Publications

Kohn-Sham density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. The recent development of the strongly constrained and appropriately normed (SCAN) functional has renewed the interest in ab initio simulations of liquid water, yielding promising results that are, however, still unable to reproduce all the experimental data. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of coupled cluster theory, the “gold standard” for chemical accuracy. Building upon the accuracy and efficiency of DC-SCAN within a many-body formal- ism, we introduce a data-driven many-body potential energy function, the MB-SCAN(DC) PEF, that is able to quantitatively reproduce coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, the properties of liquid water calculated from molecular dynamics simulations carried out with the MB- SCAN(DC) PEF are found to be in excellent agreement with the experimental data, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the condensed phase. Since the many-body formalism adopted by the present MB-SCAN(DC) PEF for water is general, we believe it can open the door to the routine development of data-driven many-body PEFs for predictive simulations of generic (small) molecules in the gas, liquid, and solid phases.

Recently, a family of cobalt pentapyridine complexes of the type [(R-PY5Me2)Co(H2O)])(CF3SO3)2, (R = CF3, H, or NMe2; PY5Me2 = 2,6-bis(1,1-di(pyridin-2-yl)ethyl)pyridine) were shown to catalyze the electrochemical generation of hydrogen from neutral aqueous solutions using a mercury electrode. We now report that the CF3 derivative of this series, [(CF3PY5Me2)Co(H2O)](CF3SO3)2 (1), can also operate in neutral water as an electrocatalyst for hydrogen generation under soluble, diffusion-limited conditions on a glassy carbon electrode, as well as a photocatalyst for hydrogen production using either molecular or semiconductor nanowire photosensitizers. Owing to its relatively low overpotential compared to other members of the PY5 family, complex 1 exhibits multiple redox features on glassy carbon, including a one-proton, one-electron coupled oxidative wave. Further, rotating disk electrode voltammetry measurements reveal the efficacy of 1 as a competent hydrogen evolution catalyst under soluble, diffusion-limited conditions. In addition, we establish that 1 can also generate hydrogen from neutral water under photocatalytic conditions with visible light irradiation (λirr ≥ 455 nm), using [Ru(bpy)3]2+ as a molecular inorganic chromophore and ascorbic acid as a sacrificial donor. Dynamic light scattering measurements show no evidence for nanoparticle formation for the duration of the photolytic hydrogen evolution experiments. Finally, we demonstrate that 1 is also able to enhance the hydrogen photolysis yield of GaP nanowires in water, showing that this catalyst is compatible with solid-state photosensitizers. Taken together, these data establish that the well-defined cobalt pentapyridine complex [(CF3PY5Me2)Co(H2O)]2+ is a versatile catalyst for hydrogen production from pure aqueous solutions using either solar or electrical input, providing a starting point for integrating molecular systems into sustainable energy generation devices.

The negative correlation energy ${\ensuremath{\epsilon}}_{c}{(r}_{s},\ensuremath{\zeta})$ per particle of a uniform electron gas of density parameter ${r}_{s}$ and spin polarization $\ensuremath{\zeta}$ is well known, but its spin resolution into $\ensuremath{\uparrow}\ensuremath{\downarrow},$ $\ensuremath{\uparrow}\ensuremath{\uparrow},$ and $\ensuremath{\downarrow}\ensuremath{\downarrow}$ contributions is not. Widely used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available quantum Monte Carlo data. In the low-density limit for $\ensuremath{\zeta}=0,$ we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ contributions to the kinetic energy of correlation.

We use the two-electron wave functions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function $g(r)$ for a uniform electron gas, finding the exact $g(0)$ for this model and extending the results from $g(0)$ to $g(r).$ We find that the short-range $(r<{r}_{s})$ part of this $g(r)$ is in excellent agreement with quantum Monte Carlo simulations for a wide range of electron densities. We are thus able to estimate the value of the second-order ${(r}^{2})$ coefficient of the small interelectronic-distance expansion of the pair-distribution function. The coefficients of the small-$r$ expansion of the spin-resolved ${g}_{\ensuremath{\sigma}{\ensuremath{\sigma}}^{\ensuremath{'}}}(r)$ have density or ${r}_{s}$ dependencies which we parametrize in a way that makes it easy to find their coupling-constant averages. Their spin-polarization or $\ensuremath{\zeta}$ dependencies are estimated from a proposed spin-scaling relation.

