Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces

Abstract

Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: A new ab initio dipole surface for high-temperature applications J. Chem. Phys. 136, 044320 (2012) Elegant expressions are derived for the computation of dipole and quadrupole moments of molecules using the electrostatic potential and electric field evaluated on an oriented molecular surface. These expressions are implemented for Hirshfeld surfaces, applied to various molecular crystals, and compared with the results from the quantum theory of atoms in molecules. The effect of intermolecular interactions is also explored by examining the differences between electrostatic moments derived from a periodic Hartree-Fock electron density and an electron density resulting from a superposition of noninteracting molecules. The enhancement of the dipole moment for hydrogen bonded molecular crystals is typically 30%-40% and shown to be largely independent of the partitioning scheme. Dipole moments calculated from Hirshfeld surfaces systematically underestimate those from zero-flux surfaces, a result attributed to the translation of the Hirshfeld surface relative to the zero-flux surfaces for these molecules. For acetylene and benzene, the differences between a crystal calculation and the sum of noninteracting molecules are small, and both partitioning schemes yield quadrupole and second moment results in close agreement.

Dipole Moment Enhancement in Molecular Crystals from X‐ray Diffraction Data

“…Thus, for a subset of molecules in Tables 1 and 2, we performed PHF calculations with CRYSTAL98 [20] using a polarized double zeta (DZP) basis set; [21] using the MOLSPLIT option yielded electron distributions arising from a sum of non-interacting molecules. Following the procedures outlined in detail elsewhere, [17] molecular dipole moments were obtained using two distinctly different partitioning schemes to define molecular regions: Hirshfeld surfaces [16] and Bader's QTAM. [13] For the former case, the crystalline electric field and electrostatic potential were computed at points on Hirshfeld surfaces around each molecule, obtained at a resolution of 10 points/au, and surface integration was used to determine molecular dipole moments.…”

“…As remarked previously for glycine, [17] amino acids such as this that exist in zwitterionic form in the crystal generate large electric fields because of their substantial dipole moments, but this does not translate into very large dipole enhancements, principally because the molecules are already highly polarized. We elaborate a little further on this observation below.…”

“…An alternative discrete partitioning method based on Hirshfeld's sharing function [15] defines a smooth boundary for a molecule in a crystal, [16] and we have recently shown that these molecular Hirshfeld surfaces can be exploited to obtain molecular dipole moments via two-dimensional integration of the electrostatic potential and electric field on the surface. [17] This approach also has a drawback, as it is not an exhaustive partitioning. Hence, small voids remain, which typically contain % 0.1 % of the electron count of a molecule.…”

Progress in the Understanding of Drug–Receptor Interactions, Part 2: Experimental and Theoretical Electrostatic Moments and Interaction Energies of an Angiotensin II Receptor Antagonist (C30H30N6O3S)

“…[52,53] In the case of a non-symmetric molecule, such as 1, the six components of the second moment tensor are all independent and their relationship to charge contraction/expansion along a particular direction defined by some structural elements (e.g., a bond axis) is not as straightforward as in simpler cases. [46,52,54] …”

“…By considering the QTAIM value as the best experimental estimate of the dipole moment and the MCG-B3LYP value as the reference, the dipole moment enhancement, occurring upon crystallisation as a consequence of both crystal field effects and intermolecular interactions, is about 87 %, whereas, with respect to the MOG-B3LYP value, the enhancement is reduced to 48 %, again high, but quite close to the range of 30-40 % reported in the literature as typical for hydrogen-bonded systems. [46,47] In an attempt to calculate the ab initio value of m in the crystal, we performed fully periodic DFT calculations on the 17 K experimental geometry with the CRYSTAL2003 program. [30] However, as this version of the code (the only one that can handle a structure as large as 1) does not include QTAIM analysis of the electron density, we could only derive a value for the dipole moment from the periodic Mulliken DMA, as retrieved from the wavefunction of the CRYSTAL2003 program by the code PAMoC.…”