endowed with the fundamental requirement of origin invariance. Densities characterized by such a property can be integrated all over the configuration space to obtain electric dipole polarizability and optical rotatory power. Corresponding maps visualize domains mainly involved in the molecular response. The diagonal components of origin-independent density tensor functions that, on integration, yield corresponding electric dipole polarizability tensor of benzene, naphthalene, phenanthrene and ovalene, have been computed, confirming the ubiquitous presence of counter-polarization regions in the proximity of the atomic nuclei. They are associated with toroidal electron currents, induced by time derivative of the electric field of impinging radiation. Electron (de)localization in these systems is readily observed and estimated. The optical rotation density of the carbonyl chromophore is studied in detail. Its essential feature is the separation in quadrants of alternating sign of density about the CO bond. The presence of an extrachromophoric perturbation determines asymmetry in the extension of the quadrant distribution, thus causing optical rotation.

Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics

By means of quantum mechanics and quantum electrodynamics applied to coupled harmonic Drude oscillators, we study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions, as considered within the employed Drude model for both non-retarded and retarded regimes. For the first case, we present an exact solution for two coupled oscillators obtained by diagonalizing the corresponding quantum-mechanical Hamiltonian and demonstrate that the external field can control the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by quantum electrodynamics, our analysis shows that field-induced electrostatic and polarization energies remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded case. For interacting species modeled by quantum Drude oscillators, the developed framework based on quantum mechanics and quantum electrodynamics yields the leading contributions to molecular interactions under the combined action of external and vacuum fields.

Origin-Independent Densities of Static and Dynamic Molecular Polarizabilities

The notion of the electric dipole polarizability density function of atoms and molecules has been considered. The current density induced by the time derivative of the electric field of monochromatic light allows for a new definition of the electric dipole polarizability density, which is translationally invariant. This translational invariance provides the physical meaning that was lacking in previous defined polarizability densities. The new polarizability density has been implemented at the TD-DFT level of theory. The origin independence has been proven in silico to hold regardless of the basis set size. Two emblematic molecules, i.e., CO and N₂, which in many respects display similar electric response, have been studied in detail. The substantial differences, which have been highlighted in the topology of the parallel and perpendicular polarizability density tensor components of CO and N₂, are grossly hidden by compensation, when integration is carried out to get the molecular properties.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r₀ in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H₂ in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, α_xx and α_zz show the expected functional forms, to leading order in r^-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.

The collision-induced polarizability of a pair of hydrogen molecules

Collision-induced light scattering, impulsive stimulated scattering, and subpicosecond-induced birefringence all depend on the transient changes Deltaalpha in molecular polarizabilities that occur when molecules collide. Ab initio results for Deltaalpha are needed to permit comparisons with accurate experimental results for these spectra and for refractive index virial coefficients and dielectric virial coefficients. In this work, we provide results for Deltaalpha for a pair of hydrogen molecules, treated at CCSD(T) level, with an aug-cc-pV5Z (spdf) basis set. Our values replace the best previous ab initio results for the variation of Deltaalpha with intermolecular separation, the self-consistent-field results obtained by Bounds [Mol. Phys. 38, 2099 (1979)] with a relatively small (3s2p) basis set for H2. For the six geometrical configurations studied by Bounds, the inclusion of correlation and improvements in the basis tend to increase both the trace Deltaalpha(0)0 and the anisotropy Deltaalpha2m of the pair polarizability. The change in the anisotropy is relatively small, but our values for the trace differ by factors of 2 or more from Bounds' results. For use in computing experimental line shapes, intensities, and virial coefficients, we have calculated Deltaalpha for 18 different relative orientations of a pair of H2 molecules, with the intermolecular separation R ranging from 2 a.u. (3 a.u. for a linear pair) to 10 a.u. The H2 bond length is fixed at the vibrationally averaged internuclear separation in the ground state r=1.449 a.u. Our results agree well with the CCSD(T) results for Deltaalpha obtained by Maroulis [J. Phys. Chem. A 104, 4772 (2000)] for two pair configurations of H2...H2 (linear and T-shaped) at a fixed internuclear distance of R=6.5 a.u. in a [6s4p1d] basis. As the intermolecular distance increases (for R>or=8 a.u.), the spherical-tensor components of Deltaalpha converge to the results from a long-range model that includes dipole-induced-dipole (DID) interactions, higher-multipole induction, nonuniformity of the local field, hyperpolarization, and van der Waals dispersion. Deviations from the first-order DID model are still evident for R between 8 and 10 a.u. in most orientations of the pair. At shorter range, overlap damping, exchange, and orbital distortion reduce both Deltaalpha0(0) and Deltaalpha(2)0 below their long-range limiting forms.