The Effect of the Electronic Structure Method and Basis Set on the Accuracy of the Electric Multipoles Computed With the Distributed Multipole Analysis (DMA)
Authors: Oliveira Roberta Siqueira Soldaini , Oliveira Marco Aurélio Souza , Borges Itamar 
Published: September 2023

Abstract
Context An accurate description of the molecular charge density is crucial for investigating intra- and inter-molecular properties. Among the different ways of describing and analyzing it, the widely used distributed multipole analysis (DMA) is an accurate method for decomposing the molecular charge density into atom-centered electric multipoles (monopole, dipole, quadrupole, and so on) that have a direct chemical interpretation. In this work, DMA was employed to decompose the molecular charge density of six chemically distinct molecules, namely, (2R)-2-amino-3-[(S)-prop-2-enylsulfinyl] propanoic acid (AAP), 4-amine-2-nitro-1,3,5 triazole (ANTA), (RS)-Propan-2-yl methylphosphonofluoridate (SARIN), chloromethane (CLMET) and 2-aminoacetic acid (GLY) into monopole, dipole, and quadrupole values. A hypothetical variation of ANTA built by exchanging all the nitrogen atoms with phosphorus that we named 4-phosphine-2-phosphite-1,3,5-phosphorine (ANTAP) was also studied. These molecules have different chemical structures bearing distinct carbon skeletons, electronegative atoms, and electron-withdrawing/donating groups. We found that although DFT multipole values can depend considerably on the exchange-correlation functional for specific atomic sites, the associated root-mean-square errors (RMSE) compared to benchmark MP4 mainly were about 10-4 - 10-6The most significant variations were for monopoles and dipoles of sites highly polarized by adjacent atoms, and to a lesser degree, for the quadrupoles. The double hybrid B2PLYP and the hybrid meta M06-2X functionals, as expected in the framework of Jacob’s ladder, overall give the most accurate results among the DFT methods. The MP2 DMA multipole values have an RMSE in relation to the MP4 benchmark mainly in the range , thus representing a lower computational cost to obtain results with similar good accuracy without the ambiguity of choosing a DFT functional. The deviations of the HF multipoles from the benchmark in most cases were less than 20%, in agreement with the well-known fact that non-correlated charge densities have a slight dependence on the electronic correlation. We also confirmed that DMA values have a small dependence on the size of the basis set: deviations did not exceed 5% in most cases. However, the dependence of the DMA values on the size of the basis set increases with the rank of the electric multipole. To compute accurate values of DMA multipoles of an atom bonded to very electronegative atoms, especially dipoles (a measure of polarization) and quadrupoles (a measure of electron delocalization), a large basis set including diffuse functions is necessary. Despite that, for a given polarized basis set, the choice of the basis set to compute accurate DMA multipole values is not critical.
Methods The molecular charge densities were computed using the electronic structure methods Hartree-Fock (HF), MP2, MP4, DFT/PBE, DFT/B3LYP, DFT/B3PW91, DFT/M06-2X, and DFT/B2PLYP implemented in the Gaussian 09 package. MP4 was the benchmark method. The DMA multipoles were obtained with the GDMA program of Stone. The 6-311G++(d,p) basis set was used for the production calculations, and the augmented correlation-consistent Dunning’s hierarchy of basis sets were employed to evaluate the dependence of the DMA multipoles on the basis set size.