The large quadrupole of water molecules

Abstract

Many quantum mechanical calculations indicate water molecules in the gas and liquid phase have much larger quadrupole moments than any of the common site models of water for computer simulations. Here, comparisons of multipoles from quantum mechanical∕molecular mechanical (QM∕MM) calculations at the MP2∕aug-cc-pVQZ level on a B3LYP∕aug-cc-pVQZ level geometry of a waterlike cluster and from various site models show that the increased square planar quadrupole can be attributed to the p-orbital character perpendicular to the molecular plane of the highest occupied molecular orbital as well as a slight shift of negative charge toward the hydrogens. The common site models do not account for the p-orbital type electron density and fitting partial charges of TIP4P- or TIP5P-type models to the QM∕MM dipole and quadrupole give unreasonable higher moments. Furthermore, six partial charge sites are necessary to account reasonably for the large quadrupole, and polarizable site models will not remedy the problem unless they account for the p-orbital in the gas phase since the QM calculations show it is present there too. On the other hand, multipole models by definition can use the correct multipoles and the electrostatic potential from the QM∕MM multipoles is much closer than that from the site models to the potential from the QM∕MM electron density. Finally, Monte Carlo simulations show that increasing the quadrupole in the soft-sticky dipole-quadrupole-octupole multipole model gives radial distribution functions that are in good agreement with experiment.

Figure 1

Charge distributions of moments, from left to right: μ₀, a linear dipole; Θ₀, a linear quadrupole; Θ₂, a square quadrupole; Ω₀, a linear octupole; and Ω₂, a cubic octupole, in which positive charge is blue and negative charge is red.

Figure 2

Electron density of three highest occupied MOs of QM∕4MM. (a) 1b₂ (b) 3a₁ (c) 1b₁ (HOMO).

Figure 3

Difference in electron density of the molecule from free atoms for QM∕4MM at the B3LYP∕6-31G^** level (a) parallel and (b) perpendicular to the plane of the molecule.

Figure 4

Electrostatic potential around a water molecule parallel (top) and perpendicular (bottom) to the plane of the molecule for (a) the electron density for QM∕4MM, (b) a multipole expansion to the octupole for QM∕4MM, (c) TIP4P∕2005, and (d) TIP5P. Horizontal and vertical range from –6 to + 6 atomic units, contours from –0.1 to 0.1 at an interval of 0.01 au with positive contours in blue and negative in red, and the potential within 0.90 Å of the oxygen or 0.37 Å of either hydrogen is set equal to zero. Gray circles at 1.4 and 2.8 Å from the oxygen.

Figure 5

Electrostatic potential at 2.8 Å from the central water molecule in QM∕4MM as a function of polar angle from the z-axis (a) parallel and (b) perpendicular to the plane of the molecule for the electron density at the MP2∕aug-cc-pVQZ level (×), a moment expansion to the quadrupole (dashed line), octupole (red line), hexadecapole (black line), TIP4P∕2005 (green line), TIP5P (blue line).

Figure 6

Radial distribution functions for the SSDQO model with QM∕4MM moments scaled to μ₀ = 2.12 D with σ = 3.5 Å and ε = 0.145 kcal∕mol in a 9-6 Lennard-Jones potential (red line) and TIP4P∕2005 moments with σ = 3.5 Å and ε = 0.15 kcal∕mol in a 9-6 Lennard-Jones potential (green line).