Errors in kinetic and exchange contributions to the molecular bonding energy are assessed for approximate density functionals by reference to near-exact Hartree-Fock values. From the molecular calculations of Allan et al.and of Lee and Ghosh, it is demonstrated that the density-gradient expansion does not accurately describe the noninteracting kinetic contribution to the bonding energy, even when this expansion is carried to fourth order and applied in its spin-density-functional form to accurate Hartree-Fock densities. In a related study, it is demonstrated that the overbinding of molecules such as ${\mathrm{N}}_{2}$ and ${\mathrm{F}}_{2}$, which occurs in the local-spin-density (LSD) approximation for the exchange-correlation energy, is not attributable to errors in the self-consistent LSD densities. Contrary to expectations based upon the Gunnarsson-Jones nodality argument, it is found that the LSD approximation for the exchange energy can seriously overbind a molecule even when bonding does not create additional nodes in the occupied valence orbitals. LSD and exact values for the exchange contribution to the bonding energy are displayed and discussed for several molecules.

The ground-state correlation energy per particle in a uniform electron gas with spin densities ${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$ and ${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$ may be expressed as ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$)=I(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$)${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(0,${\mathit{r}}_{\mathit{s}}$), where ${\mathit{r}}_{\mathit{s}}$=[3/4\ensuremath{\pi}(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)${]}^{1/3}$ is the density parameter and \ensuremath{\zeta}=(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)/(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$) is the relative spin polarization. We find an analytic expression for the spin-scaling factor (SSF) I(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$) in the high-density limit ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0. It decreases from the value 1 at \ensuremath{\zeta}=0, approaching the value 1/2 with slope -\ensuremath{\infty} as \ensuremath{\zeta} approaches 1. A simple approximation to this SSF which displays the correct qualitative behavior is ${\mathit{g}}^{3}$(\ensuremath{\zeta}), where g(\ensuremath{\zeta})=[(1+\ensuremath{\zeta}${)}^{2/3}$+(1-\ensuremath{\zeta}${)}^{2/3}$]/2. We find that g(\ensuremath{\zeta}) is the SSF for the coefficient of the \ensuremath{\Vert}\ensuremath{\nabla}n${\mathrm{\ensuremath{\Vert}}}^{2}$/${\mathit{n}}^{4/3}$ term of the spin-density gradient expansion of the exchange energy, and a good approximation to the SSF for that of correlation: ${\mathit{scrC}}_{\mathit{x}}$(\ensuremath{\zeta})/${\mathit{scrC}}_{\mathit{x}}$(0)=g(\ensuremath{\zeta}) and ${\mathit{scrC}}_{\mathit{c}}$(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0)/${\mathit{scrC}}_{\mathit{c}}$(0, ${\mathrm{r}}_{\mathrm{s}}$\ensuremath{\rightarrow}0)\ensuremath{\approxeq}g(\ensuremath{\zeta}). We also find that the \ensuremath{\Vert}\ensuremath{\nabla}\ensuremath{\zeta}${\mathrm{\ensuremath{\Vert}}}^{2}$ contribution to the correlation energy is always negligible.

Since long-range electron-electron correlation is treated properly in the random phase approximation (RPA), we define short-range correlation as the correction to the RPA. The effects of short-range correlation are investigated here in the local spin density (LSD) approximation and the generalized gradient approximation (GGA). Results are presented for atoms, molecules, and jellium surfaces. It is found that (1) short-range correlation energies are less sensitive to the inclusion of density gradients than are full correlation energies, and (2) short-range correlation makes a surprisingly small contribution to surface and molecular atomization energies. In order to improve the accuracy of electronic-structure calculations, we therefore combine a GGA treatment of short-range correlation with a full RPA treatment of the exchange-correlation energy. This approach leads to jellium surface energies close to those of the LSD approximation for exchange and correlation together (but not for each separately).